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Problem 24901

For the exponential function $f$ , find $f^{-1}$ analytically al
$f(x) = 9^x - 1$
$f^{-1}(x) =$
(Simplify your answer.)
Use the graphing tool to graph both $f$ and $f^{-1}$ . Click to enlarge graph

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Problem 24902

8. From a can of milk containing 37.50 litres of milk, the milkman delivers 29.535 litres to one marriage hall, If he is to supply 33.80 litres of milk to the next marriage hall, then how much more milk should be added to the milk left in the can?

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Problem 24903

Find the value of $x$ . $45^\circ$ $83^\circ$ $x^\circ$

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Problem 24904

After 15 minutes this patient (Q11) is not adequately anesthetized, you now administer one cartridge of 2% lidocaine, 1:100,000 epinephrine, buffered with 0.1 mL of 8.4% sodium bicarbonate.
a) How many total mL of drug have they now received? b) How many mg per mL in an 8.4% buffering agent (BA)? c) How many mg per cartridge of an 8.4% buffering agent (BA)? d) How many mg of each drug have they received? e) How many total mg of drug have they received? f) How many more mg of local anesthetic could this pt have? g) What is the limiting drug? h) What will you document in the chart for this appointment (including dosages from Q11)

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Problem 24905

$\text{Use the method of cylindrical shells to find the volume of the region bounded by } x = 2 + (y-5)^2 \text{ and } x = 3, \text{ when revolved around the } x\text{-axis.}$

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Problem 24906

Solve the inequality for $y$ . $-5.4 > 0.8 + y$ Simplify your answer as much as possible.

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Problem 24907

Douglas Corporation plans to sell 24,000 units of Product A during July and 30,000 units during August. Sales of Product A during June were 25,000 units. Past experience has shown that end-of-month inventory should equal 3,000 units plus 30% of the next month's sales. On June 30 this requirement was met. Based on these data, how many units of Product A must be produced during the month of July?
Multiple Choice 22,200 25,800 24,000 28,800

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Problem 24908

13. The article "Extravisual Damage Detection: Defining the Standard Normal Tree" (Photogrammetric Engr. and Remote Sensing, 1981: 515-522) discusses there use of color infrared photography in identification of normal trees in Douglas fir stands. Among data reported were summary statistics for green-filter analytic optical densitometric measurements on samples of both healthy and diseased trees. For a sample of 69 healthy trees, the sample mean dye-layer density was 1.028, and the sample standard deviation was 0.163. a. Calculate a $95\%$ (two-sided) CI for the true average dye-layer density for all such trees. b. Suppose the investigators had made a rough guess of 0.16 for the value of $s$ before collecting late a $95\%$ (two-sided) confidence interval for the proportion of all dies that pass the probe.

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Problem 24909

$T_B = 1600 \text{ N} \cdot \text{m}$ $60 \text{ mm}$ $36 \text{ mm}$ $T_A = 800 \text{ N} \cdot \text{m}$ $250 \text{ mm}$ $375 \text{ mm}$ $400 \text{ mm}$
The aluminum rod AB ( $G = 27 \text{ GPa}$ ) is bonded to the brass rod BD ( $G = 39 \text{ GPa}$ ). Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A.

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Problem 24910

Concentration of $CO_2$ in the Atmosphere
Levels of carbon dioxide ( $CO_2$ ) in the atmosphere are rising rapidly, far above any levels ever before recorded. Levels were around 280 parts per million in 1800, before the Industrial Age, and had never, in the hundreds of thousands of years before that, gone above 300 ppm. Levels are now over 400 ppm. The table below shows the rapid rise of $CO_2$ concentrations over the 55 years from 1960-2015 (data also available in Carbon Dioxide). We can use this information to predict $CO_2$ levels in different years.
| Year | $CO_2$ | |---|---| | 1960 | 316.91 | | 1965 | 320.04 | | 1970 | 325.48 | | 1975 | 331.11 | | 1980 | 338.75 | | 1985 | 346.12 | | 1990 | 354.39 | | 1995 | 360.82 | | 2000 | 369.55 | | 2005 | 379.80 | | 2010 | 389.90 | | 2015 | 400.81 |
Concentration of carbon dioxide in the atmosphere
Click here to the dataset associated with this question. Use the 3 e version of the dataset.
If using StatKey, the data needed is preloaded in the drop-down menu in the upper left corner. Click here to access StatKey.
Dr. Pieter Tans, NOAA/ESRL, http://www.esrl.noaa.gov/gmd/ccgg/trends/. Values recorded at the Mauna Loa Observatory in Hawaii.
(a) What is the explanatory variable? What is the response variable? * Year is the explanatory variable and $CO_2$ concentration is the response variable. $CO_2$ concentration is the explanatory variable and Year is the response variable.
(b) Use technology to find the correlation between year and $CO_2$ levels. Round your answer to three decimal places.
(c) Use technology to calculate the regression line to predict $CO_2$ from year. Round your answer for the intercept to one decimal place and your answer for the slope to three decimal places. $CO_2 =$ + (Year)
(d) Interpret the slope of the regression line, in terms of carbon dioxide concentrations. The slope tells the predicted number of years for the $CO_2$ level to go up by that amount. The slope tells the predicted number of years for the $CO_2$ level to go up by one. The slope tells the predicted $CO_2$ level one year later. The slope tells the predicted change in $CO_2$ level one year later.
(e) What is the intercept of the line? Round your answer to one decimal place. The intercept is ____ (Does it make sense in context?)
(f) Use the regression line to predict the $CO_2$ level in 2003. Use rounded slope and the intercept from part (c). Then round your answer to one decimal place. $CO_2$ level in 2003: ____
Use the regression line to predict the $CO_2$ level in 2005. Use rounded slope and the intercept from part (c). Then round your answer to one decimal place. $CO_2$ level in 2005:
(g) Find the residual for 2010. Use rounded slope and the intercept from part (c). Then round your answer to two decimal places. Residual for 2010:

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Problem 24911

The amount of carbon-14 present in animal bones after $t$ years is given by $A(t) = A_0 e^{-0.00012t}$ . A sample of fossil had 28% of the carbon 14 of a contemporary living sample. Estimate the age of the sample.
The age of the sample is ___ years. (Round to the nearest year as needed.)

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Problem 24912

If $5c - 2 = 3c$ , then $24c =$ [basic] A. 6 B. 8 C. 16 D. 24

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Problem 24913

5. Um sistema de comunicações é constituido por um cabo de 160 Km . Considere que a potência entregue ao cabo é de 5 W e que existem m repetidores ao longo do cabo. Cada repetidor tem um ganho de \mathbf{8 0 ~ d B ~ e ~ a ~ p o t e ̂ n c i a ~ m i ́ n i m a ~ a ~ s u a ~ e n t r a d a ~ e ́ ~ d e ~} 40 \mu \mathrm{~W}. Considere $\boldsymbol{\alpha}$ (atenuação provocada pelo cabo) igual a 2db/Km. Determine: a. O número de repetidores a instalar e a posição de cada um no sistema, de modo a que a potencia entregue a saida seja de pelo menos 2 W b. Mostre qual a relação entre a potência expressa em dBm e dBw c. Mostre que se $|\mathrm{H}(\mathrm{f})|=-3 \mathrm{~dB}$ , entäo $|\mathrm{H}(\mathrm{f})|=1 / 2^{0.5}$ d. Indique que tipos de distorção na transmissão

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Problem 24914

10. Choose ONE of the following questions.
A bus company has 4000 passengers daily, each paying a fare of $\$2$ . For each 15 cent increase in price, the company estimates it will lose 40 passengers. If the company needs to take in $\$10,450$ per day to stay in business, what fare should be charged?

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Problem 24915

The two triangles below are similar.
$28^\circ$ 2 2 B 10 D $76^\circ$ $28^\circ$ 5 10 X $76^\circ$ $76^\circ$ 1 $76^\circ$ W Complete the similarity statement. $\triangle VWX \sim \triangle$ C

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Problem 24916

Weights of 2 samples of patients were measured and following results are obtained: \begin{tabular}{ccc} Sample Size & Mean \\ \begin{tabular}{ccc} 1 & 30 & 70 \\ 2 & 70 & $x$ \end{tabular} \end{tabular}
If both groups were combined and the combined mean is 84 , then the mean of the second sample is: a. 74

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Problem 24917

$A=\left(\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ 1 & 1 & 1 & 1 \\ -2 & -2 & 3 & 3 \\ 1 & 2 & -2 & -3 \end{array}\right)$ (a) Use the elimination method to evaluate $\operatorname{det}(A)$ . (b) Use the value of $\operatorname{det}(A)$ to evaluate $\left|\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ -2 & -2 & 3 & 3 \\ 1 & 2 & -2 & -3 \\ 1 & 1 & 1 & 1 \end{array}\right|+\left|\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ 1 & 1 & 1 & 1 \\ -1 & -1 & 4 & 4 \\ 2 & 3 & -1 & -2 \end{array}\right|$

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Problem 24918

A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips vary in size, it is difficult to fill the bags to the exact weight desired. However, the bags pass inspection so long as the standard deviation of their weights is no more than 4 grams. A quality control inspector wished to test the claim that one batch of bags has a standard deviation of more than 4 grams, and thus does not pass inspection. If a sample of 28 bags of potato chips is taken and the standard deviation is found to be 4.6 grams, does this evidence, at the 0.025 level of significance, support the claim that the bags should fail inspection? Assume that the weights of the bags of potato chips are normally distributed.
Step 3 of 3: Draw a conclusion and interpret the decision.
Answer 2 Points Tables Keypad Keyboard Shortcuts
We reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.025 level of significance that the bags should fail inspection.
We reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the bags should fail inspection.

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Problem 24919

1. Evaluate $\operatorname{Lim}_{x \rightarrow 2}\left(\frac{x^{2}-x-2}{x^{2}-4}\right)$
2. Evaluate $\operatorname{Lim}_{x \rightarrow 3}\left(\frac{x^{2}-1}{x-1}\right)$
3. Find the limits of the polynomial $\operatorname{Lim}_{x \rightarrow 2}\left(\frac{x^{2}+x-2}{x^{2}-3 x+2}\right)$
4. Evaluate $\operatorname{Lim}_{1} \cdots\left(\frac{x^{3}-2 x+1}{3 x^{3}+4 x^{2}-1}\right)$
5 Evaluate $\operatorname{Lim}_{101}\left(\frac{\operatorname{Sin} x}{x}\right)$ (1). Using the L'Hospital Rule, solve the limit Evaluate $\operatorname{Lim}_{x \rightarrow( }\binom{x^{3}+2 x^{2}-4 x+7}{5 x^{3}-4 x^{2}+8 x-9}$
7. Limit $\operatorname{Sin} 3$ - "." $\operatorname{Sin} 4 . x$ $\therefore \operatorname{limmit} \frac{\left(13 x^{2}-5 x+1\right)-3}{x-1}$
4. $\operatorname{limit}^{x^{2}-(a+1) x+a} \begin{array}{c}x^{3}-a^{3}\end{array}$
10. $\operatorname{Limit}_{x \rightarrow 10} \frac{\log x}{x}$

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Problem 24920

1) Find $f^{(12)}(0)$ of $f(x) = x \sin x^2$ 2) Find $f^{(20)}(0)$ of $f(x) = \sin(4x^2)$ 3) Find $f^{(24)}(0)$ of $f(x) = e^{4x^3}$ 4) Find $f^{(36)}(0)$ of $f(x) = \cos \sqrt{x}$ 5) Find $f^{(40)}(0)$ of $f(x) = \ln(1+x^2)$ 6) Find $f^{(15)}(0)$ of $f(x) = x^2 e^x$

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Problem 24921

Heaven left the internet cafe traveling 4 mph . Then, 3 hours later, Miranda left traveling the same direction at 10 mph . How long until Miranda catches up with Heaven?
Complete the table below, using the variable $t$ to represent the time until Miranda catches up with Heaven: \begin{tabular}{|c|c|c|c|} \hline & Rate & Time & Distance \\ \hline Heaven & & & \\ \hline Miranda & & & $\square$ \\ \hline \end{tabular}
Using the table, write an equation to represent this situation: $\square$ The solution to the equation is $\square$ hours.

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Problem 24922

$f(x) = (4x - 2)^2 (2x^2 + 1)^3$ .
Find $f'(x)$ , and then evaluate $f'$ at $x = 2$ and $x = -2$ .
$f'(2) =$
$f'(-2) =$

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Problem 24923

Determine if the values of the variables listed are solutions of the system of equations. $\begin{cases} 2x - y = 7 \\ 3x + 5y = -9 \end{cases}$ $x = 2$ , $y = -3$ ; $(2, -3)$
Is $(2, -3)$ a solution of the system of equations? Yes No

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Problem 24924

Is $x = 3$ , $y = \frac{1}{3}$ a solution of the given system of equations?
$\begin{cases} 4x - 6y = 10 \\ \frac{1}{3}x - 2y = -\frac{1}{3} \end{cases}$
Is the first equation satisfied? Yes No

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Problem 24925

Is $x = 2$ , $y = \frac{1}{3}$ a solution of the given system of equations? $\begin{cases} 5x - 6y = 8 \\ \frac{1}{3}x - 4y = -\frac{2}{3} \end{cases}$ Is the first equation satisfied? Yes No

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Problem 24926

Is $x = 2$ , $y = \frac{1}{3}$ a solution of the given system of equations? $\begin{cases} 5x - 6y = 8 \\ \frac{1}{3}x - 4y = -\frac{2}{3} \end{cases}$ Is the first equation satisfied? Yes No Is the second equation satisfied? No Yes As a result, is $x = 2$ , $y = \frac{1}{3}$ a solution of the given system of equations? Yes No

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Problem 24927

Question Watch Video Show Examples
Ava launches a toy rocket from a platform. The height of the rocket in feet is given by $h(t)=-16 t^{2}+24 t+112$ where $t$ represents the time in seconds after launch. After how many seconds does the rocket hit the ground?
Answer Attempt 1 out of 3 $\qquad$ seconds Submit Answer

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Problem 24928

$4x + 3z = 31$ $4y - z = -17$ $-x - 3y + 4z = 25$ $x = 4$ , $y = -3$ , $z = 5$ ; $(4, -3, 5)$
Is $(4, -3, 5)$ a solution of the system of equations?
A. No, the solutions does not satisfy any of the equations. B. No, the solution does not satisfy either $4x + 3z = 31$ or $4y - z = -17$ . C. No, the solution does not satisfy either $4y - z = -17$ or $-x - 3y + 4z = 25$ . D. No, the solution does not satisfy $4x + 3z = 31$ . E. No, the solution does not satisfy $4y - z = -17$ . F. No, the solution does not satisfy either $4x + 3z = 31$ or $-x - 3y + 4z = 25$ . G. No, the solution does not satisfy $-x - 3y + 4z = 25$ . H. Yes, this is a solution to the system of equations.

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Problem 24929

Question
Solve for all values of $x$ by factoring. $x^{2}+x-16=x$
Answer Attempt 1 out of 3

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Problem 24930

$2x + y = 5$ $4x + 2y = 3$ Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is $x =$ and $y =$ . (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered pairs, they can be expressed as $\{(x,y) | x =$ , $y$ is any real number\}. (Simplify your answer. Type an expression using $y$ as the variable as needed.) C. The system is inconsistent. Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.

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Problem 24931

Use the Trapezoidal Rule to find $T_{n}$ using the indicated value of $n$ . Round to three decimal places. $\int_{0}^{1} \frac{1}{x^{2}+1} d x ; n=4$ A. $T_{4}=0.783$ B. $T_{4}=0.970$ C. $T_{4}=1.383$ D. $T_{4}=1.566$

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Problem 24932

6) Javier is making a recipe that requires 160 mL of 40% pure fruit juice. He has 25% pure fruit juice solution and a 50% pure fruit juice solution. How many milliliters of each solution should he mix to obtain the needed solution?

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Problem 24933

Graphically solving a system of linear equations 3 ph the system below and write its solution. $\left\{\begin{array}{l} -2 x+y=5 \\ y=\frac{1}{4} x-2 \end{array}\right.$
Note that you can also answer "No solution" or "Infinitely many" solutions.
Solution: No Infinitely solution many Explanation Check O 2024 McGraw Hill LLC. All Rights Reserved. Terms of

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Problem 24934

Solve the equation $2 x^{2}-19 x+2=-10 x$ to the nearest tenth.
Answer Attempt 1 out of 3 (ค) Additional Solution $\Theta$ No Solution

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Problem 24935

$2x - y = 0$ $6x + 3y = 30$ Select the correct choice below and, if necessary, fill in any answer boxes in your choice. A. The solution is $x =$ and $y =$ . (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered pairs, they can be expressed as $\{(x,y) | x =$ , $y$ is any real number\}. (Simplify your answer. Type an expression using $y$ as the variable.) C. The system is inconsistent. Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system.

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Problem 24936

Scanned with CamScanner
Find the numerical value of $\left[\sum n^{2} \delta[n+1]\right]$ : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

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Problem 24937

Solve the system of equations. If the system has no solution, say that it is inconsistent. $\begin{cases} x + 4y = 8 \\ 6x + 24y = 48 \end{cases}$ Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The solution is $x =$ and $y =$ . (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered pairs, they can be expressed as $\{(x,y) | x =$ , y any real number\}. (Simplify your answer. Type an expression using $y$ as the variable as needed.)
C. The system is inconsistent.

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Problem 24938

9 Matching 5 points Put the following steps to using the AED in order. 1 2 3 4 5 Complete 100 compressions per minute until help arrives or Preform CPR as advised by the AED Complete check, call, care and send someone to get the AED Follow directions given by AED Remove clothing and attach pads correctly As soon as the AED is available turn it on and follow the voice prompts

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Problem 24939

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

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Problem 24940

EXERCICE 1: Une bille ponctuelle S de masse $m$ est suspendue à un fil inextensible de longueur $l$ et de masse négligeable attaché en un point O. On écarte le fil d'un angle $\theta_0$ à partir de la position d'équilibre puis on l'abandonne sans vitesse initiale
1. Donner l'expression de la vitesse de la bille S: a) Au moment où le fil fait avec la verticale un angle $\theta_1$ . b) Au moment où le fil passe par la verticale.
2. Le fil étant écarté du même angle $\theta_0$ à partir de la position d'équilibre, on lance la bille avec une vitesse initiale $V_0$ déterminer l'angle maximal $\theta_m$ de remontée de la bille.
3. Quelle est la valeur minimale $V_{0m}$ de la vitesse initiale $V_0$ pour que la bille puisse faire au moins un tour ? Données : $l =$ $50$ cm; $\theta_0 = 60^\circ$ ; $V_0 = 1,2$ m.s $^{-1}$ ; $g = 10$ m.s $^{-2}$

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Problem 24941

Решите уравнение: $\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}$

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Problem 24942

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.

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Problem 24943

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is \$600 and the annual interest rate is 3.7%?
Interest = $\$$ [ ? ]
Round your answer to the nearest hundredth.

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Problem 24944

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$ $2x + y + z = -4$ $-2x + 3y - 3z = -2$
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution is $x =$ _, $y =$ _, and $z =$ _. (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(x,y,z) | x =$ _, $y =$ _, $z$ any real number\}. (Simplify your answers. Type expressions using $z$ as the variable as needed.)
C. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(x,y,z) | x =$ _, $y$ any real number, $z$ any real number\}. (Simplify your answer. Type an expression using $y$ and $z$ as the variables as needed.)
D. The system is inconsistent.

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Problem 24945

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$
$2x + y + z = -4$
$-2x + 3y - 3z = -2$

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Problem 24946

Find real numbers a, b, and c so that the graph of the function $y = ax^2 + bx + c$ contains the points $(-1,6)$ , $(2,7)$ , and $(0,3)$ .
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution is $a =$ , $b =$ , and $c =$ . (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(a,b,c) | a =$ , $b =$ , c any real number\}. (Simplify your answers. Type expressions using c as the variable as needed.)
C. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(a,b,c) | a =$ , b any real number, c any real number\}. (Simplify your answer. Type an expression using b and c as the variables as needed.)
D. There is no solution.

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Problem 24947

Complete the sentence below. An $m$ by $n$ rectangular array of numbers is called a(n) _____.
An $m$ by $n$ rectangular array of numbers is called a(n) column index. matrix. row index. entry.

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Problem 24948

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _ matrix.
The matrix used to represent a system of linear equations is called a(n) _ matrix. coefficient augmented invertible resulting

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Problem 24949

Complete the sentence below. The notation $a_{35}$ refers to the entry in the _ row and _ column of a matrix.
The notation $a_{35}$ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

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Problem 24950

Diberi $6^{3 x-2}=1296$ , cari nilai $x$ . Given $6^{3 x-2}=1296$ , find the value of $x$ .

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Problem 24951

Ahmad, Khaled and Ali are three partners in partnerships, divided profit and loss 1-2-2 respectively, on 31/12/2018 they agrees to liquidate the partnerships on the same dates the Balance Sheet as follows
| Assets | amount | Liabilities &Capital | amounts | |---|---|---|---| | cash | 10,000 | Accounts payable | 20,000 | | Non cash assets | 45,000 | Ahmad capital | 11,000 | | | | Khaled capital | 8,500 | | | | Ali capital | 15,500 | | total | 55,000 | total | 55,000 |
Others information;- 1- All non-cash assets are sold cash for \$30,000 2- Liquidation expenses are paid for cash \$10,000 3- Khaled are insolvent partners 4- All liabilities are paid cash
Instructions: prepare the liquidation statements

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Problem 24952

Find the amount of work done if an object is pushed horizontally 70 m by a force of 25 N directed $60^{\circ}$ above the horizontal. Give the exact answer. Do not round.
The amount of work done is $\square$ $\mathrm{N} \cdot \mathrm{m}$ $\sqrt{\square}$ ㅁ

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Problem 24953

When a circular plate of metal is heated in an oven, its radius increases at a rate of $0.03$ cm/min. At what rate is the plate's area increasing when the radius is $57$ cm?
The rate of change of the area is _______ $\text{cm}^2$ /min. (Type an exact answer in terms of $\pi$ .)

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Problem 24954

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is \$680 and the annual interest rate is 3.6%? Interest = $[ ? ]$ Round your answer to the nearest hundredth.

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Problem 24955

Solve by completing the square: $z^{2}=12 z+1$

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Problem 24956

Find the value of $x$ for $3^{x-2}=81^{x}$ . Jawapan / Answer:

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Problem 24957

Solve for $x$ : $\begin{array}{l} \log _{6} x+\log _{6}(x+4)=5 \\ x= \end{array}$

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Problem 24958

Use the given function and the given interval to complete parts $\mathbf{a}$ and $\mathbf{b}$ . $f(x)=2 x^{3}-27 x^{2}+108 x \text { on }[2,7]$ a. Determine the absolute extreme values of $f$ on the given interval when they exist. b. Use a graphing utility to confirm your conclusions. a. What is/are the absolute maximum/maxima of $f$ on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The absolute maximum/maxima is/are $\square$ at $x=$ $\square$ . (Use a comma to separate answers as needed. Type exact answers, using radicals as needed.) B. There is no absolute maximum of $f$ on the given interval.

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Problem 24959

Mixed Review e made a smoothie with 1 cup of yogurt, 3 tablespoons of peanut butter, 2 teaspoons of chocolate syrup, and 2 cups of crushed ice.
**Kiran tried to double this recipe. He used 2 cups of yogurt, 6 tablespoons of peanut butter, 5 teaspoons of chocolate syrup, and 4 cups of crushed ice. He didn't think it tasted right. Describe how the flavor of Kiran's recipe compares to Clare's recipe.
*How should Kiran change the quantities that he used so that his smoothie tastes just like Clare's?

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Problem 24960

John collects the running times of some athletes and records the data in the table below. \begin{tabular}{|c|c|} \hline Time $(z$ seconds) & Frequency \\ \hline $50<z \leq 60$ & 7 \\ \hline $60<z \leq 70$ & 4 \\ \hline $70<z \leq 80$ & 3 \\ \hline $80<z \leq 90$ & 7 \\ \hline \end{tabular}
Find the mean of the data in the table. Give your answer correct to 1 decimal place where appropriate.

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Problem 24961

Find the exact values of the following. a) $\sin\frac{7\pi}{6} =$ b) $\sin\left(\frac{4\pi}{3}\right)$ c) $\cos\frac{3\pi}{4}$

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Problem 24962

Note: You may need to assume the fact that $\lim_{M \to +\infty} M^n e^{-M} = 0$ for all $n$ .
Decide whether or not the given integral converges.
$\int_{-\infty}^{-8} \frac{1}{x^2} dx$
The integral converges. The integral diverges.
If the integral converges, compute its value. (If the integral diverges, enter DNE.)

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Problem 24963

4. Find the measure of each angle, to the nearest degree.
a) $\tan \theta = 1.5$ b) $\tan A = \frac{3}{4}$ c) $\tan B = 0.6000$ d) $\tan W = \frac{4}{5}$ e) $\tan C = 0.8333$ f) $\tan \theta = \frac{6}{7}$ g) $\tan X = 3.0250$ h) $\tan \theta = \frac{15}{9}$

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Problem 24964

Exercice 1 :
1) Trace en vert le symétrique de cette figure par la symétrie de centre O. 2) Trace en rouge l'image de cette figure par la translation qui transforme A en B. 3) Trace en noir l'image de cette figure par la rotation de centre O, d'angle $60^\circ$ dans le sens anti-horaire.
Exercice 2 :
1) Trace en vert le symétrique de cette figure par rapport à la droite (d). 2) Trace en rouge l'image de cette figure par la translation qui transforme C en O'. 3) Trace en noir l'image de cette figure par la rotation de centre O, d'angle $90^\circ$ dans le sens antihoraire.

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Problem 24965

(c) Estimate $\int_0^6 (x^2 + 1) dx$ using a right-hand sum with $n = 3$ (i.e. $R_3$ ).
Round your answer to two decimal places.
$R_3 =$

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Problem 24966

Question 5 (Mandatory) (1 point) In $\triangle \mathrm{DEF}, d=36 \mathrm{~m}, e=48 \mathrm{~m}$ and $f=55.3 \mathrm{~m}$ . State which unknown measurements you can use the cosine law to directly solve for, and determine their measures to the nearest degree or metre, whichever is appropriate.

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Problem 24967

$-6(2 r-2)=-8 r+40$

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Problem 24968

6. The table below give the number of homes (in thousands) build each year in a developing suburb. Find the rate of change between 2004 and 2007 using the table.
Year | Homes (thousands) ---|--- 2004 | 7.1 2005 | 8.4 2006 | 9.2 2007 | 10.3 2008 | 11

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Problem 24969

Determine the following indefinite integral. Check your work by differentiation. $\begin{array}{c} \int \sqrt[13]{r^{7}} d r \\ \int \sqrt[13]{r^{7}} d r=\square \end{array}$ $\square$

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Problem 24970

Question 8 (Mandatory) (1 point) Wendy, Karen, and Steve are playing soccer. Karen has the ball. Karen and Wendy are 3.3 m apart. Karen and Steve are 5.5 m apart. The angle between the lines from Wendy to Karen and Wendy to Steve is $70^{\circ}$ . Karen wants to pass the ball between Steve and Wendy. To the nearest degree, what is the angle between the lines from Karen to Steve and Karen to Wendy?

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Problem 24971

Use integration by substitution to solve the integral below. Use C for the constant of integration.
$\int e^{x^6+3} \cdot 6x^5 dx$
Answer 4 Points
Choose the correct answer from the options below.
$e^{x^6+3} + C$
$36e^{x^6+3}x^{10} + 30e^{x^6+3}x^4 + C$
$e^{6x^5} + C$
$e^{\frac{1}{7}x^7+3x} + C$

See Solution

Problem 24972

The digit 3 in which number represents a value of 3 tens? Choose 1 answer: A 6,300 B 8.35 C 732.9

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Problem 24973

The Scott family takes a walk together every night after dinner. It takes them 5 minutes to walk 4 blocks.
Complete the table.
Minutes 5 _ _ 30 Blocks walked 4 12 16 ___
Graph the data from the table.

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Problem 24974

Solve the following pair of simultaneous equations: $\begin{aligned} 3 x+y & =19 \\ x-y & =1 \end{aligned}$

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Problem 24975

Solve $\begin{aligned} 4 y+x & =27 \\ y-x & =3 \end{aligned}$

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Problem 24976

The weights of badgermoles in the Earth Kingdom are normally distributed, with mean weight 1150 kg and standard deviation 50 kg . Find the probability that a badgermole caught at random has a weight greater than 1260 kg . z Table Link 0.0122 0.0162 0.0158 0.0150

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Problem 24977

Consider the following. $f(x)=x^{4}-3 x^{2}-4$
Find all the zeros of the function. (Enter your answers as a comma-separated li $x=$ $\square$

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Problem 24978

2) $\lim_{x \to 1} \frac{\ln{x^2}}{x^2 - 1}$

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Problem 24979

$3)\ \log{(x^2+1)}-x=0$

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Problem 24980

Area under a Curve
30. Find the first-quadrant area bounded by the curve $y=x^{2}+1$ , the $y$ -axis, and the lines $y$ $=3$ and $y=6$ .

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Problem 24981

The vectors $\mathbf{u}$ and $\mathbf{v}$ have the same direction. a. Find $\|\mathbf{u}\|$ . b. Find $\|v\|$ . c. Is $\mathbf{u}=\mathbf{v}$ ? Explain. a. $\|\mathbf{u}\|=$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

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Problem 24982

Question 3
Find the average rate of change of the function $f(x)=\frac{7}{3 x+6}$ , on the interval $x \in[3,5]$ . Average rate of change $=$ $\square$ Give an exact answer. Submit Question

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Problem 24983

Suppose a drawer contains four green socks, five red socks, and three white socks. We draw one sock from the drawer and it is equally likely that any one of the socks is drawn. Find the probabilities of the events in parts (a)-(e).
a. Find the probability that the sock is red. (Type an integer or a simplified fraction.)
b. Find the probability that the sock is green or white. (Type an integer or a simplified fraction.)
c. Find the probability that the sock is brown. (Type an integer or a simplified fraction.)
d. Find the probability that the sock is not green. (Type an integer or a simplified fraction.)
e. We reach into the drawer without looking to pull out four socks. What is the probability that we get at least two socks of the same color? (Type an integer or a simplified fraction.)

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Problem 24984

65) $f(x) = \frac{x^2 - 6x + 2}{x+8}$
A) $x = y + 6$ B) $y = x - 14$ Objective: (4.5) Find Oblique Asymptote of Rational Function
Solve.
66) $x^2 - 9x + 20 > 0$
A) $(5, \infty)$ B) $(-\infty, 4) \cup (5, \infty)$ Objective: (4.6) Solve Quadratic Polynomial Inequality
List the critical values of the related function. Then solve the inequality.
67) $\frac{1}{x+6} > 0$
A) No critical values; $\emptyset$ B) $-6; (-\infty, -6)$ Objective: (4.6) Solve Rational Inequality I

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Problem 24985

Solve the following system of equations. $-3x+y=17$ $7x+y=-23$ $x=$ $y=$

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Problem 24986

8. How long does it take a 720 Watt electric drill to transform 45,000 J of energy? [2 marks] $W = 720 W$ $t_W = 95,000$ $E_t = W \times t$ $t = 62.5 s$ $45000 = \frac{720t}{720}$

See Solution

Problem 24987

5. $KLMN \sim PQRS$ ; find $x$ $KN = 7x - 9$ $LM = 4x + 4$ $QP = 48$ $RS = 60$
3. $MNP \sim QRP$ ; find $PR$ $MN = 24$ $NP = x + 8$ $QR = 28$ $RP = 3x - 9$
6. $ARST \sim AYSZ$ ; find $YZ$ $AR = 3x - 7$ $RS = 2x + 2$ $AY = 40$ $YZ = Z5$
4. $ABCD \sim AFGE$ ; find $FE$ $BC = 39$ $CD = 42$ $FG = 4x + 2$ $FE = 5x - 2$

See Solution

Problem 24988

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.

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Problem 24989

13. $\begin{aligned} -60 & =x-16 \\ -60+\square & =x-16+ \end{aligned}$

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Problem 24990

$Pollution\ and\ altitude:\ In\ a\ random\ sample\ of\ 331\ cars\ driven\ at\ low\ altitudes,\ 52\ of\ them\ exceeded\ a\ standard\ of\ 11\ grams\ of\ particulate\ pollution\ per\ gallon\ of\ fuel\ consumed.\ In\ an\ independent\ random\ sample\ of\ 85\ cars\ driven\ at\ high\ altitudes,\ 23\ of\ them\ exceeded\ the\ standard.\ Can\ you\ conclude\ that\ the\ proportion\ of\ high-altitude\ vehicles\ exceeding\ the\ standard\ differs\ from\ the\ proportion\ of\ low-altitude\ vehicles\ exceeding\ the\ standard?\ Let\ p_1\ denote\ the\ proportion\ of\ low-altitude\ vehicles\ exceeding\ the\ standard\ and\ p_2\ denote\ the\ proportion\ of\ high-altitude\ vehicles\ exceeding\ the\ standard.\ Use\ the\ \alpha = 0.01\ level\ of\ significance\ and\ the\ P-value\ method\ with\ the\ TI-84\ Plus\ calculator.$
$Part:\ 0/4$
$Part\ 1\ of\ 4$
$State\ the\ appropriate\ null\ and\ alternate\ hypotheses.$
$H_0:$
$H_1:$
$This\ hypothesis\ test\ is\ a\ (Choose\ one)\ test.$

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Problem 24991

1 Fill in the Blank 1 point An equation is shown. $(\frac{27}{8})^{-\frac{2}{3}} = \frac{a}{b}$ Find the value of each variable. a = type your answer... b = type your answer...

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Problem 24992

12. Marco has $2 \frac{1}{8}$ bags of soil to put in his garden. Each bag of soil will cover $78 \frac{2}{5} \mathrm{ft}^{2}$ . How many square feet will Marco be able to cover if he uses all these bags of soil?

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Problem 24993

Question Watch Video Show Examples As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 5 Second number: 4 Answer Attempt 1 out of 20 $5 \cdot \boxed{\phantom{0}} = 4$ Submit Answer

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Problem 24994

Exer. 21-24: Use polar coordinates to find the limit, if it exists. $21 \lim _{(x, y) \rightarrow(0,0)} \frac{x y^{2}}{x^{2}+y^{2}}$ $22 \lim _{(x, y) \rightarrow(0,0)} \frac{x^{3}-y^{3}}{x^{2}+y^{2}}$ $23 \lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}+y^{2}}{\sin \left(x^{2}+y^{2}\right)}$ $24 \lim _{(4, y) \rightarrow(0,0)} \frac{\sinh \left(x^{2}+y^{2}\right)}{x^{2}+y^{2}}$

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Problem 24995

A cone with a base having a radius of 10 inches has a volume of 261.67 cubic inches. What is the approximate height of the cone? 2.0 inches 2.5 inches 4.5 inches 5.0 inches

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Problem 24996

Suppose that the functions $f$ and $g$ are defined as follows. $f(x) = x-5$ $g(x) = \sqrt{3x-4}$
Find $\frac{f}{g}$ and $f+g$ . Then, give their domains using interval notation.

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Problem 24997

For the region formed by the functions $f(x)=x^{2}-2 x-2$ and $g(x)=5$ on the interval $[-1,2]$ , use definite integrals to find the area of the region. Answer: The area is $\square$ Hint: Follow Example 2.

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Problem 24998

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions. $\begin{array}{r} -10 x-3 y=17 \\ 4 x-9 y=8 \end{array}$

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Problem 24999

24. The drama club sold all the tickets for its annual production in three days. The club sold 143 tickets the first day and 295 tickets the second day. If the drama club sold 826 tickets, how many tickets were sold on the third day of sales? Solve the equation $438+t=826$ for the number of tickets, $t$ , sold on the third day of ticket sales.

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Problem 25000

Find the amount that results from the given investment. $\$ 300$ invested at 5\% compounded daily after a period of 4 years
After 4 years, the investment results in \\square$ . (Round to the nearest cent as needed.)

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Solve

Problem 24901

For the exponential function fff, find f−1f^{-1}f−1 analytically alf(x)=9x−1f(x) = 9^x - 1f(x)=9x−1f−1(x)=f^{-1}(x) = f−1(x)=(Simplify your answer.)Use the graphing tool to graph both fff and f−1f^{-1}f−1. Click to enlarge graph

Problem 24902

8. From a can of milk containing 37.50 litres of milk, the milkman delivers 29.535 litres to one marriage hall, If he is to supply 33.80 litres of milk to the next marriage hall, then how much more milk should be added to the milk left in the can?

Problem 24903

Find the value of xxx. 45∘45^\circ45∘ 83∘83^\circ83∘ x∘x^\circx∘

Problem 24904

Problem 24905

Problem 24906

Solve the inequality for yyy. −5.4>0.8+y-5.4 > 0.8 + y−5.4>0.8+y Simplify your answer as much as possible.

Problem 24907

Problem 24908

Problem 24909

Problem 24910

Problem 24911

Problem 24912

If 5c−2=3c5c - 2 = 3c5c−2=3c, then 24c=24c =24c= [basic] A. 6 B. 8 C. 16 D. 24

Problem 24913

Problem 24914

Problem 24915

The two triangles below are similar.28∘28^\circ28∘ 2 2 B 10 D 76∘76^\circ76∘ 28∘28^\circ28∘ 5 10 X 76∘76^\circ76∘ 76∘76^\circ76∘ 1 76∘76^\circ76∘ W Complete the similarity statement. △VWX∼△\triangle VWX \sim \triangle△VWX∼△ C

Problem 24916

Problem 24917

Problem 24918

Problem 24919

Problem 24920

Problem 24921

Problem 24922

f(x)=(4x−2)2(2x2+1)3f(x) = (4x - 2)^2 (2x^2 + 1)^3f(x)=(4x−2)2(2x2+1)3.Find f′(x)f'(x)f′(x), and then evaluate f′f'f′ at x=2x = 2x=2 and x=−2x = -2x=−2.f′(2)=f'(2) =f′(2)=f′(−2)=f'(-2) =f′(−2)=

Problem 24923

Problem 24924

Is x=3x = 3x=3, y=13y = \frac{1}{3}y=31​ a solution of the given system of equations?{4x−6y=1013x−2y=−13\begin{cases} 4x - 6y = 10 \\ \frac{1}{3}x - 2y = -\frac{1}{3} \end{cases}{4x−6y=1031​x−2y=−31​​Is the first equation satisfied? Yes No

Problem 24925

Is x=2x = 2x=2, y=13y = \frac{1}{3}y=31​ a solution of the given system of equations? {5x−6y=813x−4y=−23\begin{cases} 5x - 6y = 8 \\ \frac{1}{3}x - 4y = -\frac{2}{3} \end{cases}{5x−6y=831​x−4y=−32​​ Is the first equation satisfied? Yes No

Problem 24926

Problem 24927

Problem 24928

Problem 24929

QuestionSolve for all values of xxx by factoring. x2+x−16=xx^{2}+x-16=xx2+x−16=xAnswer Attempt 1 out of 3

Problem 24930

Problem 24931

Problem 24932

6) Javier is making a recipe that requires 160 mL of 40% pure fruit juice. He has 25% pure fruit juice solution and a 50% pure fruit juice solution. How many milliliters of each solution should he mix to obtain the needed solution?

Problem 24933

Problem 24934

Solve the equation 2x2−19x+2=−10x2 x^{2}-19 x+2=-10 x2x2−19x+2=−10x to the nearest tenth.Answer Attempt 1 out of 3 (ค) Additional Solution Θ\ThetaΘ No Solution

Problem 24935

Problem 24936

Scanned with CamScannerFind the numerical value of [∑n2δ[n+1]]\left[\sum n^{2} \delta[n+1]\right][∑n2δ[n+1]] : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

Problem 24937

Problem 24938

Problem 24939

Solve the following inequality algebraically. −3x2+5x>−3x−3-3 x^{2}+5 x>-3 x-3−3x2+5x>−3x−3Answer Attempt 1 out of 3 □\square□

Problem 24940

Problem 24941

Решите уравнение: cos⁡(6πx5)=2x2+2x−35\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}cos(56πx​)=2x2+2x−35​

Problem 24942

Assume that a procedure yields a binomial distribution with a trial repeated n=30n=30n=30 times. Use the binomial probability formula to find the probability of x=5x=5x=5 successes given the probability p=′15p='15p=′15 of success on a single trial. Round to three decimal places.

Problem 24943

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is \$600 and the annual interest rate is 3.7%?Interest = $\$$[ ? ]Round your answer to the nearest hundredth.

Problem 24944

Problem 24945

Solve the given system of equations. If the system has no solution, say that it is inconsistent.x−3y+4z=5x - 3y + 4z = 5x−3y+4z=52x+y+z=−42x + y + z = -42x+y+z=−4−2x+3y−3z=−2-2x + 3y - 3z = -2−2x+3y−3z=−2

Problem 24946

Problem 24947

Complete the sentence below. An mmm by nnn rectangular array of numbers is called a(n) _____.An mmm by nnn rectangular array of numbers is called a(n) column index. matrix. row index. entry.

Problem 24948

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _______ matrix.The matrix used to represent a system of linear equations is called a(n) _______ matrix. coefficient augmented invertible resulting

Problem 24949

Complete the sentence below. The notation a35a_{35}a35​ refers to the entry in the _______ row and _______ column of a matrix.The notation a35a_{35}a35​ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

Problem 24950

Diberi 63x−2=12966^{3 x-2}=129663x−2=1296, cari nilai xxx. Given 63x−2=12966^{3 x-2}=129663x−2=1296, find the value of xxx.

Problem 24951

Problem 24952

Find the amount of work done if an object is pushed horizontally 70 m by a force of 25 N directed 60∘60^{\circ}60∘ above the horizontal. Give the exact answer. Do not round.The amount of work done is □\square□ N⋅m\mathrm{N} \cdot \mathrm{m}N⋅m □\sqrt{\square}□​ ㅁ

Problem 24953

When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.030.030.03 cm/min. At what rate is the plate's area increasing when the radius is 575757 cm?The rate of change of the area is _______ cm2\text{cm}^2cm2/min. (Type an exact answer in terms of π\piπ.)

Problem 24954

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is \$680 and the annual interest rate is 3.6%? Interest = \([ ? ]\) Round your answer to the nearest hundredth.

For the exponential function $f$ , find $f^{-1}$ analytically al
$f(x) = 9^x - 1$
$f^{-1}(x) =$
(Simplify your answer.)
Use the graphing tool to graph both $f$ and $f^{-1}$ . Click to enlarge graph

Find the value of $x$ . $45^\circ$ $83^\circ$ $x^\circ$

Solve the inequality for $y$ . $-5.4 > 0.8 + y$ Simplify your answer as much as possible.

If $5c - 2 = 3c$ , then $24c =$ [basic] A. 6 B. 8 C. 16 D. 24

The two triangles below are similar.
$28^\circ$ 2 2 B 10 D $76^\circ$ $28^\circ$ 5 10 X $76^\circ$ $76^\circ$ 1 $76^\circ$ W Complete the similarity statement. $\triangle VWX \sim \triangle$ C

$f(x) = (4x - 2)^2 (2x^2 + 1)^3$ .
Find $f'(x)$ , and then evaluate $f'$ at $x = 2$ and $x = -2$ .
$f'(2) =$
$f'(-2) =$

Is $x = 3$ , $y = \frac{1}{3}$ a solution of the given system of equations?
$\begin{cases} 4x - 6y = 10 \\ \frac{1}{3}x - 2y = -\frac{1}{3} \end{cases}$
Is the first equation satisfied? Yes No

Is $x = 2$ , $y = \frac{1}{3}$ a solution of the given system of equations? $\begin{cases} 5x - 6y = 8 \\ \frac{1}{3}x - 4y = -\frac{2}{3} \end{cases}$ Is the first equation satisfied? Yes No

Question
Solve for all values of $x$ by factoring. $x^{2}+x-16=x$
Answer Attempt 1 out of 3

Solve the equation $2 x^{2}-19 x+2=-10 x$ to the nearest tenth.
Answer Attempt 1 out of 3 (ค) Additional Solution $\Theta$ No Solution

Scanned with CamScanner
Find the numerical value of $\left[\sum n^{2} \delta[n+1]\right]$ : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

Решите уравнение: $\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}$

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is \$600 and the annual interest rate is 3.7%?
Interest = $\$$ [ ? ]
Round your answer to the nearest hundredth.

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$
$2x + y + z = -4$
$-2x + 3y - 3z = -2$

Complete the sentence below. An $m$ by $n$ rectangular array of numbers is called a(n) _____.
An $m$ by $n$ rectangular array of numbers is called a(n) column index. matrix. row index. entry.

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _ matrix.
The matrix used to represent a system of linear equations is called a(n) _ matrix. coefficient augmented invertible resulting

Complete the sentence below. The notation $a_{35}$ refers to the entry in the _ row and _ column of a matrix.
The notation $a_{35}$ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

Diberi $6^{3 x-2}=1296$ , cari nilai $x$ . Given $6^{3 x-2}=1296$ , find the value of $x$ .

Find the amount of work done if an object is pushed horizontally 70 m by a force of 25 N directed $60^{\circ}$ above the horizontal. Give the exact answer. Do not round.
The amount of work done is $\square$ $\mathrm{N} \cdot \mathrm{m}$ $\sqrt{\square}$ ㅁ

When a circular plate of metal is heated in an oven, its radius increases at a rate of $0.03$ cm/min. At what rate is the plate's area increasing when the radius is $57$ cm?
The rate of change of the area is _______ $\text{cm}^2$ /min. (Type an exact answer in terms of $\pi$ .)

Solve by completing the square: $z^{2}=12 z+1$

Find the value of $x$ for $3^{x-2}=81^{x}$ . Jawapan / Answer:

Solve for $x$ : $\begin{array}{l} \log _{6} x+\log _{6}(x+4)=5 \\ x= \end{array}$

Find the exact values of the following. a) $\sin\frac{7\pi}{6} =$ b) $\sin\left(\frac{4\pi}{3}\right)$ c) $\cos\frac{3\pi}{4}$

(c) Estimate $\int_0^6 (x^2 + 1) dx$ using a right-hand sum with $n = 3$ (i.e. $R_3$ ).
Round your answer to two decimal places.
$R_3 =$

$-6(2 r-2)=-8 r+40$

6. The table below give the number of homes (in thousands) build each year in a developing suburb. Find the rate of change between 2004 and 2007 using the table.
Year | Homes (thousands) ---|--- 2004 | 7.1 2005 | 8.4 2006 | 9.2 2007 | 10.3 2008 | 11

Determine the following indefinite integral. Check your work by differentiation. $\begin{array}{c} \int \sqrt[13]{r^{7}} d r \\ \int \sqrt[13]{r^{7}} d r=\square \end{array}$ $\square$

The Scott family takes a walk together every night after dinner. It takes them 5 minutes to walk 4 blocks.
Complete the table.
Minutes 5 _ _ 30 Blocks walked 4 12 16 ___
Graph the data from the table.

Solve the following pair of simultaneous equations: $\begin{aligned} 3 x+y & =19 \\ x-y & =1 \end{aligned}$