Browse Math problems Studdy Solved!

Problem 51901

Fast computer: Two microprocessors are compared on a sample of 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are as follows: \begin{tabular}{ccccccc} \hline & \multicolumn{6}{c}{ Code } \\ \hline & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Processor A & 28.9 & 17.1 & 21.8 & 17.6 & 20.5 & 26.4 \\ \hline Processor B & 22.4 & 18.1 & 28.9 & 28.4 & 24.7 & 27.5 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Find a $98 \%$ confidence interval for the difference between the mean speeds. Let $d$ represent the speed of processor A minus the speed of processor B . Use the TI-84 Plus calculator. Round the answers to two decimal places.
A 98\% confidence interval for the difference between the mean speeds is $\square$ $<\mu_{d}<$ $\square$ .

See Solution

Problem 51902

$\text{What are the most common ages of people at the bowling alley?}$ $\square$ $\text{What is the median age of people at the bowling alley?}$ $\square$

See Solution

Problem 51903

If $f(x)=e^{x} \sin x$ , then $f^{\prime}(x)=$

See Solution

Problem 51904

Find the discontinuities.
5. $f(x)=\frac{x-2}{x^{2}-3 x+2}$

See Solution

Problem 51905

Amanda filled her gas tank three times last week. Here are the amounts of gas she bought (in gallons). $8.62,14.4,9$
What is the total amount of gas Amanda bought last week? $\square$ gallons

See Solution

Problem 51906

Brake wear: For a sample of 9 automobiles, the mileage (in 1000 s of miles) at which the original front brake pads were worn to $10 \%$ of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to $10 \%$ of their original thickness. The results were as follows: \begin{tabular}{ccc} \hline Car & Rear & Front \\ \hline 1 & 41.6 & 32.6 \\ 2 & 35.8 & 26.7 \\ 3 & 46.4 & 37.9 \\ 4 & 46.2 & 36.9 \\ 5 & 38.8 & 29.9 \\ 6 & 51.8 & 42.3 \\ 7 & 51.2 & 42.5 \\ 8 & 44.1 & 33.9 \\ 9 & 47.3 & 36.1 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Construct a $90 \%$ confidence interval for the difference in mean lifetime between the front and rear brake pads. Let $d$ represent the mileage of the rear pads minus the mileage of the front ones. Round the answers to two decimal places.
A $90 \%$ confidence interval for the mean difference in lifetime between front and rear brake pads is $\square$ $<\mu_{d}<$ $\square$ .

See Solution

Problem 51907

33 In un rettangolo la base è lunga $(2 x+1) \mathrm{cm}$ e l'altezza 6 cm . Determina $x$ in modo che il rettangolo abbia area minore di quella di un quadrato di lato 4 cm . $\left[-\frac{1}{2}<x<\frac{5}{6}\right]$

See Solution

Problem 51908

$\frac{x+5}{x}-\frac{9}{8}=0$
Select the correct choice below and, if necessary, fill in

See Solution

Problem 51909

Factorise fully $12 a c-4 a$ $\square$
Submit Answer

See Solution

Problem 51910

2. Résoudre dans $\mathbb{N} X \mathbb{N}$ le système suivant: $\left\{\begin{aligned} C_{x}^{y} & =C_{x}^{y+1} \\ 4 C_{x}^{y} & =5 C_{x}^{y-1} \end{aligned}\right.$

See Solution

Problem 51911

What is the solution to this equation? $x-12=-4$ A. $x=-16$ B. $x=16$ C. $x=8$ D. $x=-8$

See Solution

Problem 51912

Write the following number in standard decimal form. four hundredths

See Solution

Problem 51913

Find the indefinite integral. $\int x^{-8} d x$ $\square$ $+C$

See Solution

Problem 51914

Assume that an investor has formed a portfolio of two assets; asset $A$ and asset B. if he invested $30 \%$ of his wealth in asset $A$ . If the return on asset $A$ is $20 \%$ and the return on the asset B is $40 \%$ , the weight of the wealth invested in asset $B$ is 40\% 70\% We cannot find the weight 60\%

See Solution

Problem 51915

(iii) If $y=\frac{1}{2 x}-\frac{1}{3 x^{2}}+\frac{1}{4 x^{3}}$ . Find $\frac{d y}{d x}$ (i) Find the equation of the tangent and of the normal to the curve function $y=f(x)=x^{3}+2 x^{2}+1$ at $x=-1$ on it

See Solution

Problem 51916

\begin{tabular}{|c|c|c|} \hline FRACTION & DECIMAL & PERGENT \\ \hline 1/9 & a. ? & b.? \\ \hline c. ? & 0.444 & d. ? \\ \hline e. ? & 0.125 & 12.5 \\ \hline f. ? & g. ? & 16.6 \\ \hline $3 / 8$ & h. ? & i. ? \\ \hline j. ? & k. ? & 88.8 \\ \hline 1.? & 0.777 & m. ? \\ \hline $1 / 5$ & n. ? & o.? \\ \hline p. ? & 666 & q. ? \\ \hline \end{tabular}

See Solution

Problem 51917

(Chapter 5 plus sections 0.1 and 0.4 )
Solve using the substitution method. $\begin{aligned} x-y & =-2 \\ 6 x+8 y & =-26 \end{aligned}$

See Solution

Problem 51918

In the provided box, type in the two Capital letters and one word used by our textbook that fill in the blanks. Separate each with a space. Spelling of the word counts. For example: $X$ connects $Y$
The notation for conditional probability is $(P(B \mid A)$ which reads as the conditional probability of event $\qquad$ will occur $\qquad$ that the event $\qquad$ has already occurred.
Type your answer here $\square$

See Solution

Problem 51919

What is the solution to this equation? $-15 x=90$ A. $x=-105$ B. $x=105$ C. $x=6$ D. $x=-6$

See Solution

Problem 51920

A high school principal wanted to know if there was a difference in absences for 9 th grade, 10 th grade, 11 th grade, or 12 th grade among students with less than a 2.0 GPA. She took a random sample of $\mathrm{n}=5$ students from each grade and compared absences among the four grades using ANOVA. The data are below: \begin{tabular}{|c|c|c|c|} \hline 9 th grade & 10th grade & 11 th grade & 12 th grade \\ \hline 6 & 10 & 17 & 15 \\ 9 & 12 & 8 & 16 \\ 6 & 11 & 11 & 12 \\ 7 & 11 & 14 & 12 \\ 7 & 14 & 15 & 12 \\ \hline \end{tabular}
2. Calculate the degrees of freedom Between Groups $\left(\mathrm{df}_{\mathrm{BG}}\right)$
3. Calculate the degrees of freedom Within Group ( $\mathrm{df}_{\mathrm{WG}}$ )
4. Calculate the Sum of Squares total ( $\mathrm{SS}_{\text {tot }}$ )
5. Calculate the Sum of Squares Between Groups $\left(\mathrm{SS}_{\mathrm{BG}}\right)$
6. Calculate Sum of Squares Within Groups (SSWG)
7. Calculate Mean Square Between Group $\left(\mathrm{MS}_{\mathrm{BG}}\right)$
8. Calculate Mean Square Within Group (MSwG)
9. Calculate the F statistic
10. Using the table in the back of the book, find the critical value for $F$ ( $\mathrm{F}_{\text {crit }}$ ) with $\alpha=.05$
11. Calculate the Tukey HSD (using $\alpha=.05$ )
12. Which of the following is the appropriate statistical conclusion?

See Solution

Problem 51921

Use the quadratic formula to solve the equation. $x^{2}+4 x+20=0$

See Solution

Problem 51922

Directions: Read the following statements. Select the choice that correctly interprets the given information.
1. Water is draining out of a conical tank with height $h$ and radius $r$ at a rate of 8 cubic liters per second. A) $\frac{d h}{d t}=8$ B) $\frac{d h}{d t}=-8$ C) $\frac{d V}{d t}=-8$ D) $\frac{d V}{d t}=8$
2. The area of a circle with radius $r$ is increasing. Find the rate that the radius is changing when the circumference of the circle is increasing at a rate of 4 inches per second. A) $\frac{d A}{d t}=4$ B) $\frac{d C}{d t}=4$ C) $\frac{d r}{d t}=4$ D) $\frac{d C}{d t}=4 \pi$
3. A 30 foot ladder is sliding down a wall at a rate of 2 feet per second. Find the rate that the base of the ladder is moving away from the wall when the top of the ladder is 18 feet up on the wall. A) $\frac{d x}{d t}=-2$ B) $\frac{d y}{d t}=-2$ C) $\frac{d z}{d t}=-2$ D) $\frac{d y}{d t}=2$
4. A triangle with base $b$ and height $h$ is expanding such that its area is increasing at the rate $4 \mathrm{~m}^{2} / \mathrm{s}$ . A) $\frac{d A}{d t}=4$ B) $\frac{d b}{d t}=4$ C) $\frac{d h}{d t}=4$ b) $\frac{d t}{d A}=4$
5. A spherical rock erodes over time due to winds and rain. The radius of the rock is changing at a rate of $3 \mathrm{in} / \mathrm{year}$ . Find the rate that the volume of the rock is changing when the surface area (A) of the rock is $400 \mathrm{in}^{2}$ . A) $\frac{d A}{d t}=3$ B) $\frac{d r}{d t}=3$ C) $\frac{d V}{d t}=-3$ D) $\frac{d r}{d t}=-3$

See Solution

Problem 51923

The tables represent the functions $f(x)$ and $g(x)$ . \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{f}(\boldsymbol{x})$ \\ \hline-3 & -5 \\ \hline-2 & -3 \\ \hline-1 & -1 \\ \hline 0 & 1 \\ \hline 1 & 3 \\ \hline 2 & 5 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{g}(\boldsymbol{x})$ \\ \hline-3 & -13 \\ \hline-2 & -9 \\ \hline-1 & -5 \\ \hline 0 & -1 \\ \hline 1 & 3 \\ \hline 2 & 7 \\ \hline \end{tabular}
Which input value produces the same output value for the two functions? $x=-3$ $x=-1$ $x=0$ $x=1$

See Solution

Problem 51924

$\begin{array}{l}y=\frac{7}{8} x-9 \\ y=-\frac{3}{4} x+4\end{array}$

See Solution

Problem 51925

Absorption rates: In a study to compare the absorption rates of two antifungal ointments (labeled " A " and " B "), equal amounts of the two drugs were applied to the skin of 14 volunteers. After six hours, the amounts absorbed into the skin (in $\mu \mathrm{g} / \mathrm{cm}^{2}$ ) were measured. The results were as follows: \begin{tabular}{ccc} \hline Subject & A & B \\ \hline 1 & 3.31 & 2.34 \\ 2 & 2.38 & 2.45 \\ 3 & 2.82 & 2.40 \\ 4 & 2.03 & 2.70 \\ 5 & 2.26 & 1.98 \\ 6 & 3.57 & 1.88 \\ 7 & 3.27 & 2.75 \\ 8 & 3.65 & 1.57 \\ 9 & 2.74 & 1.94 \\ 10 & 3.28 & 2.51 \\ 11 & 3.73 & 2.55 \\ 12 & 4.34 & 2.09 \\ 13 & 3.59 & 2.62 \\ 14 & 3.45 & 2.48 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Construct a $98 \%$ confidence interval for the mean difference between the amounts absorbed. Let $d$ represent the amount absorbed by drug A minus the amount absorbed by drug B. Use the TI-84 Plus calculator and round the answers to three decimal places.
A 98\% confidence interval for the mean difference between the amounts absorbed is $\square$ $<\mu_{d}<$ $\square$ .

See Solution

Problem 51926

Directions: For the following problems, differentiate with respect to $t$ . Do not simplify.
6. $2 s=(3 r-4)^{5}$
7. $x^{2}=\sqrt{3-2 z}$
8. $\tan (\theta)=\frac{y}{x}$
9. $e^{2 x}=\ln (4 y+3)$
10. $x y=4$
11. $x^{2}+y^{2}=z^{2}$
12. $\cos (\theta)=\frac{x}{17}$
13. $P(x)=\frac{5 x}{3 x-4}$
14. $V=\frac{1}{3} \pi r^{2} h$
15. $2 h=\frac{1}{4}\left(r^{2}-6\right)$
16. $\frac{x+2 y}{x}=x^{2} y$
17. $A=\frac{1}{2} b h$

See Solution

Problem 51927

Suppose that the function $g$ is defined, for all real numbers, as follows. $g(x)=\left\{\begin{array}{ll} \frac{1}{2} x^{2}-5 & \text { if } x \neq 2 \\ 2 & \text { if } x=2 \end{array}\right.$
Find $g(-4), g(2)$ , and $g(4)$ . $\begin{array}{l} g(-4)= \\ g(2)= \\ g(4)= \end{array}$

See Solution

Problem 51928

12. [0/2 Points] DETAILS MYNOTES TANAPCALCBR10 6.1.016.MI.SA. PREVIOUS ANSWERS
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral. $\int 4 u^{1 / 8} d u$
Step 1 Recall the rule for the Indefinite Integral of a Constant Multiple of a Function, which states that for a constant $c$ , the following holds. $\int c f(u) d u=c \int f(u) d u$
Applying this rule gives the following result. $\int 4 u^{1 / 8} d u=\square \times \text { (D) } \int u^{1 / 8} d u$

See Solution

Problem 51929

12. [0/2 Points] DETAILS MYNOTES TANAPCALCBR10 6.1.016.MI.SA. PREVIOUS ANSWERS
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Find the indefinite integral. $\int 4 u^{1 / 8} d u$
Step 1 Recall the rule for the Indefinite Integral of a Constant Multiple of a Function, which states that for a constant $c$ , the following holds. $\int c f(u) d u=c \int f(u) d u$
Applying this rule gives the following result. $\int 4 u^{1 / 8} d u=\square \times \text { (D) } \int u^{1 / 8} d u$

See Solution

Problem 51930

The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The diagram to the right represents the corner lot. The children's path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot.

See Solution

Problem 51931

Directions: Solve for area and perimeter in each of the following problems. 1) 2) 3) $\square$

See Solution

Problem 51932

Find the equation of the tangentizine at the given poin 7. $x^{2}-y^{2}=27$ at $(6,-3)$

See Solution

Problem 51933

Question 4
Factor $4 x^{6} y^{4}+12 x^{5} y^{5}+4 x^{4} y^{3}$

See Solution

Problem 51934

9. Given the points $(5,10$ , $) and (7,20)$ :
Part A: Find the slope of the line that contains the points. Slope =
Part B: Find the equation of the line that contains the points. Equation:

See Solution

Problem 51935

To find the x intercept let A y-o B X-O C xandy Continue

See Solution

Problem 51936

Solve for $d$ in the proportion. $\begin{array}{l} \frac{6}{4}=\frac{d+5}{6} \\ d=\square \end{array}$

See Solution

Problem 51937

What is the slope of the line represented by the equation $f(t)=2 t-6$ ? The slope is 2 and the $y$ -intercept is -6 . The slope is -6 and the $y$ -intercept is 2 . The slope is 2 and the $y$ -intercept is 6 . The slope is 6 and the $y$ -intercept is 2 .

See Solution

Problem 51938

Ind the number of solutions by graphing the system of equations. Select "None" if applicable. (Hint: Rewrite the system of equations into familiar forms to raph.) $\begin{array}{l} \ln 6=2 \ln x-\ln y \\ x^{2}+y^{2}-8 y+7=0 \end{array}$
Number of solutions: $\square$ None

See Solution

Problem 51939

12. A 0.025 kg object vibrates at the end of a spring. If the maximum displacement of the object is 0.030 cm , and its period is 0.50 s , what is the maximum acceleration of the object?

See Solution

Problem 51940

$\left(\frac{5 f^{9} g^{4} h^{2}}{f^{2} h^{3}}\right)^{0}$

See Solution

Problem 51941

Determine whether the outcome is a Type I error, a Type II error, or a correct decision. A test is made of $H_{0}: \mu=15$ versus $H_{1}: \mu>15$ . The true value of $\mu$ is 17 , and $H_{0}$ is not rejected.
The outcome of the test is a (Choose one) Type I error correct decision Type II error

See Solution

Problem 51942

Jack collects the running times of some athletes and records th in the table below. \begin{tabular}{|c|c|} \hline Time $(x$ seconds) & Frequency \\ \hline $30<x \leq 35$ & 17 \\ \hline $35<x \leq 40$ & 18 \\ \hline $40<x \leq 45$ & 11 \\ \hline $45<x \leq 50$ & 5 \\ \hline $50<x \leq 55$ & 14 \\ \hline \end{tabular}
Select the class interval containing the median. $30<x \leq 35$ $35<x \leq 40$ $40<x \leq 45$ $45<x \leq 50$ $50<x \leq 55$

See Solution

Problem 51943

Find each root that is a real number. $-\sqrt{100}$

See Solution

Problem 51944

$x^{2}+39 x+380=0$ $x_{1}=$ $\square$ Round your answer to 2 decimal places. $x_{2}=$ $\qquad$ Round your answer to 2 decimal places.

See Solution

Problem 51945

A sign shows that the distance to Las Vegas is 22 miles. A traveler wants to know what this distance is in kilometers. Help the traveler by completing the parts below. (a) Let $x$ be the unknown number of kilometers. Using the values below, create a proportion that can be used to find $x$ . Use the conversion 1 mile $=1.6$ kilometers.
Values: $\square$ 1 $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ (b) Use the proportion from part (a) to find the distance to Las Vegas in kilometers. Do not round any computations. $\square$ kilomete

See Solution

Problem 51946

\begin{array}{|c|c|c|c|c|c|c|} \hline \multicolumn{2}{|c|}{\text{Morning}} & \multicolumn{2}{c|}{\text{Afternoon}} & \multicolumn{2}{c|}{\text{Night}} & \text{Total} \\ \hline \text{Start} & \text{Stop} & \text{Start} & \text{Stop} & \text{Start} & \text{Stop} & \\ \hline 9:00 & 11:00 & 12:00 & 3:00 & & & \\ \hline 9:00 & 11:30 & 12:30 & 3:00 & & & \\ \hline 9:00 & & & 2:00 & & & \\ \hline 9:00 & 11:30 & 12:30 & 3:00 & & & \\ \hline & & & & & & \\ \hline & & & & & & \\ \hline \end{array}
Calculate the total time for each row in the table. The time should be calculated based on the start and stop times provided for the morning and afternoon sessions. The night session is not included in this calculation. Provide the total time in hours and minutes for each row.

See Solution

Problem 51947

art A: Knowledge and Understanding [1] Which of the following is true about $y=-2(x+3)^{2}-7$ in its transformation from $y$ a. a vertical stretch of $-1 / 2$ (b) a horizontal a vertical translation of 3 translation of 7 1) areflection about the $y$ -axis units left unit up [2] What is the equation in factored form of the graph of the parabola $(A)$ below? $\begin{array}{l} y=9(x+4)(x+2) \quad y-4(x+4)(x+2)) \\ (-3,4) \Rightarrow 4=9(-3+4)(-3+2) \\ 4=a(1)(-1) \\ 4=-9 \end{array}$ [2] What is the equation in vertex form of the graph of the parabola (B) at right? $\begin{array}{ll} y=a(x-3)^{2}+2 & 10-2=49 \\ (1,10) \Rightarrow 10 & =9(1-3)^{2}+2 \\ x, y & =4 a \\ 10 & =a(-2)^{2}+2 \\ 10 & =4 a+2 \end{array} \quad \begin{array}{ll} a & y=2(x-3)^{2}+2 \end{array}$ $x 4=0 \Rightarrow$ $x-1=0$ $-3(x+4)(x-1)=0$ are: 3. [1] The roots of the equation $-3(x+4)(x-1)=0$ are: (a.) $(-4,0)(1,0)$ b. $(\sigma,-4)(0,-1)$ c. $(0.1)(0,1)$ d. 4.8
4. [1] What are the number of roots for the equation $-5 x^{2}+20 x-14=0$ a. 0 b. 1 $2 \quad a=-50$ d. $b=20$ $c=-t h$
5. [1] The parabola $x^{2}-4 x+7$ has (3. No real roots c. Branches not roots

See Solution

Problem 51948

Solve for $w$ . $|3 w+6|=-12$
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $w=$ $\square$
No solution

See Solution

Problem 51949

Use the Law of Sines to find the length of angle $B$ to the nearest whole degree: $\text { Given: } \begin{aligned} & A=117^{\circ} \\ & b=15.3 \mathrm{~m} \\ & a=20.0 \mathrm{~m} \end{aligned}$

See Solution

Problem 51950

2. Which graph appears to show a linear proportional relationship between $x$ and $y$ ?

See Solution

Problem 51951

اذا كان T: $T: \mathfrak{R}^{3} \rightarrow \mathfrak{R}^{3}$ حيث $T(x, y, z)=(x+2 y+3 z, 4 x+8 y+12 z, 3 x+2 y+z)$ 1 2. اوجد نواه ومدى التحويل. 3. اوجد القيم المميزة، والفضاءات المميزة لمصفوفة التحويل الخطي 4. اوجد المصفوفة القطرية D التي تشابه مصفوفة التحويل الخطي A واوجد المصفوفة P بحيث ان D = P

See Solution

Problem 51952

The cost of producing $x$ units of a product is given by $C(x)=800+80 x-80 \ln (x), \quad x \geq 1$
Find the minimum average cost.
Minimum Average Cost $=$ $\square$ Preview My Answers Submit Answers
You have attempted this problem 0 times.

See Solution

Problem 51953

$\frac{y^{-6}}{y^{-10}}$
Simplify. a

See Solution

Problem 51954

Use the information in the Table 3.19 to answer the next eight exercises. The table shows the political party affiliation of each of 67 members of the US Senate in June 2012, and when they are up for reelection. \begin{tabular}{|l|l|l|l|l|} \hline Up for reelection: & Democratic Party & Republican Party & Other & Total \\ \hline November 2014 & 20 & 13 & 0 & \\ \hline November 2016 & 10 & 24 & 0 & \\ \hline Total & & & & \\ \hline \end{tabular}
Table 3.19 101.
What is the probability that a randomly selected senator has an "Other" affiliation? 102.
What is the probability that a randomly selected senator is up for reelection in November 2016? Access for free at https://openstax.org 103.
What is the probability that a randomly selected senator is a Democrat and up for reelection in November 2016? 104.
What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?

See Solution

Problem 51955

Julie is visiting Canada from England. She brought $£ 1000$ . Maria is visiting Canada from Mexico. She brought MX\ $15000. Lia Lei is visiting Canada from China. She brought CN¥20 000. Who has the most money to spend? Show your work.$ $\begin{array}{l} £ 1 \doteq \mathrm{C} \$ 1.650 \\ \mathrm{MX} \$ 1 \doteq \mathrm{C} \$ 0.081 \\ \mathrm{CN} ¥ 1 \doteq \mathrm{C} \$ 0.152 \end{array}$ $

See Solution

Problem 51956

Binomials and trinomials in fractions should be factored after inverting the divisor. $\begin{array}{l} \frac{x^{2}-9}{2 x^{2}-2 x} \cdot \frac{3 x}{x^{2}-x-6} \div \frac{x^{2}+3 x}{x^{2}+7 x+10}= \\ \frac{x^{2}-9}{2 x^{2}-2 x} \cdot \frac{3 x}{x^{2}-x-6} \cdot \frac{x^{2}+7 x+10}{x^{2}+3 x}= \\ \frac{(x+3)(x-3)}{\frac{2 x(x-1)}{2}} \cdot \frac{3 x}{\frac{(x+2)(x-3)}{1} \cdot \frac{(x+5)(x+2)}{x(x+3)}=} \\ \frac{3(x+5)}{2 x(x-1)}=\frac{3 x+15}{2 x^{2}-2 x} \end{array}$
Invert and change to multiplication.
Factor and cancel.
Multiply.
Work these problems.
1. $\frac{2}{3} \cdot \frac{4}{3} \div \frac{12}{9}=$
2. $\frac{4 a^{2}}{5 b} \div \frac{2 a}{b^{2}}=$
3. $\frac{a^{2}-b^{2}}{a^{2}-a b} \cdot \frac{2 a^{2}-2 a}{a-1} \div \frac{a+b}{a^{2}}=$
4. $\frac{a}{b} \div \frac{a}{b}=$
5. $\frac{a}{b^{2}} \div \frac{a^{2}}{b}=$
6. $\frac{x^{5}}{y^{2}} \div \frac{x^{6}}{y^{3}}=$

See Solution

Problem 51957

```latex \begin{array}{l} \text{Name: Taleah Jones} \\ \text{Identify the constant of proportionality. Find your answer on the coloring grid and color the square according to the square in the problem.} \\ \begin{array}{l} B \\ E 1 \\ 18 \\ 3 \\ \hline \end{array} c \\ \begin{array}{|c|c|c|c|} \hline x & 2 & 3 & 4 \\ \hline y & 24 & 36 & 48 \\ \hline \end{array} \\ \begin{array}{|c|c|} \hline \multicolumn{2}{|l|}{\begin{array}{l} E \\ \text{Stage:} \# (x) \end{array}} \\ \hline \begin{array}{l} 2^{2} \|^{2} \sqrt[3]{n} \\ \text{Total number of sides (t)} \end{array} & \\ \hline \end{array} \\ F \\ 6 \\ \text{Sarah bought 3 pounds of grapes for \$2.25. Dan bought 4 pounds of grapes for \$3.00.} \\ \text{Pounds or Bananas:} \\ 3y = 2x \\ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text{Hours} \\ (x) \end{array} & 3 & 6 & 9 \\ \hline \begin{array}{c} \text{Miles} \\ (y) \end{array} & 180 & 360 & 540 \\ \hline \end{array} \\ \text{red} \\ H \\ \text{light green} \end{array}

See Solution

Problem 51958

Exercice 2 PARTIE A Le système d'alarme d'une entreprise fonctionne de telle sorte que, si un danger se présente, l'alarme s'active avec une probabilité de 0,97 . La probabilité qu'un danger se présente est de 0,01 et la probabilité que l'alarme s'active est de 0,01465 . On note $A$ l'évènement «l'alarme s'active» et $D$ l'événement «un danger se présente ». On note $\bar{M}$ l'évènement contraire d'un évènement $M$ et $P(M)$ la probabilité de l'évènement $M$ .
1. Représenter la situation par un arbre pondéré qui sera complété au fur et à mesure de l'exercice.
2. a. Calculer la probabilité qu'un danger se présente et que l'alarme s'active. b. En déduire la probabilité qu'un danger se présente sachant que l'alarme s'active. Arrondir le résultat à $10^{-3}$ .
3. Montrer que la probabilité que l'alarme s'active sachant qu'aucun danger ne s'est présenté est 0,005 .
4. On considère qu'une alarme ne fonctionne pas normalement lorsqu'un danger se présente et qu'elle ne s'active pas ou bien lorsqu'aucun danger ne se présente et qu'elle s'active. Montrer que la probabilité que l'alarme ne fonctionne pas normalement est inférieure à 0,01 . PARTIE B Une usine fabrique en grande quantité des systèmes d'alarme. On prélève successivement et au hasard 5 systèmes d'alarme dans la production de l'usine. Ce prélèvement est assimilé à un tirage avec remise. On note $S$ l'évènement «l'alarme ne fonctionne pas normalement» et on admet que $P(S)=0,00525$ . On considère $X$ la variable aléatoire qui donne le nombre de systèmes d'alarme ne fonctionnant pas normalement parmi les 5 systèmes d'alarme prélevés. Les résultats seront arrondis à $10^{-4}$ .
1. Donner la loi de probabilité suivie par la variable aléatoire $X$ et préciser ses paramètres.
2. Calculer la probabilité que, dans le lot prélevé, un seul système d'alarme ne fonctionne pas normalement.
3. Calculer la probabilité que, dans le lot prélevé, au moins un système d'alarme ne fonctionne pas normalement.
PARTIE C Soit $n$ un entier naturel non nul. On prélève successivement et au hasard $n$ systèmes d'alarme. Ce prélèvement est assimilé à un tirage avec remise. Déterminer le plus petit entier $n$ tel que la probabilité d'avoir, dans le lot prélevé, au moins un système d'alarme qui ne fonctionne pas normalement soit supérieure à 0,07 .
Exercice 3 Partie A : études de deux fonctions On considère les deux fonctions $f$ et $g$ définies sur l'intervalle $[0 ;+\infty[$ par : $f(x)=0,06\left(-x^{2}+13,7 x\right) \quad \text { et } \quad g(x)=(-0,15 x+2,2) \mathrm{e}^{0,2 x}-2,2 \text {. }$
On admet que les fonctions $f$ et $g$ sont dérivables et on note $f^{\prime}$ et $g^{\prime}$ leurs fonctions dérivées respectives.
1. On donne le tableau de variations complet de la fonction $f$ sur l'intervalle $[0 ;+\infty[$ . \begin{tabular}{|c|ccc|} \hline $x$ & 0 & 6,85 & $+\infty$ \\ \hline $f(x)$ & & & $f(6,85)$ \\ & & & \\ \hline \end{tabular}

See Solution

Problem 51959

Find the length of side $a$ to the nearest tenth of a meter:
Law of Cosines: $a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A$

See Solution

Problem 51960

Find the exact value of $\tan \frac{\theta}{2}$ for the angle $\theta$ shown in the right triangle:
Given: $\tan \frac{\theta}{2}= \pm \sqrt{\frac{1-\cos \theta}{1+\cos \theta}}$ $\tan \frac{\theta}{2}=\frac{\sin \theta}{1+\cos \theta}$ $\tan \frac{\theta}{2}=\frac{1-\cos \theta}{\sin \theta}$

See Solution

Problem 51961

3. 7 0 \longdiv { 5 , 5 9 1 }

See Solution

Problem 51962

Convert the complex number to polar form: $4-4 i$

See Solution

Problem 51963

Convert the complex number to rectangular form: $z=7 \operatorname{cis} 120^{\circ}$

See Solution

Problem 51964

Find all $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ such that: $3 \sin ^{2} \theta+2 \sin \theta-1=0$

See Solution

Problem 51965

Use a calculator to approximate $y=\csc ^{-1}(2.8842912)$ to the nearest thousandth of a radian:

See Solution

Problem 51966

Use an identity to re-write the expression as a single function: $2 \sin (16 u) \cos (16 u)$

See Solution

Problem 51967

A box with a square base and open top must have a volume of $171500 \mathrm{~cm}^{3}$ . We wish to find the dimensions of the box that minimize the amount of material used.
First, find a formula for the surface area of the box in terms of only $x$ , the length of one side of the square base. [Hint: use the volume formula to expitess the height of the box in terms of $x$ .] Simplify your formula as much as possible. $A(x)=$ $\square$ Next, find the derivative, $A^{\prime}(x)$ . $A^{\prime}(x)=$ $\square$ Now, calculate when the derivative equals zero, that is, when $A^{\prime}(x)=0$ . [Hint: multiply both sides by $x^{2}$ .] $A^{\prime}(x)=0$ when $x=$ $\square$ We next have to make sure that this value of $x$ gives a minimum value for the surface area. Let's use the second derivative test. Find $A^{\prime \prime}(x)$ . $A^{\prime \prime}(x)=$ $\square$ Evaluate $A^{\prime \prime}(x)$ at the $x$ -value you gave above. $\square$ NOTE: Since your last answer is positive, this means that the graph of $A(x)$ is concave up around that value, so the zero of $A^{\prime}(x)$ must indicate a local minimum for $A(x)$ . (Your boss is happy now.)

See Solution

Problem 51968

that could each be used to solve the probliem, Mers Nia has 5 times as many pictures parnted as her sister, Jade/Nia has 20 pictures painted. How many pictures does Jade have painted?

See Solution

Problem 51969

A set of data items is normally distributed with a mean of 500 . Find the data item in this distribution that corresponds to a given z-score of 2 , with a standard deviation of 40 : Original data value is: 580 Original data value is: 420 Original data value is: 540 Original data value is: 502

See Solution

Problem 51970

A particular circle in the standard $(x, y)$ coordinate plane has an equation of $(x-5)^{2}+y^{2}=38$ . What are the radius of the circle, in coordinate units, and the Goordinates of the center of the circle?

See Solution

Problem 51971

Use any appropriate algebraic techniques combined with trigonometric identities to simpli the expression: $\frac{1}{\cos \theta}-\cos \theta$

See Solution

Problem 51972

Question 5
A rectangle is inscribed with its base on the $x$ -axis and its upper corners on the parabola $y=10-x^{2}$ . What are the dimensions of such a rectangle with the greatest possible area?
Width = $\square$ Height = $\square$ Question Help: Video

See Solution

Problem 51973

A doctor wants to estimate the mean HDL cholesterol of all 20 - to 29 -year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with $99 \%$ confidence assuming $\mathrm{s}=11.6$ based on earlier studies? Suppose the doctor would be content with $90 \%$ confidence. How does the decrease in confidence affect the sample size required?
Click the icon to view a partial table of critical values.
A $90 \%$ confidence level requires 23 subjects. (Round up to the nearest subject.) How does the decrease in confidence affect the sample size required? A. Decreasing the confidence level decreases the sample size needed. B. The sample size is the same for all levels of confidence. C. Decreasing the confidence level increases the sample size needed.

See Solution

Problem 51974

Use the difference formula for cosine to simplify $\cos \left(\theta-\frac{\pi}{2}\right)$ as a single function of $\theta$ :

See Solution

Problem 51975

Find the reference angle for $\theta=-455^{\circ}$ :

See Solution

Problem 51976

9. Delia ordered 18 bores of red ballowns and 12 boxes of blue baltogens for a proty. She ordered a totai of 240 balions. fiow many balloons are in each bow? their (4) 6 (C) 7 (8) 8 (D) 9

See Solution

Problem 51977

Identify each number as prime or composite. Then list all the factors. 5) 2 6) 37 7) 27 8) 54 9) 19 10) 63

See Solution

Problem 51978

Use a system of linear equations to solve the following problem. A new restaurant is to contain two-seat tables and four-seat tables. Fire codes limit the restaurant's maximum occupancy to 58 customers. If the owners have hired enough servers to handle 18 tables of customers, how many of each kind of table should they purchase?
Write a system of linear equations using the given information. Choose correct answer below. A. $\left\{\begin{array}{l}x-y=58 \\ 2 x-4 y=18\end{array}\right.$ B. $\left\{\begin{array}{l}2 x+4 y=58 \\ x+y=18\end{array}\right.$ C. $\left\{\begin{array}{l}2 x-4 y=58 \\ x-y=18\end{array}\right.$ D. $\left\{\begin{array}{l}x+y=58 \\ 2 x+4 y=18\end{array}\right.$
They should purchase $\square$ two-seat tables and $\square$ four-seat tables.

See Solution

Problem 51979

3. Tipo 3: Equaçöes Exponenciais com Logaritmos
Resolva: a) $3^{\log _{3}(x)}=81$ . Estratégia: Reduza a base: $3^{\log _{3}(x)}=3^{4} \Longrightarrow \log _{3}(x)=4$ . b) $5^{2 x}=25^{x+1}$ .
Estratégia: Transforme $25=5^{2}: 5^{2 x}=5_{\downarrow}^{2(x+1)}$ .

See Solution

Problem 51980

Solve the system by the substitution method. $\begin{aligned} x+y & =3 \\ y & =x^{2}-6 x+9 \end{aligned}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ 3. (Type an ordered pair. Use a comma to separate answers if needed.) B. There is no solution.

See Solution

Problem 51981

5377cd673btesfib5tda18248e
Desmos | Beautition. The National Archive. Answer Attempt 1 out of 6

See Solution

Problem 51982

Create four (4) problems that include fractions. Solve the probl using estimation.
Each problem must contain: - at least three (3) fractions - two (2) must include the addition of fractions - two (2) must include subtraction of fractions. - an explanation of your reasoning process for each problem

See Solution

Problem 51983

1. Simples: a) $\log _{4}(x)=2$ . b) $\log _{3}(x+2)=\log _{3}(7)$ . c) $2 \log _{2}(x)=\log _{2}(32)$ .
2. Intermediários: a) $\log _{2}(x)+\log _{2}(x+3)=4$ . b) $\log _{5}(x+4)-\log _{5}(x)=1$ .

See Solution

Problem 51984

Use transformations to graph the function. $q(x)=-(x+2)^{2}+5$

See Solution

Problem 51985

$a_{1}{ }_{1}$ What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth? (1) 1.00 (3) -0.93 (2) 0.93 (4) -1.00

See Solution

Problem 51986

Solve \& State weather the system is inconsistent or equations are dependen $\begin{array}{c} 5 x+y=-5 \\ -15 x-3 y=a \end{array}$

See Solution

Problem 51987

8. $\frac{1}{3}=\frac{-}{9}$

See Solution

Problem 51988

10. $3 a^{2} b \div \frac{3 x}{4 x-y}$

See Solution

Problem 51989

3) A stmple of gas occupies a volume of 800 mL when the pressure is 680 mm Hg . What pressure will cause the gas to occupy a volume of 700 mL . assuming that there is no change in the temperature?
3. $\qquad$
Banles

See Solution

Problem 51990

A number, $v$ , is decreased by 10 and the result is then multiplied by 3 . The final result is greater than the original number.
Write and solve an inequality to show the possible values that $v$ could take.

See Solution

Problem 51991

$\text{They } \qquad \text{wheat for the last three days. The land is looking bare.}$ \text{Select one:} \begin{itemize} \item[a.] \text{harvested} \item[b.] \text{have been harvesting} \item[c.] \text{has harvested} \item[d.] \text{have harvested} \end{itemize} $1 \, V \, P$

See Solution

Problem 51992

7) $\frac{7.1 \times 10^{6}}{8.2 \times 10^{1}}$

See Solution

Problem 51993

(6) i sample of gas occupies a volume of 2.00 L when the pressure is 2.00 atm . If the pressure is changed to 1.50 atm. what volume will the gas occupy. assuming that there is no change in the temperature?
6. $\qquad$ A : Baries

See Solution

Problem 51994

$5 /-x=12$

See Solution

Problem 51995

Delia ordered 18 bowes of red balloons and 12 bover of thive beileonstor apert She ordered a total of 240 balloona How many balloons are in each box? (A) 6
C 7

See Solution

Problem 51996

The road outside of Butch's house, when seen from above, takes on the shape the graph of $y=x^{3}$ where both $x$ and $y$ are measured in feet. The end of Butch's driveway (where he gets onto the road) is at the origin which we will call the point H (for home).
One day Butch goes for a drive on this road, leaving home sometime in the mid-afernoon when the traffic is virtually nonexistent. Butch's position on the road can be thought of as the point B with coordinates $(x, y)$ where both $x$ and $y$ are differentiable functions of time, say $x(t)$ and $y(t)$ . At some time, not long after leaving home, Butch passes through the point where $x=2$ . At that instant his $x$ -coordinate is increasing at a rate of 2 feet per second. a) What is the rate of change of Butch's $y$ -coordinate at this instant?
24 ft/sec b) At this same instant, what is rate of change of the slope of the line that passes through B and $H$ ? $a^{b}$ $\frac{a}{b}$ $\sqrt{a}$ $|a|$ $\pi$ $\sin (a)$ III

See Solution

Problem 51997

Use the conversion facts above to find an approximate equivalic
17. $6 \mathrm{ft} \approx$ $\qquad$ cm
15. 3 in. $\approx$ $\qquad$ cm
16. $2 \mathrm{fl} \mathrm{oz} \approx$ $\qquad$ mL
20. $60 \mathrm{~mL} \approx$ $\qquad$ fl Oz
18. $4 \mathrm{~m} \approx$ $\qquad$ in.
19. $7 \mathrm{~L} \approx$ $\qquad$ qt
23. $8.8 \mathrm{lb}=$ $\qquad$ kg
21. $78 \mathrm{in} . \approx$ $\qquad$ m
22. $120 \mathrm{~cm} \approx$ $\qquad$ ft

See Solution

Problem 51998

What is the value of $a$ in this equation? $4=\frac{a}{5}$

See Solution

Problem 51999

5 (c) An astronaut drinks $\frac{1}{2}$ gallon of water each day. How many gallons of water will the astronaut drink in 5 days? $\qquad$
Answer: $\square$ gallon (s)

See Solution

Problem 52000

Solve the formula for x . $\begin{array}{l} \frac{1}{g}+\frac{1}{n}=\frac{1}{x} \\ x=\square \end{array}$

See Solution

Math

Problem 51901

Problem 51902

Problem 51903

If f(x)=exsin⁡xf(x)=e^{x} \sin xf(x)=exsinx, then f′(x)=f^{\prime}(x)=f′(x)=

Problem 51904

Find the discontinuities.5. f(x)=x−2x2−3x+2f(x)=\frac{x-2}{x^{2}-3 x+2}f(x)=x2−3x+2x−2​

Problem 51905

Amanda filled her gas tank three times last week. Here are the amounts of gas she bought (in gallons). 8.62,14.4,98.62,14.4,98.62,14.4,9What is the total amount of gas Amanda bought last week? □\square□ gallons

Problem 51906

Problem 51907

33 In un rettangolo la base è lunga (2x+1)cm(2 x+1) \mathrm{cm}(2x+1)cm e l'altezza 6 cm . Determina xxx in modo che il rettangolo abbia area minore di quella di un quadrato di lato 4 cm . [−12<x<56]\left[-\frac{1}{2}<x<\frac{5}{6}\right][−21​<x<65​]

Problem 51908

x+5x−98=0\frac{x+5}{x}-\frac{9}{8}=0xx+5​−89​=0Select the correct choice below and, if necessary, fill in

Problem 51909

Factorise fully 12ac−4a12 a c-4 a12ac−4a □\square□Submit Answer

Problem 51910

2. Résoudre dans NXN\mathbb{N} X \mathbb{N}NXN le système suivant: {Cxy=Cxy+14Cxy=5Cxy−1\left\{\begin{aligned} C_{x}^{y} & =C_{x}^{y+1} \\ 4 C_{x}^{y} & =5 C_{x}^{y-1} \end{aligned}\right.{Cxy​4Cxy​​=Cxy+1​=5Cxy−1​​

Problem 51911

What is the solution to this equation? x−12=−4x-12=-4x−12=−4 A. x=−16x=-16x=−16 B. x=16x=16x=16 C. x=8x=8x=8 D. x=−8x=-8x=−8

Problem 51912

Write the following number in standard decimal form. four hundredths

Problem 51913

Find the indefinite integral. ∫x−8dx\int x^{-8} d x∫x−8dx □\square□ +C+C+C

Problem 51914

Problem 51915

(iii) If y=12x−13x2+14x3y=\frac{1}{2 x}-\frac{1}{3 x^{2}}+\frac{1}{4 x^{3}}y=2x1​−3x21​+4x31​. Find dydx\frac{d y}{d x}dxdy​ (i) Find the equation of the tangent and of the normal to the curve function y=f(x)=x3+2x2+1y=f(x)=x^{3}+2 x^{2}+1y=f(x)=x3+2x2+1 at x=−1x=-1x=−1 on it

Problem 51916

Problem 51917

(Chapter 5 plus sections 0.1 and 0.4 )Solve using the substitution method. x−y=−26x+8y=−26\begin{aligned} x-y & =-2 \\ 6 x+8 y & =-26 \end{aligned}x−y6x+8y​=−2=−26​

Problem 51918

Problem 51919

What is the solution to this equation? −15x=90-15 x=90−15x=90 A. x=−105x=-105x=−105 B. x=105x=105x=105 C. x=6x=6x=6 D. x=−6x=-6x=−6

Problem 51920

Problem 51921

Use the quadratic formula to solve the equation. x2+4x+20=0x^{2}+4 x+20=0x2+4x+20=0

Problem 51922

Problem 51923

Problem 51924

y=78x−9y=−34x+4\begin{array}{l}y=\frac{7}{8} x-9 \\ y=-\frac{3}{4} x+4\end{array}y=87​x−9y=−43​x+4​

Problem 51925

Problem 51926

Problem 51927

Problem 51928

Problem 51929

Problem 51930

Problem 51931

Directions: Solve for area and perimeter in each of the following problems. 1) 2) 3) □\square□

Problem 51932

Find the equation of the tangentizine at the given poin 7. x2−y2=27x^{2}-y^{2}=27x2−y2=27 at (6,−3)(6,-3)(6,−3)

Problem 51933

Question 4Factor 4x6y4+12x5y5+4x4y34 x^{6} y^{4}+12 x^{5} y^{5}+4 x^{4} y^{3}4x6y4+12x5y5+4x4y3

Problem 51934

9. Given the points (5,10(5,10(5,10,)and(7,20)) and (7,20))and(7,20) :Part A: Find the slope of the line that contains the points. Slope =Part B: Find the equation of the line that contains the points. Equation:

Problem 51935

To find the x intercept let A y-o B X-O C xandy Continue

Problem 51936

Solve for ddd in the proportion. 64=d+56d=□\begin{array}{l} \frac{6}{4}=\frac{d+5}{6} \\ d=\square \end{array}46​=6d+5​d=□​

Problem 51937

What is the slope of the line represented by the equation f(t)=2t−6f(t)=2 t-6f(t)=2t−6 ? The slope is 2 and the yyy-intercept is -6 . The slope is -6 and the yyy-intercept is 2 . The slope is 2 and the yyy-intercept is 6 . The slope is 6 and the yyy-intercept is 2 .

Problem 51938

Problem 51939

12. A 0.025 kg object vibrates at the end of a spring. If the maximum displacement of the object is 0.030 cm , and its period is 0.50 s , what is the maximum acceleration of the object?

Problem 51940

(5f9g4h2f2h3)0\left(\frac{5 f^{9} g^{4} h^{2}}{f^{2} h^{3}}\right)^{0}(f2h35f9g4h2​)0

Problem 51941

Problem 51942

Problem 51943

Find each root that is a real number. −100-\sqrt{100}−100​

Problem 51944

x2+39x+380=0x^{2}+39 x+380=0x2+39x+380=0 x1=x_{1}=x1​= □\square□ Round your answer to 2 decimal places. x2=x_{2}=x2​= \qquad Round your answer to 2 decimal places.

Problem 51945

Problem 51946

Problem 51947

Problem 51948

Solve for www. ∣3w+6∣=−12|3 w+6|=-12∣3w+6∣=−12If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". w=w=w= □\square□No solution

Problem 51949

Use the Law of Sines to find the length of angle BBB to the nearest whole degree: Given: A=117∘b=15.3 ma=20.0 m\text { Given: } \begin{aligned} & A=117^{\circ} \\ & b=15.3 \mathrm{~m} \\ & a=20.0 \mathrm{~m} \end{aligned} Given: ​A=117∘b=15.3 ma=20.0 m​

Problem 51950

2. Which graph appears to show a linear proportional relationship between xxx and yyy ?

If $f(x)=e^{x} \sin x$ , then $f^{\prime}(x)=$

Find the discontinuities.
5. $f(x)=\frac{x-2}{x^{2}-3 x+2}$

Amanda filled her gas tank three times last week. Here are the amounts of gas she bought (in gallons). $8.62,14.4,9$
What is the total amount of gas Amanda bought last week? $\square$ gallons

33 In un rettangolo la base è lunga $(2 x+1) \mathrm{cm}$ e l'altezza 6 cm . Determina $x$ in modo che il rettangolo abbia area minore di quella di un quadrato di lato 4 cm . $\left[-\frac{1}{2}<x<\frac{5}{6}\right]$

$\frac{x+5}{x}-\frac{9}{8}=0$
Select the correct choice below and, if necessary, fill in

Factorise fully $12 a c-4 a$ $\square$
Submit Answer

2. Résoudre dans $\mathbb{N} X \mathbb{N}$ le système suivant: $\left\{\begin{aligned} C_{x}^{y} & =C_{x}^{y+1} \\ 4 C_{x}^{y} & =5 C_{x}^{y-1} \end{aligned}\right.$

What is the solution to this equation? $x-12=-4$ A. $x=-16$ B. $x=16$ C. $x=8$ D. $x=-8$

Find the indefinite integral. $\int x^{-8} d x$ $\square$ $+C$

(iii) If $y=\frac{1}{2 x}-\frac{1}{3 x^{2}}+\frac{1}{4 x^{3}}$ . Find $\frac{d y}{d x}$ (i) Find the equation of the tangent and of the normal to the curve function $y=f(x)=x^{3}+2 x^{2}+1$ at $x=-1$ on it

(Chapter 5 plus sections 0.1 and 0.4 )
Solve using the substitution method. $\begin{aligned} x-y & =-2 \\ 6 x+8 y & =-26 \end{aligned}$

What is the solution to this equation? $-15 x=90$ A. $x=-105$ B. $x=105$ C. $x=6$ D. $x=-6$

Use the quadratic formula to solve the equation. $x^{2}+4 x+20=0$

$\begin{array}{l}y=\frac{7}{8} x-9 \\ y=-\frac{3}{4} x+4\end{array}$

Directions: Solve for area and perimeter in each of the following problems. 1) 2) 3) $\square$

Find the equation of the tangentizine at the given poin 7. $x^{2}-y^{2}=27$ at $(6,-3)$

Question 4
Factor $4 x^{6} y^{4}+12 x^{5} y^{5}+4 x^{4} y^{3}$

9. Given the points $(5,10$ , $) and (7,20)$ :
Part A: Find the slope of the line that contains the points. Slope =
Part B: Find the equation of the line that contains the points. Equation:

Solve for $d$ in the proportion. $\begin{array}{l} \frac{6}{4}=\frac{d+5}{6} \\ d=\square \end{array}$

What is the slope of the line represented by the equation $f(t)=2 t-6$ ? The slope is 2 and the $y$ -intercept is -6 . The slope is -6 and the $y$ -intercept is 2 . The slope is 2 and the $y$ -intercept is 6 . The slope is 6 and the $y$ -intercept is 2 .

$\left(\frac{5 f^{9} g^{4} h^{2}}{f^{2} h^{3}}\right)^{0}$

Find each root that is a real number. $-\sqrt{100}$

$x^{2}+39 x+380=0$ $x_{1}=$ $\square$ Round your answer to 2 decimal places. $x_{2}=$ $\qquad$ Round your answer to 2 decimal places.

Solve for $w$ . $|3 w+6|=-12$
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". $w=$ $\square$
No solution

Use the Law of Sines to find the length of angle $B$ to the nearest whole degree: $\text { Given: } \begin{aligned} & A=117^{\circ} \\ & b=15.3 \mathrm{~m} \\ & a=20.0 \mathrm{~m} \end{aligned}$

2. Which graph appears to show a linear proportional relationship between $x$ and $y$ ?

The cost of producing $x$ units of a product is given by $C(x)=800+80 x-80 \ln (x), \quad x \geq 1$
Find the minimum average cost.
Minimum Average Cost $=$ $\square$ Preview My Answers Submit Answers
You have attempted this problem 0 times.

$\frac{y^{-6}}{y^{-10}}$
Simplify. a

Find the length of side $a$ to the nearest tenth of a meter:
Law of Cosines: $a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A$

Convert the complex number to polar form: $4-4 i$

Convert the complex number to rectangular form: $z=7 \operatorname{cis} 120^{\circ}$

Find all $\theta$ in the interval $\left[0^{\circ}, 360^{\circ}\right)$ such that: $3 \sin ^{2} \theta+2 \sin \theta-1=0$

Use a calculator to approximate $y=\csc ^{-1}(2.8842912)$ to the nearest thousandth of a radian:

Use an identity to re-write the expression as a single function: $2 \sin (16 u) \cos (16 u)$

A particular circle in the standard $(x, y)$ coordinate plane has an equation of $(x-5)^{2}+y^{2}=38$ . What are the radius of the circle, in coordinate units, and the Goordinates of the center of the circle?

Use any appropriate algebraic techniques combined with trigonometric identities to simpli the expression: $\frac{1}{\cos \theta}-\cos \theta$

Question 5
A rectangle is inscribed with its base on the $x$ -axis and its upper corners on the parabola $y=10-x^{2}$ . What are the dimensions of such a rectangle with the greatest possible area?
Width = $\square$ Height = $\square$ Question Help: Video

Use the difference formula for cosine to simplify $\cos \left(\theta-\frac{\pi}{2}\right)$ as a single function of $\theta$ :