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Problem 40601

11. Algebra, STD2 A4 2014 HSC 26d
Draw each graph on the grid below and hence solve the simultaneous equations. (3 marks) $\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}$ (3 marks)

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Problem 40602

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Figure A and Figure B represent examples of different types of chemical bonding. Identify the descriptions and properties Chat best represent each figure. All of the descriptions and properties may not be used.
Figure A nonpolar covalent equal sharing of electrons
Figure B unequal sharing of electrons Answer Bank $\mathrm{N}-\mathrm{H}$ bond $\mathrm{Na}-\mathrm{Cl}$ bond $\mathrm{Cl}-\mathrm{Cl}$ bond ionic transfer of electrons

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Problem 40603

$f(x)=x^{2}+4-12$
Entrada...

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Problem 40604

The price-demand and cost functions for the production of microwaves are given as $p=235-\frac{x}{90}$ and $C(x)=26000+60 x,$ where $x$ is the number of microwaves that can be sold at a price of $p$ dollars per unit and $C(x)$ is the total cost (in dollars) of producing $x$ units. (A) Find the marginal cost as a function of $x$ . $C^{\prime}(x)=$ (B) Find the revenue function in terms of $x$ . $R(x)=$ $\square$ (C) Find the marginal revenue function in terms of $x$ . $R^{\prime}(x)=$ $\square$ (D) Evaluate the marginal revenue function at $x=1500$ . $R^{\prime}(1500)=$ $\square$ (E) Find the profit function in terms of $x$ . $P(x)=$ $\square$ (F) Evaluate the marginal profit function at $x=1500$ . $P^{\prime}(1500)=\square$

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Problem 40605

Use an algebraic approach to find the solutions to the equation $6 \sin ^{2} x(6 \sin x-1)=0$ , where $0 \leq x \leq 2 \pi$ . Give the solution correct to the nearest hundredth.

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Problem 40606

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}$

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Problem 40607

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-3} y^{-5}}{a^{-3}}\right)^{-5}$

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Problem 40608

A retail store estimates that weekly sales $s$ and weekly advertising costs $x$ (both in dollars) are related by $s=60000-430000 e^{-0.0005 x}$
The current weekly advertising costs are 2000 dollars and these costs are increasing at the rate of 300 dollars per week. Find the current rate of change of sales. Rate of change of sales $=$ $\square$

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Problem 40609

Answer all of the following questions. (1) What is the domain of $f(x)=\frac{3}{x+4}$ ? Explain how you reached your conclusion. (2) Consider the graph of $f(x)=\frac{3}{x+4}$ shown below. What do you think is the range of $f(x)$ ?

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Problem 40610

A price $p$ (in dollars) and demand $x$ for a product are related by $2 x^{2}-2 x p+50 p^{2}=16200$
If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand. Rate of change of demand = $\square$

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Problem 40611

Calculate the slope and enter it below to aim the X Wing and destroy all TIE-Fighters. \begin{tabular}{|l|l|} \hline Slope & Aim Left or Right \\ \hline & \\ \hline \end{tabular}
Fire

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Problem 40612

Solve the equation $8 \sin (2 \theta)=7$ for the smallest positive value of $\theta$ . Give your answer in radians and degrees. Round your answers to three decimal places.

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Problem 40613

Simplify. $\left(\frac{4 x^{2}}{y^{3}}\right)^{3}\left(\frac{4 x^{8}}{y}\right)^{-2}$

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Problem 40614

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by $C=80000+30 x, \quad R=200-\frac{x^{2}}{40}$ where the production output in one week is $x$ calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:
Rate of change in cost $=$ $\square$
Rate of change in revenue $=$ $\square$
Rate of change in profit = $\square$

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Problem 40615

$\sqrt{2 x}+3=9$

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Problem 40616

Add. $\left(6 x^{3} y-6 x y+5\right)+\left(8 x^{3} y+6 x y+5 x\right)$

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Problem 40617

If 28600 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual:
Your answer is $\square$ (b) Semiannual:
Your answer is $\square$ (c) Monthly:
Your answer is $\square$ (d) Daily:
Your answer is $\square$ (e) Continuously:
Your answer is $\square$

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Problem 40618

Word Problems: Problem 14 (1 point) In 2010, the population of a country was $1 million and growing at a rate of 1.5% per year. Assuming the percentage growth rate remains constant express the population P. in millions, as a function of t the number of years after 2010. P= f(t)= million people help (formulas) Preview My Answers Submit Answers

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Problem 40619

14 Mark for Review
The function $f(t)=60,000(2)^{\frac{t}{40}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
Answer Preview:

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Problem 40620

3. La forme suivante est composée d'un rectangle, un demi-cercle, et un triangle. Détermine l'aire totale de la forme, arrondie au dixième près.

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Problem 40621

$10 \times 12=$

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Problem 40622

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. $f(x)=x^{3}+2 x+1$
Find $f^{\prime}(x)$ . $\begin{array}{l} f(x)=x^{3}+2 x+1 \\ f^{\prime}(x)=\square \end{array}$

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Problem 40623

Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. $10^{5+2 y}+8500=94,000$ There is no solution, $\}$ . The exact solution set is $\square$
$\log$ $\square{ }^{\circ l o g}$

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Problem 40624

Question 7
Evaluate the following expressions.
1 (a) $\log _{3} 3^{13}=$ $\square$ (b) $\log _{3} 81=$ $\square$ (c) $\log _{4} 256=$ $\square$ (d) $\log _{5} 5^{10}=$ $\square$

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Problem 40625

In 2010, the population of a country was 81 million and growing at a rate of $1.5 \%$ per year. Assuming the percentage growth rate remains constant, express the population, $P$ , in millions, as a function of $t$ , the number of years after 2010. $P=f(t)=$ $\square$ million people help (formulas)

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Problem 40626

a) $\log _{5} x=3$

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Problem 40627

A ladder seven meters in length leans against a building. If the angle of elevation of the ladder with the ground $70^{\circ}$ , how far up the wall does the ladder reach? 6.57 meters 5.18 meters 4.98 meters 2.39 meters

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Problem 40628

If 28600 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods. (a) Annual:
Your answer is $\square$ (b) Semiannual:
Your answer is $\square$ (c) Monthly:
Your answer is $\square$ (d) Daily:
Your answer is $\square$ (e) Continuously:
Your answer is $\square$

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Problem 40629

In the rectangle below, $K M=4 x+2, J L=5 x-7$ , and $m \angle N J M=54^{\circ}$ . Find $J N$ and $m \angle K N L$ .

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Problem 40630

A retail store estimates that weekly sales $s$ and weekly advertising costs $x$ (both in dollars) are related by $s=60000-430000 e^{-0.0005 x}$
The current weekly advertising costs are 2000 dollars and these costs are increasing at the rate of 300 dollars per week. Find the current rate of change of sales.
Rate of change of sales = $\square$ 2372.96

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Problem 40631

=autosave\#questio... ns that the particle moved approximately 30.00 meters to the left. that $v(t)=t^{2}-t-20=(t-5)(t+4)$ and so $v(t) \leq v \quad 0$ on the interval $[1,5]$ and $v(t)$ nus, from this equation, the distance traveled is $\begin{aligned} \int_{1}^{7}|v(t)| d t & =\int_{1}^{5}[-v(t)] d t+\int_{5}^{7} v(t) d t \\ & =\int_{1}^{5}\left(-t^{2}+t+20\right) d t+\int_{5}^{7}\left(t^{2}-t-20\right) d t \end{aligned}$ $=\left[-\frac{t^{3}}{3}+\frac{t^{2}}{2}+20 t\right]_{1}^{5}+\left[\frac{t^{3}}{3}-\frac{t^{2}}{2}-20 t\right]$ $=\frac{725}{3}$ Your answer is correct.

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Problem 40632

2. Determine the approximate degree measure, to the nearest tenth, for each angle. a) 1.24 b) 2.82 c) 4.78 d) 6.91

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Problem 40633

The function given by $y=f(x)$ shows the value of $\$ 5000$ invested at $5 \%$ interest compounded continuously, $x$ years after the money was originally invested. (Round your answers to the nearest cent.) Value of $\$ 5000$ with Continuous Compounding at $5 \%$
Part: $0 / 3$
Part 1 of 3 (a) Find the average amount earned per year between the 5 th year and the 10 th year.
The average amount earned between the 5 th year and 10 th year is $\$ 364.80$ per year. $\square$
Part: 1 / 3 $\square$
Part 2 of 3 (b) rind the average amount earned per year between the 20 th year and the 25 th year.
The average ampunt earned between the 20 th year and 25 th year is $\$$ per vear. $\square$

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Problem 40634

Fill in the blank to complete the trigonometric formula. $\sin u \cos v=$

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Problem 40635

? （ webassign.net
6. [-/5 Points] DETAILS MY NOTES TANFIN12 6.2.030.
Refer to the following Venn diagram.
Find the following. (a) $n\left(A \cup B^{C}\right)$ $\square$ (b) $n\left[A \cap(B \cup C)^{C}\right]$ $\square$ (c) $n\left(A^{C}\right)$ $\square$ (d) $n\left[(A \cup B \cup C)^{c}\right]$ $\square$ (e) $n\left(A^{C} \cup B^{C} \cup C^{C}\right)$ $\square$ Stow My Work

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Problem 40636

Problems 4B (10 points) In 2018 Juan bought 6 apartment units at a price of $\$ 175,000$ . He spent approximately $\$ 15,000$ to renovate each apartment. He sold half of the flats in 2021 at a price of $\$ 200,000$ each. Juan sold the other half in 2023 at $\$ 380,000$ per apartment. Juan had to pay $15 \%$ as profit tax. (a) Calculate Juan's net profit after tax return on his investment in 2021 and 2023. (b) Calculate Juan's profit if he had sold all of his apartment units in 2021.

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Problem 40637

- For $f(x)=\frac{9}{x-8}$ and $g(x)=\frac{1}{x}$ , find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $\mathrm{g} \circ \mathrm{g}$ (a) $(f \circ g)(x)=$ $\square$ (Simplify your answer.)

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Problem 40638

Exercice 1 1- Effectuer, en binaire, les opérations suivantes : a) $7 \mathrm{~B}_{(16)}+56,4(8)$ b) $\mathrm{A} 9_{(16)}-33_{(4)}$
2- Effectuer en octal : $726_{(8)}-535_{(8)}$ et en hexadécimal : $3 \mathrm{AD}_{(16)}+\mathrm{BOFF}_{(16)}$ . 3- Déterminer la base B sachant que $(25)_{\mathrm{B}}=(10111)_{2}$ 4- Convertir $94_{(10)}$ en binaire puis recopier et compléter le tableau suivant : \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Chiffres du nombre en base 2 & & & & & & & & \\ \hline Rang du chiffre & & & & & & & & \\ \hline Poids de chiffre & & & & & & & & \\ \hline Valeurs & & & & & & & & \\ \hline \end{tabular}
5- Déterminer x et y tel que : $(3 x 2, y 3)_{6}=(134,25)_{10}$ 6- Effectuer les conversions suivantes : a) $180_{(10)}=\mathrm{N}_{(2)}=\mathrm{N}_{(16)}$ b) $7 \mathrm{C}, \mathrm{B}_{(16)}=\mathrm{N}_{(8)}=\mathrm{N}_{(10)}$ c) $1010,011_{(2)}=\mathrm{N}_{(10)}=\mathrm{N}_{(8)}=\mathrm{N}_{(16)}$

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Problem 40639

4. An airplane is travelling at $500 \mathrm{~km} / \mathrm{h}$ due south when it encounters a win from $W 45^{\circ} \mathrm{N}$ at $100 \mathrm{~km} / \mathrm{h}$ . a. What is the resultant velocity of the airplane? b. How long will it take for the airplane to travel 1000 km ?

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Problem 40640

Evaluate the integral. Use $C$ (upper case) for the constant of integration. $\int \frac{8 x+9}{\sqrt{16-x^{2}}} d x$

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Problem 40641

Solve the equation. (Find all solutions of the equation in the interval $[0,2 \pi)$ . Enter your answers as a comma-separated list.) $\begin{array}{l} 4 \tan (2 x)-4 \cot (x)=0 \\ x=\square \end{array}$

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Problem 40642

Kristen invests \ $5,000 in a bank. The bank pays$ 6 \%$ interest compounded monthly. To the nearest tenth of a year, how long mus she leave the money in the bank for it to double?

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Problem 40643

Consider the following. line: passes through $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right): x=x_{1}+t\left(x_{2}-x_{1}\right), y=y_{1}+t\left(y_{2}-y_{1}\right)$ Find a set of parametric equations to represent the graph of the line. (Enter your answers as a comma-separated list of equations.) line: passes through $(1,3)$ and $(-7,4)$

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Problem 40644

B. Assume that one-year interest rate is $11 \%$ in the USA while the one. year interest rate in Ghana is $34 \%$ . A USA bank is prepared to buy tho Ghana Cedi at a discount of $13 \%$ one year from now. An investor wity $\$ 1,000,000$ in USA is considering whether it is worthwhile to take advantage of covered interest arbitrage. Assume a spot rate of $\$ 1$ to GHe1.4.
Required: i Determine whether covered interest arbitrage is worthwhile. (12 marks) ii. Give two reasons why the investor should not attempt covent

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Problem 40645

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r \cos (\theta), \quad y=k+r \sin (\theta)$

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Problem 40646

Find an equation of the hyperbola that has vertices $(0,0)$ and $(0,-16)$ and foci $(0,2)$ and $(0,-18)$ .
Equation: $\square$ $=1$

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Problem 40647

The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 64.4 for a sample of size 26 and standard deviation 19.4. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a $95 \%$ confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places. $\square$ $<\mu<$ $\square$

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Problem 40648

Assume that a sample is used to estimate a population mean $\mu$ . Find the $80 \%$ confidence interval for a sample of size 41 with a mean of 38.5 and a standard deviation of 18.5. Enter your answer as an openinterval (i.e., parentheses) accurate to 3 decimal places.
80\% C.I. = $\square$ The answer should be obtained without any preliminary rounding.

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Problem 40649

A factor of $x^{3}+15 x^{2}+71 x+105$ is $x+5$ $x-5$ $x-7$ $x-3$

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Problem 40650

$x+x=$

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Problem 40651

7. Why do radian measurements not have a unit indicated? [2 marks]

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Problem 40652

Interest rate is a percentage periodically applied to a sum of money to determine the amount of interest to be added to that sum
Select one: True False

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Problem 40653

Suppose the average US salary is $\$ 41,000$ . If a sample of 50 people are randomly surveyed then there is a $95 \%$ chance that the $95 \%$ confidence interval for the mean US salary will have a lower bound less than 41,000 and an upper bound greater than $41,000$ . True False

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Problem 40654

Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. $\begin{array}{c} 67^{\circ} 30^{\prime} \\ \sin \left(67^{\circ} 30^{\prime}\right)=\square \\ \cos \left(67^{\circ} 30^{\prime}\right)=\square \\ \tan \left(67^{\circ} 30^{\prime}\right)=\square \end{array}$

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Problem 40655

A political candidate has asked you to conduct a poll to determine what percentage of people support her. From a random sample of 500, 324 said they would support the candidate. A $95 \%$ confidence interval is constructed. a) In words, define the random variable $X$ $X$ is the proportion of people from the sample who support the candidate $X$ is the number of people from the sample who support the candidate $X$ is the number of people from the population who support the candidate b) In words, define the random variable $\hat{P}$ $\hat{P}$ is the proportion of people from the population who support the candidate $\hat{P}$ is the proportion of people from the sample who support the candidate $\hat{P}$ is the number of people from the sample who support the candidate

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Problem 40656

A project requires an initial investment of $\$ 300,000$ . It is expected to produce after-tax cash flows of $\$ 100,000$ in the first year. The after-tax cashflows are expected to increase by $\$ 10,000$ annually reaching $\$ 140,000$ in year 5 when the project will be scrapped. What is the project's NPV if discount rate is $12 \%$ ?
Multiple Choice \ $153,855 \$141,471 \$133,584$ \ $107,425$ $\$ 124,448$

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Problem 40657

Basisaufgaben
Berechne das Volumen des Kegels mit den gegebenen Größen. a) $\mathrm{r}=2 \mathrm{~cm} ; \mathrm{h}=7 \mathrm{~cm}$

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Problem 40658

8. A given sinusoidal function has an amplitude of 8 , an axis at $y=12$ , a period of $9 \pi$ , and a maximum at $x=3 \pi$ . Determine an equation for the function, and find all intersections of the function and $y=16$ between $x=-5 \pi$ and $x=12 \pi$ . [ 8 marks]

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Problem 40659

project initially costs $\$ 100,000$ to get stairted and has a discount rate of $9 \%$ . It has a useful life of five years. You expect the project to have a NPV of $\$ 15,000$ . nat would be the equal yearly cashflow generated by the project need to be to reach the target NPV
Multiple Choice \ $30,785.59 \$29,565.63 \$29,006.36 \$28,693.57$ \ $28,075.47$

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Problem 40660

12.1 HW Question 5, 10.1.9 HW Score: $6.9 \%, 2$ of 29 points Part 2 of 6 Points: 0 of 1 Save
Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between $x$ and $y$ . $\mathbf{b}$ . Find the value of the correlation coefficient $r$ and determine whether there is a linear correlation. $\mathbf{c}$ . Remove the point with coordinates $10-$ $(10,2)$ and find the correlation coefficient r and determine whether there is a linear correlation. d . What do you conclude about the possible effect from a single pair of values? Click here to view a table of critical values for the correlation coefficient. a. Do the data points appear to have a strong linear correlation? No Yes b. What is the value of the correlation coefficient for all 10 data points? $\mathrm{r}=$ $\square$ (Simplify your answer. Round to three decimal places as needed.)
Table of Critical Values $\square$ \begin{tabular}{|c|c|c|} \hline n & $\alpha=.05$ & $\alpha=.01$ \\ \hline 4 & . 950 & . 990 \\ \hline 5 & . 878 & . 959 \\ \hline 6 & . 811 & . 917 \\ \hline 7 & . 754 & .875 \\ \hline 8 & . 707 & . 834 \\ \hline 9 & . 666 & . 798 \\ \hline 10 & . 632 & . 765 \\ \hline 11 & . 602 & . 735 \\ \hline 12 & . 576 & . 708 \\ \hline 13 & . 553 & . 684 \\ \hline 14 & . 532 & . 661 \\ \hline 15 & . 514 & . 641 \\ \hline 16 & . 497 & . 623 \\ \hline 17 & . 482 & . 606 \\ \hline 18 & - . 468 & . 590 \\ \hline 19 & . 456 & .575 \\ \hline 20 & . 444 & . 561 \\ \hline 25 & . 396 & .505 \\ \hline 30 & . 361 & . 463 \\ \hline 35 & . 335 & 430 \\ \hline 40 & . 312 & . 402 \\ \hline 15 & 304 & 270 \\ \hline \end{tabular} Get more help -

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Problem 40661

At distribution with 7 degrees of freedom is graphed below. The region under the curve to the right of $t_{0.9}$ is shaded. The area of this region is 0.9
Find the value of $t_{0.9}$ . Round your answer to three decimal places. $t_{0.9}=$ $\square$

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Problem 40662

Enter the values of the sample size, the point estimate of the mean, the sample standard deviation, and the critical value you need for your $90 \%$ confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". \begin{tabular}{|l|l|} \hline \begin{tabular}{l} Sample size: \\ $\square$ \end{tabular} & \\ \hline \begin{tabular}{l} Point estimate: \\ $\square$ \end{tabular} & \\ \hline \begin{tabular}{l} Sample standard deviation: \\ $\square$ \end{tabular} & \\ \hline \begin{tabular}{l} Critical value: \\ $\square$ \end{tabular} & \multicolumn{1}{|c|}{ Margin of error: } \\ \hline Compute & \\ \hline \end{tabular} Save For Later Submit Assi Check

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Problem 40663

Use the product-to-sum formulas to rewrite the product as a sum or difference. $8 \cos 2 \theta \cos 4 \theta$ $\square$

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Problem 40664

Solve the equation by using the square root property. $(3 p+2)^{2}=8$
The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.

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Problem 40665

Use the sum-to-product formulas to find the exact value of the expression. $9 \cos 120^{\circ}+9 \cos 60^{\circ}$
Step 1 Factor out the constant. $9 \cos 120^{\circ}+9 \cos 60^{\circ}=$ $\square$ $\left(\cos 120^{\circ}+\cos 60^{\circ}\right)$

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Problem 40666

1. Find $\frac{d y}{d x}$ in terms of $t$ for the following parametric equations. (i) $\quad x=t^{4}+t$ and $y=t^{3}-2 t$ (ii) $x=e^{3 t}+2$ and $y=2 t^{2}+t$ (iii) $x=4 t^{3}-t$ and $y=t^{2}+8 t$
2. Find $y$ for the following, by using the given substitution. (i) $\quad y=\int x \sqrt{x^{2}+2} d x \quad$ , let $u=x^{2}+2$ (ii) $y=\int x \sqrt{1-x^{2}} d x$ , let $u=1-x^{2}$ (iii) $y=\int \frac{-3-3 x^{2}}{2-3 x-x^{3}} d x \quad$ , let $u=2-3 x-x^{3}$
3. Consider the function $x^{3}-x^{2} y+2 y^{2}=8$ (i) Differentiate the function implicitly and show that $\frac{d y}{d x}=\frac{2 x y-3 x^{2}}{4 y-x^{2}}$ (ii) Find the tangent equation to the curve $x^{3}-x^{2} y+2 y^{2}=8$ at the point $(2,0)$ .
4. Consider the function $4 y^{3}-3 x^{2} y+x=1$ (i) Differentiate the function implicitly and show that $\frac{d y}{d x}=\frac{6 x y-1}{12 y^{2}-3 x^{2}}$ (ii) Find the normal equation to the curve $4 y^{3}-3 x^{2} y+x=1$ at the point $(0,1)$ .
5. Find the point of intersection between the curve $y=9-x^{2}$ and the straight line $y-x-3=0$ shown in Figure 1 below.
Hence, find the area bounded by the curve and the straight line.
Figure 1
6. Find the point of intersection between the two curves $y=x^{2}+2 x+2$ and $y=-x^{2}+2 x+10$ . Hence, find the area bounded by the two curves.

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Problem 40667

Determine all values of $a$ for which the following set of vectors is dependent or independent. You can select 'always', 'never', ' $a=$ ', or ' $a \neq$ ', then specify a value or comma-separated list of values. $\left\{\left[\begin{array}{c} 1 \\ 3 \\ -1 \\ a \end{array}\right],\left[\begin{array}{l} 1 \\ 3 \\ 0 \\ 1 \end{array}\right],\left[\begin{array}{l} 2 \\ 6 \\ 1 \\ 2 \end{array}\right]\right\}$
Dependent: Always
Independent: Always SUBMIT AND MARK SAVE AND CLOS

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Problem 40668

Question 4 [10 points] Determine all values of $a$ for which the following set of vectors is dependent or independent. You can select 'always', 'never', ' $a=$ ', or ' $a \neq$ ', then specify a value or comma-separated list of values. $\left\{\left[\begin{array}{c} a \\ 1 \\ -2 \\ -3 \end{array}\right],\left[\begin{array}{c} 2 \\ 6 \\ 1 \\ -5 \end{array}\right],\left[\begin{array}{c} 4 \\ -8 \\ -10 \\ -2 \end{array}\right]\right\}$
Dependent: Always Independent: Always

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Problem 40669

Здесь всюоду $A, B, \ldots$ , это какие-то непустые подмножества на прямой $\mathbb{R}$ . (1) Используя лишь определение компактности доказите, что (a) прямая $\mathbb{R}$ не компактна,

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Problem 40670

Suppose that $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{4}$ is such that its action on a vector $\left[\begin{array}{c}x \\ y \\ z\end{array}\right]$ is given below: $T\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} x+3 y+3 z \\ -x-2 y-4 z \\ 2 x+5 y+6 z \\ 3 x+8 y+9 z \end{array}\right]$
Find the matrix $M_{D B}(T)$ that represents $T$ relative to the bases $B$ and $D$ shown below: $\begin{array}{l} \left.B=\left\{\begin{array}{l} 1 \\ 2 \\ 2 \end{array}\right],\left[\begin{array}{c} 1 \\ 3 \\ 1 \end{array}\right],\left[\begin{array}{c} 0 \\ 2 \\ -3 \end{array}\right]\right\} D=\left\{\left[\begin{array}{c} 1 \\ 1 \\ -2 \\ 0 \end{array}\right],\left[\begin{array}{c} -1 \\ 0 \\ 1 \\ -1 \end{array}\right],\left[\begin{array}{c} 1 \\ 1 \\ -3 \\ 1 \end{array}\right],\left[\begin{array}{c} 0 \\ 1 \\ 0 \\ -1 \end{array}\right]\right\} \\ M_{D B}(T)=\left[\begin{array}{lll} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right] \end{array}$

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Problem 40671

$\frac{y}{21}=4$

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Problem 40672

множество А компактно, где $A=\left\{\frac{2}{3}\right\} \cup\left\{\frac{2 n^{2}-3 n+1}{3 n^{2}-n+10}, n=1,2,3, \ldots\right\}$

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Problem 40673

A point is given in polar coordinates. Convert the point to rectangular coordinates. $(x, y)=(\square)$

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Problem 40674

Find the slope of the tangent line to the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ at the point $(x, y)$ . slope $=$ $\square$
Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), ( $-2,5)$ . Enter none if there are no such points.) slope is undefined at $\square$

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Problem 40675

(2) Докажите, что переселение любого семейства компактных подмнозеств компактно.

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Problem 40676

The heart rate of runners during a long distance race is approximately normal. The table below shows the heart rates of a random sample of 9 such runners. Find the point estimate. $\begin{array}{lllllllll} 116 & 122 & 106 & 132 & 126 & 149 & 109 & 145 & 134 \end{array}$ $\square$ (round to 1 decimal place)

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Problem 40677

Докажите, что множество $[0,1) \cap \mathbb{Q}$ не компактно.

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Problem 40678

All changes saved
The power, $P$ , dissipated when a 11 -volt battery is put across a resistance of $R$ ohms is given by $P=\frac{121}{R}$
What is the rate of change of power with respect to resistance? rate of change $=$

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Problem 40679

\begin{tabular}{|l|l|l|} \hline 4 & Ist das Dreieck mit den Seitenlängen $x=12 \mathrm{~m}, y=13 \mathrm{~m}, z=25 \mathrm{~m}$ rechtwinklig? & $1,5 /$ \\ \hline 5 & Der Rasen in einem Bundesligastadion ist 105m lang und 68m breit. Ist die & \\ \hline \end{tabular}

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Problem 40680

The number of seconds $X$ after the minute that class ends is uniformly distributed between 0 and 60 . Round all answers to 4 decimal places where possible. a. What is the distribution of $X$ ? $X \sim U($ , $\square$ ) then the sampling distribution is b. Suppose that 38 classes are clocked. What is the distribution of $\bar{x}$ for this group of classes? $\bar{x} \sim N($ $\square$ $\square$ c. What is the probability that the average of 38 classes will end with the second hand between 27 and 31 seconds? $\square$

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Problem 40681

Example 4: a 3.34 g sample of a hydrate has the formula $\mathrm{SrS}_{2} \mathrm{O}_{3} \cdot \times \mathrm{H}_{2} \mathrm{O}$ , and contains 2.30 g of $\mathrm{SrS}_{2} \mathrm{O}_{3}$ . Find the value of $x$

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Problem 40682

a. $\lim _{x \rightarrow 2} \frac{x^{4}-5 x-6}{4 x-8}=$

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Problem 40683

$y=6 x+3$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 1 & $\square$ \\ \hline 3 & $\square$ \\ \hline 6 & $\square$ \\ \hline 8 & $\square$ \\ \hline \end{tabular}

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Problem 40684

(ii) $\int \sqrt{\csc x} \cos ^{3} x d x$

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Problem 40685

b. $\lim _{x \rightarrow 1} \frac{\sqrt{2 x-1}-1}{5 x-5}$

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Problem 40686

5) A rectangular metal sheet shrinks while maintaining its shape, such that its length decreases at a rate of $3 \mathrm{~cm} / \mathrm{second}$ and its width decreases at a rate of $2 \mathrm{~cm} / \mathrm{second}$ . Find the rate of change of its area with respect to time when its length is 6 cm and its width is 5 cm .

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Problem 40687

+ BRERCICES. On introduth dans une flole jaugere de 250 mL une imasse de $1,29 \mathrm{~g}$ de chlorure de cobal hydraté CoCt2, $6 H 20$ ef on remplit aver de l'eau distillée jusqu'au tralt de jauge.
1. Calculer la concentration molaire de la solution S obtenue.
2. Ecrire I'équation de clissolution.
3. En dédulre les concentiations molntres des lons présents dans la solutlon.
EYERCICEF:
1. Donner les formules des ions suivants : sulfate ; Carbomate ; Phosplasle ; Nitrate.
2. Donner les formules statistiques des composés suivants : a : Chlorure d'Aluminium ba altrate de fer $/ l$ c: Sullate de potassium d: Hydrosyde de sodtum
3. Ecifre les réactions de dissolution des composés loniques sulvants: Na2504 CuC? $V 2=100 \mathrm{~mL}$ d'une solutlon CuSO 4 à concentration $\mathrm{C} 2=5.10-2 \mathrm{~mol}$ . $\mathrm{L}-1$ . Détermalare la concentratlon des difrérents lons présents dans le melange. of EXTRCTCE 7 Les usages de I'actde chlorlayditque sont maltiples : décapage ef détantrage des métaux, I des zarbies et des pierres, debouchage et dictaithage de camalisadons, de WC ... II est vendu directenseat dins le commerce eu boutelles plostiques de 1 L . L'étiquette préclse: : $30 \%$ infilusum. Je pourcentage masilque siguifle que 100 g de solutio 30 g de chlorure d'hydrogene.
1. Qaelles précautions fant-ll piendre pour utillser cette polution?
2. Lit deasité de li solution est de 1,17. Calculer la concentration molatre babals ap chlorure d'hydrogène. quatre parts d'ean goun' une part d'aclale. Que vaudia la concentration molatre de la solut alnsi ebtenue?

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Problem 40688

5. $T_{1}, T_{2}$ dan $T_{3}$ adalah tiga sebutan berturatan suatu janjang $T_{1}=7$ dan $T_{n=1}=T_{n}+4$ bagi $n \geqslant 1$ . Cari sebutan Ke-17. (3 markah) $T_{1}=7$

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Problem 40689

b) selesaikan persamaan $\sqrt{x-2}=\sqrt{x}-1$ [3 markah]

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Problem 40690

1. Find the equations of the tangent line to the ellipse, $\frac{(x+2)^{2}}{4}+\frac{(y-3)^{2}}{9}$ when $x=-3$ .

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Problem 40691

2. If $x=-3, y=4$ and $z=-5$ , then verify each of the following: (a) $|x+z| \leq|x|+|z|$ (b) ly- (c) $|x y z|=|x| \cdot|y| \cdot|z|$ (d) $\left|\frac{\mathrm{x}}{\mathrm{z}}\right|=$

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Problem 40692

19. Find the exact value of $3-2 . \dot{9}$ .

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Problem 40693

LG 1 P3-10 Statement of retained earnings Hayes Enterprises began 2015 with a retained earnings balance of $\$ 1,151,000$ . During 2015 , the firm earned $\$ 528,000$ after taxes. From this amount, preferred stockholders were paid $\$ 98,000$ in dividends. At yearend 2015 , the firm's retained earnings totaled $\$ 1,324,000$ . The firm had 100,000 shares of common stock outstanding during 2015. a. Prepare a statement of retained earnings for the year ended December 31, 2015, for Hayes Enterprises. (Note: Be sure to calculate and include the amount of cash dividends paid in 2015.) b. Calculate the firm's 2015 earnings per share (EPS). c. How large a per-share cash dividend did the firm pay on common stock during 2015?

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Problem 40694

parent punction: $y=x^{3}$ find the equation with $(-4,-1),(-5,-2),(-6,-3)$ Descrive the trans formation that were applied to the parent function

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Problem 40695

23. In the figure, the line $k x+4 y-12=0$ cuts the $\mathrm{x}-\mathrm{axis}$ at A and the $\mathrm{y}-\mathrm{axis}$ at B . If the area of $\triangle \mathrm{OAB}$ is 6 square units, then $k=$ Av) 1 B. 3 C. 5 D. 7

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Problem 40696

Guided Practice
2. Find the area of the Shaded Region to the nearest tenth.

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Problem 40697

the information given in the picture below. The height of the tree is approxi Zoom
B 34.6 m
D 3.64 m
ANSWER

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Problem 40698

What is angle for the point $M(0,-1)$ ? A -270 B 180 C 90 D 270
SUBMIT ANSWER

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Problem 40699

The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is $54 \mathrm{ft}^{2}$ . Find the dimensions of the rectangle.

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Problem 40700

Given $\operatorname{Tan}(B)=3 / 4$ and $B$ is in quadrant 3 then $\cos (B)=$
A $-3 / 5$ B $-4 / 5$
C $3 / 5$ D $4 / 5$ (E) $5 / 3$

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Math

Problem 40601

11. Algebra, STD2 A4 2014 HSC 26dDraw each graph on the grid below and hence solve the simultaneous equations. (3 marks) y=2x+1x−2y−4=0\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}y=2x+1x−2y−4=0​ (3 marks)

Problem 40602

Problem 40603

f(x)=x2+4−12f(x)=x^{2}+4-12f(x)=x2+4−12Entrada...

Problem 40604

Problem 40605

Use an algebraic approach to find the solutions to the equation 6sin⁡2x(6sin⁡x−1)=06 \sin ^{2} x(6 \sin x-1)=06sin2x(6sinx−1)=0, where 0≤x≤2π0 \leq x \leq 2 \pi0≤x≤2π. Give the solution correct to the nearest hundredth.

Problem 40606

Simplify. Write the answer using positive exponents only. (x−8x−3)−9\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}(x−3x−8​)−9

Problem 40607

Simplify. Write the answer using positive exponents only. (x−3y−5a−3)−5\left(\frac{x^{-3} y^{-5}}{a^{-3}}\right)^{-5}(a−3x−3y−5​)−5

Problem 40608

Problem 40609

Answer all of the following questions. (1) What is the domain of f(x)=3x+4f(x)=\frac{3}{x+4}f(x)=x+43​ ? Explain how you reached your conclusion. (2) Consider the graph of f(x)=3x+4f(x)=\frac{3}{x+4}f(x)=x+43​ shown below. What do you think is the range of f(x)f(x)f(x) ?

Problem 40610

Problem 40611

Calculate the slope and enter it below to aim the X Wing and destroy all TIE-Fighters. \begin{tabular}{|l|l|} \hline Slope & Aim Left or Right \\ \hline & \\ \hline \end{tabular}Fire

Problem 40612

Solve the equation 8sin⁡(2θ)=78 \sin (2 \theta)=78sin(2θ)=7 for the smallest positive value of θ\thetaθ. Give your answer in radians and degrees. Round your answers to three decimal places.

Problem 40613

Simplify. (4x2y3)3(4x8y)−2\left(\frac{4 x^{2}}{y^{3}}\right)^{3}\left(\frac{4 x^{8}}{y}\right)^{-2}(y34x2​)3(y4x8​)−2

Problem 40614

Problem 40615

2x+3=9\sqrt{2 x}+3=92x​+3=9

Problem 40616

Add. (6x3y−6xy+5)+(8x3y+6xy+5x)\left(6 x^{3} y-6 x y+5\right)+\left(8 x^{3} y+6 x y+5 x\right)(6x3y−6xy+5)+(8x3y+6xy+5x)

Problem 40617

Problem 40618

Problem 40619

14 Mark for ReviewThe function f(t)=60,000(2)t40f(t)=60,000(2)^{\frac{t}{40}}f(t)=60,000(2)40t​ gives the number of bacteria in a population ttt minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?Answer Preview:

Problem 40620

3. La forme suivante est composée d'un rectangle, un demi-cercle, et un triangle. Détermine l'aire totale de la forme, arrondie au dixième près.

Problem 40621

10×12=10 \times 12=10×12=

Problem 40622

Problem 40623

Problem 40624

Question 7Evaluate the following expressions.1 (a) log⁡3313=\log _{3} 3^{13}=log3​313= □\square□ (b) log⁡381=\log _{3} 81=log3​81= □\square□ (c) log⁡4256=\log _{4} 256=log4​256= □\square□ (d) log⁡5510=\log _{5} 5^{10}=log5​510= □\square□

Problem 40625

Problem 40626

a) log⁡5x=3\log _{5} x=3log5​x=3

Problem 40627

A ladder seven meters in length leans against a building. If the angle of elevation of the ladder with the ground 70∘70^{\circ}70∘, how far up the wall does the ladder reach? 6.57 meters 5.18 meters 4.98 meters 2.39 meters

Problem 40628

Problem 40629

In the rectangle below, KM=4x+2,JL=5x−7K M=4 x+2, J L=5 x-7KM=4x+2,JL=5x−7, and m∠NJM=54∘m \angle N J M=54^{\circ}m∠NJM=54∘. Find JNJ NJN and m∠KNLm \angle K N Lm∠KNL.

Problem 40630

Problem 40631

Problem 40632

2. Determine the approximate degree measure, to the nearest tenth, for each angle. a) 1.24 b) 2.82 c) 4.78 d) 6.91

Problem 40633

Problem 40634

Fill in the blank to complete the trigonometric formula. sin⁡ucos⁡v=\sin u \cos v=sinucosv=

Problem 40635

Problem 40636

Problem 40637

Problem 40638

Problem 40639

Problem 40640

Evaluate the integral. Use CCC (upper case) for the constant of integration. ∫8x+916−x2dx\int \frac{8 x+9}{\sqrt{16-x^{2}}} d x∫16−x2​8x+9​dx

Problem 40641

Solve the equation. (Find all solutions of the equation in the interval [0,2π)[0,2 \pi)[0,2π). Enter your answers as a comma-separated list.) 4tan⁡(2x)−4cot⁡(x)=0x=□\begin{array}{l} 4 \tan (2 x)-4 \cot (x)=0 \\ x=\square \end{array}4tan(2x)−4cot(x)=0x=□​

Problem 40642

Kristen invests \5,000inabank.Thebankpays5,000 in a bank. The bank pays 5,000inabank.Thebankpays6 \%$ interest compounded monthly. To the nearest tenth of a year, how long mus she leave the money in the bank for it to double?

Problem 40643

Problem 40644

Problem 40645

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x=h+rcos⁡(θ),y=k+rsin⁡(θ)x=h+r \cos (\theta), \quad y=k+r \sin (\theta)x=h+rcos(θ),y=k+rsin(θ)

Problem 40646

Find an equation of the hyperbola that has vertices (0,0)(0,0)(0,0) and (0,−16)(0,-16)(0,−16) and foci (0,2)(0,2)(0,2) and (0,−18)(0,-18)(0,−18).Equation: □\square□ =1=1=1

Problem 40647

Problem 40648

Problem 40649

A factor of x3+15x2+71x+105x^{3}+15 x^{2}+71 x+105x3+15x2+71x+105 is x+5x+5x+5 x−5x-5x−5 x−7x-7x−7 x−3x-3x−3

Problem 40650

x+x=x+x=x+x=

Problem 40651

7. Why do radian measurements not have a unit indicated? [2 marks]

11. Algebra, STD2 A4 2014 HSC 26d
Draw each graph on the grid below and hence solve the simultaneous equations. (3 marks) $\begin{array}{l} y=2 x+1 \\ x-2 y-4=0 \end{array}$ (3 marks)

$f(x)=x^{2}+4-12$
Entrada...

Use an algebraic approach to find the solutions to the equation $6 \sin ^{2} x(6 \sin x-1)=0$ , where $0 \leq x \leq 2 \pi$ . Give the solution correct to the nearest hundredth.

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-8}}{x^{-3}}\right)^{-9}$

Simplify. Write the answer using positive exponents only. $\left(\frac{x^{-3} y^{-5}}{a^{-3}}\right)^{-5}$

Answer all of the following questions. (1) What is the domain of $f(x)=\frac{3}{x+4}$ ? Explain how you reached your conclusion. (2) Consider the graph of $f(x)=\frac{3}{x+4}$ shown below. What do you think is the range of $f(x)$ ?

Calculate the slope and enter it below to aim the X Wing and destroy all TIE-Fighters. \begin{tabular}{|l|l|} \hline Slope & Aim Left or Right \\ \hline & \\ \hline \end{tabular}
Fire

Solve the equation $8 \sin (2 \theta)=7$ for the smallest positive value of $\theta$ . Give your answer in radians and degrees. Round your answers to three decimal places.

Simplify. $\left(\frac{4 x^{2}}{y^{3}}\right)^{3}\left(\frac{4 x^{8}}{y}\right)^{-2}$

$\sqrt{2 x}+3=9$

Add. $\left(6 x^{3} y-6 x y+5\right)+\left(8 x^{3} y+6 x y+5 x\right)$

14 Mark for Review
The function $f(t)=60,000(2)^{\frac{t}{40}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
Answer Preview:

$10 \times 12=$

Question 7
Evaluate the following expressions.
1 (a) $\log _{3} 3^{13}=$ $\square$ (b) $\log _{3} 81=$ $\square$ (c) $\log _{4} 256=$ $\square$ (d) $\log _{5} 5^{10}=$ $\square$

a) $\log _{5} x=3$

A ladder seven meters in length leans against a building. If the angle of elevation of the ladder with the ground $70^{\circ}$ , how far up the wall does the ladder reach? 6.57 meters 5.18 meters 4.98 meters 2.39 meters

In the rectangle below, $K M=4 x+2, J L=5 x-7$ , and $m \angle N J M=54^{\circ}$ . Find $J N$ and $m \angle K N L$ .

Fill in the blank to complete the trigonometric formula. $\sin u \cos v=$

Evaluate the integral. Use $C$ (upper case) for the constant of integration. $\int \frac{8 x+9}{\sqrt{16-x^{2}}} d x$

Solve the equation. (Find all solutions of the equation in the interval $[0,2 \pi)$ . Enter your answers as a comma-separated list.) $\begin{array}{l} 4 \tan (2 x)-4 \cot (x)=0 \\ x=\square \end{array}$

Kristen invests \ $5,000 in a bank. The bank pays$ 6 \%$ interest compounded monthly. To the nearest tenth of a year, how long mus she leave the money in the bank for it to double?

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r \cos (\theta), \quad y=k+r \sin (\theta)$

Find an equation of the hyperbola that has vertices $(0,0)$ and $(0,-16)$ and foci $(0,2)$ and $(0,-18)$ .
Equation: $\square$ $=1$

A factor of $x^{3}+15 x^{2}+71 x+105$ is $x+5$ $x-5$ $x-7$ $x-3$

$x+x=$

Interest rate is a percentage periodically applied to a sum of money to determine the amount of interest to be added to that sum
Select one: True False

Basisaufgaben
Berechne das Volumen des Kegels mit den gegebenen Größen. a) $\mathrm{r}=2 \mathrm{~cm} ; \mathrm{h}=7 \mathrm{~cm}$

At distribution with 7 degrees of freedom is graphed below. The region under the curve to the right of $t_{0.9}$ is shaded. The area of this region is 0.9
Find the value of $t_{0.9}$ . Round your answer to three decimal places. $t_{0.9}=$ $\square$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $8 \cos 2 \theta \cos 4 \theta$ $\square$

Solve the equation by using the square root property. $(3 p+2)^{2}=8$
The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.

$\frac{y}{21}=4$

множество А компактно, где $A=\left\{\frac{2}{3}\right\} \cup\left\{\frac{2 n^{2}-3 n+1}{3 n^{2}-n+10}, n=1,2,3, \ldots\right\}$

A point is given in polar coordinates. Convert the point to rectangular coordinates. $(x, y)=(\square)$