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Problem 28601

What is the probability of drawing an orange marble first from a jar with 8 purple and 3 orange marbles?

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Problem 28602

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

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Problem 28603

Convert the proton mass $M_{p} = 1.673 \times 10^{-27} \mathrm{~kg}$ and neutron mass $M_{n} = 1.675 \times 10^{-27} \mathrm{~kg}$ . Find their mass difference.

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Problem 28604

Solve the inequality: $\frac{(x-4)^{2}}{x^{2}-4} \geq 0$ . List intervals and signs in interval notation.

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Problem 28605

What is the probability of drawing a purple marble after keeping one orange marble from a jar with 8 purple and 3 orange marbles?

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Problem 28606

Convert the distances $d_{1} = 349000000000000000 \mathrm{~km}$ , $d_{2} = 45000000000000 \mathrm{~km}$ , $d_{3} = 427000000000000000 \mathrm{~km}$ to scientific notation and find the total distance traveled.

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Problem 28607

Calculate the area by multiplying 138.2 km by 3.5 km. What is the product?

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Problem 28608

Find the density of an object with mass 25025 kg and volume 22 m $^{3}$ . Use correct significant figures in your answer.

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Problem 28609

Find the probability of drawing an orange marble and then a purple marble from a jar with 8 purple and 3 orange marbles.

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Problem 28610

Solve the inequality $(x-7)^{2}/(x^{2}-36) \geq 0$ and list intervals with signs in each. Use interval notation.

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Problem 28611

Calculate the product of 3250 cm and 0.550 cm.

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Problem 28612

374 km ÷ 12 h =

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Problem 28613

Find the coordinates of $\mathrm{C}^{\prime}$ if point C is (0, -3) and transformed by $(x, y) \longrightarrow (y+4,-x)$ .

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Problem 28614

Calculate the fraction $\frac{25^{\circ} \mathrm{C}}{6.6 \mathrm{~s}}$ considering significant figures.

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Problem 28615

Calculate the total weight by adding $192.88 \mathrm{~kg}$ and $56.7 \mathrm{~kg}$ .

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Problem 28616

What is the probability of being either a sophomore or junior if students are equally likely to be in any class? Options: 0.44, 0.50, 0.25, 0.625.

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Problem 28617

Calculate the product of 2500 cm and 50 cm: $2500 \, \text{cm} \times 50 \, \text{cm}$ .

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Problem 28618

Find the perimeter of a square park with area $25x^{2}+70x+49$ . What is the perimeter when $x=8$ ft?

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Problem 28619

Calculate 82300 km - 9.721 km.

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Problem 28620

What is the probability that a student majors in either Performing Arts or Humanities? Options: 0.77, 0.26, 0.23, 1.00

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Problem 28621

Rearrange the equation $\frac{-3 r+2}{-6 r+5}=4 s$ to solve for $r$ .

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Problem 28622

Convert 640 mph to meters per second. Use the conversion $1.0$ mile $=1.6$ km to find the British missile velocity.

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Problem 28623

Alyssa wants to know her savings traveling to the Moon vs. Mars. Find savings using distances $d_{1}=1.22 \times 10^{8} \mathrm{~km}$ , $d_{2}=8.12 \times 10^{5} \mathrm{~km}$ , fuel rate $=1.54 \times 10^{3} \mathrm{~km} / \mathrm{L}$ , and cost $\$ 3.23 \times 10^{2}$ per liter.

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Problem 28624

Alyssa wants to know her fuel savings by traveling to the Moon vs. Mars. Round trip distances: $d_{1} = 1.22 \times 10^{8} \mathrm{~km}$ , $d_{2} = 8.12 \times 10^{5} \mathrm{~km}$ . Fuel efficiency: $1.54 \times 10^{3} \mathrm{~km/L}$ , cost: \$3.23 \times 10^{2} per liter. Calculate savings.

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Problem 28625

Solve the inequality: $\frac{x+8}{x-3} \leq 1$ . List intervals and signs in each interval in interval notation.

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Problem 28626

Find the sum of the coefficients of $P(x) + Q(x)$ where $P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3$ and $Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7$ .

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Problem 28627

Solve the inequality $\frac{x+8}{x-3} \leq 1$ . List intervals and signs. Provide the solution in interval notation.

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Problem 28628

Find the amount of apple $y$ for cranberry amounts $t$ using the ratio 3:5. Complete the table for $t = 525$ .

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Problem 28629

Solve the inequality $\frac{x+4}{x-2} \leq 1$ and list intervals with signs in interval notation.

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Problem 28630

A car costs \$28,100 with a 6% sales tax. Find the tax paid and total cost.

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Problem 28631

An unbiased coin is tossed. What is the probability of getting (a) heads, (b) tails? Use $P(H) = \frac{1}{2}$ and $P(T) = \frac{1}{2}$ .

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Problem 28632

Calculate the percent increase in life expectancy from 28 years in the Stone Age to 71 years in 2016. Round to the nearest integer.

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Problem 28633

A fair six-sided die is rolled. Find the probability of getting: (a) a '4', (b) a '1' or '6', (c) a prime number, (d) a multiple of 10.

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Problem 28634

Solve the inequality:
$\frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0$
Identify intervals and their signs, then list in interval notation.

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Problem 28635

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

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Problem 28636

Find the percent decrease from a regular sofa price of \ $570 to a sale price of \$490.20:$ \%$

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Problem 28637

Find the total cost of a \$719 tablet on sale for 14\% off with a 6\% sales tax. Round to two decimal places.

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Problem 28638

Solve the inequality:
$\frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0$
List intervals and their signs in ascending order.

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Problem 28639

Find the real zeros of $f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3$ and factor $f$ over the reals.

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Problem 28640

Calculate the simple interest owed on a principal of \$ 710 at a rate of 2\% for 2 years. Round to the nearest cent.

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Problem 28641

Calculate the future value $A$ of a loan with principal $P=\$2000$ , interest rate $r=3.0\%$ , and time $t=3$ months.

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Problem 28642

Find the molarity of the KCl solution made from 1.5 g in 50 mL. Molar mass of KCl is 65.598 g/mol.

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Problem 28643

Solve the equation $3 x^{4}-58 x^{3}+280 x^{2}-438 x+117=0$ . What are the real solutions? A. $x=$ ; B. No real solutions.

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Problem 28644

Find the perimeter of triangle $ABC$ with vertices at $A(-1, -2)$ , $B(4, 1)$ , and $C(1, -3)$ .

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Problem 28645

Calculate the finance charge for August using an average daily balance method with a starting balance of \$260 and 17% interest. Transactions: Aug 6: -\$89, Aug 14: +\$130, Aug 16: +\$18, Aug 23: +\$32. Round to the nearest cent. Finance charge: \$\square.

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Problem 28646

A box has 6 blue, 8 green, and 7 red cards. Find the probabilities: (a) red, (b) not green, (c) yellow.

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Problem 28647

1. Find $F_{30}$ .
2. Calculate $F_{10} + F_{20} + F_{5}$ .
3. Solve $3 F_{18} - 2 F_{10}$ .
4. Determine $F_{21} - 5 F_{7}$ .
5. Find $\frac{4 F_{5} + F_{11}}{2}$ .
6. Calculate $\frac{3 F_{13}}{6}$ .
7. What is $\mathrm{F}_{75} * 0$ ?
8. Compute $10 \mathrm{~F}_{6} * 3$ .
9. Find $\frac{F_{35}}{2}$ .
10. Calculate $\frac{F_{29}}{3} * 3$ .

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Problem 28648

Find the derivative $f^{\prime}(x)$ of $f(x)=x^{3}+4 \sqrt{x}+\frac{1}{x}+2$ and the tangent line at $x=1$ .

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Problem 28649

Find the complex zeros of $f(x)=x^{3}-15 x^{2}+79 x-145$ . Provide exact answers using radicals and $i$ .

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Problem 28650

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

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Problem 28651

A Boeing 777-300 has 4 First, 48 Business, 28 Premium economy, and 184 Economy seats. Find the probability that a random passenger (i) is in Premium economy and (ii) is not in Business class.

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Problem 28652

Find $\mathrm{n}$ using the future value of an annuity formula with $\mathrm{A}=\$ 18,500$ , $R=\$ 800$ , $r=8.0\%$ . $n=\square$

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Problem 28653

To get your guitar back, you paid \$1472 after borrowing \$720. What is the annual interest rate? Round to the nearest whole number.

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Problem 28654

How much to invest now at 12% simple interest to have \$2,000 in 6 years? Round up to the nearest cent.

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Problem 28655

$\frac{5 x-3}{2}=6$

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Problem 28656

$3 \frac{3}{8} \div 2 \frac{1}{4}=$

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Problem 28657

Multiply. $\frac{1}{4} \times \frac{1}{2}=$ $\square$

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Problem 28658

a) Find the slope of the tangent to $g(x)=\frac{6 x^{2}-9 x}{x-8}$ at $x=6$ . b) Find the equation of the tangent to $f(x)=-8 x^{2}-56 x+4$ that is parallel to the tangent in a). Express in slope $y$ -intercept form.

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Problem 28659

Find the derivative of $y=3 x^{-7 \sqrt{x}}$ . Be sure to include parentheses around the arguments of any logarithmic functions in your answer.
Provide your answer below: $y^{\prime}=$

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Problem 28660

Tho number of bacteria growing in an incubation culture increases with time according to $n(t)=6900(2) t$ , where is time in days. Find the number of bacteria when $x=0$ and $x=3$ .

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Problem 28661

Evaluate. $3^{0}=$ $\square$ Submit

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Problem 28662

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

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Problem 28663

Find a linearly independent set of vectors that spans the same subspace of $\mathbb{R}^{4}$ as that spanned by the vectors $\left[\begin{array}{l} 2 \\ 2 \\ 0 \\ 1 \end{array}\right], \quad\left[\begin{array}{c} -4 \\ -2 \\ 2 \\ -5 \end{array}\right], \quad\left[\begin{array}{c} 3 \\ 2 \\ -1 \\ 3 \end{array}\right], \quad\left[\begin{array}{c} 7 \\ 6 \\ -1 \\ 5 \end{array}\right]$
A linearly independent spanning set for the subspace is: $\left\{\begin{array}{l} {\left[\begin{array}{l} \square \\ \square \\ \square \\ \square \end{array}\right],\left[\begin{array}{l} {\left[\begin{array}{l} \square \\ \square \\ \square \\ \square \end{array}\right]} \end{array}\right\} . . . . . . . . . . . ~} \\ \square \end{array}\right]$

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Problem 28664

Evaluate the expression when $x=-3$ . $x^{2}+8 x-7$

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Problem 28665

Evaluate the expression when $y=4$ . $y^{2}-5 y+6$

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Problem 28666

Module Knowitedge Grest Ouestion 12
A chemist carefully measures the amount of heat needed to raise the temperature of a 691.0 g sample of a pure substance from $36.9^{\circ} \mathrm{C}$ to $51.6^{\circ} \mathrm{C}$ . The experiment shows that 47.7 kJ of heat are needed. What can the chemist report for the specific heat capacity of the substance? Be sure your answer has correct number of significant digits. [! $\mathrm{J} \cdot \mathrm{g}^{-1} \cdot \mathrm{~K}^{-1}$ $\square \square$

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Problem 28667

$80 \times 20=1$

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Problem 28668

You wish to test the following claim $\left(H_{1}\right)$ at a significance level of $\alpha=0.05$ . $\begin{array}{l} H_{o}: p=0.54 \\ H_{1}: p \neq 0.54 \end{array}$
You obtain a sample of size $n=707$ in which there are 374 successful observations. What is the test statistic for this sample? (Report answer accurate to two decimal places.) test statistic $=$ $\square$ What is the $p$ -value for this sample? (Report answer accurate to four decimal places.) p -value = $\square$ The $p$ -value is... less than (or equal to) $\alpha$ greater than $\alpha$
This test statistic leáds to a decision to... reject the null accept the null fail to reject the null
As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.54 . There is not sufficient evidence to warrant rejection of the claim that the population proportion is not equal to 0.54 . The sample data support the claim that the population proportion is not equal to 0.54 . There is not sufficient sample evidence to support the claim that the population proportion is not equal to 0.54 .

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Problem 28669

(1 point)
Find the slope of the tangent line to the curve $3 \sin (x)+3 \cos (y)-3 \sin (x) \cos (y)+x=4 \pi$ at the point $(4 \pi, 7 \pi / 2)$ . $(-4+4 p i) / 3$ Preview My Answers Submit Answers

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Problem 28670

A road perpendicular to a highway leads to a farmhouse located 2 mile away. An automobile traveling on the highway passes through this intersection at a speed of 45 mph .
How fast is the distance between the automobile and the farmhouse increasing when the automobile is 1 miles past the intersection of the highway and the road?
The distance between the automobile and the farmhouse is increasing at a rate of $\square$ miles per hour. Preview My Answers Submit Answers

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Problem 28671

23. Evaluate the functions. a) $\sin \frac{4 \pi}{3}$ b) $\tan (-225)$ c) $\sec \frac{11 \pi}{6}$ d) $\sec \frac{9 \pi}{2}$ e) $\sin (-510)$

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Problem 28672

12) $\int\left(\frac{x}{2}+3\right)\left(x^{2}+12 x\right)^{6} d x$

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Problem 28673

A company is doing a hypothesis test on the variation in quality within one supplier. Assume the population is normally distributed. A sample of 14 products was selected. The sample mean was 7 and the sample standard deviation was 1.83 . Test to see if the standard deviation in quality is less than 2.09 by answering the following questions. Assume a significance level of 0.01 . 1) What is the null hypothesis? $H_{0}$ : $\square$ ?V $\square$ 2) What is the alternative hypothesis? $H_{1}$ : $\square$ ?v $\square$ $\square$ 3) What is the test statistic value (to 2 decimals)? $\square$ 4) What is the $p$ -value (to 4 decimals)? $\square$ 5) State your decision. Accept $H_{0}$ Do Not Reject $H_{0}$ Reject $H_{0}$ 6) State your conclusion. There is not enough evidence that the standard deviation in quality is less than 1.83. There is not enough evidence that the standard deviation in quality is less than 2.09. There is enough evidence that the standard deviation in quality is less than 1.83. There is enough evidence that the standard deviation in quality is less than 2.09.

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Problem 28674

4. $\int_{0}^{11-x} d x=$ (a) $\frac{1}{2} \ln 2$ (b) $2 \ln 2+1$ (c) $2 \ln 2-1$ (d) $\frac{1}{2} \ln 2-1$

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Problem 28675

What is the probability that a wo-digit number selected at random will be a multiple of 5 and not a multiple of 3? A. $3 / 17$ B. 2/15 10 $\geqslant 99$ C. $4 / 21$ D. $5 / 19$

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Problem 28676

Digitalis is a technology company that makes high-end computer processors. Their newest processor, the luteA, is going to be sold directly to the public. The processor is to be sold for $\$ 3900$ , making Digitalis a profit of $\$ 547$ . Unfortunately there was a manufacturing flaw, and some of these luteA processors are defective and cannot be repaired. On these defective processors, Digitalis is going to give the customer a full refund. Suppose that for each luteA there is an $11 \%$ chance that it is defective and an $89 \%$ chance that it is not defective. (If necessary, consult a $\underline{l i s t}$ of formulas.)
If Digitalis knows it will sell many of these processors, should it expect to make or lose money from selling them? How much?
To answer, take into account the profit earned on each processor and the expected value of the amount refunded due to the processor being defective. Digitalis can expect to make money from selling these processors. In the long run, they should expect to make $\square$ dollars on each processor sold. Digitalis can expect to lose money from selling these processors. In the long run, they should expect to lose $\square$ dollars on each processor sold. Digitalis should expect to neither make nor lose money from selling these processors.

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Problem 28677

Probability Permutations and combinations: Problem type 2
Answer the questions below. (If necessary, consult a $\underline{\text { list of formulas.) }}$ (a) 74 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed? $\square$ (b) To log on to a certain computer account, the user must type in a 3-letter password. In such a password, no letter may be repeated, and only the lower case of a letter may be used. How many such 3-letter passwords are possible? (There are 26 letters in the alphabet.) $\square$

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Problem 28678

5. Simplify (a) $l(A, B, C, D)=\pi(0,2,5,7,8,10,13,15)$ (0.5 mark) (b) $T(A, B, C, D)=\Sigma(1,3,4,6,9,11,12,14)$ ( 0.5 mark)
6. (a) An alternating current is defined by the equation: $i=25 \operatorname{Sin} 100 \pi t m A$ . Determine its mean value over half-a-cycle and the root-mean square values over a cycle. (0.5 mark) (b) A body has an initial velocity of $100 \mathrm{~m} / \mathrm{s}$ and it is subjected to a retardation of $25 \mathrm{~m} / \mathrm{s}^{2}$ .
Find the mean value of the velocity of the body during its forward motion. (0.5 mark) Scanned with OKEN Scan
7. (a) Find the position of the centroid of the area bounded by the curve $y=3 x^{2}$ , and the $x$ -axis and the ordinates $x=0$ and $x=2$ (0.5 mark) (b) For the first quadrant area bounded by the curve $y=10-x^{2}$ . Find the moment of inertia w.r.t. the $y$ -axis (0.5 mark)
8. (a) Determine the co-ordinates of the centroid of the area lying between the curve $y=5 x-x^{2}$ and the $x$ -axis (0.5 mark) (b) Find the moment of inertia about the $x$ -axis of the region bounded by $y=x^{2}$ and $y=x-1$ (0.5 mark)
9. A d.c circuit comprises four closed loops. Applying Kirchhoff's laws to the closed loops give the following equations for the current flow in milliamperes: $\begin{aligned} 4 i_{1}+3 i_{2}+i_{3}-i_{4} & =14 \\ 2 i_{1}+5 i_{2}+2 i_{3}+i_{4} & =17 \\ i_{1}+4 i_{2}+4 i_{3}+6 i_{4} & =20 \\ 3 i_{1}+i_{2}-i_{3}+5 i_{4} & =12 \end{aligned}$
Use the Gaussian elimination method to Solve for $i_{1}, i_{2}, i_{3}$ , and $i_{4}$ . (1 mark)
10. Use simplex method to solve $\begin{aligned} \text { Maximize } z & =7 x_{1}+5 x_{2} \\ \text { Subjected to } & 2 x_{1}+x_{2} \leq 10 \\ & 4 x_{1}+3 x_{2} \leq 24 \\ & x_{1} \geq 0, x_{2} \geq 0 \end{aligned}$ (1 mark)

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Problem 28679

The random variable $(X, Y)$ has a normal distribution with mean $(0,0)$ and covariance matrix $\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \square_{\text {Alox }}$ a) Determine the values of $a$ for which $X-a Y$ and $X+a Y$ are independent. b) Determine the mean, covariance matrix, and density of the variable $(X-Y, X+Y)$ . c) What is the distribution of the variable $X+3 Y+2$ ?

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Problem 28680

Find the mean, variance, and standard deviation for each of the values of $n$ and $p$ when the conditions for the binomial distribution are met. Round your answers to three decimal places as needed.
Part 1 of 4 (a) $n=13, p=0.67$
Mean: $\mu=8.710$ Variance: $\sigma^{2}=2.873$ Standard deviation: $\sigma=1.695$
Part 2 of 4 (b) $n=1080, p=0.09$ $\begin{aligned} \text { Mean: } \mu & =97.2 \\ \text { Variance: } \sigma^{2} & =88.452 \\ \text { Standard deviation: } \sigma & =9.405 \end{aligned}$
Part: $2 / 4$
Part 3 of 4 (C) $n=590, p=0.23$ $\begin{aligned} \text { Mean: } \mu & =\square \\ \text { Variance: } \sigma^{2} & =\square \\ \text { Standard deviation: } \sigma & =\square \end{aligned}$

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Problem 28681

Which of the following is true? $\sqrt{2}$ is a rational number. 0 is neither a rational number nor an irrational number. $-\sqrt{16}$ is an irrational number. $1 . \overline{3}$ is a rational number but not an integer.

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Problem 28682

Systems of Linear Equations: Tutorial 13 of 26 ? Question Plane $A$ is descending toward the local airport at a rate of 2,500 feet/minute. It is currently at an altitude of 12,000 feet. Plane $B$ is ascending from the same airport at a rate of 4,000 feet/minute. It is currently at an altitude of 1,000 feet. This system of equations models this real-world situation, where $x$ represents the time in minutes and $y$ represents the altitude in thousands of feet: $\begin{array}{l} y=12-2.5 x \\ y=1+4 x \end{array}$
Graph the lines of the two equations, and mark the point of intersection for the two lines. In approximately how many minutes will the two planes be at the same altitude? At what altitude will they be?

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Problem 28683

The product of two consecutive, nonnegative integers is 342 . Find the integers and separate them with a comma.

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Problem 28684

Aufgaben zum Einsetzungsverfahren 1) Lose wie in Beispiel 1: a) $\left\lvert\, \begin{array}{l}4 x+2 y=8 \\ y=8 x-1\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}2 x+y=6 \\ y=-4 x\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}6 x+y=-4 \\ y=-3 x+2\end{array}\right.$ 2) Lóse wie in Beispiel 2: a) $\left\lvert\, \begin{array}{l}x+y=11 \\ x=-3\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}x-5 y=-16 \\ -5 x+20 y=40\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}2 x+3 y=-30 \\ x=-2 y-30\end{array}\right.$ 3) Lơse wie in Beispiel 3: a) $\left\lvert\, \begin{array}{l}4 x+7 y=-8 \\ 4 x+3 y=8\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}3 x+8 y=9 \\ 5 x-8 y=15\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}7 x+19 y=-3 \\ 12 x+19 y=22\end{array}\right.$ (mache jeweils die Probe und überprüfe somit dein Ergebnis!)

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Problem 28685

Assignment 6a Question 10 of 10 (1 point) | Question Attempt: 1 of 1 Time Remaining: 1:15:00 $=1$ $=2$ 3 5 $\equiv 6$ $=7$ $=8$ 10
Family Farming A family owns a large farm. The probability that they plant $5,6,7$ , or 8 field sections in a season is $0.28,0.36,0.4$ , and -0.04 , respective Find the expected value for the field sections planted.
The expected value is $\square$ field sections planted.

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Problem 28686

Place the following in order of increasing $I E_{1}$ .
N F As A) $\mathrm{N}<\mathrm{As}<\mathrm{F}$ B) $\mathrm{As}<\mathrm{N}<\mathrm{F}$ C) $\mathrm{F}<\mathrm{N}<\mathrm{As}$ D) $\mathrm{F}<\mathrm{As}<\mathrm{N}$ E) As $<\mathrm{F}<\mathrm{N}$

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Problem 28687

Question 10 of 15 (1 point) I Question Attempt: 1 of 1
The top 14 speeds, in miles per hour, for Pro-Stock drag racing over the past two decades are listed below. Find the median speed. $\begin{array}{lllllllllllllll} 180.3 & 202.0 & 190.0 & 201.6 & 190.7 & 201.5 & 192.6 & 201.4 & 193.5 & 201.4 & 194.6 & 199.2 & 195.8 & 196.2 \end{array}$ Send data to Excel 201.4 195.8 194.9 196.0

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Problem 28688

$\lim _{x \rightarrow \infty}\left(\frac{2 x^{2}-3}{x^{2}-5 x+3}\right)$

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Problem 28689

Backspace
A stone fall from a railroad overpass which is 36 ft high into the path of a train which is approaching the overpass with uniporm speced It the stone falls when the train is 50 ft away from the overpass and thestome hit the gmind just as the train anives at that spot, how fast is the train movin

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Problem 28690

A34 De hoeveelheid water op aarde wordt geschat * op 1385 miljoen kubieke kilometer $\left(\mathrm{km}^{3}\right)$ . Bijna al dit water is zout en bevindt zich in de zeeën en oceanen. Slechts een klein deel van het water is zoet. Daarvan is het grootste deel aanwezig in de vorm van ijs, voornamelijk in de ijskappen op de polen en in gletsjers. De rest van het zoet water zit in meren en rivieren, is grondwater of is als waterdamp in de lucht aanwezig. De waterkringloop is een gesloten systeem waarbij geen water verloren gaat. Dit betekent dat de totale hoeveelheid water, in welke verschijningsvorm dan ook, constant is. De ijskappen en gletsjers bevatten 2,1\% van al het water op aarde. Dat is $68,7 \%$ van de totale hoeveelheid zoet water. a Hoeveel $\mathrm{km}^{3}$ zoet water is er op aarde? Hoeveel $\mathrm{m}^{3}$ is dat per aardbewoner? Gebruik dat er 7,7 miljard mensen op aarde zijn.

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Problem 28691

Monroe High School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent.
Here are the positions and the people interested in each. \begin{tabular}{|c|l|} \hline Position & \multicolumn{1}{|c|}{ People interested } \\ \hline Faculty member & Mrs. Rodriguez, Ms. Scott, Dr. Miller \\ \hline Male student & Bob, Boris, Carlos, Justin, Dante, Shen \\ \hline Female student & Maya, Latoya, Laura, Rachel, Carmen, Martina \\ \hline Parent & Dr. Lopez, Mr. Green, Ms. Anderson, Ms. Martinez \\ \hline \end{tabular}
Based on this list, how many ways are there to fill the four committee positions? $\square$

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Problem 28692

5. In the diagram below, triangle $A C D$ has points $B$ and $E$ on sides $A C$ and $A D$ , respectively, such that $B E \| C D, A B=1, B C=3.5$ , and $A D=18$ . What is the length of $A E$ , to the nearest tenth? 1) 14.0 2) 5.1 3) 3.3 4) 4.0

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Problem 28693

Random Variables and Distributions Standard normal values: Basic
Suppose $Z$ follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of $c$ so that the following is true. $P(Z \leq c)=0.1379$
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. $\square$

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Problem 28694

14. Given the following complex numbers find $z_{1}+z_{2}, z_{1} \cdot z_{2}$ and $\frac{z_{1}}{z_{2}}$ : $\begin{array}{l} z_{1}=-3-4 i \\ z_{2}=-2 \sqrt{3}+2 i \end{array}$

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Problem 28695

\begin{tabular}{|c|c|c|c|} \hline & \multicolumn{2}{|r|}{} & ;ديف \\ \hline & ب) بر عدد صحيح يك عدد كويا است. (1). & \begin{tabular}{l} در ستى يا نادرستى هر عبارت را مشخص كنيد \\ ج) بز ركتر ين عدد صحيح منفى دو رقمى •ا- مي باشد. \end{tabular} & 1 \\ \hline \end{tabular}

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Problem 28696

$\lim _{x \rightarrow 0} \frac{\sqrt{2}-\sqrt{1+\cos x}}{\sin ^{2} x}$

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Problem 28697

8. Bella's Bakery is known for its delectable desserts. They sell slices of cake for $\$ 3.25$ dollars each. If a whole cake yields 12 slices, and the bakery sells 7.5 cakes in a day, how much money does the bakery make from cake sales alone?

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Problem 28698

ne two fair spinners below each have four equal sections. The diagram shows every possible total whe the results from the two spinners are added together.
What is the probability of the total being 7 ? Give your answer as a fraction.

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Problem 28699

線分 $A B$ 上に 2 点 $\mathrm{P}, \mathrm{Q}$ がある。 $A P: P B=\frac{\sqrt{14}}{3}: \sqrt{\frac{7}{2}}$ , $\mathrm{AQ}: \mathrm{QB}=\sqrt{\frac{5}{3}}: \sqrt{\frac{3}{5}}$ であるとき, $\mathrm{AP}: \mathrm{PQ}$ を最も簡単な整数比で表せ。

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Problem 28700

Which of the following numbers is written in scientific notation? $10 \times 10^{5}$ $5.13 \times 10^{5}$ 10 5.13
Choose the correct answer below. A. $10 \times 10^{5}$ B. $5.13 \times 10^{5}$ C. 5.13

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Solve

Problem 28601

What is the probability of drawing an orange marble first from a jar with 8 purple and 3 orange marbles?

Problem 28602

Evaluate −73x+10-\frac{7}{3} x + 10−37​x+10 when x=6x = 6x=6.

Problem 28603

Convert the proton mass Mp=1.673×10−27 kgM_{p} = 1.673 \times 10^{-27} \mathrm{~kg}Mp​=1.673×10−27 kg and neutron mass Mn=1.675×10−27 kgM_{n} = 1.675 \times 10^{-27} \mathrm{~kg}Mn​=1.675×10−27 kg. Find their mass difference.

Problem 28604

Solve the inequality: (x−4)2x2−4≥0\frac{(x-4)^{2}}{x^{2}-4} \geq 0x2−4(x−4)2​≥0. List intervals and signs in interval notation.

Problem 28605

What is the probability of drawing a purple marble after keeping one orange marble from a jar with 8 purple and 3 orange marbles?

Problem 28606

Problem 28607

Calculate the area by multiplying 138.2 km by 3.5 km. What is the product?

Problem 28608

Find the density of an object with mass 25025 kg and volume 22 m3^{3}3. Use correct significant figures in your answer.

Problem 28609

Find the probability of drawing an orange marble and then a purple marble from a jar with 8 purple and 3 orange marbles.

Problem 28610

Solve the inequality (x−7)2/(x2−36)≥0(x-7)^{2}/(x^{2}-36) \geq 0(x−7)2/(x2−36)≥0 and list intervals with signs in each. Use interval notation.

Problem 28611

Calculate the product of 3250 cm and 0.550 cm.

Problem 28612

374 km ÷ 12 h =

Problem 28613

Find the coordinates of C′\mathrm{C}^{\prime}C′ if point C is (0, -3) and transformed by (x,y)⟶(y+4,−x)(x, y) \longrightarrow (y+4,-x)(x,y)⟶(y+4,−x).

Problem 28614

Calculate the fraction 25∘C6.6 s\frac{25^{\circ} \mathrm{C}}{6.6 \mathrm{~s}}6.6 s25∘C​ considering significant figures.

Problem 28615

Calculate the total weight by adding 192.88 kg192.88 \mathrm{~kg}192.88 kg and 56.7 kg56.7 \mathrm{~kg}56.7 kg.

Problem 28616

What is the probability of being either a sophomore or junior if students are equally likely to be in any class? Options: 0.44, 0.50, 0.25, 0.625.

Problem 28617

Calculate the product of 2500 cm and 50 cm: 2500 cm×50 cm2500 \, \text{cm} \times 50 \, \text{cm}2500cm×50cm.

Problem 28618

Find the perimeter of a square park with area 25x2+70x+4925x^{2}+70x+4925x2+70x+49. What is the perimeter when x=8x=8x=8 ft?

Problem 28619

Calculate 82300 km - 9.721 km.

Problem 28620

What is the probability that a student majors in either Performing Arts or Humanities? Options: 0.77, 0.26, 0.23, 1.00

Problem 28621

Rearrange the equation −3r+2−6r+5=4s\frac{-3 r+2}{-6 r+5}=4 s−6r+5−3r+2​=4s to solve for rrr.

Problem 28622

Convert 640 mph to meters per second. Use the conversion 1.01.01.0 mile =1.6=1.6=1.6 km to find the British missile velocity.

Problem 28623

Problem 28624

Problem 28625

Solve the inequality: x+8x−3≤1\frac{x+8}{x-3} \leq 1x−3x+8​≤1. List intervals and signs in each interval in interval notation.

Problem 28626

Find the sum of the coefficients of P(x)+Q(x)P(x) + Q(x)P(x)+Q(x) where P(x)=3x4−2x3+4x2−6x+3P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3P(x)=3x4−2x3+4x2−6x+3 and Q(x)=−x4+5x3−2x2−3x+7Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7Q(x)=−x4+5x3−2x2−3x+7.

Problem 28627

Solve the inequality x+8x−3≤1\frac{x+8}{x-3} \leq 1x−3x+8​≤1. List intervals and signs. Provide the solution in interval notation.

Problem 28628

Find the amount of apple yyy for cranberry amounts ttt using the ratio 3:5. Complete the table for t=525t = 525t=525.

Problem 28629

Solve the inequality x+4x−2≤1\frac{x+4}{x-2} \leq 1x−2x+4​≤1 and list intervals with signs in interval notation.

Problem 28630

A car costs \$28,100 with a 6% sales tax. Find the tax paid and total cost.

Problem 28631

An unbiased coin is tossed. What is the probability of getting (a) heads, (b) tails? Use P(H)=12P(H) = \frac{1}{2}P(H)=21​ and P(T)=12P(T) = \frac{1}{2}P(T)=21​.

Problem 28632

Calculate the percent increase in life expectancy from 28 years in the Stone Age to 71 years in 2016. Round to the nearest integer.

Problem 28633

A fair six-sided die is rolled. Find the probability of getting: (a) a '4', (b) a '1' or '6', (c) a prime number, (d) a multiple of 10.

Problem 28634

Solve the inequality: x2(2+x)(x+3)(x+7)(x−1)≥0 \frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0 (x+7)(x−1)x2(2+x)(x+3)​≥0 Identify intervals and their signs, then list in interval notation.

Problem 28635

Calculate the slope between the points (18,-12) and (-11,17). Use the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

Problem 28636

Find the percent decrease from a regular sofa price of \570toasalepriceof$490.20:570 to a sale price of \$490.20: 570toasalepriceof$490.20:\%$

Problem 28637

Find the total cost of a \$719 tablet on sale for 14\% off with a 6\% sales tax. Round to two decimal places.

Problem 28638

Solve the inequality: x2(4+x)(x+6)(x+7)(x−2)≥0 \frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0 (x+7)(x−2)x2(4+x)(x+6)​≥0 List intervals and their signs in ascending order.

Problem 28639

Find the real zeros of f(x)=7x4+6x3−22x2−18x+3f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3f(x)=7x4+6x3−22x2−18x+3 and factor fff over the reals.

Problem 28640

Calculate the simple interest owed on a principal of \$ 710 at a rate of 2\% for 2 years. Round to the nearest cent.

Problem 28641

Calculate the future value AAA of a loan with principal P=$2000P=\$2000P=$2000, interest rate r=3.0%r=3.0\%r=3.0%, and time t=3t=3t=3 months.

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

Convert the proton mass $M_{p} = 1.673 \times 10^{-27} \mathrm{~kg}$ and neutron mass $M_{n} = 1.675 \times 10^{-27} \mathrm{~kg}$ . Find their mass difference.

Solve the inequality: $\frac{(x-4)^{2}}{x^{2}-4} \geq 0$ . List intervals and signs in interval notation.

Find the density of an object with mass 25025 kg and volume 22 m $^{3}$ . Use correct significant figures in your answer.

Solve the inequality $(x-7)^{2}/(x^{2}-36) \geq 0$ and list intervals with signs in each. Use interval notation.

Find the coordinates of $\mathrm{C}^{\prime}$ if point C is (0, -3) and transformed by $(x, y) \longrightarrow (y+4,-x)$ .

Calculate the fraction $\frac{25^{\circ} \mathrm{C}}{6.6 \mathrm{~s}}$ considering significant figures.

Calculate the total weight by adding $192.88 \mathrm{~kg}$ and $56.7 \mathrm{~kg}$ .

Calculate the product of 2500 cm and 50 cm: $2500 \, \text{cm} \times 50 \, \text{cm}$ .

Find the perimeter of a square park with area $25x^{2}+70x+49$ . What is the perimeter when $x=8$ ft?

Rearrange the equation $\frac{-3 r+2}{-6 r+5}=4 s$ to solve for $r$ .

Convert 640 mph to meters per second. Use the conversion $1.0$ mile $=1.6$ km to find the British missile velocity.

Solve the inequality: $\frac{x+8}{x-3} \leq 1$ . List intervals and signs in each interval in interval notation.

Find the sum of the coefficients of $P(x) + Q(x)$ where $P(x) = 3x^4 - 2x^3 + 4x^2 - 6x + 3$ and $Q(x) = -x^4 + 5x^3 - 2x^2 - 3x + 7$ .

Solve the inequality $\frac{x+8}{x-3} \leq 1$ . List intervals and signs. Provide the solution in interval notation.

Find the amount of apple $y$ for cranberry amounts $t$ using the ratio 3:5. Complete the table for $t = 525$ .

Solve the inequality $\frac{x+4}{x-2} \leq 1$ and list intervals with signs in interval notation.

An unbiased coin is tossed. What is the probability of getting (a) heads, (b) tails? Use $P(H) = \frac{1}{2}$ and $P(T) = \frac{1}{2}$ .

Solve the inequality:
$\frac{x^{2}(2+x)(x+3)}{(x+7)(x-1)} \geq 0$
Identify intervals and their signs, then list in interval notation.

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Find the percent decrease from a regular sofa price of \ $570 to a sale price of \$490.20:$ \%$

Solve the inequality:
$\frac{x^{2}(4+x)(x+6)}{(x+7)(x-2)} \geq 0$
List intervals and their signs in ascending order.

Find the real zeros of $f(x)=7x^{4}+6x^{3}-22x^{2}-18x+3$ and factor $f$ over the reals.

Calculate the future value $A$ of a loan with principal $P=\$2000$ , interest rate $r=3.0\%$ , and time $t=3$ months.

Solve the equation $3 x^{4}-58 x^{3}+280 x^{2}-438 x+117=0$ . What are the real solutions? A. $x=$ ; B. No real solutions.

Find the perimeter of triangle $ABC$ with vertices at $A(-1, -2)$ , $B(4, 1)$ , and $C(1, -3)$ .

Find the derivative $f^{\prime}(x)$ of $f(x)=x^{3}+4 \sqrt{x}+\frac{1}{x}+2$ and the tangent line at $x=1$ .

Find the complex zeros of $f(x)=x^{3}-15 x^{2}+79 x-145$ . Provide exact answers using radicals and $i$ .

Find the $x$ -intercepts of the parabola with vertex $(6,27)$ and $y$ -intercept $(0,-81)$ . Round to the nearest hundredth.

Find $\mathrm{n}$ using the future value of an annuity formula with $\mathrm{A}=\$ 18,500$ , $R=\$ 800$ , $r=8.0\%$ . $n=\square$

$\frac{5 x-3}{2}=6$

$3 \frac{3}{8} \div 2 \frac{1}{4}=$

Multiply. $\frac{1}{4} \times \frac{1}{2}=$ $\square$

a) Find the slope of the tangent to $g(x)=\frac{6 x^{2}-9 x}{x-8}$ at $x=6$ . b) Find the equation of the tangent to $f(x)=-8 x^{2}-56 x+4$ that is parallel to the tangent in a). Express in slope $y$ -intercept form.

Find the derivative of $y=3 x^{-7 \sqrt{x}}$ . Be sure to include parentheses around the arguments of any logarithmic functions in your answer.
Provide your answer below: $y^{\prime}=$

Tho number of bacteria growing in an incubation culture increases with time according to $n(t)=6900(2) t$ , where is time in days. Find the number of bacteria when $x=0$ and $x=3$ .

Evaluate. $3^{0}=$ $\square$ Submit

Radieal Cube root of an integer
Find the value of $\sqrt[3]{1000}$ $\square$

Evaluate the expression when $x=-3$ . $x^{2}+8 x-7$

Evaluate the expression when $y=4$ . $y^{2}-5 y+6$

$80 \times 20=1$

23. Evaluate the functions. a) $\sin \frac{4 \pi}{3}$ b) $\tan (-225)$ c) $\sec \frac{11 \pi}{6}$ d) $\sec \frac{9 \pi}{2}$ e) $\sin (-510)$

12) $\int\left(\frac{x}{2}+3\right)\left(x^{2}+12 x\right)^{6} d x$

4. $\int_{0}^{11-x} d x=$ (a) $\frac{1}{2} \ln 2$ (b) $2 \ln 2+1$ (c) $2 \ln 2-1$ (d) $\frac{1}{2} \ln 2-1$