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2 years ago

How do you do #1 & #2 ?

Mathematics

1 answer:

Alexeev081 [22]2 years ago

7 0

$Answer: \\ 1. \: x = \frac{ {32}^{2} }{24} = \frac{128}{3} \\y = \sqrt{ {24}^{2} + {32}^{2} } = 40\\ z = \frac{32 \times 40}{24} = \frac{160}{3} \\ \\ 2. \: x = \sqrt{( {4 \sqrt{5} )}^{2} - {8}^{2} } = 4$

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Four buses carrying 146 high school students arrive to Montreal. The buses carry, respectively, 32, 44, 28, and 42 students. One

Naily [24]

Answer:

The expected value of X is $E(X)=\frac{2754}{73} \approx 37.73$ and the variance of X is $Var(X)=\frac{226192}{5329} \approx 42.45$

The expected value of Y is $E(Y)=\frac{73}{2} \approx 36.5$ and the variance of Y is $Var(Y)=\frac{179}{4} \approx 44.75$

Step-by-step explanation:

(a) Let X be a discrete random variable with set of possible values D and probability mass function p(x). The expected value, denoted by E(X) or $\mu_x$ , is

$E(X)=\sum_{x\in D} x\cdot p(x)$

The probability mass function $p_{X}(x)$ of X is given by

$p_{X}(28)=\frac{28}{146} \\\\p_{X}(32)=\frac{32}{146} \\\\p_{X}(42)=\frac{42}{146} \\\\p_{X}(44)=\frac{44}{146}$

Since the bus driver is equally likely to drive any of the 4 buses, the probability mass function $p_{Y}(x)$ of Y is given by

$p_{Y}(28)=p_{Y}(32)=p_{Y}(42)=p_{Y}(44)=\frac{1}{4}$

The expected value of X is

$E(X)=\sum_{x\in [28,32,42,44]} x\cdot p_{X}(x)$

$E(X)=28\cdot \frac{28}{146}+32\cdot \frac{32}{146} +42\cdot \frac{42}{146} +44 \cdot \frac{44}{146}\\\\E(X)=\frac{392}{73}+\frac{512}{73}+\frac{882}{73}+\frac{968}{73}\\\\E(X)=\frac{2754}{73} \approx 37.73$

The expected value of Y is

$E(Y)=\sum_{x\in [28,32,42,44]} x\cdot p_{Y}(x)$

$E(Y)=28\cdot \frac{1}{4}+32\cdot \frac{1}{4} +42\cdot \frac{1}{4} +44 \cdot \frac{1}{4}\\\\E(Y)=146\cdot \frac{1}{4}\\\\E(Y)=\frac{73}{2} \approx 36.5$

(b) Let X have probability mass function p(x) and expected value E(X). Then the variance of X, denoted by V(X), is

$V(X)=\sum_{x\in D} (x-\mu)^2\cdot p(x)=E(X^2)-[E(X)]^2$

The variance of X is

$E(X^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{X}(x)$

$E(X^2)=28^2\cdot \frac{28}{146}+32^2\cdot \frac{32}{146} +42^2\cdot \frac{42}{146} +44^2 \cdot \frac{44}{146}\\\\E(X^2)=\frac{10976}{73}+\frac{16384}{73}+\frac{37044}{73}+\frac{42592}{73}\\\\E(X^2)=\frac{106996}{73}$

$Var(X)=E(X^2)-(E(X))^2\\\\Var(X)=\frac{106996}{73}-(\frac{2754}{73})^2\\\\Var(X)=\frac{106996}{73}-\frac{7584516}{5329}\\\\Var(X)=\frac{7810708}{5329}-\frac{7584516}{5329}\\\\Var(X)=\frac{226192}{5329} \approx 42.45$

The variance of Y is

$E(Y^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{Y}(x)$

$E(Y^2)=28^2\cdot \frac{1}{4}+32^2\cdot \frac{1}{4} +42^2\cdot \frac{1}{4} +44^2 \cdot \frac{1}{4}\\\\E(Y^2)=196+256+441+484\\\\E(Y^2)=1377$

$Var(Y)=E(Y^2)-(E(Y))^2\\\\Var(Y)=1377-(\frac{73}{2})^2\\\\Var(Y)=1377-\frac{5329}{4}\\\\Var(Y)=\frac{179}{4} \approx 44.75$

8 0

3 years ago

Joanne works two jobs to pay for college. She tutors for $25 per hour and also works as a receptionist for $12 per hour. Due to

il63 [147K]

Answer: C. $t+r\leq 25$

$25t+12r\geq 200$

Step-by-step explanation:

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work=t+r

Since she can work up to 25 hours.

Thus $t+r\leq 25$

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning =$ $25t+12r$

Since she must earn $200.

Then $25t+12r\geq 200$ .

Therefore, the required system of inequality will be

$t+r\leq 25$

$25t+12r\geq 200$

4 0

3 years ago

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A candy company makes boxes of chocolates. Each box has 32 chocolates total. Of those 32 chocolates 14 of them have nuts. If the

Agata [3.3K]

Answer: 266

Step-by-step explanation: This is a ratio problem. If there are 14 chocolates with nuts out of every 32 chocolates, you can use this as a ratio and set it up as a proportion.

(1) 14 chocolates w/ nuts / 32 chocolates = n chocolates / 608 chocolates

(2) Solve for n: 8,512 = 32n; n = 266

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3 years ago

Please help I am dying<br><br> Points=30 <br> And I will thank you and mark you brainliest

dedylja [7]

Answer:

1120 ounces

Step-by-step explanation:

5 stone= 5*14 pounds= 70 pounds

70 pounds= 70*16 ounces= 1120 ounces

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3 years ago

Please help!!! Please help!!! Please help!!!

Elis [28]

Answer:

See explanation.

Step-by-step explanation:

Tyler wrote everything correct, except he multiplied some incorrectly. 2x times 5 is 10x, not 7x. And 3 times 5 is 15, not 8. The bottom left and right boxes are incorrect.

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2 years ago

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