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3 years ago

Box has 10 M&M candies: 5 red and 5 blue.

1 answer:

5 0

If we use the formula P(A and B) = P(A)×P(B) and the data given we can say that the operation will be like this: P(Red and Blue)= 5(total of candies) / 10 (it means 5 per 2 which are the 2 variable(blue and red)) + 5/10 = 10/10 or what is the same 1. The probability is 1

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the sum of three numbers is 131. The second of three numbers is seven more than twice the first. The third number is 12 less tha

spin [16.1K]

No. 1 = x
No. 2 = 2x+7
No. 3 = x-12

Answer:

x+(2x+7)+(x-12) = 131

From there you solve to get the numbers:

34, 75 and 22

3 0

2 years ago

Determine how long it will take an airplane to travel 2000 miles if it flies 200 miles per hour, 400 miles per hour, and 600 mil

AveGali [126]

I will use 'hr' to mean hour and 'hrs' to mean hours.

<u>The airplane flies:</u>

200 miles per hr

400 miles per hr

600 miles per hr

Average speed = Total distance ÷ total time

= (200 + 400 + 600)miles ÷ 3hrs = 400miles/hr

Time = Distance ÷ Average speed

= 2000miles ÷ 400miles/hr = 5hrs

7 0

3 years ago

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

Two acute triangles are similar. Which of the following must the similar triangle have?

abruzzese [7]

B is the only one that makes sense if you break them each down. An Acute doesnt have every Pair of angles congruent, the don't have to have proportional side lengths, and it can't have a right angle or it would be a right triangle.

7 0

2 years ago

Read 2 more answers

the tickets are 90 dollars in all adults 7 kids 12 kids are 2/3 cost of adults tickets. What is the cost of the adult tickets

svetoff [14.1K]

I hope it helps. .........

3 0

3 years ago