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3 years ago

What is the probability that she chose the four students so that exactly ONE of them is a junior?

Mathematics

1 answer:

8090 [49]3 years ago

3 0

Answer:

B) 0.246

Step-by-step explanation:

The desired probability is the sum of the probabilities of each of the ways one junior can be chosen. If we let a, b, c, d represent the ratio of juniors in classes 1 to 4, then this probability is ...

p(1 junior) = (a)(1-b)(1-c)(1-d) + (1-a)(b)(1-c)(1-d) + (1-a)(1-b)(c)(1-d) + (1-a)(1-b)(1-c)(1-d)

We can simplify this a little bit to ...

p(1 junior) = (1-a)(1-b)(1-c)(1-d) × (a/(1-a) +b/(1-b) +c/(1-c) +d/(1-d))

___

So, for {a, b, c, d} = {9/15, 12/15, 6/15, 3/15} = {3/5, 4/5, 2/5, 1/5} the probability of interest is ...

p(1 junior) = (2/5·1/5·3/5·4/5) × (3/2 + 4/1 + 2/3 + 1/4) = 24/625 × 77/12

p(1 junior) = 154/625 ≈ 0.246

_____

<em>Comment on the sum we're computing</em>

Each of the probabilities in the first sum above is ...

p(junior in given class) · p(not a junior in the other 3 classes)

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Determine if triangle XYZ with coordinates X (1, 1), Y (5, 6), and Z (6, 2) is a right triangle. Use evidence to support your cl

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We will use the formula for distance;

XY = $\sqrt{ ( x_{Y}- x_{X} )^{2}+y_{Y}- y_{X} )^{2} } = \sqrt{ (1-5 )^{2}+(1-6 )^{2} } = \sqrt{ 16+25 } = \sqrt{41}$
Applying the same formula
YZ = $\sqrt{17}$
XZ = $\sqrt{26}$

XZ^2 + YZ^2 is not equal with XY^2 which means the triangle is not right.

In order to make the triangle right, we have to take X and Z on the same x-line which means Z will be (6, 1) and Z and Y to be on the same y-line which means Y will be (6, 6). The point will be:
X(1, 1)
Y(6, 6)
Z(6, 1)

XY = $\sqrt{50}$
YZ = $\sqrt{25}$
XZ = $\sqrt{25}$

It means that: YZ^2+XZ^2=XY^2 and the triangle is right.

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4 years ago

Compute the exact value of the function for the given x-value without using a calculator. (2 points) f(x) = 5x for x = -1

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Answer:

The exact value of the function for the given x-value is of -5.

Step-by-step explanation:

In this question, we compute the numeric value of the function f(x) for x = -1, that is, we replace every instance of x in the function by -1.

f(x) = 5x for x = -1

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The exact value of the function for the given x-value is of -5.

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3 years ago

Harmons and Smiths are having a sale on apples. Harmons charges $1.25 for 5 apples. Smiths charges $2.04 for 6 apples. Find the

8090 [49]

Answer:

0.09

Step-by-step explanation:

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Then subtract the answers 0.34-0.25=0.09

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3 years ago

Douglas bought a $20 game card at a

satela [25.4K]

Answer:

Douglas can race the go-karts at least 3 times.

Step-by-step explanation:

Given that:

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Amount Douglas wants to left = $7.75

Let,

x be the times Douglas can ride go-kart.

20 - 3.50x ≤ 7.75

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$\frac{3.50x}{3.50}\leq \frac{12.25}{3.50}\\x\leq 3.5$

Hence,

Douglas can race the go-karts at least 3 times.

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