18:a = 14:21 what does a equal?

Complete the following.

Otrada [13]

Answer:

Step-by-step explanation:

1) the triangle is a right angle triangle.

From the given right angle triangle,

With 67° as the reference angle,

x represents the adjacent side of the right angle triangle.

17 represents the opposite side of the right angle triangle.

To determine x, we would apply

the Tangent trigonometric ratio.

Tan θ = opposite side/adjacent side.

Therefore,

Tan 67 = 17/x

xTan 67 = 17

x = 17/Tan 67

x = 17/2.3559

x = 7.22

2) From the given right angle triangle, with 24° as the reference angle,

x represents the opposite side of the right angle triangle.

12 represents the adjacent side of the right angle triangle.

To determine x, we would apply

the Tangent trigonometric ratio.

Tan θ = opposite side/adjacent side.

Therefore,

Tan 24 = x/12

x = 12Tan 24

x = 12 × 0.4452

x = 5.34

4 0

4 years ago

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

This Zscore is how many standard deviations the value of the measure X is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

So

$Z = \frac{X - \mu}{\sigma}$

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$

The standard deviation of a sample of n young man is given by the following formula

$s = \frac{\sigma}{\sqrt{n}}$

We want to have $s = 0.167$

$0.167 = \frac{2.8}{\sqrt{n}}$

$0.167\sqrt{n} = 2.8$

$\sqrt{n} = \frac{2.8}{0.167}$

$\sqrt{n} = 16.77$

$\sqrt{n}^{2} = 16.77^{2}$

$n = 281.23$

We need a sample of at least 282 young men.

6 0

3 years ago

Roll a number cube. If the number cube comes up odd, you win the same number of points as the number on the cube. If the number

laila [671]

Answer:

–0.5

Step-by-step explanation:

Expected value is found by multiplying the probabilities of each roll by the amount won or lost with each roll.

The odd rolls are 1, 3 and 5. The probability of rolling a 1 is 1/6, and the value is 1; this gives us 1/6(1) = 1/6.

The probability of rolling a 3 is 1/6, and the value is 3; this gives us 1/6(3) = 3/6.

The probability of rolling a 5 is 1/6, and the value is 5; this gives us 1/6(5) = 5/6.

Rolling any even number gives us the same value. The probability of rolling an odd number is 3/6, and the value is -4; this gives us 3/6(-4) = -12/6.

Together we have

1/6+3/6+5/6-12/6 = 4/6+5/6-12/6 = 9/6-12/6 = -3/6 = -0.5

5 0

3 years ago

Read 2 more answers

The formula for the volume of a sphere is v= 4/3 m^3 what is the formula solved for r ?

Softa [21]

Answer:

3V

r = ∛ ( ---------- )

4π

Step-by-step explanation:

Please, enclose the fraction 4/3 inside parentheses, to eliminate any possibility of misreading this fraction. Also note that this formula MUST include "pi," symbolized by π.

V = (4/3) π r³ This formula does NOT include "m," which is a unit of measurement, not a variable.

Our task is to solve this formula for the radius, r.

Divide both sides by (4/3) π, to isolate r³. This results in:

v (4/3) π r³

------------- = -----------------

(4/3) π (4/3) π

V 3V

Then r³ = -------------- = --------

(4/3) π 4π

and r is found by taking the cube root of the above result:

3V

r = ∛ ( ---------- )

4π

4 0

4 years ago

Please answer and explain how you received that answer, these are the three problems I had trouble with out of 18

Varvara68 [4.7K]

9) x.14 = 6.26 ==> 14x=156 ==> x=11.1

12) OAB = Right Triangle : (27+24)² = 24² + AB² (Pythagoras)
==> 51² =24² + AB² ==> 2,601 = 576 + AB² ==> AB² = 2,601 - 576 = 2,025
==> AB² = 2015 AND AB =√2025 = 45
Sorry I can't read the last page

5 0

3 years ago