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12345 [234]
3 years ago
14

7. what is the value of x

Mathematics
2 answers:
frozen [14]3 years ago
8 0

Answer:

x = 18.5

Step-by-step explanation:

tangent is opposite over adjacent

tan 51 = x/15

solve for x

be sure your calculator is in Degree mode.

x = tan 51 * 15

andrew-mc [135]3 years ago
7 0

Answer:

x ≈ 18.52

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan51° = \frac{opposite}{adjacent} = \frac{x}{15}

Multiply both sides by 15

15 × tan51° = x, thus

x ≈ 18.52 ( to 2 dec. places )

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A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000
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Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

p_1=X_1/n_1=494/1000=0.494

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

p_2=X_2/n_2=552/1000=0.552

The difference between proportions is (p1-p2)=-0.058.

p_d=p_1-p_2=0.494-0.552=-0.058

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022

Then, the margin of error is:

MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

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