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2 years ago

PLEASE HELP NOW 20pts........

Mathematics

2 answers:

OlgaM077 [116]2 years ago

6 0

x = 4y – 2

1.5x + 5y = 1152

julia-pushkina [17]2 years ago

6 0

Answer:

number of tickets of $5 sold = 418 and number of tickets of $1.5 sold = 105

Step-by-step explanation:

Let y be the number of $5 tickets sold and x be the number of $1.50 tickets sold.

Now from the statement " Number of $1.50 tickets sold was 2 less than the four times the number of $5 tickets sold".

Equation will be x = 4y - 2

4y - x = 2 ---------(1)

For second equation statement is " The pep club raised $1152 from the ticket sales".

Equation will be 5y + (1.50)x = 1152 -------(2)

Now we multiply equation (1) by 1.5 and add it to equation (2)

6y - 1.5x + (5y + 1.5x) = 3 + 1152

11y = 1155

y = 105

Now we put y = 105 in equation (1)

x = 4×105 - 2

x = 420 -2

x = 418

Therefore, number of tickets of $5 sold = 418 and number of tickets of $1.5 sold = 105

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Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

Step-by-step explanation:

(a)

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Given:

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The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

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The critical value of z for a 90% confidence level is:

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Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)$

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

Interpretation:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

(b)

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Given:

X = 440

n = 1000

Confidence level = 95%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{440}{1000}=0.44$

The critical value of z for a 95% confidence level is:

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Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

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There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

The confidence level
Sample size
Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of z in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

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