John deposited $2860 in a bank that pays 9% interest, compounded monthly. Find the amount he will have at the end of 3 years.

In an apartment complex with 28 units, 19 of the renters keep a pet. What percentage does not keep a pet?

Aleks04 [339]

If 19 out of 28 renters keep a pet, there are $28-19 = 9$ renters who don't keep a pet.

Whenever you have a subset of some set, and you want to know which percentage of the set the subset represents, you simply have to compute

$\dfrac{\text{number of elements in the subset}}{\text{number of elements in the set}}\times 100$

So, in your case, you're wondering what percentage of 28 does 9 represent. So, the formula becomes

$\dfrac{9}{28}\times 100 = 0.32\overline{142857}\times 100 = 32.\overline{142857} \approx 32.14\%$

6 0

1 year ago

Hich expression is equivalent to -4(7 - 2m) + 11m?

Sholpan [36]

Answer:

$- 4(7 - 2m) + 11m \\ = - 28 + 8m + 11m \\ = \boxed{19m - 28}$

Expression (19m-28) is equivalent to -4(7 - 2m) + 11m.

3 0

1 year ago

Counter example. The sum of three fractions with odd numerators is never 1/2

kolbaska11 [484]

1/6 + 1/6 + 1/6 = 3/6 = 1/2

8 0

2 years ago

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A certain article indicates that in a sample of 1,000 dog owners, 610 said that they take more pictures of their dog than of the

lbvjy [14]

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)

Let X = number of dog owners who take more pictures of their dog than of their significant others or friends.

Given:

X = 610

n = 1000

Confidence level = 90%

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:

$\hat p=\frac{X}{n}=\frac{610}{1000}=0.61$

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

$z_{\alpha/2}=z_{0.10/2}=z_[0.05}=1.645$

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)

Let X = number of dog owners who are more likely to complain to their dog than to a friend.

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:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

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:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)$

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend is (0.42, 0.46).

Interpretation:

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).

4 0

1 year ago

Find the value of 3 + 5 × (2 − 1).

Alenkasestr [34]

Step 1 (simplify):
3+5x(2-1)
8 x 1

Step 2 (solve):
8 x 1 = 8

8 is your answer. Hope this helps :)

8 0

1 year ago

Read 2 more answers