Width = x
Length = x+18

Assuming the table is rectangular:
Area = x(x + 18)

Therefore:
x(x + 18) ≤ 175
x^2 + 18x ≤ 175

Using completing the square method:
x^2 + 18x + 81 ≤ 175 + 81
(x + 9)^2 ≤ 256
|x + 9| ≤ sqrt(256)
|x + 9| ≤ +-16
-16 ≤ x + 9 ≤ 16
-16 - 9 ≤ x ≤ 16 - 9
-25 ≤ x ≤ 7

But x > 0 (there are no negative measurements):

Therefore, the interval 0 < x ≤ 7 represents the possible widths.

3 0

2 years ago

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Researchers from Dartmouth Medical School conducted a study in 2003 to look at the connection between watching actors smoking in

docker41 [41]

Answer:

The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

Step-by-step explanation:

A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.

The (1 - α) % confidence interval for the population proportion (p) is given by:

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

The information provided is:

$n = 6522\\\hat p=0.38\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table for the critical value.

Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:

$CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.38\pm 1.96\times \sqrt{\frac{0.38(1-0.38)}{6522}}\\=0.38\pm 0.0118\\=(0.3682, 0.3918)\\\approx (0.37, 0.40)$

Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

8 0

2 years ago

I have a hat that contains six nickels and five pennies. I draw coins from the hat at random, without replacement. Find the prob

Rzqust [24]

6 nickels and 3 pennies

8 0

2 years ago