A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each

Answer:

50 years

Detailed breakdown:

Applying the simple interest formula:

PRT/100

Where P is the principal amount ($5000)

R represents the interest rate (4)

T signifies the time (x- unknown)

The total amount after time T is double the initial investment = 5000 * 2 = 10000

(5000 * 4 * x) / 100 = 10000

20000x / 100 = 10000

20000x = 100 * 10000

20000x = 1,000,000

x = 1,000,000 / 20,000

x = 50

It will require 50 years

Answer:

Step-by-step explanation:

Proceed to your table

B refers to the base of the triangle,
and a signifies the length of the two identical sides.

The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.

Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1

The ratio of women to men is 34 to 382. To find the total sales, we compute 382 multiplied by 2.50, resulting in $955. For women, the calculation is 34 multiplied by 1.25, which equals $42.50. Therefore, summing these amounts gives us $955 + $42.50 = $997.50.

Answer:

a) Null and alternative hypothesis

b) Point estimate d = -$78

c) Test statistic t = -2.438

P-value = 0.0113

Reject H0. This indicates that the average automobile premium in Pennsylvania is lower than in the nation.

Step-by-step breakdown:

This is a statistical test for the average population mean.

The hypothesis posits that car insurance in Pennsylvania is notably less expensive compared to the national average.

Accordingly, the null and alternative hypotheses are:

The significance level is set at 0.05.

The sample size is n=25.

The sample mean equates to M=1425.

A point estimate of the difference between the Pennsylvania mean premium and the national average can be computed using the sample mean:

Given that the standard deviation of the population is unknown, we approximate it using the sample standard deviation, which is s=160.

The estimated standard error of the mean is determined with the formula:

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size stand at:

This constitutes a left-tailed test, with 24 degrees of freedom and t=-2.438, rendering the P-value as (per a t-table):

As the P-value (0.0113) falls below the significance level (0.05), the results prove significant.

Thus, the null hypothesis obtains dismissal.

At a 0.05 significance level, there's sufficient evidence to assert that car insurance in Pennsylvania costs notably less than the national average.