The U. S. Department of Agriculture claims that the mean cost of raising a child from birth to age 2 by husband-wife families in the United States is $13,120. A random sample of 500 children (age 2) has a mean cost of $12,925 with a standard deviation of $1745. At α=.10, is there enough evidence to reject the claim? (Adapted from U. S. Department of Agriculture Center for Nutrition Policy and Promotion).

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 13120

For the alternative hypothesis,

µ ≠ 13120

This is a 2 tailed test

Since the population standard deviation is not given, the t test would be used to determine the test statistic. The formula is

t = (x - µ)/(s/√n)

Where

s = sample standard deviation

x = sample mean

µ = population mean

n = number of samples

From the information given,

µ = $13120

x = $12925

n = 500

s = $1745

t = (12925 - 13120)/(1745/√500) = - 2.5

Degree of freedom = n - 1 = 500 - 1 = 499

Using the t score calculator to find the probability value,

p = 0.012

Since α = 0.10 > p = 0.012, it means that there is enough evidence to reject the claim

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x