The standard form of the equation that represents the number of quarters, q, and the number of dimes, d, that Austin has in his

Answer:

Step-by-step explanation:

a) According to the included image, the smaller section measures 16ft², and the larger section is 50 ft². The formula for the area of a square is side × side = side².

For the smaller section: Area = side²

16 = side²

side = √16 = 4 ft

For the larger section: Area = side²

50 = side²

side = √50

The overall length of the shed is the small area plus the large area = 4 + √50

The total length of the shed equates to 4 + √50

b) All square roots of integers unless they are perfect squares are irrational numbers, thus 4 + √50 is irrational. All such values fall within the set of real numbers, categorizing  4 + √50 as an irrational and real number.

Response:

Detailed explanation:

For private institutions,

n = 20

Average, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(sum of (x - mean)²/n

Sum of (x - mean)² = (43120 - 34623.05)^2 + (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public institutions,

n = 20

Average, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Sum of (x - mean)² = (25469 - 25063.15)^2 + (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This involves two independent samples. Define μ1 as the mean out-of-state tuition for private institutions and μ2 as the mean out-of-state tuition for public institutions.

The random variable represents μ1 - μ2 = the difference between the mean out-of-state tuition for private vs. public institutions.

The hypothesis is established as follows. The correct choice is

-B. H0: μ1 = μ2; H1: μ1 > μ2

As the sample standard deviation is known, the test statistic is calculated using the t test formula:

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The method for finding degrees of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

The probability value is obtained from the t test calculator. It is

p value = 0.000065

Given that alpha, 0.01 > the p value, 0.000065, we will reject the null hypothesis. Hence, at a significance level of 1%, the mean out-of-state tuition for private institutions is statistically significantly greater than that of public institutions.

The y-coordinate of P' is -10.

Step-by-step explanation:

It is given that triangle PQR has vertices at P(–2, 6), Q(–8, 4), and R(1, –2).

The translation rule is

To determine the image of point P, referred to as P', we must substitute the coordinates of P(-2,6) to arrive at;

Thus, the y-coordinate of P' is -10.