Since obtaining measurements of the human brain is difficult with living subjects, Gladstone (1905) used cadavers to investigate if there was a relationship between a subject's head size (in cubic centimeters) and his or her brain weight (in grams). This linear regression model was fit using 50 randomly selected cadavers from Gladstone's study, where X is the predictor variable head size and Yˆ is the predicted response variable brain weight. The standard error of the slope coefficient for this model, SEb, is 0.0233. Yˆ=342.0134+0.2585X

Using this regression line, suppose Gladstone wishes to conduct a two‑tailed t ‑test to test the hypothesis that subjects with larger head sizes will have either smaller or larger brain weights. Let =0.05 and assume that all of the necessary conditions are met for this linear regression model. Let β represent the slope of the population regression line.

Required:
Compute the t-statistic and its corresponding.

.

step-by-step explanation:

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

the answer is c

step-by-step explanation: i took a test with this question on it

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3