69. A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is . a. at least 20%, when in fact, it is less than 20%. b. 20%, when in fact, it is 20%. c. less than 20%, when in fact, it is 20%. d. less than 20%, when in fact, it is less than 20%

a. at least 20%, when in fact, it is less than 20%.

Step-by-step explanation:

Type 1 Error is to reject null hypothesis when it is actually true.

Here the null hypothesis is fewer than 20% of Evergreen Valley College (EVC) students attended the show.

In mathematics fewer than 20% means less than  20%.

So the null hypothesis is that less than 20 % students attended the show.

We have to reject this hypothesis .

We can reject this hypothesis when we assume that the % is greater than or equal to 20 %

At least  20% means greater than or equal to 20%.

So the best choice is option a.

at least 20%, when in fact, it is less than 20%.

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form