Darius is studying the relationship between mathematics and art. he asks friends to each draw a "typical” rectangle. he measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. the points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). which equation could darius use to determine the length, in centimeters, of a "typical” rectangle for a given width in centimeters?
a. y = 0.605x + 0.004
b. y = 0.959x + 0.041
c. y = 1.518x + 0.995

Option A

Step-by-step explanation:

Given that Darius is studying  the relationship between mathematics and art. He asks friends to each draw a "typical” rectangle. x the length, y the width are known.

xy

6.112

58.1

9.115.2

6.510.2

7.411.3

10.917.5

slope0.605311851

Intercept0.004221583

Hence regression equation would be

y = 0.605x +0.004

Option A is the right answer

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.