MATHEMATICS HIGH SCHOOL

Which pair of variables can possibly be correlated (as opposed to associated)?SAT scores and college grade point averages



religious affiliation and number of offspring



marital status and personal income



favorite band and peer likability as measured on a 5-point scale

Answers

Answer 1
Answer: We can look at each of the options to see whether or not the pair of variables can be correlated or associated. The most logical answer is the first option.

SAT scores and college grade point averages: The relationship between the variables can produce a linear relationship i.e., there is a direct relationship between one variable to the other.
Answer 2
Answer:

Answer:

See image

Step-by-step explanation:

Plato

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What number goes between 44 and 88 and right before 76?
HELP ME FIND X AND Y: 2x = 4y + 6 and 3x - y = -1
Solve for x: (125^2x)(5x) = 25^3

What is the final balance for the investment? $1200 for 3 years at 3% compounded annually A.
$1311.27

B.
$72.00

C.
$2636.40

D.
$1272.00

Answers

The amount is $1311.27 and the interest is $111.27.

What multiplies to make 12 and adds up to 16

Answers

To solve Q.15, remember to multiply the first numerical coefficient, in this case 3 to -12, to find the numbers to multiply and get that product. The middle term represents the sum the same two numbers must add to.

For example:

3r^2 - 16r - 7 = 5
3r^2 - 16r - 12 = 0

What 2 numbers multiply to give you -36, and add to give you -16, are -18 and +2, since -18 • 2 = -36, and -18 + 2 = -16.

3r^2 - 18r + 2r - 12 = 0
Factor
3r(r - 6) + 2(r - 6) = 0
(3r + 2)(r - 6) = 0
r = 6

3r + 2 = 0
3r = -2
r = -2/3.

Your 2 solutions for r are -2/3 and 6.

The length of a rectangle is 7 mm longer than its width. Its perimeter is more than 62 mm. Let w equal the width of the rectangle. Write an expression for the length in terms of the width.
Use these expressions to write an inequality based on the given information.
Solve the inequality, clearly indicating the width of the rectangle

Answers

We know that the length (L) of the rectangle in question is 7mm longer than its width (W). Let's represent that as the following:
L=7+W

A rectangle's perimeter (the total sum of its sides) will be made my 2 sides representing the length  (2L) and 2 sides representing the width (2W).  We also know that this rectangle's perimeter is greater than 62. Since eventually we are solving for W, let's state all expressions in terms of W:
2L=2(7+W)
2(7+W)+2W>62
14+2W+2W>62
14+4W>62
4W>62-14
4W>48
W>48/4
W>12
If the rectangle's perimeter is greater than 62, then the width  will be greater than 12. Let's confirm this:
Perimeter=2L+2W
P=2(7+12)+2(12)
P=14+24+24
P=62
So we can see that if the perimeter is to surpass 62, W needs to be greater than 12 and L ( which is also 7+W) needs to be greater than 19.

Final answer:

The length of the rectangle is expressed as w + 7 mm. The inequality for the perimeter is 2(w + w + 7) > 62. The solution for the inequality reveals that the width, w, must be more than 12mm.

Explanation:

The question is asking for an expression for the length of a rectangle in terms of the width and an inequality based on the perimeter. We are given that the length of the rectangle is 7 mm longer than its width, and its perimeter is more than 62 mm.

The width of the rectangle is defined as w. We can express the length as w + 7 mm, since it is 7 mm longer than the width.

The perimeter of a rectangle is calculated as 2 times the sum of its width and length, so we form the inequality: 2(w + w + 7) > 62.

To solve it, we simplify the left side: 4w + 14 > 62. We then subtract 14 from both sides, getting 4w > 48. Finally, we divide both sides by 4, which gives us w > 12. Therefore, the width of the rectangle must be more than 12 mm.

Learn more about Inequalities here:

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$3450 is invested into an account earning 2.27% interest for 5 years. Compounded monthly.

Answers

$3,536.65 I believe

Which polynomial is a difference of squares? A.x2 – 16x + 64
B.x2 + 4
C.9x2 – x – 36
D.25x2 – 36

Answers

Answer

D.25x2 – 36


Explanation

A. x² – 16x + 64

product = 64

sum = -16

factors: -8 and -8

x² – 16x + 64  = x² - 8x - 8x + 64

                       = x(x - 8) - 8(x - 8)

                        = (x - 8)(x-8) = (x-8)²      ⇒ Not a difference of squares


B.x² + 4 = (x² + 2²) ⇒ Not a difference of squares


C.9x² – x – 36

product = - 324

sum = -1

Factors: none

9x² – x – 36  ⇒ Has no perfect roots.


D.25x² – 36

25x² – 36 = (5x)² - 6²   ⇒ This is the difference of squares.

Hello,

Answer D

25x²-36=(5x)²-6²

A tent is in the shape of a triangular prism. The front and back are isosceles triangles with base 6 feet and height 4 feet. The surface area of the entire tent is 104 square feet. What is the depth of the tent?

Answers

If  surface area of the entire tent is 104 square feet then the depth of the tent is approximately 4.44 feet.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The tent can be divided into three rectangular faces and two triangular faces. Let the depth of the tent be denoted by "d".

The area of each triangularface is (1/2) base x height = (1/2) x 6 x 4 = 12 square feet.

The area of each rectangular face is length x width = d x 6 feet.

Therefore, the total surfacearea of the tent is:

2 x 12 square feet (for the triangular faces) + 3 x (d x 6 feet) square feet (for the rectangular faces) = 24 + 18d

We know that the total surface area of the tent is 104 square feet, so:

24 + 18d = 104

Subtract 24 from both sides.

18d = 80

Divide both sides by 18.

d = 80/18 ≈ 4.44 feet

Therefore, if  surface area of the entire tent is 104 square feet then the depth of the tent is approximately 4.44 feet.

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the depth is 5 feet of the tent
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