MATHEMATICS
HIGH SCHOOL

Answer:

Hello There!

Mode: Number that occurs most often in a set of numbers.

When we look at our set of numbers, we can see that the number 32 occurs more than any other number in the set of numbers.

The mode of the numbers is 7

Answer: The mode would be 32 because it shows up three times which is more than any other number. 32 is represented more than the other numbers

HIGH SCHOOL

A triangular bookself has a base of 10 inches,12 inches and 18 inches. Will the bookself fit in the corner of a square living room

Answer:

No, if fit means that the sides of the book case need to be flush with the wall, which means that the sides of the bookcase are touching the wall and the bookcase fits perfectly in that spot

Step-by-step explanation:

A square room will have corners that meause 90°, so we need to see if any of the vertices of the bookcase measure 90°. All right triangles have a 90° in them, so we can use Pythagorean Theorem to solve this.

Pythagorean Theorem is a² + b² = c², where a and b are the legs, and c is the hypotenuse. Since the hypotenuse is always the longest side, for our bookshelf, 10 and 12 are the legs, and 18 would be the hypotenuse if it is a right triangle. Plug the values in to see if the equation is true or false

10² + 12² = 18²

100 + 144 = 324

244 ≠ 324 so the bookcase does not form a right angle, and won't fit in the corner of the room

COLLEGE

Use even and odd properties of the trigonometric functions to find the exact value of the expression. sin(−π6)

Answer:

sin(-π/6) = -1/2

Step-by-step explanation:

sin(π/6) = 1/2 is a value we have memorized.

sin(-π/6) = -sin(π/6) = -1/2

COLLEGE

0 If x and y vary inversely and y=6 as x=7, what is the constant of variation?

Answer:

k = 42

Step-by-step explanation:

given that x and y vary inversely then the equation connecting them is

y = ← k is the constant of variation

To find k use the condition y = 6 when x = 7

k = yx = 6 × 7 = 42

HIGH SCHOOL

What quadrilaterals are also parallelogram

Trapozoids are types of quadrilaterals that are parallelograms because the have four sides that are parallel. Their angles are also congruent.

MIDDLE SCHOOL

73 is 20% of what number?

20% = 73/x * 100%

20%/100% = 73/x

0.20 = 73/x

x = 73/0.20

x = 365

20%/100% = 73/x

0.20 = 73/x

x = 73/0.20

x = 365

Make an equation.

'is' is an equal sign

20% = 0.20

'of' is multiplication

'what number' is 'x'

So we have:

Multiply:

Divide 0.20 to both sides:

'is' is an equal sign

20% = 0.20

'of' is multiplication

'what number' is 'x'

So we have:

Multiply:

Divide 0.20 to both sides:

HIGH SCHOOL

An archer’s arrow follows a parabolic path. The height of the arrow f(x) is given by f(x) = -16x^2 + 200x + 4, in feet. Find the maximum height of the arrow.

The maximum height is the greatest value of the function, or the y-coordinate of the vertex.

The maximum height of the arrow is 629 feet.

The maximum height of the arrow is 629 feet.

MIDDLE SCHOOL

The slope of the line containing the points (6, 4) and (-5, 3) is:

A. 1/11

B. 1

C. -1

Answer:

1/11

Step-by-step explanation:

MIDDLE SCHOOL

: The Imbrium Basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by

{d0 < d < 3805774}. What does this tell you about the basin?

Answer:

Part a)

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) see the explanation

Part c)

Step-by-step explanation:

The complete question is

On the moon, the time, in seconds, it takes for an object to fall a distance, d, in feet, is given by the function f(d) = 1.11√d.

Part a: determine f(2) and explain what it represents.

Part b: The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}. What does this tell you about the basin.

Part c: how long would it take a rock to drop from the rim to the bottom of the basin?

Let

f(d) -----> the time in seconds it takes for an object to fall

d -----> distance in feet

we have

Part a): Determine f(2) and explain what it represents

we know that

f(2) represent the time in seconds it takes for an object to fall a distance of 2 feet

For d=2 ft

substitute in the function above and solve for f(2)

therefore

It takes 1.57 seconds for an object to fall a distance of 2 feet

Part b) The imbrium basin is the largest basin on the moon. A reasonable domain for the height above the lowest point in the basin is given by {d|0 ≤ d ≤ 3805774}

What does this tell you about the basin?

The height of the basin is greater than or equal to 0 ft and less than or equal to 3,805,774 ft

so

The maximum height of the basin is 3,805,774 ft

Part c) How long would it take a rock to drop from the rim to the bottom of the basin?

we know that

The distance from the rim to the bottom of the basin is equal to the maximum height of the basin

so

substitute the value of d in the function f(d)

MIDDLE SCHOOL

Four friends go out to lunch and decide to split the bill evenly. The bill comes to $48.20. How much does each person owe?

Four friends go out to lunch and they agree to split the bill evenly.

so now you have to divide the price by 4 because there's four people.

$48.20. / 4.

so your answer is $12.05 that's so much each person will pay for their share of bill.

so now you have to divide the price by 4 because there's four people.

$48.20. / 4.

so your answer is $12.05 that's so much each person will pay for their share of bill.

Answer:

They each have to pay $12.05

Step-by-step explanation:

If you have a calculator put in $48.20 and divide that by 4 and you'll get 12.05 which is how much everyone would pay