Mathematics High School

Simplify the expression. Write your answer as a power.

Answers

Answer 1

Answer:

π^8

Step-by-step explanation:

π^30/π^22= π^8

Related Questions

A sphere with a 2-inch radius is packed in a cube so that all sided touch. How much empty space is left in the cube?.

Answers

The volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

What is a cube?

It is defined as three-dimensional geometry that has six square faces and eight vertices.

We have a sphere with a 2-inch radius is packed in a cube so that all sided touch.

The volume of the sphere = (4πr³)/3 = (4π(2)³)/3 = 33.51 cubic inches

The side length of the cube = 4 inches

Because diameter of the sphere is 4 inches and all sided touch to the cube face.

Volume of the cube = 4³ = 64

The volume of the empty space = 64- 33.51 = 30.49 cubic inches

Thus, the volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.

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A computer generates 50 integers from 1 to 8 at random. The results are recorded in this table.

Outcome 1 2 3 4 5 6 7 8
Number of times outcome occurred

5 8 9 7 4 6 5 6
What is the experimental probability of the computer generating a 2 or a 4?

12%

15%

22%

30%

Answers

The experimental probability of the computer generating a 2 or a 4 is 30% option fourth is correct.

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A computer generates 50 integers from 1 to 8 at random.

Total number of outcomes = 5+8+9+7+4+6+5+6 = 50

Computer generating a 2 = 8

Computer generating a 4 = 7

P(computer generating a 2) = 8/50

P(computer generating a 4) = 7/50

P(computer generating a 2 or a 4) = 8/50 + 7/50 = 15/50 or

= 0.3×100

= 30%

Thus, the experimental probability of the computer generating a 2 or a 4 is 30% option fourth is correct.

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'the largest prime number that is a factor of 42'
is multiplied by
'the smallest prime number that is a factor of 28'

Answers

The answer is 14, since 7x2=14.

Answer:

14.

Step-by-step explanation:

42 = 2 8 3 * 7

Largest prime factor = 7

28 = 2 * 2 * 7

Smallest prime factor = 2

Answer = 2*7 = 14.

Jeremy finished 3/5 of his homework what percent of homework did he finish

Answers

Answer:

60%

Step-by-step explanation:

Percent means per hundred. Change to "per hundred"

3/5 = 6/10 = 60/100

3/5 is 60%

Divide 3/5 means 3÷5...

3÷5 = .6

Change decimal to percent by multiplying by 100.

.6 × 100 = 60

60%

Answer:

60%

Step-by-step explanation:

well if they only finished 3/5 it’s going to be

60/100 = 60%

P+d= 19 9p+ 5.50d= 150 solve the system of equations , step by step

Answers

Answer:

d=6 & p=13

Step-by-step explanation:

1. P+d=19

×9

2. 9p +5.50d=150

×1

9p+9d=171

9p +5.50d=150

3.5d=21

d=6

Substituting d=6 in 1.

P+6=19

P=13

The sum of three consecutive intergers is 189 what are the integers

Answers

Answer:

62, 63, 64

Step-by-step explanation:

The middle integer of three consecutive integers will be the average of them. That is, it will be their sum, divided by 3.

The middle integer is 189/3 = 63.

The three consecutive integers are 62, 63, 64.

_____

Additional comment

If you'd like to write an equation that tells you the same thing, let x represent the middle integer. Then the lower one is x-1, and the upper one is x+1. Their sum is ...

(x-1) +x +(x+1) = 189

3x = 189 . . . . . . . . . . . . simplify

x = 189/3 = 63 . . . . . . . divide by the coefficient of x

(x-1) = 63-1 = 62 . . . . . . find the other two integers

(x+1) = 63+1 = 64

How do I find the radius/x of a shaded region with it's area and/or angle measurement?

Answers

Answer:

[tex]x \approx 9.823\ ft[/tex]

Step-by-step explanation:

Remember that the area of a sector is defined as:

[tex]A = \frac{\theta}{360^\circ}\times \pi r^2[/tex]

In this problem, we are given the area [tex]A[/tex], and the angle [tex]\theta[/tex]. We can set up an equation to solve for the radius, which is x:

[tex]A = \frac{\theta}{360^\circ}\times \pi r^2\\128 = \frac{152}{360}\times \pi r^2\\128 \times \frac{360}{152} = \pi r^2\\\frac{5760}{19} = \pi r^2\\r = \sqrt{\frac{5760}{19 \pi}}\\r \approx 9.823[/tex]

Answer:

r ≈ 9.8 feet

Step-by-step explanation:

Formula of A Sector

Area (Sector) = πr² × θ/360°

Substitute the given values in the formula to find r.

128 = 3.14 × r² × 152/36040.76 = r² × 19/45r² = 1834.2/19r² = 96.54r ≈ 9.8 feet

Layla owns a small business selling clothing. She knows that in the last week 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card. Based on these results, express the probability that the next customer will pay with something other than a credit card as a decimal to the nearest hundredth.

Answers

Total cards=52+20+11=83

Probability of paYing in credit card

11/830.13

P(Not paying in credit card)

1-0.130.87

The probability that the next customer will pay with something other than a credit card is 0.87.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Layla owns a small business selling clothing. She knows that in the last week, 52 customers paid cash, 20 customers used a debit card, and 11 customers used a credit card.

Based on these results we have;

Total cards=52+20+11=83

Probability of paying in credit card;

11/83

0.13

Now, P(Not paying in credit card)

1-0.13

0.87

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If (8^2)p = 8^4, what is the value of p?

2
3
4
6

Answers

Answer:

Step-by-step explanation:

8²p=8^4

64p=4096

p=64

p could also equal 2

8^2x2=8^4

Answer: P = ^2

Step-by-step explanation:

8^4= 4096

8^2= 64

4096/64=64

(8^2)^2= 8^4

4096 = 4096

I'm good how's life!

Complete the table by giving the length and area for each
width. (The width is the side perpendicular to the building.)
width (feet) length (feet)
area (square feet)
10
30
40
W
of the play area

Answers

The values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.

What is the area of the rectangle?

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We know the perimeter of the rectangle = 2(w+l)

The sum of w+w+l = 120 (given)

2w + l = 120

From the above equation, we can calculate the l of the rectangle:

We have w = 10 feet

l = 100 feet

Area = 10×100 = 1000 square feet

When w = 30

l = 60 feet

Area = 60×30 = 1800 square feet

When w = 40

l = 40 feet

Area = 40×40 = 1600 square feet

Thus, the values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.

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serious car accident and broke both wrists.

what is the absolute value of 62

Answers

Answer:

62, since positive doesn't change to negative.

General rule nth term)
6;11;16; 21; .....

Answers

Answer:

The rule is increase by 5. That means the next term would be 26.

How far does the unicycle move if the wheel turns once?

Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?

Answers

The unicycle would move 2.512 meters if the wheel turns once

The wheel needs to rotate completely 40 times in order for Pierre to travel 100m

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

a) The circumference of the wheel = π * diameter = 3.14 * 80 cm = 251.2 cm = 2.512 m

The unicycle would move 2.512 meters if the wheel turns once

b) For a 100m race:

Number of wheel rotation = 100 m / 2.512 m = 39.8

The wheel needs to rotate completely 40 times in order for Pierre to travel 100m

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how to find slope within two sets of points

Answers

The slope within two sets of points is calculated using the slope equation [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

What is slope?

The slope of a line or points is the rate of change of the line.

This in other words means that, the vertical change per unit horizontal change

Assume that the points are given as:

(x1, y1) and (x2, y2)

The slope (m) of the points is:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Hence, the equation of two sets of points is [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Answers

Top company would accept the order as it increases the total profit of the corporation by $90000

How to illustrate the information?

As a company as a whole, Tops corporation will accept orders if the contribution margin increases by accepting orders.

a. The contribution margin will be:

= sales price - variable cost of manufacturing department - variable cost of marketing department

= $400 - [$2400*1000/10000units] - $70

= $400 - $240 - $70

= $90

Therefore, the increase in profit will be:

= $90 × 1000

= $90000

Top company would accept the order.

b. The marketing department will accept the order as it increases its profit by $400000-$370000 = 30000.

c. The manufacturing division manager would accept the order as it increases its profit by $60000. This was gotten as:

= (300 × 1000) - (240 × 1000)

= 300000 - 240000

= 60000

The other parts of the question include:

The company has just received an offer to buy 1,000 units of the product this month at a price of $400 per unit. The Marketing Division manager suggests that for the special order only, the transfer price be set at 50 percent of the sales price, or $200 per unit. Instead, assume the transfer price is unchanged from the current transfer price.

Required:

a. Does Tops Corporation want to accept this order?

b. Will the Marketing Division manager be willing to accept this order?

c. Will the Manufacturing Division manager be willing to accept this order?

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can someone help me with this? thank you!

Answers

Answer:

240cm³

Step-by-step explanation:

To find our answer we will multiply the volume, width, and height.

4 · 20 · 3 = 240. Therefore, 240cm³ is our answer.

Have a good day!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate its volume ~

Volume of a rectangular prism is :

[tex]\qquad \sf \dashrightarrow \:v = l \cdot w\cdot h[/tex]

[tex]\qquad \sf \dashrightarrow \:v = 20 \cdot 4\cdot 3[/tex]

[tex]\qquad \sf \dashrightarrow \:v = 240 \: \: cm {}^{3} [/tex]

Write an expression to represent:
"5 times the sum of 12
and a number"

Answers

5 (12 + x)

Step-by-step explanation:

Answer:

5(12+X)

Step-by-step explanation:

I need an answer for this:
stirring a hot cup of tea causes a metal spoon to get warm which statement best explains why the spoon gets warm?

Answers

Answer:

here we go

Step-by-step explanation:

Stirring a cup of hot tea causes a metal spoon to get warm. Which statement best explains why the spoon gets warm? Heat energy transfers from the hot tea to the spoon.

Answer:

The molecules at the end of the spoon, in turn, collide with the molecules in the adjacent, cooler part, passing the kinetic energy on. This continues through the spoon until the handle molecules are also heated.

Step-by-step explanation:

Stay safe, stay healthy and blessed.Have a good day !Thank you

Angles 1 and 2 are supplementary

Angle 1 = 30°

Answers

Answer:

Angle 2 = 150°

Step-by-step explanation:

▪︎ Measures of supplementary angles add up to 180°.

Therefore,

Angle 1 + Angle 2 = 180°

Angle 1 = 30°

6x + 33 = 6x + 36 ( subtract 33 from both sides )

6x = 6x + 3 ( subtract 6x from both sides )

0 = 3 ← not possible

This indicates the equation has no solution

]

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