Which of the ratios below is equivalent to 1:3? Select all that apply.
A) 4:12
B) 6:18
C) 6:2
D) 8:24
E) 5:8

The length of the apothem of the pentagon is approximately 11 meters.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc.

Here, we have,

To solve this problem, we can use the formula for the area of a regular pentagon:

A = (5/2) × s × a

Where A is the area of the pentagon, s is the length of one side, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

We know that the area of the pentagon is 118.25 square meters and the length of one side is 4.3 meters. We can substitute these values into the formula and solve for the apothem:

118.25 = (5/2) × 4.3 × a

Divide both sides by (5/2) x 4.3:

a = 118.25 / ((5/2) × 4.3)

 = 118.25 / 10.75 ≈ 11 meters

Therefore, the length of the apothem of the pentagon is approximately 11 meters.

Learn more about polygon here:

brainly.com/question/24464711

#SPJ1

Answer:

88 are boys

Step-by-step explanation:

220 times 3/5 = 132

220-132 =88

The number of boys in the 7th grade is B = 88 boys

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is = number of boys

Substituting the values in the equation , we get

If three-fifths of the students are girls, then two-fifths must be boys, since the total fraction of students is equal to 1

On simplifying the equation , we get

To find the number of boys in the 7th grade, we can start by calculating the fraction of boys:

( 2/5 ) x 220 = 88

Hence , there are 88 boys in the 7th grade.

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

To learn more on Transformation click:

https://brainly.com/question/11709244

#SPJ1

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

Step-by-step explanation: x=-2.      -3•-2=6+3=9

Step-by-step explanation:

C = Amount (A) - Principal (P)

Where

C is the compound interest

To find the amount we use the formula

\(A = P ({1 + \frac{r}{100} })^{n} \)

where

P is the principal

r is the rate

n is the period / time

From the question

P = Rs 12, 000

r = 5%

n = 3 years

Substitute the values into the above formula

That's

\(A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} \)

We have the answer as

Compound interest = 13891.50 - 12000

Hope this helps you

52 Step-by-step explanation:

Bello bought a motor-bike for $8.50. if there was a discount of 20%, what was the marked price of the motor-bike?​

100% - 20% = 80% or 0.8

0.8 * 8.5 = $6.8

Answer: 6 dollars and 80 cents #6.80

Step-by-step explanation:

with the 20% off you save #1.7 and you subtract that from the original price to find the answer.

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

Learn more about expression at https://brainly.com/question/1859113

#SPJ1

Answer:

The radius of this sphere is \(3\).

Step-by-step explanation:

The volume of a sphere of radius \(r\) is:

\(\displaystyle V = \frac{4}{3}\, \pi\, r^{3}\).

The surface area of a sphere of radius \(r\) is:

\(A = \pi\, (2\, r)^{2}\).

Equate the right-hand side of these two expressions and solve for \(r\):

\(r = 3\).

In other words, the radius of this sphere is \(3\).

The desired monthly yield at the retirement time will be equal to $565,714.28.

Compound Interest may be defined as the interest earned by the bank on the basis of principle and also accumulated interest which increases exponentially and not linearly with respect to time. In calculating compound interest, the amount earned at the end of first year becomes principle for the next year and so on. Compound interest can be calculated, annually, half-yearly or quarterly etc.

Time for which work is planned = 40 years, Principle = $4500 and APR = 8.4% = 0.084/12 = 0.007.

The value of n = 12 × 25 = 300

The amount can be calculated by the formula A = P/r [1 - (1 + r) ⁻ⁿ]

A = (4500/0.007) [1 - (1 + 0.007) ⁻³⁰⁰]

A = 642,857.14 [1 - 0.12]

A = 642,857.14 × 0.88

A = $565,714.28 which is required amount.

Learn more about Compound Interest at:

brainly.com/question/13463611

#SPJ9

Complete Question:

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 8.4% compounded monthly. What monthly deposits are required to achieve the desired monthly yield at retirement?

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

sept one

Step-by-step explanation:

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

Learn more about rules of exponents here : brainly.com/question/11975096

#SPJ1

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Step-by-step explanation:

I've shown the process in the picture

hope it helps

Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

For more such questions on Unit pricing, click on:

https://brainly.com/question/29023044

#SPJ8

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

Read more about polynomial here:https://brainly.com/question/8021175

#SPJ1

Answer:

2sqr3, the first option

Step-by-step explanation:

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

im not sure just yet

The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

Read more on mean here; https://brainly.com/question/21479395

#SPJ1

Answer: the answer is 21

Step-by-step explanation:

first, u divide the odd and positive numbers last u divide the both answers and it should be the answer

The volume of the shaded portion of the cone is V = 621.667 inches³

Given data ,

Let the volume of the shaded region be V

Now , the volume of the larger cone be A

Let the volume of the smaller cone be B

Volume of Cone = ( 1/3 ) πr²h

V = A - B

And , A = ( 1/3 ) ( 9 )² ( 25 )

On simplifying , we get

A = ( 1/3 ) ( 81 ) ( 25 )

A = 675 inches³

And , B = ( 1/3 ) ( 4 )² ( 10 )

B = ( 160/3 ) inches³

So , Volume of shaded region V = A - B

V = 675 inches³ - ( 160/3 ) inches³

V = ( 1,865/3 ) inches³

V = 621.667 inches³

Hence , the volume of cone is 621.667 inches³

To learn more about cone click :

https://brainly.com/question/1984638

#SPJ1

Answer:

0.00079

Step-by-step explanation:

Leading zeroes dont count as sig figs, just round the final value and that gives your answer in 2 sig figs.

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

o.2222

Step-by-step explanation:

just divide one by five

hope that helps

Answer:

7

Step-by-step explanation:

7, 7, 7, 11, 15, 18

The mode is the number that appears most.

Answer: 7

Answer:

7

Step-by-step explanation:

The mode is the most frequently occurring value in a set of data. In this case, the number 7 occurs twice, which is more than any other number, so the mode is 7. It is worth noting that if there were no values that occurred more than once, then there would be no mode for the data set. In this case, the data set has a single mode, but it is possible for a data set to have multiple modes if there are multiple values that occur with the same highest frequency.

Answer:

B, C and F

Step-by-step explanation:

A constant is where a variable or number is on its own

B - 2x-4 (4 is the constant)

C - 8x+y (y is the constant)

F - 7+4x (7 is the constant)