Simplify the expression below. Determine the value of the exponent for y.

The area of circle C, which passes though points W and Z is 324π square meters.

The center of the outer circle, Point D, is where we want to calculate the area of the circle has a WZ diameter and WC and CZ radii.

That YZ = YD = 10 cm is known.

Let DC = x and CY = 10 - x

The outer circle's radius can be expressed as 8 + 8 + x or 10 + 10 - x, which we can equate to determine its value of x

8 + 8 + x = 10 + 10 - x

Simplify

16 + x = 20 - x

Subtract 16 on both side, we get

x = 4 - x

Add x on both side, we get

2x = 4

Divide by 2 on both side, we get

x = 2

As a result, the circle's radius is

= 8 + 8 + x

= 16 + x

= 16 + 2

= 18 cm

The area of circle = πr²

The area of circle = π(18)²

The area of circle = 324π

Thus, the circle's area is 324π square meters.

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The complete question is:

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.

What is the area of circle C, which passes though points W and Z?

A. 81

B. 164

C. 324

D. 1296

Answer: true

Step-by-step explanation:

true

[tex]10[/tex] pupils mean in age from sum [tex]150[/tex] to [tex]15[/tex] years.

The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from the scaling factor) of a dataset. This indicator of central tendency is usually referred to as the "average".

Just dividing the total number of values inside a data collection by the sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table may be utilized in the computation. Often, average is referred to as mean or mathematical mean. Mean is only a way of summarizing the sample's average.

Mean age [tex]=[/tex] (sum of ages) / (number of students)

Mean age [tex]= 150 / 10[/tex]

Mean age [tex]= 15[/tex]

Therefore, the mean age of the [tex]10[/tex] students is [tex]15[/tex] years.

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Answer:

Step-by-step explanation:

The corresponding points of each triangle are equal distance from the line y = -2

The expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.

The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the rectangle has two sides with a length (9.5c+6.2d) and two sides with a length (5.1c−3.4d).

Therefore, the perimeter can be calculated by adding the lengths of all four sides:

Perimeter = (9.5c+6.2d) + (9.5c+6.2d) + (5.1c−3.4d) + (5.1c−3.4d)

Simplifying and combining like terms, we get:

Perimeter = 2(9.5c+6.2d) + 2(5.1c−3.4d)

Perimeter = 19c + 12.4d + 10.2c − 6.8d

Perimeter = 29.2c + 5.6d

Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.

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The possible combination for three-course meals to be chosen from given the restriction is equal to 16.

The restriction that can only choose either a dessert or an appetizer,

Have two choices for the first course.

For the second course,

Have 4 choices for the soup.

For the third course,

Have 3 choices for the main course,

And since can only choose one of the remaining two categories (dessert or appetizer),

Have 2 choices for the third course.

Using the multiplication principle of counting,

The total combinations of number of three-course meals possible under these conditions by multiplying the number of choices for each course,

= Number of choices for the first course × Number of choices for the second course × Number of choices for the third course

= 2 × 4 × 2

= 16

Therefore, there are 16 possible combination for three-course meals that can be chosen.

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Step-by-step explanation:

If the simple interest rate is 4% per year, then the interest earned each year is calculated by multiplying the principal amount by the interest rate.

The interest earned in one year is:

Interest = Principal x Rate = $6000 x 0.04 = $240

After four years, the total interest earned is:

Total Interest = Interest x Time = $240 x 4 = $960

Therefore, the total amount Mr. Khan can withdraw after four years is:

Withdrawal Amount = Principal + Total Interest = $6000 + $960 = $6960

Answer:

If the simple interest rate was 4% per year, we can use the formula for simple interest to calculate the amount of interest Mr. Khan earned on his $6000 deposit:

Simple interest = P * r * t

Where P is the principal (the initial amount deposited), r is the interest rate (as a decimal), and t is the time (in years).

In this case, P = $6000, r = 0.04, and t = 4. Substituting these values into the formula, we get:

Simple interest = $6000 * 0.04 * 4 = $960

The total amount Mr. Khan can withdraw after four years is the sum of his initial deposit and the interest earned:

Total amount = Principal + Interest

Total amount = $6000 + $960 = $6960

Therefore, Mr. Khan can withdraw $6960 from his bank account after four years if the simple interest rate was 4% per year.

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Answer:D. x=125

Step-by-step explanation:

Answer:D

Step-by-step explanation:

125/5= 25

Number of apples that teacher has now is zero

Subtraction is a mathematical operation that involves taking away one quantity from another. It is one of the four basic arithmetic operations, along with addition, multiplication, and division. Subtraction is usually represented using the "-" symbol.

If the teacher had 1 apple and gave 1 apple to Tommy, then the total number of apples the teacher has now can be calculated using subtraction

Teacher's apples after giving one to Tommy = Teacher's apples before - Apples given to Tommy

Teacher's apples after giving one to Tommy = 1 - 1

Teacher's apples after giving one to Tommy = 0

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Answer:

Step-by-step explanation: add all of them together

The height of the trapezoid can be found by dividing the area (6,350 cm2) by the average of the two bases (100 cm). The height is 63.5 cm.

The formula used to find the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two bases and h is the height. We are given the area (A) and the lengths of both bases (b1 and b2). All we need to do is solve for h.

To do this, we first need to find the average of the two bases. The average of the two bases is the sum of the two bases divided by two. In this case, the longer base (b1) is 115 cm and the shorter base (b2) is 85 cm, so we can calculate the average as (115 + 85) ÷ 2 = 100 cm.

We can now substitute this value into the area formula and solve for h. A = (1/2)(100)h, so h = A ÷ (1/2)(100). Plugging in the area given (6,350 cm2), we get h = 6,350 ÷ (1/2)(100) = 63.5 cm. The height of the trapezoid is 63.5 cm.

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Answer:

We can find the value of Y when k = 5/4 by substituting k = 5/4 in the given expression for Y:

Y = 16 × 10^8 × k

Y = 16 × 10^8 × (5/4)

Y = 20 × 10^8

To express this in standard form, we can convert it to scientific notation:

Y = 2.0 × 10^9

Step-by-step explanation:

y^(5/4) = (16×10^(8k))^(5/4)

remember all the rules of exponents :

an exponent of an exponent : we multiply both exponents.

x^(a/b) =

[tex] \sqrt[b]{ {x}^{a} } = ({ \sqrt[b]{x} })^{a} [/tex]

and

(a×b)^c = a^c × b^c

so, with that we can do the trick here :

y^(5/4) = (16×10^(8k))^(5/4) =

= 16^(5/4) × 10^(8k × 5/4)

16^(5/4) =

[tex] \sqrt[4]{ {16}^{5} } = ( \sqrt[4]{16} )^{5} = ( \sqrt[4]{ {2}^{4} })^{5} = {2}^{5} = 32[/tex]

10^(8k × 5/4) = 10^(40k/4) = 10^(10k)

so, the result is

32 × 10^(10k)

[tex]32 \times {10}^{10k} [/tex]

Answer:

A

Step-by-step explanation:

The answer is A because the numbers only go under category A

Answer:

12.52 ounces

Step-by-step explanation:

Leftovers= 23.9-11.38

=12.52 ounces

Answer:

This means that a cylinder has two kinds of surface areas -Total Surface Area (TSA) and Curved Surface Area (CSA). For a cylinder whose base radius is 'r' and height is 'h': TSA of cylinder = 2πr2 + 2πrh (or) 2πr (r + h) CSA of cylinder = 2πrh.

Answer:

u ≈ 13.3

Step-by-step explanation:

tan34° = [tex]\frac{9}{u}[/tex] ( multiply both sides by u )

u × tan34° = 9 ( divide both sides by tan34° )

u = [tex]\frac{9}{tan34}[/tex] ≈ 13.3 ( to 1 decimal place )

the value of the expression -2-(-9)-(-2) is 9.

To solve the expression -2-(-9)-(-2), we can simplify it using the rules of arithmetic:

A double negative becomes a positive. So, -(-9) becomes +9.

Subtracting a negative is the same as adding the positive. So, -(-2) becomes +2.

Using these rules, we can simplify the expression as follows:

-2 - (-9) - (-2) = -2 + 9 + 2

= 9

Therefore, the value of the expression -2-(-9)-(-2) is 9.

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Answer:

To calculate the expected value of the game for the player, we need to find the probability of each possible outcome and the corresponding payoff or cost, and then multiply each probability by its payoff or cost, and sum the results. Let's first find the probability of each possible outcome:

- Probability of drawing two green marbles: (6/14) * (5/13) = 0.164

- Probability of not drawing two green marbles: 1 - 0.164 = 0.836

If both marbles are green, the player wins $25, so the payoff is $25. If not, the player must donate $10 to the animal shelter, so the cost is -$10. Therefore, the expected value of the game for the player is:

Expected value = (Probability of winning * Payoff) + (Probability of losing * Cost)

Expected value = (0.164 * $25) + (0.836 * -$10)

Expected value = $4.10 - $8.36

Expected value = -$4.26

The expected value of the game for the player is -$4.26, which means that on average, the player can expect to lose $4.26 per game. Therefore, playing this game is not a good bet for the player.

Answer:

a = 4, b = 5

Step-by-step explanation:

we need to complete the square to get it in that form.

x^2 - 8x + 21

= x^2 - 8x + 16 + 5

= (x-4)^2 + 5

a = 4, b = 5

Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.

To find the volume of a cone, we use the following formula:

V = 1/3 * π * r² * h

where V is the volume of the cone, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.

To use the formula, we simply substitute the given values for r and h into the formula and simplify. Make sure that the radius and height are measured in the same units. The resulting volume will be in cubic units.

The formula for the volume of a cone is:

V = 1/3 * π * r² * h

where π is pi (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.

Substituting the given values, we get:

V = 1/3 * 3.14 * 9² * 12

= 1/3 * 3.14 * 81 * 12

= 3.14 * 324

= 1017.36

Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.

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Jenny must have used at least 1600 minutes of her phone service to incur a minimum monthly fee of $96.36. This can be calculated by solving the inequality $24 + 0.06x ≥ $96.36 where x is the number of minutes.

Rearranging this equation to 0.06x ≥ $72.36 and solving for x gives us the result x ≥ 1600.
Given that, For her phone service, Jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. The least she has been charged in a month is $96.36.To find the possible numbers of minutes she has used her phone in a month.

Inequality for $96.36 is(0.06m + 24) ≥ 96.36where m is the number of minutes used. In order to solve the above inequality, we will simplify it first(0.06m + 24) ≥ 96.360.06m + 24 - 24 ≥ 96.36 - 24.060.06m ≥ 72.36m ≥ 72.36/0.06m ≥ 1206So, the possible numbers of minutes she has used her phone in a month is greater than or equal to 1206 minutes. Answer: $\boxed{m≥1206}$

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The two inference we can make from this data is the proportion of females who prefer makeup and the significant difference in makeup preference between different groups of female.

Based on the sample of 100 females regarding makeup preference, Sam could make the following inferences:

1. The proportion of females who prefer makeup can be estimated. Sam can calculate the proportion of females in her sample who preferred makeup and use that as an estimate of the proportion in the population. For example, if 70 out of the 100 females in the sample preferred makeup, then Sam could estimate that 70% of females in the population prefer makeup.

2. Sam could also determine if there is a significant difference in makeup preference between different groups of females. For example, she could compare the proportion of females who prefer makeup in different age groups or different ethnic groups.

To find out how many out of 375 people prefer lipstick, we need to know the proportion of people in the sample who prefer lipstick. If this information is not available, we cannot accurately determine the number of people who prefer lipstick out of 375.

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The number of pages in each issue of the technology magazine is 74 pages.

The number of pages in each issue of the sports magazine is s and the number of pages in each issue of the technology magazine is t.

To solve this problem, we have to write a system of equations using the given information. We have to find s and t.

System of equations can be used to find s and t; 12s = 10t + 32 and t = s + 18

The given sports magazine prints 12 issues per year and the technology magazine prints 10 issues per year.

The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. That means we can write an equation based on the information given for the number of pages in all the issues of the sports magazine and the technology magazine.

12s = 10t + 32

We also know that each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. That means we can write another equation based on the information given for the number of pages in each issue of the sports magazine and the technology magazine.

t = s + 18

Now, we can solve for s and t by substituting t = s + 18 in the first equation: 12s = 10(s + 18) + 32

12s = 10s + 180 + 32

12s - 10s = 180 + 32s = 56

So, the number of pages in each issue of the sports magazine is 56 pages. And, the number of pages in each issue of the technology magazine is: t = s + 18t = 56 + 18t = 74 pages.

So, each issue of the technology magazine contains 74 pages.

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The expression that makes the equation true= 4 x (2 + 3).

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

Hence, The expression that makes the equation true=

4 x (2 + 3).

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Answer:

a

Step-by-step explanation:

none

Answer:

Greg's account earned 80$ because 0.10×800=80 80+800=880 total

Answer: The volume of the recycling bin can be calculated by multiplying the area of the base by the height of the bin.

Given that the area of the base is 72 ft² and the height is 14 feet, we can use the formula:

Volume = Area of Base × Height

Substituting the given values, we get:

Volume = 72 ft² × 14 feet

Volume = 1008 cubic feet

Therefore, the volume of the recycling bin is 1008 cubic feet.

Step-by-step explanation:

Not answer but helpful:

The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.

What is stem-and-leaf plots?

A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.

here,

For the given data set:

Stem Leaf

0         4

1         1, 3, 3

2         0, 0, 0, 6, 7

3         0, 0, 0, 7

The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.

Answer:

48

Step-by-step explanation:

a² - 16

a = 8

8² - 16 = 64 - 16 = 48

So, the answer is 48

Answer: 240°

Step-by-step explanation:

The sum of the angles in a circle adds up to 360°, and the central angles are congruent to its arcs, so what we have is arcGFE + arcGHE = 360°, but we know arcGHE adds up to 120°. This makes our equation arcGFE + 120° = 360°, which means arcGHE = 240°