Please help and please show how you worked this out

Answer:

5

Step-by-step explanation:

The pair of functions that are inverses of each other is:

O A. f(x) = 1/2 - 18 and g(x) = x + 18

For two functions to be inverses of each other, the composition of the functions should result in the identity function.

In other words, if we apply one function and then the other to a given input, we should obtain the original input.

Let's verify this for the given pair of functions:

f(x) = 1/2 - 18

g(x) = x + 18

To check if they are inverses, we can compose them:

g(f(x)) = g(1/2 - 18)

       = (1/2 - 18) + 18

       = 1/2

As we can see, applying the functions in reverse order results in the original input, which is 1/2. Therefore, the functions f(x) = 1/2 - 18 and g(x) = x + 18 are inverses of each other.

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Answer:

1/3

Step-by-step explanation:

This answer is unintuitive, but stick with me.

If a family has 2 children, and each can be a boy (B) or a girl (G), there are 4 possible combinations:

BB BG GB GG

We know that this family doesn't have 2 girls, leaving us with 3 options:

BB BG GB

Because the order is unspecified, all 3 of these options are possible. Only one has two biys out of 3 possibilities, so it is 1/3.

Answer:

-80

Step-by-step explanation:

→ Complete the multiplication

20 × 8 = 160

→ Complete the take away

3 - 5 = -2

→ Divide the two answers from each other

160 ÷ -2 = -80

Angles p and q are complementary, which means that their sum is equal to 90 degrees. Let's assume the size of angle q is x degrees. Since p is four times the size of q, we can write the equation p = 4q.

To find the size of q, we need to substitute the value of p in terms of q into the equation for the sum of the angles: p + q = 90.

Substituting 4q for p, we get:

4q + q = 90

Combining like terms:

5q = 90

To solve for q, we divide both sides of the equation by 5:

q = 90/5

Simplifying:

q = 18

Therefore, the size of angle q is 18 degrees.

when angles p and q are complementary and p is four times the size of q, the size of angle q is 18 degrees.

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The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

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The percentage gain of the company is calculated to be 10%.

The percentage gain is calculated by multiplying the fraction of the gain and the initial amount by 100.

we shall calculate for the percentage gain of the company as follows:

gain = $33 - $30 = $3

initial amount = $30

percentage gain = ($3/$30) × 100

percentage gain = (1/10) × 100

percentage gain = 10%

Therefore, the percentage gain of the company is calculated to be 10%.

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Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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Answer:

x = 53.15

Step-by-step explanation:

use Pythagoras theorem

first find for the triangle that has both sides given and then solve for the other

On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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Answer:

Step-by-step explanation:

So the sign means that y has to be less than or equal to x plus 9

if you wanted an answer an example could be

y = 1

x = 10

this works because if implemented into the equation

1 ≤ 10 + 9 which is true

The shortest route would be taking County Line Road. This is because it directly connects Takoda's house to The Sportsplex without any detours. On the other hand, if Takoda takes Highway 4 and then Route 6, he would be taking a longer route that includes an additional road, resulting in more distance traveled.

Based on the given information, we need to determine which route is the shortest:

County Line Road or Highway 4 and then Route 6.

To determine the shortest route, we would need to compare the distances of both routes.

However, the distances of the routes are not provided in the question.

Therefore, without the information about the distances, we cannot accurately determine which route is the shortest.

To make an informed decision, we would need to consider factors such as traffic conditions, speed limits, and any other relevant information that may affect the efficiency of each route.

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Any smooth curve connecting two points is called an arc. The correct option is c.

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

\(\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}\)

where

θ is the angle, that arc creates at the centre of the circle in degree.

If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.

Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.

Hence, the correct option is c.

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The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

Any five-sided polygon or 5-gon is referred to as a pentagon. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

We have,

Any five-sided polygon or 5-gon is referred to as a pentagon. A basic pentagon's interior angles add up to 540°. A pentagon might be straightforward or self-intersecting.

We know the formula for the area of a pentagon, therefore, the area of the pentagon PQRST can be written as,

A = 1/4 * √5(5+25)*a²

Given that the side of the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, therefore, the area of the pentagon ABCDE can be written as,

ABCDE = 1/4 * √5(5+25)* 6a²

ABCDE = 36 * A

Hence, The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

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complete question:

Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which

statement is true?

A.

The area of pentagon ABCDE IS 6 times the area of pentagon PQRST.

B.

The area of pentagon ABCDE is 12 times the area of pentagon PQRST.

C.

The area of pentagon ABCDE is 36 times the area of pentagon PQRST.

D.

The area of pentagon ABCDE IS 216 times the area of pentagon PQRST.​

\(\huge \orange{F =G.\frac{xy}{r^2}}\)

Step-by-step explanation:

Answer:

f(-8) = -512, f(8) = 2

Step-by-step explanation:

Substitute x = -8 and 8 into the function, taking into account the rules of the function.

For x = -8, x < 0 so the value is equal to the cube of -8, which is -512.

For x = 8, x > 0 so the value is equal to the cube root of 8, which is 2.

Hey there! :)

We are given the piecewise function:

\( \displaystyle \large{f(x) = \begin{cases} {x}^{3} \: \: (x < 0) \\ \sqrt[3]{x} \: \: (x > 0) \end{cases}}\)

To evaluate the value of function at x = -8 and x = 8, we know that -8 is less than 0 and 8 is greater than 0.

Therefore, if we want to evaluate the value of function at x = -8; we use the x^3 since it's given x < 0 for the function and for x = 8; we use the cube root of x since it's given x > 0.

Evaluate x = -8

From the piecewise function:

\( \displaystyle \large{f(x) = \begin{cases} {x}^{3} \: \: (x < 0) \\ \sqrt[3]{x} \: \: (x > 0) \end{cases}}\)

Since -8 is less than 0, we use x^3.

\( \displaystyle \large{f( - 8) = {( - 8)}^{3} } \\ \displaystyle \large{f( - 8) = - 512} \)

Evaluate x = 8

From the piecewise function, since 8 is greater than 0, we use the cube root of x.

\( \displaystyle \large{f(8) = \sqrt[3]{8} }\)

To evaluate the cube root, first we prime-factor the number.

\( \displaystyle \large{f(8) = \sqrt[3]{2 \cdot 2 \cdot 2} }\)

Since it's a cube root, we pull three 2's out of the cube root and write only one 2.

\( \displaystyle \large{f(8) =2}\)

Answer

Let me know if you have any questions!

Answer: The expression (st)(6) means to substitute the value of 6 into the function (st) which is the composition of two functions s and t. The order of applying the functions is crucial, so the first function s will be applied to the result of the second function t after being applied to the 6. So the correct equivalent of (st)(6) is s(t(6))

Step-by-step explanation:

Answer:

To find the perimeter (or arc length) of an ellipse, you'll need to use an elliptic integral

The perimeter is a distance around the outlines or edge of any shape. A practical example of measuring the perimeter of an ellipse would be the distance you cover when you walk along the edges of an elliptical-shaped field. Or the length of fence you need to surround it

The amount of waste a cylinder can hold nearest to the whole number is 3 cubic feet.

We have,

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A cylindrical hazardous waste container has a diameter of 1.5 feet and a height of 1.6 feet.

The amount of waste a cylinder can hold will be given by the volume of the cylinder.

The volume of the cylinder will be

V= π/4 * d²h

We have

d = 1.5 ft

h = 1.6 ft

Then

Volume =π/4 * 1.5² *1.6

             = 2.82 ft^3

             =3ft^3

Hence, The amount of waste a cylinder can hold nearest to the whole number is 3 cubic feet.

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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To find multiple of 3 and 5 we need to add 15 to the previous multiple of 15.

To find multiples of 3 and 5, you can use the following steps:

1. Start with the number 3 and 5, respectively.
2. Add 3 or 5 to the previous number to get the next multiple. For example, 3 + 3 = 6, 6 + 3 = 9, and so on. Similarly, 5 +    5 = 10, 10 + 5 = 15, and so on.
3. Repeat step 2 until you have found the desired number of multiples.

Here are the first 10 multiples of 3 and 5:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Note that some numbers, such as 15 and 30, are multiples of both 3 and 5. These are called common multiples.

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Answer:

w t f

Step-by-step explanation:

Answer: $48.06

Step-by-step explanation:

Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.

Answer:

You would pay $48.06

Step-by-step explanation:

27*0.78 = 21.06

27 + 21.06 = 48.06

Answer:

1.0014 Miles

Step-by-step explanation:

The light travels at 186,291 miles per second (~300,000 km/s), and speed of sound in dry air is equal to 0.21 - 0.22 miles per second (0.33-0.35 km/s), as it varies with the temperature. We can notice the lightning almost immediately even though the storm is far from us, but the thunder needs around 5 seconds to travel one mile and approximately 3 seconds to travel one kilometer. Thanks to this seven orders of magnitude difference in sound and light propagation, we can easily estimate the storm distance

Answer:

This explanation is not good, can you please break it down so we can see how you guys got this answer?

Step-by-step explanation:

The slope of the line that passes through (5, 8) and (11, 5) in its simplest form is - 1/2

The slope of a line refers to the change in the dependent variable (y) as a result of a change in the independent variable (x).

The slope can be found by the formula:

= Change in y / Change in x

Given the points, (5, 8) and (11, 5):

Change in y = (5 - 8)

Change in x = (11 - 5)

The slope can therefore be found to be:
= (5 - 8 ) / (11 - 5)

= -3 / 6

= - 1/2 in simplest form

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Answer:

<B=105°

Step-by-step explanation:

as it's an isosceles trapezoid. AD parallel to BC

ACCORDING TO THE QUESTION

75°+<B=180°

<B=180°-75°

<B=105°

Answer:

y=1/2x-4

Step-by-step explanation:

subtract 4x from the left side and the right side. It becomes:

-8y=-4x+32

divide -8 from both sides and it becomes:

y=1/2x-4