what is the domain and range of a cubic function ?

Thus, we get a total of 27 seven-digit phone numbers that begin with a three-digit prefix that has the property you described.

We need to find all seven-digit phone numbers that begin with a three-digit prefix that equals the product of the last four digits.

To do this, we can start by noting that the three-digit prefix can be written as XYZ, where X, Y, and Z are digits. We also know that the last four digits must have a product of XYZ. Let's call the last four digits W, P, Q, and R. Then we have:

W x P x Q x R = XYZ

We can simplify this equation by dividing both sides by XYZ:

(W x P x Q x R) / XYZ = 1

Now we can start counting the number of possible phone numbers that satisfy this equation. We can do this by systematically trying out different values for X, Y, and Z and seeing how many possibilities we get for W, P, Q, and R. Here are the possibilities:

X = 1: In this case, we need to find all four-digit numbers that have a product of 1YZ. The only possibility is 1111, which gives us one seven-digit phone number.

X = 2: In this case, we need to find all four-digit numbers that have a product of 2YZ. The possibilities are 2222, 2211, and 2111. This gives us three seven-digit phone numbers.

X = 3: In this case, we need to find all four-digit numbers that have a product of 3YZ. The possibilities are 3333, 3311, 3222, 3211, and 3111. This gives us five seven-digit phone numbers.

X = 4: In this case, we need to find all four-digit numbers that have a product of 4YZ. The possibilities are 4444, 4322, 4311, and 4222. This gives us four seven-digit phone numbers.

X = 5: In this case, we need to find all four-digit numbers that have a product of 5YZ. The possibilities are 5555, 5422, 5411, 5322, and 5311. This gives us five seven-digit phone numbers.

X = 6: In this case, we need to find all four-digit numbers that have a product of 6YZ. The possibilities are 6666, 6511, and 6422. This gives us three seven-digit phone numbers.

X = 7: In this case, we need to find all four-digit numbers that have a product of 7YZ. The only possibility is 7777, which gives us one seven-digit phone number.

X = 8: In this case, we need to find all four-digit numbers that have a product of 8YZ. The possibilities are 8644 and 8633. This gives us two seven-digit phone numbers.

X = 9: In this case, we need to find all four-digit numbers that have a product of 9YZ. The possibilities are 9999, 9811, and 9722. This gives us three seven-digit phone numbers.

Adding up all of the possibilities, we get a total of 27 seven-digit phone numbers that begin with a three-digit prefix that has the property you described.

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The three posts can be given in 4080 ways among 17 students.

It is given that the number of people available to choose the posts from is 17.

There are three posts here- president, vice president, and secretary.

Now, if we choose a candidate for President first, there are 17 students available.

Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.

At, last there are 15 students available to choose the secretary from as two students already hold a post.

Hence, the number of ways to select the President, Vice-President, and Secretary are-

17 X 16 X 15 ways

Therefore we get

4080 ways.

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Answer:

W(2W-19)

Step-by-step explanation:

let length = L

length= L feet

let Width= W

from the question,

twice the width = 2W

then L = 2W-19

the area of the rectangle

Area= length × width

Area= 2W-19×W

Area= 2W^2-19W

Area= W(2W-19)

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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In the linear model n = 2x + 13, the slope of 2 represents the average increase in the number of shots made per hour of practice. It indicates that for every additional hour spent practicing, the team is expected to make, on average, 2 more shots during a game.

In the given linear model, n represents the average number of shots the team makes during a game, while x represents the number of hours spent practicing during the week. The equation n = 2x + 13 suggests that the number of shots made during a game is directly related to the hours of practice.

The slope of the linear model, which is 2 in this case, represents the rate of change in the number of shots made per hour of practice. It indicates that for every additional hour spent practicing, the team is expected to make, on average, 2 more shots during a game. The positive slope suggests a positive correlation between practice hours and the number of shots made.

In practical terms, the slope of 2 implies that consistent practice and additional hours dedicated to training have a positive impact on the team's performance, resulting in an increase in the number of shots made during a game.

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Probably b

Sorry if its wrong tho

The correct linear parent function is,

⇒ y = x

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

To find the linear parent function.

Now, We know that;

A line is of the form x to the first power.

Here, 1/x is not x to the first power and makes a curve.

And, |x| makes a v shape

Also, x³ is a curve.

Hence, The correct linear parent function is,

⇒ y = x

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's solve ~

If it passes through x, then let's find x when y = 0

\(\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6\)

\(\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0\)

\(\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0\)

\(\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0\)

So, required values of x are 3 and -2

Now, let's differentiate the equation to get slope slope for tangent ~

\(\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)\)

\(\qquad \tt \dashrightarrow \: m = 2 x - 1\)

Now, plug in the values of x to find slopes of tangents

\(\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1\)

\(\qquad \tt \dashrightarrow \: m_1 = 6 - 1\)

\(\qquad \tt \dashrightarrow \: m _1 = 5\)

and

\(\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1\)

\(\qquad \tt \dashrightarrow \:m_2 = - 4- 1\)

\(\qquad \tt \dashrightarrow \:m_2 = - 5\)

We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'

\(\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1\)

\(\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}\)

\(\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}\)

and

\(\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1\)

\(\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}\)

\(\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}\)

\(\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}\)

Now, write the equations of normals using point slope form :

Normal 1 : passing through (3 , 0), and slope = -1/5

\(\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)\)

\(\qquad \tt \dashrightarrow \:5y = - (x - 3)\)

\(\qquad \tt \dashrightarrow \:5y = - x + 3\)

\(\qquad \tt \dashrightarrow \:x + 5y - 3 = 0\)

and

Normal 2 : passing through (-2 , 0), and slope = 1/5

\(\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))\)

\(\qquad \tt \dashrightarrow \:5y = x + 2\)

\(\qquad \tt \dashrightarrow \ x - 5y + 2 = 0\)

That's all for Aunty ~ hope it helps !

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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The derivative of H(z) is H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)].

To differentiate the function H(z) = ln[(d^2-z^2)/(d^2+z^2)]^(1/2), we will use the chain rule and the power rule of differentiation.

First, we can simplify the expression inside the natural logarithm using the laws of exponents:

[(d^2-z^2)/(d^2+z^2)]^(1/2) = [(d^2-z^2)^(1/2)/(d^2+z^2)^(1/2)]

Now we can differentiate H(z) as follows:

H'(z) = d/dz [ln[(d^2-z^2)/(d^2+z^2)]^(1/2)]

= (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * d/dz [(d^2-z^2)/(d^2+z^2)]

Using the quotient rule, we can simplify the derivative:

d/dz [(d^2-z^2)/(d^2+z^2)] = [(2z)(d^2+z^2) - (d^2-z^2)(2z)]/(d^2+z^2)^2

= -4zd^2/(d^2+z^2)^2

Substituting this back into H'(z), we get:

H'(z) = (1/2)[(d^2+z^2)^(1/2)/(d^2-z^2)^(1/2)] * (-4zd^2/(d^2+z^2)^2)

= -2zd^2/[(d^2-z^2)(d^2+z^2)]

Therefore, the derivative of H(z) is:

H'(z) = -2zd^2/[(d^2-z^2)(d^2+z^2)]

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Answer:

y = -2x + 3

Step-by-step explanation:

Step 3 is incorrect because it states that if all the sides of two figures are proportional then those two figures are similar.

Step 6 is incorrect because it states that if needed, we should reflect A B C D over segment WX. This is incorrect because reflection is not required to prove two figures are similar.

A segment is part of a market that is specifically targeted for a product or service. It is defined by characteristics such as demographics, geography, buying behavior, and interests. Segmentation helps companies to identify their target market and direct their marketing activities accordingly.

We can prove two figures are similar using a sequence of transformations that includes translations, rotations, and dilations, but not reflections. Reflection may be used to help visualize similar figures, but it is not necessary to prove that they are similar.

from the question:

Step 3 is erroneous since it implies that two figures are identical if all of their sides are proportionate. This isn't always the case because two figures can resemble one another without having sides that are proportional. When two figures of the same shape, such as two squares or two circles, proportional sides can only ensure that the two figures are identical.

Step 6 is erroneous because it instructs us to reflect A, B, C, and D over segment WX if necessary. This is false since the similarity between two figures can be established without thought. Using a series of transformations that includes translations, rotations, and dilations but not reflections, we may demonstrate the similarity of the two figures. Reflection may be employed to aid in seeing related figures, but it is not required to establish their similarity.

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Answer:

Lets say h is the horses speed. It would be H \(\leq\)4

Answer:

48

Step-by-step explanation:

The given parameters are;

The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services

The number of students that do all three activities = 3

The number of students that do two or more activities = 21

The number of the students that participate in music = Half of the students

The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3

Let x represent a common number factor of participants in each of the given three activities, we have;

5·x participate in debate, A

4·x participate in music, B

3·x participate in community service, C

We get;

The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C

Given that the number of students that do two or ore activities = 21, we have;

(A∩B)∪(A∩C)∪(B∩C) = 21

However, we have;

(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C

∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3

(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27

∴ -(A∩B) - (A∩C) - (B∩C) = -27

Therefore;

A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3

5·x + 4·x + 3·x - 27 + 3 = 12·x - 24

The total number of students = A∪B∪C = 12·x - 24

The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2

∴ 4·x = (12·x - 24)/2

8·x = 12·x - 24

12·x - 8·x = 24

4·x = 24

x = 24/4 = 6

The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48

The data that has a variation, or mean absolute deviation, similar to the data set in the given dot plot is option D.

Deviation describes the extent of the Stata change, do plot in D has the same distribution with the example given to they must have the most similar Mean Absolute deviation.

A data set's mean absolute deviation (MAD) is the average distance between each data value and the mean. A data set's fluctuation can be described using mean absolute deviation. The mean absolute deviation tells us how "spread out" the values in a data collection are.

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Answer:

To graph the inequality y ≤ x - 2 on the axes, you would:

Plot the line y = x - 2 on the graph. The line will be a straight line passing through the point (-2,0) and has a slope of 1.

Determine the direction of the inequality symbol. Since it is a less-than-or-equal-to symbol, we will shade the region that is less than or equal to the line.

Shade the region that is less than or equal to the line in the graph. In this case, the region above the line y = x - 2.

The line is solid, it's not dotted.

Note: The graph will be a straight line that is tilted towards the top right of the coordinate axes, the region above the line will be shaded.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

(a)

\(\sqrt{3}\) × \(\sqrt{6}\)

= \(\sqrt{3(6)}\)

= \(\sqrt{18}\)

= \(\sqrt{9(2)}\)

= \(\sqrt{9}\) × \(\sqrt{2}\)

= 3\(\sqrt{2}\)

(b)

\(\sqrt{8}\) × \(\sqrt{18}\)

= \(\sqrt{8(18)}\)

= \(\sqrt{144}\)

= 12

_________

\( \sqrt{3} \times \sqrt{6} = ...\)

\( = \sqrt{3 \times 6} \)

\( = \sqrt{18} \)

\( = \sqrt{9} \sqrt{2} \)

\( = \bold{3 \sqrt{2}} \)

.

\( \sqrt{8} \times \sqrt{18} = ...\)

\( = \sqrt{8 \times 18} \)

\( = \sqrt{144} = \bold{12}\)

Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

Answer:

D

Step-by-step explanation:

7

4

2   last option

Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

Answer:

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Step-by-step explanation:

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

a)

The given condition makes a right-angle triangle as shown below,

The tan function,

tanθ = 6/25

θ = 14.50°

b)

When a player is 5 feet closer means (20 feet far)

tanθ = 6/20

θ = 16.70°

c)

As the player gets closer the angle becomes more and more.

Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".

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Answer:

124 Minutes or 2 hours 4 Minutes

Step-by-step explanation:

If there are 60 minutes in an hour and we are trying to go from 2:08 to 4:12 then we can add 2 hours which is 120min to make it 4:08. the we can add the final 4 min and get 124min.

Answer:

A) Changing the measurement unit.

Step-by-step explanation:

"Changing the measurement unit" is the correct answer because when you convert from feet to inches, you are essentially changing the unit of measurement from a larger unit (feet) to a smaller unit (inches) within the same system of measurement (length or distance). It involves multiplying the value in feet by a conversion factor to obtain the equivalent value in inches. This process is commonly used in math, science, and everyday life when dealing with different units of measurement.

So first you find 10% which is 34.5

Then you multiply 10% by 4 to get 40% which is = 138s

Yw

Answer:

t ≥ 13

Step-by-step explanation:

t + 20 ≥ 33

subtract 20 from each side

he will run at least another 13 miles

Answer:

2

24

5

4

Step-by-step explanation:

The given recipe makes 8 bags.

To make 16 bags, Lily needs twice as many ingredients because 8 + 8 = 16.

Since 1 cup of raisins makes 8 bags, 2 cups of raisins will make 16 bags.

To show the mathematical way:

Variable w = number of cups of raisins

1/8 = w/16

Cross multiply

1 × 16 = 8 × w

16 = 8w

2 = w

2 cups of pretzels makes 8 bags so 6 cups of preztels will make how many bags?

Set up an equation:

Variable x = number of bags

2/8 = 6/x

Cross multiply

2 × x = 8 × 6

2x = 48

x = 24

6 cups of pretzels will make 24 bags.

If 0.5 cup of pecans = 2.5 cups of crackers, then 1 cup of pecans = y cups of crackers?

Variable y = number of cups of crackers

Set up equation:

0.5/2.5 = 1/y

Cross multiply

0.5 × y = 2.5 × 1

0.5y = 2.5

y = 5

1 cup of pecans will need 5 cups of crackers

2 cups of pretzels = 8 bags, so 1 cup of preztels = z bags?

Variable z = number of bags

Set up equation:

2/8 = 1/z

Cross multiply

2 × z = 8 × 1

2z = 8

z = 4