there are n contestants in a talent tv show numbered 1, 2, 3, ···, n, waiting to be called at the stage. let x be the number of a randomly selected contestant, so that x has pmf

Using the arithmetic operation of division -

a) 3 people can be fed by 1 pizza.

b) Maria would need 11 pizzas for 33 people.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pizzas ordered = 8

The number of people are = 24.

Number of people that can be fed if 1 pizza was there =

Number of people = Number of people that came/ Number of pizza

Use the arithmetic operation of division -

Number of people = 24/8

Number of people = 3

Therefore, 3 people can be fed.

Now, the number of people = 33

Number of pizzas required for 33 people can be obtained as -

Use the arithmetic operation of division -

Number of pizzas = Number of people/ Number of people fed by 1 pizza

Number of pizzas = 33/3

Number of pizzas = 11

Therefore, Maria will require 11 pizzas.

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Answer:

m∠QRT = 47°

m∠TRS = 133°

Step-by-step explanation:

Because points Q, R, and S are collinear, ∠QRT and ∠TRS are supplementary. This means that:

m∠QRT + m∠TRS = 180°

Plug-in the known values and simplify:

3x + 5 + 10x - 7 = 180

13x - 2 = 180

13x = 182

x = 14

Now that you have the value of x, plug them into the values of the angles:

m∠QRT = 3x+ 5

              = 3(14) + 5

              = 42 + 5

              = 47°

m∠TRS = 10x - 7

             = 10(14) - 7

             = 140 - 7

             = 133°

To double-check:

133° + 47° = 180°     ☺

Answer:

The 2nd answer is the correct answer

Step-by-step explanation:

Hope this helps:)

Answer: Its the second choice

Step-by-step explanation: square area is base x height; the base is 12 the height is 4. triangle area = (base x height)/ 2; base is 12, times 4 (height), then divide by 2

Answer:

A

Step-by-step explanation:

The range of the given function from the given graph are: all values of y that are greater than or equal to -3. Therefore, the correct option is option D.

It is seen to be best practice to define the word "range" the first time it appears in a book or article because it might have several different meanings. When the word "range" is used in older literature, it frequently refers to what is today known as the codomain.

If more recent texts use the phrase "range" at all, they typically do so to refer to what is now known as the image. Several contemporary novels shouldn't use the term "range" at all to avoid any misunderstandings.

A function's range is the set of each of its potential outputs1,2,3,4. That's the output that the function generates when all of its inputs are used3,5. The range of the given function from the given graph are: all values of y that are greater than or equal to -3.

Therefore, the correct option is option D.

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Your question is incomplete but most probably your full question was,

What is the range of the function shown in the graph?

Answer:

f(5)=5²-2(5)

=25-10

=15

replace the x with five

From the given picture, we can note that

Similarly,

In the same way, we have

and finally,

The start = 1 is the number of rabbit pairings after one month. Each female rabbit births three pairs of rabbits starting in the third month. We can count rabbit pairs at month's end by analysing the trend. After a year, we can count all rabbits, male and female.

a. The initial condition So = 1 represents the number of rabbit pairs alive at the end of the first month. This means that initially, there is one pair of rabbits in the field.

b. To compute the number of rabbit pairs at the end of each month, we follow the given rules. After the first month, the pair of rabbits is still too young to reproduce, so S1 remains 1. In the second month, they still cannot reproduce, so S2 remains 1 as well. However, at the end of the third month, the female rabbit can give birth, resulting in three new pairs of rabbits. Therefore, S3 becomes 1 (initial pair) + 3 (new pairs) = 4. In the fourth month, each of the four female rabbits can give birth, resulting in 3 * 4 = 12 new pairs. So, S4 becomes 4 (existing pairs) + 12 (new pairs) = 16. Following this pattern, we can calculate S5, S6, and so on.

c. We can observe a recurrence relation in the sequence: Sn = Sn-1 + 3 * Sn-3, where n > 3. This relation states that the number of pairs at the end of the nth month is equal to the number of pairs at the end of the previous month (Sn-1) plus three times the number of pairs three months ago (Sn-3).

d. To find the total number of rabbits at the end of the year, we sum up the number of rabbit pairs for each month from the 1st to the 12th month. At the end of the 12th month, we can calculate the total number of rabbits by multiplying the number of pairs by 2 (to account for both male and female rabbits in each pair).

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Answer:

(2•5y to the 7th power)

Step-by-step explanation:

Step 1:  (2y to the 4th power • 5) • y to the 3rd power

Step 2:  (2•5y to the 4th power) • y to the 3rd power

Step 3:  3.1    y to the 4th power multiplied by y to the 3rd power = y to the  (4 + 3) power = y to the 7th power

Final answer:  (2•5y to the 7th power)

The expression \(2y^{4} * 5y^{3}\)  is equal to 10\(y^{7}\).

When two expressions with exponents are multiplied, it is called multiplying exponents. The multiplication of exponents involves certain rules depending upon the base and the power.

When the terms with the same base are multiplied, the powers are added, i.e., \(a^{m}\) × \(a^{n}\) = \(a^{{m+n}}\)

According to the question

\(2y^{4} * 5y^{3}\)

Now,

Using the multiplying exponent rule :

the terms with the same base are multiplied, the powers are added, i.e., \(a^{m}\) × \(a^{n}\) = \(a^{{m+n}}\)

Therefore,

As, base y is common in both the terms

= 10\(y^{4+3}\)

= 10\(y^{7}\)

Hence, the expression \(2y^{4} * 5y^{3}\)  is equal to 10\(y^{7}\).

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Answer:

6

Step-by-step explanation:

diameter = 2 radius

3*2 = 6

Answer:

6

Step-by-step explanation:

r = d/2        Multiply both sides by 2

2*r = d

r = 3

2*3 = d

d = 6

Answer:

N would equal anything lower than -4 for example, -5 or -6

Step-by-step explanation:

yw

Answer:

C

Step-by-step explanation:

Multiplying the numerator and the denominator by the same constant, we get an equivalent fraction, as follows:

Then, -6/4 is equivalent to -3/2

Answer:

SA= 289.56 m^2

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:

\(c = \pm\sqrt{43}\)

»»————-　★　————-««  

Here’s why:

I am assuming that the two is an exponent.  

⸻⸻⸻⸻

\(\boxed{\text{Solving for 'c'...}}\\\\c^2 = 43\\----------------\\\rightarrow \sqrt{c^2} = \sqrt{43}\\\\\rightarrow \boxed{c = \pm\sqrt{43}}}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.

The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.

In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.

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To find the standard form of the equation of an ellipse, we need to know the center, the lengths of the major and minor axes, and the orientation of the ellipse.

Given that the center is (1, 8) and the vertices are (1, 0) and (1, 16), we can see that the major axis is vertical and has a length of 16 (since the distance between the vertices is the length of the major axis). Therefore, the length of the minor axis is 2c = 8 (where c is the distance from the center to one of the foci).

To find c, we can use the relationship a^2 = b^2 + c^2, where a is half the length of the major axis (8 in this case) and b is half the length of the minor axis (4 in this case).

a^2 = b^2 + c^2
8^2 = 4^2 + c^2
c^2 = 48
c = sqrt(48) = 4sqrt(3)

Now we have all the information we need to write the standard form of the equation of the ellipse. Since the major axis is vertical, we have the equation:

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

where (h, k) is the center of the ellipse, a is half the length of the major axis (8 in this case), and b is half the length of the minor axis (4 in this case).

Plugging in the values, we get:

(x - 1)^2 / (4^2) + (y - 8)^2 / (8^2) = 1

Simplifying, we get:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1

Therefore, the standard form of the equation of the ellipse is:

(x - 1)^2 / 16 + (y - 8)^2 / 64 = 1.
Given the center (h, k) = (1, 8), vertices (1, 0) and (1, 16), and the relation a = 2c, we can determine the standard form of the ellipse equation.

From the vertices, we can see that the ellipse is vertically oriented. The distance between the center and a vertex is the major radius "a." Therefore, a = 8 (half of the distance between the vertices).

Since a = 2c, we can solve for c:
c = a / 2 = 8 / 2 = 4.

Now, we can find the minor radius "b" using the relationship a² = b² + c²:
64 = b² + 16
b² = 48

Finally, the standard form of the ellipse equation is:

((x - h)² / b²) + ((y - k)² / a²) = 1

Substitute the values of h, k, a, and b:

((x - 1)² / 48) + ((y - 8)² / 64) = 1

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The pair of variables with an inverse relationship is y = 1/x. This relationship can be seen by graphing the two variables on a coordinate plane and observing the shape of the graph.

As x increases, y decreases and as x decreases, y increases. This is because the equation y = 1/x can be written as y = c/x, where c is a constant. Since c is a constant, as the value of x increases, the value of y decreases, and vice versa.

For example, if x = 4, then y = 1/4, or 0.25. If x increases to 8, then y decreases to 1/8, or 0.125. On the other hand, if x decreases to 2, then y increases to 1/2, or 0.5. As can be seen, as x increases, y decreases, and as x decreases, y increases, which shows the inverse relationship between the two variables.

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Answer:

(h, k )

Step-by-step explanation:

given the standard form of an absolute function

f(x) = a| x - h | + k , then

vertex = (h, k )

The standard form of an absolute value function is f(x) = a|x - h| + k, where (h,k) is the vertex of the absolute value function.

The correct option is (h,k).

The term "function" refers to a relationship between a set of inputs and outputs. Just one output is connected to each input in a function, which connects inputs in that manner. Every function has a domain, co-domain, and range.

In general, the standard form of an absolute value function is given as:

f(x) = a |x - h| + k

where:

a is a non-negative constant that determines the shape and direction of the V-shaped graph of the absolute value function

h is the horizontal shift of the graph of the function from the origin (if h > 0, the graph shifts to the right; if h < 0, the graph shifts to the left)

k is the vertical shift of the graph of the function from the origin (if k > 0, the graph shifts up; if k < 0, the graph shifts down)

The vertex of the absolute value function is the point where the graph changes direction, that is, the point where the graph changes from sloping downwards to sloping upwards or vice versa.

Since the vertex is the point of the absolute value function where the graph changes direction, it lies at the center of the V-shaped graph. Thus, the vertex is located at the point (h,k).

Therefore, in the standard form f(x) = a |x - h| + k, (h,k) represents the coordinates of the vertex of the absolute value function.

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Answer:

Even

Step-by-step explanation:

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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The integer that represents the change in the worker's position is -43, indicating a downward movement of 43 feet.

The worker in the silver mine descended 43 feet, and the change in the worker's position can be represented by the integer -43.
When we use integers to represent positions, negative values indicate downward movement. In this case, the negative value -43 indicates that the worker moved downwards by 43 feet.
To better understand this concept, let's consider a number line. Imagine that the starting position is 0, and moving to the right represents going upwards while moving to the left represents going downwards.
If the worker descends 43 feet, they would move to the left on the number line by 43 units. This can be represented as -43.
It's important to note that in the context of this question, the worker's change in position is represented by a negative value because they moved downwards.
In summary, the integer that represents the change in the worker's position is -43, indicating a downward movement of 43 feet.

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Answer:

1. Fact that all individuals are created equal and are endowed by their creator with certain unalienable rights is a clear statement in the Declaration of Independence.

2. Aim of having a government is to safeguard these rights,  the people have the right and the duty to alter, abolish, or over through that government.

3. The Decoration of Independence lists the grievances that the government has failed to resolve and reconcile with the colonies.

4. The decree was made to become an autonomous nation and the motives for asserting independence are listed in the grievances.

Answer:

(27, 9)

Step-by-step explanation:

Hope that helps!

Answer:(27, 9)

Step-by-step explanation:

The exact volume of the cylinder is 1,846.32 cubic inches

Cylinder:

Radius, r = 7 in

Height, h = 12 in

Cone:

Radius, r = 7 in

Height, h = 12 in

Volume of a cylinder = πr²h

= 3.14 × 7² × 12

= 3.14 × 49 × 12

= 1,846.32 cubic inches

Volume of a cone = 1/3πr²h

= 1/3 × 3.14 × 7² × 12

= 1/3 × 3.14 × 49 × 12

= 1,846.32/3

= 615.44 cubic inches

Hence, the approximate volume of the cone to the nearest tenth is 615.4 cubic inches

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In the linear equation -1/4(x -1) = 2/3x + 2, the value of x is -21/11

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

In the given equation -1/4(x -1) = 2/3x + 2, we can solve for the value of x

-1/4(x -1) = 2/3x + 2

collect like terms

-1/4x + 1/4 = 2/3x + 2

2/3x + 1/4x = 1/4 - 2

(11/12)x = - 7/4

x = - 21 / 11

The value of x is -21/11

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