Using the region names in the image below, select all regions that represent:

A ∩ B' ∩ C'

3 group Venn Diagram with Roman numeral labeled regions

A intersection not B intersection not C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.

The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is  [tex]f(x) = x^3 - 76x + 210.[/tex]

To write a polynomial function in factored form with the given roots, we can use the factored form equation:

f(x) = (x - r1)(x - r2)(x - r3)...

Where r1, r2, r3 represent the roots of the polynomial.

Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:

f(x) = (x - 7)(x + 10)(x - 3)

Expanding this equation will give us the polynomial function in factored form:

[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]

[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]

[tex]= (x^2 + 3x - 70)(x - 3)[/tex]

[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]

[tex]= x^3 - 76x + 210[/tex]

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Answer:

Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4

The period of the trigonometric function in this problem is given as follows:

A) 540º.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().

For which the parameters are given as follows:

The coefficient B for the equation is given as follows:

B = 2/3.

Hence the period of the function is given as follows:

2π/(2/3) = 3π = 540º.

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3/5 is the fraction between the numbers 1/3 and 87/100

A number line is a graphical representation of numbers that can be used to understand and visualize numerical relationships. It is a straight line that extends infinitely in both directions and is usually drawn horizontally.

Writing the fractions as percentage:

1/3 * 100 = 33.3%

87/100 = 87%

This shows that the required number must be between 33.3% and 87%

From the given options:

3/5 * 100 = 3 * 20

3/5 * 100 = 60%

Hence the value in between the numbers 1/3 and 87/100 is 3/5

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A. The function f is injective.

B. The function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

To prove that the function f is injective, we need to show that if f(x) = f(y), then x = y.

Let f(x) = f(y). Then we have:

x / (1 + x) = y / (1 + y)

Cross-multiplying, we get:

x(1 + y) = y(1 + x)

x + xy = y + xy

Now, subtract xy from both sides:

x = y

Since x = y when f(x) = f(y), we can conclude that the function f is injective.

(b) To prove or disprove that the function f is surjective, we need to determine whether for every y ∈ Q, there exists an x ∈ N such that f(x) = y.

Consider the case where y = 1/2. We need to find x ∈ N such that:

f(x) = x / (1 + x) = 1/2

Cross-multiplying, we get:

2x = 1 + x

Subtract x from both sides:

x = 1

In this case, there exists an x ∈ N (x = 1) such that f(x) = 1/2. However, we need to consider all y ∈ Q. Let's try another case.

Consider the case where y = 1. There is no x ∈ N that satisfies the following equation:

f(x) = x / (1 + x) = 1

Cross-multiplying, we get:

x = 1 + x

Subtract x from both sides:

0 = 1

This is a contradiction, so there is no x ∈ N such that f(x) = 1. Therefore, the function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

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Answer:

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and

y represent the cost per pound of the vanilla coffee beans.

6x + 5y = 77.50

20x + 13y = 234.50, both of these are given.

Rewrite these equations so you can eliminate one of the variables;

60x + 50y = 775, Multiply both sides of the equation by 10

60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

y = 6.5

Solve for x,

6x + 5(6.50)= 77.50

x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and

the cost per pound of the vanilla coffee beans is $6.50.

The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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The experimental probability of the computer generating a 3 or a 5 is given as follows:

20%.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes in the table is given as follows:

90.

The desired number of outcomes is given as follows:

10 + 8 = 18.

Hence the experimental probability is given as follows:

p = 18/90 = 0.2 = 20%.

The problem is given by the image presented at the end of the answer.

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The slope and y-intercept include the following:

Slope = 2.

y-intercept = -1.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the linear equation:

-6x + 3y =-3

By making y the subject of formula, we have:

3y = 6x - 3

y = 2x - 1

By comparison, the slope and the y-intercept include the following:

Slope, m = 2.

y-intercept, b = -1.

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Answer: [tex]x\approx 6.2[/tex]

Step-by-step explanation:

Detailed explanation is attached below.

The mode of the data is 0

Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.

It provides an accurate description of the entire data.

The three major measures of central tendency are given as;

The mode is defined as the measure of central tendency representing the most occurring number in a given data set

From the information given, we have;

0, 4 , 3, 4, 0, 9, 1

Then, the mode is 0

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Using substitution method to solve the system of linear equation, the number of calculator is 50 and calender is 30

The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.

To solve this problem, we can set the variables for this;

Let;

To write the system of linear equations;

x + y = 80 ...eq(i)

12x + 10y = 900 ...eq(ii)

Part B;

Using substitution method;

From equ(i)

x + y = 80

x = 80 - y ...equ(iii)

Put equ(iii) into equ(ii)

12(80 - y) + 10y = 900

y = 30

x = 50

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the solution to the equation log2x + log4x + log16 = 7  the logarithms using the properties of Logarithms is x ≈ 53.408.

To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.

First, we can use the property loga + logb = log(ab) to combine the logarithms:

log2x + log4x + log16 = log(2x * 4x * 16)

Next, we simplify the expression inside the logarithm:

log(2x * 4x * 16) = log(32x^3)

Now, our equation becomes:

log(32x^3) = 7

To eliminate the logarithm, we can rewrite the equation in exponential form:

32x^3 = 10^7

Simplifying further:

32x^3 = 10,000,000

Now, we can solve for x by dividing both sides of the equation by 32:

x^3 = 10,000,000 / 32

x^3 = 312,500

To find the value of x, we take the cube root of both sides:

x = ∛312,500

x ≈ 53.408

Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.

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The transformations to the parent function are given as follows:

The parent function for this problem is given as follows:

y = 1/x.

The transformed function for this problem is given as follows:

y = 3/(x + 5) - 3.

Hence the  transformations to the parent function are given as follows:

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The probability of getting Two Tails is 0.1 or 10%.

Let's assume that '2. Tails' appeared x times.

According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.

The total number of tosses is 360. We can express this information in an equation:

x + 3x + 6x = 360

Simplifying the equation:

10x = 360

x = 36

Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.

To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:

Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses

= 36 / 360

= 0.1

Therefore, the probability of getting Two Tails is 0.1 or 10%.

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The portion of scores that are between 59 and 91 is 98%.

The portion of exam scores that are less than 67 is 16%.

The portion of exam scores that are between 67 and 91 is 82%.

A normal distribution curve is a type of probability distribution that is commonly used in statistics to represent a large set of data. It is also known as a bell curve. The curve is bell-shaped, symmetrical, and smooth.

Comparing the exam score diagram in the question, to a standard normal distribution curve, we will have the following;

The portion of scores that are between 59 and 91 is;

= 100% - (59 to 43 portion)

= 100% - 2%

= 98%

The portion of exam scores that are less than 67 is;

= (67 to 59) + (59 to 43)

= 14% + 2%

= 16%

The portion of exam scores that are between 67 and 91 is ;

= (67 to 75) + (75 to 83) + (83 to 91)

= 34% + 34% + 14%

= 82%

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The horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

To answer the question, we need to use trigonometry. In this case, we can use the sine function, which relates the opposite side of a right triangle to its hypotenuse. In this case, the ladder is the hypotenuse, and the horizontal distance between the base of the ladder and the wall is the opposite side.

The angle formed by the ladder and the ground is the angle of interest.

Let x be the horizontal distance between the base of the ladder and the wall. Then, using the sine function, we have:

sin(64 degrees) = x/18

Multiplying both sides by 18, we get:

x = 18 sin(64 degrees) ≈ 16.2 feet

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.

It is important to note that when using trigonometry, we need to use the appropriate trigonometric function depending on the sides and angles we are given. In this case, we were given the hypotenuse and the angle opposite the horizontal distance, so we used the sine function.

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For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.

For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.

hopes thats help thank you

The interval representing the range of the graphed function in this problem is given as follows:

a) (0, ∞).

From the image of the problem, the output y of the function is composed by the positive values, hence the interval representing the range is given as follows:

(0, ∞).

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The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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The calculated measure of the red arc in ⊙C is 11

From the question, we have the following parameters that can be used in our computation:

The congruent circles

From the circles, we have

Centers = C and P

Also, we have

Corresponding segments are equal segments

Using the above as a guide, we have the following:

QR = LM

Where

LM = 11

This gives

QR = 11

Hence, the value of QR is 11

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The scatter plot that accurately describes the data is given as follows:

Scatter plot A.

The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:

(Input, Output).

The input and output variables for this problem are given as follows:

Hence the points are given as follows:

(13, 23), (17, 17), (21, 17), ..., (70,30).

And all these points are marked on the scatter plot given by option A.

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Answer:

Angles 1 and 8 are alternate exterior angles.

Answer: 2^(4/5)=16

Step-by-step explanation:

log a (b)=c

this converts to:

a^c=b

so...

2^(4/5)=16

Answer:

[tex]\huge\boxed{\sf 0.00008\ km}[/tex]

Step-by-step explanation:

= 8 cm

= 8 / 100,000 km

[tex]\rule[225]{225}{2}[/tex]

Answer:

0.00008

80 cm is 0.0008 so you know I just assumed

The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.

We are given that;

Orange juice cup= 6

Pineapple juice cup=3

Now,

PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:

32 fluid ounces = 32 / 8 cups = 4 cups

The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.

PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:

8 pints = 8 * 2 cups = 16 cups

Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T

Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.

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Answer: 2916 cubic feet

Step-by-step explanation:

V=(4/3)*3*(9^3)

V=(4/3)*3*729

V=2916

Answer:

We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1

Now we can substitute this value into the original equation and simplify:

y = -3 + tan(1/2 (0 + π/2))

y = -3 + 1

y = -2

The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down

The depth of water when the tank is on its side is 4.2 cm.

We are given that;

tank measurement is 13*8*17

Now,

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.

To find the volume of water in the tank when it is upright. To do this, you multiply the depth of water by the area of the base:

Volume = Depth * Area Volume = 9 cm * (13 cm * 8 cm) Volume = 936 cm^3

This volume does not change when you put the tank on its side. However, the area of the base does change. Depending on which side you put the tank on, the area of the base will be either 13 cm by 17 cm or 8 cm by 17 cm. Let’s assume you put the tank on its longer side, so that the area of the base is 13 cm by 17 cm.

Now, you can find the depth of water by dividing the volume by the area:

Depth = Volume / Area Depth = 936 cm^3 / (13 cm * 17 cm) Depth= 4.2 cm

Therefore, by the cube answer will be 4.2cm.

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