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 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 number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ben originally filled out 8 more applications than Henry.

Let the number of applications filled by Henry be x.

Now, x+8

Then each boy filled out 3 additional applications, bringing the total to 28.

Here, x+3+x+8+3=28

2x+14=28

2x=14

x=7

So, x+8=15

Therefore, the number of applications filled by Henry is 7 and the number of applications filled by Ben is 15.

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The total change in size of the tumor in the first 3 months is 13.5 cubic millimeters. The average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.

The total change in size of the tumor in the first 3 months can be calculated by subtracting the size at the beginning (4.5 cubic millimeters) from the size at the end of the 3-month period (S(3) = 4.5 * 3 = 13.5 cubic millimeters). Therefore, the total change in size of the tumor in the first 3 months is 13.5 cubic millimeters.

To calculate the average rate of change in the size of the tumor in the first 3 months, we need to divide the total change in size (13.5 cubic millimeters) by the time (3 months).

Therefore, the average rate of change of the tumor in the first 3 months is 4.5 cubic millimeters per month.

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Answer:

Step-by-step explanation:

maybe you typed the question wrongly or some

^^

Answer:

the 3 answer is the right one

If a and b are integers that divide c and are relatively prime, then ab divides c. If a and b are not relatively prime, then ab need not divide c.

If a and b are integers that divide c, this means that c is divisible by both a and b. Additionally, if a and b are relatively prime, this means that they have no common factors besides 1. In this case, since a and b both divide c, then it follows that their product, ab, also divides c.

However, if a and b are not relatively prime, this means that they have common factors besides 1. In this case, the common factors of a and b may not divide c, so it is not necessarily true that ab divides c.

For example, if a = 6, b = 8, and c = 24, then 6 and 8 both divide 24, but 6 and 8 are not relatively prime (they have a common factor of 2). In this case, 6 * 8 = 48 does not divide 24.

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Answer:

P = 5x + 29

Step-by-step explanation:

Let's call the length of one side of the triangle "a".

According to the problem, another side is 14 more than three times the length of the bottom of the triangle, so it can be expressed as 3x + 14.

The last side is 15 more than the bottom of the triangle, so it can be expressed as x + 15.

The perimeter of the triangle is the sum of all three sides, so:

P = x + (3x + 14) + (x + 15)

Simplifying:

P = 5x + 29

The ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1) is 8:1, and the coordinates of the point are 8/3 and -1/9

The given data is, the line 2x+3y-5= 0 and the points are (8, -9) and (2, 1)

Let us consider the ratio to be α: 1

To find the values of a and b we need to use the midpoint formula:

[tex]X=\frac{m_1x_1+m_2x_2}{m_1+m_2} ,\frac{m_1y_1+m_2y_2}{m_1+m_2}[/tex]

For Points (8,–9) and (2, 1) by applying the section formula we get,

[tex]X=\frac{2\alpha +8}{\alpha +1} ,y=\frac{\alpha -9}{\alpha -1}[/tex]

Given equation of line is 2x + 3y–5 = 0 substitute the values of x,y in the equation of line:

[tex]X=2(\frac{2\alpha +8}{\alpha +1} )+3(\frac{\alpha -9}{\alpha -1})-5=0[/tex]

4α+16+3α-27-5α-5

2α=16

α=8

Hence the ratio is 8:1.

Also, the coordinates are

[tex]X=\frac{2\alpha +8}{\alpha +1}=\frac{2(8) +8}{8+1}=\frac{24}{9}=\frac{8}{3} \\\\ y=\frac{\alpha -9}{\alpha -1}=\frac{8-9}{8-1}=\frac{-1}{9}[/tex]

∴ The coordinates are (x,y) = (8/3,-1/9).

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The equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, 22000t + 70000r = 2000000, we are asked to solve it for, Solve for t and r

The given equation is

22000t + 70000r = 2000000

Solving for t, we get,

22000t + 70000r = 2000000

22000t = 2000000 - 70000r

22t = 2000 - 70r

11t = 1000 - 35r

t = (1000-35r) / 11

Solving for r, we get,

22000t + 70000r = 2000000

70000r = 2000000 - 22000t

70r = 2000 - 22t

35r = 1000-11t

r = (1000-11t) / 35

Hence, the equation given, when solved for t and r given expression, t = (1000-35r) / 11 and r = (1000-11t) / 35 respectively.

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The vertex of the hyperbolic mirror is (17, 8.5). To find the vertex of a hyperbolic mirror, you need to find the midpoint between its two foci.

In this case, the focus has coordinates (17, 0) and the mount at the top edge of the mirror has coordinates (17, 17). To find the midpoint, you average the x-coordinates and the y-coordinates.

The x-coordinate of the midpoint is: (17 + 17) / 2 = 17.

The y-coordinate of the midpoint is: (0 + 17) / 2 = 8.5

Therefore, the vertex of the hyperbolic mirror is (17, 8.5).

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The value of f(3) in the function is 67

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

f(a) = 4^a + 3

The function notation f(3) implies that the value of a is 3

Substitute the known values in the above equation, so, we have the following representation

f(4) = 4^3 + 3

Evaluate the exponents

f(4) = 64 + 3

So, we have

f(4) = 67

Hence, the solution is 67

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The right expression will be -3x + 3 = 3( 1 - x ) for the given expressions.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that there are different expressions the correct expression choice is calculated s below:-

-3x + 3 = 3( 1 - x )

-3x + 3 = 3 - 3x

-3x + 3 = -3x + 3

Hence, the correct ex[ression would be -3x + 3 = 3( 1 - x ).

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The values of x are 13 and -1. Option A

Algebraic expressions are defined as  expressions that have terms, variables, coefficients, constants and factors.

They are made up of arithmetic operations.

Given that;

(x - 7)²= 36

expand the bracket

x² - 7x - 7x + 49 = 36

collect like terns

x² - 14x + 49 = 36

x² - 14x + 13

Factorize the expression

(x² - 13x) + (x - 13)

Factor the common terms

x(x - 13) + 1(x - 13)

x = 13. x = -1

Hence, the values are 13 and -1

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A score of 100 and a standard deviation of 15 for an intelligence test indicate that:

the scores are normally distributed, which means that the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.

Typically, in a normal distribution, 68% of scores fall within one standard deviation of the mean (85 to 115 in this case), 95% of scores fall within two standard deviations of the mean (70 to 130), and 99.7% of scores fall within three standard deviations of the mean (55 to 145).

This information can be used to describe how the scores are distributed as follows:

Therefore: the majority of scores are clustered around the mean (100) and the spread of scores decreases as the deviation from the mean increases.

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The line best models line l is x=4, the correct option is A.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

Given;

The graph shown in the figure.

Now,

On the graph the x coordinate is 4 throughout

So, x=4

On the graph the y coordinate is continous

Therefore, the graph function will be x=4

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Answer:

Given f(x) = 3x - 3 and g(x) = -x, to find g(f(x)), we first need to substitute f(x) into g(x).

So, g(f(x)) = g(3x - 3) = -(3x - 3) = -3x + 3.

The number of batches of muffins she can make will be 5.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a berry farm, Clayton picks 1¹/₄ cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins.

The number of the batches of muffins can be calculated as:-

Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )

Number = [  ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )

Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]

Number = 5

Therefore, the number of batches of muffins will be 5.

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The angle x in the heptagon is 98 degrees.

The polygon above has 7 sides. Therefore, the name of the polygon is heptagon. Therefore, the sum of interior angles of a polygon can be represented as follows:

sum of interior angles of a polygon = 180(n - 2)

where

Therefore,

sum of interior angles of the heptagon =  180(7- 2)

sum of interior angles of the heptagon = 180(5)

sum of interior angles of the heptagon = 900 degrees

Hence, let's find x as follows:

122 + 146 + 142 + 140 + 110 + 142 + x = 900

x = 900 - 802

x = 98 degrees

Hence,

x = 98 degrees

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The function that is graphed is (c) y = x² + 2    if x < 1 and y = -x + 2  if x ≥ 1

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

The graph

On the graph, we can see that the first curve is a quadratic function,

Also, it has an open circle at x = 1

So, we have:

x² + 2    if x < 1

Next, we have a linear equation with a closed circle at x = 1

So we have:

y = -x + 2 for x ≥ 1

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The  y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount. The y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].  It will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

From the given data,

A super large tank was initially filled with brine solution of 20 liters.

At some point, fresh water starts to flow in at a rate of 8 liters per minute, and the well mixed solution flows out at half of the rate.

The initial value problem (IVP) to describe the above problem can be set up as follows:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒y(0)=20

Where y(t) represents the amount of salt in the tank t minutes after the process started, and y(0) = 20 represents the initial amount.

Part II:

To solve the IVP, we need to find y(t) for a given t. This can be done using numerical methods or analytical methods, such as separation of variables. Using separation of variables, we have:

⇒[tex]\frac{d}{dt} y(t)=\frac{1}{2} (8-y(t))[/tex]

⇒[tex]\frac{dy}{dt}=\frac{1}{2}(8-y)[/tex]

⇒2dy = (8 - y) dt

⇒2dy = (8 - y)dt

Integrating both sides with respect to t, we get:

⇒∫2dy = ∫(8 - y)dt

⇒2y = 8t - (1/2)y^2 + C

where C is a constant of integration. Using the initial condition y(0) = 20, we can find the value of C:

⇒[tex]2y=8t-\frac{1}{2}y^{2} +C[/tex]

⇒[tex]2y=8t-\frac{1}{2}y^{2} +20[/tex]

Solving for y, we get:

⇒[tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex]

Therefore, the y(t) is [tex]y(t) = 4 + 8t - \frac{1}{2} y^2[/tex].

Part III:

To find the time it takes for the amount of salt in the tank to be reduced to 20% of the initial amount, we can solve for t when y(t) = 0.2 * y0:

⇒[tex]y(t) = 4 + 8t -\frac{1}{2}y^2 = 0.2 * y0[/tex]

⇒[tex]4 + 8t - \frac{1}{2} y^2 = 0.2 * 20[/tex]

Solving for t, we get:

⇒t =[tex]\frac{1}{8}[/tex](4 - 0.2 * 20) = approximately 6.875 minutes.

Hence, it will take approximately 6.875 minutes for the amount of salt in the tank to be reduced to 20% of the initial amount.

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The missing length is 6.

8

4

2

10

From the numbers shown above, it is found that the difference from one length to the other is  2.

Therefore, the missing length is 6.

Length is described as a measure of distance.

In the International System of Quantities, length is also a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.

In conclusion, the base unit for length is the meter in the International System of Units system the base unit for length is the meter.

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Answer:

-5

Step-by-step explanation:

well you could just impute the 0 for x

f(0)= 3(0)-5

multiply 3 and 0 to get 0

0-5

subtract 5 from 0 to get = -5

Answer: 5/3

Step-by-step explanation:

f(x) has to be 0

Therefore 3x-5 = 0

3x=5

3x/3 = 5/3

x = 5/3

Answer:

Minimum = -1

Maximum = 3

Step-by-step explanation:

∛-10+9 = ∛-1 = -1

∛18+9 = ∛27 = 3

If a family has 3 children of different ages and all combinations of boys and girls are considered equally likely:

a) the sample space and probability measure that describes the gender of the three children in their birth order is:  1/8.

b) Assuming we see the parents with two girls and there is no other information beyond that, the probability that the child we have not yet seen is a boy is: 1/4.

c). If we see the parents with two girls, and the parents tell us that these are the two youngest children, the probability that the oldest child we have not yet seen is a boy is: 1/8

a) The sample space for the genders of three children can be represented as a set of strings of length 3, each consisting of B (for boy) or G (for girl).

The total number of combinations of boys and girls is 2^3 = 8. Each combination has the same likelihood of occurring, so each combination can be assigned a probability of 1/8. So the sample space and probability measure can be described as:

Sample space: {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

Probability measure: P(BBB) = P(BBG) = P(BGB) = P(BGG) = P(GBB) = P(GBG) = P(GGB) = P(GGG) = 1/8

b) Assuming we see the parents with two girls, the possible combinations for the genders of the three children are:

The probability of the third child being a boy is 1/2. So, given two girls, the probability that the child we have not yet seen is a boy is:

c) Assuming we see the parents with two girls and they tell us that these are the two youngest children, the possible combinations for the genders of the three children are:

The only possible combination is GBG, so the probability of the oldest child being a boy is 1. So, given two girls and that they are the youngest children, the probability that the oldest child we have not yet seen is a boy is:

Complete Question:

"Suppose a family has 3 children of different ages and all combinations of boys and girls are considered equally likely.

a) Precisely formulate the sample space and probability measure that describes the gender of the three children in their birth order.

b) Given that the parents have two girls and no other information is available, what is the probability that the remaining child is a boy?

c) If the parents have two girls and they inform us that they are the two youngest children, what is the probability that the oldest child is a boy?"

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The compound interest and the amount are $2349980000 and $2.35 * 10⁹

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

Principal = $20,000

Rate = 800% per minute = 8

Duration = 12 seconds

n = 20 i.e. every 3 seconds

The amount is calculated as

A =  P(1 + r/n)^(nt)

So, we have

A = 20,000(1 + 8/20)^(20*12)

A = 2.35 * 10⁹

So, we have

Interest = 2.35 * 10⁹ - 20000

Interest = 2349980000

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a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

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The expected number of sales (per 100 calls) can be calculated by finding the mean or average of the sales data. To find the mean, add up all the sales values and divide by the number of sales values.

To find the expected number of sales per 100 calls, we need to find the average sales made by the sales personnel. We can do this by adding up all the sales values and dividing by the number of sales values.

The sum of sales values is:

14 + 23 + 18 + 26 + 25 + 28 + 24 + 25 + 23 + 21 + 22 + 26 + 17 + 17 + 23 + 25 + 24 + 19 + 28 + 21 + 19 + 23 + 20 + 24 + 32 + 22 + 31 + 21 + 25 + 20 + 19 + 23 + 22 + 22 + 20 + 16 + 25 + 18 + 27 + 20 + 25 + 14 + 11 + 22 + 28 + 21 + 18 + 28 + 21 + 20 +21 + 15 + 22 + 16 + 20 + 22 + 17 + 20 + 19 + 22 + 21 + 26 + 25 + 18 + 25 + 16 + 30 + 20 + 22 + 14 + 30 + 25 + 25 + 21 + 33 + 19 + 24 + 18 + 15 + 30 + 19 + 34 + 27 + 26 + 24 = 1135

And the number of sales values is:

60

So, the mean or average sales per 100 calls can be calculated as follows:

1135 / 60 = 18.92

Rounding to 2 decimal places, the expected number of sales (per 100 calls) is 22.47.

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There are 4840 yards in two and three-fourths miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 mile is equal to 1760 yards.

Therefore, The number of yards in two and three-fourths miles can be obtained by multiplying the unit equivalent of one mile with two and three-fourths miles which is,

= 1760×[tex]2\frac{3}{4}[/tex] yards.

= 1760×(11/4) miles.

= 440×11 yards.

= 4840 yards.

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Answer: 4840

Step-by-step explanation:

The intersection point is the solution of inequalities is (15, 7.5).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are 13x+37y≤481 -----(i) and 27x+21y≤567 -----(ii)

Here, x≥4 and y≥2

From the graph we can see that, inequalities are intersecting at (15, 7.5)

Therefore, the intersection point is the solution of inequalities is (15, 7.5).

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