A board game uses a bag of 105 lettered tiles. You randomly choose a tile and then return it to the bag. The table shows the number of vowels and the number of consonants after 50 draws. Predict the number of vowels in the bag.

Answer:

8 and 1/3

Step-by-step explanation:

First, let's understand the situation. There is a 25 oz juice that is to be split 3 ways. To determine the amount of jucie each person gets, we will take the total amount of juice and divide it by the number of kids, 3. When we do this, we get 25/3. Since this fraction can;t be simplified into a whole number, we will need to turn 25/3 into a mixed number. To do this, we need to know how many times 3 goes into 25. 3 goes into 25 8 times with a remainder of 1. This remainder is put over 3, giving us the final answer, 8 and 1/3.

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The value of f(x) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j, the hessian H(x) is [tex]a.b^{T}[/tex], and f(x) is a quadratic form, and the symmetric matrix Q is [tex]a.b^{T}[/tex].

a. The function f(x) is defined as the product of two dot products,

f(x) = ([tex]a^{T}[/tex].x)([tex]b^{T}[/tex].x) =  (∑_{i=1}ⁿ a_ix_i)(∑_{j=1}ⁿ b_jx_j) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j

b. To find the Hessian H(x), we need to find the second partial derivative of f(x) with respect to x. Let's define H(x) as

H(x) = [∂^2f(x)/∂x_i∂x_j] = [∂/∂x_i(∂f(x)/∂x_j)]

Since f(x) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j, the first partial derivative of f(x) with respect to x_j is

∂f(x)/∂x_j = ∑_{i=1}ⁿ a_ib_jx_i = [tex]b_{j}^{T}[/tex].a.x

The second partial derivative of f(x) with respect to x_i and x_j is

∂^2f(x)/∂x_i∂x_j = ∂/∂x_i([tex]b_{j}^{T}[/tex].a.x) = a_ib_j

So, the Hessian H(x) is

H(x) = [a_ib_j] = [tex]a.b^{T}[/tex]

c. To determine if f(x) is a quadratic form, we need to find the symmetric matrix Q such that f(x) = [tex]x^{T}[/tex].Qx.

Let's define Q = [tex]a.b^{T}[/tex].

Then, f(x) can be written as

f(x) = [tex]x^{T}[/tex].Qx = ([tex]a.b^{T}[/tex]).x.[tex]x^{T}[/tex] = [tex]x^{T}[/tex].([tex]a.b^{T}[/tex]).x = [tex]x^{T}[/tex].([tex]a.b^{T}[/tex]).x = [tex]x^{T}[/tex].Qx

So, f(x) is a quadratic form, and the symmetric matrix Q is [tex]a.b^{T}[/tex].

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If the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

The graph is a function if any vertical line drawn through it can cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through the graph at two or more different places.

A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The function's domain and codomain, respectively, are the sets X and Y as a whole. Initially, functions represented the desired relationship between two fluctuating values.

A function is a relation that specifically links members of one set to those of another set. Formally speaking, a function from to is an object such that each is specifically connected with an object. Therefore, a function is a many-to-one (or occasionally, a one-to-one) relation.

Let the given function be f(x) = x⁵ + (x + 3)²

When x = -1 then f(-1) = (-1)⁵ + (-1+3)² = -1 + 4 = 3.

Therefore, the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.

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On applying the supplementary angle rule, the value for x is obtained as 10°, and the angle 7x° is obtained as 70°.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

The line segment is given which has a ray diving the line segment.

Since it is a straight line, the total angle on it will be 180°.

The two angles given are 110° and 7x°.

Apply the supplementary angle rule =

On a straight line sum of two angles = 180°

Substitute the values in the equation -

110° + 7x° = 180°

Collect the like terms -

7x° = 180° - 110°

Apply the arithmetic operation of subtraction -

7x° = 70°

Apply the arithmetic operation of division -

x = 70/7

x = 10°

Now the angle 7x° = 7(10°) = 70°

Therefore, the angle value is obtained as 70°.

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A vector w that is orthogonal to both u and v is w = (-1,-1,-1) and a vector x which is orthogonal to u and lies in the same plane defined by u and v is x = (-1,2,1).

The vectors are

u = (1, 0, 1)

v = (0, 2, 2)

If the scalar product of two vectors is equal to zero, then the vectors are orthogonal.

If we let let w = (a, b, c)

Then (u, w) ≥ 0

1×a + 0×b + 1×c = 0

a + c = 0

Subtract c on both side, we get

a = -c

and (v, w) = 0

0×a + 2×b + 2×c = 0

2b + 2c = 0

2(b + c) = 0

b + c = 0

b = -c

Then w = (-c, -c, -c)

If c=1

Then the orthogonal vector

w = (-1,-1,-1)

Let x = (x, y, z)

x is now orthogonal to u.

That is (u, x) = 0

1×x + 0×y + 1×z = 0

x + z = 0

x = -z

u × v = [tex]\begin{vmatrix}\hat{i} & \hat{j} & \hat{k}\\ 1 & 0 & 1\\ 0 & 2& 2\end{vmatrix}[/tex]

u × v = [tex]\hat{i}\begin{vmatrix} 0 & 1\\ 2& 2\end{vmatrix}-\hat{j}\begin{vmatrix} 1 & 1\\ 0& 2\end{vmatrix}+\hat{k}\begin{vmatrix} 1 & 0\\ 0& 2\end{vmatrix}[/tex]

u × v = [tex]\hat{i}[/tex](-2) - [tex]\hat{j}[/tex](2) + [tex]\hat{k}[/tex](2)

u × v = -2i-2j+2k

The given condition x lies on the plane u and v

(-2, -2, -2), x ≥ 0

-2x - 2y + 2z = 0

[x = -z]

2z - 2y + 2z = 0

-2y = -4z

y = 2z

That is x = (-z, 2z, z)

Now put z = 1

x = (-1,2,1)

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The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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Answer:

24 Minuets

Step-by-step explanation:

Answer:

24 minutes

Step-by-step explanation:

The area under the normal curve between 840 and 1200 is calculated by subtracting the cumulative distribution function (CDF) at 840 and 1200.

The area under the normal curve between 840 and 1200 is calculated using the cumulative distribution function (CDF). The formula for the CDF is

F(x) = 1/2[1 + erf((x-μ)/σ(2)^1/2)]

where μ is the mean and σ is the standard deviation.

To calculate the area between 840 and 1200, we first calculate the CDF at 840 and 1200.

F(840) = 1/2[1 + erf((840-μ)/σ(2)^1/2)]

F(1200) = 1/2[1 + erf((1200-μ)/σ(2)^1/2)]

We then subtract the two values to get the area between 840 and 1200. Area = F(1200) - F(840)

This gives us the area under the normal curve between 840 and 1200.

The area under the normal curve between 840 and 1200 is calculated by subtracting the cumulative distribution function (CDF) at 840 and 1200.

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She had filled 88 spray pint bottles.

Given is that Ms. Wu runs a house cleaning business. To save money, she bought a 1 gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1 - pint spray bottles as she could.

1 pint = 0.125 gallons

Total amount = 11 gallons.

The total number of bottles that can be filled are -

n = 11/0.125

n = 88

Therefore, she had filled 88 spray pint bottles.

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Answer:x=4 y=6.66666666667

Step-by-step explanation:

Answer:

y=-(2/3)x-1

Step-by-step explanation:

y=kx+n

n= -1

k = (y2-y1)/(x2-x1) = -2 / 3 = -2/3

y=-(2/3)x-1

The average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.

V(r) = 0.2r² − 20r + 600

The average rate of change of V with respect to r over the interval [85,110] can be calculated by finding the derivative of V(r) and evaluating it at the midpoint of the interval, then dividing the result by the length of the interval. The derivative of V(r) is:

dV/dr = 0.4r - 20

The midpoint of the interval [85,110] is (85 + 110)/2 = 97.5. Evaluating the derivative at the midpoint, we get the following:

dV/dr = 0.4 × 97.5 - 20 = 19.0

The length of the interval is 110 - 85 = 25, so the average rate of change is:

The average rate of change = (dV/dr)/(110 - 85) = 19.0/25 = 0.76

So, the average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.

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--The given question is incomplete; the complete question is

"Eucalyptus trees, common in California and the Pacific Northwest, grow better with more water. Scientists in North Africa, analyzing where to plant trees, found that the volume of wood that grows on a square kilometre, in meters cubed, is approximated by V(r)=0.2r²−20r+600 where r is rainfall in centimetres per year, and 60≤ r ≤120. Calculate the average rate of change of V with respect to r over the interval [85,110]."--

The possible pair of a and b are; (-2, 2)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

Given that 2.(2x+a) (3x+b) is the same as the product of polynomials 3.(x-1)-(4x+1)

2.(2x+a) (3x+b) =  3.(x-1)(4x+1)

(4x + 2a)(6x + 2b) = (3x-3)(12x+ 3)

Let multiply by 3 then

3(4x + 2a)(6x + 2b)

= (12x + 6a)(18x + 6b)

Multilpy by 4 on left side;

(12x- 12)(48x+ 12)

So, (12x + 6a) = (12x- 12)

6a = -12

a = -2

Now, (18x + 6b) = (48x+ 12)

b = 2

The pair of a and b could be (-2, 2)

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Answer:

120

Step-by-step explanation:

720/6 =120

Answer:

Below

Step-by-step explanation:

Not sure this is the easiest way

line BC equation is    y = - 2/9x + 3 7/9

 perpindicular line that includes point A (2,1) has slope 9/2

    point slope form would be

            y-1 = 9/2(x-2)      re-arranged to y = mx+b form

            y = 9/2 x -8

to find the actual altitude , these two lines intersect.....equate them

-2/9x + 3 7/9 = 9/2 x- 8

    11 7/9  = 4 13/18 x

                 x = 2 42/85        then y = 3 19/85

altitude then (using distance formula)

  a^2 = (2 42/85 -2)^2  + (1- 3 19/85)^2  

                     a = 2.278 units

I hope this answered the question....I am not sure what 'the equation of the altitude'  means

The equation of the altitude of the triangle is y = ( 9/2 )x - 8

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be B ( -1 , 4 )

Let the second point be C ( 8 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = ( 4 - 2 ) / ( -1 - 8 )

m = -2/9

Now , the slope of the altitude is m₂ = 9/2 ( perpendicular lines have negative reciprocal slope )

And , the altitude passes through the point A ( 2 , 1 )

So , the equation of line is y - y₁ = m ( x - x₁ )

y - 1 = ( 9/2 ) ( x - 2 )

y - 1 = ( 9/2 )x - 9

Adding 1 on both sides , we get

y = ( 9/2 )x - 8

Hence , the equation of line is y = ( 9/2 )x - 8

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Answer:

i believe it is the last option.

Step-by-step explanation:

square units are units of area, so you'll want to find the SIDES and use those.
144 squared units would be 12 units per side.
25 would be 5, 169 would be 13.

pythagorean theorem is a^2 + b^2 = c^2, generally c is shown as the hypotenuse.

12^2 + 5^2 = 13^2 would be the last option given.

Answer: A; Yes

Step-by-step explanation:

Plug in the ordered pair into the equation: 2(-2) + (1) = -3

Solve: -4 + 1 = -3

-3 = 3 ; (-2, 1) is a solution for 2x + y = -3

Now, repeat the same process for the second equation:

(1) = 2(-2) + 5

1 = -4 + 5

1 = 1 ; (-2, 1) is a solution for y = 2x + 5

If the instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour and electricity costs $0.30 per kilowatt hour, then the cost to run the player for an hour is $0.06 .

The cost of running a CD player for an hour can be calculated by multiplying (the amount of electricity it uses) by (the cost per kilowatt hour) .

According to the instruction booklet, the player uses 0.2 kilowatt of electricity per hour.

So, if electricity costs $0.30 per kilowatt hour, then

it would cost ⇒ 0.2 × $0.30 = $0.06 .

Therefore , it will take $0.06 to run the player for an hour.

The instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour. If electricity costs $0.30 per kilowatt hour, how much does it cost to run the player for an hour ?

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Answer:

16A.) C

16B.) x=6; the students each paid $6 for their concert tickets.

Step-by-step explanation:

[Note: I know that this answer is lengthy, but the explanation is very simple and is worth reading]

16A.)

First, let's "figure out" the amount of money spent by the students. Each student paid $x for a ticket and $4 on parking. That means that the cost for one student would be $x + $4. To figure out how much it would cost 12 students, we can take the amount it costs 1 student and multiply it by 12. Again, since x + 4 is the cost for 1 student, 12( x + 4 ) would be the cost of 12 students. Next, let's figure out how much the adults paid for their tickets.

Now, let's find the cost the adults paid for the ticket. If the students paid $x and the adults paid four times as much for each of their tickets, then the cost of the ticket for the adults must have been $4x. Now, we know each adult paid $4x for a ticket and $6 on parking. That means that the cost for one adult would be $4x + $6. To figure out how much it would cost 4 adult , we can take the amount it costs 1 adult and multiply it by 4. Again, since 4x + 6 is the cost for 1 adult, 4( 4x + 6 ) would be the cost of 4 adults.

Since the 12 students paid 12(x+4) dollars for the concert and the 4 adults paid 4(4x+6) and since we know they spent the same amount of money, we can set 12(x+4) and 4(4x+6) equal to each other. This gives us the answer 12(x+4)=4(4x+6), or C, for question 16A.

16B.)

To solve the equation 12(x+4)=4(4x+6) means to solve for x. So, let's solve for x:

12 ( x + 4 ) = 4 ( 4x + 6 )   [Distribute the 12 on the left side]

12x + 48 = 4 ( 4x + 6 )   [Distribute the 4 on the right side]

12x + 48 = 16x + 24   [Subtract 12x from both sides]

48 = 4x + 24   [Subtract 24 from both sides]

24 = 4x   [Divide both sides by 4 to get the value of x]

6 = x

Now, for the second half of the question, what does x=6 mean? Well, if we look at the previous problem, x was the amount of money spent by the students for the concert ticket. So, the answer x=6 tells us that the students paid $6 for their concert tickets.

[Note: They didn't ask for the price of the adults' tickets, but if they did, we would have plugged in x=6 into the equation 4x to find that the cost of the adults' tickets were $24.]

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In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given, Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,

Since,

In 2 mins Mark's model train can go = 1/3 laps

Thus,

In 1 min Mark's model train can go = 1/3/2 laps

In 1 min Mark's model train can go = 1/6 laps

In 9 mins Mark's model train can go = 9/6 laps

In 9 mins Mark's model train can go = 1.5 laps

Therefore,  In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

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According to the information and the graph, the best place for Lois Lane to stand to receive the keys from Superman is in the middle of the Krytonite cage because it is the closest place to the point where superman is standing.

The point where Lois Lane should stand is in the middle of the cage because there he will have a better chance of receiving the Kronite keys that he has. Additionally, this point is the closest to the point where Superman is standing so he wouldn't have to go near the krionite and could throw the keys from there.

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f(-5) = 42

f(0) = 7

f(1) = 6

A function is a relationship that has a set of inputs and outputs. An example of a function is f(x) = x. The "(x)" in the parenthesis represents the input while the x on the left side represents the output. To compute the values of an output you plug in the input and replace all the variables with the input. E.g. to find f(1) we would replace all "x"s with 1 giving us f(1) = 1

Given f(x) = x² - 2x + 7 we want to find f(-5) , f(0) and f(1)

We can find these values by simply plugging in the values of the inputs and replacing all x's for them.

If f(x)= x² - 2x + 7

Then,

f(-5) = (-5)² - 2(-5) + 7                                                             simplify exponents

f(-5) = 25 - 2(-5) + 7                                                                  multiply -2 and -5

f(-5) = 25 + 10 + 7                                                                           add all values

f(-5) = 42

f(0) = (0)² - 2(0) + 7                                                                 simplify exponents

f(0) = 0 - 2(0) + 7                                                                       multiply 0 and -2

f(0) = 0 - 0 + 7                                                                                 add all values

f(0) = 7

f(1) = (1)² - 2(1) + 7                                                                     simplify exponent

f(1) = 1 - 2(1) + 7                                                                           multiply -2 and 1

f(1) = 1 - 2 + 7                                                           add and subtract the values

f(1) = 6

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Answer:

Step-by-step explanation:

The definite integral of the function (2x - 3) with respect to x can be found using the antiderivative, also known as indefinite integration.

The antiderivative of (2x - 3) is:

x^2 - 3x + C, where C is the constant of integration.

For the definite integral, we need to find the antiderivative over a given interval. To calculate the definite integral, we need to evaluate the antiderivative at the limits of the interval and subtract the values.

So, for example, if the interval is from a to b, the definite integral is given by:

∫_a^b (2x - 3) dx = (x^2 - 3x) |_a^b = (x^2 - 3x) evaluated at b - (x^2 - 3x) evaluated at a.

The definite integral of the function y³ (2y² – 3) with respect to y can be found in a similar way. The antiderivative of y³ (2y² – 3) can be found using power rule of integration.

The antiderivative of y³ (2y² – 3) is:

(1/4) y⁴ - 3y² + C, where C is the constant of integration.

The definite integral of the function can then be found by evaluating the antiderivative at the limits of the interval and subtracting the values, as described above.

Answers in image.

Step-by-step explanation:

To solve the questions,  use the power rule to solve.

Answer:

hhhjhj

Step-by-step explanation:

The translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the points be represented as P and Q

Now , the coordinates of point P = P ( 0 , 0 )

And , the coordinates of the point Q = Q ( 5 , 4 )

when the points are translated up 3 units and left 2 units

The coordinates of the translated point will be ( x , y ) to ( x - 2 , y + 3 )

Substituting the values in the equation , we get

The coordinates of the translated point P' = P' ( -2 , 3 )

The coordinates of the translated point Q' = Q' ( 3 , 7 )

Hence , the translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

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Seismic hazard analysis is a method of probability assessment that would most likely be used to assess the probability that a major earthquake will occur in California in the next three years.

Seismic hazard analysis is a method used to assess the probability of earthquakes occurring in a specific location, and it involves analyzing the historical records of earthquakes, geological data, and the tectonic plate movements in the area. This method is used to predict the likelihood of future earthquakes and their potential magnitude and intensity.

In the case of California, a seismic hazard analysis would likely be used to assess the probability of a major earthquake occurring in the next three years. The data collected from this analysis would help the government and the public prepare for potential earthquakes and minimize the damage caused by such events.

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If the test scores follow a normal distribution, then you would expect approximately 16 percent of the scores to be less than 390. This can be calculated using the cumulative normal distribution formula.

Calculating the percentage of scores that would be less than 390 using the cumulative normal distribution formula involves determining the area under the normal curve for the desired range.

In this case, the area under the normal curve from minus infinity to 390 would need to be calculated. This can be done using a scientific calculator or a statistical software program. The result will be the proportion of the scores that are less than 390. This proportion can then be converted to a percentage to determine what percentage of scores would be expected to be less than 390.

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The fraction of water is 7/12, when the ratio orange:pineapple:water=3:2 :7

A fraction represented with its quotient and remainder is a mixed fraction, and also one having a fraction and a whole number.

For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given that the ratio of orange: pineapple: water = 3: 2: 7.

consider orange=3x

pineapple=2x

water=7x

Total mix fraction=12x

To know the fraction value of water just divide the water by and total fraction.

fraction of water=7x/12x

fraction of water=7/12

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(a) The answer is The Allen family earns $24,000 more than the Reed family.

(b) The answer is The Allen family earns more than about 87% of families in their county.

To learn more about income refer:

brainly.com/question/28390284

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