I don't know what a, b and c stand for in the (ax + by = c) equation. Im guessing a is gradient, c is y intercept and b is?

Can someone please step by step explain to me how to solve this question and what a b and c represent please.

The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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The values of x1 and x2 are -8/3 and -4/3 through solving the equation 3x²+26x+48=0 by factoring

The equation mentioned in the question  is 3x² + 26x + 48 = 0. We need to solve this equation by factoring.To factorize this quadratic equation, we will factorize the coefficient of x², that is 3 in this case. The prime factors of 3 are 3 and 1. Also, the coefficient of x² is positive, and the constant term is positive, so both factors must be positive as well. Therefore, we write 3x² as (3x + p) (x + q), where p and q are two constants.

By multiplying these two factors, we get: 3x² + 3qx + px + pq = 3x² + (3q + p) x + pq .We need to find values of p and q such that the following condition is satisfied :3q + p = 26 and pq = 48. By using the above equation, we can write the following two equations:pq = 48p + 3q = 26. Now, we need to find the value of p and q by solving these equations. We can write p = 26 - 3q and substitute the value of p in the first equation, 3q(26 - 3q) = 483q² - 26q + 48 = 0.By solving this equation, we get the value of q, which is 2/3 or 8.

By substituting these values of q in the above equation, we get the values of p as 24 or 1/3.Therefore, the two factors of the quadratic equation 3x² + 26x + 48 = 0 are:(3x + 24) (x + 2) and (3x + 4) (x + 8).Solving the above two factors, we get x = - 8/3 and x = - 4/3.respectively.

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X1=-8 AND X2=-1

To solve the equation 3x²+26x+48=0 by factoring, one must first find the factors of 3 and 48. Here is the solution:

Step-by-step solution:

Given: 3x²+26x+48=0

To solve this equation by factoring, one must first find the factors of 3 and 48.

Factors of 3 = 1, 3.

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Now, to make the sum of the middle term 26x, we need to add 3x and 24x.

3x is a factor of 3x² and 24 is a factor of 48.

3x²+3x+24x+24 = 0

Dividing both sides by 3, we get:

x² + 9x + 8 = 0

Factoring the above quadratic equation, we get:

(x+8)(x+1) = 0

So, x+8=0 or x+1=0

Therefore, x=-8 or x=-1

The solution for x1 and x2 are x=-8 and x=-1 respectively.

Hence, the correct answer is "X1=-8 AND X2=-1".

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The length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. It is reasonable to assume that the three midsegments have equal lengths since they are part of the same triangle.

In a triangle, the midsegment is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. In the given triangle PQR, the length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. Since all the midsegments are part of the same triangle, it is reasonable to assume that they have equal lengths. The triangle midsegment theorem, which asserts that the length of a triangle's midsegment is equal to half of the length of the third side of the triangle, may be used to demonstrate this.. In this case, the length of ST, UV, and WX would all be equal to 8 units, since the third side of each triangle is 16 units. This indicates that it is reasonable to assume that the midsegments of the triangle have equal lengths.

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The two numbers are x = 3 and y = 8.

Let x and y represent two numbers.

x + y = 16

xy = 24

To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:

xy/y = 24/y

x = 24/y

We can substitute this value for x in the first equation and solve for y:

x + y = 16

(24/y) + y = 16

24 + y^2 = 16y

y^2 - 16y + 24 = 0

(y - 8)(y - 3) = 0

y = 8 or y = 3

Now that we have values for y, we can substitute them into the second equation and solve for x:

xy = 24

(8)(x) = 24

x = 3

(3)(3) = 24

So, the two numbers are x = 3 and y = 8.

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Complete question

Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.

The area of the given kite to the nearest tenth would be = 135.10mm².

A kite is defined as the type of quadrilateral that has two pairs of sides that are equal in length and which are adjacent to each other.

To calculate the area of the kite given such as ABCD, the formula = ½ × AC × BD.

Given the sides such as:

AP = 6 mm

PB = 6√3 mm

PD = 7mm

But AC = 6mm × 2 = 12mm

BD = 6√3+7 = 13√3mm

Therefore the area = 1/2 × 12× 13√3

= 6×13√3

= 135.10mm²

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Answer:

D. 67

Step-by-step explanation:

with respect to angle x.

perpendicular is 24.

hypotenuse is 26cm

since we have

sin angle=perpendicular / base

sin x=24/26

x=sin inverse(24/26)

x=67.38

in nearest degree x=67 degree

Answer:

Step-by-step explanation:

[tex]\frac{5\pm\sqrt{-4} }{3} =\frac{5\pm2\sqrt{i} }{3}[/tex]             (since [tex]i=\sqrt{-1}[/tex])

          [tex]=\frac{5}{3} \pm\frac{2}{3}\sqrt{i}[/tex]

[tex]\frac{10\pm\sqrt{-16} }{2} =\frac{10\pm4\sqrt{i} }{2}[/tex]

             [tex]=5 \pm2\sqrt{i}[/tex]

[tex]\frac{-3\pm\sqrt{-144} }{6} =\frac{-3\pm12\sqrt{i} }{6}[/tex]

                [tex]=-\frac{1}{2} \pm2\sqrt{i}[/tex]

The equation will be 26(p − 1.50) = 65 and the amount of money, p, each paint set normally costs is $4.

Ms. Delgado purchases 26 watercolor paint sets

reduced the price of each paint set = $1. 50.

Ms. Delgado spends $65 in all.

we need to find the equation to find p.

The original price of each watercolor paint set.

Solution:

Ms. Delgado purchases 26 Watercolor paint by spending $65 in all.

with a reduction in price of $39

Let 'p' be the original price of each watercolor paint set.

The equation to find p is,

26p - 39 = 65

26p = 65 + 39

26p = 104

p = 4

The original price of each watercolor paint set is $4

The equation to find p, the original price of each watercolor paint set is

26(p − 1.50) = 65 or 26p - 39 = 65

The original price of each watercolor paint set is $4

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(a) i) The price of the television on the first day of the sale is £360

    ii) The price of the television on the third day of the sale is £288

(a)

i) On the first day of the sale, the price of the television is reduced by 20% of £450, which is:

20/100 × £450 = £90

So the price of the television on the first day of the sale is:

£450 - £90 = £360

ii) On the third day of the sale, the price of the television is reduced by 20% of the price on the second day of the sale. To find the price on the second day, we need to calculate the reduction on the first day and subtract it from the original price:

Reduction on first day = 20/100 × £450 = £90

Price on second day = £450 - £90 = £360

On the second day of the sale, the price of the television is reduced by 20% of £360, which is:

20/100 × £360 = £72

So the price of the television on the third day of the sale is:

£360 - £72 = £288

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70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. To find the time it takes to find a parking space 70% of the time, we need to find the z-score that corresponds to the 70th percentile.

Using a z-table, we find that the z-score corresponding to the 70th percentile is 0.52. Using the formula z = (x - μ) / σ, where x is the value we are trying to find, μ is the mean, and σ is the standard deviation, we can plug in the values and solve for x:

0.52 = (x - 5) / 2

x - 5 = 0.52 * 2

x - 5 = 1.04

x = 6.04

Therefore, 70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

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By dragging the number cards to form the lowest sum possible and substituting that sum into the formula for x, we can make the value of x as small as possible.

The formula for x is x = (a + b + c + d)/4. In order to minimize the value of x, we should aim to make the sum of a, b, c, and d as small as possible. To do this, we can drag the number cards to form the lowest sum possible. For example, if the number cards are 5, 6, 7, and 8, we can drag them to form the sum of 26 (5 + 6 + 7 + 8 = 26). To calculate the value of x, we can substitute the sum of the numbers in the formula and divide it by 4. In this example, x = (26/4) = 6.5. By using this strategy, we can minimize the value of x and make it as small as possible.

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Complete question:

What is the smallest value for x when you drag the number cards?

is it a option ? or no cuz im a litlle confused

Thus, the cοοrdinates οf Pοint S after dilatiοn with sοurce as the center as well as a scale factοr οf 12 are (24, 36). Take nοte that nοne οf the answer chοices fit this result, hence they are all errοneοus.

There are nο measurements like length, width, οr thickness fοr a pοint. A star inside the sky οffers us a nοtiοn οf pοint. The tip οf a ruler, the pοinted end οf a pencil, and the pοinted pοint οf a needle are sοme further examples οf pοints.

Pοint S's cοοrdinates are (2, 3).

We can use the given equatiοns tο dο a dilatiοn with οrigin as the center and a scale parameter οf 12:

(x', y') = (kx, ky)

Wherein (x, y) are the pοint's initial cοοrdinates, (k), the iteratiοns, and (x', y'), the new cοοrdinates fοllοwing dilatiοn.

Inputting the values results in:

(x', y') = (122, 123)

= (24, 36)

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The probability that the next chew Myesha removes from the bag will be a flavor other than lime is 82%.

What is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent the degree of uncertainty about whether the event will occur or not.

Out of the 17 times Myesha performed the experiment, a lime chew was selected 3 times. Therefore, the probability that the next chew Myesha removes from the bag will be a lime chew is 3/17.

To find the probability that the next chew Myesha removes from the bag will be a flavor other than lime, we need to subtract the probability of getting a lime chew from 1.

P(flavor other than lime) = 1 - P(lime)

P(flavor other than lime) = 1 - 3/17

P(flavor other than lime) = 14/17

To express this probability as a percent to the nearest whole number, we multiply by 100 and round to the nearest integer:

P(flavor other than lime) = 14/17 x 100

P(flavor other than lime) = 82.35

P(flavor other than lime) ≈ 82%

Therefore, the probability that the next chew Myesha removes from the bag will be a flavor other than lime is approximately 82%.

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The area of composite figure composed of a sector and triangle is 95.52 cm²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

To get the area of the composite figure, we add the area of the sector to the area of the triangle.

Area of circle sector = (Ф / 360) * π * radius²

but Ф = 82°, radius = 10 cm, π = 3.14, hence:

Area of circle sector = (82 / 360) * 3.14 * 10² = 71.52 cm²

Area of triangle = (1/2) * base * height

but base = 6 cm, height = 8 cm, therefore:

Area of triangle = (1/2) * 6 * 8 = 24 cm²

Area of composite figure = 24 cm² + 71.52 cm² = 95.52 cm²

The area of composite figure is 95.52 cm²

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7 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat for two events based on laws of probability multiplication.

The probability multiplication method can be used to determine the number of persons who own both a dog and a cat if we assume that owning either one is an independent occurrence.

We are aware that 15 out of the 30 people—or 50%—have cats. Also, 12 out of the 30 people, or 40%, are dog owners. The likelihood of owning both a cat and a dog is just the sum of the probabilities of owning both a cat and a dog if we believe that these events are unrelated:

P(having a dog and a cat) = P(having a cat) * (owning a dog)

P (having a dog and a cat) equals (15/30) * (12/30).

P(having a dog and a cat) = 0.25

7.5 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat. We cannot allow a fraction of a person to possess both a cat and a dog though, as we are dealing with a discrete number of people. As a result, we can round to the next whole number or down. As there cannot be a half of a person in this situation, we would round down to 7 people having both a dog and a cat.

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After calculations, we find that the company saves a total of $12 x 160 = $1,920 per month by having Alex work instead of a paid employee.

In this scenario, the company has three unpaid interns, including P. Alex, who are working in exchange for college credit. This means that the company does not have to pay these interns any salary or wages.

If the company were to hire a paid employee instead of having an intern like Alex work, they would have to pay that employee $12 per hour for the work that needs to be done. This is the amount that the company would have to spend in wages for each hour worked by the employee.

Now, we know that Alex works for the full 8 hours per day, and for 20 workdays in a month. This means that she works a total of 8 x 20 = 160 hours in a month.

Therefore, the total amount of money the company would have to pay a paid employee for the same amount of work that Alex does would be $12 per hour x 160 hours = $1,920.

Since Alex is working for the company without any payment, the company saves the entire amount of $1,920 per month that they would have had to pay a paid employee to do the same work.

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Answer:

(6, -1)

Step-by-step explanation:

The midpoint formula, (y2+y1)/2 and (x2+x1)/2 will help us find our answer. So (2-4)/2= -1 and (7+5)/2=6, so (6,-1) is the midpoint of segment AB.

The simplified expression of (x - 4)/2(x - 3) - (x - 1)/2x is -3/(2x).

The given expression (x - 4)/2(x - 3) - (x - 1)/2x can be simplified to;

(x - 4)/(2x - 6) - (x - 1)/2x

To solve this expression, we need to first find a common denominator for the two fractions.

The least common multiple of the denominators 2x and 2x - 6 is;

2x( x - 3)

So we'll multiply the first fraction by (x - 3)/(x - 3) and the second fraction by (x - 3)/(x - 3) to get a common denominator:

((x - 4)/(2x - 6)) · ((x - 3)/(x - 3)) - ((x - 1)/(2x)) · ((x - 3)/(x - 3))

Now we can combine the numerators over the common denominator:

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

Expanding the parentheses and combining like terms, we get:

(x² - 7x + 12 - x² + 4x - 3)/(2x(x - 3))

Simplifying the numerator, we get:

(-3x + 9)/(2x(x - 3))

Now we can factor out a -3/2 and simplify:

(-3/2) · (x - 3)/(x(x - 3))

The (x - 3) terms cancel out, leaving us with:

(-3/2) · 1/x

= -3/(2x)

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He can feed 15 cows till 36 days because earlier he feed 12 cows till 42 days. So we see we uses the concepts inversely proportional.

In this type of proportional is if their are two quantities then if first one is increase then automatically second one is decrease.

Suppose if a, b are two variables , and if they are indirectly proportional then we can write it as a ∝ 1/b , that means xy = k(where k is constant).

Let number of day be x days.

and, total number of cows = 12 + 3 (After he buy 3 more cow)

then, Number of cows and the number of days are inversely proportion.

So, we can write  [tex]\frac{12}{15} = \frac{x}{45}[/tex]

[tex]= x * 15 = 12 * 45[/tex]

[tex]\implies x = 36\ days[/tex]

So, He can feed 15 cows till 36 days.

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Question in English :

A farmer has feed to feed his 12 cows for 45 days. if he buys 3 more cows, How long does the feed last?

The amounts of each type of animal are given as follows:

The amounts are obtained solving a system of equations, for which the variables are given as follows:

In this year's winter mammal census, the total number of wolves and deer counted 495, hence:

x + y = 495.

x = 495 - y.

Last year 7 times as many deer and 9 times as many wolves were counted for a total of 3775 mammals, hence:

7x + 9y = 3775.

Replacing the first equation into the second, the value of y is given as follows:

7(495 - y) + 9y = 3775

2y = 310

y = 310/2

y = 155.

Then the value of x is given as follows:

x = 495 - 155

x = 340.

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The sample standard deviation of Ervin's scores is 41.81.

In this problem, we are given the scores of 7 games bowled by Ervin, and we are asked to calculate the sample standard deviation of these scores. To calculate the sample standard deviation, we first need to calculate the sample mean, which is the sum of the scores divided by the number of games:

mean = (155 + 165 + 138 + 172 + 127 + 193 + 142) / 7 = 138.57

Next, we need to calculate the variance, which is the sum of the squared differences from the mean, divided by the number of games minus one:

variance = [(155-138.57)² + (165-138.57)² + (138-138.57)² + (172-138.57)² + (127-138.57)² + (193-138.57)² + (142-138.57)²] / (7-1) = 1749.62

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

standard deviation = √(variance) = √(1749.62) = 41.81

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The correct option is a low return rate; eliminating interviewer bias. Mail surveys have the concern of low return rate but have the advantage of eliminating interviewer bias.

A mail survey is a form of a self-administered survey in which the questionnaire is sent to the respondent through the post. Mail surveys are convenient because they allow participants to respond on their schedule and in the privacy of their own homes.

Mail surveys have the concern of a low return rate but have the advantage of eliminating interviewer bias. The concern of mail surveys is a low return rate. One of the greatest advantages of mail surveys is that they do not require any interaction between the researcher and the respondent. Mail surveys' response rate is typically lower than phone or face-to-face surveys. However, it eliminates interviewer bias.

Interviewer bias occurs when the interviewer's characteristics or behavior have an impact on the participant's responses. Interviewer bias can occur in face-to-face interviews or phone surveys. Respondents may attempt to please the interviewer or present themselves in a more favorable light than they otherwise would in order to avoid social disapproval.

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To solve for x, we need to simplify the left side of the equation by combining like terms and then isolate x on one side of the equation.

First, let's combine the like terms:

5x + 3x = 8x

-7 + 27 = 20

So the equation simplifies to:

8x + 20 = 180

Next, let's isolate x by subtracting 20 from both sides:

8x + 20 - 20 = 180 - 20

8x = 160

Finally, we can solve for x by dividing both sides by 8:

8x/8 = 160/8

x = 20

Therefore, the solution for x is 20.

Answer:

x>1 or x≥4

Step-by-step explanation:

-2x+5>3 or x-5≥-1

-2x>3-5 or x≥-1+5

-2x>-2 or x≥4

-2x/-2>-2/-2 or x≥4

x>1 or x≥4

To determine whether it is valid to claim that the amount of is lower, we need to compare this probability to our chosen cut-off for unusual events, which is 5%.

To find the probability of randomly selecting 37 with a mean of   [tex]0.897 g[/tex]  or less, we need to calculate the z-score and look up the corresponding probability in the standard normal distribution table.

Where X is the sample mean   [tex](0.897 g),[/tex] μ is the population mean (0.951 g), σ is the population standard deviation [tex](0.299 g)[/tex]  , and n is the sample size (37).

Plugging in the values, we get:

[tex]z = (0.897 - 0.951) / (0.299 / sqrt(37)) = -1.731[/tex]

Looking up the corresponding probability in the standard normal distribution table, we find that   [tex]P(Z < -1.731) = 0.0419[/tex] (rounded to 4 decimal places).

Since the calculated probability is greater than 5%, we cannot reject the null hypothesis that the mean amount of has not changed. In other words, the evidence is not strong enough to support the claim that the amount of nicotine is lower.

Therefore, the probability of randomly selecting 37 with a mean of  [tex]0.897 g[/tex] or less is [tex]0.0419[/tex] .

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[tex] \boxed{ \tt \purple{ x \: = \frac{1}{3} }}[/tex]

_________

[tex] \texttt{3x = 1} \\ \tt \blue{ x = \frac{1}{3} }[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps-

There will be enough room for Mike since the diagonal is more than 13 inch

The diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. It passes through the center of the cuboid and represents the longest distance between any two points in the cuboid.

If the diagonal is less than 13 inch then there will not be enough room if otherwise then there will be enough room

To find the diagonal of a cuboid, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In a cuboid, if we label the length, width, and height

diagonal = √(length^2 + width^2 + height^2)

diagonal = √(10^2 + 8^2 + 12^2)

diagonal = √308

diagonal = 17.5 to 1 decimal place

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Answer:

y=2x -5 is the answer of above mentioned questions

Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

What is Hamilton's method?

To use Hamilton's method, we need to calculate each state's priority by dividing its population by the geometric mean of its current seat and the next higher integer seat.

Then, we assign seats based on priority until we reach the total number of seats (in this case, 100).

State Population Standard Quota

A              5.6                      18

B              6.8                      22

C              3.6                      12

D              3.2                      10

E              5.2                      17

To calculate priorities, we first find the geometric mean of the current seat and the next higher integer seat for each state:

State A: sqrt(18*19) ≈ 18.49

State B: sqrt(22*23) ≈ 22.94

State C: sqrt(12*13) ≈ 12.68

State D: sqrt(10*11) ≈ 10.49

State E: sqrt(17*18) ≈ 17.89

Then, we divide each state's population by its corresponding priority:

State A: 5.6/18.49 ≈ 0.303

State B: 6.8/22.94 ≈ 0.296

State C: 3.6/12.68 ≈ 0.284

State D: 3.2/10.49 ≈ 0.305

State E: 5.2/17.89 ≈ 0.291

We then assign seats based on priority, starting with the highest priority and rounding down to the nearest integer:

State D: 30 seats

State A: 18 seats

State E: 17 seats

State B: 22 seats

State C: 13 seats

This adds up to 100 seats, as required.

Therefore, the apportionment under Hamilton's method is:

State Apportionment

A             18

B             22

C             13

D             30

E             17

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