Town A and Town were located close to each other, and recently merged into one city. Town A had a population with 12% whites. Town B had a population with 10% whitesAfter the merge, the new city has a total of 5000 residents, with 10.56% whitesHow many residents Town A and Town used to have?

The rule of dilation is a dilation by a scale factor of 2

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

The scale factor is calculated as

Scale factor  = A'/A

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

Scale factor  = (2, 2)/(1, 1)

Evaluate

Scale factor  = 2

Hence, the rule of dilation is (2x, 2y)

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The information given in the table is the number of bullseyes hit by each team in a dart competition.

The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.

The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer

We have,

The information given in the table is the number of bullseyes hit by each team in a dart competition.

The organizer wants the display to show the performance of each team in hitting the bullseye in the competition.

The display will allow the audience to compare the performance of different teams and draw conclusions about which team performed better in hitting the bullseye.

The display will be analyzed by comparing the number of bullseyes hit by each team.

The team with the highest number of bullseyes will be considered the best performer, while the team with the lowest number of bullseyes will be considered the worst performer.

The audience may also analyze the performance of each team in relation to their expectations or previous performance in similar competitions.

Thus,

The information on the data displayed and its analysis is given above.

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The intervals that could be used based on the information will be:

The frequency distribution will be:

Interval Frequency

0-3. 2

4-7. 6

8-11. 4

12-16 8

Lastly, it should be noted that to work out which bar is the tallest, we must compare the frequencies of all the intervals. In our case here, the interval with a frequency of 8, 12-16, has the highest value and therefore its bar will be the tallest in the histogram.

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The slope of f(x) is less than the slope of g(x).

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know two points on a line, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values.

So the slope of f(x) is:

a = (3 - 0)/(0 + 2) = 3/2

And g(x) = (4/5)*x - 2

So here the slope is 4/5

We can see that clearly the slope of g(x) is larger.

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4.) The statement that is not true about the cube box is that the volume of the box is one square foot. That is option C.

5.) All the possible dimensions of the bottom layers include the following;

when length= 4 units; width = 3units

when length = 3 units; width = 4 units

when length = 2 units; width = 6 units

To calculate the volume of a cube box the formula that should be used = a³

where a = 1³

volume = (1×1×1) = 1ft³

The area of the cube = 6(a²)

But a = 1

area = 6(1²)

= 6ft²

Therefore the wrong statement is that the volume of the box is one square foot instead of 1ft³.

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Polynomial M is 2(x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/72)[tex]a^{2}[/tex] + by

To find the polynomial M, we need to rearrange the equation given to us. We can start by adding M to both sides of the equation to isolate the constant term. This gives us:

2[tex]x^{2}[/tex] - (1/3)ax + by = M

Now, we have the polynomial M in terms of x, a, b, and y. However, this is not in its simplest form yet. We can simplify this further by factoring out the coefficient of x. This gives us:

2([tex]x^{2}[/tex] - (1/6)ax) + by = M

Now, we can complete the square inside the brackets to get a perfect square trinomial. This means taking half of the coefficient of x, squaring it, and adding it and subtracting it inside the brackets. This gives us:

2((x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/144)[tex]a^{2}[/tex]) + by = M

Simplifying this further, we get:

2(x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/72[tex]a^{2}[/tex] + by = M

Therefore, the polynomial M is given by:

M = 2(x - [tex](\frac{1}{12}a)^{2}[/tex]  - (1/72)[tex]a^{2}[/tex] + by

This is the final answer for the polynomial M.

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The y-values are 5, 2, 1, 2, 5, 10 and 17.

Given that an equation of a curve, y = x²+1, we need to find the values of the y-intercept corresponding to the given x-intercept,

So,

y = x²+1

Putting the values of x,

x = -2,

y = (-2)²+1

y = 5

(-2, 5)

x = -1

y = (-1)²+1

y = 2
x = 0,

y = (0)²+1

y = 1

x = 1

y = 2

x = 2,

y = 2²+1

y = 5

x = 3,

y = 3²+1

y = 10

when x = 4,

y = 4²+1

y = 17

Hence, the y-values are 5, 2, 1, 2, 5, 10 and 17.

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Step-by-step:

ANALYSIS:

From the question, we know that...

• 310m from his home to the meeting

• Average speed RETURNING: 7 mph LESS than the speed he went on

• Total time = 12 hours

• Rate of speed = ?

-Round off to the nearest TENTH-

EXPLANATION:

Speed = Distance / Time

• S = 310/12

• S = 25.83333... mph

• S = 25.83 (round off)

Then it says that speed returning is -7 from the speed he went on, so...

• 25.83 - 7 = 18.83 mph

Rounding off to the nearest TENTH:

18.83 = 18.8 mph

Final Answer : 18.8 mph

The probability that they win the next game and player on the New York Liberty being over 73 inches​ is 53% and 50%

We are given that;

Games= 35/35

Now,

We can use the past performance of the Knicks as an estimate of their probability of winning a game. They won 35 games out of 65 games, so their probability of winning a game is:

P(win) = 35/65 P(win) = 0.538

To find the experimental probability of a player being over 73 inches, we need to count how many players are over 73 inches and divide by the total number of players. There are six players who are over 73 inches, so the experimental probability is:

P(over 73 inches) = 6/12 P(over 73 inches) = 0.5

Therefore, by probability the answer will be 53% and 50%.

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Answer:

A. 115

B. 65

C. 115

D. 65

E. 115

F. 665

G. 115

Step-by-step explanation:

a straight line is a 180 degree angle. If one of 2 angles is 65 degrees the other angle will be 115 because 180-65= 115

since both lines on the graph are parallel the angles will be coresponding.

The requried probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

Standardize 85 and 115 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 85:

z = (85 - 100) / 15 = -1

For 115:

z = (115 - 100) / 15 = 1

So we want to find the probability that a standard normal random variable Z is between -1 and 1. Using a standard normal distribution table or a calculator, we can find that this probability is 0.6827.

Since IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, the probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.

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Answer: 55/60

Step-by-step explanation:

Answer:

Step-by-step explanation:

Points on line= (-4,5) and (1,2)

use slope formula: M= y2-y1 divided by X2-X1

Filling into the formula: M=2-5 divided by 1+4

M (slope) = -3/5

The translation is of 5 units to the right and 3 units down, it can also be written as:

(x, y) ---> (x + 5, y - 3)

To study the translation, just look at some vertex in both figures.

The top left vertex of F is at (2, 7)

And the top left vertex at G is (7, 4)

Taking the difference between these, we will get:

(7, 4) - (2, 7) = (5,, - 3)

Then the translation from F to G can be defined as:

(x, y) ---> (x + 5, y - 3)

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The total area of the table runner is 858 square inches

Given that Table Runner has an overall length of 72" and a width of 13",

Area = length ×width

=60×13

=780 sq in

Area of triangle = 1/2×base ×height

=1/2×13×6

=39

There are two triangles so area is 2(39) = 78

Total area is 936+78

=858 square inches

Hence, the total area of the table runner is 858 square inches

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Answer:

-34/3

Step-by-step explanation:

I've provided the explanation from my e-board in a picture below

Answer:1/25

Step-by-step explanation:100/25=4. So 1/25 of the box.

The percent of saline solution in brand B  is 10.83%

Let's assume that brand B has x gallons of the 100% saline solution.

The amount of salt in brand A is 18% of 6 gallons = 0.18 * 6 = 1.08 gallons.

When the two brands are mixed, the total volume of the mixture is 6 + x gallons, and the total amount of salt is 1.08 + x gallons.

Since the resulting mixture is 18 gallons of 8% saline solution, we can set up the equation:

(1.08 + x) / (6 + x) = 0.08

Solving for x, we get:

1.08 + x = 0.48 + 0.08x

0.92x = 0.6

x = 0.65

So, brand B has 0.65 gallons of the 100% saline solution.

Therefore, the percent of saline solution in brand B is:

0.65 / 6) * 100% = 10.83%, which rounded to the nearest whole number is 11%.

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The type of transformation shown is vertical translation. That is option D.

Transformation of geometrical figures or points is the manipulation of a given figure to take the same shape but with different direction of its original angles.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given a polygon ABDC.

It is transformed to another polygon with the same size A'B'D'C'.

Here the polygon ABDC is just moved downwards as it is and mark is as A'B'D'C'.

In rotation or reflection transformation, the points will change it's correspondent place.

Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.

Since the shifting is done vertically, it is vertical translation.

Hence the transformation is vertical translation.

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Answer:

  8

Step-by-step explanation:

Brenda sold 2 brass signs of the 10 signs she sold this week. You want an estimate of the number of brass signs she will sell out of the next 40.

We expect the proportion of brass signs to remain the same, so the number (x) of brass signs in the next 40 signs is expected to be ...

  x/40 = 2/10

  x = 40(2/10) = 8

We estimate Brenda will sell 8 brass signs out of the next 40 signs she sells.

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A graph is a visual representation or diagram that shows facts or values in an ordered way. The only graph that satisfies the above shape is the third one.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between multiple items are frequently represented by the points on a graph. The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects. The only graph that satisfies the above shape is the third one.

Therefore, the correct option is option C.

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

Answer:

  8 cm³

Step-by-step explanation:

You want the volume of Prism B similar to Prism A, where the volume of Prism A is 216 cm³, its height is 9 cm, and the height of Prism B is 3 cm.

The ratio of volumes is the cube of the ratio of heights:

  (Prism B volume)/(Prism A volume) = ((Prism B height)/(Prism A height))³

  (Prism B volume)/(216 cm³) = ((3 cm/(9 cm))³ = 1/27

  Prism B volume = (216 cm³)·(1/27) = 8 cm³

The volume is 8 cubic centimeters.

Answer:

The answer is D. 60

Step-by-step explanation:

We can use the formula for calculating z-score to find out how many points Gregor scored on the Stats exam. The z-score formula is:

z = (x - μ) / σ

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

We know that the population mean (μ) is 75 points and the population standard deviation (σ) is 5 points. We also know that Gregor's z-score (z) is -3. Substituting these values into the formula, we get:

-3 = (x - 75) / 5

Simplifying the equation, we get:

-15 = x - 75

Adding 75 to both sides, we get:

x = 60

Therefore, Gregor scored 60 points on the Stats exam. The answer is (D) 60.

The volume of the smaller box is 900 cm³.

We have,

The dimensions of the smaller box are half the dimensions of the larger box.

Length = 24/2 = 12 cm

Width = 10/2 = 5 cm

Height = 30/2 = 15 cm.

The volume of the smaller box is the product of these dimensions:

Volume = length × width × height

= 12 cm × 5 cm × 15 cm

= 900 cm³

Therefore,

The volume of the smaller box is 900 cm³.

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The area of the face of a clock with a circumference of 14 inches is approximately 15.6 square inches. This is calculated using the formula for the area of a circle, which is πr², where r is the radius of the circle.

To find the area of the face of the clock, we need to use the formula for the area of a circle, which is

A = πr²

where A is the area of the circle, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle.

Since the circumference of the clock is 14 inches, we can use the formula for the circumference of a circle to find the radius

C = 2πr

14 = 2πr

r = 14 / (2π)

r = 2.227 in (approx)

Now that we know the radius, we can use the formula for the area of a circle

A = πr²

A = 3.14 x (2.227)²

A = 15.6 sq in (approx)

Therefore, the area of the face of the clock is approximately 15.6 square inches.

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The new mixture contains 34% peanuts. The correct option is A

The idea of weighted averages can be applied.

First, let's determine the mixture's entire weight:

Total weight = 4 kg + 12 kg = 16 kg

We can now calculate how many peanuts there are overall in the mixture:

Total weight in kilograms is =  (4 kg) (0.16) + (12 kg) (0.40)

= 0.64 kg + 4.80 kg

= 5.44 kg.

Finally, we can find the percentage of peanuts in the mixture:

Percent of peanuts = (Total amount of peanuts / Total weight) x 100%

= (5.44 kg / 16 kg) x 100

   = 34%

Therefore, the new mixture contains 34% peanuts, which is option A.

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The interval that is likely to contain the exact percent of all US adults who would support the policy is 0.7 ± 0.022.

Since the sample size is large (n = 2000) and the proportion of respondents who support the policy is 0.7, we can use the normal distribution to approximate the sampling distribution of the sample proportion.

The margin of error is ±2.2%, which means that we need to construct a 95% confidence interval. The critical value for a 95% confidence interval with a two-tailed test is approximately 1.96.

The formula for a confidence interval for a population proportion is:

sample proportion ± z* (standard error)

sqrt((sample proportion * (1 - sample proportion)) / n)

Substituting the values:

Therefore, the 95% confidence interval for the percentage of all U.S adults who would support a national policy requiring rooftop solar panels to be installed on all new homes is 0.678 - 0.722.

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The solutions to the equation [tex]x^{2}[/tex] - 6x = 7 are x = 7 and x = -1.

To solve the equation [tex]x^{2}[/tex] - 6x = 7, we need to first bring all the terms to one side, so subtracting 7 from both sides gives us [tex]x^{2}[/tex] -6x - 7 = 0.

Next, we can use the quadratic formula, which is x = (-b ± [tex]\sqrt{b^{2}-4ac}[/tex]) / 2a, where a, b, and c are the coefficients of the quadratic equation a[tex]x^{2}[/tex]+bx+c=0.

In this case, a=1, b=-6, and c=-7, so plugging these values into the formula gives us x = (6 ± [tex]\sqrt{6^{2}-4(1)(-7) }[/tex]) / 2(1).

Simplifying further, we get x = (6 ± [tex]\sqrt{64}[/tex]) / 2, which can be written as x = 3 ± [tex]\sqrt{16}[/tex].

Therefore, the solutions to the equation [tex]x^{2}[/tex]-6x=7 are x = 3 + [tex]\sqrt{16}[/tex] = 3 + 4 = 7 and x = 3 - [tex]\sqrt{16}[/tex] = 3 - 4 = -1.

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Find the limit...

[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )[/tex]

Factor the top and bottom of the expression.

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{(x+2)(x-2)}{3x(x-2)} )[/tex]

Cancel the common factor "(x-2)."

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{x+2}{3x} )[/tex]

Now plug in the limit.

[tex]\Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{2+2}{3(2)} ) \Longrightarrow \lim_{x \to 2} tan^{-1}(\frac{4}{6} )=\boxed{tan^{-1}(\frac{2}{3} )}[/tex]

[tex]\lim_{x \to 2} tan^{-1}(\frac{x^2-4}{3x^2-6x} )=\boxed{\boxed{tan^{-1}(\frac{2}{3} )}} \therefore Sol.[/tex]

Thus, the limit is solved.

The radius of the circle is 6 inches and the circumference is 30.84 in

For a circle of radius R, the circumference is given by:

C = (pi*R + 2*R)

Where pi = 3.14

For the given semicircle, we can see that the diameter is 12 inches. Then the radius is half of that, we will get.

R = D/2 = 12in/2 = 6 inches.

Now we can replace that in the circumference formula to get.

C = (3.14*6in + 2*6in)

C = 30.84 in

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