How many
1/4-foot cubes would fill the inside of the prism?
​Write the answer in the box.

The factorized form of the equation is 3((3x + 10)(9x - 10) ) = 0.

The given quadratic equation is simplified as follows;

81x² + 180x - 200 = 100

Collect similar terms together;

81x² + 180x = 100 + 200

81x² + 180x = 300

81x² + 180x - 300 = 0

Factorize the equation by using a common factor;

3(27x² + 60x - 100) = 0

Factorize further as follows;

3(27x² + 90x - 30x - 100) = 0

3( 9x (3x + 10) - 10(3x  + 10) )= 0

3((3x + 10)(9x - 10) ) = 0

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Answer:

Step-by-step explanation:

The difference between the median math test score in the morning and the afternoon is 9.5

The median can simply be described as the middle number in a given set of data when the values are arranged in an order from least to the greatest values.

From the information given, we have that;

The math scores for the afternoon test were;

55, 70, 76, 85, 95

The math scores for the morning test were;

70, 80.5, 85.5, 90.5 and 95.5

Hence,

The median for the afternoon test = 76

The median for the morning test =85.5

The difference between the values would be = 85.5 - 76 = 9. 5

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Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1

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

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

Evaluating the like terms, we have

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

Cancel out the common factors

So, we have

(x - 2) = 1

Add 2 to both sides

x = 3

Hence, the solution is 3

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Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

Step-by-step explanation:

We have the system of equations:

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

-1/x + 8/y = -6 -----(2)

We can use the substitutions u = 1/x and v = 1/y to rewrite the equations in terms of u and v. Substituting, we get:

u + 2v = 1 -----(3)

-u + 8v = -6 -----(4)

Now we can solve the system in terms of u and v. Adding equations (3) and (4) gives:

2v = -5

Dividing both sides by 2, we get:

v = -5/2

Substituting this value of v into equation (3) gives:

u + 2(-5/2) = 1

Simplifying:

u - 5 = 1

u = 6

Therefore, we have u = 6 and v = -5/2.

To find the solution set in terms of x and y, we substitute back:

u = 1/x, so 6 = 1/x, and x = 1/6

v = 1/y, so -5/2 = 1/y, and y = -2/5

Therefore, the solution set to the original system is x = 1/6 and y = -2/5.

The total cost of the art supplies without the coupon is:

2 paint brushes x $10.50 per brush = $21.00

1 dozen colored pencils x $7.88 per dozen = $7.88

1 sketch book x $16.12 per book = $16.12

Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00

With the $15.00 off coupon, the total cost becomes:

$45.00 - $15.00 = $30.00

The amount saved by using the coupon is:

$45.00 - $30.00 = $15.00

The percentage saved can be calculated as:

Percentage saved = (Amount saved / Total cost without coupon) x 100%

Percentage saved = ($15.00 / $45.00) x 100%

Percentage saved = 33.33%

Therefore, the customer saved 33.33% by using her coupon.

We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:

Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:

Total momentum before = Total momentum after

(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)

Simplifying and solving for v, we get:

v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg

v = 2.85 m/s

Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.

Answer:

Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.

Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.

From the problem, we know that the sum of the areas of the two carpets is 720 square feet:

x^2 + y^2 = 720

We also know that the difference of the areas of the two carpets is 432 square feet:

x^2 - y^2 = 432

We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:

x^2 = y^2 + 432

Substituting this expression for x^2 into the first equation, we get:

y^2 + 432 + y^2 = 720

Simplifying and solving for y, we get:

2y^2 = 288

y^2 = 144

y = 12

Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:

x^2 + 144 = 720

x^2 = 576

x = 24

Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.

Step-by-step explanation:

The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.

The graph of the solution set of -48 < -8t is shown below.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Next, we would determine the solution to the given inequality as follows;

2.5x ≥ 20

x ≥ 20/2.5

x ≥ 8 (Sebastian was wrong)

-48 < -8t

-48/-8 < -8t/-8

6 < t

t > 8

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Answer:

0

Step-by-step explanation:

By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.

In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:

A''(x, y) = (4, - 1) + (- 3, - 2)

A''(x, y) = (1, - 3)

B''(x, y) = (1, 1) + (- 3, - 2)

B''(x, y) = (- 2, - 1)

C''(x, y) = (0, - 3) + (- 3, - 2)

C''(x, y) = (- 3, - 5)

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By solving equations we get to know that your cousin bought 356 shares of BP and 1448 shares of Exxon.

Initial investment:

x shares of BP at $90.75 per share + y shares of Exxon at $87.25 per share = $97,918.25

Sale of shares:

x shares of BP at $82.75 per share + y shares of Exxon at $61.25 per share = $74,090.25

We now have two equations with two variables, which we can solve using either substitution or elimination

0.875x($90.75) + 0.875y($87.25) = $85,648.23

x($82.75) + y($61.25) = $74,090.25

0.875x($90.75) - x($82.75) = $11,558.98 - 0.875y($87.25) + y($61.25)

0.875x($8) = $11,558.98 - 0.875y($26)

7x = $11,558.98 - $22.75y

We can then substitute this expression for "x" into either of the original equations to solve for "y".

(7($11,558.98 - $22.75y))/$8 + y($87.25) = $97,918.25

$81,763.03 - $19.9375y + $87.25y = $97,918.25

$7.0125y = $10,155.22

y = 1448

and x = 356

Hence, your cousin bought 356 shares of BP and 1448 shares of Exxon.

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The Cost of the blue paint that would cover the shaded area = $0.495

The Cost of the white paint that would cover the triangular shapes = $0.6678

Recall the following formulas:

Area of a circle = πr²

Area of a triangle = 1/2 * base * height.

Area the blue paint will cover = 2(1/2 * base * height) = 2(1/2 * 1.5 * 1)

= 1.5 ft²

Cost of the blue paint = 1.5 * 0.33 = $0.495

Area the blue paint will cover = πr² - area of the two triangles

= 3.14 * 1.5² - 1.5 = 5.565 ft²

Cost of the white paint = 5.565 * 0.12 = $0.6678

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Answer: C

Step-by-step explanation:

Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.

The histogram is solved and the data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.

Given data ,

Let the number of observations of each interval is:

1 to 5: 2 observations.

6 to 10: 5 observations.

11 to 15: 2 observations.

16 to 20: 6 observations.

21 to 25: 1 observations.

Let the maximum range be represented as M

And , there are two similarly high bins for the histogram , hence the distribution can be said to be bimodal, with maximum range given as follows

M = 25 - 5

M = 21 - 1

M = 20

Hence , the histogram is solved

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The density in trees per acre upon completion will be 500 trees per acre.

In this scenario, let's say the landscaping provider donates 2750 seedlings.

Density of trees per acre = Total number of trees / Total area of land

Hence, applying the formula leads us to:

Density of trees per acre = 2750 trees / 5.5 acres

The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.

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Answer:

Step-by-step explanation:

Let A(-2,-3), B(-4,-4).

Line f(x) = y = ax + b (C)

The line passes through these points so when substituting their coordinates into (C), we get:

-3 = -2a + b

-4 = -4a + b

Solving this set of equations gives us a = 1/2; b = -2.

So the equation of this line is  [tex]f(x)=\frac{1}{2}x-2[/tex]

D. The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is given as follows: 0.7340 = 73.40%.

E. The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is given as follows: 0.0968 = 9.68%.

F. The 75th percentile for the height of giraffes is given as follows: 18.54 ft.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 18, \sigma = 0.8[/tex]

The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is the p-value of Z when X = 18.5, hence:

Z = (18.5 - 18)/0.8

Z = 0.625

Z = 0.625 has a p-value of 0.7340.

The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is the p-value of Z when X = 19.9 subtracted by the p-value of Z when X = 19, hence:

Z = (19.9 - 18)/0.8

Z = 2.375

Z = 2.375 has a p-value of 0.9912.

Z = (19 - 18)/0.8

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

Hence:

0.9912 - 0.8944 = 0.0968 = 9.68%.

The 75th percentile is X when Z = 0.675, hence:

0.675 = (X - 18)/0.8

X - 18 = 0.8 x 0.675

X = 18.54 ft.

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The value of the expression is 28 2/3

To determine the value of addition, we need to know that fractions are described as part of a whole number or variables.

From the information given, we have that;

1/9 times 3 to the 3rd power

This is represented as;

(1/9 × 3)³

Divide the values, we get

(3)³

Find the cube

27

Then, we have;

27 + 2(1/6+2/3)

Solve the bracket

27 + 2( 1+ 4 /6)

27 + 2(5/6)

Divide the values

27 + 5/3

81 + 5/3

86/3

Divide the values

28 2/3

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Answer:

The Correct answer is D and F

The cost of shelving Nathaniel’s DVD collection is 15.75×27=$425.25.

We are given that;

Dimensions =7.5in, 5.3in, 0.6in

To find the cost of shelving Nathaniel’s DVD collection, we need to find how many shelves he needs and multiply that by the price of each shelf. To find how many shelves he needs, we need to find how many DVDs can fit on one shelf and divide that by the total number of DVDs.

Since the shelves are 31.5 inches wide and the DVDs are 5.3 inches wide, we can fit 5.331.5​≈5.94 DVDs on one shelf. We round this down to 5 DVDs per shelf because we cannot fit a partial DVD on a shelf.

Since Nathaniel has 132 DVDs in his collection, he needs 5132​=26.4 shelves. We round this up to 27 shelves because we cannot use a partial shelf.

Therefore, by algebra the answer will be 15.75×27=$425.25.

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The width of the brochure is 3/2 inches and the height is 10 inches.

Let's assume that the width of the brochure is x and the height is y.

The area of the brochure is given as 30 square inches:

xy = 30

The perimeter of the brochure is given as 23 inches:

2x + 2y = 23

We can use the second equation to solve for one variable in terms of the other.

2x + 2y = 23

2x = 23 - 2y

x = (23 - 2y)/2

Now we can substitute this expression for x into the equation for the area:

xy = 30

[(23 - 2y)/2]y = 30

23y/2 - y^2 = 60/2

y^2 - 23y/2 + 30 = 0

We can solve for y using the quadratic formula:

y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)

y = [23/2 ± sqrt(529/4 - 120)]/2

y = [23/2 ± sqrt(289/4)]/2

y = [23/2 ± 17/2]/2

y = 10 or y = 3/2

Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.

So, y = 10 and

x = (23 - 2y)/2 = (23 - 20)/2 = 3/2

Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.

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The probability that fewer than 30% of the rolls result in a two is given as follows:

0.3085 = 30.85%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:

n = 50, p = 2/6 = 1/3 = 0.3333.

The mean and the standard error are given as follows:

The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:

Z = (0.3 - 0.3333)/0.0667

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

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Answer: 1/2

Step-by-step explanation:

The fraction equivalent of 0.5 is 1/2.

To convert it into a mixed number, we can divide the numerator by the denominator:

1 ÷ 2 = 0 with a remainder of 1

So, the mixed number is 0 1/2.

The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487

The total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7

The probability formula will be applied ed as

P = required outcome / Total possible outcomes

From the information that is provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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The question is incomplete, Complete question probably will be  is:

The table shows the​ distribution, by age and​ gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.

The probability is ___.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

After 0.50 hours, the cyclist's new elevation is h = 1.8 km.

Since the cyclist is riding downhill, we can use the formula h = h0 - Vt sin θ to calculate her new elevation. In this formula, h0 represents her initial elevation, V her speed, t her time, and θ her angle of descent. We are given h0 = 1.9 km, V = 25 km/hr, t = 0.50 hours, and θ = 2°.

h = 1.9 km - (25 km/hr)(0.50 hours)(sin 2°)

h = 1.9 km - (25 km/hr)(0.50 hours)(0.03492)

h = 1.8282 km

h ≈ 1.8 km

Therefore, after 0.50 hours, the cyclist's new elevation is h = 1.8 km.

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The triangle with 2 angles as 90° is not possible and the statement is false.

Given data ,

Let the triangle be represented as ∠ABC

Now , the measures of the angles of the triangle are

A triangle has two 90° angles and a side 12 centimeters in length

So , ∠ABC = ∠BAC = 90°

And , For a Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Therefore, a triangle cannot be formed with 2 angles as 90°

Hence, the statement, the third angle is 90° is False

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