The volume of the triangular pyramid below is 240 units. Find the value of a.
Answer: =
12
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The number of times the Team Olympus could have tied is not given in the below options

Given data ,

Let's use "W" for the number of victories and "T" for the number of ties. The information available indicates that Team Olympus played 19 games and earned a total of 28 points.

Team Olympus receives three points for each victory, so three victories would result in a total of nine points.

Team Olympus receives one point for each tie, making the sum of the tie-related points (T) equal to one times the number of ties.

We may construct the following equation using the information provided:

3W + 1T = 28   be equation (1)

Now , Since Team Olympus played 19 games in total, the total number of games (W + T) should be equal to 19.

W + T = 19   be equation (2)

Subtracting equation (2) from equation (1) , we get

2W = 9

Divide by 2 on both sides , we get

W = 4.5 wins

And , the supplied possibilities (3, 4, 2, 5, 0) do not add up to a total of 28 points, hence none of them are acceptable answers for Team Olympus.

Hence , in this situation, Team Olympus could not have tied many times

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The equation of tangent line related to the parametric equations is equal to y = 3 · x - 22.

In this question we find the case of two parametric equations evaluated at t = - 1, whose tangent line equation must be found. Equation of the tangent line is introduced below:

y = m · x + b

Where:

First, determine the slope of the tangent line:

dx / dt = 1 + 2 · t

dx / dt = 1 - 2

dx / dt = - 1

dy / dt = 2 · t - 1

dy / dt = - 2 - 1

dy / dt = - 3

m = (dy / dt) / (dx / dt)

m = (- 3) / (- 1)

m = 3

Second, evaluate the parametric functions at t = - 1:

x = - 1 + (- 1)² + 8

x = 8

y = (- 1)² - (- 1)

y = 2

Third, determine the intercept of the tangent line:

b = y - m · x

(m = 3, x = 8, y = 2)

b = 2 - 3 · 8

b = 2 - 24

b = - 22

Fourth, write the equation of the tangent line:

y = 3 · x - 22

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The box plot that represents the data is the second box plot.

To find the box plot, look for the measure that is different in both box plots and you will find it to be the value of Q1.

Therefore find the value of Q1 in the data by Ellen by first arranging the riders in order :

0, 0, 2, 2, 3, 4, 6, 8, 8, 9, 11, 14, 16

Q1 would be at the 25 th percentile :

= 25 / 100 x 13

= 3.25 position

Q1 is therefore 2 which makes the correct box plot the second one which shows the Q1 value as 2.

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Answer:

Step-by-step explanation:

To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.

First, let's calculate the mean of the original data set:

Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67

Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:

31, 39, 50, 50, 70, 82

The median is the middle value, which is 50.

Now, let's add Becky's earnings of $23 to the data set:

31, 39, 50, 50, 70, 82, 23

The new data set has 7 values. Let's calculate the new mean:

Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14

The new mean is less than the original mean, so we can eliminate options A and C.

Now let's calculate the new median. We need to arrange the data set in order:

23, 31, 39, 50, 50, 70, 82

The median is still 50.

Therefore, the answer is option D: The mean decreases and the median remains the same.

Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.

Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.

In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:

Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet

To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:

Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles

Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

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The student is correct because we can factorize x² - x - 56 to get (x - 8)(x + 7).

How to Factorize an Expression?

In order to determine if -56 is the integer that can replace the box in the expression, we can try to factorize the expression and see if it works.

Factorize x² - x - 56 using the sum-product pattern:

x² - x - 56

Take out the common factors from each pair:

(x² + 7x) - (8x - 56)

x(x + 7) -8(x + 7)

Rewrite in factored form:

(x - 8)(x + 7)

Thus, this shows that the student is correct.

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The value of y when x = 2 is -2.

We are given that;

x = 4

y = -1

Now,

To write an equation relating x and y for inverse variation, you can use the formula123:

xy = k

where k is a constant.

To find the value of k, you can use the given values of x and y:

x = 4

y = -1

xy = k

(4)(-1) = k

k = -4

So, the equation relating x and y is:

xy = -4

To find y when x = 2, you can substitute x = 2 in the equation and solve for y:

xy = -4

(2)y = -4

y = -4/2

y = -2

Therefore, by the given equations the answer will be -2.

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The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.

Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.

Let's begin by calculating the total cost of producing 400 brownies a day:

Cost per brownie = 25 cents = 0.25 dollars

Total cost = 400 × 0.25 = 100 dollars

To make a daily profit of at least $420, the total revenue should be:

Total revenue = Total cost + Minimum profit

Total revenue = 100 + 420 = 520 dollars

The minimum selling price per brownie to achieve this revenue can be calculated as:

Selling price per brownie = Total revenue / Number of brownies produced

Selling price per brownie = 520 / 400

Selling price per brownie = 1.3 dollars

Therefore, the minimum selling price is $1.30 per brownies.

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The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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The number of miles that he would have saved instead would be = 8.6 miles

The amount of miles he traveled south = 7 miles

The amount of miles he traveled east = 5 miles

To calculate the number of miles he would have saved, the Pythagorean formula is used;

That is :

C² = a²+ b²

a = 7

b =5

c² = 7²+5²

= 49+25

= 74

c = √74

= 8.6 miles

Therefore, he would have travelled 8.6 miles instead of 12 miles.

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K's value is around 0.055 to three decimal places.

Let's first use the given information to set up two equations:

A(0) = 23 (the initial population in millions)

A(6) = 32 (the population 6 years later in millions)

Substituting these values into the exponential growth function A = 23e^(kt), we get:

[tex]23 = 23e^(k0) = > e^{(k0)} = 1\\32 = 23e^{k*6}[/tex]

Dividing the second equation by the first, we get:

[tex]32/23 = e^{6k}[/tex]

Taking the natural logarithm of both sides, we get:

ln(32/23) = 6k

Solving for k, we get:

k = ln(32/23)/6

k ≈ 0.055

Rounding to three decimal places, we get k ≈ 0.055.

Therefore, the value of k to three decimal places is approximately 0.055.

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Answer:

1. s < 40

2. w ≤ 12

3. D ≥ 110

4. D ≤ 3 1/2

5. w ≥ 30

6. m ≥ 45

7. t ≠ 21

8. c < 45

9. D > 1/5

10. s ≠ 45 5/6

11. h ≥ 48

12. P ≠ 5

1. radius = 13cm

2. Diameter = 27.2cm

3. Diameter = 24m

4.  Radius = 24. 5m

The formula used for determining the area and also the circumference of a circle is given thus;

For the  area of a circle, we have;

A = πr²

Given that the parameters are;

For the circumference of a circle, we have;

C = 2πr

To calculate the  diameter of a circle, we have the formula;

Diameter = 2Radius

Now, substitute the values for each

1. radius = diameter/2 = 26/2

radius = 13cm

2. When the radius = 13.6m

diameter = 2(13.6) = 27.2m

3. When the radius = 12m

diameter = 2(12) =  24m

4. When the diameter  = 49m

Then, radius 49/2 = 24. 5m

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Answer:

The 3rd one or C

Step-by-step explanation:

A       B

C      D

Answer:

6 × 3 = 18

18 ÷ 2 = 9

Therefore, the expression 6 × 3 ÷ 2 simplifies to 9

Step-by-step explanation:

To simplify the expression, we follow the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right.There

are no parentheses or exponents,so we multiply 6 by 3 to give us 18.

Then we divide 18 by 2 to give us 9.

There for the Expression simplifies to 9.

HOPE IT HELPS.

PLEASE MARK ❣️‼️ ME AS BRAINLIEST .

The perimeter and the area of each composite figure are, respectively:

Case 1: p = 77.6 cm, A = 304 cm²

Case 2: p = 25.1 ft, A = 28 ft²

Case 3: p = 42 mi, A = 52.5 mi²

Case 4: p = 56.5 in, A = 179.424 in²

In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we find the perimeter and the area of each figure:

Case 1

p = 2 · (18.8 cm) + 2 · (20 cm)

p = 77.6 cm

A = (15.2 cm) · (20 cm)

A = 304 cm²

Case 2

p = 10 ft + 8.1 ft + 7 ft

p = 25.1 ft

A = 0.5 · (10 ft) · (5.6 ft)

A = 28 ft²

Case 3

p = 17.5 mi + 6 mi + 18.5 mi

p = 42 mi

A = 0.5 · (17.5 mi) · (6 mi)

A = 52.5 mi²

Case 4

p = 20 in + 13.9 in + 15 in + 7.6 in

p = 56.5 in

A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)

A = 98.8 in² + 31.982 in² + 48.642 in²

A = 179.424 in²

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Answer:

There are 300 students at East High School.

Step-by-step explanation:

East High School has 1/10 as many students as West High School, which means that the number of students at East High School is equal to 1/10 of the number of students at West High School.

To find out how many students are at East High School, we can multiply the number of students at West High School by 1/10:

East High School = West High School x 1/10East High School = 3000 x 1/10East High School = 300

Therefore, there are 300 students at East High School.

Answer:

East High School has 1/10 × 3,000 = 300 students.

Answer:

Step-by-step explanation:

The population density of the neighborhood is 12000 people per square mile.

Total number of people = 1250

Number of city blocks = 30

Length of the block, l = 1/16 mile

Width of the city block, w = 1/18 mile

Area of one block, A = l x w

A = (1/16) x (1/18)

A = 1/288 square mile

Total area of all the 30 blocks, A' = 30 x A

A' = 30/288 square mile

So, the population density,

D = Total no.of people/A'

D = 1250/(30/288)

D = 1250 x 288/30

D = 12000 people per square mile.

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Sample Response: Use the inverse operation to isolate the variable. Undo the subtraction of 4 by adding 4 to both sides of the equation. –4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. Check the solution by substituting 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, so 13 is the solution.

Step-by-step explanation:

–4 + 4 = 0, and 9 + 4 is 13. The solution is q = 13. check it by taking 13 for q in the original equation, and then simplify. 13 – 4 is 9 and 9 = 9 is a true statement, 13 is the answer

The standard form of the equation of the circle with a radius of 7 and center at (0, 0) will be x² + y² = 49.

Given that:

The center is at the origin.

Radius, r = 7

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

Substitute h = 0, k = 0, and r = 7, then we have

(x - 0)² + (y - 0)² = 7²

x² + y² = 49

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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 = 515, \sigma = 125[/tex]

The proportion of scores less than 675 is the p-value of Z when X = 675, hence:

Z = (675 - 515)/125

Z = 1.28

Z = 1.28 has a p-value of 0.8997.

Hence the percentage is 89.97%.

The proportion of scores greater than 550 is one subtracted by the p-value of Z when X = 550, hence:

Z = (550 - 515)/125

Z = 0.28

Z = 0.28 has a p-value of 0.6103.

1 - 0.6103  = 0.3897, hence the amount is given as follows:

E(X) = 1000 x 0.6103 = 610.

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If "∠A" is complementing angle "∠B" and "∠C" is complementing "∠B", then the true statement is (a) ∠A ≅ ∠C, because both the angles have the same measure.

The "Complementary-Angles" are two angles that add up to 90 degrees, which is also known as a right-angle. When two angles are complementary, they are said to complement each other.

Since the angles : ∠A and ∠C are both complementary to ∠B, we can write :

⇒ ∠A + ∠B = 90°,

⇒ ∠B + ∠C = 90°,

Next, We subtract "∠B" from both sides of each equation,
We get;

⇒ ∠A = 90° - ∠B,

⇒ ∠C = 90° - ∠B,

We see that the measure of the angle "A" and angle "C" is same.

Therefore, ∠A and ∠C have the same measure, option (a) is the correct answer.

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The given question is incomplete, the complete question is

If ∠A is a complementary angle of ∠B and ∠C is a complementary angle of ∠B, then which of the following statements is true?

(a) ∠A ≅ ∠C

(b) ∠A ≅ ∠B

(c) ∠A + ∠C ≅ ∠B

(d) ∠B ≅ ∠C

Answer: Translation

Step-by-step explanation:

      To get from the pre-transformation shape (red) to the transformed image (blue), a translation takes place. This is where the shape is not rotated, reflected, or stretched, but simplify "slided" or "shifted" somewhere else.

The solutions to y = –8x for x = 2, 4, and 8 are (2, –16), (4, –32), (8, –64), hence, option D is correct.

We are given the equation y = -8x and asked to find the solutions for x = 2, 4, and 8. To find the solutions, we substitute the given values of x into the given linear equation and solve for y.

For x = 2, we have,

y = -8x

y = -8(2)

y = -16

Therefore, the solution for x = 2 is (2, -16).

For x = 4, we have,

y = -8x

y = -8(4)

y = -32

Therefore, the solution for x = 4 is (4, -32).

For x = 8, we have,

y = -8x

y = -8(8)

y = -64

Therefore, the solution for x = 8 is (8, -64).

Putting these solutions together, we get {(2,-16), (4,-32), (8,-64)}. Hence, the correct answer is option D.

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The value of the missing lengths are;

a. b =  17. 32, c = 20

b. x = 8. 49, y = 8.49

Note that the different trigonometric identities are;

These identities have their ratios written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have;

tan 30 = 10/b

cross multiply the values

b = 17. 32

Also, we have;

sin 30 = 10/c

cross multiply the values

c = 20

b. Using the sine identity

sin 45 = x/12

cross multiply the values

x = 8. 49

Also,

cos 45 = y/12

cross multiply

y = 8. 49

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The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet

Similar triangles are triangles that have the same shape but may have different sizes.

The length of the shadow cast by the building = 30 feet

Rob's height = 6 feet

The length of Rob's shadow = 2 feet long

The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;

Let h represent the height of the building, we get;

h/30 = 6/2 = 3

h = 30 × 3 = 90

The height of the building is 90 feet tall

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The value of the number is 18. Option A

To determine the product of the expression, we need to consider that;

Algebraic expressions are described as those mathematical expressions that are composed of terms, their coefficients, the variables and the factors and constant values.

These expressions are also made up of mathematical operations. These operations are;

From the information given, we have that;

The product of six and a number is 108

Let the number be x, we have;

6x = 108

Divide sides by the coefficient

x = 18

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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:   [1/5x-4+2y]+[2/5x+5-4y] simplifies to 3/5x - 2y + 1.

Step-by-step explanation:

To simplify the given expression, we need to combine like terms.

The like terms are the ones with the same variable parts.

Let's first simplify the expression inside the brackets separately:

[1/5x-4+2y] = 1/5x + 2y - 4

[2/5x+5-4y] = 2/5x - 4y + 5

Now, we can combine the simplified expressions:

[1/5x + 2y - 4] + [2/5x - 4y + 5]

= 1/5x + 2y - 4 + 2/5x - 4y + 5

= (1/5 + 2/5)x + (2y - 4y) - 4 + 5

= 3/5x - 2y + 1

Therefore, [1/5x-4+2y]+[2/5x+5-4y] simplifies to 3/5x - 2y + 1.

The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

We have to given that;

The rational expressions is,

⇒ 4x/(x+6) times (x-8) / (x-6)

Now, We can multiply as;

⇒ 4x/(x+6) times (x-8) / (x-6)

⇒ 4x/(x+6) × (x-8) / (x-6)

⇒ 4 (x - 8) / (x + 6) (x - 6)

⇒ (4x -32) / (x² - 6²)

⇒ (4x - 32) (x² - 36)

Thus, The value of the product of the rational expressions is,

⇒ (4x - 32) (x² - 36)

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