Samantha is designing a new three-dimensional puzzle in the form of a square pyramid. She knows that the design and the general formula for finding the volume are as follows, where h is the height and a is the side length of the base. All of her measurements are in centimeters.

An illustration of a pyramid, with the height of h and width a.

Samantha's puzzle must have a certain volume and height, but she needs to determine the side length of the base to complete the design. Which equation can Samantha use to find the side length of the base in terms of the volume and height of her puzzle?

The consumers' surplus at a price level of $1 for the price-demand equation is -1072.5.

Given that price-demand equation p= D(x) = 20-0.1x, we need to find the consumers' surplus at a price level of $1.

So,

From the equation we have,

20-0.1x = 1

0.1x = 19

x = 190

Therefore, the equilibrium point = (190, 1) = (xe, Pe)

Now,

Cs = [tex]\int\limits^{x_e}_0 {D(x)} \ dx\, -Pexe[/tex]

[tex]\int\limits^{190}_0 {20-0.1x} \ dx\, -(190)[/tex]

= 20-0.1{9025}-190

= -1072.5

Hence the consumers' surplus at a price level of $1 for the price-demand equation is -1072.5

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The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)

:: No. of rotations = 48

:: Circumference of a circle = ( 2 x π x r )

where, r is radius of the circle

So, as,

Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]

Therefore,

Distance = (2 x π x 0.3) x (48)

Distance = 2 x (3.14) x 0.3 x 48

Distance = 90.432 meters

When rounded off to the nearest meter,

Distance = 90 meters.

So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

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Answer:

2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

Step-by-step explanation:

To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:

2 1/4 = (2 × 4 + 1) / 4 = 9 / 4

1 1/2 = (1 × 2 + 1) / 2 = 3 / 2

Now we can divide by multiplying by the reciprocal of the second fraction:

(9/4) / (3/2) = (9/4) * (2/3)

We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:

(9/4) * (2/3) = (33/4) * (2/13) = 9/2

So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]

[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]

[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]

[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]

[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]

• Check the attached image.

[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]

[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]

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The type of distribution pictured in this histogram is skewed.

A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.

In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.

There are two types of skewed distributions: positively skewed and negatively skewed.

The distribution in the image is positively skewed as its is pulled towards the left.

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Answer: 15 x 162 = 2430$

The percent of the area that is not covered is 80 percent

In mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².

area of tent

= (10 - 0) * (6 - (-3))

= 90

The area of the campsite would be:

(25 - (-5) x (10 - (-5))

= 450

Then the area would be 450 - 90

= 360

the percentage that is not covered by tent = 360 / 450 x 100

= 80 percent

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To represent z+9=14, we can start by subtracting 9 from both sides of the equation:

z + 9 - 9 = 14 - 9

Simplifying the left side of the equation gives:

z = 5

Therefore, the solution to the equation z+9=14 is z=5.

Answer:

300

Step-by-step explanation:

The measure of angle IHE is 23°.

Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:

mHJF = mGHJ = 134°

We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:

mHJF + mFJI + mIHE = 180°

Substituting the values we know, we get:

134° + mFJI + mIHE = 180°

Simplifying the equation, we get:

mFJI + mIHE = 46°

We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:

mGHJ + mHJF + mFJI = 180°

Substituting the values we know, we get:

134° + mFJI + mFJI = 180°

Simplifying the equation, we get:

2mFJI = 46°

Dividing both sides by 2, we get:

mFJI = 23°

Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:

mFJI + mIHE = 46°

23° + mIHE = 46°

Subtracting 23° from both sides, we get:

mIHE = 23°

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Complete Question:

If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?

Answer:

Option D.   [tex]g(x)=5(0.8)^{x}+2[/tex]

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

3.4.1) (8x^2)(6x^2 - 4x) = 48x^4 - 32x^2

3.4.2) 48x^4 - 32x^2 = (16x^2)(3x^2 - 2)

3.4.3) Length = 16(2^2) = 16(4) = 64

Width = 3(2^2) - 2 = 3(4) - 2

= 12 - 2 = 10

Area = 64(10) = 640

If a spinner divided into three equal sections marked A A and Z is spun 570 times .  The number of  times it will be expected to land on an A is 380 times.

Since the spinner has three equal sections in which two of them are marked A.  The probability of landing on an A in a single spin will be 2/3  while the probability of landing on Z  will be 1/3.

So,

Expected number of time E(A) =Number of spins x Probability of landing on A

Expected number of time E(A) = 570 x (2/3)

Expected number of time E(A)  = 380

Therefore the Expected number of time E(A) is 380 times.

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The total amount in the acount in 5 years is approximately $13,321.76.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.75/100

r = 0.0575

Plug the given values into the above formula and solve for A.

[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]

A = $13,321.76

Therefore, the accrued amount is $13,321.76.

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The value of the height of the entire climbing frame is 11.99 feet

To determine the value, we need to know the different trigonometric identities.

These identities are;

From the information given, we have that;

In the triangle, the parameters are;

Hypotenuse is the distance between the architect and frame

The angle is 63.43

Adjacent is 6 feet

Using the tangent identity, we have;

tan 63.43 = h/6

cross multiply, we get;

h = tan (63. 43) × 6

Find the tangent value and substitute, we have;

h = 1. 99 × 6

Multiply the values, we have;

h = 11. 99 feet

Then, the height of the entire climbing frame is 11. 99 feet

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Complete question:

'The architect stands 6 feet from climbing frame, looking up at the top of the frame at an angle of 63.43" It is 5 and half feet from ground to the architect's eyes: The vertical distance from eye level to the top of the climbing frame is feet: The height of the entire climbing frame is feet:'

If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)ᵗ

where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.

Plugging these values into the formula, we get:

A = 60(1 + 0.015)¹⁰

A ≈ 71

t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.

Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.

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The objective function that can be used to maximize the profit is Profit = 15a + 8b

Let a is the number of units of product A and b is the number of units of product B.

Profit = 15a + 8b

This function represents the total profit earned by producing a units of product A and b units of product B

Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.

To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function

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The values of the matrices operations are [tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex] and [tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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

[tex]G = \left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right][/tex]

Also, we have

[tex]F = \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Using the above as a guide, we have

[tex]4G + 2F = 4\left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right] + 2 \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Evaluate the sum

[tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex]

Next, we have

[tex]D = \left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right][/tex]

Also, we have

[tex]B = \left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

The matrix expression is then represented as

[tex]4D - 3B= 4\left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right] - 3\left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

Evaluate

[tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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The probability that event A or B takes place is P ( A ∪ B ) = 6/17

Given data ,

Let the probability that event A or B takes place is P ( A ∪ B )

Now , the probability of A is P ( A ) = 2/17

And , the probability of B is P ( B ) = 4/17

where P ( A ∩ B ) = 0

On simplifying the equation , we get

P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

So , P ( A ∪ B ) = 2/17 + 4/17

P ( A ∪ B ) = 6/17

Hence , the probability is 6/17

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Answer:

39270

Step-by-step explanation:

When the first person is picked, there is a 1 in 35 chance that it will be Person 1. If they are selected, that leaves 34 people left in the pool. After Person 2 is selected, there are 33 people left in the pool for Person 3.

35*34*33=39270

The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.

To determine the caloric content, we will assign algebraic notations to each of the dessert types.

1 Icecream + 2 Blueberry pie =   790 calories

3 icecream + 2 Blueberry pie = 1290 calories

Now the first equation will be subtracted from the second equation as follows:

2 icecream = 500 calories

So, 1 ice cream is 250 calories.

Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.

Complete question:

Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.

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The size of matrix cM is given as follows:

9 x 10.

When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.

The parameters for this problem are given as follows:

Hence the size of matrix cM is given as follows:

9 x 10.

(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).

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The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.

Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.

The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

So, the lines with the same slope but a different y-intercept are said to be parallel.

Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.

We thus have:

y = 8x + b

6 = 8(7) + b

6 = 56 + b

b + 56 = 6

b + 56 - 56 = 6 - 56

b = -50

The equation is: y = 8x - 50

Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.

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Correct question:

Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).

The class mark of the modal class is: 25

From the given histogram, the following Frequency Distribution is obtained:

Class Interval Mid point Frequency

625-675 650 3

676-726 701 5

727 - 777 752 7

778 - 828 803 8

829 - 879 854 6

880 - 930 905 2

931 - 981 956 0

982 - 1032 1007 1

b. To find the lower class limit of the first class:

First class: 625

c. The upper limit of the first class is:

First class: 676

The class mark of the modal class is:

The modal class is: 803

The class mark is upper limit + lower limit/2

Thus, 828-778/2

=> 50/2

The class mark of the modal class is: 25

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Answer: 100.48 cubic feet

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Lateral surface contains B,C and D (because A and E are bases)

A (lateral surface area) = 70 + 70 + 56 = 196 cm^2

Answer:

245 inches

Step-by-step explanation:

Yards->Inches

1 yard = 36 inches

Therefore, 6 yards = 36 x 6 = 216 inches

Feet->Inches

1 feet = 12 inches

Therefore, 2 feet = 2 x 12 = 24 inches

Adding all inches,

=> 216 + 24 + 5

=> 245 inches