BRAINLIEST! HURRY! What is the volume of the prism?



Enter your answer, as a mixed number in simplest form, in the box.


_ cm³

Answer:

measure of angle MPQ is 125

Step-by-step explanation:

1) Corresponding angles are congruent

5x=3x+50

2x=50

x=25

2) Substitute back into the equation

3(25)+50 = 125

The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.

In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.

If there are n points and k transformations, then the required number of multiplications is n × k.

This is because each point needs to be multiplied by the composite transformation matrix k times.

Therefore, the total number of multiplications is n × k.

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Answer:

Commutative property

The Commutative property is most simply shown with: a x b = b x a. In multiplication, the values can shift or "commute" in any order

To solve triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

c^2 = a^2 + b^2 - 2ab*cos(C)

We are given B, a, and b, so we can solve for c as follows:

c^2 = 25^2 + 41^2 - 2(25)(41)cos(64)

c^2 = 625 + 1681 - 2135cos(64)

c^2 = 1829 - 2135*cos(64)

c^2 = 311.90

Taking the square root of both sides, we get:

c ≈ 17.7

So the length of side c is approximately 17.7 units.

To find the measures of angles A and C, we can use the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:

a/sin(A) = b/sin(B) = c/sin(C)

We know a, b, and c, and we just solved for c, so we can use the Law of Sines to solve for angles A and C:

a/sin(A) = c/sin(C)

sin(A) = asin(C)/c

A = sin^{-1}(asin(C)/c)

A = sin^{-1}(25*sin(C)/17.7)

Similarly,

b/sin(B) = c/sin(C)

sin(B) = bsin(C)/c

B = sin^{-1}(bsin(C)/c)

B = sin^{-1}(41*sin(C)/17.7)

To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

C = 180 - A - B

Using a calculator, we get:

A ≈ 41.6 degrees

B ≈ 74.1 degrees

C ≈ 64.3 degrees

Therefore, the measures of the angles in triangle ABC are approximately:

A ≈ 41.6 degrees

B = 64 degrees

C ≈ 64.3 degrees

And the lengths of the sides are approximately:

a = 25

b = 41

c ≈ 17.7

The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.

The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.

This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.

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p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.

Answer:

(a) To find the value of a and d, we use the formula for the sum of first n terms of the arithmetic series A which is given by:Sn = n/2[2a + (n-1)d]We are also given that Sn = 15 + 2n. So we can equate these two expressions to get:15 + 2n = n/2[2a + (n-1)d]Multiplying both sides by 2 and simplifying, we get:30 + 4n = n[2a + (n-1)d]Expanding the brackets and simplifying, we get:2an + nd - d + 30 = 2n^2Rearranging terms, we get:2a = 2n^2 - nd + d - 30Now we also know that the first term of the series A is a. So we can substitute this value of a in the formula above to get:a = (2n^2 - nd + d - 30)/2Simplifying, we get:a = n^2 - (n-1)d - 15Therefore, we have found the values of a and d in terms of n. (b) To find the 20th term of A, we use the formula for the nth term of an arithmetic series which is given by:an = a + (n-1)dSubstituting the value of a and d that we found in part (a) we get:a20 = (20^2 - 19d - 15) + 19dSimplifying, we get:a20 = 391 - dTherefore, the 20th term of A is given by a20 = 391 - d.(c) Given that S2p - 2Sp = 1 + S(p-1), we can use the formula for the sum of first n terms of an arithmetic series which we used in part (a) to get:2p/2[2a + (2p-1)d] - 2p/2[2a + (p-1)d] = 1 + p/2[2a + (p-2)d]Simplifying, we get:2apd = d(p^2 - 3p + 2)Dividing both sides by d and simplifying, we get:2ap = p^2 - 3p + 2Rearranging terms, we get:p^2 - 3p + (2-2ap) = 0This is a quadratic equation with coefficients a=1, b=-3, and c=2-2ap. We can use the quadratic formula to solve for p:p = [3 ± sqrt(9 - 4(1)(2-2ap))]/2Simplifying, we get:p = [3 ± sqrt(4ap + 1)]/2Therefore, we have found the value of p in terms of a.

Answer:

Step-by-step explanation:

everything is resolved with the expression:

20^2 x 6 = 2400 cm^2

There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.

To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.

In this case, n = 15 and r = 3.

Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.

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The probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

The 10-sided die has 10 faces, each marked with a unique number from 1 to 10. When we talk about the probability of rolling a particular number, we're asking what the chances are of that number coming up when the die is rolled.

In this case, the question asks for the probability of rolling a number 10 or less, which means we're interested in the probability of rolling any number from 1 to 10. Since all the possible outcomes are numbers from 1 to 10, the probability of rolling a number 10 or less is certain, or 1.

This is because the sum of probabilities of all possible outcomes of an experiment is always 1.

Similarly, the probability of rolling a number greater than 10 is impossible, or 0. This is because there are no possible outcomes greater than 10 on the 10-sided die. In general, the probability of an event that cannot occur is always 0.

So, the probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

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 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.

given

A =  πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):

A₁ = π(4a-6)²

If we condense this phrase, we get:

A₁ = π(16a² - 48a + 36)

A₂ = π(4a-6)²

A₂ = π(16a² - 48a + 36)

A₃ = π(4a-6)²

A₃ = π(16a² - 48a + 36)

A₄ = π(4a-6)²

A₄ = π(16a² - 48a + 36)

We can add up the areas of each of the four circles to determine their combined area:

A1 + A2 + A3 + A4 Equals A total

A total is equal to π (16a2 - 48a + 36) +  π(16a2 - 48a + 36) +  π(16a2 - 48a + 36).

 π(64a2 - 192a + 144) = A total

 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

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out of the families that have DS, 20 have both, so subtract them from the absolute to get 124 - 20 = 104.

out of the families that have WII, 20 have both, so subtract them from the all-out to get 186 - 20 = 166.

you presently have 3 classifications that are unadulterated.

104 own DS in particular.

266 own WII in particular.

20 own both.

the complete that possesses either a DS or a WII however not both is equivalent to 104 + 266 = 370.

you need to subtract 20 from every classification since it is remembered for both.

it is remembered for DS and it is remembered for WII.

Market surveys are apparatuses to straightforwardly gather criticism from the interest group to grasp their qualities, assumptions, and prerequisites. Marketers foster previously unheard-of techniques for impending items/benefits however there can be no affirmation about the outcome of these methodologies.

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the complete question is:

A company conducted a marketing survey for families with young children and found that 124 families own a Nintendo DS and 186 families own a Nintendo Wii. If 20 own a Wii and a DS, how many own either a Wii or DS, but not both?

The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.

With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.

Regular pentagons have a number of distinctive features, including:

A regular pentagon has 108 degree internal angles that are all equal.

A standard pentagon's outside angles are all 72 degrees in angle.

A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.

Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.

First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:

s = r * √(3)

where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:

s = 5 * √(3)

simplifying, we get:

s ≈ 8.7 meters

Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:

A = (1/2) * b * h

where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:

h = (1/2) * s * √(3)

Plugging in the value for s, we get:

h ≈ 7.5 meters

Now we can calculate the area of one of the triangles:

A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters

Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:

A = 6 * (s²) * √(3)/4 + 3 * A

Plugging in the values we calculated, we get:

A ≈ 96.9 square meters

Rounding to the nearest square meter, we get:

A ≈ 97 square meters

Therefore, the answer is A. 97 m².

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Answer:

-45

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 0.0625 g/cm^3

Formula for density: d= mass/volume

we have mass m=50g

volume of rectangular prism = length x height x width

volume of book = 5cm x 16cm x 10cm = 800cm^3

density = mass / volume

density = 50g/800cm^3

density = 0.0625 g/cm^3

Answer:

90, 86, and 92 are three options

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.

It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.

Here,

Let's begin by giving the unknowns variables:

x = number of vehicles

Van count = 4 times

Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).

The value of x can be determined using the second bit of knowledge:

=> 4x/3 = (205 - 11x)/2

When we simplify this solution, we obtain:

=> 8x = 3(205 - 11x)

=> 8x = 615 - 33x

=> 41x = 615

=> x = 15

We can now determine the quantity of vans:

Van count = 4x = 4(15) = 60

Consequently, the parking lot has 60 trucks.

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the concentrations of nitrogen, phosphate, and potassium in the mixture are 13.33%, 13.67%, and 8%, respectively. To find the concentrations of nitrogen, phosphate, and potassium in the mixture, we need to calculate the total amount of each nutrient in the two bags and then divide by the total weight of the mixture.

First, let's calculate the amount of each nutrient in the 10 pound bag of 12-12-12:

Nitrogen: 12% of 10 pounds = 1.2 pounds

Phosphate: 12% of 10 pounds = 1.2 pounds

Potassium: 12% of 10 pounds = 1.2 pounds

Next, let's calculate the amount of each nutrient in the 5 pound bag of 16-17-0:

Nitrogen: 16% of 5 pounds = 0.8 pounds

Phosphate: 17% of 5 pounds = 0.85 pounds

Potassium: 0% of 5 pounds = 0 pounds

Now, let's add up the total amount of each nutrient in the two bags:

Nitrogen: 1.2 + 0.8 = 2 pounds

Phosphate: 1.2 + 0.85 = 2.05 pounds

Potassium: 1.2 + 0 = 1.2 pounds

Finally, let's divide the total amount of each nutrient by the total weight of the mixture (10 + 5 = 15 pounds) and express the answers as percentages:

Nitrogen: (2 / 15) x 100% = 13.33%

Phosphate: (2.05 / 15) x 100% = 13.67%

Potassium: (1.2 / 15) x 100% = 8%

Therefore, the concentrations of nitrogen, phosphate, and potassium in the mixture are 13.33%, 13.67%, and 8%, respectively.

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Answer:

A

Step-by-step explanation:

The area of the equilateral triangle is 36√3 square units

What is area of the equilateral triangle?

Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.

In an equilateral triangle, the center, the centroid, and the circumcenter coincide.

The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.

The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.

So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.

The area of an equilateral triangle with side length s is given by:

A = (s² * √3) / 4

Substituting s = 12, we get:

A = (12² * √3) / 4

= 36√3

Therefore, the area of the equilateral triangle is 36√3 square units.

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The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:

Step-by-step explanation:

Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.

Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.

Here,

1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.

To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:

Range = 83 - 5 = 78

2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.

Therefore, the correct answer is: The median is the best measure of center because there are outliers present.

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Let's denote the width and length of the pool by “w” and “l” respectively. Then, the width of the pool and deck combined would be:So the equation that represents the total area of the pool and deck as binomials is [tex]: A = 2(L + 8)(2L + 8)[/tex]

Let's start by drawing a diagram of the rectangular pool and the surrounding deck:

 ___________  Pool Length (L)

|           |

|           |

|           |

|           |

W|___________|

| Deck Width|

|    = 4ft  |

|___________|

We know that the width of the pool (W) is twice its length (L), so we can write:

[tex]W = 2L[/tex]

We also know that the deck is 4ft wide on each side, so the total width of the pool and deck is:

[tex]W_total = W + 8 = 2L + 8[/tex]

And the total length of the pool and deck is:

[tex]L_total = L + 8[/tex]

The total area of the pool and deck can be found by multiplying the total width by the total length:

[tex]A = W_total \times L_total[/tex]

Substituting our expressions for W_total and L_total, we get:

[tex]A = (2L + 8) * (L + 8)[/tex]

Expanding the brackets, we get:

[tex]A = 2L^2 + 24L + 64[/tex]

So the equation that represents the total area of the pool and deck is:

2L^2 + 24L + 64

To represent the sides of the shape as binomials, we can factor out a common factor of 2 from the quadratic expression:

[tex]A = 2(L^2 + 12L + 32)[/tex]

Then we can write the sides of the shape as:

[tex]L + 8[/tex]   and [tex]2L + 8[/tex]

Therefore, So the equation that represents the total area of the pool and deck as binomials is: [tex]A = 2(L + 8)(2L + 8)[/tex]

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The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.

This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.

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The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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The length of Tanya's mural is 28 feet.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

Area = length × width

We know that the area of Tanya's mural is 224 square feet, and the height of the mural is 8 feet.

So we can use these values to find the length of the mural:

Area = length × width

224 = length × 8

To solve for the length, we can divide both sides of the equation by 8:

length = 224 ÷ 8

length = 28 feet

Therefore, the dimension of the length is 28 feet.

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The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.

We have,

In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.

Each section is divided into quarters.

If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:

SW 1/4:

This represents one-fourth of the section.

The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.

NE 1/4:

The NE 1/4 of Section 13 is also 160 acres.

NW 1/4:

The NW 1/4 of Section 13 is 160 acres.

To find the total acreage, add up the individual acreages:

160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)

= 480 acres

Therefore,

The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.

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Teresa needs to buy two new tires for her mountain bike.

With a budget of $120, she will likely spend within $25 of that amount.

To help her find the best deal, Teresa should first research what type of mountain bike tire she needs. She can look at the bike's current tires to determine the size, or she can look up the bike model and size online. She should then research prices at a variety of local bike shops and online retailers to compare costs.

Once she finds the best price, Teresa should look for discounts and coupon codes that she can use to reduce the cost of her tires. She should also make sure she is aware of any extra costs, such as shipping and taxes.

With some research and savvy shopping, Teresa should be able to find two mountain bike tires that fit within her budget of $120 and that will keep her bike running smoothly.

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Answer:

500 vehicles

Step-by-step explanation:

let t represent number of tolls and v represent number of vehicles.

given that t varies directly with v then the equation relating them is

t = kv ← k is the constant of variation

to find k use the condition t = 129 from v = 20 , then

129 = 20k ( divide both sides by 20 )

6.45 = k

t = 6.45v ← equation of variation

when t = 3225 , then

3225 = 6.45v ( divide both sides by 6.45 )

500 = v

the number of vehicles is 500