What is the volume of this frustum?

ANSWER

1/35

EXPLANATION

First we have to find how many ways you can pick 3 horses out of 7. For the first place you have 7 horses that can be there. For the second place, you have 6 horses (you already placed one horse) and for the third place you have 5 horses. The number of ways to pick 3 horses - in order - from 7 horses is:

Now we want to know the permutations for 3 horses. Once you have picked one combination out of the 210 combinations of 3 horses, there are many ways to arrange them. This is:

Let 'A' be the event where the gambler wins his bet:

We can simplify this fraction:

Answer:

i thank 180 or 115×31=

Step-by-step explanation:

i am not sure sorry):

the answer is on the picture

Answer:

Evan needs enough paint to cover 448in^2

He needs enough soil to fill 768in^3

Step-by-step explanation:

Answer:

here's the answer to your question

Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

Answer:

979.72

Step-by-step explanation:

First find the amount of tax

895.95 * 9.35%

Change to decimal form

895.95 * .0935

83.771325

Rounding to the nearest cent, tax is 83.77

Add this to the cost of the tx

895.95 +83.77

979.72

Answer:

All of them are not vertical angles.

Step-by-step explanation:

Because they are not directly vertical from each other.

Answer:

Bottom left

Step-by-step explanation:

It covers the most points

The coins of each type are 346 nickels, 165 dimes and 173 quarters. when a newspaper carrier has $6.85 charge  by substitution method.

Let x = number of quarters

Then, x-4 = number of dimes and 5x = number of nickels

So, 0.05(5x) + 0.10(x-4) + 0.25x = 6.85

0.6x - 0.4 = 6.85

0.6x = 7.25

x = 12

There are 12 quarters, 8 dimes, and 60 nickels (or)

x = 8 + D(dimes)

D = Q -8

N(nickels) = 2Q

N + D + Q = 685

2Q + Q-8 + Q = 685

4Q = 685+ 8 = 693

Q = 693/4 = over 173

D= over 165

N= over 346

174+ 165 + 346 = 685

the answer is 346 nickels, 165 dimes and 174 quarters.

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We know that y varies directly with x.

First we need to find the constant of variation

7=14k

k= 7/14

k=1/2

the equation that relates x and y is

Answer:

(3−5)(+1)

Step-by-step explanation:

I hope this helps you and please mark me as brainliest

Answer:

The answer is ( p + 1 ) ( 3p - 5 )

Step-by-step explanation:

The lengths of the sides of the cube is,

⇒ side = 7 inches

We have to given that;

A cube has a volume of 343 in³.

Since, We know that;

Volume of cube is,

⇒ V = side³

Hence, Substitute all the values, we get;

⇒ 343 = side³

⇒ side = ∛343

⇒ side = 7 inches

Thus, The lengths of the sides of the cube is,

⇒ side = 7 inches

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The correct option for calculating the percentage change in x from x₁ to x₂ is:

c) 100(∆x / x₁)

Percentage change is a measure that calculates the relative difference between two values, typically expressed as a percentage. It is used to determine the magnitude and direction of the change between an initial value and a final value.

The formula for calculating the percentage change is:

Percentage change = (Change in value / Initial value) * 100

In this case, the change in x is represented as ∆x, and the initial value is x₁. Therefore, the formula becomes:

Percentage change = (∆x / x₁) * 100

Therefore, Option c) matches this formula and correctly calculates the percentage change in x.

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Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

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30-degree is the smallest value of the \(\theta\\\).

If sin(θ) = 1/2 and 0° < θ < 180°, then we know that θ is an acute angle in the first or second quadrant of the unit circle, since sine is positive in those quadrants.

To find the value of θ, we can use the inverse sine function (sin^-1) on both sides of the equation:

\(sin^{-1}(sin(\theta)) = sin{^-1}(1/2)\)

θ = 30° or 150°

Since 0° < θ < 180°, the smaller value of θ is 30°.

Therefore, the smaller value of θ is 30°.

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Rui Feng invested approximately $45,644.91.

To find the original amount invested by Rui Feng, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal amount (the original investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that Rui Feng received $5,800 as interest at the end of 3 years, we can calculate the final amount:

A = P + I

A = P + $5,800

Using the formula for compound interest and rearranging the equation, we can solve for the principal amount (P)

P = A - $5,800

Substituting the values into the formula, we have:

P = $5,800 / (1 + 0.04/2)^(2*3)

P = $45,644.91 (rounded to two decimal places)

Therefore, Rui Feng invested approximately $45,644.91 originally.

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We can observe that this table corresponds to the addition table of the cyclic group Z₅, which consists of the integers modulo 5. Therefore, the factor group 3Z/15Z is isomorphic to the cyclic group Z₅.

To find the factor group 3Z/15Z and determine its elements and table, we need to consider the cosets of 15Z within 3Z.

The cosets of 15Z within 3Z are obtained by adding elements of 15Z to the elements of 3Z. Since 3Z consists of all multiples of 3, and 15Z consists of all multiples of 15, we can express the elements of 3Z/15Z as:

3Z/15Z = {3n + 15m | n, m ∈ Z}

To find the distinct cosets, we need to consider the possible values of n and m. Since n and m can take any integer value, we can list the distinct left cosets as follows:

3Z + 15Z = {0, 3, 6, 9, 12}

Each element in the factor group represents a distinct coset. Now, we can write the table for the factor group by performing the group operation (addition) on its elements:

```

+ |   0   |   3   |   6   |   9   |   12

---------------------------------------

0 |   0   |   3   |   6   |   9   |   12

---------------------------------------

3 |   3   |   6   |   9   |   12  |   0

---------------------------------------

6 |   6   |   9   |   12  |   0   |   3

---------------------------------------

9 |   9   |   12  |   0   |   3   |   6

---------------------------------------

12|   12  |   0   |   3   |   6   |   9

```

We can observe that this table corresponds to the addition table of the cyclic group Z₅, which consists of the integers modulo 5. Therefore, the factor group 3Z/15Z is isomorphic to the cyclic group Z₅.

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The average rate of change of fuel efficiency = -3 gallon per hour

Fuel efficiency of the cooper when driving at a speed of 75 mph = 29 miles per gallon

Fuel efficiency of the cooper when driving at a speed of 60 mph = 34 miles per gallon

Let y₁ = 75 mph, y₂ = 60 mph

and x₁ = 29 miles/gallon , x₂ = 34 miles /gallon

Then the average rate of change of fuel efficiency = (y₂-y₁)/(x₂-x₁)

                                                        = (60 - 75)/(34-29)

                                                        = -3 gallon per hour

This means that the fuel efficiency dropped as the speed dropped from 75 mph tp 60 mph.

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Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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The area of Jimmy's rectangular room is approximately 27.7241 square yards.

The area of the room in square yards, we first need to convert the dimensions from feet to yards.

Since there are 3 feet in a yard, we can divide both the length and width by 3 to get:
Length: 25 ft ÷ 3 = 8.33 yards (rounded to two decimal places)
Width: 10 ft ÷ 3 = 3.33 yards (rounded to two decimal places)

Now we can find the area by multiplying the length and width in yards:
Area = 8.33 yards x 3.33 yards
Area = 27.7241 square yards (rounded to four decimal places)

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We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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 By multiplying matrices B and A, we obtain the product BA. Using BA, we can solve the system of equations y + 2z = 7, x - y = 3, and 2x + 3y + 4z = 17.the values of x, y, and z are -1, 2, and 1 respectively

To find the product BA, we multiply matrix B with matrix A. The resulting matrix will have the same number of rows as B and the same number of columns as A. The product BA will be used to solve the given system of equations.
The product BA can be computed by multiplying each row of matrix B by each column of matrix A and summing the results. The resulting matrix will be:
Now, we can use the product BA to solve the system of equations:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.

1 -1 2
2 3 1
0 4 2
We can rewrite this system of equations as:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
By comparing the coefficients of x, y, and z in the system of equations with the entries in the matrix BA, we can determine the values of x, y, and z.
Solving the system of equations using matrix BA, we get:
x = -1,
y = 2,
z = 1.
Therefore, the values of x, y, and z are -1, 2, and 1 respectively.

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The complete question is:
Given A=
⎣2 2 -4|
|-4 2 -4|
|2 -1 5|
, B=
⎣1 -1 0|
⎢2 3 4|
⎢0 1 2|
, find BA and use this to solve the system of equations y+2z=7, x−y=3, 2x+3y+4z=17.

The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

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Therefore, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is approximately 0.3174 or 31.74%.

To find the probability that the mean thickness in the 16 measurements, denoted as x, is farther than 3 units away from the target value, we can use the Central Limit Theorem and the properties of the normal distribution.

Given:

Mean thickness (μ) = 200 units

Standard deviation (σ) = 12 units

Sample size (n) = 16

First, we need to calculate the standard error of the mean (SE):

SE = σ / √n

SE = 12 / √16

= 3

Next, we calculate the z-score corresponding to a deviation of 3 units from the target value:

z = (x - μ) / SE

z = (3 - 0) / 3

= 1

Now, we need to find the probability of the mean thickness being farther than 3 units away from the target value, which corresponds to the area in the tails of the normal distribution.

Using a standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of 1 in the right tail:

P(Z > 1) ≈ 0.1587

Since we are interested in both tails (farther than 3 units in either direction), we multiply this probability by 2:

P(|Z| > 1) = 2 * 0.1587 = 0.3174

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Answer:

  $4.80

Step-by-step explanation:

You want to know the finance charge on a balance of $480 if the APR is 12%.

The monthly finance charge is the product of the monthly interest rate and the balance. The monthly interest rate is 1/12 of the annual rate.

  finance charge = (1/12 · 12%) · $480 = 0.01 · $480 = $4.80

The finance charge on the next monthly statement is $4.80.