What is the area of the base, B,
of the prism?
B = 12 ft²
What is the volume, V, of the prism?
V= ? ft³
4 ft
6 ft
3 ft

Answer:

Solution given:

we have

setup price =$30

as rate for 1 print tickets =$1.05/tickets

so

for t

t=$30+$1.05*t

is a required expression.

the

cost of 300 tickets:

300 tickets =$30+$1.05*300=$345

$345is the cost of 300 tickets.

Answer:

huh? no they cant both be 30 at the same time is cindy is 2 years older than marie....

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

4 times 8 = 32. 56 - 32 = 24. 24 divided by 4 = 6.

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

The propagated error in the measurement of the side of the cube is 0.001.

We know that,

the volume of a cube is dependent on the length of the edge, s, which is given by the equation,

V = \(s^{3}\).

With this we determine that the given cube has an edge of 27 = \(s^{3}\)

⇒ s = 3 inches.

Now we can acquire the differential of the equation for the volume of the cube with the following equations.

V = \(s^{3}\)

dV = d(\(s^{3}\))

dV = 3\(s^{2}\) ds

We have given that volume of the cube is 0.027.

That is dV = 0.027 and s = 3

we simply plug in the given and then solve for ds to determine the error in the measurement of the edge of the cube.

dV = 3\(s^{2}\) ds

0.027 = 3(3)²ds

0.027 = 27ds

0.001 = ds

Therefore, there is an error in measurement of the edge of the cube up to 0.001 inches.

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Answer:

221

Step-by-step explanation:

Make a proportion.

182/14 = x/17

182 x 17 divided by 14 is 221

Answer:

221 points

Step-by-step explanation:

We can set up a ratio of points to games

182:14

We can simplify this ratio into

13:1

This means he can score 13 points in 1 game. Now we can set up an equation to find how many he will score in 17 games.

\(\frac{13}{1} =\frac{x}{17} \)

Cross multiply

x=221

He will score 221 points

Answer:im not 100% sure but this is the answer i got 937.5

Step-by-step explanation:

The length of the rectangular plot of land is 153 feet. This problem will be solved using the basics of rectangles. The width of the rectangular plot of land is w. As given, the length of the fence is 32 feet longer than the width. So, the length of the rectangular plot of land is w + 32 feet. If the landowner has a total of 548 feet of fence that he can use, then the perimeter of the rectangular plot of land can be calculated using the given data.

The perimeter of the rectangular plot of land can be calculated as follows: Perimeter of a rectangle = 2(l + w)Here, l is the length of the rectangular plot of land and w is the width of the rectangular plot of land. So, the equation can be written as follows:2(w + 32 + w) = 548Simplifying the above equation:2w + 32 = 2742w = 242w = 121So, the width of the rectangular plot of land is 121 feet. As per the given data, the length of the rectangular plot of land can be calculated as follows: l = w + 32l = 121 + 32l = 153. So, the length of the rectangular plot of land is 153 feet.

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Answer:

58.33

Step-by-step explanation:

8.33 per hour

Mulitply by 7 and get 58.33

The contractor does not have enough concrete to finish the job. The conical pile of concrete mix has a volume of approximately 183.17 cubic yards, which is less than the required 78 cubic yards.

To determine if the existing conical pile of concrete contains enough material, we need to calculate the volume of the pile and compare it to the required volume of 78 cubic yards.

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where V is the volume, π is approximately 3.14159, r is the radius of the base, and h is the height of the cone.

Given that the diameter of the pile is 22 feet, the radius is half the diameter, which is 11 feet. The height of the pile is 12 feet.

Using the formula, we can calculate the volume of the pile:

V = (1/3) * 3.14159 * (11^2) * 12

V ≈ 1664.71 cubic feet

To convert the volume to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):

Volume in cubic yards = 1664.71 / 27 ≈ 61.65 cubic yards

Since the volume of the existing conical pile is approximately 61.65 cubic yards, it is not enough to meet the required volume of 78 cubic yards. Therefore, the contractor needs additional concrete to complete the construction job.

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The average rate of change over the interval from x = 2 to x = 4 is 2.

The average rate of change for a function over an interval is the slope of the secant line that connects the two points on the graph. The average rate of change can be found by using the formula:

Average Rate of Change = (y2 - y1) / (x2 - x1)

For the given function, the average rate of change over the interval from x = 2 to x = 4 can be found by substituting the appropriate values into the formula:

Average Rate of Change = (f(4) - f(2)) / (4 - 2)

Substituting the function values, we get:

Average Rate of Change = (6 - 2) / (4 - 2)

Simplifying, we get:

Average Rate of Change = 4 / 2

Therefore, the average rate of change over the interval from x = 2 to x = 4 is 2.

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Answer:

rita and john are susseful the job

js school

Answer:

its an undefined slope.

Step-by-step explanation:

After answering the provided question, we can conclude that the average (arithmetic mean) of 2x and 2y is 48.

The mean of a dataset is the sum of all values divided by the total number of values; this is also known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the total number of values in the dataset by the sum of those values yields this result. Calculations can be performed using both raw data and data that has been combined into frequency tables. The average of a number is referred to as its average. It is simple to calculate: Divide the total number of digits by the number of digits. the total divided by the count.

The average (arithmetic mean) of 2x and 2y is 48.

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The Jacobian for this transformation is

\(J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}\)

with determinant \(|J| = 12\), hence the area element becomes

\(dA = dx\,dy = 12 \, du\,dv\)

Then the integral becomes

\(\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv\)

where \(R'\) is the unit circle,

\(\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1\)

so that

\(\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv\)

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

\(\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}\)

Then

\(\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}\)

The shape is a four sided polygon with two pairs of parallel sides. The vertices of the parallelogram are A(1,4), B(3,0), C(1,-4) and D(-1,0). It has two pairs of equal length sides, one pair of which is parallel to the x-axis and the other is parallel to the y-axis.

To calculate the area of the parallelogram, we need to calculate the length of each side first. The length of the sides AB and CD can be calculated using the distance formula as follows:

AB = \(sqrt((3-1)^2 + (0-4)^2) = sqrt(4 + 16) = sqrt(20) = 4.472.\)

Similarly,

CD = \(sqrt((1- (-1))^2 + (-4 - 0)^2) = sqrt(4 + 16) = sqrt(20) = 4.472.\)

The length of the sides AD and BC can be calculated in a similar manner. Now, to calculate the area, we use the formula: Area = base * height. Thus, the area of the parallelogram is 4.472 * 4.472 = 20.03 square units.

Area = base * height = 4.472 * 4.472 = 20.03 square units

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Answer:13 1/8

(Decimal: 13.125)

Step-by-step explanation:

Answer:18 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=

10

+

1

2

+

8

+

1

8

Solving the whole number parts

10

+

8

=

18

Solving the fraction parts

1

2

+

1

8

=

?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

4

8

+

1

8

=

5

8

Combining the whole and fraction parts

18

+

5

8

=

18

5

8

The x- and y-intercepts of the graph of x + y = 18 both have the values of 18

The x-intercept of the function is the point or points where the graph of the function crosses the x-axis i.e. the point where the function equals 0

The equation of the graph is given as

x + y = 18

To calculate the x-intercept, we set the value of y to 0

This is represented as

y = 0

So, we have the following equation

x + 0 = 18

Evaluate the like terms

x = 18

To calculate the y-intercept, we set the value of x to 0

This is represented as

x = 0

So, we have the following equation

0 + y = 18

Evaluate the like terms

y = 18

This means that the x-intercept has a value of 18 and the y-intercept has a value of 18

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The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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\(g( \sqrt{55} ) = ( \sqrt{55} ) {}^{2} + 11 = 55 + 11 = 66\)

\(f(g(55)) = f(66) = \sqrt{66 - 2} = \sqrt{64} = 8\)

The value of the function f(g(√55)) is 3√7.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

We have the function:

f(x) = √ (x - 2)

and, g(x) = x² + 11.

As, g(√55)

= (√55)² + 11

= 55 + 11

= 66

So, f(g(√55))

= √ (65 - 2)

= √63

= 3√7

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Answer:

Step-by-step explanation:

To find the slope, pick any two points fromthe line.

(2,2)  & (0,-4)

x₁ = 2 & y₁ = 2

x₂ = 0 & y₂ = - 4

\(\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}\)

          \(\sf =\dfrac{-4-2}{0-2}\\\\\\ =\dfrac{-6}{-2}\\\\\\=3\)

Slope = 3

At y-intercept x = 0.

From the graph, y-intercept = -4

Equation of the line: y = mx + b

y = 3x - 4

Answer:

32

Step-by-step explanation:

With the ratio 8:4 we can assign variables.

8x+4x=96

12x=96

x=8

Subsitute to ratio: 8x:4x

64:32

32 orange packages

Hope this helps

Answer:

divide both side of inequality by 4 but don't flip the symbol

Answer:

20&22

Step-by-step explanation:

let the numbers be X and X+2.

By question, X×(X+2)=440

or, X^2+2X=440

or, X^2+2X-440=0

or, X^2+(22-20)X-440=0

or, X^2+22X-20X-440=0

or, X(X+22)-20(X+22)=0

or, (X+22)(X-20)=0

Either,X-20=0 Or, X+22=0

•°•X=20(true) •°• X=-22(false)

•°•X=20

•°•X+2=20+2=22

•°• The two consecutive even numbers are 20 and 22.

9514 1404 393

Answer:

  the difference of squares is 24(3n+2), so a multiple of 24

Step-by-step explanation:

The sequence has a first term of 7 and a common difference of 6, so the n-th term is ...

  a[n] = a1 +d(n -1)

  a[n] = 7 + 6(n -1)

  a[n] = 6n +1

Then the (n+1)-th term is ...

  a[n+1] = 6(n+1) +1 = 6n +7

The difference of the squares of these terms is ...

  a[n+1]^2 -a[n]^2 = (6n+7)^2 -(6n+1)^2

  = (36n^2 +84n +49) -(36n^2 +12n +1)

  = 72n +48

  = 24(3n +2) . . . . . always a multiple of 24

The difference of squares of terms n and n+1 is 24(3n+2), a multiple of 24.

_____

Check

The difference between squares for n=1 and n=2 is 13^2 -7^2 = 169 -49 = 120. The formula tells us the difference is 24(3·1 +2) = 24·5 = 120, in agreement.

The largest area a rectangle can have when inscribed in a semicircle of radius 2 is 4 square units.

The dimensions of this rectangle are 2 units by 2 units. This occurs when the sides of the rectangle are parallel to the diameter of the semicircle, so that each vertex of the rectangle lies on the circumference of the semicircle.

The length of the rectangle is equal to the diameter of the semicircle, or 2 units, and its width is half the diameter, or 2/2 = 1 unit. The area of this rectangle is equal to the length times the width, or 2 * 1 = 2 square units.

Since the rectangle is inscribed in a semicircle, its dimensions must be equal, so the largest area rectangle that can be inscribed in a semicircle of radius 2 has sides of length 2 units and an area of 4 square units.

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The total length of craft wire used by Samantha is 10x + 9

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let's call the length of the smaller quadrilateral's 6-centimeter side "x".

Then the length of the corresponding side in the larger quadrilateral would be 6+3=9 centimeters, since the scale factor is 3.

To find the total length of craft wire used, we need to add up the lengths of all the sides in both quadrilaterals.

The smaller quadrilateral has four sides, each with a length of x.

The larger quadrilateral also has four sides, but only one of them has a different length (9 cm), while the other three sides are simply 3 times longer than the corresponding sides in the smaller quadrilateral.

So the total length of craft wire used by Samantha is:

4x + 9 + 3x + 3x + 3x

Simplifying this expression, we get:

10x + 9

Hence,  the total length of craft wire used by Samantha is:

10x + 9

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If the degree of freedom is 24, your sample size when conducting a t-test for dependent means must be 25. Option C is the correct answer.

The sample size when conducting a t-test for dependent means depends on the specific study design and the level of significance desired, and cannot be determined solely based on the degrees of freedom.

However, if we assume that the sample size is equal for both groups, then the formula to calculate the degrees of freedom for a t-test for dependent means is:

df = n - 1

Where "n" is the number of pairs of observations in the sample.

Therefore, if the degree of freedom is 24, then the number of pairs of observations in the sample would be:

n = df + 1 = 24 + 1 = 25

Hence, the answer is 25.

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