Cooper decides to estimate the volume of a grapefruit by modeling it as a sphere. He measures its radius as 6.7 cm. Find the grapefruit's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.

Answer:

see explanation

Step-by-step explanation:

using the property of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

3x²[tex]y^{5}[/tex] × 4x³[tex]y^{7}[/tex] ( separate like parts in the product )

= 3 × 4 × x² × x³ × [tex]y^{5}[/tex] × [tex]y^{7}[/tex]

= 12 × [tex]x^{(2+3)}[/tex] × [tex]y^{(5+7)}[/tex]

= 12[tex]x^{5}[/tex][tex]y^{12}[/tex]

Rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.

What is Circumference?

Circumference is a term used in geometry to refer to the distance around the edge of a circle or any circular object. It is the total length of the boundary or perimeter of the circle. The circumference is determined by the diameter or radius of the circle, and it is calculated using the formula:

Circumference = π × diameter

The circumference of the tire is equal to the distance it travels in one revolution. Since the diameter of the tire is 28 inches, its radius is 14 inches. Therefore, the circumference of the tire is:

C = 2πr = 2π(14 inches) = 28π inches

To convert the distance of 500 feet to inches, we multiply by the conversion factor 12 inches/foot:

500 feet × 12 inches/foot = 6000 inches

Now we can find the number of revolutions of the tire:

number of revolutions = distance traveled / circumference of tire

number of revolutions = 6000 inches / 28π inches ≈ 214 revolutions

Therefore, rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.

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One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.

A= [ 1 1 1] [ 1 2 3] [ 4 5 6] and v = [ 2 ] [ 3 ] [ -1]​​. To find the image of v under TA, we simply multiply A and v to get:

TA = [ 1 1 1] [ 2 ] = [ 4 ]
[ 1 2 3] [ 3 ] [ 7 ]
[ 4 5 6] [ -1]​​ [ 17 ]

So the image of v under TA is [ 4 7 17 ].

To find vectors w that are different from v but that get mapped to the same image, we can use the equation TA*w = TA*v. Since TA*v = [ 4 7 17 ], we can set up the following system of equations:

1w1 + 1w2 + 1w3 = 4
1w1 + 2w2 + 3w3 = 7
4w1 + 5w2 + 6w3 = 17

Solving this system of equations will give us all the possible vectors w that get mapped to the same image as v. One possible solution is w = [ 1 2 0 ], which is different from v but gets mapped to the same image.

To find all vectors z that get mapped to zero, we can use the equation TA*z = 0. This gives us the following system of equations:

1z1 + 1z2 + 1z3 = 0
1z1 + 2z2 + 3z3 = 0
4z1 + 5z2 + 6z3 = 0

Solving this system of equations will give us all the possible vectors z that get mapped to zero. One possible solution is z = [ -3 2 1 ], which gets mapped to zero under TA.

Finally, to write down a nontrivial linear dependence relation between the columns of A, we can use the equation c1*A1 + c2*A2 + c3*A3 = 0, where A1, A2, and A3 are the columns of A and c1, c2, and c3 are constants. One possible solution is c1 = 1, c2 = -2, and c3 = 1, which gives us the linear dependence relation A1 - 2A2 + A3 = 0.

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Three rational expressions that simplify to (x)/(x+1) are:

1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)

To simplify these expressions, we can combine like terms in the numerator and denominator:

1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)

As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.

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The predicted value of the car in the year 2009 is $6,232.

First we need to use the formula for exponential decay:

V(t) = V0 × e^(-rt)

Where

We know that the car was purchased in 2000 for $27,600, and that its value in 2004 was $8,300. Therefore, we can use these values to solve for the rate of decay:

$8,300 = $27,600 × e^(-r x 4)

e^(-4r) = 0.3

Taking the natural logarithm of both sides:

-4r = ln(0.3)

r = -0.3567

Now that we have the rate of decay, we can use the same formula to predict the value of the car in 2009, which is 9 years after the initial purchase:

V(9) = $27,600 × e^(-0.3567 x 9) = $6,232

Therefore, the predicted value of the car in the year 2009 is $6,232.

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The amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.

Either of a triangle's two sides that are equal in length is said to be isosceles. This characteristic equates to the triangle's two angles being equal. Two of the sides and two of the angles of an isosceles triangle are equal. An isosceles triangle has three sides that are all the same length, have the same angles, and meet at symmetrical corners. Two right-angle triangles are produced if a perpendicular line is traced from the junction of two equal sides to the base of the unequal side.

The area of the triangle is given as:

A = 1/2(b)(h)

Here, the base = 6 and height = 8 in.

Thus, the area of the triangle is:

A = 1/2(6)(8)

The figure consists of 2 similar triangles. So, the area of the second triangle is added to get the final area.

A = [1/2(6)(8)].2

Hence, the amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.

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The correct classification for 11+8i is a complex number.√−81 can be expressed as the complex number 9i.

The number 11+8i is a complex number. This is because it has both a real part (11) and an imaginary part (8i). A complex number is any number that can be expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. Therefore, the correct classification for 11+8i is a complex number.

To express √−81 as a complex number, we can use the fact that √−1 = i. So, √−81 = √(81)*√(−1) = 9*i = 9i. Therefore, √−81 can be expressed as the complex number 9i.

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The other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

Given that x = -9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0, we can use the determinant of the matrix to find the other roots. The determinant of the matrix is given by:

| (x,3,7)(2,x,2)(7,6,x) | = x(x*x - 2*6) - 3(2*x - 7*2) + 7(2*6 - 7*x)

= x^3 - 12x - 3(2x - 14) + 7(12 - 7x)

= x^3 - 12x - 6x + 42 + 84 - 49x

= x^3 - 67x + 126 = 0

Since x = -9 is a root, we can divide the polynomial by (x + 9) to get:

(x^3 - 67x + 126) / (x + 9) = x^2 - 9x - 14

Now we can use the quadratic formula to find the other two roots:

x = (-(-9) ± √((-9)^2 - 4(1)(-14))) / (2(1))

x = (9 ± √(81 + 56)) / 2

x = (9 ± √137) / 2

Therefore, the other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.

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Answer:

Step-by-step explanation:

There are four methods of sampling namely Random sampling,Stratified sampling, Cluster sampling and Multistage sampling. Let’s look at them one by one.

Random sampling - When each subject of the population is equally likely to be included in the sample, the sampling method is called random sampling.

Stratified sampling- Under this, the data are first divided into stratas. Each stratum consists of homogeneous subjects and strata are heterogeneous among themselves. Samples are randomly taken from each strata. Example- In an investigation of mortality rate of the insured, we can first subdivide the data into males and females and then take sample from each group. Here, male and female groups represent stratas.

Cluster sampling- Under this we first divide the data into clusters that are homogeneous among themselves and then select few of them and sample all observations from the randomly selected clusters. For example- suppose we want to take a sample of people's weight in a specific city. We observed that the areas in that city are similar to each other , so instead of travelling to each area and collecting data we can select few areas and then take observations from all people of those areas.

Multistage sampling - This adds one more stage to cluster sampling. Unlike cluster sampling where we sample all observations from the selected clusters, In multistage sampling we randomly sample observations from each selected cluster.

I hope this helped.

The linear system has a unique solution for all values of a except √(97/13), and infinitely many solutions or no solution for a = √(97/13).

To find the values of a for which the linear system has a unique solution, infinitely many solutions, or no solution, we can use the determinant of the coefficient matrix. The determinant of a 3x3 matrix is given by:

|A| = adg - beh + cfi - 3fci - 2c - 3ebh - 2b - 3dag - 2a

For a unique solution, the determinant of the coefficient matrix must be nonzero. For infinitely many solutions or no solution, the determinant must be zero.

For the given system, the coefficient matrix is:

⎡⎣⎢​1 2 −32 −1 54 1 a2−14​⎤⎦⎥

The determinant of this matrix is:

|A| = (1)(-1)(a2-14) - (2)(5)(4) - (-3)(-1)(1) - (3)(4)(a2-14) - (2)(1)(-3) - (3)(2)(4) - (2)(-1)(-3)

Simplifying this expression gives:

|A| = -a2 + 14 - 40 - 3 - 12a2 + 168 - 6 - 24 - 6

|A| = -13a2 + 97

For a unique solution, |A| ≠ 0:

-13a2 + 97 ≠ 0

13a2 ≠ 97

a2 ≠ 97/13

a ≠ √(97/13)

For infinitely many solutions or no solution, |A| = 0:

-13a2 + 97 = 0

13a2 = 97

a2 = 97/13

a = √(97/13)

Therefore, the linear system has a unique solution for all values of a except √(97/13), and infinitely many solutions or no solution for a = √(97/13).

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The value of x is 9.75

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Therefore, the other side of the small triangle = √12²+9² = √ 144+81 = √225 = 15

15/9+x = 12/15

225 = 12(9+x)

225/12 = 9+x

18.75 = 9+x

x = 18.75 -9

x = 9.75

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An engineer is hired to design a bridge to carry traffic across the river.  The length of the bridge is 324.35 meters.

To find the distance from point A to point B, we can use the Law of Sines. This states that the ratio of the length of a side of a triangle to the sine of the opposite angle is equal for all sides and angles of the triangle. In this case, we have:

AC/ sin(B) = AB/ sin(C)

We can plug in the given values and solve for AB:

250 m/ sin(49°52') = AB/ sin(90°)

Simplifying and rearranging, we get:

AB = (250 m * sin(90°))/ sin(49°52')

Using a calculator, we find that sin(90°) = 1 and sin(49°52') ≈ 0.7705. Plugging these values back into the equation, we get:

AB = (250 m * 1)/ 0.7705

AB ≈ 324.35 m

Therefore, the distance from point A to point B, and the length of the bridge, should be approximately 324.35 meters.

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Using synthetic division, the value of g(1) is 37.

To find g(1) using synthetic division, we need to divide the polynomial g(z) by the binomial (z - 1). The process of synthetic division is as follows:

1. Write down the coefficients of the polynomial g(z): 28, -9, -26, 10, 34
2. Write down the value of z that we are plugging in, which is 1, in the leftmost column.
3. Bring down the first coefficient, which is 28, to the bottom row.
4. Multiply the value in the bottom row by the value of z, which is 1, and write the result in the next column.
5. Add the value in the top row to the value in the bottom row and write the result in the bottom row.
6. Repeat steps 4 and 5 until all the columns are filled.
7. The last value in the bottom row is the remainder, and the values in the bottom row before the remainder are the coefficients of the quotient polynomial.

The synthetic division table looks like this:

1 | 28  -9  -26  10  34
|       28   19   -7   3
 | 28  19    -7   3   37

The remainder is 37, so g(1) = 37.

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Answer:

6

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6  

Answer: The two triangles created by the bank shot are similar.

Step-by-step explanation: The measures of the triangles are as follows:

Triangle 1:

Angle A = 53.14 degrees, Angle B = 36.86 degrees, Angle C = 90 degrees

Triangle 2:

Angle A = 53.14 degrees, Angle B = 36.86 degrees, Angle C = 90 degrees

Yes, the two triangles are similar.

Using the given percentage we can see that there are 78 filled pages.

We know that there are 800 cards and each page holds 8 cards, then the number of pages is:

N = 800/8 = 100

And we know that 22% of the album is empty, then 78% (the complement) of the album is filled, this means that the number of filled pages is given by the formula below.

F = 100*(78%/100%) = 100*0.78 = 78

We divide the percentage by 100% to make it a decimal number, so we can use it in the operation.

There are 78 filled pages in the album.

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Answer:

x=25°

Step-by-step explanation:

please mark as brainliest

Answer:

See below.

Step-by-step explanation:

We are asked to find the value of x, and what these 2 angles are.

We know that these angles are Vertical Angles.

Vertical Angles are angles that are opposite of each other and are equal. They're equal due to the two straight lines crossing over each other at the same angle.

These angles aren't Adjacent Angles because they aren't next to each other. These angles don't share a common side. (Ray)

Since Vertical Angles are equal:

[tex]75 = 4x - 25[/tex]

Simplify for x:

[tex]100=4x\\25 = x[/tex]

x will equal 25°.

The center height of the tent is 1.57 meters.

Triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry. Triangles come in a variety of forms, including equilateral, isosceles and scalene. The sum of the three interior angles of a triangle is always 180°, making it one of the few geometric shapes whose angles add up to a fixed number. Triangles are the strongest shape, making them ideal for construction and engineering projects.

Using the formula for the volume of a triangular prism, V = B x H x L, we can determine the center height, h, of the tent:

V = B x H x L
12.6 = 2.8 x H x 4.5
H = 12.6 ÷ (2.8 x 4.5)
H = 1.57 meters

Therefore, the center height of the tent is 1.57 meters.

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The equation that models the objective function for the cost,  C=1x+.80y. (A)

This equation is the correct model because it represents the cost, C, as a function of the number of x and y items. The cost of each x item is $1, and the cost of each y item is $0.80.

Therefore, the total cost will be the sum of the cost of x items and the cost of y items, which is represented by the equation C=1x+.80y.

In contrast, options B, C, and D do not accurately represent the cost as a function of the number of x and y items. Option B includes a subtraction of the cost of y items, which would not accurately represent the total cost.

Options C and D include incorrect coefficients for the cost of x and y items, which would also not accurately represent the total cost.

Therefore, the correct equation to model the objective function for the cost, C, is option A. C=1x+.80y.

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It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.

Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):

E = 10h

$1 = 10h

h = $1/10

Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.

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Carys earns one dollar in one-tenth of an hour, or six minutes.

The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.

Set E (the amount earned) to $1 and solve for h (the number of hours):

E = 10h

$1 = 10h

h = $1/10

As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.

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Ben is incorrect because, all of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.

A polygon is a geometric shape with a limited number of sides and two dimensions. The sides or edges of a polygon are formed by joining end-to-end segments of a straight line to form a closed shape. The intersection of two line segments, which results in an angle, is referred to as a vertex or corners.

The formula for calculating an interior angle in a regular polygon with n sides is (n-2) x 180 / n.

An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.

Substituting the angle in Ben's expression:

xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°

9x - 27° = 108

We observe that none of the value of x results in 108 degrees.

Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.

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The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.

Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.

Here we have

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour

The bale given is

                          Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

Here, number of customers = 2 + 4 + 6 + 8 = 20

No of customers that choose chocolate creamer = 6 + 8 = 14

The percentage of customers that put chocolate creamer

=  [ 14/20 ] × 100 =  70%

Therefore,

The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

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Answer: 70%

Step-by-step explanation:

Answer:2

Step-by-step explanation:

20 divided by 10 equals 2

1). The statement " If in the year 2000 the price index is 120 and the value of the price index in 2001 is 125, it implies that there was a 5% increase in the price level in 2001." is true. Percentage change = (New price index - Old price index) / Old price index x 100, Plugging in the values from the question:Percentage change = (125 - 120) / 120 x 100 = 4.17%. Therefore, there was a 4.17% increase in the price level in 2001. 2). The statement " The weighted aggregate price index assigns a lower weight to the items that are sold in higher quantities." is  False. This is false because these items have a greater impact on the overall price level

The price index measures the change in prices of a basket of goods and services from one period to another. In this case, the price index in 2000 is 120 and the price index in 2001 is 125. To calculate the percentage change in the price level, you can use the formula:

The weighted aggregate price index assigns a higher weight to the items that are sold in higher quantities. This is false because these items have a greater impact on the overall price level. For example, if the price of a popular item, such as gasoline, increases, it will have a greater impact on the overall price level than if the price of a less popular item, such as a luxury car, increases.

Therefore, the weighted aggregate price index assigns a higher weight to the items that are sold in higher quantities to accurately reflect their impact on the overall price level.

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The solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].

To solve for u in the equation [tex]82-u=266[/tex], we can use the additive property of equality. The additive property of equality states that if you add the same value to both sides of an equation, the equation will still be true.

Step 1: We can start by isolating the variable u on one side of the equation. To do this, we can add u to both sides of the equation:

[tex]82-u+u=266+u[/tex]

Step 2: Simplify the equation by canceling out the u terms on the left side of the equation:

[tex]82=266+u[/tex]

Step 3: Next, we can use the additive property of equality again to isolate the variable u on one side of the equation. To do this, we can subtract 266 from both sides of the equation:

[tex]82-266=266+u-266[/tex]

Step 4: Simplify the equation by canceling out the 266 terms on the right side of the equation:

[tex]-184=u[/tex]

Step 5: The final step is to write the solution in the form of u=____. We can do this by simply switching the sides of the equation:

[tex]u=-184[/tex]

Therefore, the solution to the equation [tex]82-u=266[/tex] is [tex]u=-184[/tex].

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An investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.

Value is a term used to describe the worth of something, either in terms of money, or in terms of importance or usefulness. Value can be determined in terms of the amount of money something is worth, or the level of importance or usefulness it has to someone. When something has a high value, it means that it is worth a lot of money or has a high level of importance or usefulness.

The value of an investment of $1,000 after 3 years at an annual interest rate of 7.5%, compounded annually, can be calculated using the following formula:

Future Value (FV) = Present Value (PV) × (1 + r)ⁿ

Where PV is the present value of the investment ($1,000 in this case), r is the annual interest rate (7.5%) and n is the number of years (3).

Using this formula, we can calculate the future value of the investment after 3 years as follows:

FV = $1,000 × (1 + 0.075)³

FV = $1,000 × 1.23228

FV = $1,232.28

Therefore, an investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.

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As you have two side lengths but no angle measures, the Pythagorean Theorem should be used to obtain the value of x.

Then the value of x is given as follows:

x = 36.3.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

x² + 19² = 41²

x = sqrt(41² - 19²)

x = 36.3.

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The only value of y that is a solution to the equation 40=5-7y is y=-5.

To identify solutions to a linear equation in one variable, we can plug in the given values of y and see if the equation is true.

For the first value of y, let's plug in y=1:
40=5-7(1)
40=5-7
40=-2

This equation is not true, so y=1 is not a solution to the equation.

Now let's try y=2:
40=5-7(2)
40=5-14
40=-9

This equation is also not true, so y=2 is not a solution to the equation.

Finally, let's try y=-5:
40=5-7(-5)
40=5+35
40=40

This equation is true, so y=-5 is a solution to the equation.

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