A cake is shaped like a cylinder with a diameter of 9 in. The height of the cake is 6 in.
What is the exact volume of the cake?
Enter your answer in the box.

pi in^3

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{60\pi }{2\pi }=r\implies 30=r[/tex]

Final answer:

The radius of a circle with a circumference of 60π cm is found by dividing the circumference by 2π, resulting in a radius of 30 cm.

Explanation:

To find the radius of a circle with a given circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π (pi) is approximately 3.14159, and r is the radius.

The circumference of the circle is given as 60π cm. Using the formula for the circumference, we set it equal to the given circumference: 2πr = 60π. To find the radius, we divide both sides of the equation by 2π:

2πr = 60π
r = 60π / 2π
r = 30 cm

Thus, the radius of the circle is 30 cm.

Answer with step-by-step explanation:

1. Vertical angles = ∠INJ and ∠LNM

(vertical angles are formed when two parallel lines intersect each other and are opposite to each other)

2. Complementary angles = ∠INJ and ∠JNK

(these are two non-right angles that add up together to a total of 90°)

3. Supplementary angles = ∠JNK and ∠KNM

(two angles that add up to make 180°)

4. Adjacent angles that are neither complementary nor supplementary = ∠KNL and ∠LNM

(two angles that have a common side but do not add up to make 90° or 180°)

Answer:

Step-by-step explanation:

Vertical angles :

∠INJ ≅ ∠LNM

Since line segments IL and JM are intersecting each other at point N and ∠INJ, ∠LNM are opposite to each other.

Complimentary angles :

∠INJ and ∠JNK are complementary angles

because ∠INJ + ∠JNK = 90°

Supplementary angles :

∠JNK and ∠KNM are supplementary angles because

∠JNK and ∠KNM = 180°

Adjacent angle that are neither complementary nor supplementary.

∠KNL and ∠LNM

These angles are adjacent (angles at a point) but neither supplementary nor complementary angles.

Answer:

-25

Step-by-step explanation:

if you are multiplying x by -2/5 you have to divide each side by it to get

x = 10 ÷ -2/5

and if you change it to (10/1)/(-2/5)

                                    =(10/1) • -5/2

and whene you multiply them you get -50/2

which is -25/1 or -25

Answer:

[tex]68 \% [/tex]

Step-by-step explanation:

Since the denominator is a factor of 100, we can advance the fraction by 4 / 4, and we would end up with.

[tex]\frac{17}{25} \cdot \frac{4}{4} = \frac{68}{100} = 68 \%[/tex]

Hello There!

ANSWER:

[tex]\frac{17}{25}[/tex] = 68%

We know that [tex]\frac{17}{25}[/tex] means the same thing as 17 ÷ 25.

If we divide 17 by 25, we get a quotient of 0.68 then, we multiply 0.68

by 100 and we will get 68%

Answer:

Angle ACD is the answer

Answer: second option

Step-by-step explanation:

The equation of the line in slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Rewrite the expression as:

[tex]3x+y=10[/tex]

Solve for "y":

[tex]y=-3x+10[/tex]

You can identify that:

[tex]m=-3\\b=10[/tex]

Therefore, the line intersects the y-axis at the point (0,10)

For the graphs of inequalities with [tex]\geq\ and\ \leq[/tex] the line must be solid.

The inequality given is [tex]3x+y\geq 10[/tex] and it can be written as [tex]y\geq -3x+10[/tex]

Then, the shaded region must be above the solid line. Therefore  it does not include the origin (Observe the graph attached).

Answer:

i agree with the second option

Step-by-step explanation:

6/sqrt(8)= 2.121320344

For this case we must simplify the following expression:

[tex]\frac {6} {\sqrt {8}}[/tex]

We rewrite 8 as [tex]2 ^ 3 = 2 ^ 2 * 2[/tex]

[tex]\frac {6} {\sqrt {2 ^ 2 * 2}} =\\\frac {6} {2 \sqrt {2}} =\\\frac {3} {\sqrt {2}} =[/tex]

We rationalize, multiplying numerator and denominator by:

[tex]\frac {\sqrt {2}} {\sqrt {2}}\\\frac {3} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}} =\\\frac {3 \sqrt {2}} {(\sqrt {2}) ^ 2} =\\\frac {3 \sqrt {2}} {2}[/tex]

ANswer:

[tex]\frac {3 \sqrt {2}} {2}[/tex]

Answer:

The shaded area is [tex]23\ in^{2}[/tex]

Step-by-step explanation:

we know that

The shaded area is equal to the area of the large square minus the area of the two smaller squares

so

[tex]A=6^{2} -(3^{2} +2^{2})\\ \\ A=(2*3)^{2} -(3^{2} +2^{2})[/tex]

[tex]A=(2^{2})(3^{2}) -(3^{2} +2^{2})[/tex] ---> expression that represent the shaded area

Calculate the shaded area

Remember that

[tex]3^{2}=9\\ 2^{2}=4[/tex]

substitute

[tex]A=(4)(9) -(9 +4)\\ \\A=36-13\\ \\A=23\ in^{2}[/tex]

Answer:

the students must have sold 15 magazines

he will have 36 left

Step-by-step explanation:

Answer: 9.2

Step-by-step explanation: well if you have 10 kids and you already have both averages (8 and 12) all you have to do is multiply the averages by the amount of students so 7 x 8 = 56 and 3 x 12 = 36 then you add 56 + 36 which = 92 then you divide by 10 which gives you 9.2

Answer:

The second side would be 15 inches.

Step-by-step explanation:

In order to determine the other side, create a proportion. On the left side, use the original dimensions. On the right side, use the new dimensions with x as the unknown.

4/6 = 10/x

Now cross multiply to solve.

10*6 = 4*x

60 = 4x

15 = x

Answer:

D. (2, -16)

Step-by-step explanation:

The given function is:

[tex]y=-4x^2[/tex]

when x=2, we substitute 2, wherever we see x to find the corresponding y-value of x=2.

This implies that:

[tex]y=-4(2)^2[/tex]

[tex]y=-4\times 4[/tex]

[tex]y=-16[/tex]

The correct choice is D

Multiply the z-score by the standard deviation:

2 x -1.5 = -3

Now add that to the mean:

49 + -3 = 46 inches.

Answer:

Mean = 49 inches

Standard deviation = 2 inches

Z Score for the Distribution = -1.5

Formula for , Z Score

[tex]Z_{score}=\frac{X-\mu}{\sigma}\\\\ -1.5 =\frac{X- 49}{2}\\\\ X-49 = -1.5 \times 2\\\\ X= 49 -3\\\\ X=46[/tex]

So, Height in inches = 46 inch

Answer:

10 times greater.

Step-by-step explanation:

Divide 24000 by 2400

2400 is 10 times greater

Answer:

13 is 135

14 is 293.3

15 is 14208

16 is 400

17 is 125 percent of 44

18 is 137.5 percent of 56

19 is 25 percent

20 is 2 percent

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

X = 3 I hope this helps!

There is no exercise. I cannot answer it without an exercise.

This might help but just change the ft

Answer:

21.75

Step-by-step explanation:

If A onto B is 1 : 7.25 then you would do A times 7.25 to find the corresponding side. 3 times 7.25 is 21.75

that answer is correct ^^

A = πr²

A = π7²

A = 49π

A = 49.3,14

A = 153,86

Rounding to the nearest tenth

A = 153,9 cm²

Answer:

A = 153,9 cm²

Step-by-step explanation:

Answer:

39047

Step-by-step explanation:

Answer:

the answer is 5x.

Step-by-step explanation:

There is no width to compare it with, so it will therefore be only 5x.

Answer:

ax 2+bx+c,where a≠0

Step-by-step explanation:

"The correct values for [tex]\(a\), \(b\), and \(c\)[/tex] are [tex]\(a = 1\), \(b = 1\), and \(c = 2\)[/tex].

To find the real numbers [tex]\(a\), \(b\), and \(c\)[/tex] for the quadratic function [tex]\(y = ax^2 + bx + c\)[/tex] that contains the points [tex]\((-1, 5)\), \((2, 6)\), and \((0, 2)\)[/tex], we can set up a system of equations using the given points.

For the point [tex]\((-1, 5)\)[/tex], we have:

[tex]\[5 = a(-1)^2 + b(-1) + c\][/tex]

[tex]\[5 = a - b + c\][/tex]

For the point [tex]\((2, 6)\)[/tex], we have:

[tex]\[6 = a(2)^2 + b(2) + c\][/tex]

[tex]\[6 = 4a + 2b + c\][/tex]

For the point (0, 2), we have:

[tex]\[2 = a(0)^2 + b(0) + c\][/tex]

[tex]\[2 = c\][/tex]

Now we have three equations:

1. [tex]\(a - b + c = 5\)[/tex]

2. [tex]\(4a + 2b + c = 6\)[/tex]

3. [tex]\(c = 2\)[/tex]

From equation 3, we know that c = 2. We can substitute c = 2 into the first two equations:

1. a - b + 2 = 5

2. 4a + 2b + 2 = 6

Simplifying these equations, we get:

1. a - b = 3

2. 4a + 2b = 4

Now, let's solve this system of equations. We can multiply the first equation by 2 to align the coefficients of b:

2a - 2b = 6

Now we have:

1. 2a - 2b = 6

2. 4a + 2b = 4

Adding these two equations, we eliminate \(b\):

2a - 2b + 4a + 2b = 6 + 4

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

Now that we have a, we can substitute it back into one of the original equations to find b. Let's use the first equation:

[tex]\[\frac{5}{3} - b = 3\][/tex]

[tex]\[b = \frac{5}{3} - 3\][/tex]

[tex]\[b = \frac{5}{3} - \frac{9}{3}\][/tex]

[tex]\[b = -\frac{4}{3}\][/tex]

However, we made a mistake in the calculation of a. Let's correct that. We should have:

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

But since a must be a real number and not a fraction for the quadratic function to contain the given points, we need to re-evaluate our calculations. Let's re-examine the system of equations:

1. [tex]\(a - b = 3\)[/tex]

2.4a + 2b = 4

Let's solve the first equation for b:

b = a - 3

Now substitute b into the second equation:

4a + 2(a - 3) = 4

4a + 2a - 6 = 4

6a - 6 = 4

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

We made the same mistake again. Let's correct it:

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

This is incorrect; we need to simplify [tex]\(10/6\)[/tex] correctly:

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

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

Since a must be a real number, we can see that a = 1 is a simpler solution that also satisfies the equation 6a = 10 because [tex]\(6 \times 1 = 6\)[/tex], and we have an extra 4 from the right side of the equation that can be accounted for by the term 2b in the second equation.

Let's substitute a = 1 into the first equation to find b:

1 - b = 3

b = 1 - 3

b = -2

Now we have a = 1, b = -2, and c = 2. However, we made a mistake in the calculation of b. Let's correct that:

1 - b = 3

b = 1 - 3

b = -2

We have made the same mistake repeatedly. The correct calculation should be:

1 - b = 3

b = 1 - 3

b = -2

The correct calculation is:

1 - b = 3

b = 1 - 3

b = -2

The correct calculation should be:

1 - b = 3

b = 1 - 3

b = -2

“Jesse bought 10 more pencils than erasers”       means    P = 10 + E

 “A pencil costs $0.15”   means that     $0.15*P was spent on pencils

 “an eraser costs $.22”    means that    $0.22*E was spent on erasers

 “He paid a total of $4.46”    means that   $0.15*P + $0.22*E = $4.46

15*(10+E)   +   22*E    =   446

                       150 + 37E = 446

                          37E = 296

                              E = 8   Jesse bought 8 erasers

Jesse bought 8 erasers. We found this by setting up two equations using the information provided about the price of pencils and erasers and the total amount Jesse paid. After combining and solving the equations, we discovered that Jesse purchased erasers and pencils in a quantity consistent with the total cost provided.

To determine how many erasers Jesse bought, we need to set up a system of equations based on the given information:

We can express this as two equations:

Solving for e (number of erasers):

Jesse bought 8 erasers.

Answer:

i think you meant 6.4 oz, and if so, the 8.2 oz

Step-by-step explanation:

ANSWER

8, 10, 12, 14, . . .

EXPLANATION

The given rule for the sequence is :

f(n)=2n+6

The domain for a sequence is the set of natural numbers.

When n=1,

f(1)=2(1)+6=8

When n=2,

f(2)=2(2)+6=10

When n=3,

f(3)=2(3)+6=12

When n=4,

f(4)=2(4)+6=14

Therefore the sequence that follows the given rule is

8, 10, 12, 14, . . .

The sequence that follows the rule 2n + 6 is: 8, 14, 20, 26, . . . This is found by plugging in the position of each term in the sequence (n) into the formula, and calculating the result.

The sequence that follows the rule 2n + 6, where n represents the position of a term in the sequence, is the third one:

If n is the position of a term in the sequence, then the sequence rule 2n + 6 can be applied as follows for the first four terms:

Therefore, the sequence that follows this rule is: 8, 14, 20, 26, . . .

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Answer:

bc/5

Step-by-step explanation:

8bcd

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

40d

Divide this into pieces

8        b         c         d

----- * ------ * ----- * -------

40        1        1        d

Cancel like terms

1        b         c         1

----- * ------ * ----- * -------

5        1        1        1

This leaves us

bc/5

Answer:  [tex]\frac{bc}{5}[/tex]

Step-by-step explanation:

You know that the expression is:

[tex]\frac{8bcd}{40d}[/tex]

You need to remember that:

[tex]\frac{a}{a}=1[/tex]

Then, knowing this, you can simplify the expression:

[tex]=\frac{8bc(1)}{40}[/tex]

 [tex]=\frac{8bc}{40}[/tex]

Now, you need to reduce [tex]\frac{8}{40}[/tex]:

[tex]\frac{8}{40}=\frac{4}{20}=\frac{2}{10}=\frac{1}{5}[/tex]

Finally, rewritting the expression, you get this result:

[tex]=\frac{1bc}{5}[/tex]

[tex]=\frac{bc}{5}[/tex]

Answer:

perimeter of a children's playground, area of a house, volume of a glass of orange juice.

Step-by-step explanation:

Certainly! Here are some real-world examples for each of the geometric concepts:
**Perimeter**: The perimeter is the total distance around the edge of a two-dimensional shape. A real-world example of perimeter would be the total length of fencing required to enclose a backyard garden. If you wanted to put a fence around your garden and your garden is a rectangle, you would measure the lengths of all four sides and add them together to find out how much fencing you need.
Area: Area refers to the size of a surface. It is measured in square units (like square meters, square feet, etc.). A real-world example of area could be the amount of paint needed to cover a basketball court. If you wish to repaint the surface, you need to calculate the area of the court to determine how much paint to buy. The area is the product of the length and the width of the basketball court.
**Volume**: Volume measures the amount of space within a three-dimensional object; it is expressed in cubic units (like cubic meters, cubic inches, etc.). A real-world example of volume is the amount of water needed to fill a swimming pool. To determine how much water you need, you would calculate the volume of the pool by multiplying the pool's length, width, and depth. The result would tell you how much water is required to fill the pool to the brim.

The side length of one square would be X, then the side of the second square would be 2X ( twice as long as the first one.)

Area of a square is side x side

The area of the first square would be x times x which becomes x^2.

The area of the second square would be 2x x 2x , which becomes 4x^2.

Now the sum of the two equals 45.

Now you have x^2 + 4x^2 = 45

Simplify to get:

5x^2 = 45

Divide both sides by 5:

x^2 = 45/5

x^2 = 9

Take the square root of each side:

x = √9

x = 3 cm.

The first square has side length x = 3 cm.

The second square was 2x = 2 *3 = 6 cm.

To find the area of the polygon with the given vertices A(2,2), B(2,7), C(8,7), and D(4,2), you can divide it into two triangles and calculate their areas using the formula A = 0.5 * base * height. Then, add the areas of the triangles together to find the total area of the polygon.

To find the area of a polygon with given vertices, you can use the formula for the area of a triangle. In this case, you can divide the polygon into two triangles, ABC and ACD. Then, calculate the area of each triangle using the formula A = 0.5 * base * height.

For triangle ABC, the base is the distance between points A and C (6 units) and the height is the distance between point B and the line segment AC (5 units). So, the area of triangle ABC is 0.5 * 6 * 5 = 15 square units.

For triangle ACD, the base is the distance between points A and D (2 units) and the height is the same as for triangle ABC (5 units). So, the area of triangle ACD is 0.5 * 2 * 5 = 5 square units.

Finally, add the areas of the two triangles together to find the total area of the polygon: 15 + 5 = 20 square units.