Find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 8 ft. Round your answer to the nearest tenth of a cubic foot

5. 20% of students said that they enjoy Cookie Cake.

6. 25 students answered a survey regarding their favorite cake.

The percentage is defined as a ratio expressed as a fraction of 100.

The % formula is used to calculate a percentage of a whole in terms of 100.

Percentage = (Value/Total Value) × 100

Percentage of students said they like Cookie Cake:

5/(5 + 6 + 8 + 6) × 100%

5/25 × 100%

20%

The total number of students who answered this survey about their favorite Cake:

5 + 6 + 8 + 6

25

Thus, 25 students answered a survey regarding their favorite cake.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

The area of the following circle is A ≈ 153.86 square units.

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.

The circumference of a circle is the distance around the edge of the circle, and it is calculated using the formula C = 2πr, where r is the radius and π (pi) is a mathematical constant approximately equal to 3.14159. The area of a circle is the region enclosed by the circle, and it is calculated using the formula A = πr².

The diameter of the circle is 14, so the radius is half of that, which is 7.

The area of the circle is given by the formula A = πr², where r is the radius. Substituting in the values we get:

A = π(7)²

A = 49π

Therefore, the area of the circle is 49π square units. If you want to use an approximation, you can use 3.14 as an estimate for π and get:

A ≈ 153.86 square units.

To know more about area visit:

brainly.com/question/12187609

#SPJ1

The complete question is -

Answer:

Step-by-step explanation:

2(2x+2) + 2(x+4) = 36

4x+4 +2x+8 =36

6x+12= 36

6x = 36-12

6x =24

x = 4

longer side = 10

Table that represent input & output value  would be:

Input Output

44            45

45            46

46            47

To determine which table represents inputs and outputs that follow the same rule as 44+1, 44+2, and 44+3, we can simply evaluate each of the expressions and look for a pattern.

44 + 1 = 45

44 + 2 = 46

44 + 3 = 47

Therefore, the rule appears to be adding 1 to each subsequent number. We can check this by evaluating additional terms:

44 + 4 = 48

44 + 5 = 49

Based on this pattern, the correct table would be:

Input Output

44            45

45            46

46            47

To learn more about subsequent number

https://brainly.com/question/30826580

#SPJ4

Using the Gaussian elimination method, the general solution is:               [tex]\[ x = -31t + 6 \][/tex], [tex]\[ y = 5 \][/tex], [tex]\[ z = 31t \][/tex].

To solve this system of equations, we can use the Gaussian elimination method. This method involves creating a matrix with the coefficients of the equations and using row operations to reduce the matrix to a form that can be easily solved.

First, we create a matrix with the coefficients of the equations:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 2 & 3 & 2 & 3 \\ 2 & 1 & 2 & -7 \\ 1 & -3 & 2 & 10 \\ -1 & 3 & -1 & -6 \\ -1 & 3 & 2 & 6 \\ 6 & -2 & 2 & 4 \\ 3 & -1 & 2 & 2 \\ -12 & 4 & -8 & 8 \end{array} \right) \][/tex]

Next, we use row operations to reduce the matrix to a form that can be easily solved:

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & -1 & 0 & -5 \\ 0 & -4 & 1 & 11 \\ 0 & 4 & 0 & -5 \\ 0 & 4 & 1 & 7 \\ 0 & -8 & -4 & 10 \\ 0 & -4 & -1 & 5 \\ 0 & 8 & 4 & -4 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 1 & 1 & -1 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 27 \\ 0 & 0 & -4 & 50 \\ 0 & 0 & -1 & 25 \\ 0 & 0 & 4 & -44 \end{array} \right) \][/tex]

[tex]\[ \left( \begin{array}{ccc|c} 1 & 0 & 1 & -6 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 31 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -4 \\ 0 & 0 & 0 & 174 \\ 0 & 0 & 0 & 56 \\ 0 & 0 & 0 & -168 \end{array} \right) \][/tex]

From this reduced matrix, we can see that there are infinitely many solutions to this system of equations. The general solution can be written as:
[tex]\[ x = -31t + 6 \][/tex]
[tex]\[ y = 5 \][/tex]
[tex]\[ z = 31t \][/tex]
Where t is any real number.

Know more about Gaussian elimination here:

https://brainly.com/question/14529256

#SPJ11

The fourth proportion to 15/7,23/14, and 33/5 is 19.25.

To discover the fourth proportion, we require to set up a probability between the 3 presented figures and the fourth unknown variety, which we can name x.

23/1433/5 x

First, we need to transfigure all the mixed figures to unsuitable fragments

= (7/7 * 1)5/7 = 7/75/7 = 12/7

= (14/14 * 2)3/14 = 28/143/14 = 31/14

= (5/5 * 3)3/5 = 15/53/5 = 18/5

Now we're suitable to preference those values into the share

31/1418/5 x

To break for x, we're suitable to cross-multiply

12/7) * x = (31/14) *(18/5)

Simplifying

12x/ 7 = 279/14

Multiplying each aspects via7/12

x = (279/14) *(7/12)

x = 19.25

Thus, the fourth proportion to 15/7,23/14, and 33/5 is 19.25.

Learn more about proportion:-

https://brainly.com/question/870035

#SPJ4

The value of c is 10.

The value of c is 10. To find this, use the limit definition of continuity. This states that for the function to be continuous at x = 4, we must have f(4) = lim f(x) x -> 4. Thus, we can equate f(4) and lim f(x) x -> 4 to get 1/4*4 + c = -4 + 6, giving c = 10.

Learn more about continuous function

brainly.com/question/21447009

#SPJ11

An expression that looks like Sarah's expression but is not equivalent is:

10(5j + j + 3).

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2. This statement is represented mathematically by the expression x/2 + 6. Using mathematical expressions, complex puzzles can be solved.

now in the question,

We can write a look alike expression which is not equivalent is:

10(5j + j + 3).

Now translating the new expression into verbal:

Sarah gets paid $10 for every shark tooth she finds. After finding 3, she asked Jhon for help. When Jhon finds a tooth, by that time Sarah finds 5 of them.

To know more about expressions, visit:

https://brainly.com/question/14083225

#SPJ1

The spinner  probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.

Spinner Results

Color Frequency

Red 20

Blue 9

Green 19

Yellow 14

Purple 14

Total outcomes: 20 + 9 + 19 + 14 + 14

Total outcomes: 76

spinner probability = favorable outcome / total outcome

favorable outcome (red or green or purple) = 20 + 19 + 14 = 53

spinner probability = 53 / 76 = 0.69

spinner probability = 0.70

Thus, the probability that the next spin will land either red or green or purple is found 0.70 as a decimal to the nearest hundredth.

Know more about probability in spinner

https://brainly.com/question/27460972

#SPJ9

Answer:

Year 1 Depreciation:$2,000

Depreciation Percentage:20.00%

Total Depreciation:$10,000

Final Year Depreciation:$2,000

Step-by-step explanation:

P.S by teacher told me the answer

Note that the pair of numbers that solves the system of equations:

y=11x+40; and

y= -7x+9

are,  x = -31/18  ; and y = 379/18.

To solve the system of equations, we need to find the values of x and y that satisfy both equations simultaneously. One way to do this is to set the expressions for y equal to each other, since both expressions represent the same value of y.

So we have:

11x + 40 = -7x + 9

Simplifying and solving for x, we get:

18x = -31

x = -31/18

Now that we have found the value of x, we can substitute it into either equation to find the corresponding value of y. Let's use the first equation:

y = 11(-31/18) + 40

y = -341/18 + 720/18

y = 379/18

Therefore, the pair of numbers that solves the system of equations is (-31/18, 379/18).

Learn more about system of equations at:

https://brainly.com/question/21620502

#SPJ1

Answer:

66.5

Step-by-step explanation:

average the 2 together (57+76)/2

Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

To find i (the rate per period) and n (the number of periods) for the given annuity, we need to use the formula for the future value of an annuity:

FV = PMT × [(1 + i)^n - 1] / i

Where FV is the future value, PMT is the periodic payment, i is the rate per period, and n is the number of periods.

Given:
PMT = $305
i = 8.5% / 12 = 0.00708333 (since the interest is compounded monthly)
n = 7 × 12 = 84 (since there are 12 months in a year and the deposits are made for 7 years)

Plugging these values into the formula, we get:

FV = $305 × [(1 + 0.00708333)^84 - 1] / 0.00708333

FV = $305 × [1.80722 - 1] / 0.00708333

FV = $305 × 0.80722 / 0.00708333

FV = $34563.89

Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

Learn more about period

brainly.com/question/16061498

#SPJ11

The vectors are linearly independent.

The vectors u = (2,1,0), v = (-4,3,1), and w=(0,-2,-5) are linearly dependent if there exists scalars c1, c2, and c3 such that c1u + c2v + c3w = 0. To determine if this is the case, we can form a matrix with the vectors as columns and find its determinant. If the determinant is 0, then the vectors are linearly dependent. If the determinant is not 0, then the vectors are linearly independent.

The matrix formed by the vectors is:
```
| 2 -4 0 |
| 1  3 -2|
| 0  1 -5|
```

The determinant of this matrix is:
```
2(3(-5) - (-2)(1)) - (-4)(1(-5) - (0)(-2)) + 0(1(1) - (0)(3))
= 2(-15 + 2) + 4(5) + 0
= 2(-13) + 20 + 0
= -26 + 20
= -6
```

Since the determinant is not 0, the vectors are linearly independent.

Learn more about linear dependence here https://brainly.in/question/5157143.

#SPJ11

The annual interest rate on Susan's savings account is 4%.

Annual interest rate, also known as annual percentage rate is the yearly interest generated by a sum that's charged to borrowers or paid to investors We can use the simple interest formula to calculate the annual interest rate which is Simple Interest = (Principal x Rate x Time)

By plugging our values, we get.

$54 = ($900 x Rate x 1.5)

Simplifying the equation:

Rate = $54 / ($900 x 1.5)

Rate = 0.04

Rate = 4%.

Read more about interest rate

brainly.com/question/25793394

#SPJ1

Answer:

Area of a triangle =L*W

A= 45*15

A=270cm²

The equation that describes the plant's height is y = 3 + 0.5x .

The equation that describes the plant's height is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + c

Where:

m = slope

c = intercept

Plant's height = starting height + (rate of growth x number of weeks)

y = 3 + (0.5 x x)

y = 3 + 0.5x

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

To find f(x)-g(x), we need to subtract the two given functions.

f(x) = x^(2)-6x-40

g(x) = x+4

f(x)-g(x) = (x^(2)-6x-40) - (x+4)

Next, we need to distribute the negative sign to the terms inside the parentheses:

f(x)-g(x) = x^(2)-6x-40 - x - 4

Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44

Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.

To know more about polynomial click on below link :

https://brainly.com/question/11536910#

#SPJ11

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7  expression years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

Let's start by calculating the entire amount of creamer in grammes:

(Number of cartons) x (Total quantity of creamer) (Amount of creamer per box)

15 boxes x 450 grammes each box = total quantity of creamer

Total creamer weight = 6,750 g

(Total amount of creamer in grammes) / number of days (Amount of creamer consumed per day in grams)

The number of days is 6,750 grammes divided by 5 grammes each day.

The number of days is 1,350.

As a result, the 15 cartons of creamer will last for 1,350 days, or nearly 3.7 years. This implies the consumer drinks one serving of creamer per day at a weight of 5 grammes per serving.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

Answer: 50%

Step-by-step explanation: There are 5 out of 10 employees at the water slide. 10 in this situation is going to be 100%

since there is only 5 out of 10 employees that are temporary

it would be 50%

Answer: 50%

Step-by-step explanation:

The value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100) is 1,350.98.

To find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100), we need to simplify and perform the arithmetic operations.

Multiplying each term in the expression, we get:

1 × 1,000 = 1,000

3 × 100 = 300

5 × 10 = 50

9 × 1/10 = 0.9

8 × 1/100 = 0.08

Adding up all the terms, we get:

1,000 + 300 + 50 + 0.9 + 0.08 = 1,350.98

In summary, to find the value of the expression, we multiply each term by its respective coefficient, then add up all the terms. In this case, the result is 1,350.98.

To learn more about expression click on,

https://brainly.com/question/27850538

#SPJ4

Complete question is:

Find the value of the expression (1×1,000)+(3×100)+(5×10)+(9×1/10)+(8 x 1/100)?

Answer:

c landing on 1 is the answer

hope it helps u mark me BRAINLIST

The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)

To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:

A' = k * (A - O) + O

B' = k * (B - O) + O

where k is the scale factor, O is the center point of dilation, and A and B are the original points.

In this case, k = 2 and O = (0, 0). So we have:

A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)

B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)

Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.

So, the answer is option (A) OA (-8, 2) and B (-2, 6).

Learn more about coordinates here:https://brainly.com/question/17206319

#SPJ1

Answer:

Step-by-step eEIKxplanation:

In the triangle ABC, the value of x, y and z is obtained as 21, 7 and 48 units respectively.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangle ABC is given.

The measure of AB is given as 16 + z units.

The measure of AD is given as 16 units.

The measure of DB is given as z - 16 units.

The measure of BE is given as 21 units.

The measure of BC is given as x units.

The measure of AC is given as 14 units.

According to the midpoint theorem, the length of DE is -

DE = 1/2 (AC)

y = 1/2 (14)

y = 7 units

Therefore, the value of y is obtained as 7 units.

Now according to indirect measurement -

AB / AC = BD / DE

Substitute the values in the equation -

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 48

Therefore, the value of z is obtained as 48 units.

Now according to indirect measurement -

BC / AC = BE / DE

Substitute the values in the equation -

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Therefore, the value of x is obtained as 21 units.

To learn more about triangles from the given link

brainly.com/question/25215131

#SPJ1

Answer:

x = 21

y = 7

z = 32

Step-by-step explanation:

DE = 1/2 (AC)

y = 1/2 (14)

y = 7

AB / AC = BD / DE

Substitute values

16 + z / 14 = z - 16 / 7

7(16 + z) = 14(z - 16)

112 + 7z = 14z - 224

7z - 14z = -224 - 112

-7z = -336

z = 32

BC / AC = BE / DE

Substitute values

21 + x / 14 = 21 / 7

7(21 + x) = 14 × 21

147 + 7x = 294

7x = 294 - 147

7x = 147

x = 21

Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex] feet represents the distance between the two staircases on the tree. Thus, option c is correct.

The Pythagorean theorem states that the square length of the hypotenuse, or the side that faces the right angle, of a right triangle is equal to the sum of the square lengths of the other two sides. The following can be expressed mathematically: [tex]a^2 + b^2 = c^2[/tex] where "c" represents the length of the hypotenuse and "a" and "b" represent the measurements of the two sides of the right triangle.

given

Assume the tree is h feet tall, the higher ladder is 3 feet long, and the lower ladder is x feet long.

Using the Pythagorean formula, we can create two equations:

With regard to the narrower staircase,  x² + h² = (3.5)

Use the formula for the higher ladder. (3x)²+ h²= (7.5)².

The formulas are as follows, simplified: 12.25 x² + 9.25 x² + 56.25

To remove h2, we can solve for x in the first equation and y in the second equation: 8x² = 44.

Finding the value of x is as follows:   [tex]x = \sqrt{(5.5) } = 2.34[/tex]

Therefore, [tex]h = \sqrt{(12.25 - x^2)} = 3.73[/tex]  feet represents the distance between the two staircases on the tree.

To know more about Pythagorean theorem visit:

brainly.com/question/14930619

#SPJ1

Complete question:

Two ladders are placed at different locations on a coconut palm tree so that lights can be installed, as pictured below. The length of the taller ladder is three times the length of the shorter ladder. The shorter ladder is placed 3.5 feet from the base of the tree while the taller ladder is placed 7.5 feet from the base of the tree. What is the distance on the tree between the two ladders?

O 4.59 feet

O 9.78 feet

O 3.73 feet

O 8.96 feet

We are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.

The critical numbers of a function are the points where the derivative of the function is either zero or undefined. To find the critical numbers of the given function f(x) = x^2/(3-x), we need to first find its derivative:

f'(x) = (2x(3-x) - (-1)x^2)/ (3-x)^2 = (6x - x^2 - x^2)/ (3-x)^2 = (6x - 2x^2)/ (3-x)^2

Now, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined. f'(x) is undefined when the denominator (3-x)^2 is equal to 0, which occurs when x = 3. f'(x) is equal to 0 when the numerator 6x - 2x^2 is equal to 0:

6x - 2x^2 = 0
2x(3 - x) = 0
x = 0 or x = 3

However, we are only interested in the critical numbers on the interval [1,3], so we can disregard x = 0. Therefore, the critical numbers of the function f(x) on the interval [1,3] are x = 3.

Answer: 3

Learn more about critical numbers

brainly.com/question/29743892

#SPJ11

Answer:

IQR - 31

You first need to find the median. After find the middle number in the numbers before and after your median. This will give you your first and third quartile. Add these together then divide by two. This will give your IQR.

The conditional expectation of Y given that X is less than or equal to 1/2 is calculated by taking the weighted average of the possible values of Y, with the weights being the probabilities of X being less than or equal to 1/2 for each value of Y.
The formula for E(Y | X<=1/2) is:
E(Y | X<=1/2) = ∑y P(Y=y | X<=1/2) * y
To find P(Y=y | X<=1/2), we can use the formula:
P(Y=y | X<=1/2) = P(X<=1/2 | Y=y) * P(Y=y) / P(X<=1/2)
We can then plug in the values for each possible value of Y and calculate the conditional expectation.

For example, if Y can take on the values 0, 1, and 2, and the probabilities of X being less than or equal to 1/2 for each value of Y are 0.2, 0.5, and 0.3, respectively, and the probabilities of Y being 0, 1, and 2 are 0.4, 0.3, and 0.3, respectively, then:
E(Y | X<=1/2) = (0.2 * 0.4 / 0.5) * 0 + (0.5 * 0.3 / 0.5) * 1 + (0.3 * 0.3 / 0.5) * 2
E(Y | X<=1/2) = 0 + 0.3 + 0.36
E(Y | X<=1/2) = 0.66

Therefore, the conditional expectation of Y given that X is less than or equal to 1/2 is 0.66.

To know more about conditional expectation refer here:

https://brainly.com/question/4434964

#SPJ11