A pyramid has a square base and a height of 6 ft. The volume of the pyramid is 162 ft^3. Let s be the length of a side of the pyramid's base.
A) In terms of s, the area of the base is ____________ .
B) The formula for the volume of a pyramid gives the equation ___________.
C) Solving this equation shows that s = __________

Answers

Answer 1

Answer:

[tex](a)s^2\\(b)162=2s^2\\(c)s=9$ ft[/tex]

Step-by-step explanation:

(a)Base Area

Side length of square base=s

Area of a Square of side length s=[tex]s^2$ ft^2[/tex]

(b)

Height =6 ftVolume=[tex]162 $ ft^3.[/tex]

Volume of a Pyramid[tex]=\frac{1}{3}X$Base Area X Height[/tex]

Substituting the given values, we have:

[tex]162=\frac{1}{3}Xs^2 X 6\\\\162=2s^2[/tex]

(c)Solving the equation derived from (b)

[tex]162=2s^2\\$Divide both sides by 2\\s^2=81\\s^2=9^2\\s=9$ ft[/tex]

Solving this equation shows that s =9 ft.


Related Questions

An online store furniture sells chairs for $200 each and tables for $500 each.

Answers

Answer: what is the question?

Step-by-step explanation:

The area of a parrellogram is 31.5ft and height is 6.3ft. What is the length of the base

Answers

Answer:

Area = base × height

31.5 = base × 6.3

base = 5 ft

Answer:

5 feet

Step-by-step explanation:

The area formula is A = b * h, where A is the area, b is the length of the base, and h is the height. Since we want to know the length of the base, we are solving for b. Thankfully, we know that A = 31.5 and h = 6.3. When we plug them into the equation, we get 31.5 = b * 6.3. Because we want b on one side without any coefficients and numbers on the other side, we can divide the equation by 6.3 on both sides. The equation will remain the same because we are doing the same thing to both sides. When we divide, we get b = 31.5 / 6.3 = 5 feet. Hope this helps!

Someone please help me

Answers

Answer:

3/19

Step-by-step explanation:

Answer:

im havijn trouble 2Step-by-step explanation:

idkmsorry

A scientist wants to find the average weight of fish living in a large pond. So she will use the weights of 25 fish from the pond to find the average weight

Answers

Answer:

Use interval estimation to compute the average weight of fish living in a large pond.

Step-by-step explanation:

In statistic, point estimation comprises of the use of sample data to estimate a distinct data value (known as a point estimate) which is to function as a "best guess" or "best estimate" of an unidentified population parameter.  

The point estimate of the population mean (µ) is the sample mean ([tex]\bar x[/tex]).

Now according to the law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ([tex]\bar x[/tex]) approaches the whole population mean (µ).

That is, [tex]\bar x[/tex] →  µ as n → ∞.

The scientist uses the weights of 25 fish from the pond to find the average weight.

The sample is large, but not large enough.

So, use interval estimation to compute the average weight of fish living in a large pond.

The interval estimation is the best way to estimate the true value of a parameter. This is because the interval of values computed for the parameter has certain probability of containing the true parameter value.

The (1 - α)% confidence interval for population mean is an interval estimate.

obteber dos números tales que la suma de uno de ellos con el doble del cuadrado del otro sea igual a 7776 , y el producto de ambos sea máximo

Answers

Answer: the numbers are 5,111.3 and 35.74

Step-by-step explanation:

I will answer this in English.

We have the numbers X and Y, ad we have that:

X + 2*Y^2 = 7776

X = 7776 -  2*Y^2

Now we also want that the product of X and Y is a maximum.

The equation of maximum product is

P(Y) = X*Y = (7776 -  2*Y^2)*Y

       = 7776*Y - 2*Y^3

Now, to find the maximum we must derivate and find the value where P'(Y) is equal to 0

P'(Y) = 7776 - 6*Y^2 = 0

7776 = 6*Y^2

Y = √(7776/6) = 35.74

Now, we replace this value in the equation for X and we can find X:

X = 7776 -  2*Y^2  = X = 7776 -  2*(35.74)^2 = 5,111.3

50 POINTS
Amber has 12n + 50 pieces of candy, her brother has 8n - 26 pieces. How many more pieces of candy does Amber have than her brother?

Answers

Answer:

i think is 64

Step-by-step explanation:

Determine the number of real solutions for each system of equations.

Answers

Answer:

1+1=2

Step-by-step explanation:

What’s the correct answer for this question?

Answers

Answer:

C

Step-by-step explanation:

In the attached file

Find the value of X, Z and Y.

Answers

Answer:

x = 5; y = 138, z= 42

Step-by-step explanation:

4x- 17 = 3 [ opposite sides of a parallelogram are equal]

4x = 3+ 17 = 20; X= 20/4 = 5

138 + Z = 180( angle on a straight line)

Z is an alternate angles to the remaining angle off 138 forming the straight line.

z= 180-138 = 42 degrees

Y = 138 [ opposite angles of a regular quadilareral been equal]

A bicycle club logged 9,860 miles. If the
29 members of the club each rode the
same number of miles, how many miles
did each member ride?

Answers

Answer:

[tex]340[/tex] miles,

Step-by-step explanation:

To find out how many miles each person rode, divide the total number by how many people there were.

[tex]9860 / 29 = 340[/tex]

Each person rode [tex]340[/tex] miles.

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer these 2 questions!

Answers

Answer:

A. [tex]G(x) = 7x^2[/tex]

D. No, because one x-value corresponds to two different y-values.

Step-by-step explanation:

If you were to vertically stretch the quadratic parent function, the correct answer would be "A," because you are stretching upwards, which in turn, also changes the y-values.

As you can see in the table, the x-value of 3 repeats, which cannot occur. Each input (x-value) can go to only one output (y-value). As a result, the table does not represent a function.

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.

Answers

Answer: A

I just love your questions. You always put "No guessing" haha.

Step-by-step explanation:

[tex]f(x)=3^x+10x\\g(x)=2x-4[/tex]

[tex](f+g)(x)=[/tex]

This basically means you have to take both functions and add them together.

[tex](f+g)(x)=(3^x+10x)+(2x-4)\\(f+g)(x)=3^x+10x+2x-4\\[/tex]

Combine like terms;

[tex](f+g)(x)=3^x+12x-4[/tex]

Given function f(x)=x^2+5, determine the value of f(f(5))

Answers

Answer:

905

Step-by-step explanation:

So your original equation is f(x) = x² + 5

First lets work with the stuff inside the parentheses.

f(5) = 5² + 5 = 30

So now you are finding,

f(f(5)) => f(30)

f(30) = 30² + 5 = 900 + 5 = 905

Exponential form of xyyzzz

Answers

Answer:

  xy²z³

Step-by-step explanation:

An exponent is a way to indicate the number of times the factor is repeated. When it is 1, it is rarely shown.

  x is repeated once, so will appear without an exponent

  y is repeated twice, so will have an exponent of 2

  z is repeated 3 times, so will have an exponent of 3

__

  xyyzzz = xy²z³

_____

In plain text, an exponent is indicated with a caret (^).

  xy^2z^3

Identify whether each of the following statements is more appropriate as a null hypothesis or an alternative hypothesis. Hypothesis: The number of hours that grade-school children spend doing homework predicts their future success on standardized tests. Hypothesis: King cheetahs on average run the same speed as standard spotted cheetahs. Hypothesis: The mean length of African elephant tusks has changed over the last 100 years. Hypothesis: The risk of facial clefts is equal for babies born to mothers who take folic acid supplements compared with those born to mothers who do not. Hypothesis: Caffeine intake during pregnancy affects mean birth weight.

Answers

Answer:

(1) Alternate Hypothesis.

(2) Null Hypothesis.

(3) Alternate Hypothesis.

(4) Null Hypothesis.

(5) Alternate Hypothesis.

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by H.

(1)

The hypothesis statement is:

"The number of hours that grade-school children spend doing homework predicts their future success on standardized tests."

According to the hypothesis statement, we known that the test to be performed is for the relationship between the number of hours that grade-school children spend doing homework and their future success on standardized tests.

So, the null hypothesis here will be that there is no relation between the two variables, or the number of hours that grade-school children spend doing homework does not predicts their future success on standardized tests.

Thus, the provided statement is a Alternate hypothesis.

(2)

The hypothesis statement is:

"King cheetahs on average run the same speed as standard spotted cheetahs."

According to the hypothesis statement, we known that the test to be performed is for the difference between the mean running speed of king cheetahs and spotted cheetahs.

The statement provided is a statement of no difference, i.e. there is no difference between the mean running speed of king cheetahs and spotted cheetahs.

Thus, the provided statement is a Null hypothesis.

(3)

The hypothesis statement is:

"The mean length of African elephant tusks has changed over the last 100 years."

According to the hypothesis statement, we known that the test to be performed is for the significance of single mean.

The null hypothesis here would be there is no change in the mean length of African elephant tusks over the last 100 years.

Thus, the provided statement is a Alternate hypothesis.

(4)

The hypothesis statement is:

"The risk of facial clefts is equal for babies born to mothers who take folic acid supplements compared with those born to mothers who do not."

According to the hypothesis statement, we known that the test to be performed is for the difference between the proportion of risk of facial clefts for babies born to mothers who take folic acid supplements and with those born to mothers who do not.

The null hypothesis here would be that there is no difference between the two risk proportions.

Thus, the provided statement is a Null hypothesis.

(5)

The hypothesis statement is:

"Caffeine intake during pregnancy affects mean birth weight."

According to the hypothesis statement, we known that the test to be performed is for the significance of single mean.

The null hypothesis of this test will be that the mean birth weight is not affected by the caffeine intake during pregnancy.

Thus, the provided statement is a Alternate hypothesis.

I need help on this

Answers

Answer:

a = 250 ; b = 10

Step-by-step explanation:

a = 5 × 10² / 2

a = 5 × 100 / 2

a = 500 / 2

a = 250

b = 2 × 10² (10-5) / 10×10

b = 2 × 100 × 5 / 100

b = 1000 / 100

b = 10

What’s the correct answer for this?

Answers

Answer:

its 7.5

Step-by-step explanation: subscribe when i have channel set

Answer:

D. = 8.1

Step-by-step explanation:

In the attached file

Determine the volume of sphere with a radius of six inches. What is the volume of the sphere in terms of π?

Answers

Answer:

288π inch³

Step-by-step explanation:

V=4

/3πr³

by substituding in formulae

4/3*216π

=288π inch³

hope this helps

plzz mark me brainliest

Which expression is equivalent to 36x2 - 25?
(18x) + (-5)
(18x)? – (5)
(6x)2 + (-5)
(6x)2 – (5)​

Answers

Answer:

The equivalent expression is: (6x + 5)*(6x - 5)

Step-by-step explanation:

This expression is called the difference of two squares.

It has the following format: [tex]a^{2} - b^{2}[/tex]

It is factored as: [tex]a^{2} - b^{2} = (a-b)*(a+b)[/tex]

In this question:

[tex]a^{2} - b^{2} = 36x^{2} - 25[/tex]

So

[tex]a^{2} = 36x^{2}[/tex], then [tex]a = \sqrt{36x^{2}} = 6x[/tex]

[tex]b^{2} = 25[/tex], then [tex]b = \sqrt{25} = 5[/tex]

So

The equivalent expression is: (6x + 5)*(6x - 5)

Answer: (6x)^2 − (5)^2

Step-by-step explanation:

edge. 2022 got it right

A farmer used fence posts to build a fence for Hazel Horse and Pauly Pony. The farmer used 262626 fence posts to build Hazel Horse's fence and 191919 fence posts to build Pauly Pony's fence.

How many fence posts did the farmer use in all?

Answers

Answer:

45

Step-by-step explanation:

19+26 fences equal 45

answer this ! please

Answers

The answer is D
2y/y+2 + 4/y+2= 2

There are 80 sixth graders, 90 7th graders, and 70 8th graders at your school. Every student gets entered in a raffle. What is the probability that a 7th grade student will win the raffle?

Answers

Answer:

P(seventh grade winner) = 3/8

Step-by-step explanation:

P(seventh grade winner) = 3/8

What is the approximate height of the cylinder ? Use 3.14 for pi and if necessary round to the nearest tenth. V= 3.14 ft 3.

Answers

Answer:

So the value of h and r are both 1 inch

Step-by-step explanation:

Volume of a cylinder = πr²h

Volume of the cylinder = 3.14 ft³

And π = 3.14

Dividingthrough by π

r²h = ft³

So the possible out come of r and h is only one because r² must be equal to one and the product of the two must be equal to one.

So the value of h and r are both 1 inch

Answer:3 ft

Step-by-step explanation:

What is The true solution to In 20 +in 5=2in x?

Answers

Answer:

  x = 10

Step-by-step explanation:

Combining the logarithms, you have ...

 ln(20·5) = ln(x²)

  100 = x² . . . . . take the antilogs

  10 = x . . . . . . . take the positive square root

_____

Alternate solution

  ln(2·2·5) +ln(5) = 2·ln(x) . . . . . . . factor 20

  2ln(2) +ln(5) +ln(5) = 2·ln(x) . . . . rearrange ln(20)

  ln(2) +ln(5) = ln(x) . . . . . . . . . . . . divide by 2

  ln(10) = ln(x) . . . . . . . . . . . . . . . . combine logs on the left

  10 = x

_____

These solutions make use of the rules of logarithms ...

  ln(ab) = ln(a) +ln(b)

  ln(a²) = 2·ln(a) . . . . . same as the first rule for a=b

what the square root of 280​

Answers

Answer:

2√70

Step-by-step explanation:

√280

Simplify:

Take out 4

2√70

Answer:

16.7332005307

Step-by-step explanation:

Rewrite  280  as  2 ^(2) ⋅ 70 .

Factor  4  out of  280 .

√ 4 ( 70 )

Rewrite  4  as  2^(2) .

√ 2 ^(2 )⋅ 70

Pull terms out from under the radical.

2√ 70

The result can be shown in multiple forms.

Exact Form:

2 √ 70

Decimal Form:

16.73320053....

Factor x3 ‒ 11x2 ‒ 7x + 77 by grouping. What is the resulting expression?


a

(x2 ‒ 7)(x ‒ 11)


b

(x2 ‒ 7)(x + 11)


c

(x2 ‒ 11)(x + 7)


d

(x2 ‒ 11)(x ‒ 7)

Answers

Answer:

A. [tex](x^{2}-7)\cdot (x-11)[/tex]

Step-by-step explanation:

The third order polynomial is factored herein:

[tex]x^{2}\cdot (x-11) - 7\cdot (x-11)[/tex]

[tex](x^{2}-7)\cdot (x-11)[/tex]

Which represents answer A.

Malik's arts and crafts shop has a bolt of crimson velvet 32 meters long. A customer came in during the morning and bought 120 centimeters of the velvet. Another customer bought an additional 14 meters during the afternoon. How much crimson velvet does Malik's shop have left? Write the answer in centimeters.

Answers

Answer:

Amount of crimson velvet left = 3200 -  120 - 1400 = 1680  cm

Step-by-step explanation:

The arts and craft shop has a bolt of crimson velvet of 32 meters long. A customer bought 120 centimetres of the velvet. In the afternoon another customer bought 14 meters. The remaining length of crimson velvet Malik shop possess after the morning and afternoon sales can be calculated below.

The total length of the crimson velvet = 32 meters. Since our answer should be in centimetre we will convert all the units to cm.

total length = 32 m

1 m = 100 cm

32 m = ?

cross multiply

total length in cm = 32 × 100 = 3200 cm

The first customer bought 120 cm

The second customer bought 14 m so let convert again.

1 m = 100 cm

14 m = ?

cross multiply

the second customer length in cm = 14 × 100 = 1400 cm

The amount left in the shop will be as follows

Amount of crimson velvet left = 3200 -  120 - 1400 = 1680  cm

What’s the correct answer for this?

Answers

Answer:

D.

Step-by-step explanation:

In the attached file

Which statements are true about the graph of the function f(x) = x2 - 8x + 5? Select three options.
The function in vertex form is f(x) = (x - 4)2 - 11.
The vertex of the function is (-8,5).
The axis of synimetry is x = 5.
The y-intercept of the function is (0,5).
ОО
The function crosses the x-axis twice.

Answers

Answer:

The answer is A, D, and E on Edge

Step-by-step explanation:

idek man but i got it right so

Answer: Option A,  D, E

(A) The function in vertex form is f(x) = (x – 4)2 – 11.

(D) The y-intercept of the function is (0, 5).

(E) The function crosses the x-axis twice.

Step-by-step explanation:

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.

i need help plz answer correctly thanks

Answers

Answer:

67

Not exactly sure on how to write it in though

Step-by-step explanation:

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