A sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.
A sphere with height h and radius r. A cylinder with height h and radius r.
What is the volume of the sphere?

The surface area of the pyramid is 34.8 in²

Since the figure is a square pyramid, its surface area, A = 4 × area of triangular face + area of square base.

Area of triangular face A' = 1/2bh where

So, A' = 1/2 × 4.3 in × 3 in

A' = 1/2 × 12.9 in²

A' = 6.45 in²

Area of square base A" = L² where L = length of base = 3 in

So, A" = (3 in)²

= 9 in²

Surface area of pyramid, A = 4A' + A"

= 4 × 6.45 in² + 9 in²

= 25.8 in² + 9 in²  

= 34.8 in²

So, the surface area of the pyramid is 34.8 in²

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we conclude that the correct option is A, the slope is:

"the average number of pounds per foot tall"

The linear equation:

y = 48.3*x - 127

Relates the height, x, and the weight, y of an adult.

Then the slope, which is 48.3, should have units of mass over height.

Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.

Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:

"the average number of pounds per foot tall"

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Answer:

$525

Step-by-step explanation:

We can find the original price by using the formula x - 0.36x = 336, where x is the original price, 0.36 is the discount percentage (converted to decimal form), and 336 is the total amount paid after the discount is applied:

[tex]x-0.36x=336\\0.64x=336\\x=525[/tex]

To check and further understand why the formula works, we can simply apply the discount to the original price and subtract the number from the original price:

525 * 0.36 = 189

525 - 189 = 336

Modeling the first formula gives us:

525 - (0.36 * 525) = 336

525 - 189 = 336

Look at the attached image above ☝️for explanation

Hope it helps! and if it's not pls tell me on the comment.

she should use 2 by 6

Step-by-step explanation:

2 divided by 6 will give 0.3 in 1d.p

Answer:

E

Step-by-step explanation:

We can find the volume either by finding the scale factor between the two figures and multiplying the first cylinder's volume by it or simply finding the diameter of the second cylinder and doing the equation for volume of a cylinder.

I chose the second way to work out.

Since the two cylinders are similar, we can simply set up a proportion to find the diameter, d, of the second cylinder:

[tex]\frac{6}{d}=\frac{4.5}{6}\\ \\ 4.5d=36\\ d=8[/tex]

The formula for volume of a cylinder is [tex]V=\pi r^2h[/tex]

The radius is simply d/2 so the radius of the second cylinder is 8/2 or 4.

Thus, we have

[tex]V=\pi *4^2*6\\V=\pi *16*6\\V=96\pi \\V=301.59[/tex]

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )

m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0

The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

m = ( y₂ - y₁) / (x₂ - x₁)

It is given that the two points are (6, 2) and (-18, 2).

The two-point can be represented as,

(x₁, y₁  ) = (6, 2)

(x₂, y₂ ) =(-18, 2)

The slope of the line can be obtained as,

m = ( y₂ - y₁) / (x₂ - x₁)

m = (2-2) / (-18-6)

m =0 / -24

m =0

Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.

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Answer:

-7

Step-by-step explanation:

[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]

[tex]f(1)[/tex] is [tex]81.[/tex]

To find  f(1):

f(n 1) = one-half(n).

f(3) = 9.

[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]

A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]

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Answer:

36

Step-by-step explanation:

Assuming I understand the question correctly

[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]

We have the recursive relationship

[tex]f(n+1) = \frac{1}{2} f(n)[/tex]

[tex]f(3) = 9[/tex]

[tex]f(3) = \frac{1}{2} f(2)[/tex]

[tex]f(2) = \frac{1}{2} f(1)[/tex]

So

[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]

So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]

Verifying

If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18

f(3) = (1/2) f(2) = (1/2)(18) = 9

Answer:

The third one as they have no links really

Answer:

4

Step-by-step explanation:

h(x) = -1/3x+2 where we need to find -4h(9)

h(9): x = 9

h(x) = -1/3(9) + 2

h(x) = -3 + 2

h(x) = -1

-4h(9) is -4h(x):

-4(-1) = 4

The length of edge FC in the triangular prism is: 12 cm.

Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).

Considering the image given showing a right triangular prism, we have the following:

Volume of triangular prism = 900 cubic centimeters

Length of triangular base = FC = ?

Height of triangular base = 10 centimeters

Height of the prism = 15 centimeters

Plugin the values

900 = 1/2(FC × 10 × 15)

900 = 1/2(FC × 150)

Multiply both sides by 2

2(900) = 2(1/2(FC × 150))

1,800 = FC × 150

Divide both sides by 150

1,800/150 = FC × 150/150

12 = FC

FC = 12 cm

The length of edge FC is: 12 cm.

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Answer: 12

Step-by-step explanation:

Answer: 42

Step-by-step explanation:

angle t is 42 degrees

Answer:

  ∠T = 42°

  PT = 14.4

  QT = 19.4

Step-by-step explanation:

An angle and its adjacent side are given in the right triangle. The other two sides can be found using trig relations. The third angle can be found using the angle sum theorem.

The mnemonic SOH CAH TOA is intended to remind you of the relations between sides of a right triangle and the trig functions of its angles. The relations relevant to this triangle are ...

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

  Tan = Opposite/Adjacent   ⇒   Opposite = Adjacent×Tan

Then the missing side lengths are ...

  QT = QP/cos(Q) = 13/cos(48°) ≈ 19.4282 ≈ 19.4

  PT = PQ×tan(Q) = 13×tan(48°) ≈ 14.43796 ≈ 14.4

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means the acute angles in a right triangle are complementary.

  ∠T = 90° -48° = 42°

The solution to the triangle is ...

  ∠T = 42°

  PT = 14.4

  QT = 19.4

__

Additional comment

The attachment shows the solution from one of many available triangle solvers. Some calculators have triangle solver functions built in.

There are 18c4 ways that RSM wants to send 4 of its 18 teachers into a conference. that means there are 3060 ways to send

there are 18 teachers and RSM wants to send 4 mem out of 18

so, we use combinatorics for this

Combinatorics is the branch of Mathematics dealing with the study of finite or countable discrete structures. It includes the enumeration or counting of objects having certain properties. Counting helps us solve several types of problems such as counting the number of available IPv4 or IPv6 addresses.

It is used to find solutions easily for possible ways of a problem

For that we are using the formula for combinatorics

NCr = n!/ (r! (n – r)!)

similarly 18c4 = 18!/ (4! (18 – 4)!)

                       = 3060

Therefore , there are 3060 ways that RSM wants to send 4 of its 18 teachers into a conference.

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Answer:

6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on

Step-by-step explanation:

PLEASE GIVE BRAINLIEST OR 5 ⭐

Answer:

25%

Step-by-step explanation:

Each flip has a 50% probability of landing heads.  Two in a row would be (50%)*(50%) = 25%

[Note:  25% of $40 is $10].  Don't waste your time.

Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.

Answer: In 2 pounds there are 0.907 kilograms.

According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

[tex]k=1+log_{2} n[/tex]

Here, n is equal to 66 and by substituting the value to the equation we get:

[tex]k=1+log_{2} (66)[/tex]

k = 7.0444

k ≈ 7

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The probability that the last marble removed is non-red is 2/3.

According to the given question.

Total number of marbles in a bucket = 3

And, a person arbitary pulls out each marble one at a time.

So, there are 6 possible sequences of removing 3 marbles.

Let R be the red marble, B be the blue marble and G be the green marble.

The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.

Let A denotes the event of removing the non-red marbles at the last.

The favorable cases for event A are: RBG, RGB, BRG and GRB.

As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Thereofre,

The probability that the last marble removed is non-red

= 4/6

= 2/3

The probability that the last marble removed is non-red is 2/3.

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Answer:

-15 would be the answer because if it's below sea level it would have a negative sign in front of 15

Step-by-step explanation:

Answer:

4230.44

Step-by-step explanation:

Answer:

2/5 or 0.4

Step-by-step explanation:

First we have to make equation into the gradient slope form :

y=mx+c    m is gradient and c is y-intercept

15y-6x=8

First we add 6x to both sides :

15y = 6x+8

Now we divide both sides by 15 :

y = 6x+8 / 15

Split the fraction on the right :

y = 6x/15 + 8/15

6x/15 = 6/15x

Our gradient will be 6/15 = 2/5 or 0.4

Hope this helped and have a good day

Part A

Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,

[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]

Part B

[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]

Answer:

the second option L = 0.05F + 10

Step-by-step explanation:

the first one

F = 0.05L + 10

does not make any sense, as for length = 10 the force has to be 0. but this function here gives us

0.05×10 + 10 = 0.5 + 10 = 10.5

which is clearly not 0. so, this is wrong.

the second one is correct.

L = 0.05F + 10

it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.

the third

L = 0.05F

fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.

the fourth

F = 0.05L

fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.

The value of a = 11

What is complex numbers ?

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = [tex]\sqrt{( a - c)^{2} + (b -d )^{2} }[/tex]

put values in the formula -

[tex]\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }[/tex] = 29

square both sides

[tex]{(a + 9)^{2} + (21)^{2} } = 29^{2}[/tex]

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

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The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.

According to the given question.

The linear form of the function is

f(x) = mx + b

Also, the function is passing through the points (0, 5) and (1, 20).

So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.

Now,

At (0, 5)

f(0) = m(0) + b

⇒ 5 = 0 + b

⇒ b = 5 ..(i)

Also,

at (1, 20)

f(1) = m(1) + b

⇒ 20 = m + 5     (from i)

⇒ m = 20 - 5

⇒ m = 15

Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by

f(x) = 15(x) + 5   (on substituting the vale of m and b in f(x) = mx + b).

⇒ f(x) = 15x + 5

Hemce, the formula of the function is f(x) = 15x + 5.

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Considering the given function in the problem, it is found that:

a. 9.6 offspring survive to maturity when there are 12 female rabbits in the population.

b. At least 18 female rabbits are required for there to be 13 offspring.

The function gives the relationship between the number of adult female rabbits F and the number of offspring R as follows:

[tex]R = 3 + \frac{350F}{F + 625}[/tex]

When there are 12 female rabbits, we have that F = 12, hence:

[tex]R = 3 + \frac{350 \times 12}{12 + 625} = 9.6[/tex]

9.6 offspring survive to maturity when there are 12 female rabbits in the population.

For at least 13 offspring, we have that the number of rabbits needed is given as follows:

[tex]R \geq 13[/tex]

[tex]3 + \frac{350F}{F + 625} \geq 13[/tex]

[tex]\frac{350F}{F + 625} \geq 10[/tex]

[tex]350F \geq 10F + 6250[/tex]

[tex]F \geq \frac{6250}{340}[/tex]

[tex]F \geq 18[/tex]

At least 18 female rabbits are required for there to be 13 offspring.

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The system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

The system of equation are equations that contains more than two equation and unknown.

Let the two unknown numbers x and y

If the sum of two numbers is 84, hence;

x +y = 84

y = -x + 84

If the square of the first number is 6 more than the second number, hence;

x² = y + 6

Substitute equation 2 into 2 to have:

x² = y + 6

x² = (-x+84) + 6

x² = -x+84 + 6

x² +x+84 + 6  = 0

x² +x + 90 = 0

Hence the system of equations to find the value of x, the first number, and y, the second number are;

y = -x + 84

y = x² + 6

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