The volume of a cylinder is 480 cm. The height of the cylinder is 30 cm. What is the radius of the
cylinder?
The radius of the cylinder is cm. (Simplify your answer.)

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

                Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

               All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

  X = 1 red marble:

        P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

        P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

        P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

        P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

        P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

        P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

          X :         1                 2                3

       P (X):       0.3            0.6              0.1

- The expected value E(X) for the given random variable X is:

                E ( X ) = ∑Xi*P(Xi)

                           = 1*0.3 + 2*0.6 + 3*0.1

                           =1.8

- The variance Var(X) for the given random variable X is:

                Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

                               = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

                               = 0.36

- The standard deviation for the given random variable X is:

                σ = √Var(X)

                σ = √0.36

                σ = 0.6

The expected value, the variance, and the standard deviation of the given random variable X are 1.8, 0.36, and 0.6 respectively and this can be determined by using the given data.

Given :

X is the number of red marbles that Suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones.

The total number of outcomes are:

[tex]\rm \; ^5C_3=10[/tex]

The probability of random variable X are as follows:

X = 1 red marble

P(X = 1) = [tex]\rm \; ^3C_1 \times ^2C_2[/tex] = 0.3

X = 2 red marbles

P(X = 2) = [tex]\rm \; ^3C_2 \times ^2C_1[/tex] = 0.6

X = 3 red marbles

P(X = 3) = [tex]\rm \; ^3C_3[/tex] = 0.1

So, the expected value is given by:

[tex]\rm E(X) = \sum X_i \times P(X_i)[/tex]

        [tex]= 1\times 0.3+2\times 0.6 + 3 \times 0.1[/tex]

        = 1.8

Now, the variance is given by:

[tex]\rm Var(X) = \sum X^2_i \times P(X_i)-(E(X))^2[/tex]

           [tex]=1^2\times 0.3+2^2\times 0.6+3^2 \times 0.1-1.8^2[/tex]

           = 0.36

Now, the standard deviation is given by:

[tex]\rm \sigma=\sqrt{Var(X)}[/tex]

[tex]\rm \sigma = \sqrt{0.36}[/tex]

[tex]\sigma = 0.6[/tex]

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Answer:

The domain is the set of inputs, the range is the set of outputs

The true statements are options (A) f(x) has a domain of all real numbers, and (C) g(x) has a domain of all real numbers.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

A. True: The function f(x) = (4)ˣ has a domain of all real numbers, as exponentiation is defined for any real number exponent.

B. False: The function g(x) = (4)⁻ˣ has a range of y ≥ 0, since exponentiation with negative exponent results in a positive number for any real number x.

C. True: The function g(x) = (4)⁻ˣ has a domain of all real numbers, as exponentiation is defined for any real number exponent.

D. False: The function h(x) = -(4)ˣ has a range of y ≤ 0, since exponentiation with positive exponent results in a positive number for any real number x, and multiplying it by -1 results in a negative number.

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The question seems to be incomplete, the complete question would be as:

Consider the three functions: f(x) = (4)ˣ, g(x) = (4)⁻ˣ, and  h(x) = –(4)ˣ

Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.

A. f(x) has a domain of all real numbers.

B. g(x) has a range of y < 0.

C. g(x) has a domain of all real numbers.

D. h(x) has a domain of x > 0.

Answer:

6

Step-by-step explanation:

for 12 papers?

12 is the total amount

2 is the amount of piles

12 divided by 2 is 6.

there are 6 papers in each pile

Final answer:

To find out the number of papers in each pile, divide the dozen papers by the two piles, resulting in 6 papers per pile.

Explanation:

The question asks about dividing papers into two piles with an equal number of papers in each pile. Since it mentions there are 12 papers in total on the desk, we know that the number 12 represents a dozen, which is a common grouping for small objects to make counting and handling more efficient. To find out how many papers are in each pile, we simply divide the total number of papers by the number of piles. There are 2 piles on the desk, so we would perform the following calculation:

Therefore, each pile contains 6 papers.

Answer:

(a)25% of 100 < 75% of 100

(b)25% of -100 > 75% of -100

Step-by-step explanation:

If Lillian says that 25% of a number will always be less than 75% of any other number.

We are required to complete two inequality one of which supports and the other refutes the statement.

Support

Let our number be 100

25% of 100 < 75% of 100

25<100

This is true.

Refute

Let our number be -100

25% of -100 > 75% of -100

-25>-100

Therefore, for negative numbers, the inequality will not be true as:

-25>-100.

Answer: Approximately 33 feet

Step-by-step explanation: Please refer to the attched diagram.

The 20ft ladder is placed on the wall at an agle of 85° with the ground.

If the person on the ladder were to lean back and fall to the ground (rotating the ladder away from the wall), then the distance he would have covered before he hits the ground is depicted by the arc as shown in the diagram. The ladder upon touching the ground would remain the same, which is 20 feet. So what the question requires is the length of the arc made during the fall, and the length of the ladder both on the wall an on the floor would be the radius (20 ft) while the angle subtended by the arc is 95° ( angles on a straight line equals 180, that is 85 + 95 = 180)

Therefore the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 95 and r = 95

Length of arc = (95/360) x 2 x 3.14 x 20

Length of arc = (19/72) x 125.6

Length of arc = 2386.4/72

Length of arc = 33.1444

Length of arc ≈ 33 feet (To the nearest foot)

The person on the ladder would have travelled approximately 33 feet before he/she hits the ground.

The person falls a distance of approximately 19.924 feet.

In this question, we must determine the vertical distance travelled by the person ([tex]y[/tex]), in feet. Let consider that the ladder is set between a horizontal ground and a vertical wall.

Then, the vertical distance is determined by the following trigonometric expression:

[tex]y = l\cdot \sin\theta[/tex] (1)

Where:

If we know that [tex]l = 20\,ft[/tex] and [tex]\theta = 85^{\circ}[/tex], then the vertical distance travalled by the person:

[tex]y = (20\,ft)\cdot \sin 85^{\circ}[/tex]

[tex]y \approx 19.924\,ft[/tex]

The person falls a distance of approximately 19.924 feet.

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Answer:

The area of the bedroom actually is 453.75 sq ft.

Step-by-step explanation:

Given that,

A blueprint shows the master bedroom to be 5 inches long and 3 inches wide.

The scale on blueprint is 2 inches : 11 feet.

It means 2 inches = 11 feet.

Then,

1 inches [tex]=\frac{11}{2}[/tex] feet = 5.5 feet.

So,

The length of the bedroom is 5 inches = (5×5.5) feet=27.5 feet

The wide of the bedroom is 3 inches = (3×5.5) feet= 16.5 feet

The area of the bedroom actually is = length × wide

                                                            =(27.5×16.5) square ft

                                                            =453.75 square ft

Final answer:

To find the area of the actual bedroom, you need to use the scale provided on the blueprint. By setting up ratios and solving for the actual length and width, you can find that the area of the actual bedroom is 453.75 square feet.

Explanation:

To find the area of the actual bedroom, we need to use the scale provided on the blueprint. The scale states that 2 inches on the blueprint represents 11 feet in reality. So, we can set up a ratio to find the actual length and width of the master bedroom:

Length ratio: 2 inches ⁠∩⁠ 11 feet = 5 inches ⁠∩⁠ x feet
Width ratio: 2 inches ⁠∩⁠ 11 feet = 3 inches ⁠∩⁠ y feet

By cross-multiplying and solving for x and y, we can find that x = 27.5 feet and y = 16.5 feet. Therefore, the actual length of the bedroom is 27.5 feet and the actual width is 16.5 feet. To find the area, we simply multiply the length and width: Area = 27.5 feet × 16.5 feet = 453.75 square feet.

Answer:

it will take 20hrs to fill the pool

Answer:

It would take 20 hours to fill the pool.

Step-by-step explanation:

We are give the Dimensions of the Pool. Recall that Volume of a Rectangular Prism is V = l*w*h which will return 800[tex]m^{3}[/tex]. Using Dimensional Analysis and recalling that the rate is being pumped at a rate of [tex]\frac{40m^{3}}{h}[/tex],   [tex]\frac{m^{3} }{\frac{m^{3}}{h} } = h[/tex] so, just divide the Volume by the Rate given since they are under the same units: [tex]\frac{16*10*5}{40} = \frac{800}{40} = 20 hours[/tex].

Answer:

6

Step-by-step explanation:

area is base times height so 3 times 2 is 6

Hello there!

The area of the purple rectangle is 6 m^2, because 3x2 is 6, and the area of the green one is 24 m^2. Add them together to get the total area:

24 + 6 = 30 m^2

:)

Answer:

p= 8

Step-by-step explanation:

1/2 p = 4

p = 2(4)

Answer:

p=8

Step-by-step explanation:

This will ake the problem 8/2 which is the same as 4.  

Thus, 8 is your answer.

Leave 5 stars if this helped.

Answer:

B

Step-by-step explanation:

Answer:

4 hammers

Step-by-step explanation:

Please refer to the attached image for explanations

Answer: True

Step-by-step explanation:

If you draw a vertical number line, the numbers in it will infinitely extend in both directions (up and down), having the zero 0 as the neutral number (the origin).

Then, the numbers that are above the origin are the positive integers and represent the distance of an object above zero, while the numbers below the origin are the negative integers and represent perfectly the distance of an object underground (below the origin).

The statement is true, negative numbers can be used to represent the distance of an object below a reference point, such as underground relative to the surface.

True or false? You can represent the distance of an object underground using negative numbers.

The statement is true. In mathematics, especially when dealing with physical situations like displacements and positions, using negative numbers to indicate direction is a common practice. We often choose a frame of reference and a positive direction at the beginning of a problem. In this context, for example, if we define the surface of the ground as our reference point and the direction away from the center of the Earth (upwards) as positive, then it would take sense to use negative numbers to represent the distance of an object that is located underground, indicating it is below the reference point.

Answer:

Straight line joining (0,6) and (24,0)

Step-by-step explanation:

y = (-1/4)x + 6

Make a straight line passing through:

y = 0 + 6 = 6

(0,6)

And

0 = (-1/4)X + 6

-6 = -x/4

x = 24

(24,0)

sorry honey but i dot have a graph to you how but

all you do is  start at 6 positive and then mark a point one down and 4 to left and mark other point and then draw a line through it

Answer:

Since h(max) is less than 30 ft, it will never reach a height of 30ft

The maximum height it can reach is 11.25ft.

Step-by-step explanation:

Given;

The height equation of the rock;

h = -16t^2 +20t +5

To determine whether it would reach 30 ft, we need to find its maximum height. Which is at;

dh/dt = 0

dh/dt = -32t +20 = 0

At Maximum height.

t = 20/32

We then substitute into the height equation.

h(max) = -16(20/32)^2 + 20(20/32) +5

h(max) = 11.25 ft

Since h(max) is less than 30 ft, it will never reach a height of 30ft

The maximum height it can reach is 11.25ft.

Answer:

There are no real solution to the equation [tex]h = -16t^2 +20t +5[/tex] when h = 35 ft.

Step-by-step explanation:

Here we have the equation for the height of the rock in ft given as

[tex]h = -16t^2 +20t +5[/tex]

For the rock to reach 30 ft we must have

[tex]30 = -16t^2 +20t +5[/tex]

That is [tex]0 = -16t^2 +20t +5 - 30 = -16t^2 +20t -25[/tex]

[tex]0 = -16t^2 +20t -25[/tex] or

[tex]16t^2 -20t +25 = 0[/tex]

From which it is observed that since the root of the equation is given by the quadratic formula

b² should be greater than 4·a·c  however

(-20)²[tex]\ngeqslant[/tex] (4×16×25)

Hence the equation has only imaginary roots.

Answer:

  5012

Step-by-step explanation:

Five thousand: 5000

Twelve: 12

Five thousand twelve: 5000 +12 = 5012

_____

Comment on "and"

I was taught to reserve the use of "and" for indicating a decimal point. For example, "five thousand and twelve hundredths" = 5000.12

Final answer:

The number five thousand and twelve is written in numerical form as 5012, with 'five thousand' representing 5000 and 'twelve' adding 12.

Explanation:

The number five thousand and twelve written in numerical form is 5012.

When converting numbers from word form to figure form, it is essential to identify the value of each word in the context of place value. In this case:

Thus, combining those two values brings us to the total figure of 5012.

Answer:

20x + 12y -21

Step-by-step explanation:

Do the operation and put in the another side.

Answer:

4(5x+3y-7) = [20x] + [12y] + [- 28]

Step-by-step explanation:

4(5x+3y-7)

1) Distribute the 4 to each term in the parenthesis.

4(5x) + 4(3y) + 4(-7)

2) Multiply.

20x + 12y - 28 ← Final Answer

Answer:

a.  total cost including discount = 64.47

b. sales would be greater if tax was added before

Step--step explanation:

The total cost of the shirts including the discount is $64.57 and  total cost of the shirts including the 6.5% sales tax would be greater if the tax was applied after a 15% discount is taken, rather than before.

percentage, a relative value indicating hundredth parts of any quantity.

The cost of one shirt after a 15% discount is $9.99 - ($9.99 x 0.15) = $8.49.

The cost of two shirts costing $11.99 each after a 15% discount

2 x ($11.99 - ($11.99 x 0.15)) = $20.38.

The cost of two shirts costing $21.00 each after a 15% discount

2 x ($21.00 - ($21.00 x 0.15)) = $35.70.

Therefore, the total cost of the shirts including the discount

$8.49 + $20.38 + $35.70

= $64.57.

If the tax is applied before the discount, then the taxable amount would be the original price of the shirts, which is $9.99 + (2 x $11.99) + (2 x $21.00) = $84.97.

The tax on this amount at 6.5% would be $5.52.

After the 15% discount, the total cost of the shirts would be $64.57, which includes the $5.52 tax.

Therefore, the total cost of the shirts after the discount and tax

$59.05 + $5.52 = $64.57.

The total cost of the shirts including the 6.5% sales tax would be greater if the tax was applied after a 15% discount is taken, rather than before.

Hence,  the total cost of the shirts including the discount is $64.57 and  total cost of the shirts including the 6.5% sales tax would be greater if the tax was applied after a 15% discount is taken, rather than before.

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Answer:

A rate

Step-by-step explanation:

Its a ratio that compares unlike units.

Answer:

8 busses

Step-by-step explanation:

just divide 412 by 57 and you get 7.228070175438596 witch you round up to 8

Answer:

You need 8 buses

Step-by-step explanation:

Divide 412 by 57 and you will get the answer

I hope this will  help u

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Answer:

3 cm

Step-by-step explanation:

3 cm converted to mm would be 30 mm which is bigger than 25 mm

Answer:

Step-by-step explanation:

Answer: x = -1

Step-by-step explanation:

1) x - 5 = 36 -7x -49

2) x - 5 = -13 -7x

3) x + 7x =- 13 +5

4) 8x =- 8

5) x = -1

Please mark this as the brainliest answer! :) I hope this helped! <3

Answer:

correct option is  C. $399,060

Step-by-step explanation:

given data

balloon mortgage = 7/23

initial payments = $915

time = 30 year

new payments = $895

solution

we know here that 7/23 is that loan has fixed rate =  first 7  years.

so that initial payments for 7 years is here

initial payment = 7 × 12 × 915

initial payment = $76860

and

payments for 30 years when refinance her balloon

payments for 30 year = 30 × 12 × 895

payments for 30 year = $322200

so total financed cost paid for her house is

total financed cost =  $76860 + $322200  

total financed cost = $399,060

so correct option is  C. $399,060

Final answer:

To determine the total financed cost of Margaret's house, one must sum the payments made during the initial balloon mortgage and the subsequent 30-year mortgage, totaling $399,060 (Option C).

Explanation:

The total financed cost that Margaret paid for her house can be calculated by adding the payments made during her initial 7-year balloon mortgage period to the payments for the 30-year mortgage she refinanced into.

For the balloon mortgage: 7 years = 84 months. Therefore, the total paid during this period is 84 months × $915/month = $76,860.

For the refinanced mortgage: 30 years = 360 months. Hence, the total paid after refinancing is 360 months × $895/month = $322,200.

Adding these two amounts gives us the total financed cost which is $76,860 + $322,200 = $399,060. The answer to the student’s question is C. $399,060.

Answer:

the equation would be

28÷(11.50+5.50)

hope this helps :)

Answer:

28=5.50h+11.50

Step-by-step explanation:

Answer: 4ft too the 2 power

Step-by-step explanation:

Answer:

2

Step-by-step explanat

the average of wieght od the kittens in the slether?

C. w= 3V/lh

D. V/B=h/3

E. V=w^2h/3

The equation that can describe a square pyramid include:

It should be noted that a square pyramid simply means a pyramid that has a square base.

The equations that could describe a square pyramid include w = 3v/lh, v/b = h/3, and v = w²h/3. When the top is above the center of the square, it's a right square pyramid.

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Answer:

B

Step-by-step explanation:

2/36=1/18=0,056 it's too easy

The probability that the sum adds to 2 or 12 is P = 0.056.

We have two number cubes, each one has 6 outcomes, so the total number of outcomes is:

C = 6*6 = 36 outcomes.

Now, we need to find the number of outcomes that add up to 2 or 12, these are:

Dice 1  dice 2    sum

  1           1            2

  6          6           12

So 2 out of 36 outcomes add up to 2 or 12, so the probability is:

P = 2/36 = 0.056

So the correct option is B.

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Answer: 20 pesos.

Step-by-step explanation: Your basically dividing 500 by 25. Hope this was helpful. :)

Answer:

20 ₱ (Pesos)

Step-by-step explanation:

$500 to Mexican Pesos

$25 = ₱1

25*4*5 = 1*4*5

$500 = 20 ₱