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Solve for x in the diagram below

If its radius measures 15 units. Then the height of the cone will be 53 units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The volume of a right cone is 3975π cubic units.

If its radius measures 15 units.

Then the height of the cone will be

The volume of the cone is given as

Volume = 1/3 x π x r² x h

Then we have

3975π = 1/3 x π x 15² x h

 11925 = 225 x h

        h = 53 units

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Answer: If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.

Step-by-step explanation:

If the corresponding angles of two triangles are not congruent, then the triangles are not congruent.

A contrapositive statement is when you take the original statement, "flip" it around, and write the opposite of the original statement. Here's an example:

Original statement: The grass is wet because it was raining.

Contrapositive statement: It was not raining, so the grass is not wet.

Notice how we "flipped" the original sentence around, as wrote it's "opposite".

Answer:

7,200

Step-by-step explanation:

I hope this helps!

The Census Bureau conducts a detailed examination of housing and residential finance every ten years.

The Census Bureau's comprehensive housing and residential finance survey, conducted every ten years, is designed to measure levels of residential mortgage debt and provide data for assessing the effectiveness of the current residential finance system in promoting the goal of a decent home and suitable living environment for every American. The study collects data on residential mortgage debt levels and examines the performance of the current residential financing system.

The survey provides national and regional estimates and helps policymakers to make informed decisions about housing and residential finance policies.

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The question is an example of theoretical probability, since it does not involve actually selecting marbles from the bag, while empirical probability is based on actual observations or experimental data.

Theoretical probability is the probability of an event based on mathematical analysis or reasoning, without actually performing an experiment or collecting data.

Here given question is an example of theoretical probability.

Theoretical probability is the probability of an event based on a theoretical or mathematical calculation, without actually performing an experiment or collecting data. In this case, we can calculate the probability of choosing a blue marble by dividing the number of blue marbles (8) by the total number of marbles;

the total number of marbles in the bag = 7 + 8 + 9 = 24

P(Blue) = 8/24 = 1/3

This calculation is based on theoretical probability, since it does not involve actually selecting marbles from the bag to determine the proportion of blue marbles. In contrast, empirical probability is based on actual observations or experimental data.

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Answer:

11 months

Step-by-step explanation:

Nate needs $850 total, and he already has $300. So, the money left that he needs is 850-300 which is $550.

Now, he can save $50 each month, and we need to find the amount of months, x, it will take to reach his goal.

He needs $550, to the equation is:

50x=550

We need to isolate x, so we divide both sides by 50.

x=11

It will take Nate 11 months to save for the trip.

Answer:

11 months

Step-by-step explanation:

850-300=550

550÷50=11

The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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Answer:

The answer is m=-2 or m=7.

Step-by-step explanation:

The steps to solve this equation are below:

Factor: to get (m+2)(m−7)=0.

m+2=0 or m−7=0

m=−2 or m=7. So, your answer is m=-2 or m=7.

Answer:

m = 7

m = -2

Step-by-step explanation:

ax^2 + bx + c

1m^2 - 5m - 14

a = 1

b = -5

c = -14

-b ± √b^2 - 4ac/2a

-(-5) ± √(-5)^2 - 4(1)(-14)/2(1)

5 ± √25 + 56/2

5 ± √81/2

5 ± 9/2

5 + 9/2

14/2 = 7

5 - 9/2

-4/2 = -2

Answer:

19 folders

Step-by-step explanation:

8 + 6 + 5 = 19

Answer:

34

Step-by-step explanation:

substitute x = 6, y = - 2 into the expression

5x - 2y

= 5(6) - 2(- 2)

= 30 + 4

= 34

The expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

What is a number line?

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

In the given number line, the distance between point A and point B is 5.

Now we have to check each option

| 3 | + | -2 | = 3 + 2  = 5

| -2 + 3 | = | 1 | = 1

| -3 - 2 | = | -5 | =5

3 - ( -2 ) = 3+ 2 = 5

| 3 - ( -2 ) | = |3 + 2| = 5

Hence, the expressions that are equal to the distance between point A and point B would be

| 3 | + | -2 |

| -3 - 2 |

3 - ( -2 )

| 3 - ( -2 ) |

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The maximum amount of water that the pool can hold is 1000 cubic feet.

To find the maximum amount of water that the rectangular prism swimming pool can hold, we need to calculate its volume.

The volume of a rectangular prism is given by:

V = l x w x h

where l is the length, w is the width, and h is the height of the prism.

Given the dimensions of the swimming pool, we have:

l = 16 feet

w = 12.5 feet

h = 5 feet

Therefore, the volume of the swimming pool is:

V = l x w x h

V = 16 feet x 12.5 feet x 5 feet

V = 1000 cubic feet

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Answer:

Step-by-step explanation:

The estimated cost to attend this college for 1 semester is $9114

3974+400+3240+1500=9114

Nola would have to pay for 8 semesters if she attends for 4 years.

4x2=8

The estimated cost for Nola to attend this college for 4 years is $72912

9114x8=72912

Answer:

The answer is  B

Step-by-step explanation:

sorry it is wrong

Answer:

B. Parallelogram

Step-by-step explanation:

It should look something like this which is a parallelogram.

Parallogram is like a rectangle or square that is kinda slanted.

    ________

  /                /

/_______/

Answer:

$648.00

Step-by-step explanation:

==>Given:

Squared living room of 9m by 9m

Cost of purple carpet per m² = $8.00

==>Required:

Cost of buying carpet to cover the squared living room

==>Solution:

Find the area of the room:

Area of squared room = 9m × 9m = 81m²

Find cost of purple carpet that would cover 81m²:

Let x be the cost of carpet required to cover the room.

Thus,

1m² = $8.00

81m² = x

cross multiply

1*x = 8.00*81

x = 648

Cost of purple carpet to cover the living room = x = $648.00

a. The normal model for IQ scores would be a bell-shaped curve, also known as a Gaussian distribution, centered at a mean of 100 and with a standard deviation of 16. The curve should be labeled "IQ Scores" and include tick marks at the mean (100) and at one standard deviation above and below the mean (84 and 116, respectively).

Using the 68-95-99.7 rule, the area under the curve between each pair of tick marks represents the percentage of scores falling within those ranges. b. According to the 68-95-99.7 rule, the central 95% of IQ scores should be found within two standard deviations of the mean. Since the standard deviation is 16, we can calculate the interval by adding and subtracting two standard deviations from the mean: 100 - (2 * 16) to 100 + (2 * 16). This gives us the range of 68 to 132, meaning that we should expect the central 95% of IQ scores to fall within this interval.

c. To determine the percentage of people with IQ scores above 116, we can calculate the area under the curve to the right of the IQ score 116. We can use statistical tables or software to find the corresponding z-score for 116 and then look up the percentage associated with that z-score. Based on the standard normal distribution, the percentage of people with IQ scores above 116 would be the complement of the percentage below 116.

d. To calculate the percentage of people with IQ scores between 84 and 116, we can find the area under the curve between these two values. Similar to the previous calculation, we can convert the IQ scores to z-scores, look up the corresponding percentages, and subtract the lower percentage from the higher percentage to obtain the desired percentage.

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if the interest rate rises by 0.6%, the fund would be exposed to a loss of approximately 0.0594% of its current value. Please note that this is a generalized calculation and the actual loss may vary depending on the specific characteristics of the portfolio.

The loss that the pension fund would be exposed to if the interest rate rises by 0.6% can be calculated using the concept of duration. Duration measures the sensitivity of the value of a portfolio to changes in interest rates.
In this case, the portfolio has a duration of 9.9 years. This means that for every 1% change in interest rates, the value of the portfolio will change by approximately 9.9%. Since the interest rate is currently 5.3% and it is expected to increase by 0.6%, the total change in interest rates would be 0.6%.
To calculate the loss, we multiply the change in interest rates by the duration and the current value of the portfolio. So, the loss would be:
Loss = (Change in interest rates) * (Duration) * (Current value of the portfolio)

In this case, the change in interest rates is 0.006 (0.6% expressed as a decimal), the duration is 9.9 years, and the current value of the portfolio is not given. Therefore, we cannot calculate the exact loss without knowing the current value of the portfolio.
However, we can provide a general formula to calculate the loss as a percentage of the current value of the portfolio:
Loss % = (Change in interest rates) * (Duration)
Using the given values, the loss % would be:
Loss % = 0.006 * 9.9 = 0.0594

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The volume of the cube with the shortest possible side lengths is 216 cubic inches.

If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.

side length of cube = diameter of sphere

side length of cube = 2 x radius of sphere

side length of cube = 2 x 3 inches

side length of cube = 6 inches

The volume of the cube can be calculated using the formula below.

V = s³

where V = volume and s = side length of cube

V = (6 inches)³

V = 216 cubic inches

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You bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

Let's assume you bought x stamps that cost 45 cents each and y stamps that cost 30 cents each.

From the given information, we can create two equations:

The total number of stamps is 10: x + y = 10.

The total cost is $4.20: 45x + 30y = 420 (since the cost is given in cents).

Now we can solve this system of equations to find the values of x and y.

We can multiply the first equation by 30 to eliminate y:

30x + 30y = 300.

Now we have a system of equations:

30x + 30y = 300,

45x + 30y = 420.

Subtracting the first equation from the second equation, we get:

45x + 30y - (30x + 30y) = 420 - 300,

15x = 120,

x = 120/15,

x = 8.

Substituting the value of x back into the first equation:

8 + y = 10,

y = 10 - 8,

y = 2.

Therefore, you bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

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According to the given question we have The value of k that makes the function f continuous at x = 2 is -2.

To determine the value of k that makes the function f continuous at x = 2, we need to evaluate the limit of the function at x = 2 from both sides and ensure that they are equal.

First, let's evaluate the limit as x approaches 2 from the left side (x < 2). We have:

lim (x->2-) f(x) = lim (x->2-) (x^2 - 5x + k) = 2^2 - 5(2) + k = -2 + k

Next, let's evaluate the limit as x approaches 2 from the right side (x > 2). We have:

lim (x->2+) f(x) = lim (x->2+) (4 - 4x + k) = 4 - 4(2) + k = -4 + k

For the function to be continuous at x = 2, these two limits must be equal. Therefore, we have:

-2 + k = -4 + k

Solving for k, we get:

k = -2

Therefore, the value of k that makes the function f continuous at x = 2 is -2.

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Answer:

2/3

Step-by-step explanation:

rise over run

Answer:

1)D 2)C 3)A 4)B 5) A

Step-by-step explanation:

1) The area rectangle is 36x^2 -1

We know ,

A= l*b

=36x^2 -1

=(6x)^2 -1

=(6x+1) (6x-2)

This the value of l,b respectively.

So, Perimeter of rectangle is 2(l+b)

P=2(6x+1) + 2(6x-1)

=24x

2)The area of square is 4(x+5)^2

We know,

A=l^2

=4(x+5)^2

=4(x^2 + 10x + 25)

=(2x+10)^2

This is the value of l=2x+10.

So, Perimeter of square is 4l

P=4(2x+10)

=8x+40

3)The fully factorized form is

= -2x^2 + 10x +12

= -2x^2 + 12x -2x +12

= -2x(x-6) -2(x-6)

= -2(x-6) (x+1)

4)The fully factorized form is

=x^4 -81

=(x^2)^2 -9^2

=(x^2 + 9) (x^2 - 9)

=(x^2 + 9) (x^2 - 3^2)

=(x^2 + 9) (x + 3) (x - 3)

5)The fully factorized form is

= 5x^4 - 320

= 5(x^4 - 64)

= 5((x^2)^2 - 8^2)

= 5(x^2 + 8) (x^2-8)

Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

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Answer:

Ang SAgot ay pukingina ka

Given:

Center of a circle is (3,9).

Solution point is (-2,21).

To find:

The standard form of the circle.

Solution:

Radius is the distance between center (3,9) and the solution point (-2,21).

\(r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(r=\sqrt{(-2-3)^2+(21-9)^2}\)

\(r=\sqrt{(-5)^2+(12)^2}\)

\(r=\sqrt{25+144}\)

On further simplification, we get

\(r=\sqrt{169}\)

\(r=13\)

The radius of the circle is 13 units.

The standard form of a circle is

\((x-h)^2+(y-k)^2=r^2\)

Where, (h,k) is the center and r is the radius.

Putting h=3, k=9 and r=13, we get

\((x-3)^2+(y-9)^2=(13)^2\)

\((x-3)^2+(y-9)^2=169\)

Therefore, the standard form of the circle is \((x-3)^2+(y-9)^2=169\).

Answer:

4.81 divided by 0.74=6.5       61.32 divided by 1.4= 43.8

Step-by-step explanation: