If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?

143
314
14 ⋅ 3
14 ⋅ 14 ⋅ 14
PLEASE ANWSER !!!!!
(100 points given)

Answer:

3/4 - 5/12

Step-by-step explanation:

first you make the demoninators the same so 3*4=12

and if you *3 you do it to the numerator

so its 9/12-5/12

the unsimplified fraction is 4/12

if wanted simplified version its 1/3

\(\frac{3}{4}-\frac{5}{12}\\\)

First make the denominators equal so you can easily add the numerators

Common Factor of 4 and 12: 12

So multiply \(\frac{3}{4}\) with 3 for both numerator and denominator (4*3=12, to make denominator equal)

\(\frac{9}{12} - \frac{5}{12} =\frac{4}{12}\)

Simplify further

\(\frac{4}{12} =\frac{1}{3}\)

\(\frac{1}{3}\) is the answer

Hope it helps!

Answer:32+ 1.21

Step-by-step explanation:

if you really want an awser you would take all the nubers and sfhgkjfqipjghwpkrejvhbwptijgbqkejnvwpigtnjuvrepiufgnjwrekjbhartio

Answer:

Step-by-step explanation:

Answer:

This is also known as the Counting rule.

The Fundamental Counting Principle is used in determining all the possible outcomes and the total possible ways different events can be combined with each other. It is usually done by multiplying all the events together to get the total possible outcome. Doing this also helps in determining the sample space of a probability.

For example there are events a, b and c. The total sample space or possible outcome will be a*b*c.

Answer:

a) 0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

b) The 75th percentile for the age of United States Presidents on the day of inauguration is 61.

c) 0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3.

This means that \(\mu = 56, \sigma = 7.3\)

(a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

This is the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 56}{7.3}\)

\(Z = 0.55\)

\(Z = 0.55\) has a pvalue of 0.7088

0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

(b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration.

This is X when Z has a pvalue of 0.75. So X when Z = 0.675.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.675 = \frac{X - 56}{7.3}\)

\(X - 56 = 0.675*7.3\)

\(X = 61\)

The 75th percentile for the age of United States Presidents on the day of inauguration is 61.

(c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Now, by the Central Limit Theorem, we have that \(n = 4, s = \frac{7.3}{\sqrt{4}} = 3.65\)

This is the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{60 - 56}{3.65}\)

\(Z = 1.1\)

\(Z = 1.1\) has a pvalue of 0.8643

0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Answer:

C

Step-by-step explanation:

To find this answer you simply perform the division and see which one gives you 32

In this case 8/25=0.32 or 32%!

Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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Answer:

I think its C

Step-by-step explanation:

Answer:  the answer is 2.5

Step-by-step explanation:

Answer:

w= 5/2 inches or 2 1/2 inches

Step-by-step explanation:

area = length × width (w)

45/4 = 9/2 × w

45/4 =9w/2

45×2 = 9w×4

90 = 9w×4

9w= 90/4= 45/2

w= 45/2 × 1/9

w= 5/2 inches or 2 1/2 inches

Answer: The answer is 8/5

Answer:

Each person gets 8/5 part of cookie

Answer:

1,000,000 + 300,000 + 20,000  + 5,000 + 800  + 60 + 4  

Step-by-step explanation:

Answer: The reason they do this is water refraction. I don't know if this was a question or not, but here you go.

Answer:

Step-by-step explanation:

Given two points:

The distance between them is the difference of y- coordinates since x- coordinates are same:

The figure is indeed symmetric and the number of lines of symmetry the snowflake has is C. Yes; 6 lines of symmetry.

Generally a snowflake is hexagonal and has 6-way radial symmetry. Thus, one can rotate it 60 degrees (the sixth of full rotation) and it still appears the same.

So, overall, this means that a snowflake holds 6 lines of symmetry which divide it into two identical halves reflecting each other. Consequently, it can be rotated in 60-degree increments and still holds identicality. Akin to this final property, the snowflake artifact possesses six uniquely divided

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Answer:

24

Step-by-step explanation:

first you replace m with 3

like this:

2(3)2+12

then you multyply 2*3*2

and get this:

6*2+12

12+12

=24

Hey there!

2m^2 + 12

= 2(3)^2 + 12

3^2

⇒3 * 3

⇒ 9

= 2(9) + 12

= 18 + 12

= 30

Therefore, your answer is: 30

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

We are given the following equation

Let us solve the equation for x.

Step 1:

Add 12 to both sides of the equation to eliminate 12 on the left side of the equation.

Therefore, the value of x is 7

Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

Answer:

Step-by-step explanation:

25

Answer:

The volume is 997.62 cubic units..

Step-by-step explanation:

We are given the following details:

The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.

Side of hexagonal base, a = 8 units

Altitude of pyramid, h = 18 units

We have to find the volume of pyramid.

Formula:

\(V = \dfrac{1}{3} \times B \times h\)

Where, B is the area of base of pyramid.

h is the height/altitude of pyramid

To calculate B:

Here, base is a hexagon with side 8 units.

\(\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}\)

Here, a = 8 units

\(\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}\)

Putting values of B and h in Formula of volume:

\(\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}\)

Hence, the volume is 997.62 cubic units.

Answer:

A

Step-by-step explanation:

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

From the graph, the x coordinate 2, have a y coordinate of 120. Hence:

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

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Answer:

10 teachers= 120 students

Step-by-step explanation:

2 teachers= 24 students

divide 24 and 2 which 12

1 teacher= 12 students

multiply 10 and 12 which equals to 120

10 teachers= 120 students.

Pls mark as brainliest, thank u.

The graph that correctly represents the given linear equation is the one in option D.

A general linear equation is:

y = m*x + b

Where m is the slope and b is the y-intercept.

In this case, we know that the slope is -2/3 and the y-intercept is 1, then we can replace:

m = -2/3

b = 1

So the linear equation becomes:

y = -(2/3)*x + 1

Notice that when x = 0, the value of y is 1, and the slope is negative, thus, the line goes downwards. With that in mind we can conclude that the correct graph is the one in option D.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

0.1102 = 11.02% probability of x >= 0.337 if the windows meet the standards.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The standards for glass thickness call for the glass to average 0.325 inch with a standard deviation equal to 0.065 inch.

This means \(\mu = 0.325, \sigma = 0.065\)

Sample of 44

This means that \(n = 44, s = \frac{0.065}{\sqrt{44}}\)

What is the probability of x >= 0.337 if the windows meet the standards?

This is 1 subtracted by the p-value of Z when X = 0.337. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.337 - 0.325}{\frac{0.065}{\sqrt{44}}}\)

\(Z = 1.225\)

\(Z = 1.225\) has a p-value of 0.8898

1 - 0.8898 = 0.1102

0.1102 = 11.02% probability of x >= 0.337 if the windows meet the standards.

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

2

Step-by-step explanation:

1+1=2

9514 1404 393

Answer:

  3

Step-by-step explanation:

The square root function (√) only gives positive values, so graphs 1 and 4 make no sense.

When x = -3, the y-value is 0, consistent with graph 3.

Answer:

D. x^3

Step-by-step explanation:

1. Volume of cube = width*length*height

2. width, length, and height of a cube are all the same. In this case, it's x.

3. multiply x * x * x to get x^3

Answer:

D

Step-by-step explanation:

The equation for volume of a cube is l*w*h.

If we plug in l and w and h equaling x, we get:

x*x*x. When you multiply a number by itself, you get that number to the power of however many times it is multiplied. Therefore, x*x*x = x^3