The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Final answer:

After receiving $38,000 and investing it at a 6.0 percent interest rate per year for 10 years, the student will have approximately $68,052.19 in 12 years.

Explanation:

To find out how much the student will have in 12 years after receiving $38,000 and investing it for 10 years at a 6.0 percent interest rate per year, we need to calculate the future value of the investment using the formula for compound interest.

The formula for the future value FV of an investment over time is given by:

FV = PV * (1 + r)^n

Where:

PV = Present Value of the investment (the initial amount of money)

r = annual interest rate (expressed as a decimal)

n = number of years the money is invested

In this case:

PV = $38,000

r = 0.06 (which is 6.0 percent expressed as a decimal)

n = 10

Plugging these values into the formula, we get:

FV = $38,000 * (1 + 0.06)^10

FV = $38,000 * (1.06)^10

FV = $38,000 * 1.790847

FV = $68,052.186

Therefore, the student will have approximately $68,052.19 in 12 years.

Answer:

23.78

Step-by-step explanation:

Answer:

(x-6)(x-1)

Step-by-step explanation:

this is the correct answer on ape x

Answer:

(x-6)(x-1)

Step-by-step explanation:

In this experiment, the type of nail polish represents B. the explanatory variable.

The nail polish brands—Bella, Primrose, Shine, and Glo—are the explanatory variables in the experiment that is being discussed. These are the many conditions or treatments that are being investigated to find out how they affect a certain result.

The primary aim of the experiment is to compare how each type of nail polish performs or is perceived, which requires manipulating the nail polish type and observing the results.

The response variable (or dependent variable) is the outcome that is measured in response to the explanatory variables. This could be factors like durability, appearance, user satisfaction, or any other measurable characteristic related to the nail polish.

Thus, the nail polish brands are the explanatory variables because they are the categories being compared. The response variable would be whatever metric is used to evaluate the performance or characteristics of these nail polishes.

Complete Question:

Select the correct answer. A cosmetics company decides to compare its new nail polish product, Bella, with three other nail polish bra experiment, participants are divided into four groups. Each group of women is asked to wear nail polish from one of the four brands. The results for Primrose, Shine, and Glo are compared with those for Bella, and a conclusion is drawn. What does the type of nail polish represent in this case?                                                                                                                                                                    A. the control group                                                                                                                                                        B. the explanatory variable                                                                                                                                            C. the response group                                                                                                                                                    D. the response variable

The slant height of a cone with a radius of 7 meters and a surface area of 395.64 square meters is approximately 11 meters, which corresponds to option C.

To find the slant height of a cone when you know the radius (r) and the surface area, you can use the formula for the surface area of a cone, which is spelled out as A = πrs + πr², where A is the surface area, r is the radius, and s is the slant height. In this case, you know that the surface area (A) is 395.64 square meters and the radius (r) is 7 meters. So, you can rearrange the formula to solve for the slant height(s) : A - πr² = πrs => (A - πr²)/πr = s.

Insert the values into the formula: s = (395.64 - 3.14*7²) / (3.14*7). By performing these calculations, you'll find that the slant height is approximately equal to 11, which corresponds to option C.

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The required down payment for a condominium priced at $102,000, with a 5% down payment, is $5,100. This is calculated by multiplying the price of the condominium by 0.05. Therefore, the down payment amount is $5,100.

The price of the condominium is $102,000, and the bank requires a 5% down payment. To find the required down payment, we need to calculate 5% of the condominium's price.

Step-by-step solution:

Therefore, the required down payment for the condominium is $5,100.

Final answer:

The product of (g-7)(g-2) is found by applying the Distributive Property, which results in g² - 9g + 14.

Explanation:

To use the Distributive Property to find the product (g−7)(g−2), we need to multiply each term in the first parenthesis by each term in the second parenthesis. This gives us:

g × g = g²

g × (−2) = − 2g

(−7) × g = − 7g

(−7) × (−2) = 14

Combining these we get g² - 2g - 7g + 14. Simplifying by combining like terms, we obtain:

g² - 9g + 14

Therefore, the product (g−7)(g−2) using the Distributive Property is g² - 9g + 14.

C. There is one outlier that indicates an unusually large number of cars were in the parking lot that day.

~ SourCreamAndOnion

A square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q. the size of angle AQB 90 degrees.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

square ABCD and midpoints M and N are marked on CB and CD, respectively. Draw AM and BN, which meet at Q.

To show triangles ABM and BNC are congruent

AB = BC  

BM = NC

angle B = angle C

Thus, triangles ABM and BNC are congruent by (SAS).

To find ∠AQB

∠AQB =∠ QMB + ∠MBQ   (exterior angles of a triangle)

        = ∠BNC + ∠MBN   (corresponding angles of congruent triangles)

       = 90 degrees   (exterior angle of triangle BNC)

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Answer:

In a linear programming graph, the best optimal solution always occur at a point called:

Extreme Point.

Step-by-step explanation:

As we know that the optimal solution is the solution that is a feasible solution and satisfies the objective function.

The objective solution always exist at the corner point of the feasible region and the objective function is either a minimization or a maximization function and hence such a point will is a objective solution is called a extreme point.

Answer:

The guinea pig is 210 mm longer than Naomi's fish

or

The guinea pig is 21 cm longer than Naomi's fish

Step-by-step explanation:

Remember that

1 cm=10 mm

Convert cm to mm

guinea pig ------> 25 cm=25*10=250 mm

Subtract the length of Naomi's fish from the length of her guinea pig

so

250-40=210 mm

Convert to cm

210 mm=210/10=21 cm

It depends on the number. Generally, it is false, expect in a few certain cases, such as 2 for example, as:

2 + 2 = 4

2 x 2 = 4

however, most other numbers do not work, such as, for example, 5

5 + 5 = 10

5 x 5 = 25

So it really depends on what "x" is.

hope this helps

The expression 6y² - 48 + 42y is factored by first rearranging the terms, finding the GCF, and then factoring the resulting trinomial to get 6(y + 8)(y - 1).

To factor the expression 6y² - 48 + 42y, the first step is to rearrange the terms in descending powers of y, which gives us 6y² + 42y - 48. Next, we can look for a greatest common factor (GCF) among the three terms. Observing that each term is divisible by 6, we can factor out 6:

6(y² + 7y - 8)

Now, we need to factor the trinomial within the parentheses. We are looking for two numbers that multiply to give -8 (coefficient of y² times constant term), and add to 7 (coefficient of y term). The numbers +8 and -1 satisfy these conditions:

6(y + 8)(y - 1)

Thus, the original expression 6y² - 48 + 42y factors to 6(y + 8)(y - 1).

To find out how many years until Tevin's age is 5 times Katherine's age, we set up an equation and solve for x, finding that it will take 13 years.

The question is asking us to find out how many years until Tevin's age is 5 times Katherine's age. Let's denote the number of years until this happens as 'x'.

Currently, Tevin is 202 and Katherine is 30.

In x years, Tevin will be 202 + x years old and Catherine will be 30 + x.

Therefore, we want to find x such that:

202 + x = 5(30 + x)

This can be solved as follows:

202 + x = 150 + 5x

Now, we subtract 5x from both sides:

202 - 4x = 150

Subtract 202 from both sides:

-4x = -52

Divide by -4:

x = 13

Therefore, it will take 13 years for Tevin's age to be 5 times Katherine's age.

Answer with explanation:

Outlier, in a data set are those real numbers called variates , if we consider two consecutive real numbers in that data set, when data is arranged in ascending or descending order the difference looks filthy,or ambiguous.

For, example , 13,45,  23.45, 35.45, 49.45,55.45, 80.45.

So, we can say that ,applying the above definition , 80.45 is an outlier.

Outliers affect the mean and Standard deviation.

→If you discard 50 % of the data , to get the better result in an experiment,the data set will become smaller and getting accurate result will be a task similar to catch a  ruffian who is riding in a four wheeler and you are running behind him on footsteps.

→Similarly, Examining a smaller random sample of the population will not give accurate result.

Most of the Outliers lie either on right or left of Data set when arranged in ascending or descending order.

To overcome the effect of an outlier,we should consider large sample to get better result, as leaving some variates from right or left will have little effect on the result.

Option B: Examine a larger random sample of the population.

The potential dimensions that could represent the original photograph and its enlargements, with the length being 1 2/5 times the width, are 5 by 7 inches for the original photograph, and 20 by 28 inches and 10 by 14 inches for the enlargements.

To find the dimensions of Sally's original photograph and the enlargements with the area having the given ratio of length to width as 1 2/5, we need to understand the relationship between the area of two similar objects and their linear dimensions. We are given that the original photograph has an area of 35 square inches, and the enlargements have areas of 140 and 560 square inches. With the length being 1 2/5 times the width in each case, we can work out the possible dimensions for these photographs.

Now, let's consider the list of dimensions provided and determine which ones correspond to an area ratio that matches the original photograph or the enlargements:

Conclusively, only some of the dimensions given match the requirements: 5 inches by 7 inches for the original photograph, 20 inches by 28 inches and 10 inches by 14 inches for the enlargements. They adhere to the concept that the ratio of their areas equals the ratio of the squares of their linear dimensions due to scaling.

Answer:

[tex]3.75\ cm^{3}[/tex]  or  [tex]3\frac{3}{4}\ cm^{3}[/tex]

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

we know that

The volume of a rectangular prism is

[tex]V=LWH[/tex]

In this problem we have

[tex]L=2\frac{1}{2}\ cm=\frac{2*2+1}{2}=\frac{5}{2}\ cm[/tex]

[tex]W=2\frac{1}{2}\ cm=\frac{2*2+1}{2}=\frac{5}{2}\ cm[/tex]

[tex]H=5\ cm[/tex]

substitute in the formula

[tex]V=(\frac{5}{2})(\frac{5}{2})(5)=\frac{125}{4}=31.25\ cm^{3}[/tex]

step 2

Find the difference between the volume of the prism and the volume of the storage container

[tex]35\ cm^{3}-31.25\ cm^{3}=3.75\ cm^{3}[/tex]

[tex]3.75=3\frac{3}{4}\ cm^{3}[/tex]

Answer:

3.75

Step-by-step explanation:

:>

The length of the longest side of the rectangular prism is approximately

10 centimeters.

The correct option is D.

In three-dimensional space, a prism is a polyhedron where two ends are similar.

To solve the equation 2x³ + 14x² +12x =400, we first need to rearrange it to the standard form of a cubic equation:

2x³ + 14x² +12x - 400 = 0

We can use a graphing calculator to find the real solutions of this equation, which are approximately x = -8.75, x = 2.16, and x = 5.59.

Since the dimensions of the rectangular prism are x + 1, 2x, and x + 6, we need to find the maximum value of the expression (x + 1)(2x)(x + 6) over the interval [2.16, 5.59]. We can set up a system of inequalities to find this maximum value:

2.16 ≤ x ≤ 5.59

(x + 1)(2x)(x + 6) ≥ 400

Using a graphing calculator, we can graph the function f(x) = (x + 1)(2x)(x + 6) and find the maximum value over the interval [2.16, 5.59]. The maximum value occurs at x ≈ 4.98, and the value of the function at this point is approximately 469.83.

Therefore, the length of the longest side of the rectangular prism is approximately 4.98 + 6 = 10.98 centimeters, which is closest to answer choice D) 10 centimeters.

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