Answer step by step

1.Avas school took a field trip. A total of 32 vehicles were needed for the trip.Some students took the bus, and some students car-pooled. There are 27 people on each bus and 3 people on each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?

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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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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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:

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The family's weekly income is $1500.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

A Family spends 240.00 per week on food. If this is 16% of their income.

let,

x = weekly income (in dollars)

16% of x = amount spent on food per week

16% of x = 240

(16/100)*x = 240

0.16*x = 240

0.16*x/0.16 = 240/0.16

x = 1500

Hence, The family's weekly income is $1500.

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The simplified value of the product of [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

We know when we have the same radical we can simply multiply the values.

Given, [tex]\sqrt[3]{24}\times\sqrt[3]{45}[/tex].

= [tex]\sqrt[3]{24\times45}[/tex].

= [tex]\sqrt[3]{2\times2\times2\times3\times3\times3\times5}[/tex].

= [tex]2\times3\sqrt[3]{5}[/tex].

= [tex]6\sqrt[3]{5}[/tex].

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The length of 4 skateboards is 3 2/3 yards.

1 feet = 1/3 yards

5/2 x 1/3 = 5/6 yards

The second step is to multiply 5/6 yards by 4

5/6 x 4 = 20 / 6 = 3 2/3 yards

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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 graph the equation 8x - 5y = 40, find the x-intercept and y-intercept. The x-intercept is (5,0) and the y-intercept is (0,-8). Plot these points and draw a straight line passing through them.

To graph the equation 8x - 5y = 40 using intercepts, we need to find the x-intercept and y-intercept. The x-intercept is the point where the line intersects the x-axis, so let y = 0 and solve for x. The y-intercept is the point where the line intersects the y-axis, so let x = 0 and solve for y.

Setting y = 0, we get 8x - 5(0) = 40, which simplifies to 8x = 40. Solving for x, we find x = 5. So the x-intercept is (5, 0).

Setting x = 0, we get 8(0) - 5y = 40, which simplifies to -5y = 40. Solving for y, we find y = -8. So the y-intercept is (0, -8).

Plotting the x-intercept (5, 0) and the y-intercept (0, -8) on a graph, we can draw a straight line passing through these two points, which is the graph of the equation 8x - 5y = 40.

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Mary and Jerry's number will be 39 and 50.The sum of their numbers is 89.Which shows that the obtained answer is correct.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

Let, Mary’s number be x

Mary’s number is eleven more than Jerry’s

Jerry's number is x+11

From the given condition sum of their numbers is 89.

[tex]x + (x + 11) = 89\\\\ 2x + 11 = 89\\\\ 2x = 89 - 11\\\\ 2x = 78\\\\ \frac{2x}{2} = \frac{78}{2} \\\\ x = 39[/tex]

Jerry's number will be;

[tex]x+11 \\\\ 39+11 \\\\ 50[/tex]

Hence the Mary and Jerry's number will be 39 and 50.

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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

Answer:

If we need all the rows to be equal, all we are doing is dividing.

20/1= 20

20/2= 10

20/4=5

20/5=4

20/10=2

20/20=1

We have 6 different ways to divide 20!

Given is the price increase of a ticket from 50p to 60p.

Using the concept of fractions, we can find the ratio of new price to old price as follows :-

[tex] \frac{new \;\; price}{old \;\; price} = \frac{60p}{50p} =\frac{6}{5} [/tex]

So the increase in price is [tex] \frac{6}{5} [/tex] times old price of the ticket.

Using the formula of percentage, we can find the percentage change in price as follows :-

[tex] Percentage = \frac{(new\;\;price \;-\; old\;\;price) }{old \;\; price}*100 \\\\
Percentage = \frac{60p-50p}{50p}*100 \\\\
Percentage = \frac{10p}{50p}*100 \\\\
Percentage = 20\;\% [/tex]

Hence, Percentage increase is 20% of the original price.

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.