Mathematics College

A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?

Answers

Answer 1

First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:

where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.

Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:

A = 5*18 + 3*20 + 5*18

A = 90 + 60 + 90

A = 240

Then, the area is 240 in^2

Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:

[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]

Now, to find the volume convert 30 in to yards:

[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]

Finally, multiply the previous result by the area of the figure:

[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]

Related Questions

If I take a 45 min. break at 2:15pm what time do I come back?

Answers

The break time is 2:15 pm.

The time interval for break is 45 min.

Determine the time at which interval ends.

[tex]\begin{gathered} 2\colon15+00.45=2\colon60 \\ =3\colon00 \end{gathered}[/tex]

So break ends (individual come back) at 3:00.

What is the area of this triangle?
Pls help :(

Answers

24
Remember the formula
A=1/2(B)(H)

what is the answer to 65y=12

Answers

In this case, we have a equation with one unknown value (y)

all you have to do is to isolate y

Let's see

65 y=12

[tex]\begin{gathered} 65y=12 \\ \text{divide each side by }65 \\ \\ \frac{65y}{65}=\frac{12}{65} \\ \\ y=\frac{12}{65} \\ \end{gathered}[/tex]

so the solution is y=12/65

I really hope it helps

Write this trinomial in factored form. 5a² - 30 - 14

Answers

[tex]5x^2-3x-14[/tex]

replace x with a for this exercise

we use this formula to factor

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

where a=5, b=-3 and c=-14

[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]

we have two roots

[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]

and

[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]

so the simplified equation is

[tex](x-2)(x+\frac{7}{5})[/tex]

now replace x for a

[tex](a-2)(a+\frac{7}{5})[/tex]

Kia rides her bicycle at 20 miles per hour. Which equation represents the situation? Leth represent the hours traveled. Let d represent the distance traveled. Od 2012 Oh= 200 Od 20 h O h = 20 -

Answers

Velocity= 20 miles/hour

What is the polar form of the equation? What type of polar curve is this?

Answers

The curve is given to be:

[tex]x^2+y^2+12y=0[/tex]

We can rewrite the equation in the form:

[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]

Using the Completing the Square method, we have the equation to be:

[tex]\frac{\left(x-0\right)^2}{6^2}+\frac{\left(y-\left(-6\right)\right)^2}{6^2}=1[/tex]

Therefore, the ellipse's center is (0, -6).

(2-5). (6.0)Find the midpoint

Answers

Let:

(x1,y1)=(2,-5)

(x2,y2)=(6,0)

The midpoint is given by:

[tex]\begin{gathered} xm=\frac{x1+x2}{2} \\ xm=\frac{2+6}{2} \\ xm=\frac{8}{2}=4 \\ ym=\frac{-5+0}{2}=-\frac{5}{2}=-2.5 \end{gathered}[/tex]

Therefore the midpoint is:

M = (4 , -5/2) or M = (4, -2.5)

Solve 3 (4x - 7) * 7x - 10 0 12x - 7 12x - 21 12x + 21

Answers

Answer:

12x-21

Explanation:

Given the expression

3 (4x-7)

On expanding using distributive law;

3(4x-7)

3(4x) - 3(7)

12x - 21

Hence the result required is 12x-21

23.What is the missing piece of information required to provethese triangles congruent?a) QYQYb) NYPYC) ZN 2 Pd) QY is the perpendicular bisector

Answers

In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.

The missing information, that can also be seen in the picture, is that we have a shared side that is QY.

If we applied the reflexive property, we know that:

[tex]QY\cong QY[/tex]

and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.

Answer: QY = QY (Option A).

Can someone help me out??

Answers

The correct option for the missing sides of given triangles is-

Part 1: x = 30Part 2: x = 21Part 3: x = 49Part 4: x = 22What is termed as the similar triangles?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size.

For the given question,

The dimension of the two triangles are given with the missing sides.

Part 1: In the given rectangles;

5/3 = x/18

x = 30

Part 2: In the given rectangles;

9/x = 3/7

x = 21

Part 3: In the given triangles;

x/63 = 7/9

x = 49

Part 4: In the given triangles;

16/x = 8/11

x = 22

Thus, the missing sides of the given shapes are found.

To know more about similar triangles, here

https://brainly.com/question/14285697

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110,169 is larger than 110,72

Answers

110,169 is larger than 110,72

This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.

110,169 is larger than 110,72

This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week.

Answers

The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent variable

The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,

W = W(n) = Pb'

Here P = 106 and b = 1.04

Hence the required formula is,

⇒ W = 106 × 1.04ⁿ

Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

Learn more about the algebraic expression here :

brainly.com/question/21751419

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The question seems to be incomplete the correct question would be

Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit

Answers

In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:

[tex]GF=HE[/tex]

Substituting we get:

[tex]z+10=2z[/tex]

Now, we solve for "z". First, we subtract "z" from both sides:

[tex]\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}[/tex]

Therefore, the value of "z" is 10.

The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =

For part c) and e), Is the assumption of normal necessary? NoYes

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem: