Ziyad is hoping to start his own lawn care business in Gettysburg, PA. Gettysburg has about 2,400 households. Ziyad went to
three different gas stations in Gettysburg and asked every tenth adult if they would be interested in using lawn care services
in the future. Of the adults he surveyed, 92 said yes, 51 said no, and 17 said they weren't sure.
Based on his results, how many households in Gettysburg are likely interested in using lawn care services?

Answer:

Step-by-step explanation:

There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:

P = 2w + l; solving for l and filling in our length of fencing gives us:

l = 148 - 2w

The area then for this will be:

A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:

[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:

[tex]A=-2w^2+148w[/tex]

The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.

To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:

[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:

[tex]-2(w^2-74w)=0[/tex]

The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:

[tex]-2(w^2-74w+1369)=...[/tex]

But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:

[tex]-2(w^w-74w+1369)=-2738[/tex]

The left side can be simplified down to a perfect square binomial:

[tex]-2(w-37)^2=-2738[/tex]

Now we'll add over the -2738:

[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.

9514 1404 393

Answer:

  14

Step-by-step explanation:

Use the formula with n=3.

  h(3) = h(3-2) +h(3-1)

  h(3) = h(1) +h(2)

  h(3) = -6 +20 . . . . . substitute the given values

  h(3) = 14

there should be a cross multiplication

3(8x)=2

expanding bracket

24x=2

multiple both sides by 24

x=1/12

Answer:

two dollars

Step-by-step explanation:

12-8=4/2=2

Answer:

Answer. so the answer is 15. you got 15 questions right.

Step-by-step explanation:

Answer:

3:20

Step-by-step explanation:

6000:40,000

find HCF (2000)

divide both sides by 2000

3:20

Answer:

39

Step-by-step explanation:

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The scale factor is the ratio of corresponding dimensions:

  (6 cm)/(9 cm) = 2/3

Answer:

We say that a function is increasing on an interval if the function values increase as the input values increase ...

Step-by-step explanation:

Answer:

$8.25

Step-by-step explanation:

I don't know how to explain it to you but if I'm wrong tell me I'll try it aagain.

9514 1404 393

Answer:

  1) 2/3

  2) 5x/2

Step-by-step explanation:

The fraction simplification process involves finding the largest common factor in the numerator and denominator, then dividing that from both.

1)

  [tex]\dfrac{8}{12}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{2}{3}\cdot\dfrac{4}{4}=\dfrac{2}{3}\cdot1 =\boxed{\dfrac{2}{3}}[/tex]

__

2)

  [tex]\dfrac{15x^2}{6x}=\dfrac{5x\cdot3x}{2\cdot3x}=\dfrac{5x}{2}\cdot\dfrac{3x}{3x}=\dfrac{5x}{2}\cdot1=\boxed{\dfrac{5x}{2}}[/tex]

Answer:

328 is the surface area

Step-by-step explanation:

Answer:

Is 3(b+c) equivalent expressions?

A. True

Answer:

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Step-by-step explanation:

Manufacturer’s claim that the average nicotine content does not exceed 3.5 mg

This means that the null hypothesis is given by:

[tex]H_{0}: \mu = 3.5[/tex]

And the alternate hypothesis is:

[tex]H_{a}: \mu > 3.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

3.5 is tested at the null hypothesis

This means that [tex]\mu = 3.5[/tex]

A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams.

This means that [tex]n = 8, X = 4.2, \sigma = 1.4[/tex]

Value of the z-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{4.2 - 3.5}{\frac{1.4}{\sqrt{8}}}[/tex]

[tex]z = 1.41[/tex]

Pvalue of the test:

We are testing if the mean is higher than 3.5.

The sample mean found is of 4.2, and we have to find the probability of finding a sample mean at least as large as this, which is 1 subtracted by the pvalue of z = 1.41.

z = 1.41 has a pvalue of 0.9207

1 - 0.9207 = 0.0793

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Answer:

The top number in a fraction. Shows how many parts we have. (The bottom number is the Denominator and shows how many equal parts the item is divided into.)

Step-by-step explanation:

Answer:

n+18

Step-by-step explanation:

Answer: n+18

Step-by-step explanation:

CONCEPT:

- a increased by b=a+b

- a decreased by b= a-b

- a multiply by b=ab

- a divided by b=a/b

SOLVE:

A number n increased by 18

(n) increased by (18)

n+18

Hope this helps!! :)

Please let me know if you have any questions

Answer:

the answer is 20+6h=15+8h

Answer:

The car gets 35 miles per gallons.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

We want to solve the equation:

[tex]5\sin(2x)=3\cos(x)[/tex]

To do so, we can rewrite the equation.

Recall the double-angle identity for sine:

[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]

By substitution:

[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]

Distribute:

[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]

We can subtract 3cos(x) from both sides:

[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]

And factor:

[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.

Answer:

A. cosx(10sinx-3)=0

Step-by-step explanation:

5(2sinxcosx)=3cosx

10sinxcosx-3cosx=0

cosx(10sinx-3)=0

Answer:

3,268,584

Step-by-step explanation:

1^12 is 1

Answer:

[tex]y = 4*5^x[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex](x_2,y_2) = (1,20)[/tex]

Required

Determine the exponential equation

An exponential equation is of the form: [tex]y = ab^x[/tex]

In: [tex](x_2,y_2) = (1,20)[/tex]

[tex]20 = ab^1[/tex]

[tex]20 = ab[/tex] ---- (1)

In: [tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex]\frac{4}{125} = ab^{-3}[/tex] --- (2)

Divide (1) by (2)

[tex]20/\frac{4}{125} = \frac{ab}{ab^{-3}}[/tex]

[tex]20/\frac{4}{125} = b^4[/tex]

[tex]20*\frac{125}{4} = b^4[/tex]

[tex]5*125 = b^4[/tex]

[tex]625 = b^4[/tex]

Take 4th roots of both sides

[tex]\sqrt[4]{625} = b[/tex]

[tex]5 = b[/tex]

[tex]b = 5[/tex]

Substitute [tex]b = 5[/tex] in [tex]20 = ab[/tex]

[tex]20 = a * 5[/tex]

Solve for a

[tex]a = 20/5[/tex]

[tex]a = 4[/tex]

Hence, the equation is:

[tex]y = 4*5^x[/tex]

Answer:

2.9

Step-by-step explanation:

3.6 - 0.7 = 2.9

Answer:

2.9 ｡◕‿◕｡ make as brainlest

explain

3.6 - 0.7 =2.9

Answer:

87

Step-by-step explanation:

87 because 15 times 6 equals 90 but take away the 1.50 from eah hou and you get 87

Answer:

72. If the second 3cm has some relevance, leave a note and I'll come back and modify my answer.

Step-by-step explanation:

Givens

L = 6 cm

W = 3 cm

H = 2 cm

I don't know what the extra 3 cm is for.

Formula

SA = 2*L*W + 2*L*H + 2*H*W

SA = 2*6*3 + 2*6*2 + 2*2*3

SA = 36 + 24 + 12

SA = 72

Answer:

Step-by-step explanation:

Using Cramer’s Rule, the value of x is 0

We have:

2/5X + 1/4Y = 9/20

2/3X + 5/12 = 3/4

Represent as a matrix

[tex]\left[\begin{array}{cc}2/5&1/4\\2/3&5/12\end{array}\right] \left[\begin{array}{c}9/20&3/4\end{array}\right][/tex]

Start by calculating the determinant of the matrix

A = 2/4 * 5/12 - 2/3 * 1/4

Evaluate the product

A = 5/24 - 1/6

Evaluate the difference

A = (5 - 4)/24

|A| = 1/24

Next, replace the last column with the first

[tex]\left[\begin{array}{cc}9/20&1/4\\3/4&5/12\end{array}\right][/tex]

Calculate the determinant

|x| = 9/20 * 5/12 - 1/4 * 3/4

Evaluate the product

|x| = 3/16 - 3/16

Evaluate the difference

|x| = 0

The value of x is then calculated as:

x = |x|/|A|

So, we have:

x = 0/(1/24)

Evaluate

x = 0

Hence, the value of x is 0

Read more about Cramer's rule at:

https://brainly.com/question/11198799

#SPJ1

0 and no solutions are both wrong, but dont know the acrual answer lol

Answer:

9.76

Step-by-step explanation:

area of a rectangle = length * breadth

length = (2x + 3)

breadth = x

given area is 220 sq. inches.

thus,

220 = x * (2x+3)

220 = 2x² +3x

2x² + 3x -220 = 0

x = (-b + √ ( b²-4ac) ) ÷ 2a

x = ( -3 + √ ( 3² - 4*2*220) ) ÷ 2*2

x =9.76