An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage, is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2 inches. The statistician will determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. What are the appropriate hypotheses?

H0: μ = 76.4 versus Ha: μ < 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ < 77.1, where μ = the true mean height of all trucks
H0: μ = 76.4 versus Ha: μ > 77.1, where μ = the true mean height of all trucks

Answer:

10%

Step-by-step explanation:

I think it's right lol but I could be wrong I forgot a lot of this stuff

but out of all the data it goes from 22-42 so 20 points in total

there is only 2 of the data points behind 24, so it is 2/20 or 10%

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

The average rate of change of a function over the interval [tex][a,b][/tex] is equal to [tex]\frac{f(b)-f(a)}{b-a}[/tex], hence:

[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}[/tex]

Therefore, the average rate of change of [tex]f(x)[/tex] over the interval [tex][5,9][/tex] is [tex]\frac{9}{2}[/tex].

Part B

Do the same thing as in Part A:

[tex]\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4[/tex]

Therefore, the average rate of change of [tex]g(x)[/tex] over the interval [tex][0.25,1][/tex] is [tex]-4[/tex].

Part C

To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).

The average rates of change are:

For a function f(x), the average rate of change on the interval [a, b] is:

[tex]r = \frac{f(b) - f(a)}{b -a}[/tex]

a) Here we have:

[tex]r = \frac{F(9) - F(5)}{9 - 5} = \frac{14 - (-4)}{4} = 4.5[/tex]

b) Now we look at g(x) on the interval [0.25, 1]

Notice that g(0.25) = 5 and g(1) = 2

Then we have:

[tex]r = \frac{2 - 5}{1 - 0.25} = -4[/tex]

c) That average rate of change means that, in average, in that interval in each second the height decreases by 4 ft.

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Answer:

30:9 or if you want it simplified 10:3

Step-by-step explanation:

Answer:

Step-by-step explanation:

D 18,000

Answer:

$104

Step-by-step explanation:

$260 - 60% = $104

Step-by-step explanation:

so,

1cm : 4m

that means the factor is 1/400 (as 1 m = 100 cm).

also to remember : 1 m² = 100cm×100cm = 10,000 cm²

the area of a rectangle is

length × width

if both dimensions are shortened by a factor (1/400) in our case :

length×1/400 × width×1/400 =

= length × width × 1/400² = length × width × 1/160,000

that means the area of the actual tennis court is

160,000 times the area of the blueprint picture :

160,000 × 16.25 = 2,600,000 cm² = 260 m²

we now know that the actual length of the tennis court is 400 times the length of the blueprint length :

400 × 6.25 = 2,500 cm = 25 m

Answer:

[tex]x\geq -3[/tex]

Step-by-step explanation:

We can start by combining like terms:

[tex](3x-7x)+(-5+2)\leq 9\\-4x-3\leq 9[/tex]

We want to isolate x, so we must add 3 and divide by -4:

[tex](-4x-3\leq 9)+3\\(-4x\leq 12)/-4\\\\x\geq -3[/tex]

Because we had to divide by -4, the inequality sign had to flip.

Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the data in the question;

2x + 3 = -1

First, we collect like terms.

2x = -1 - 3

2x = -4

divide both sides by 2
2x/2 = -4/2

x = -4/2

x = -2

Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.

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Answer:

x = 2, y = 1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}2x+2y=6\\ 3x-y=5\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Isolate\;x\;for\;2x+2y=6:x=3-y}[/tex]

[tex]\mathrm{Substitute\:}[/tex]

[tex]\begin{bmatrix}3\left(3-y\right)-y=5\end{bmatrix}[/tex]

[tex]\mathrm{Simplfy}[/tex]

[tex]\begin{bmatrix}9-4y=5\end{bmatrix}[/tex]

[tex]\mathrm{Isolate\;y\;for\;9-4y=5:y=1}[/tex]

[tex]\mathrm{For\:}x=3-y\;\mathrm{Substitute\:}y=1[/tex]

[tex]x=3-1[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x=2[/tex]

[tex]\mathrm{The\:Answers\:to\:the\:system\:of\:equations\:are:}[/tex]

[tex]x=2,\:y=1[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check Answer:

Since [tex]x =2 , y =1[/tex]

[tex]2(2)+2(1)[/tex]

[tex]4 + 2[/tex]

[tex]= 6[/tex]

True

[tex]3(2) - (1)[/tex]

[tex]6 -1[/tex]

[tex]5[/tex]

True

Hence, [tex]x = 2, y = 1[/tex]

~Lenvy~

Answer:

224

Step-by-step explanation:

7×8×4= 224 that is the answer

The coordinates of Omega house is (3/2, 1)

Data;

To find the coordinates of Omega house, we can use the formula of midpoint of a line since Omega house falls between Forsyth Tech and Stadium

[tex]x,y = (\frac{x_1+ x_2}{2} , \frac{y_1+y_2}{2})[/tex]

We can substitute the values and solve for both x and y coordinates.

[tex]x = \frac{x_1+x_2}{2} \\x = \frac{7 + (-4)}{2} = \frac{3}{2}[/tex]

The value of the y-coordinate is

[tex]y = \frac{-5+ 3}{2} = 1[/tex]

The coordinates of Omega house is (3/2, 1)

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Answer:

c 6

Step-by-step explanation:

since angles are equal then the sides can be equal

(AB÷PQ)=(AC÷PR)

(20÷5)=(24÷X)

4=24÷X

X=6

Answer:

0.728 to nearest thousandth.

Step-by-step explanation:

3(3 squared2 -4)

= 9√2 - 12

= 0.728 to nearest thousandth.

Answer:

Let the amount invested at 3% = x

Let the amount invested at 6% = y.

From the total amount invested, we get this equation.

x + y = 18

Now we look at the interest earned.

The 3% account earns 0.03x

The 6% account earns 0.06y

5% on the entire amount is 0.05 * 18 = 0.9

This gives us the second equation.

0.03x + 0.06y = 0.9

Now we have a system of 2 equations in 2 unknowns.

x + y = 18

0.03x + 0.06y = 0.9

Solve the first equation for y:

y = 18 - x

Replace 18 - x for y in the second equation.

0.03x + 0.06y = 0.9

0.03x + 0.06(18 - x) = 0.9

0.03x + 1.08 - 0.06x = 0.9

-0.03x + 1.08 = 0.9

-0.03x = -0.18

x = 6

Answer: He invested $6 at 3%

The surface area is the sum of the areas of the faces of a figure. We can break this figure down into 3 different shapes: the base rectangle, the rectangles that come to a point, and the two triangles.

Area of a Rectangle = base x height

Area of a Triangle = 1/2 x base x height

Base rectangle = 24 x 12 = 288

Rectangles that come to a point = 2(12 x 13) = 2(156) = 312

---There are two rectangles, which is why I multiplied the area by 2.

Triangles = 2(1/2 x 24 x 5) = 2(1/2 x 120) = 2(60) = 120

Surface Area = sum of all the areas of the faces

Surface Area = 288 + 312 + 120 = 720 in^2

Answer = 720 in^2

Hope this helps!

Answer:B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The line on B is at the Y coordinate -6.

Horizontal is the X

Vertical is the Y

Answer:

$1.5 per water bottle.

Step-by-step explanation:

One energy bar is equal to $2.

$2 * 22 players is equal to $44.

$44 - $77 is equal to $33.

$33 ÷ 22 players is $1.5.

the reason I divided $33 by 22 players is because you need to know how many dollars did he pay for each bottle of water so you divide the amount of dollars by the amount of players to get the amount of dollars of each water bottle.

There was 42 biscuits in the boxes

[tex]======================================[/tex]

Negative numbers are always less than positive ones.

Do you remember the symbol for "less than"? That's right, "<" :)

Hence,

-6<3

Because

-6 is negative (the - sign tells us that)

3 is positive

[tex]===================================[/tex]

~DiamondS~

Answer:

She can make 2 groups of six, with five cookies remaining

Step-by-step explanation:

First, divide 17 by 6 to get 2 5/6. The whole number is the number of groups she can make, and the fraction is how many are left over. She can make two groups, with five left over.

Hopefully this helps - let me know if you have any questions!

Answer:

2 groups with 5 left over.

Step-by-step explanation:

to solve, take 17 and divide it by 2. since we only have 17 cookies, we round down no matter what. to get the left over, multiply 2 by 6, then subtract by 17.

please mark as brainlest.

Answer:

Yes Girlie, you need to multiply by x and divide by 15!!!!!!!!!

Step-by-step explanation:

Answer:

s=7

p=3s

Step-by-step explanation:

The perimeter is the side length times 3

So the equation would be p=3s

Plug in 21 for p

21=3s

That means s=7

The fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

Slope of a line = change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given the following points:

(4, 9) and (0, 5)

Slope of the line would be:

Slope = (5 - 9)/(0 - 4)

Slope = (-4)/(-4)

Slope = 1

Therefore, the fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

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Answer: They are all less than 1

13% = 0.13 is less than 1

So is 0.125

And so is [tex]\frac{1}{5} = 0.2[/tex]

Same goes for 10% = 0.10

Answer: 22 ft

Step-by-step explanation:

The path that the dog can walk if he maximally extends his leash is the path of a semi-circle, which has a radius of 7ft.

The distance along a full circle is given by the circumference of the circle, which is related to the radius. To find the length of the path that the dog walks, we evaluate half the circumference.

[tex]\begin{aligned}&D=\frac{C}{2} \\&D=\frac{2 \pi r}{2} \\&D=\pi r \\&D=7 \pi \\&D \approx 22\end{aligned}[/tex]

Therefore, the dog can walk about 22 ft if he extends the leash as far as it can go.

Answer: A

Step-by-step explanation:

Answer:

y = 4

Step-by-step explanation:

because 5 x 4 = 20 and 20 × 4 = 80 and so on y is equal to four