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. The statistician plans to test the hypotheses, H0: μ = 76.4 versus Ha: μ > 76.4, where μ = the true mean height of all trucks. Are the conditions for inference met?

No, the random condition is not met.
No, the 10% condition is not met.
No, the Normal/large sample condition is not met.
Yes, all conditions for inference are met.

Answer:

The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4

Step-by-step explanation:

Answer:

-14x + 6 (option D)

Step-by-step explanation:

To solve the given equation, you first need to distribute the negative 3.

So, you need to multiply

(4x)(-3)  ;  (-2)(-3)

(4x)(-3)= -12x

(-2)(-3)= 6

So, your new, distributed, equation would be:

-12x + 6 - 2x

If we combine like terms (-12x - 2x), our new equation will be:

-14x + 6

Answer:

The answer is A since it does the same movements twice. Think of it like flipping a coin, then actually taking the coin and flipping it back over regardless of what it lands on.

Step-by-step explanation:

Hope this helps have a good rest of your day

Answer:

Domain: -5, -2, 1, 5

Range: 10, 11, 4, 10

To get the function, you need to create an equation.

Step-by-step explanation:

For example, f(x)= 10x. "x" equals your y value, and "10" is where you plug in your range, or in other words, your y-values.

Answer:

78.5

Step-by-step explanation:

The probability of scoring 1 , 3 or 5 points is 78.5% ( optionD)

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it's 100% in percentage.

probability is expressed as;

probably = sample space/total outcome

The area of the square is expressed as;

A = l²

= 20 × 20

= 400cm²

The area of the biggest circle is 314 cm²

The probability of scoring 1, 3 or 5

= 314/400 = 0.785

in percentage = 0.785 × 100

= 78.5%

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#SPJ3

Answer:

114

Step-by-step explanation:

just add all sides together.

Answer:

91 cm

Step-by-step explanation:

Perimeter is adding all of the side lengths:

8+32+10+10+4+4+23=91

Don't forget to add the unit:

91 cm

Answer:

9. (a) 1/4

   (b) remove 3 alphabet cards

   (c)  add 4 number cards

10.  1/8

Step-by-step explanation:

Question 9

Given:

⇒ total number of cards = 8 + 10 + 6 = 24 cards

[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]

(a) P(picture card) = 6/24 = 1/4

(b) P(alphabet card) = 10/24 = 5/12

If we remove 3 alphabet cards from the box

⇒ number of alphabet cards = 10 - 3 = 7

⇒ total number of cards = 24 - 3 = 21

Therefore, P(alphabet card) = 7/21 = 1/3

(c)  P(number card) = 8/24 = 1/3

If we add 4 number cards to the box:

⇒ number of number cards = 8 + 4 = 12

⇒ total number of cards = 24 + 4 = 28

Therefore, P(number card) = 12/28 = 3/7

--------------------------------------------------------------------

Question 10

Given:

⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²

As PR = SD = 4cm

Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²

P(point lies in ΔSDR) = 8/128 = 1/16

P(point lies in ΔPRQ) = 8/128 = 1/16

P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8

Answer:

(2,-12)

Step-by-step explanation:

Correct equations:

  8x+y=4

 -2x-8=y

------------------

Rearrange the first equation:

8x+y=4

y=4-8x

Now use this value of y in the second equation:

-2x-8=y

-2x-8=4-8x

6x = 12

x = 2

When x = 2:

y=4-8x

y=4-8(2)

y = -12

(2,-12)

--

One can also graph the two equations and find the point they intersect.  See the attached graph.

Answer:

2n= 53

and you divide both sides by 2

2n/2 =53/2

2 divided by 2 is 1 and 53 divided 2 is 26.5

n= 26.5

Answer:

4x/(x+1)(x2+x+6)

Step-by-step explanation:

Answer:

20 meters

Step-by-step explanation:

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:

2 m/s or 7.2 km/h

Step-by-step explanation:

Time = 50 seconds

Distance = 100 meters

Velocity = distance/time = 100/50 = 2 m/s or 7.2 km/h

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[tex] \large \rm{s = \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = \cancel \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = 2 m/s \: or \: 7.2km/h }[/tex]

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Answer:

The answer is 12

Step-by-step explanation:

1/2x 12 = 6

6/2-2+11 = 12

The final answer is 12

Answer:

since there are 30 students as a whole and 20 boys make up part of the class, you can assume that there are 10 girls in the class. since the mean mark for boys is 62 I think the mean mark for girls would be 8%

Step-by-step explanation:

Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.

An equation is an expression used to show the relationship between two or more numbers and variables.

Ginger and Caleb each have $0.75

Ginger does not have any quarters. He might have 7 dimes and 7 pennies.

Caleb does not have any dimes. He can have 3 quarters and 2 pennies.

Ginger can have 7 dimes and 7 pennies while Caleb can have 3 quarters and 2 pennies.

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Answer: Yes

Step-by-step explanation:

Step #1: Lacey has 2 3/4 yards of wrapping paper remaining. She has six boxes to wrap, each of which requires 3/8 of a yard of paper. First, you must find the total number of yards of wrapping paper needed for six boxes.

Number of boxes * Number of wrapping paper required for each box

6 x 3/8 = 9/4

Step #2: Subtract the number of yards of wrapping paper remaining by the total number of wrapping for 6 boxes.

2 3/4 - 9/4 = 1/2

Step #3: Determine and solve whether Lacey will have enough wrapping paper left to also wrap a book that requires 1/2 yard of paper. To solve, subtract the remaining amount of wrapping paper by the amount of wrapping required for a book.

1/2 - 1/2 = 0

So, yes Lacey will have just enough wrapping paper to also wrap a book that requires 1/2 yard of paper.

The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6).

In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:

P'(x,y) = P(x,y) + T(x,y)   (1)

Where:

If we know that P(x,y) = (5, -6) and T(x,y) = (-4, 0), then the image point is:

P'(x,y) = (5, -6) + (-4, 0)

P'(x,y) = (1, -6)

The image point of P(x,y) = (5, -6) after applying a horizontal reflection is P'(x,y) = (1, -6). [tex]\blacksquare[/tex]

Statement is incorrect and poorly formatted. Correct form is shown below:

What is the image point of (x, y) = (5, -6) after the transformation of translating horizontally the point -4 units to the y-axis?

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Answer:

Step-by-step explanation:

To make a guess as to the volume, it may be easier to guess in cups rather than centimeters or inches. One may visualize that a 12 ounce soda can is about 1.5 cups. This is equivalent to 354.88 cubic centimeters or 21.656 cubic inches.

Answer:

184

Step-by-step explanation:

80% of 230

0.8x230

8×23

=184

Check the picture below.

Answer:

x - 7 [tex]\leq[/tex] -28

Step-by-step explanation:

I guarantee you that this is correct. It's pretty simple to understand.

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Step-by-step explanation:

(2x - 3)×4

random number multiplied by 2, then minus 3 from that result, and multiply that result by 4.

Answer:

70

Step-by-step explanation:

20x(1+150%)

28x(1+1.5)

28x2.5

70

Answer:

The answer is D

Step-by-step explanation:

The parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.

It is given that the two functions one is the parent function [tex]\rm y = \sqrt[3]{-x}[/tex] and the transformed function [tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex].

It is required to find the transformation rules.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have parent function:

[tex]\rm y = \sqrt[3]{-x}[/tex]

and transformed function:

[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]

If we multiply the parent function with a negative value it will f(x) over the x axis.

By the transformation rules of the function y = -f(x) reflects f(x) over x-axis.

After applying the transformation to the parent function:

[tex]\rm y = -\sqrt[3]{-x}[/tex]

By the transformation rules of the function if multiply the function with less than the unit value it will be compressed by the multiplied factor ie.

y = k f(x) and k<1, the function will be compressed by the k factor hence:

[tex]\rm y = -0.4\sqrt[3]{-x}[/tex]  (after applying the second transformation)

As we can see the transformed function is subtracted by -2

By rules of transformation, for y=f(x-A) it would be a horizontal translation of 'A' unit to the right.

After applying this transformation we get:

[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]  which is a transformed function derived after applying the transformation to the parent function.

Thus, the parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.

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21b-32+7b-20b=

21b + 7b - 20b - 32

       8b            - 32

Hello!

21b-32+7b-20b=

21b +7b -20b -32

= 28b -20b - 32

= 8b -32

The amount of plywood needed to build the garbage bin is the surface area. Therefore, the amount of plywood needed is 90884 cm².

The wooden box is a rectangular prism. The amount of plywood used to construct the wooden box is the surface area of the box.

Therefore,

surface area of rectangular prism = 2(lw + lh + hw)

where

l = 156 cm

w = 122 cm

h = 95 cm

surface area of rectangular prism = 2((156 × 122) + (156 × 95) + (122 × 95))

surface area of rectangular prism = 2(19032 + 14820 + 11590)

surface area of rectangular prism = 2(45442)

surface area of rectangular prism = 90884 cm²

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