A truck averages 23 mpg. Gas costs $2.28 per gallon. How much would it cost to pay for the gas if this truck made a trip of 2,093 miles?

Answer:

25

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2 + b^2 = c^2

We know the two legs and want to find the hypotenuse

15^2+ 20 ^2 = c^2

225 + 400 = c^2

625 = c^2

Taking the square root of each side

sqrt(625) = c^2

25 = c

Step-by-step explanation:

a) The Roughly shape of the probability model is bell shaped or symmetric

( normal )

(b) Roughly, guess the center (mean) of the probability model

The mean is 5/10 =0.5

Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .

(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.

Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .

3*5 ≡ 15 ≡ 3 (mod 12)

3*7 ≡ 21 ≡ 9 (mod 12)

3*9 ≡ 27 ≡ 3 (mod 12)

5*7 ≡ 35 ≡ 11 (mod 12)

5*9 ≡ 45 ≡ 9 (mod 12)

7*9 ≡ 63 ≡ 3 (mod 12)

Your table should look like the attached.

It's unclear what you're supposed to evaluate for part (b)...

Answer:

Length of Shortest Side = 12 inches

Step-by-step explanation:

Length of Shortest Side = L = 3x

Length of Longest Side = W = 5x-4

Condition:

2L+2W = Perimeter

2(3x)+2(5x-4) = 56

6x+10x-8 = 56

16x-8 = 56

Adding 8 to both sides

16x = 56+8

16x = 64

Dividing both sides by 14

=> x = 4

Now,

Length of the Shortest Side = L = 3(4) = 12 inches

Length of the Longest Side = W = 5(4)-4 = 16 inches

Answer:

12 inches

Step-by-step explanation:

The length is the longest side.

The width is the shortest side.

Length : [tex]l=5x-4[/tex]

Width : [tex]w=3x[/tex]

Apply formula for the perimeter of a rectangle.

[tex]P=2l+2w[/tex]

[tex]P=perimeter\\l=length\\w=width[/tex]

Plug in the values.

[tex]56=2(5x-4)+2(3x)[/tex]

[tex]56=10x-8+6x[/tex]

[tex]56=16x-8[/tex]

[tex]64=16x[/tex]

[tex]4=x[/tex]

The shortest side is the width.

[tex]w=3x[/tex]

Plug in the value for x.

[tex]w=3(4)[/tex]

[tex]w=12[/tex]

Answer:

62

Step-by-step explanation:

Sn=1/2(3n^2+7n)

S1=1/2(3+7)=5

S2=1/2(3*4+7*2)=26/2=13

We know

S1=a1=5

S2=a1+a2=13

S2-s1=a1+a2-a1

13-5=a2

a2=8

We know d=a2-a1

d=8-5=3

nth term of AP =an=5+(n-1)3

an= 2+3n

Therefore 20th term =

a20= 2+3(20)=62

Hence 20th term of AP is 62

I hope this helps

Answer:

1800

Step-by-step explanation:

Hello,

First of all we need to find the prime factorisation of the numbers.

18 = 2 * 3 * 3

40 = 2 * 2 * 2 * 5

75 = 3 * 5 * 5

It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3

Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1800

Step-by-step explanation:

→ First of all we need to find the prime factorisation of the numbers.

18 = 2 × 3 × 3 or 2 × 3²

40 = 2 × 2 × 2 × 5 or 2³ × 5

75 = 3 × 5 × 5 or 5² × 3

→ Now find the number that appear twice or more and write them down

3 and 3 from 18

2, 2 and 2 from 40

5 and 5 from 75

→ Now multiply all of these numbers together

3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800

Answer:

  b ≈ 101.52

Step-by-step explanation:

Given two sides and the angle between, the Law of Cosines is useful.

  b^2 = a^2 +c^2 -2ac·cos(B)

  b^2 = 105^2 +9^2 -2·105·9·cos(65°) ≈ 10307.251

  b ≈ √10307.251

  b ≈ 101.52

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.

Answer:

12345824.4

Step-by-step explanation:

I'm not really sure. I just did 1240x637x15.63=12345824.4

answer:

53,445.1 gallons of water

Step-by-step explanation:

im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps

Answer:

Angle 2= 45

Angle 3= 45

Angle 4= 135

Angle 5= 135

Angle 6= 45

Angle 7= 45

Angle 8= 135

Answer:

Your correct answer is 3.75

Step-by-step explanation:

0.25 x 15 = 3.75

Answer:

3.75

Step-by-step explanation:

You can do this many ways. Write a table that looks like this:

0.25

   15

--------

Ignore all decimal points. Multiply the 5's together and carry the 2 to the next column. Multiply 2 x 5 + 2, write the second digit (which is 2) and carry the 1. Multiply 0 by 5 + 1 = 1, so your top number should be 125. Then, multiply all the numbers by the 1. 5 x 1 = 5; 2 x 1 = 2; 0 x 1 = 0. We now have something that looks like:

   0.25

       15

   --------

    1  2  5

0  2  5

Add these numbers together and add the decimal point 2 numbers from the right, since that's what was in the original decimal.

    1  2  5

0  2  5

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

    3.75

Answer:

B. 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5

Answer:

The slope of line is -1.

Step-by-step explanation:

This equation is in the form Y=mx+b form, where m is the slope of the line. in this equation, -1 is m.

Answer:

[tex]\huge\boxed{x=\pm4.5}[/tex]

Step-by-step explanation:

The quadratic formula of

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]

substitute

[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]

Answer:

The sampling is dependent because an individual selected for one sample does dictate about which individual to be selected in the second sample.

The variable is qualitative because it classifies the individual.

Step-by-step explanation:

The sample is dependent as the second individual selected in the sample is dependent on the first individual selection. The sample selection is not random and is dictated. The variables selected are qualitative in nature because they identify the quality of response variable which is non numerical in nature.

Answer:

Step-by-step explanation:

Plug x as 2y-15 in the first equation and solve for y.

-5(2y-15)+4y=3

-10y+75+4y=3

-6y+75=3

-6y=-72

y=12

Plug y as 12 in the second equation and solve for x.

x=2(12)-15

x=24-15

x=9

Answer:

90°

Step-by-step explanation:

Theres a right angke beside x

And Angles on a straight line = 180 so 180-90°= 90°

Answer:

90

Step-by-step explanation:

I looked it up on the internet

Answer:

Step-by-step explanation:

In computer programming relational operators are used to check conditions, that is if one conditions matches another and returns true if the condition is met or satisfied.

Answer:

1.

A. H0 :  μ1 = μ2 = μ3

Ha : μ1 ≠ 2μ ≠ μ3

2. Test Statistics = 95%

3. Critical F-Value = 3.76

4. P-Value = 2.32

5. Conclusion : Reject the null hypothesis

6. Type of vehicle does effect the amount of green house gas emissions.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

A. H 0  μ1 = μ2 = μ3

Ha  μ1 ≠ 2μ ≠ μ3

2. Test Statistics is 95%

3. Critical F-Value is 3.76.

4. P-Value is 2.32.

5. Conclusion  Reject the null hypothesis.

6. Type of vehicle does effect the amount of green house gas emissions.

The correct order of the steps of a hypothesis test is given below.

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

All steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

For more details on hypothesis test follow the link:

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Answer:

  1

Step-by-step explanation:

David Joyner might be the first name, so you may only have to check 1 name.

Answer:

1/2

Step-by-step explanation:

i think sin 5 pi/6

[tex]sin \frac{5 \pi}{6} =sin (\frac{\pi}{2} +\frac{\pi}{3} )=cos \frac{\pi}{3} =\frac{1}{2} \\or\\sin\frac{5 \pi}{6} =sin (\pi-\frac{\pi}{6} )=sin \frac{\pi}{6} =\frac{1}{2}[/tex]

The exact Value of sin 5x/6 is 1/2.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin 5x/6

We can Split it as

sin (5π / 6) = sin (π/2 + π/3)

                  = cos π/3

                  = 1/2

Also, sin (5π / 6) = sin (π - π/6)

                  = sin π/6

                  = 1/2

Hence, the exact value is 1/2.

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Answer:

Step-by-step explanation:

29 is 6 more than K

Let's create an equation

[tex]29 = 6 + k[/tex]

Move variable to L.H.S and change its sign

Similarly, move constant to R.H.S and change its sign

[tex] - k = 6 - 29[/tex]

Calculate

[tex] - k = - 23[/tex]

Change the sign on both sides of the equation

[tex]k = 23[/tex]

Hope this helps..

Best regards!!

The equation for the statement 29 is 6 more than K is solved and K = 23

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists  mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by the statement below

29 is 6 more than K

On simplifying , we get

29 = 6 + K

Subtracting 6 on both sides , we get

K = 29 - 6

K = 23

Therefore , the value of K is 23

Hence , the equation is K = 23

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Answer:

B

Step-by-step explanation:

Answer:

The answer for this Question is Elementary

It is B.

Answer:

It is not normally distributed as it has it main concentration in only one side.

Step-by-step explanation:

So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).

So, let us begin the groupings into their different classes, shall we?

Data given:

0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.

(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.

(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31

(3). 0.4 - 0.6 : there are 2 values that falls into this category.

(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.

Class interval            frequency.

0.00 - 0.20.                   15.

0.20 - 0.40.                    2.

0.4 - 0.6.                        2.

Answer:

The answer is

Step-by-step explanation:

(4k – 4) + ( –9k – 5)

Remove the bracket and simplify

That's

4k - 4 + - 9k - 5

4k - 4 - 9k - 5

Group like terms

4k - 9k - 4 - 5

We have the final answer as

- 5k - 9

Hope this helps you

We can use FOIL to solve:

(4k - 4) + (-9k - 5)

(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)

-36k - 20k + 36k + 20

-20k + 20

Best of Luck!

Answer:

Option b = 90 degrees of freedom.

Step-by-step explanation:

So, in this particular Question we are given the following parameters or data or information which is going allow us to be able to solve this particular problem or Question;

=> "A regression analysis involved 8 independent variables"

=> "99 observations. "

Requirement : to determine the critical value of t for testing the significance of each of the independent variable's coefficient.

Hence, the formula below will used in Calculating or in the determination of the degree of freedom;

Degree of freedom= total number of observations - number of independent variables- 1.

Thus, slotting bin the values into the formula above, we have;

The degree of freedom = 99 - 8 - 1 = 90.

Answer:  8x³ + 12x² - 16x - 16

Step-by-step explanation:

  (4x² - 2x - 4)(2x + 4)

= (2x + 4)(4x² - 2x - 4)

= 2x(4x² - 2x - 4)  +  4(4x² - 2x - 4)

=   8x³ - 4x² - 8x   +  16x² - 8x - 16

=   8x³ + (-4x² + 16x²) + (-8x - 8x) - 16

=   8x³ + 12x² - 16x - 16

Answer:

false

Step-by-step explanation:

When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter