Linda pays $24.84 for 7.2 gallons of gas.
Find the unit price in dollars per gallon.
If necessary, round your answer to the nearest cent.

Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity.

a) The volume of the box ([tex]V[/tex]), in cubic centimeters, is equal to the area of the base ([tex]A[/tex]), in square centimeters, multiplied by the height of the box ([tex]h[/tex]), in centimeters. The area of the surface is the product of the width ([tex]w[/tex]) and length (l), both in centimeters:

[tex]V = w\cdot l\cdot h[/tex]  

[tex]V = (36-2\cdot x)^{2}\cdot x[/tex]   (1)

The volume of the container is [tex]V = (36-2\cdot x)\cdot x[/tex] cubic centimeters. [tex]\blacksquare[/tex]

b) We need to apply first derivative analysis and second derivative analysis to determine the dimensions of the maximum squares to be cut:

[tex]-4\cdot (36-2\cdot x)\cdot x+(36-2\cdot x)^{2} = 0[/tex]

[tex]-4\cdot x + 36-2\cdot x = 0[/tex]

[tex]6\cdot x = 36[/tex]

[tex]x = 6[/tex]

[tex]V'' (x) = -4\cdot [(-2)\cdot x+(36-2\cdot x)]-4\cdot (36-2\cdot x)\cdot x + (36-2\cdot x)^{2}[/tex]

[tex]V''(x) = 8\cdot x-4\cdot (36-2\cdot x)-4\cdot (36\cdot x-2\cdot x^{2})+(36-2\cdot x)^{2}[/tex]

[tex]V'' (6) = -48[/tex]

Since [tex]V''(6) < 0[/tex], the critical value of [tex]x[/tex] leads to a maximum.

Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity. [tex]\blacksquare[/tex]

To learn more on optimization, we kindly invite to check this verified question: https://brainly.com/question/5425085

Answer:

Hello bakugo here!

Step-by-step explanation:

I don't see anything, is there supposed to be anything here? if not

Thank you extra for FREE points! :D

Answer:

Step-by-step explanation:

Answer:

102(vertically opposite angle)

Answer:

[tex]\mathrm{No\:Solution}[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}Y=3x-2\\ Y-3x=4\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}Y=3x-2[/tex]

[tex]\begin{bmatrix}3x-2-3x=4\end{bmatrix}[/tex]

[tex]\mathrm\:{Combine\:like\:terms:[/tex]

[tex]\begin{bmatrix}-2=4\end{bmatrix}[/tex]

[tex]-2=4\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}[/tex]

[tex]\mathrm{No\:Solution}[/tex]

Answer:

1∶ 4

explanation

Check the picture below.

Answer:

  (c)  $31.75

Step-by-step explanation:

First of all, you need to use some number sense to estimate an answer.

If the $900 loan had no interest, 1/3 of it would be paid off in each of the 3 years, or about $300 each year. You will be making 12 monthly payments each year, so the amount of principal being paid with each payment is $300/12 = $25. Any answer much above this amount will not make sense, so you can immediately reject all choices except $31.75.

__

The simple interest on the loan is ...

  I = Prt = $900×0.09×3 = $243

That, too, is divided among the 36 payments, so adds ...

  $243/36 = $6.75 to each of the $25 payments we calculated above.

The monthly payment is ...

  $25 +6.75 = $31.75

Answer: y = 10

Step-by-step explanation: Hi there!

To get started, first, we have to subtract 2y from 9y on the left side.

7y + 8 = 4y + 38

Then subtract 4y on both sides.

3y + 8 = 38

Then subtract 8 on both sides

3y = 30

Finally divide by 3 on both sides.

y = 10

The answer is y = 10.

Answer: y=10

Step-by-step explanation:

9y-2y+8=4y+38

[tex]\mathrm{Add\:similar\:elements:}\:9y-2y=7y[/tex]

7y+8=4y+38

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

7y+8-8=4y+38-8

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

7y=4y+30

[tex]\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides}[/tex]

7y-4y=4y+30-4y

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

3y=30

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

[tex]\frac{3y}{3}=\frac{30}{3}[/tex]

Simplify

y=10

Answer:

B

Step-by-step explanation:

3/8 is equal to 0.375, also known as 37.5%.

The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.

The experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.

In the question, we are given that Sarah hit the ball 3 times out of the 8 times.

We are asked to find the experimental probability (as a percent) that she will hit the ball next.

As we know, the experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.

∴ The experimental probability = The number of times Sarah hit the ball/The number of times she experimented = 3/8

or, The experimental probability = (3/8)*100 % = (3*25)/2 % = 75/2 % = 37.5%.

∴ The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.

Learn more about the experimental probability at

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Answer:

54 units

Step-by-step explanation:

        We can graph the vertices given to make this easier to solve.

-> See attached.

-> This will help us in finding the lengths of the sides.

-> We can also use mathematics.

8 + 5 = 13 and 8 + 6 = 14

        Next we will find the perimeter.

-> This can be found with either of these formulas:

[] P = 2L + 2W

[] P = W + W + L + L

P = 2L + 2W

P = 2(14) + 2(13)

P = 54

The perimeter of the county is 54 units

not an answer but I’m working on the same worksheet and if u wanna work on it together than u should add my discord: kuispe#1715

Answer:

Slope = rise/run

= 1/4

Y-intercept = 0

Equation of the line:

y = 1/4x

Answer:

Conner should get 2 $ back

Step-by-step explanation:

conner should get 2$ back

Answer:

Step-by-step explanation:

Answer:

Hope this helps any!

Step-by-step explanation:

Answer:

18[tex]\pi[/tex] yd.³ or 56.54867 yd.³

Step-by-step explanation:

The volume of a cylinder can be written as: height × base, where the base of the cylinder is [tex]\pi[/tex]r².

Since the radius (r) is half the diameter, it should be 1.5 or 3/2 yd.

r = 1.5

So, the area of the base of the cylinder is 1.5²([tex]\pi[/tex]), which is equal to 2.25[tex]\pi[/tex].

Now multiply that by the height, 8 yd.

2.25[tex]\pi[/tex] × 8 = 18[tex]\pi[/tex]

The area of the cylinder is 18[tex]\pi[/tex] or 56.54867

Answer:

56.55 yd.³ OR 56.52 yd.³

Step-by-step explanation:

The formula for the volume of a cylinder is; V=πr^2h

To find the volume let's put in the values they gave us.

Now: V=π times 1.5^2 times 8

(If you don't know what pi or π is its the area of a unit circle. So the area of a circle with diameter 2 or radius 1)

Continuing the volume would be 3.141592.. * 2.25 * 8 ( '*' indicates multiplication) Now the answer after you multiply would be approx. 56.54867 which rounded would be 56.55

V=πr^2h so 3.14*2.25*8 which would be 56.52 yd.³ (if this is the way you need it ignore ANY other answers)

Answer and explanation:

The two events of choosing jolly ranchers from each bag, first and second are independent events so the probability of first event AND second event will be multiplied

First bag has 4 red 2 green and one blue

Second bag has 4 red and 2 orange

what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second

Probability = number of favourable outcomes /total number of favourable outcomes

The first bag does not have a purple jolly rancher and so probability is zero

the second bag's probability of choosing a red jolly rancher =4/6

probability of choosing a purple jolly rancher from first bag and red jolly rancher from second bag

=0*4/6=0

Answer=0

Answer:

-375.5<1200

True

Step-by-step explanation:

100-475.5 = -375.5

Brainliest please!!

Answer:

x = 15°

Step-by-step explanation:

Linear pair = 180°

⇒ (6x - 5) + (6x + 5) = 180°

⇒ 12x = 180°

⇒ x = 15°

Since line m is parallel to line n, (6x - 5) and (6x + 5) are a linear pair.

Linear pair means that the sum of two angles equaling 180°.

[tex](6x - 5) + (6x + 5) = 180[/tex]

Step-by step calculations:

Opening the parenthesis:

[tex](6x - 5) + (6x + 5) = 180 \\\\6x - 5 + 6x + 5 = 180[/tex]

Combining like terms:

[tex]6x - 5 + 6x + 5 = 180 \\\\ (6x + 6x) + (-5 + 5) = 180[/tex]

Simplify the LHS:

[tex](6x + 6x) + (-5 + 5) = 180\\\\(12x) = 180[/tex]

Divide 12 both sides and simplify:

[tex]\frac{12x}{12} = \frac{180}{12} \\\\ x = 15[/tex]

Thus, the value of x is 15.

Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.

Step 1: Find the mean

Step 2: Find each score’s deviation from the mean

Step 3: Square each deviation from the mean

Step 4: Find the sum of squares

Step 5: Apply the formula

[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}[/tex]

The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.

Step 1: Find the mean

The mean of the given data set can be written as,

[tex]Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857[/tex]

Step 2: Find each score’s deviation from the mean

1 - 3.857 = -2.857

4 - 3.857 = 0.143

2 - 3.857= -1.857

2 - 3.857= -1.857

8 - 3.857 = 4.143

7 - 3.857 = 3.143

3 - 3.857 = -0.857

Step 3: Square each deviation from the mean

-2.857² = 8.162

0.143² = 0.02

-1.857² = 3.447

-1.857² = 3.447

4.143² = 17.165

3.143² = 9.877

-0.857²= 0.735

Step 4: Find the sum of squares

8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857

Step 5: Apply the formula

[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474[/tex]

Hence, the standard deviation of the data set is 2.474.

Learn more about Standard Deviation:

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Answer:

The answer is D : 4.

Step-by-step explanation:

=2x-3>11-5x

=2x-3+5x>11

=7x-3>11

=7x>11+3

=7x>14

=7x/7>14/7

=x>2

By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.

I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.

Answer:

Step-by-step explanation:

2x-2+2=12+2

= 2x+0=14

= 2x=14

= X=14÷2

= X=7

Thank you ☺️☺️☺️☺️

Answer:

Point I is on line segment HJ; which means HI and IJ are equal.

HJ = 15

IJ = 10

Finding the length of HI, given the above statements:

Length of HI = 10 (reason: HI and IJ are congruent)

a) x(x+12) + 27
b) m(2n-3k) - 2p(3k + 2n)

Answer:

the answer is (B) I used an app to solve it

Answer:

The answer would be "B" because you have to cross multiply, which would give you: -3k = 180. Then, you have to divide 180 by -3, which would give you -60.

Answer:

I got you :)

Step-by-step explanation:

All angles of a triangle add up to 180 degrees so you can make the equation

3x-2+4x+9+3x-9=180  this equation will help you find x

I used the equation to find out that x=18.2 (i can explain this part further if you would like)

so now you know x=18.2 and all you have to do is plug in

m<H = 3 x 18.2 - 2 = 52.6

m<I =  4 x 18.2 + 9 = 81.8

M<J = 3 x 18.2 - 9 = 45.6

Hope this helps!  :)

Also to check work you can do 52.6+81.8+45.6= 180 :) you know its right because it equals 180 degrees at the end  

Answer:

3 &4

Step-by-step explanation:

Factor is something that is being multiplied together.

Answer:-0.125 or 1/8

Step-by-step explanation: :)

Answer:

-1/8

Step-by-step explanation:

1/2 times -1/4 = -1/8

Answer:

a) (-3, 0) and (7, 0)

b) If x = 7 then (7 - 7) = 0

   If x = -3 then (-3 + 3) = 0

c)  f(x) = x² - 4x - 21

   y-intercept  (0, -21)

Step-by-step explanation:

a)

x-intercepts are when f(x) = 0

Therefore, if f(x) = (x - 7)(x + 3)  then (x - 7)(x + 3) = 0

⇒ x - 7 = 0

⇒ x = 7

and

⇒ x + 3 = 0

⇒ x = -3

So x-intercepts are (-3, 0) and (7, 0)

b) If x = 7 then (7 - 7) = 0

  If x = -3 then (-3 + 3) = 0

c) Expand f(x) = (x - 7)(x + 3)

⇒ f(x) = x² + 3x - 7x - 21

⇒ f(x) = x² - 4x - 21

The y-intercept is when x = 0 ⇒  (0, -21)