5.) The price of gas last year was $1.75 per gallon. The price went up by 5%,
what is the new price for a gallon of gas?

[tex]Prove\ that\ the\ assumption \is \true for\ n=1\\1^3=\frac{1^2(1+1)^2}{4}\\ 1=\frac{4}{4}=1\\[/tex]

Formula works when n=1

Assume the formula also works, when n=k.

Prove that the formula works, when n=k+1

[tex]1^3+2^3+3^3...+k^3+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k+1)^2}{4}+(k+1)^3=\frac{(k+1)^2(k+2)^2}{4} \\\frac{k^2(k^2+2k+1)}{4}+(k+1)^3=\frac{(k^2+2k+1)(k^2+4k+4)}{4} \\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+4k^3+4k^2+2k^3+8k^2+8k+k^2+4k+4}{4}\\\\\frac{k^4+2k^3+k^2}{4}+k^3+3k^2+3k+1=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+2k^3+k^2}{4}+\frac{4k^3+12k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\\frac{k^4+6k^3+13k^2+12k+4}{4}=\frac{k^4+6k^3+13k^2+12k+4}{4}\\[/tex]

Since the formula has been proven with n=1 and n=k+1, it is true. [tex]\square[/tex]

[tex]\text{For angle N,}\\\\PQ= \text{Perpendicular.}\\\\QN = \text{Hypotenuse.}\\\\\text{Now,}\\\\\sin N = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\~~~~~~~=\dfrac{QP}{QN}[/tex]

Answer:

see the attachment photo!

3/0 and -191/32

lmk if this is wrong, I might be.

Answer:

i think its point D. So that means the answer is B. I think so because if the middle like going side to side is marked first then it must mean the positive is first and so it's point D

Answer:

223

Step-by-step explanation:

find the area for each side.

Answer:

It will be 4 30

Step-by-step explanation:

Mark me as a brainliest.

Answer: what question i don't see it but you can try reading it again and writing it down

Answer:

x = 1

Step-by-step explanation:

7x + 16 = 8x + 15

Step 1 : Subtract 15 on both sides

7x + 16 - 15 = 8x

7x + 1 = 8x

Step 2 : Subtract 7x on both sides

1 = 8x - 7x

1 = 1x

x = 1

It will take 32 minutes for the population to grow from 1,000 to 32,000.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If the population of an alien race doubles every two minutes,

1,000 x 32 = 32,000

Hence, It would take 32 minutes.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

Answer:

7x <5x-16

Step-by-step explanation:

7x-5x < 5x -16 -5x

The ratio of the area of sector abc to the area of sector dbe is 4/3

For sector abc, we have:

Angle = x

Radius  = 2r

For sector dbe, we have:

Angle = 3x

Radius = r

The area of a sector is:

[tex]Area =\frac{\theta}{360}* \pi r^2[/tex]

So, we have:

[tex]ABC =\frac{x}{360}* \pi (2r)^2[/tex]

Evaluate

[tex]ABC =\frac{x* \pi r^2}{90}[/tex]

For DBE, we have:

[tex]DBE =\frac{3x}{360}* \pi (r)^2[/tex]

Evaluate

[tex]DBE =\frac{x}{120}* \pi r^2[/tex]

The ratio of both areas is:

[tex]Ratio = \frac{x}{90}* \pi r^2 : \frac{x}{120}* \pi r^2[/tex]

Cancel out the common factors

[tex]Ratio = \frac{1}{90} : \frac{1}{120}[/tex]

Express as fraction

[tex]Ratio = \frac{120}{90}[/tex]

Divide

[tex]Ratio = \frac{4}{3}[/tex]

Hence, the ratio of the area of sector abc to the area of sector dbe is 4/3

Read more about sector areas at:

https://brainly.com/question/1582027

#SPJ4

4/3

its the answer edmentum

I think the incorrect data is the second x to the left.

Answer:

[tex]1 \div {3}^{( 30)} [/tex]

Step-by-step explanation:

There are exponent rules I posted above that are being used here.

We have (3^-6)^-5

Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.

So, we're left with 3^-30.

If you look at the photo, there's a rule for negative exponents.

Take the inverse of the base number, so 3 in this case:

1 / 3

and then make the exponent positive after taking the inverse.

So, we should get 1 / 3^30

Hope this helps!

Answer:

5

Step-by-step explanation:

You need to do 4 divided by 4 on 1 side and 20 divided by 4 on the other side

4÷4= 1 so we are left with x

20÷4= 5 so we are left with 5

Therefore x=5

Hi student, let me help you out!

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to solve the equation 4x=20.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Is x all by itself? No, there's a 4 multiplied by it.

So, we do the opposite operation.

The opposite of multiplication is..?

Division.

Thus, we divide both sides by 4.

x=5

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{When\;solving\;equations\;,\;our\;goal\;is\;to\;find\;the\;value\;of\;the\;variable,\;which\;in\;this\;case\;was\;x}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

~Just a smiley person helping fellow students :)

The net represents a cube.

The net shows a cube with a side length of 12 cm, meaning its surface area is [tex]6(12)^{2}=\boxed{864 \text{ cm}^{3}}[/tex]

Answer:

Step-by-step explanation:

The Platonic solid with six (6) square faces is the cube. Its surface area is the sum of the areas of the square faces. Each of those is the square of its edge length.

__

The 3-dimensional shape represented by the net is a cube.

The area of the cube is ...

  6 × (12 cm)² = 6 × (144 cm²) = 864 cm²

Answer:

2x + 25

Step-by-step explanation:

Let that number be x.

Step 1 : Multiply x and 2.

x * 2 = 2x

Step 2 : Add 25 and 2x.

2x + 25

Hence,

25 is added to the product of a number and 2 is 2x + 25.

Answer:

none of the answers listed are equivalent to b (22/5, 11/8, 2/5, 1/4)

Step-by-step explanation:

[tex]\frac{1}{3b} = \frac{4}{5}[/tex]

to simplify, cross multiply

(1 · 5  =  3b · 4)

(5 = 12b)

divide both sides by 12 to isolate b,

[tex]\frac{5}{12} =\frac{12b}{12}[/tex]

[tex]\frac{5}{12} = b[/tex]

None of the answers listed are equivalent to 5/12

[tex]\frac{5}{12}[/tex] [tex]\neq[/tex][tex]\frac{22}{5}[/tex]

[tex]\frac{5}{12} \neq[/tex][tex]\frac{11}{8}[/tex]

[tex]\frac{5}{12} \neq[/tex][tex]\frac{2}{5}[/tex]

[tex]\frac{5}{12} \neq[/tex][tex]\frac{1}{4}[/tex]

Answer:

V =512 m^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = 8^3

V =512 m^3

Answer:

P

Step-by-step explanation:

The middle is the middle of the angle ...point P

The amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.

x grams of 20% and 20-x grams of 35%

Hence:

0.20x+0.35(20-x)=0.26×20

0.20x-0.35x+7=5.2

Collect like terms

-0.15x=-1.80

Divide both side by -0.15x

x=-1.80/-0.15

x=12 grams of 20% or 2.4 grams pure

20-x= (20-12) =8 grams of 35% or 2.8 grams pure

Therefore the amount of grams that she must use to make the solution she needs are: 12 grams and 8 grams.

Learn more about amount of grams here:https://brainly.com/question/1107267

#SPJ1

To identify the value that goes in each box, we must perform the corresponding operation and calculate the final result.

In mathematics there are procedures such as addition (+), subtraction (-), division (÷), and multiplication (×) to solve problems. These operations are the four basic operations of mathematics.

According to the above, what we must do is identify what operation we must perform with the given numbers and then identify the result and put it in the corresponding box.

Note: This question is missing because there is some information missing. Howeve i can answer it based on my general knowledge.

Learn more about numbers in: https://brainly.com/question/17429689

#SPJ1

Answer:

1. 33.6

Step-by-step explanation:

1. Mean = total score/number of tests

         = (23+28+29+30+30+32+33+36+36+40+41+43+45+46+48)/15

         =33.6

I don't know any of the others, but I hope that this will be helpful :)

Answer:

y=4/3x+6

Step-by-step explanation:

The maximum height of the  pumpkin is 3 feet

We have given that,

A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.

The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.

We have to determine the maximum height.

At the point of maxima f'(x)=0

first, find the maxima

Therefore differentiate the given function with respect to t we get,

[tex]h'(t)=-32t+96[/tex]

h'(t)=0

Then we get,

[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]

Therefore the maximum height of the pumpkin is 3 feet.

To learn more about the maxima visit:

https://brainly.com/question/13995084

#SPJ1

Answer:

A=πr^2

Step-by-step explanation:

A=π*r^2

Where, A is area of circle

r is radius of circle

π is constant

.

Hope it's help and I think I have give brainleist answer

Answer:

πr^2

Step-by-step explanation:

it's just πr^2.

easy

Answer: -6.5

Step-by-step explanation:

First, you take the values on both sides to the power of 2 to get:

-x = x + 13

Subtract x on both sides.

-2x = 13

Divide both sides by -2.

x = -6.5

Answer:

[tex]x=-\dfrac{13}2[/tex]

Step-by-step explanation:

[tex]~~~~~\sqrt{-x} = \sqrt{x+13}\\\\\implies -x= x+13~~~~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\implies -x -x = 13\\\\\implies -2x = 13\\\\\implies x = -\dfrac{13}2\\\\\text{Verify solution:}\\\\~~~~~~~\sqrt{-\left(- \dfrac{13} 2 \right)} = \sqrt{-\dfrac{13}2 +13}\\\\\\\implies \sqrt{\dfrac{13}2} = \sqrt{\dfrac{13}2}\\\\\text{Hence, the solution is}~ x=-\dfrac{13}2[/tex]