no one answers with 20 points so here’s 60 points again lol

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Answer:

1, 4, 9, 16,25, 36, 49, 64, 81, 100, 121, 144

Step-by-step explanation: hope it helps

Answer:

1, 4, 9, 16, 25, 36

Step-by-step explanation:

Hi! So when you're looking at questions like these, you're normally going to want to find a pattern. So lets look at this problem. When you jump from the number 1 to the number 4, you increase by 3. When you jump from the number 4 to the number 9, you increase by 5. When you jump from the number 9 to the number 16, you increase by 7.

Based on this information, you can conclude that the pattern is that it is increasing by odd numbers, and the odd number is increasing by 2 each time.

Now that we know the information, we can start finding the next terms. Since the jump from 9 to 16 was 7, we know that the next number is going to be 9 away from 16, which is 25.

Now that we have that term, we can find the next. We know that the jump from 16 to 25 is 9, so we know that the next term will be 11 away from 25, which is 36.

You could keep doing this forever.

Hope this helps!!

Answer:I think it’s B

Step-by-step explanation:

If I get this wrong i’m sorry

Answer:

I am pretty sure the answer is 17

Answer:

3

Step-by-step explanation:

7.5 - 1.5 x 3

7.5-4.5

3

Answer:

my answer is (5±√10)/3

Answer:

Step-by-step explanation:

Let the amount of pineapple juice be x quarts, the concentration of juice is as following equation:

Answer:

120

Step-by-step explanation:

6*5*4=120 and boom that’s your answer

Answer:

 C.  x ≥ 5

Step-by-step explanation:

You must meet both conditions:

 (x -5) ≥ 0 and (x +2) ≥ 0

For the first condition, ...

 x ≥ 5 . . . . add 5 to both sides

For the second condition ...

 x ≥ -2 . . . . subtract 2 from both sides.

Since both conditions must be met, we must have ...

 x ≥ 5

i hope this helps :)

Answer: 1.25

Step-by-step explanation: you gotta divide 50 and 40.

Answer: 55% of the seats in the theater were filled by the 6th graders on the trip.

Step-by-step explanation:

Given: Total seats = 3100

Seats vacant=  1395

Seats occupied by 6th graders = 3100-1395 = 1705

The percentage of the seats in the theater were filled by the 6th graders on the trip = [tex]\dfrac{\text{Seats occupied by 6th graders}}{\text{Total seats}}\times100[/tex]

[tex]=\dfrac{1705}{3100}\times100\\\\= 55\%[/tex]

Hence, 55% of the seats in the theater were filled by the 6th graders on the trip.

Answer:

increase by 25%

Step-by-step explanation:

15-12=3

12÷3=4

4=25%

Answer:

y=x-5

Step-by-step explanation:

2x-2y=10

1.) subtract 2x from both sides

-2y=-2x+10

2.) Divide by -2 to get y by itself

y=x-5

Answer:

y= x+5

Step-by-step explanation:

y =mx+b is slope intercept form

Given:

The graph of an inequality.

To find:

The inequality.

Solution:

From the given graph it is clear that the boundary line is a vertical line parallel to y-axis at the distance of 3 units from the left of y-axis. So, the equation of boundary line is

[tex]x=-3[/tex]

Now, the shaded portion lies on the left of the boundary line. It means the values which are less than 0 are included in the solution set.

The boundary line is a dotted line. So, x=-3 is not included in the solution set.

So, the required inequality is

[tex]x<-3[/tex]  

Therefore, the correct option is B.

Answer:

It changes 3 inches

Step-by-step explanation:

Because every time she takes a sip it goes down, I can’t really explain it good but it changes 3 inches as she took 3 sips of water.

Answer:

Step-by-step explanation: 1 sip = 2 in

                                           3 sips = 6 in so 3 sips x 2 inches =  6 inches

Answer:

what do you actually wanna say?

Answer:5x^(2)-21x+4

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(x) would be

8

4

2

0

- 2

Answer:

$700 for 35 people but if you want to add the fee it will be $850

Answer:

-5 and -9 are the constants, can also be written -14

Given:

Amount in the savings account = 4300

Each week, Raul pays the dog sitter 30 from his savings account.

To find:

The function, f(x), that is equal to the amount of money in the account after Raul pays the dog sitter each week.

Solution:

Let x be the number of weeks.

Raul pays the dog sitter in 1 week = 30

Raul pays the dog sitter in x week = 30x

Remaining amount = Initial amount - Amount he pays the dog sitter

[tex]f(x)=4300-30x[/tex]

Therefore, the required function is [tex]f(x)=4300-30x[/tex].

Answer:

6/25

Step-by-step explanation:

Answer:

I think its

|x| = 5

Step-by-step explanation:

Answer:

|x|<5

Step-by-step explanation:

Answer:

150 ft

Step-by-step explanation:

The formula for area is, height x width (h x w) or base x height (b x h)

10 feet is the base and 15 is the height, multiply those and you get 150

Answer:

D.  9(3.1416)

Step-by-step explanation:

Answer:

a=31

Step-by-step explanation:

1/2(a-9)=11

a-9=22

a=22+9

a=31