45 points for first most detailed / accurate answer:

You are planning to make and sell 3 different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 24 candles (8 per 3 sizes).

a. Design the candles what dimensions are each size of candle? (Remember, 3sizes)
b. You want to make a profit of $100. Decide on a price for each size of candle.
c. Did you set the prices so that they are proportional to the volume of each size of candle? Why/Why not?

Answers

Answer 1
a.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions. 

I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.

With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:

V=pi(r^2)(h)

we then solve the corresponding height per candle. Let us let the value of pi be 3.14.

Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for 

r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in

b. each candle should sell for $15.00 each

($20+$100)/8=$15.00

c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes

Related Questions

the store has 53 cases of apples and oranges in a storm if there are 28 cases of apples how many cases of oranges are there in the store room

Answers

There are a total of 35 cases or oranges in the store room.

Daily output of marathon's garyville, lousiana, refinery is normally distributed with a mean of 232,000 barrels of crude oil per day with a standard deviation of 7,000 barrels. (a) what is the probability of producing at least 232,000 barrels?

Answers

50% A normal distribution is symmetric about the mean. That means that no matter what the standard deviation of a statistic, if it is normally distributed half of the time it will above the mean and half will be below. 232000 barrels is the mean and half of the time production will be above that value.

Round off446,221 to the nearest ten

Answers

the answer is 446,220

Answer:

Answer when we  round off 446,221 to the nearest ten is 446,220

Step-by-step explanation:

We need to round off 446,221 to the nearest ten.

Nearest ten to the 446,221 can be 446,220 or 446,230

Difference between 446,221 and 446,220 = 446,221 - 446,220 = 1

Difference between 446,221 and 446,230 = 446,230 - 446,221 = 9

Here the difference is minimum for 446,220

Answer when we  round off 446,221 to the nearest ten is 446,220

Write the slope intercept form of the equation of the line through the given points.
Explanation, please! Thank you!

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ -2}})\quad % (c,d) &({{ 1}}\quad ,&{{ 3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-(-2)}{1-1}\implies \stackrel{und efined}{\cfrac{3+2}{0}}[/tex]

hmmm, the slope is undefined, that means, is a vertical line then, check the picture below.

-4(n - 6) = 12

Solve the Equation.

Answers

-4(n - 6) = 12

n - 6 = -12/4   divide both sides by -4

n - 6 = -3

n = -3 + 6    add both sides by 6

n = 3

hope that helps, God bless!

The normal body temperature of a camel is 37°C. This temperature varies by up to 3°C throughout the day. Write and solve an absolute value inequality that represents the range of normal body temperatures (in degrees Celsius) of a camel throughout the day.

Answers

The range of normal body temperatures for a camel throughout the day is from 34°C to 40°C, inclusive.

To represent the range of normal body temperatures for a camel throughout the day, we'll use an absolute value inequality. Given that the normal body temperature is 37°C and it varies by up to 3°C, we can express this as:

|T - 37| ≤ 3

Where T represents the temperature of the camel throughout the day. This inequality ensures that the temperature remains within 3 degrees above or below the normal body temperature of 37°C.

To solve this inequality, we'll consider two cases:

1. When T - 37 is positive:

T - 37 ≤ 3

T ≤ 40

2. When T - 37 is negative:

-(T - 37) ≤ 3

-T + 37 ≤ 3

-T ≤ -34

T ≥ 34

Combining the two cases, the range of normal body temperatures for a camel throughout the day is 34°C to 40°C.

you invest 1600 in an account that pays an interest rate of 6.5%, what is your balance after 6 years and round your answer to the nearest hundredth.

Answers

Final answer:

To calculate the balance after 6 years with compound interest, use the formula Balance = Principal * (1 + Interest Rate)^Time. Substituting the values, we find the balance to be approximately $2,243.89.

Explanation:

To calculate the balance after 6 years, we need to use the formula for compound interest:

Balance = Principal * (1 + Interest Rate)^Time

Given that the principal (initial investment) is $1600 and the interest rate is 6.5%, we can substitute these values into the formula:

Balance = 1600 * (1 + 0.065)^6

Calculating this, we find that the balance after 6 years is approximately $2,243.89.

Final answer:

The balance after 6 years is approximately $2105.69.

Explanation:

To find the balance after 6 years, we can use the formula for compound interest:

Balance = Principal(1 + Interest Rate)^Ti

Plugging in the given values, we have:

Balance = $1600(1 + 0.065)^6

Simplifying, we get:

Balance = $1600(1.065)^6

Calculating, we find that the balance after 6 years is approximately $oxed{2105.69}.

What is the magnitude of the vector product? 4.00i + 7.00j?

Answers

The given vector is [tex]4.00 \hat{i} + 7.00 \hat{j}[/tex].

Its magnitude is
[tex] \sqrt{4.00^{2}+7.00^{2}} = 8.062[/tex]

Answer: 8.062  (nearest thousandth)

Between white pair of numbers is a product of 200 and 89 and 7

Answers

[tex]\bf 200\cdot 89\cdot 7\implies 124600 \\\\\\ \boxed{124599}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}124600\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{124601}[/tex]

what is 645 round to the nearest ten

Answers

The answer is 650 have a nice day
645 rounded to the nearest ten is 650

hope this helps

Glenn invested $22,000 at 7% interest compounded annually. How much interest will Glenn earn in 3 years?


$19,826.24

$20,837.25

$2340.23

$4950.95

Answers

Given:
P = $22,000, the principal
r = 7% =0.07, the rate
n = 1, annual compounding
t = 3 years

The value after 3 years is
[tex]A=P(1+ \frac{r}{n} )^{nt}[/tex]
That is,
A = 22000(1.07)³ = $26,950.95
Interest earned = $26,950.95 - $22,000 = $4,950.95

Answer: $4,950.95

what is the coefficient in the expression 3x/13+4?

Answers

A coefficient in the expression is a numerical or constant quantity that is placed before and multiplying the variable in an algebraic expression, for example in expression 5x + 4; 5 is the coefficient.
So in the given expression 3x/13 + 4. 3 / 13 is the coefficient of x, as 3 / 13 is multiplying with x.

Answer:3/13

Step-by-step explanation:

Just took test

What does e equal in e/2 < 3? Please help. I need a quick answer.

Answers

2.718 ≈e that is the answer to your question.

You have diving lessons every fifth day and swimming lessons every third day. Today you have both lessons. In how many days will you have both lessons on the same day again?

Answers

16 days
 because 8 +8 = 16  5+3=8

Yesterday, Chau had m baseball cards. Today, he gave 5 away. Using m , write an expression for the number of cards Chau has left.

Answers

If m = baseball cards he had yesterday, and today he got rid of 5, the expression is equal to

m - 5 = x.

As an example of what the answer is, replace m with 10.

If he had 10 baseball cards and gave away 5 today, x = 5.

The answer is m - 5 = x.

the sinclair family live 5.4 miles from southside middle school. how many feet away do they live?

Answers

Final answer:

The Sinclair family lives 28,512 feet away from Southside Middle School, calculated by multiplying 5.4 miles by the number of feet in one mile, which is 5,280 feet.

Explanation:

The Sinclair family lives 5.4 miles from Southside Middle School. To convert this distance from miles to feet, we use the conversion factor that 1 mile is equal to 5,280 feet. To find the distance in feet, we multiply the number of miles by the number of feet in one mile:

5.4 miles  imes 5,280 feet/mile = 28,512 feet.

Therefore, the Sinclair family lives 28,512 feet away from Southside Middle School.

General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate

Answers

470/2 = 235. 235c/h is the unit rate.

Answer:

The unit rate is 235 calories per hour.

Step-by-step explanation:

General house cleaning (sweeping the floor vacuuming laundry) can burn 470 calories every two hour determine the unit rate.

Unit rate means we have to find the calories burned in 1 hour.

Hence, calories burned in 1 hour = [tex]\frac{470}{2}= 235[/tex]

Answer :

The unit rate is 235 calories per hour.

An equivalent equation has been written by multiplying the second equation by 2. 4x – 9y = 7 4x – 9y = 7 2(–2x + 3y = 4) → –4x + 6y = 8

Answers

my best guess is 
x=3/2y-2
y=2/3x+4/3
depends on which one you are solving for

Answer: answer is (-19/2,-5)


Step-by-step explanation:


How to write 645,300 in expanded form using exponents?

Answers

6 × 105+4 × 104+5 × 103+3 × 102+0 × 101+0 × 100

To express 645,300 in expanded form using exponents, it is written as [tex]6x10^{5} + 4x10^{4} + 5x10^{3}+ 3x10^{2}[/tex]x, breaking down each digit by its place value and expressing each as a power of 10.

To write the number 645,300 in expanded form using exponents, we break down each digit according to its place value and then express each of these as a power of 10. The place values for the number 645,300 are as follows:

600,000 which is 6 times 100,000

40,000 which is 4 times 10,000

5,000 which is 5 times 1,000

300 which is 3 times 100

Now we express these place values using exponents:

645,300 = [tex]6x10^{5} + 4x10^{4} + 5x10^{3}+ 3x10^{2}[/tex]

This notation shows the number 645,300 written as the sum of each digit multiplied by the appropriate power of 10 based on its position in the number.

How many variables are displayed in a scatter plot

Answers

Image result for How many variables are displayed in a scatter plot
two variables
BACK.
Scatter plots are an awesome way to display two-variable data (that is, data with only two variables) and make predictions based on the data. These types of plots show individual data values, as opposed to histograms and box-and-whisker plots.

there are 24 sixth graders and 40 seventh graders. Mr chan wants to divide both grades into groups of equal size ,with the greatest possible number of students in each group. How many students should be in each group?

Answers

Here, you must find the GCF of 24 and 40 which is 8
There would be 8 in each group.

WILL GIVE BRAINEST
a bean plant grows at a constant rate for a month....

Answers

I'm fairly certain it's A. Gradient is 2, and you need to subtract the height and number of days from y and x respectively, rather than add them.

Hope this helps :)

Help me answer this? Thanks :)

Answers

An expression is undefined when you divide by zero. A simple example is 1/0 which in english is "one over zero"

You cannot have zero in the denominator. Something like 0/1 is allowed as it is equal to 0. In other words, 0/1 = 0. But 1/0 is not allowed. 

1 1/4mi = ft, can someone explain this to me

Answers

first off, we'll convert the mixed fraction to "improper" and check about, keeping in mind that, there are 5280 feet in 1mile.

[tex]\bf \stackrel{mixed}{1\frac{1}{4}~mi}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}~mi}\\\\ -------------------------------[/tex]

[tex]\bf \begin{array}{ccll} feet&miles\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 5280&1\\ f&\frac{5}{4} \end{array}\implies \cfrac{5280}{f}=\cfrac{1}{\quad \frac{5}{4}\quad }\implies \cfrac{5280}{f}=\cfrac{\frac{1}{1}}{\quad \frac{5}{4}\quad } \\\\\\ \cfrac{5280}{f}=\cfrac{1}{1}\cdot \cfrac{4}{5}\implies \cfrac{5280}{f}=\cfrac{4}{5}\implies \cfrac{5280\cdot 5}{4}=f\implies 6600=f[/tex]

Use the definition of the derivative to find the derivative of: f(t)=14−5tf(t)=14−5t.
f′(t)=
f′(t)=

Answers

[tex]\bf f(t)=14-5t\qquad \qquad \stackrel{d e f in i tion~of~a~derivative}{\lim\limits_{h\to 0}~\cfrac{f(t+h)-f(t)}{h}} \\\\\\ \lim\limits_{h\to 0}~\cfrac{[14-5(t+h)]~~-~~[14-5t]}{h}\implies \lim\limits_{h\to 0}~\cfrac{\underline{14-5t}-5h\underline{-14+5t}}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{-5\underline{h}}{\underline{h}}\implies -5[/tex]

A new computer game has been developed and 80 veteran game players will test its market potential. of sixty players liked the game, what is the probability that any veteran game player will like the new computer game

Answers

60/80 = 0.75

75% of the veteran game players liked the game

3/4  is the probability that any veteran game player will like the new computer game.

What is Probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Given,

New computer game has been developed and 80 veteran game players will test its market potential.  

In this sixty players liked the game.

We need to find the probability that any veteran game player will like the new computer game.

To find the probability we just need to divide sixty by 80.

60/80

3/4

Hence 3/4  is the probability that any veteran game player will like the new computer game.

To learn more on Probability click:

https://brainly.com/question/11234923

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Valentine purchased 200 beads for $48 to make necklaces. If she needs to buy 25 more beads,how much will she pay if she is charged the same rate?

Answers

Fire: you need you show ur understanding by Dividing ur Amount By ur Total Which is 48 ÷ 200$ and that give your rage which is 0.24 per bead.

Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71. How many items did Alex break.

Answers

576*0.05= $28.80.
Guess and check: 1.98*5=9.9
28.80-9.9=18.9- too much
1.98*3=5.94
28.80-5.94=22.86- this is the closest

So he must have broken 3 items.
Hope this helps!

Can u plz mark me as brainliest? I really need it!

Alex broke 3 glasses during the unpacking of the glasses.

As mentioned in the question, Alex was hired to unpack 576 items of glass wear, at five cents per piece unpacked. For every item broken in the process, however, Alex had to pay $1.98. At the end of the job, Alex received $22.71.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The total amount earned for 576 glasses is given as,
= 576 × 0.05
= $28.80.

Amount earned = $22.71
Amount paid by Alex for the broken glass = $28.80 - $22.71 = 6.09
Total glass broked = 6.09 / 1.98 ≈ 3

Thus, Alex broke 3 glasses during the unpacking of the glasses.

Learn more about arithmetic here:

https://brainly.com/question/11424589

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For the compound inequality x + 2 ≥ a AND x - 7 ≤ b, find values of a and b for which the only solution is x = 1.

Answers

the answer is obviously, A=45, B=57

A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?

Answers

Let the number of half dollars be x,

number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
= 0.75x + 0.5
0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
= 17

There are 17 quarters and 15 half dollars.

Let the number of half dollars be x,

number of quarters = x + 2

amount of half dollars = 0.5x

amount of quarters = 0.25(x + 2)

= 0.25x + 0.5

total amount = 0.5x + 0.25x + 0.5

= 0.75x + 0.5

0.75x + 0.5 = 11.75

0.75x = 11.25

x = 15

number of quarters = x + 2

= 15 + 2

= 17

There are 17 quarters and 15 half dollars.

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