I really need help with this. Please.

A chef has two dozen meatballs to add to a pot of sauce. Each meatball has a two-inch diameter. Before the meatballs are added, the sauce is 2 inches from the top of the 14-inch diameter pot. Will the sauce spill over when the chef adds the meatballs to the pot? Show all of your work to justify your answer.

Answers

Answer 1

Given the volume of the space in the pot and the volume of the meatballs, the sauce will not spill over.

Will the sauce spill over?

The first step is to determine the volume of the remaining space that the sauce is yet to fill. A pot usually has the shape of a cylinder, so the formula for the volume of a cylinder would be used.

Volume of a cylinder = πr²h

π x (14/2)³ x 2 = 98 in³

The second step is to determine the volume of the two dozen meatballs.

Volume of a sphere = 4/3πr³

24 x (4/3 x π x (2/2)³) = 32π in³

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Answer 2

The sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

Volume of the sauce in the pot

The volume of sauce in the pot is calculated as follows;

V = πr²h

V = π x (7)² x (2)

V = 98π in³

Volume of the two dozen meatballs

Area of 1 meatball = πr² = π x (1)² = π in²

Area of the 2 dozen = (2 x 12) x A

                                       = 24 x π in² = 24π in²

the height of each meatball = 2 in,

Volume of the 2 dozens = 2 in x 24π in² = 48π in³

Total volume of the meatball and sauce in the pot = 98π + 48π = 146π in³

Thus, the sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

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Related Questions

PLEASE SOLVE ASAP!! WILL GIVE BRAINLIEST TO QUICKEST AND FIRST ANSWER!!

Solve: 5√(x + 10) - 15 = 30

Solve: √(x + 2) + 8 = 6

Answers

1. x=71

This is solved by isolating the radical then raising each side of the equation to the power of its index.

2. NO SOLUTION

There are no values of x that make the equation true.

Answer:

1. 71

2. No solution


Summer school classes begin at 8:30 and last for two and a half hours. At what time
the classes end?

Answers

Answer:it ends at 11:00

Step-by-step explanation:8:30+2:30=11:00

Answer:

11:00

Step-by-step explanation:

8:30 + half an hour = 9:00

9:00 + 2 hours = 11:00


Factor completely 3x – 15.
3(x - 5)
3(x + 5)
3x(-15)
Prime

Answers

Answer:

A. 3(x-5)

Step-by-step explanation:

USE M-A-T-H-W-A-Y

Step-by-step explanation:

[tex]3x - 15[/tex]

Bind the expression with the common factor three .

3 ( x - 5 )

15 in
18 in
14 in
11 In
22 in






I need help on bottom three please

Answers

Answer is
18 in
Because that’s what it gave me

What is “b” in the following quadratic equation:
4x^2-3x-11=0

Answers

Answer:

The value of b in the quadratic equation is -3

Step-by-step explanation:

4x²-3x-11=0

a = 4

b = -3

c = -11

In the 2016 Rio Olympic games, the total of gold, silver and bronze medals won by China was 70.

They won:
• 18 silver medals,
• the same number of gold medals as they did bronze medals.

How many gold medals did China win?

Answers

26 gold metals

Explanation: 70 - 18 silver = 52 metals left

52/2= 26 … so 26 + 26= 52 52 + 18=70

Which gives the value of 16 divided by 2 times 4 minus 20?

Answers

Answer:

16/2×4−20 = 12

Step-by-step explanation:

NOTE : Make sure to review the order of operations

16/2×4−20 = (16÷2)×4-20

                  = 8×4-20

                  = 32-20

                  = 12

Please write the solution

Answers

Answer:

D .

Step-by-step explanation:

that is the answer to the question

catalina spent &17.50 on 10 scrunchies. what is the unit cost?

Answers

Answer:

48

Step-by-step explanation:

20 scrunchies=3 dollars

7.25 dollars = ?

1 dollar=6.66666666

0.25 dollar=1.666666666666

7*6.66666666=46.666666

What is the solution to this equation?

a/6-11=25

Answers

Answer:

a=216

Step-by-step explanation:

Victoria needs $299 to purchase a music player. She earns $4.50 per hour from her neighbor
for babysitting. She has already saved $75. Which inequality bestrepresents the minimum
number of hours she will have to babysit to earn enough money to purchase the music
player?

Answers

Answer:

4.50(x)+75=299

4/7
of a number is 36
What is the number?

Answers

[tex]\text{If the number is x,}\\\\~~~~~\dfrac 47 \cdot x =36\\\\\implies 4x = 36 \times 7\\\\\implies x =\dfrac{36 \times 7}4\\ \\\implies x = 9 \times 7\\\\\implies x = 63\\\\\text{Hence, the number is 63.}[/tex]

Answer:

[tex]\huge\boxed{\bf\:x = 63}[/tex]

Step-by-step explanation:

Given,

4/7th of a number = 36

Let's take the unknown number as 'x'.

Now,

4/7 × x = 36

Take the reciprocal of 4/7 to the other side of the equation .

x = 36 × 7/4

Cancel 36 by 4.

x = 9 × 7

Multiply the 2 numbers

x = 63

[tex]\rule{150pt}{2pt}[/tex]

explain how mid-nineteenth-century American values and social trends are conveyed in The Voyage of Life paintings by Thomas Cole. how did society influence the art? how did the art influence society?​

Answers

Answer:

Step-by-step explanation:

American values and social trends are conveyed in The Voyage of Life paintings by Thomas Cole. how did society influence the art

what is the answer to
-(-4x-7)+x=-4

Answers

Answer:

-128

Step-by-step explanation:

hope it helps srry if its wroung:>

I NEED HELPPP ON THISS ONEE PLEASSEEEE

Answers

Answer:

6 , 9

Step-by-step explanation:

- 3 x - 4y = - 54
    4x + 4y = 60
Eliminate => x = 6

x + y = 15
when x =6  ; => y = 9

Please answer for 10 points. It is a word problem.

Answers

Step-by-step explanation:

here is your answer, this is how it's solved

6)
5ft
3ft.
14ft
8 ft
I need the surface area someone help me

Answers

Answer:

258ft squared is possibly the answer

the hcf and lcm of 180, 150 and 315​

Answers

Answer:

HCF=15    LCM=6,300

Step-by-step explanation:

Answer:

HCF = 15

LCM = 6300.

Step-by-step explanation:

Write them out as a product of their prime factors:

180 = 2*2*3*3*5

150 = 2*3*5*5

315 = 3*3*5*7

Picking out the factors common to all 3 list of prime factors:

The GCF = 3*5 = 15.

To find the LCM we pick out all the numbers except if there are repeated number we only use them once, So for example  we only take 2*2 for the calculation as there is a pair of 2's in 180 and 150 factors and there is an extra 2 in 180 - so we only take 2 of the 3 2's.

LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7

= 6300.

4. One of three contestants will be randomly selected to win a prize. One of three different prizes will be randomly awarded to the contestant whose name is selected to win. The tree diagram shows all possible outcomes of this contest. Prize 1 1 Pedro Prize 2 Prize 3 Prize 1 Whitney Prize 2 Prize 3 Prize 1 Bryan Prize 2 Prize 3 What is the probability that Whitney will win Prize 2?​

Answers

The probability that Whitney will win Prize 2 will be [tex]\frac{1}{9}[/tex]. Probability is the ratio of the favorable event to the total number of events.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

The total no of the contestants=3

Randomly selection of the prize-=1

The probability that Whitney will win Prize 2 will be;

[tex]\rm P= P(A)P(B) \\\\ P=\frac{1}{3} \times \frac{1}{3}\\\\ P= \frac{1}{9}[/tex]

Hence, the probability that Whitney will win Prize 2 will be [tex]\frac{1}{9}[/tex]

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The expression below represents the perimeter, in feet, of Manual’s garden.

15 + 2x + 7 + 15 + 2x + 7

Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden.

The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7.

Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation.

Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length.

The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?

Answers

a) Shawn's error was that he Multiplied 15 by 2x only. He didn't Multiply 15 by 7

b) The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as 98 square feet

What is the perimeter?

The perimeter is defined as the sum of all the sides of the figure. Now we have The area in, square feet, of Shawn’s garden is found be calculating 15(2x + 7). Shawn incorrectly says the area can also be found using the expression 30x + 7.

The correct area =15(2x + 7).

= 30x + 105 square feet

The error in Shawn’s expression is

= 15(2x + 7)

= 30x + 7 square feet

Shawn's error was that he Multiplied 15 by 2x only. He didn't Multiply 15 by 7

The difference, in square feet, between the actual area of Shawn’s garden and the area found using his expression is given as

30x + 105 square feet - 30x + 7 square feet

= 30x + 105 - (30x + 7)

= 30x - 30x + 105 - 7

= 98 square feet

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Isaac Newton proved that fluids cool exponentially when left out in an open space. A cup of coffee was poured at a
temperature of 210°F and left on the dining room table to cool. If you start drinking it at a temperature of 150°F, 10 minutes
later, what will be the temperature be when you take the last sip 18 minutes after you poured it?

Answers

The temperature will be when you take the last sip 18 minutes after you poured it, will be 114.64 °F.

What is an exponent?

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

Isaac Newton proved that fluids cool exponentially when left out in an open space.

A cup of coffee was poured at a temperature of 210°F and left on the dining room table to cool.

If you start drinking it at a temperature of 150°F, 10 minutes later.

The exponential function is given as

[tex]\rm T_f = T_i (a)^{-t}[/tex]

Then the initial temperature will be 210°F.

[tex]\begin{aligned} 150 &= \rm 210 (a)^{-10}\\\\0.7143 &= \rm a^{-10}\\\\-0.146 &= \rm -10 \log a\\\\0.0146 &= \rm \log a\\\\\rm a &= \rm 1.0342 \end{aligned}[/tex]

Then the equation will be

[tex]\rm T_f = 210 (1.0342)^{-t}[/tex]

Then the temperature will be when you take the last sip 18 minutes after you poured it.

[tex]\rm T_f = 210 (1.0342)^{-18}\\\\T_f = 114.64 \ ^oF[/tex]

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Explain what “solution” means for a system of two linear equations. Give an example.

Answers

Answer:

A solution of a system of equations is a list of numbers x , y , z ,... that make all of the equations true simultaneously. The solution set of a system of equations is the collection of all solutions. Solving the system means finding all solutions with formulas involving some number of parameters.

Step-by-step explanation:

hope it will help you

Answer:

Step-by-step explanation:

In this context "solution" means a point whose x- and y-coordinates satisfy both equations.

If we're given the two linear equations x + y = 3 and 2x - y  = 7, we can solve them by addition and subtraction (among other methods):

3x = 3 + 7, or 3x = 10, or x = 10/3.  

Substitute this result into x + y = 3 to find the corresponding y value;  

10/3 + y = 3, or 10/3 + y = 9/3, or y = 1/3.  

Then the "solution" is the point (10/3, 1/3).

The construction workers are constructing a line of bricks. Each brick is 8 inches long. If the line of bricks must be 24 feet long, how many bricks will the construction workers need to use?

Answers

Answer:

thhe answer would only be 3 feet

Step-by-step explanation:

what’s 690 divided by 4???

Answers

172.5! hope this helps

Answer:

Step-by-step explanation:

172.5 is the correct answer.

NEED HELP SHOW WORK WILL GIVE BRAINLYEST

Answers

It would be 14 for the perimeter

What value of c makes 3x²+24x+c contain a perfect square trinomial? Is there an equation to find it or is it just guess and check?

Answers

3x^2+24x+48


*20 characters limit , ignore this.*

you and your mom enter drawing with three different prices the prizes are awarded at random is a total of 8 people entered the drawing and how many ways can you win first prize and your mom went second prize

Answers

The number of ways in which you can win first prize and your mom went the second prize will be 8. Then the correct option is D.

What are permutation and combination?

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

You and your mom enter the drawing with three different prices the prizes are awarded at random is a total of 8 people entered the drawing.

Then the number of the ways in which you can win first prize and your mom went the second prize will be

Let x be the number of different ways.

Then we have

[tex]\rm x = \ ^8C_1\\\\x = 8[/tex]

Thus, the number of ways in which you can win first prize and your mom went the second prize will be 8.

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The radius of a cylinder is 6.0 inches and the height is 9.0 inches, what is the volume of the cylinder? if the cylinder is enlarged by a linear scale factor of 3, what is the volume of the enlarged cylinder?​

Answers

Answer:

A) The volume of the cylinder is 1017.9 in³.

B) The volume of the enlarged cylinder is 27,482.7 in³.

Step-by-step explanation:

What is the volume of the cylinder?

The radius of the cylinder is r = 6 in and the height is h = 9 in.

The volume of a cylinder can be found using the formula:

V = πr²h

Substitute r = 6 and h = 9 into the formula.

V = π(6)²(9)V = π(36)(9)V = π(324)V = 1017.876

The volume of the cylinder is 1017.876 in³.

What is the volume of the enlarged cylinder?

If the cylinder is enlarged by a factor of 3, this means that each dimension is getting increased by 3.

Therefore, we need to multiply the original volume by a factor of three cubed; 3³.

V_enlarged = V · 3³V_enlarged = 1017.876 · 27 = 27482.652 in³

The volume of the enlarged cylinder is 27,482.652 in³.

At Tower Middle School, there are 14 girls and 16 boys in Mr. Bell's class. There are 17 girls and 19 boys in Ms. Carlson's class. Which of the following best compares Mr. Bell's and Ms. Carlson's classes?
A.
They have the same ratio of girls to boys because a straight line can be drawn through the points (14,16) and (17,19) on a coordinate grid.


B.
They have the same ratio of girls to boys because a straight line can be drawn through the points (14,16), (17,19), and (0,0) on a coordinate grid.


C.
They do not have the same ratio of girls to boys because a straight line cannot be drawn through the points (14,16) and (17,19) on a coordinate grid.


D.
They do not have the same ratio of girls to boys because a straight line cannot be drawn through the points (14,16), (17,19), and (0,0) on a coordinate grid.

Answers

Answer:

D.  They do not have the same ratio of girls to boys because a straight line cannot be drawn through the points (14, 16), (17, 19), and (0, 0) on a coordinate grid.

Step-by-step explanation:

In order to check if the ratio is the same, convert the ratios to (x, y) points, plot them on a graph and see if you can draw a straight line through them and the origin (0, 0).  If you can, then the ratios are the same.  If not, then the ratios are not the same.

After plotting (14, 16) and (17, 19) and (0, 0) on a graph (attached), you can see that a straight line will only go through any two of the points, but not all three.  Therefore, the ratios are not the same.

In the expression StartFraction 7 m over 9 EndFraction + 6 r minus four-fifths, what are the coefficients?
Negative four-fifths and 6
StartFraction 7 over 9 EndFraction and negative 6
StartFraction 7 over 9 EndFraction and Negative StartFraction 4 over 5 EndFraction
StartFraction 7 over 9 EndFraction and 6

Answers

Answer:

7/9 and 6

Step-by-step explanation:

The given expression is

=> [tex]\frac{7m}{9} +6r-\frac{4}{5}[/tex]

Coefficients are the numbers with variables.

So, here in this expression the coefficients are 7/9 and 6

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