Working together, two ants named Aran and Beatrice can build an ant hill in 10 hours. Aran and Charlie can build the ant hill in 12 hours. Beatrice and Charlie can build the ant hill in 15 hours. How long, in hours, will it take to build the ant hill if Aran, Beatrice, and Charlie work together?

Answers

Answer 1

Answer:

They complete the hill in 8 hours

Step-by-step explanation:

Equations:

Let's call the variables:

Aran can make build the ant hill in A hours

Beatrice can make build the ant hill in B hours

Charlie can make build the ant hill in C hours

In one hour, Aran makes 1/A of the ant hill.

In one hour, Beatrice makes 1/B of the ant hill.

In one hour, Charlie makes 1/C of the ant hill.

Aran and Beatrice build it in 10 hours, thus:

[tex]\displaystyle \frac{1}{A}+\frac{1}{B}=\frac{1}{10}\qquad\qquad[1][/tex]

Similarly:

[tex]\displaystyle \frac{1}{A}+\frac{1}{C}=\frac{1}{12}\qquad\qquad[2][/tex]

[tex]\displaystyle \frac{1}{B}+\frac{1}{C}=\frac{1}{15}\qquad\qquad[3][/tex]

We need to find the time taken for the three ants to build the anthill:

[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=[/tex]

Adding [1], [2], and [3]:

[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}[/tex]

Adding the fractions (LCM=60):

[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6}{60}+\frac{5}{60}+\frac{4}{60}[/tex]

[tex]\displaystyle \frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{6+5+4}{60}=\frac{15}{60}=\frac{1}{4}[/tex]

Dividing by 2:

[tex]\displaystyle \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}[/tex]

All ants together make 1/8 of the hill, thus they complete the hill in 8 hours


Related Questions

Taylor completed 2/3 of her homework. Riian completed 7/8 of her homework. Taylor and Riian have the same amount of homework. Who completed a greater amount of homework?

Answers

Answer:

Riian completed a greater amount of homework.

Step-by-step explanation:

The fraction 7/8 is greater than the fraction 2/3.

At 8p.m., the temperature was -9 degrees Fahrenheit. Over the next five hours, the temperature dropped by 18 degrees. What is the temperature after five hours?

Answers

Answer:

-27 if im reading the question right.

Step-by-step explanation

What is the probability of drawing an even numbered card from a standard deck of shuffled cards?
A) 20/52
B) 25/52
C) 30/52
D) 35/52

Answers

Answer:

Prob = 20/52

Step-by-step explanation:

There are 5 even number cards per suit: 2, 4, 6, 8, and 10.

and there are 4 suits in a deck, so the total of the even number card events is 5 * 4 = 20

Given that the deck has 52 cards total, then the probability of drawing an even numbered card is the number of successes (20) divided the number of total cards (52) This gives:

Prob = 20/52

which agrees with answer A) in your list.

HELP ASAPPPPP I WILL GIVE BRAINLIST

Answers

Answer:

Step-by-step explanation:

Count all writing utensils which is 16, then jus count the number of pencils

Answer:

5:16 because she has 5 pencils and a total of 16 writing utensils

Step-by-step explanation:

Gabby sells candy bars for $ 1 dollar each, and Twizzlers for 25 cents each. For every dollar she earns she gives 10 cents to charity. If She sells 42 candy bars and 45 Twizzlers, how much money will she have for herself after giving to charity? Write an expression and evaluate.

Answers

Answer:

$47.925 for herself.

Step-by-step explanation:

Answer:

Step-by-step explanation:

42+11.25 =52.35

52.35*.10

5.235$

I hope this is the right answer

4
Jared has a collection of 90 movies on DVD. If
46 of the movies are comedies, 26 are drama,
and the rest are science fiction, what percent of
the movies are science fiction?
A) 18
B) 20
C) 28
D) 32

Answers

20%

46 + 26 = 72
90 - 72 = 18

18/90 x 100 = 20


Help ASAP I’ll mark brainliest

Answers

Answer:

C. 254

Step-by-step explanation:

There are 3 different types of engineers listed in the chart, Electrical, Chemical, and Mechanical. Under the first column of math, add together the numbers for all three engineers.

85+80+89= 254

Therefore, 254 engineers chose math as their favorite subject.

What is the slope of a line that passes through the points (-2, 4) and (-6, 12)?
O-2

0

2
02

Answers

Answer:

[tex]\displaystyle m=-2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-2, 4)

Point (-6, 12)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                            [tex]\displaystyle m=\frac{12-4}{-6+2}[/tex][Slope] [Fraction] Subtract/Add:                                                                         [tex]\displaystyle m=\frac{8}{-4}[/tex][Slope] [Fraction] Divide:                                                                                    [tex]\displaystyle m=-2[/tex]

PLEASE HELP!!!! What is the slope of the line that passes through the points (2, 3) and (6, 8)

Answers

Answer:

[tex]\frac{5}{4}[/tex]

Step-by-step explanation:

to find the slope (m) of a line:

[tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]

where y₁ = 3

y₂ = 8

x₁ = 2

x₂ = 6

plug into the equation:

[tex]m = \frac{8 - 3}{6 - 2} \\m = \frac{5}{4}[/tex]

so the slope is [tex]\frac{5}{4}[/tex]

7. Are the two triangles similar? How do you know? I need this answered quick plz

Answers

Answer:

Yes, by the angle angle rule.

Step-by-step explanation:

In the first triangle,

m<C=60 degrees, and m< D=53 degrees. You know that the sum of angles in a triangle add up to 180 degrees, so solve for E. m<E= 67 degrees.

In the second triangle,

m<F=60 degrees and m<H=67 degrees.

Since both triangle have two congruent angles, you can say that the two triangles are similiar by the AA rule.

Both triangle CDE and triangle FGH are similar to each other.

Similar figures

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. All the corresponding angles of similar figures are congruent.

∠C + ∠D + ∠E = 180° (angles in a triangle)

60 + 53 + ∠E = 180

∠E = 67°

∠C = ∠F, ∠D = ∠G, ∠E = ∠H, hence both triangles are similar.

Find out more on Similar figures at: https://brainly.com/question/2644832

y = - 4x y = 2x - 1

which method is the best to solve this

Answers

Answer:

get all the varibles on one side

Step-by-step explanation:

mark me as brainliest plz thx

Tennis star Rafael Nadal lost at the Australian Open. How many Grand Slams has he won?

Answers

Answer: 22

Step-by-step explanation:

ANSWER CORRECTLY OR I WILL REPORT AND DELETE YOUR ANSWER THANK YOU Classify the questions as statistical or not statistical. How many hours did Ryan study last Saturday? How many students in my class own 2 bags? How many bags do I own? How many hours do students in my class study every day? How many cars does each person in my neighborhood own? How many houseplants does each house on my block have?

Answers

The following are statistical questions:

How many hours do students in my class study every day? How many cars does each person in my neighborhood own? How many houseplants does each house on my block have?

The following are not statistical questions:

How many hours did Ryan study last Saturday? How many students in my class own 2 bags? How many bags do I own?

What is a statistical question?

A statistical question is a question that can be answered by collecting data that varies. For example, the hours studied by students in a class would vary. Some would study for 1 hour, others 2 hours or 5 hours or 10 hours.

To learn more about statistical questions. please check: https://brainly.com/question/11253919

#SPJ1

Can someone help me with this in

Answers

Answer:

Step-by-step explanation:

Answer from text book is given but I cant understand how they get this answer using these numbers?


This was the question:
Analia wants to know which school has higher academic achievements relative to the number of teachers per student.
a) What is the Graduation rate divided by teachers per student?
b) SAT average divided by teachers per student?

So I looked up the answer after getting it wrong and this is the calculations used to come to the answer. I cant figure out how they put these 3 numbers together to get 18,947 and 11,053

Answers

Answer:

The equation is

(students x points) / teachers

5
Which equation will solve the following word problem? The professor has 390 books that he wants to display in his office. Each shelf can hold 65 books. How many shelves will he need?


390s = 65


390(65) = s


s/390 = 65


390 = 65s

Answers

Answer:

6 shelves

Step-by-step explanation:

Let the number of shelves needed be s

If the total number of books to be displayed is 390books

If Each shelf can hold 65 books, then;

1 shelf = 65books

To know the  total shelf needed;

s = 390 books

Divide both expressions

1/s = 65/390

65s = 390

Divide through by 65

65s/65 = 390/65

s = 390/65

s = 6

Hence 6 shelves will be needed

Right Triangle ABC has its right angle at C, BC = 4, and AC= 8.

What is the value of the trigonometric ratio?

cos B
csc B
tan A

Drag a value to each box to match the trigonometric ratio?

Answers

9514 1404 393

Answer:

 cos B = (√5)/5

  csc B = (√5)/2

  tan A = 1/2

Step-by-step explanation:

The length of hypotenuse AB is given by the Pythagorean theorem:

  AB² = AC² +BC²

  AB² = 8² +4² = 64 +16 = 80

  AB = √80 = 4√5

The mnemonic SOH CAH TOA can help you remember the needed ratios.

  Cos = Adjacent/Hypotenuse

  cos B = BC/AB = 4/(4√5)

  cos B = (√5)/5

__

  Sin = Opposite/Hypotenuse

  csc = 1/sin = Hypotenuse/Opposite

  csc B = AB/AC = (4√5)/8

  csc B = (√5)/2

__

  Tan = Opposite/Adjacent

  tan A = BC/AC = 4/8

  tan A = 1/2

Answer:

tan A = 1/2  

cos B = √5/5

csc B = √5/2

Step-by-step explanation: I took the test

. Which expression represents the phrase below? 4 less than the product of 8 and a number, x *

A. 8 - 7x
B. (8 + 4) - 3
C. 4 - 8x
D. 8x - 4

Answers

Answer:

8x-4

Step-by-step explanation:

4 is less meaning it is subtraction and product of 8 and x is 8x

Nathan has $40 in a savings account. The interest rate is 5% per year and is not
compounded. How much interest will he earn in 1 year?
Use the formulai = prt, where / is the interest earned, p is the principal (starting amount),
is the interest rate expressed as a decimal, and is the time in years.
Submit

Answers

Money with Nathan in his savings account = $40

Rate of interest per annum = 5%

We know that :

[tex]\color{hotpink}\tt \: simple \: interest \color{plum}= \frac{principal \times rate \times time}{100} [/tex]

In this case :

Principal = $40

Rate = 5%

Time = 1 year

Simple interest he will earn in 1 year :

[tex] =\tt \frac{40 \times 5 \times 1}{100} [/tex]

[tex] = \tt \frac{200}{100} [/tex]

[tex]\color{plum} =\tt\$ \: 2[/tex]

Amount = Principal + Interest

Amount Nathan has to pay at the end of one year :

[tex] = \tt40 + 2[/tex]

[tex]\color{plum} =\tt \$42[/tex]

Thus, at the end of 1 year Nathan has to pay $42.

Therefore, simple interest Nathan will earn in 1 year = $2

f(x) = ( - 3x² + 2 – 2)e". Find f'(x) and f''(x).
f'(2) =
f''(c)
=

Answers

Answer:

-3x²-5xeˣ-eˣ

-3eˣx²-11eˣx-6eˣ

Step-by-step explanation:

I'm going to go by the picture and not what you wrote in your title.

To find the derivative of this we have to apply the product rule

(a*b)'=

a'*b+a*b'

We plug in our numbers and get

(-3x²+x-2)'*eˣ+(-3x²+x-2)*eˣ'

Now we can evaluate the derivatives and simplify

(-3x²+x-2)'= -6x+1

eˣ'=eˣ

which means we have

(-6x+1)*eˣ+(-3x²+x-2)*eˣ

Simplify

-6xeˣ+eˣ-3x²eˣ+xeˣ-2eˣ

Combine like terms

-3x²eˣ-5xeˣ-eˣ

Now we just need to find the derivative of this

We can apply the same product rule as we did before

(-3x²eˣ)'

Let's start by factoring out the -3 to get

-3(x²eˣ)'

which is equal to

-3(x²eˣ'+x²'eˣ)

Compute this and get

-3(x²eˣ+2xeˣ)= -3x²eˣ-6xeˣ

Now let's find the derivative of the second part

(-5xeˣ)'

-5(x'eˣ+xeˣ')

-5(eˣ+xeˣ)

-5eˣ-5xeˣ

Which means we have

(-3x²eˣ-6xeˣ)+(-5eˣ-5xeˣ)-eˣ

Combine like terms and get

-3eˣx²-11eˣx-6eˣ

Write an
equivalent expression using the distributive property.
1/4(4x - 6)

Answers

Answer:

Step-by-step explanation:

Distributive property: a*(b + c)= (a*b) + (a*c)

[tex]\frac{1}{4}(4x - 6) = 4x*\frac{1}{4} - 6*\frac{1}{4}\\\\[/tex]

              [tex]= x -3*\frac{1}{2}\\\\=x - \frac{3}{2}[/tex]

3. Jalen is a lifeguard at a public swimming pool and is planning to string

flags across both diagonals of the rectangular pool. He knows the

dimensions of the pool are 50 meters by 25 meters.

What value represents the length of flag string Jalen will need to reach

across the diagonals of the pool?

Answers

Answer:

[tex]Flag = 55.90m[/tex]

Step-by-step explanation:

Given

[tex]Length = 50m[/tex]

[tex]Width = 25m[/tex]

Required

Determine the length of the flag

Because the flag crosses through opposite diagonals of the pool. Its length is the length of the diagonal of the pool.

This is calculated using Pythagoras theorem.

[tex]Flag^2 = Length^2 + Width^2[/tex]

Substitute values for Length and Width

[tex]Flag^2 = 50^2 + 25^2[/tex]

[tex]Flag^2 = 2500 + 625[/tex]

[tex]Flag^2 = 3125[/tex]

Take positive square root of both sides

[tex]Flag = \sqrt{3125[/tex]

[tex]Flag = 55.90m[/tex]

Hence, the length of the flag is approximately 55.90m

help me me me me pls

Answers

Answer:

"C" is the answer to that question

Answer:

C

Explanation:

Because I say so

si un punto está sobre el eje x cual es su valor de la ordenada

Answers

Answer:

si un punto esta sobre el eje x cual es su valor de cordenada

Step-by-step explanation:

360

I’ll give you 15 points if you know the answers to this question


Answers

It would be B)no.

Hope This Helps!

This month you make $3,881 from liquor salesfrom food, and from your gift shop. your monthly sales goal is $25,000, did you meet your goal?

Answers

Answer:

No

Step-by-step explanation:

If you add all the sales you do not meet your goal of $25,000

(9/8) to the power of 2; can some give me the answer quick please.​

Answers

Answer:

(9/8)²=

81/64.

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

The height of a building is 956 feet, which is about 479 feet higher than another building. What is the height of the second building?
The second building has a height of feet

Answers

If the first building height is 956 feet and the height of second building is 479 feet smaller than the first one
Therefore 956-479=477 feet
Height of second building is 477 feet

Square ABCD is similar to square JKLM. AB = 10, BC = 10, CD = 10, DA = 10, and JK = 15. The area of square JKLM is ____u 2

Answers

Answer:

225 square units

Step-by-step explanation:

since they are similar, all sides of JKLM are 15 units so:

15x15=225

Rahul made three Indian clay curry pots. He wants to see if he

can place them in the oven at the same time.

The diameter of the second pot is of the diameter of his first

pot.

cm wider than the diameter

The diameter of the third pot is

of his second pot.

The sum of the diameters of the three pots is 47.5 cm.


What equation represents the sum of the diameters of all three lord and what is the value of y?

Answers

Answer:2.234

Step-by-step explanation:

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