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?
Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.
We will find that working together, they need to work for 8 hours.
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Let's start by defining the variables that we will use:
A = rate at which Aran worksB = rate at which Beatrice works.C = rate at which Charlie works.Now let's see the given information:
"Aran and Beatrice can build an ant hill in 10 hours"
This can be written as:
(A + B)*10 h = 1 ant hill
"Aran and Charlie can build the ant hill in 12 hours"
This can be written as:
(A + C)*12 h = 1 ant hill
"Beatrice and Charlie can build the ant hill in 15 hours"
This can be written as:
(B + C)*15 h = 1 ant hill.
Then we have 3 equations:
[tex](A + B)*10 h = 1[/tex]
[tex](A + C)*12 h = 1[/tex]
[tex](B + C)*15 h = 1[/tex]
Where for commodity, I removed the "ant hill" unit.
Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.
I will isolate A in the first equation:
[tex]A = \frac{1}{10h} - B[/tex]
Now we can replace it in the second equation to get:
[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]
Now we can isolate C in the last equation to get:
[tex]C = \frac{1}{15h} - B[/tex]
Replacing that in the above equation we get:
[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]
This means that Beatrice alone would construct the hill in 24 hours.
Now that we know the value of B, we can use:
[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]
This means that Charlie needs 40 hours to finish the hill alone.
Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:
[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]
Now if the 3 ants work together, the total rate at which they work is:
[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]
This means that they need to work for the inverse of that rate
[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]
Working together, they need to work for 8 hours to complete an ant hill
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Answer:
Graph A is increasing more rapidly, so Dan is correct
Jonathan is building an outdoor staircase for his deck. He uses 8 screws for every 2 steps. If there are 14 steps, how many screws does Jonathan need?
Answer:
56 screws
Step-by-step explanation:
So, first we can find how many screws he needs.
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws
The screws does Jonathan need is 56 screws.
It is required to find how many screws does Jonathan need.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Jonathan uses 8 screws for every 2 steps. If there are 14 steps.
So, first we can find how many screws he needs.
According to given question we have
So, if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)
then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws.
Therefore, the screws does Jonathan need is 56 screws.
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Write the equation of a line through (-1,-5) parallel to 3x-y=5, and in slope intercept form
Answer:
y = 3x -2
Step-by-step explanation:
The general equation form is;
y = mx + b
where m is the slope and b is the y-intercept
For the equation given;
y = 3x -5
the slope from here is 3
If two lines are parallel, they have equal slopes
This mean that the slope of the line we want to calculate too is 3
Now we can use the point slope format to get the correct equation
y-y1 = m(x-x1)
y+ 5. = 3(x+ 1)
y = 3x + 3 -5
y = 3x -2
HELP ASAP!!!! PLEASE HELP!!!!
Step-by-step explanation:
[tex] \sin(c) = \frac{36}{45} = 0.8 \\ \cos(c) = \frac{27}{45} = 0.6\\ \tan(c) = \frac{36}{27} = 1.333[/tex]
In an effort to save money, you placed $20 in a jar each month for 2 years. You spent 60% on presents for your family. How much do you have left?
2.) Add unlike fractions using the butterfly method.
1 point
c) of the teacups in Lily's Tea Shop, 1/5 are teal and another 1/10 are yellow. What fraction
of the teacups are either teal or yellow?
3/10
5/10
7/10
O 1/10
Answer:
3/10
Step-by-step explanation:
1/5=2/10
2/10+1/10=3/10
Answer:
ITS 3/10 AND CAN SOMEONE PLS ANSWER MY MOST RECENT QUESTION.
You brought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
Answer:
8
Step-by-step explanation:
Answer:
Candy bars: $13
Step-by-step explanation:
$3 magazine + $13 total of candy bars = $19
in the equation x+12=30 does x=16 explain your answer
Enter the value of n for the equation 26 * 2n = 213
Answer:
4.09
Step-by-step explanation:
Please help due ASAP
Hxhdbdidhdbbr
When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer.
GIVING BRAINLIST PLEASE ANSWER CORRECT!!!
False
True
4 dogs have weights of 5.2 kg, 3.5 kg, 7 kg, and 9.74 kg. What is the total weight of the dogs? What is the average weight of the 4 dogs?
Answer:
25.14kg is the total weight
Step-by-step explanation:
Answer:
The total weight of the dogs is 25.44 kg
The average weight of the dogs are 25 kg
Step-by-step explanation:
It is right on Egenuity comment if you want another answer and have a good day :)
The diagram shows a square with a perimeter of 20 cm.
Not drawn
accurately
Eight of these squares fit together to make a rectangle.
Not drawnaccurately
What is the perimeter of the rectangle?
The perimeter of the rectangle is 70cm.
What is perimeter?Perimeter is the total length of the sides of a two-dimensional shape.
What is the formula for the perimeter of square?Perimeter of the square is given by
P = 4a
where,
a is the side length of the square.
P is the perimeter of the square.
What is the formula for the perimeter for the rectangle?Perimeter of the rectangle is given by
P = 2( l + b)
Where,
l is the of the rectangle
b is the breadth of the the rectangle
According to the given question.
We have the perimeter of the square is 20cm.
⇒ 4a = 20
⇒ a = 5cm
⇒ Each side length of the square is 5cm
And a rectangle made of 10 squares.
⇒ length of the rectangle = 5×5 = 25cm
and the breadth of the rectangle = 2 × 5 = 10cm
Therefore, the perimeter of the rectangle = 2(25 + 10) = 2 × 35 = 70cm
Hence, the perimeter of the rectangle is 70cm.
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Use complete sentences to describe why postulates are helpful.
cos 2 * (x/2) = (sec(x) + 1)/(2sec(x))
Answer:
Answer below
Step-by-step explanation:
I really hope it works
Please help!!
Will mark brainliest
Help pls this is timed!!!!!!! Pls and thank you ;P
Who supported the formation of Washington Territory out of a belief that it was America’s destiny to settle the Pacific Northwest?
A.)President Millard Fillmore
B.)Governor Isaac Stevens
C.)Oregon Territory’s northern settlers
D.)Oregon Territory’s southern settlers
Answer:
A. President Millard Fillmore
1. 10 x ____ = 180
2. 37 x 10 = ____
3. ____ tens = 650
Answer:
1. 18
2. 370
3. 65
Step-by-step explanation:
1. 180/10=18
2. 370 add a zero
3. tens means ·10 so 650/10=65
Answer:
1.)18
2.)370
3.)65 tens yw(:
What is the solution to the equation? 13 3/4+X= 7 1/ 4
Answer: x=-6 1/4
Step-by-step explanation:
A. A cylinder just fits into a cube of side length 36 m Calculate the percentage
of empty space in the box.
Answer:
21.5%
Step-by-step explanation:
volume of cube: 36x36x36
volume of cylinder: πx18²x36
Cylinder percentage: (πx18²x36) / 36x36x36 = π / 4 = 0.785
percentage of empty space: 1 - 0.785 = 0.215 (21.5%)
What was the price for one notebook?
Answer:
A notebook at the dollar store costs between 1-2 dollars
If x : 3 = 5 : 7 , then x = ………
Answer:
the answer is A which 2(1/7)
What is the value of
2021
−
2223
+
2425
?
?
Answer:
2223
Step-by-step explanation:
We need to find the value of 2021-2223+2425.
Firstly subtract 2223 from 2021.
2021-2223 = -202
Now add -202 and 2425. So,
2425 +(-202) = 2223
So, the value of 2021-2223+2425 is 2223. Hence, this is the required solution.
please answer the questions.
Answer:
1. 9 numbers (27, 36, 45, 54, 63, 72, 81, 90, 99)
2. 122 square cm
Step-by-step explanation:
break the shape into 2, find area of each, add those areas together
HELP ME PLEASE !!!
Answer:
A realistic budget is hard to come by. All budgets tell you what you should include in your monthly plan, but what about unexpected expenses? Here are some ideas for making a realistic budget, and sticking to it.
daid1784 avatar
Well, the dozens of apps, spreadsheets, and other methods just don’t account for real life and all the expenses we don’t think of. There are plenty of expenses we have that aren’t monthly that take up more of our money than we planned.
the measure of AOC is 90 find the value of x, A 30 B 10 C 11
10
Step-by-step explanation:
3x° + 46° +14°
3*10° + 46 + 14° =90
therefore the value of x is 10
The value of x on the given figure is 10.
Option D is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
From the figure,
3x + 46 + 14 = 90
Now,
Simplifying.
3x + 60 = 90
Subtracting 60 on both sides.
3x = 90 - 60
3x = 30
Dividing 3 into both sides.
x = 10
Thus,
The value of x on the given figure is 10.
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The complete question is given on the attach image.
select all relations that are functions from the choices below.
Paul won 37 super bouncy balls playing hoops at county fair. At school he gave two to every student in his math class. He only had 3 remaining. How many students are in his class?
Answer:
17 students
Step-by-step explanation:
If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.
Does the tablets shown a proportional relationship? If so, what is the value of y when x is 10?
Answer: Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x=k or y=kx.
