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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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
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.
Enter the value of n for the equation 26 * 2n = 213
Answer:
4.09
Step-by-step explanation:
in the equation x+12=30 does x=16 explain your answer
Please help!!
Will mark brainliest
At 6 a.m., the temperature is 19.4°C. Between 6 a.m. and noon, the temperature rises 3.8°C. Between noon and 6 p.m., the temperature falls 2.5°C.
What is the temperature at 6 p.m.?
1.3°C
6.3°C
13.1°C
20.7°C
Answer:
20.7°C
Step-by-step explanation:
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
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.
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.
select all relations that are functions from the choices below.
If x : 3 = 5 : 7 , then x = ………
Answer:
the answer is A which 2(1/7)
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]
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.
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 was the price for one notebook?
Answer:
A notebook at the dollar store costs between 1-2 dollars
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?
Evaluate the following when a = 4 and b = 7 (a+b)^2 - (a^2 + b^2)
Answer:
56
Step-by-step explanation:
(4+7)²-(4²+7²)=121-65
=56
Answer:
56
Step-by-step explanation:
(4 + 7)² - (4² + 7²) = 11² - (16 + 49) = 121 - 65 = 56
What is the area of this triangle?
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
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.
Learn more details about arithmetic here:
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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
Use the Law of Cosines to solve for the side BC. Round your answer to the point
nearest whole number. Write the value only *
Answer:
BC = 50
Step-by-step explanation:
Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cosy (c is BC)
c^2 = 30^2 + 21^2 - 2(30)(21)cos123
c^2 = 900 + 441 - 1260*(-0.888)
c^2 = 1341 - (-1118.841)
c^2 = 2459.841
c = 49.597
c = 50
Please help due ASAP
Hxhdbdidhdbbr
(Write an equation to go with the problem) Miranda goes to the store to buy 3 apples and some rice. The total was 6.50. If the rice cost $5.00, what was the cost per Apple?
Answer:
14.15 is the answer..comment it if that subtraction or multiple division
Answer: 3x + 5 = 6.50 is the equation where x represents the cost per apple and the cost per apple is 50 cents.
Step-by-step explanation:
In this situation we will represent the cost per apple by the variable x.
If she bought 3 apples, then 3 has to be multiply by x to find the cost so we will have the expression 3x
The rice cost $5 and she spend a total of 6.50 so 3x has to be add to 5 and it has to equal 6.50.
3x + 5 = 6.50 You can now solve for x in the equation to find the cost per apple
3x + 5 = 6.50
-5 -5
3x = 1.5
x= 0.5
This means the cost of an apple is 50 cents.
Andy played with Buzz 65% of the time. How many times did andy play with Buzz if her played with his toys 20 times?
Answer:
13
Step-by-step explanation:
yes.
Step-by-step explanation:
65/100×29
13
plz make me brainlest
what would x equal? (x=___)
Answer:
56mm
Step-by-step explanation:
they are parallelograms so the opposite sides are equal.
in the bottom parallelogram the top side length is 4x the side side length so in the top one the top side length must be 4x the side side length to be similar, so 14*4=56mm
Does (5, 6) satisfy the inequality 2x - 3y> 6?
Answer:
yes
Step-by-step explanation:
Answer:
Nope, it does not satisfy the equation.
Step-by-step explanation:
2x - 3y > 6
2(5) - 3(6) > 6
10 - 18 > 6
-8 > 6
Hope this helps and I hope u have an Amazing day!
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%)
In triangle XYZ, XY¯¯¯¯¯¯¯¯=15, YZ¯¯¯¯¯¯¯=8, ∡X=(3w−35)°, and ∡Y=52°. In triangle RST, RS¯¯¯¯¯¯¯=15, RT¯¯¯¯¯¯¯=8, ∡R=(w+17)°, and ∡S=52°. Find the angle measure for each of the four angles whose measures are not known.
A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°
B. ∡R=64°, ∡T=64°, ∡X=64°, ∡Z=64°
C. ∡R=35°, ∡T=93°, ∡X=35°, ∡Z=93°
D. ∡R=52°, ∡T=76°, ∡X=52°, ∡Z=76°
Answer:
A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.
Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:
[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]
In triangle XYZ, we can find XZ using cosine rule:
[tex]XZ^2=XY^2+YZ^2-2(XY)(YZ)cosY\\\\subtituting:\\\\XZ^2=15^2+8^2-2(15)(8)cos(52)\\\\XZ^2=141.24\\\\XZ=11.88\\\\Using\ sine\ rule:\\\\\frac{XZ}{sin(Y)}=\frac{XY}{sin(Z)}\\\\\frac{11.88}{sin(52)}=\frac{15}{sin(Z)}\\\\sin(Z)=15*sin(52) /11.88\\\\sin(Z)=0.9946\\\\Z=sin^{-1}(0.9946)\\\\Z=85^0[/tex]
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
∠X + 52 + 85 = 180
∠X + 137 = 180
∠X = 43°
∠X = 3w - 35
3w - 35 = 43
3w = 78
w = 26
In triangle RST, using sine rule:
∠R = w + 17
∠R = 26 + 17
∠R = 43°
∠R + ∠S + ∠T = 180° (sum of angles in a triangle)
43 + 52 + ∠T = 180
∠T + 95 = 180
∠T = 85°
