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?
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
Decrease 60kg by 40%
Answer:
36 KG
Step-by-step explanation:
This is how I did it:
60 x 0.6 = 36
1 = 100%
0.4 = 40%
but you have to decrease so
100% - 40% = 60%
60% = 0.6
How can this expression be written another way?
60x - 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes.
Answer:
factor using 12 (gcf)
12(5x-2)
See attached picture
Answer:
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]=2x + h[/tex]
Step-by-step explanation:
Given
[tex]f(x)= x^2 + 2[/tex]
Required
Determine: [tex]\frac{f(x+h)-f(x)}{h}[/tex]
First, we calculate f(x + h)
[tex]f(x)= x^2 + 2[/tex]
[tex]f(x+h) = (x+h)^2+2[/tex]
[tex]f(x+h) = x^2+2xh+h^2+2[/tex]
So, we have:
[tex]\frac{f(x+h)-f(x)}{h}[/tex] [tex]= \frac{x^2 + 2xh + h^2 + 2 - x^2 - 2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]= \frac{x^2 - x^2+ 2xh + h^2 + 2 - 2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex] [tex]= \frac{2xh + h^2}{h}[/tex]
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]=2x + h[/tex]
A strawberry farmer will receive 37 per bushel of strawberries during the first week of harvesting each week after that the value will drop 0.8 per bushel the farmer estimates that there are approxiamately 129 of strawberries int he fieldsand that the crop is increasing at a rate of four bushels per week when should the farmer harvest the strawberries to maximize their value? (Assume that "during the first week of harvesting" here means week 1. How many bushels of strawberries will yield the maximum value? (Round your answer to the nearest integer.)
bushels
2. What is the maximum value of the strawberries? (Round your answer to two decimal places.)
$
Answer:
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
b.)
Revenue = bx = (157)(31.4) = $ 4929.8
Step-by-step explanation:
Let number of bushes = b
The price of the bushes = x
The time to harvest = t
The revenue = y
Now given,
Price = x = 37 - (0.8)t
and
Number of bushes = b = 129 + 4t
Also,
The revenue = (Number of bushes)(Price of the bushes)
= bx
= (129 + 4t)[37 - (0.8)t]
= 129×37 - 129× (0.8)t + 4×37t - 4×0.8t²
= 4773 - 103.2t + 148t - 3.2t²
= 4773 + 44.8t - 3.2t²
⇒ y = 4773 + 44.8t - 3.2t²
Now,
[tex]\frac{dy}{dt}[/tex] = 0 + 44.8 - 6.4t
Now,
[tex]\frac{dy}{dt}[/tex] = 0
⇒ 44.8 - 6.4t = 0
⇒ - 6.4t = -44.8
⇒ 6.4t = 44.8
⇒t = [tex]\frac{44.8}{6.4} = 7[/tex]
Now,
[tex]\frac{d^{2}y }{dt^{2} }[/tex] = -6.4
As [tex]\frac{d^{2}y }{dt^{2} }[/tex] < 0 ,
It means at time t = 7 , the revenue is maximum
a.)
Number of bushes = b = 129 + 4(7) = 129 + 28 = 157 bushes
Price = x = 37 - (0.8)(7) = 37 - 5.6 = 31.4
b.)
Revenue = bx = (157)(31.4) = 4929.8
Y is directly proportional to x squared if y=20 when x=2 find y when x= 5
Answer:
y = 125
Step-by-step explanation:
Given that,
y is directly proportional to x² i.e.
[tex]y=kx^2[/tex]
k is a constant of proportionality
Put y = 20 and x = 2 in the given equation to find k.
[tex]k=\dfrac{y}{x^2}\\\\k=\dfrac{20}{(2)^2}\\\\k=5[/tex]
Now put k = 5 and x = 5 in the given equation to find y.
[tex]y=5\times (5)^2\\\\y=125[/tex]
So, the value of y is equal to 125.
Hello! I'm having a problem figuring out this problem: 6c-9d=111 5c-9d=103
I've been looking at different ways to solve it, but I'm not sure how to do it. Please, help give me a step-by-step instruction on how to figure it out. (I'll make you the most Brainliest answer.) (And, you'll get a good amount of points.)
Answer:
C=8
Step-by-step explanation:
6c-9d=111
-) 5c-9d=103
6c-5c=c
-9c+9c=0
111-103=8
(Negative+Negative=Positive)
C=8
I need Brainliest!
REASONING Tell whether the rates are equivalent.
75 pounds per 1.5 years
38.4 ounces per 0.75 year
Answer:
No, either convert pound to ounces or the other way around.
Step-by-step explanation:
Use 1 lb= 16 oz so 75 lb=16 x 75 =1200 oz ---> 1200 ounces per 1.5 years..
---> 1200 oz/1.5 years (1)
The second equation is 38.4 ounces per 0.75 years , will be the same as 76.8 ounces per 1.5 years.---->76.8 oz / 1.5 years (2)
So compare (1) and (2) are not equivalent....
The rates are not equivalent to each other..
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
Use 1 lb= 16 oz
Thus 75 lb=16 x 75 =1200 oz
Means 1200 ounces per 1.5 years..
Now 1200 oz/1.5 years ----- (1)
The second equation is 38.4 ounces per 0.75 years which will be the same as 76.8 ounces per 1.5 years.
76.8 oz / 1.5 years ----- (2)
So compare (1) and (2) are not equivalent to each other.
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A small plane has 20 rows of seats. Each row has 4 seats.
Find the total number of seats on the plane.
How many seats are on 3 small planes?
Answer:
the total number of seats on the plane
Step-by-step explanation:
Total number of seats on a small plane is 80 and 3 small planes have 240 seats in total
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the question
A small plane has rows of seats = 20
Each row have seats = 4
Total number of seats on a small plane = 20*4
= 80 seats
Therefore,
3 small planes have total seats = 3 * 80
= 240 seats
Hence, Total number of seats on a small plane is 80 and 3 small planes have 240 seats in total
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Solve and graph the inequality |4 – v| < 5.
a. Write the inequality as two inequalities without absolute value.
b. Solve the inequality and write the solution set.
c. Graph the solution on a number line.
50 points !!!!!
Answer:
-1 < v < 9Step-by-step explanation:
Given inequality
|4 - v| < 5a. The two inequalities:
1. 4 - v < 5
v > 4 - 5v > -12. 4 - v > -5
v < 4 - (-5)v < 9b. Solution is the combination of the above two:
-1 < v < 9c. The graph is attached
13. What is the slope of the line of best fit for the given
graph?
a) -0.3
b) 0.3
d) -3
c) 3
0
The shape below is a horizontal cross section of a figure. Select all the possible figures that could have this shape as a cross section. A Sphere B Rectangular Prism C Triangular pyramid D Rectangular pyramid
Answer:
D. Rectangular prism
Step-by-step explanation:
I believe the answer is D. Rectangular prism
A rectangular prism is also called a cuboid. Like cuboid, it also has three dimensions, i.e., length, width and height. So here the horizontal cross section of the figure is rectangular prism. The correct option is B.
What is a rectangular prism?A rectangular prism is defined as a three dimensional shape which has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. A geometrical box, notebooks, rooms, etc. are in the shape of a rectangular prism.
A rectangular prism has 6 faces, 12 edges and has 8 vertices. For a rectangular prism the pairs of opposite faces are identical or congruent. A prism with six faces that are rectangles and all angles are right angles is a right rectangular prism.
Thus the correct option is B.
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Determine the interval(s) where f(x) = In (9x - 81) is continuous.
Answer: (9, ∞)
Step-by-step explanation:
You cant take the natural log of a negative number, and you cant take the natural log of 0. So, to find the intervals where the function is defined, set the inside of the natural to 0.
9x - 81 = 0
x = 9
The intervals where this function is continuous is from 9 --> infinity
Kevin is driving on a long road trip. He currently has 11 gallons of gas in his car. Each hour that he drives, his car uses up 1.75 gallons of gas. How much gas would be in the tank after driving for 5 hours? How much gas would be left after t hours?
Answer:
He would have 2.75 gallons left after 5 hours.
Step-by-step explanation:
The expression (2x + 6) + x represents the perimeter of an isosceles triangle. If x represents the length of one side of the triangle, explain how you can use Distributive Property to find the length of each of the two equivalent sides?
Answer:
x+3
Step-by-step explanation:
x= one side of the triangle
(2x+6)=two sides of the isosceles triangle
Factor (2x+6) which is 2(x+3)
So, the length of each side is x+3.
What procedure can be used to solve the equation StartFraction x Over 19.3 EndFraction = 38.6, and what is the solution?
Answer: it’s number D I think let me know if I’m wrong
Step-by-step explanation:
Answer:
the answer is d.Multiply both sides by 19.3; the solution is 744.98.
Step-by-step explanation:
got it right on edge.
Find the 15th term of the geometric sequence 1, -4, 16, ...
Answer:
Answer is 268435456
Step-by-step explanation:
use an = a × ^r n-1 to find the sequence
The 15th term of the given geometric progression sequence 1, -4, 16, ... will be 268435456.
What is geometrical progression series?A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
As per the given sequence,
1, -4, 16, ...
First term a = 1
Common ratio r = -4/1 = -4
The nth term is given as ar^(n - 1)
Therefore, the 15th term will be as,
a₁₅ = 1(-4)¹⁵⁻¹
a₁₅ = -4¹⁴ = 268435456
Hence "The 15th term of the given geometric progression sequence 1, -4, 16, ... will be 268435456".
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Part B
Based on your calculations in part a, did Kelvin ski twice as long without falling as anyone else in the family?
Answer:
Yes, Kevin skied twice as long as Lori without falling.
Step-by-step explanation:
Kevin's time was 223 sec and Lori's was 110 sec.
110 x 110 = 220
Since Lori's time was 110 seconds and twice that is less than Kevin's, which was 223.
Thus we have our answer:
Yes, Kevin skied twice as long as Lori did without falling.
Hope it helps!!
700% of what number is 4,340?
Answer:
620
Step-by-step explanation:
100% must be the the answer so 700% must be 7 times that number.
4340÷7=620
Select ALL of the correct answers. COULD BE more than one answer.
Answer:
This study uses a control group
This study uses a repeated measures design
Step-by-step explanation:
Hope it help
Please mark me as brainliezt
Sorry if my answer is wrong
11. What percent of this circle is shaded if you have 1/3 and 5/12?
Answer:
Epic
Step-by-step explanation:
you can do it trust me.
What is the midpoint of the segment with endpoints (0,7) and (5,2)
Answer:
( 2.5 , 4.5 )
Step-by-step explanation:
How do I answer this?
9514 1404 393
Answer:
A. (-∞, ∞)
B. (-∞, 0) U (0, ∞)
Step-by-step explanation:
A. Though the attached calculator disagrees, the value of the derivative of f(x) is actually defined at x=0. Its value is 0. There is a discontinuity in the second derivative at x=0, but both the derivative and the function are continuous there.
differentiable on (-∞, ∞)
__
B. The derivative is discontinuous at x=0, so is undefined there. The function is differentiable everywhere else.
differentiable on (-∞, 0) U (0, ∞)
_____
The graphs of f(x) and its derivative are red and dotted orange, respectively.
The graphs of g(x) and its derivative are purple and dotted blue, respectively.
There are overlaps, which is why we chose to make some graphs dotted.
what is 1+1?
(serious question)
Answer:
2
Step-by-step explanation:
4 1/6 divided by 10
Answer:
~0.42
Step-by-step explanation:
Convert the fraction (4 1/6) to an improper fraction
25/6 = improper form
Now convert the improper fraction to a decimal
4.166666666666667
Now we can divide that by 10
4.166666666666667 ÷ 10
0.4166666666666667
And we can round that up to the nearest hundredth
4 or less, let it rest, 5 or more, let it sore
0.42
Hope this helped!
Have a supercalifragilisticexpialidocious day!
please help only answer if you know please
Answer:
a)Let the number of avocados that I brought be a and number of oranges be r.
b) a+r=28 ---(1)
a+2r=44 ---(2)
c) a+r=28
a=28-r ---(3)
sub (3) into (2), 28-r+2r=44
r=16
sub r=16 into (3), a=28-16
a=12
∴ I brought 12 avocados and 16 oranges.
If the root of x2-7x+k=0, m=1, find the value of the constant k
Answer:
hfrhghubifhvfuovhtjopugjob
Step-by-step explanation:
Un avión dispone de 24 asientos en clase A y de 62 asientos en clase B cuya venta supone un total de $15,390. Sin embargo, sólo sea han vendido 10 asientos en clase A y 40 en clase B, obteniendo un total de $8,750.
¿Cuál es precio de un asiento en cada clase? Ayuda por favor!!
Answer:HOLA I Do not speack spanish
Step-by-step explanation:
A light bulb consumes 1800 watt-hour per day. How long does it take to consume 8550 watt-hours
Answer:
4 hours and 45 minutes
Step-by-step explanation:
8550 ÷ 1800 equals 4.75 which should translate into 4 hours and 45 minutes
BRAINLIEST FOR WHOEVER SOLVES
ameliaswan
Answer:
8/22 for the first box and 2 for the second box.
Step-by-step explanation:
Because the 2 extremes are 10/5 and 8/22, those would be the two answers.
Answer:
Step-by-step explanation: