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 this one as well
Your social media ad cost $2.50 per thousand impressions. You get 3.14 billion impressions. What is your approximate bill?
The approximate bill when the social media ad cost $2.50 per thousand impressions should be $7.85.
Calculation of the approximate bill:Since Your social media ad cost $2.50 per thousand impressions. You get 3.14 billion impressions.
So here the approximate bill be like
= 2.50 (3.14)
= $7.85
hence, The approximate bill when the social media ad cost $2.50 per thousand impressions should be $7.85.
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Georgia practiced for her dance recital for 3/4 of an hour on Monday, 3/8 of an hour on Tuesday, and 5/6 of an hour on Wednesday. How much longer did she practice on Monday than on Tuesday?
Answer: 22.5 minutes
Step-by-step explanation: On Monday Georgia practiced for 3/4 of an hour and on Tuesday she practiced for 3/8 of an hour. The difference between those two is 3/8 of an hour and when you take 3/8 of 60 minutes you get 22.5 minutes
Answer: 3/8 longer or 2 times longer or 22.5 minutes longer on Monday depending on the type of answer they want.
Step-by-step explanation: 3/8 longer or 2 times longer Explanation is: Gotta find common denominator Common denominator is 8 6/8 on Monday and 3/8 on Tuesday so difference of 3/8 or twice as long 22.5 Minutes Longer explanation is: 3/4 of an hour is 45 minutes (60/4=15x3=45) 3/8 of an hour is 7.5 minutes (60/8=7.5x3=22.5) So 45-22.5= 22.5 minutes longer on Monday. In fraction form its 9/40.
Ms. Morris asked her students to each pick one or more of the following 4 numbers, all powers of 3:1,3,9,27and write the sum of the chosen numbers on a piece of paper. Students must not talk to each other about their choices.She then collected all papers, and wrote them down on the whiteboard, but no number would be written more than once. The class “won” the game if there were N numbers written down, where N was the greatest possible such numbers. What was the valueof N that Ms. Morris had in mind?
A
Step-by-step explanation:
all you have to do is answe
3x=5y-9 2y=3x+3
solve
Answer:
(1/3 ,2)
Step-by-step explanation:
If I have 4 pencils and you have 7 apples, how many pancakes can fit on the roof?....
Answer:
11 pancakes can fit on the roof =)
Step-by-step explanation:
Answer:
9000 pancakes buddy come on u should know better
aMath In comparison 1/3 to where 2/6 would be located on a number line closer to O B. the same point closer to 1 D. At O
Answer:
o represent 1/3 on a number line, we divide the gap between O and A into 3 equal parts. Let T and Q be the points of division. Then, T represents 1/3 and Q represents 2/3, because 2/3 means 2 parts out of 3 equal parts as shown below. By using the same procedure, point O represents 0/3 and point A represents 3/3.
Step-by-step explanation:
I need help with this
Answer:
Step-by-step explanation:
9/I0 x 2/2 =9/I0
Or 0.9 in decimals
Answer:
The answer is IN the question... (9/10)
Step-by-step explanation:
Ok well you multiply the numberator and denominator by 2 which makes 18/20 but OH THAT CAN BE SIMPLIFIED SO DIE FRACTION! so then you divide both sides by 2 and you get the original 9/10
plz brainliest :)
What is 3 examples of a rate?
Answer:
Step-by-step explanation: For example, if a 12 ounce can of corn costs 55 cents the rate is 55 cents for 12 ounces. The first term in ratio is measured in cents the second term in ounces
PLEASE, PLEASE HELP D:
write the linear equation given :
1. slope = 1/4; y-intercept =7
2. slope = -3; y-intercept = 2/3
3. slope = 2/3; y-intercept = 2/3
4. slope = -2; y-intercept = -1/2
5. slope = -3/4; y-intercept = -3
Answer:
Step-by-step explanation:
1. y = 1/4 x + 7
2. y = -3 x + 2/3
3. y = 2/3 x + 2/3
4. y = -2 x - 1/2
5. y = -3/4 x - 3
Convert 3,259 ml to L
Answer:
3.259 L
Step-by-step explanation:
1000 ml in 1 L
Write 23/50 as a number compared to 100
Answer:
46 blocks would be colored.
Step-by-step explanation:
23/50 = ?/100
23/50 x 2 = 46/100
A flood a creek's water level changes by −4 7/10 feet in 2 hours. What is the average change in the creek's water level per hour?
Answer:
-2.35
Step-by-step explanation:
Divide -4.7/2 = -2.35
1.How do you know you have a direct variation in the
relationship between two quantities?
Answer:
Say you have y=2x. That is direct variation and will always pass through the origin when graphed. When x is multiplied by a number, the y value will also be changed by that number. If you add a y-intercept and change y=2x to, for example, y=2x+2, the x and the y will no longer be related by a constant ratio.
Step-by-step explanation:
x2 + 8x + 20 = 0
Quadratic equation
Answer:
The answer is x = -4 ± 2i
Step-by-step explanation:
The weight of a baby dog on day one is 5 kilograms. Every day, the dog grows an additional 0.1 kilograms. How heavy the dog is after 10 days?
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The weight of the dog after 10 days is 5.9 kg.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Weight of the baby on day one = 5 kg
This can be written as,
1 day = 5 kg
The dog grows 0.1 kg each day.
This means,
On the 2nd day, we get,
2 days = 5 + 0.1
2 days = 5.1 kg
The expression for the weight of the dog on n days can be written as,
n days = 5 + (n -1) x 0.1 _____(1)
Now,
After 10 days we get,
n = 10
From (1) we get,
10 days = 5 + (10 - 1) x 0.1
10 days = 5 + 9 x 0.1
10 days = 5 + 0.9
10 days = 5.9 kg
Thus,
The weight of the dog after 10 days is 5.9 kg.
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Shea wrote the expression 5(y+2)+4 to show the amount of money five friends paid for snacks at a baseball game.Which espression is equivalent to the one shea wrote?
Answer: B. 5 ∙ y + 5 ∙ 2 + 4
Step-by-step explanation:
The options are:
a. 5 + y + 5 + 2 + 4
b. 5 ∙ y + 5 ∙ 2 + 4
c. 5 ∙ y + 5 ∙ 4 + 4
d. 5 ∙ y + 5 + 2 + 4
To solve the question, we have to expand 5(y+2)+4. This will be:
= (5 × y) + (5 × 2) + 4
= 5 ∙ y + 5 ∙ 2 + 4
= 5y + 10 + 4
= 5y + 14
Use an informal argument to find the value of a
PLEASE ANSWER FAST!!!
find the common difference of the arithmetic sequence -2,-4,-6
Answer:
-2
Step-by-step explanation:
-4-(-2) = -2
-6-(-4) = -2
What is the rate of change of the table shown?
Answer: rate of change = 2
===============================
Explanation:
Apply the slope formula. I'll use the first two columns as the two points, but you can use any two columns you want.
m = (y2-y1)/(x2-x1)
m = (9-5)/(3-1)
m = 4/2
m = 2
The slope is 2, so the rate of change is 2. Slope and rate of change describe the same thing. Each time x goes up by 1, y goes up by 2.
9. Factorize: 6x2 - 19x + 14.
Answer:
Step-by-step explanation:
Here, we want to factor the given polynomial
We have this as;
6x^2 - 19x + 14
= 6x^2 -12x-7x + 14
= 6x(x-2) -7(x-2)
= (6x-7)(x-2)
6x^2-19x + 14 = (6x-7)(x-2)
plz help due in 30mins
Answer: think a ukjuuuhb
A tip of $6.30 is what percent of a $35 bill?
16%
15%
18%
10%
Answer:A tip of $6.30 is what percent of a $35 bill? 10% , 15% , 16% , or 18% ? A tip of $6.30 is 18% percent of a $35 bill. $35.00 * 18/100 = $6.30.
Answer:
18%
Step-by-step explanation:
Solve for x in the diagram below. Will mark brainliest if your answer is correct!♡
please help it due asap
thanks
Answer:
C) AC=11.5
Step-by-step explanation:
3x-5=x+6
2x=11
x=5.5
AC=3(5.5)-5
AC=11.5
Solve the system of linear equations by substitution.
3x + y = -3 -2x + y =7
Answer:
(-2, 3)
Step-by-step explanation:
First solve one equation for y:
[tex]-2x+y=7\\y=7+2x[/tex]
Now we can substitute this equation into the other one:
[tex]3x+7+2x=-3[/tex]
Solve for x:
[tex]x=-2[/tex]
Now substitute this value into the equation [tex]y=7+2x[/tex]:
[tex]y=7+2x(-2)[/tex]
Solve for y:
[tex]7=3[/tex]
Now your solution is (-2,3)
Hope this helps! :)
X - y = 4
X + y =8
The x-coordinate of the solution to the system shown is
1. 12
2. 4
3. 6
4. 2
Answer:
3. 6
Step-by-step explanation:
X - y = 4 ( Equation 1 )
X + y =8 ( Equation 2 )
equation 1 + equation 2
; 2x = 12
x = 12÷2
x =6
hope it helps ☺️
Answer: n=6
Step-by-step explanation:
687.68 divided by 0.7
Answer:
784.14
Step-by-step explanation:
Answer:
982.4
Step-by-step explanation:
Please Brainiest It will help me get to my quest!!??!?!
6.6+1.3x-5.2x(less than or equal to) 14.4 plssss help omg
J
4. As a fund-raiser, the student council sold
T-shirts and sweatshirts. They sold a total
of 105 T-shirts and sweatshirts and raised
$1170. If the cost of a T-shirt t was $10 and
the cost of a sweatshirt s was $15, what
was the number of sweatshirts sold?
A 24
B 52
C 81
D 105