Answer: 4.5 hours
Step-by-step explanation:
First you put 60000 and change 2.5 hours into minutes then divide by that, inwhich you get 400. After getting 400 divide 108000 by 400 which equals 270, divide by 60 for hours.
It would take the same pump 4.5 hours to empty a tank containing 108,000 gallons of water.
What is an expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. An expression can also include mathematical functions, parentheses, and other symbols.
Let x be the amount of time (in hours) it takes the pump to empty a tank containing 108,000 gallons of water.
Using the direct variation formula, we can write:
time = k x capacity
Where k is the constant of variation.
We can use the given information to find k:
2.5 = k x 60000
k = 2.5 / 60000
k = 0.00004167
Now we can use this value of k to find x:
x = k x 108000
x = 4.5
Therefore, it would take the same pump 4.5 hours to empty a tank containing 108,000 gallons of water.
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A piece of paper has an area of 80 square inches. A person cuts off of the piece of
paper. Then a second person cuts off of the remaining paper. A third person cuts
off what is left, and so on.
The remaining paper after the nth person cuts off their fraction is given by:
n A(n)
0 80
1 60
2 45
3 33.75
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.After the first person cuts off 1/4, the piece of paper left is given by:
Fraction = 1/4 × 80
Fraction = 20
Remainder = 80 - 20 = 60 square inches.
After the second person cuts off 1/4, the piece of paper left is given by:
Fraction = 1/4 × 60
Fraction = 15
Remainder = 60 - 15 = 45 square inches.
After the second person cuts off 1/4, the piece of paper left is given by:
Fraction = 1/4 × 45
Fraction = 11.25
Remainder = 45 - 11.25 = 33.75 square inches.
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Complete Question:
A piece of paper has an area of 80 square inches. A person cuts off 1/4 of the piece of paper. Then a second person cuts off 1/4 of the remaining paper. A third person cuts off 1/4 what is left, and so on.
Complete the table where A(n) is the area, in square inches, of the remaining paper after the nth person cuts off their fraction.
Help ASAP
Liz sewed a quilt with an area of 900 square inches. The length of the quilt is 30 inches. What is the perimeter of the quilt? Enter your answer in the box below.
inches
Answer:
The answer is 120 inches
Step-by-step explanation:
900 is the area the area of a rectangle is A=lw
So 900=30w
900/30=w
30=w
multiply 30 by 4 to get the perimeter
The function g(x) is a transformation of the cube root parent function,
f(x)=√. What function is g(x)?
-5
1
5
f(x)
g(x)
O
5
1
1
A. g(x)=√x +4-3
OB. g(x)=√x-3-4
C. g(x)=√x + 3-4
D. g(x)=√x-4-3
We have a translation 3 units downwards and 4 units to the right. So the equation is:
g(x) = ∛(x - 4) - 3
What is the equation for the function g(x)?
We know that g(x) is a transformation of the parent cube function, which is f(x) = ∛x
If we look at the image, we can see that the graph of g(x) is exactly like the graph of f(x), but translated 3 units downwards and 4 units to the right.
A vertical translation of N units is written as:
g(x) = f(x) + N
if N > 0, the translation is upwards.If N <0, the translation is downwards.A translation of 3 units downwards is written as:
g(x)= f(x) - 3
A horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.If N <0, the translation is to the right.Then a translation of 4 units to the right is:
g(x) = f(x - 4) - 3
Replacing the function f(x) we get:
g(x) = ∛(x - 4) - 3
That is the transformed function. So the correct option is D
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Mary had 241 dollars to spend on 6 books. After
buying them she had 13 dollars.
Good for you mary.
Lol is there a question? I'll answer it if so
What is the average rate of change of f(x), represented by the table of values, over the interval [-3,4]
Answer:
Average rate of change = 3
Step-by-step explanation:
We know that the average rate of change is basically a measure of the slope of the secant line in the closed interval [a, b].here a = -3 and b = 4
f(b) = f(4) = 27f(a) = f(-3) = 6⇒ Average rate of change = f(b) - f(a) / b - a
= (27 - 6) / (4 - (-3))
= 21 / 7
= 3
Therefore, Average rate of change = 3
There are 10 seniors and 15 juniors in a gym class. What is the ratio of seniors to total students?
Answer:
for every 2 seniors there are 3 juniors or 2:3
The ratio of seniors to total students will be 2: 5.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
There are 10 seniors and 15 juniors in a gym class.
The total number of students will be given as,
Total students = 10 + 15
Total students = 25
Then the ratio of seniors to total students will be given as,
Ratio = Seniors / Total student
Ratio = 10 / 25
Ratio = 2 / 5
The ratio of seniors to total students will be 2: 5.
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Which number line shows the solution of 2x- 8>-4?
Answer:
The answer is B I just checked a math sumulater
Step-by-step explanation:
please help. I don't understand
Answer:
Length of third side is: [tex]\mathbf{8m^3-4m^2+3m}[/tex]
Step-by-step explanation:
Perimeter of triangle = [tex]18m^3+2m^2-m[/tex]
Length of side 1= [tex]5m^3+3m^2-2m[/tex]
Length of side 2= [tex]5m^3+3m^2-2m[/tex]
We need to find length of third side.
The formula used is: [tex]Perimeter \:of\:triangle=Sum\:of\:all\:sides[/tex]
Putting values and finding length of third side.
[tex]Perimeter \:of\:triangle=Sum\:of\:all\:sides\\18m^3+2m^2-m=5m^3+3m^2-2m+5m^3+3m^2-2m+Length\:of\:3rd\:side\\18m^3+2m^2-m=5m^3+5m^3+3m^2+3m^2-2m-2m+Length\:of\:3rd\:side\\18m^3+2m^2-m=10m^3+6m^2-4m+Length\:of\:3rd\:side\\Length\:of\:3rd\:side=18m^3+2m^2-m-(10m^3+6m^2-4m)\\Length\:of\:3rd\:side=18m^3+2m^2-m-10m^3-6m^2+4m\\Length\:of\:3rd\:side=18m^3-10m^3+2m^2-6m^2-m+4m\\Length\:of\:3rd\:side=8m^3-4m^2+3m[/tex]
So, Length of third side is: [tex]\mathbf{8m^3-4m^2+3m}[/tex]
Smart about slopes pls help
Answer:
Step-by-step explanation:
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
8). Slope of the line passing through (0, 4) and (-1, 6) will be,
Slope = [tex]\frac{6-4}{-1-0}[/tex]
= -2
9). Slope of a line passing through (10, 15) and (9, 0),
Slope = [tex]\frac{15-0}{10-9}[/tex]
= 15
10). Slope of a line passing through (0, -9) and (4, -7),
Slope = [tex]\frac{-9+7}{0-4}[/tex]
= [tex]\frac{1}{2}[/tex]
11). Slope of a line passing through (2, 20) and (4, 17),
Slope = [tex]\frac{20-17}{2-4}[/tex]
= [tex]-\frac{3}{2}[/tex]
what is 1000m in 2 minutes?
is this somthing that your looking for?
Question 1 options:
Find the slope of the line that passes through (7, 18) and (9, 9).
Write your answer as an improper fraction.
Answer:
9/-2
Step-by-step explanation:
im in algebra and its easy
Find the distance between the two points in simplest radical form.
(-5,8) and (-3, 1)
Given:
The two points are (-5,8) and (-3,1).
To find:
The distance between the given two points in simplest radical form.
Solution:
Distance formula: The distance between two points is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between (-5,8) and (-3,1) is
[tex]d=\sqrt{(-3-(-5))^2+(1-8)^2}[/tex]
[tex]d=\sqrt{(-3+5)^2+(-7)^2}[/tex]
[tex]d=\sqrt{(2)^2+(-7)^2}[/tex]
[tex]d=\sqrt{4+49}[/tex]
[tex]d=\sqrt{53}[/tex]
Therefore, the distance between two points (-5,8) and (-3,1) is [tex]\sqrt{53}[/tex] units.
Fiona is 7 years older than Gavin. Alex is 12 years younger than Gavin. If the total age is 73 how old is the youngest of them?
Step-by-step explanation:
hey i hope this helps
its kind of blurry but u can still see the answer
Please show work!! Will rate 5 stars and give thanks
Using proportions, we have that:
6. From the last pool, 46.43% of voters were for the candidate.
7. Janie makes the triple amount of Jenny.
8. The balance has increased by 3.02% during the year, not 3%.
9. The statement that 10% of the students in the class are men with blond hair is correct.
10. There is a intersection between the percentages of Democrats and of union members, hence we can not affirm that the sets are independent and that 18% of the voters are Democrats who are union members.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item 6, we have that:
A 40% increase is represented by 1.4x.The resulting percentage is of 65%.Hence:
1.4x = 65
x = 65/1.4
x = 46.43%.
From the last pool, 46.43% of voters were for the candidate.
For item 7, we have that 200% more than a measure is given by:
x + 2x = 3x.
As the measure by itself is of 100%, hence:
Janie makes the triple amount of Jenny.
For item 8, we have that:
The 1% increase on the first semester is represented by 1.01.The 2% increase on the second semester is represented by 1.02.Hence the yearly increase is given by:
1.01 x 1.02 = 1.0302 = 3.02%.
The balance has increased by 3.02% during the year, not 3%, because the 2% increase on the second semester is over the 1% increase in the first semester, hence the coefficients are multiplied.
For item 9, we have that:
50% of the students are men.Of the men(50%), 20% have blond hair.Hence:
0.2 x 0.5 = 0.1.
The statement that 10% of the students in the class are men with blond hair is correct.
For item 10, we have that:
45% of the voters are Democrats.40% of the voters are union members.There is a intersection between the percentages of Democrats and of union members, hence we can not affirm that the sets are independent and that 18% of the voters are Democrats who are union members.
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please help me, i genuinely don't understand
Answer:
lol
Step-by-step explanation:
need points
Answer:
not even funny
Step-by-step explanation:
u should get banned this website is for education
Find the distance d(A,B) between points A and B.
A(2,-6); B(2,2)
Reflect the figure over the line y = -2x - 3.
Plot all of the points of the reflected figure.
You may click a plotted point to delete it.
-10 -9 -8
7
-6 -5
10
-10
3 4
5
6
7
8
9
10
The coordinates of the vertices of the image of the triangular figure with vertices (-5, -3), (-2, -9), (-5, -8) are the points (3, 3), (6, -5), (7, -2)
What is a reflection transformation?A reflection transformation is one in which the image points are mirrored about a line of reflection.
The coordinates of the vertices of the triangle following a reflection about the line y = -2·x - 3 can be found as follows;
The coordinates of the vertices of the triangle are; (-5, -3), (-2, -9), (-5, -8)
The slope of the line y = -2·x - 3 is m₁ = -2, therefore, the slope, m₂ of the line of reflection is m₂ = -1/(-2) = 1/2
The equations of the line of reflection are therefore;
y = (1/2)·(x + 5) - 3 = 0.5·x - 0.5
y = 0.5·x - 0.5
The point of intersection can therefore be found as follows;
0.5·x - 0.5 = -2·x - 3
Which indicates, using an online calculator, x = -1
y = 0.5 × (-1) + 0.5 = 0
The point of intersection of the line from (-5, -3) to the image and the line of reflection is (-1, 0)
(x₁ + x₂)/2 = -1
(-5 + x₂)/2 = -1
x₂ = 3
Similarly; (y₁ + y₂)/2 = 0
(-3 + y₂)/2 = 0
y₂ = 3
The image of the point (-5, -3) following a reflection is (3, 3)
Equation of the line from point (-2, -9) is; y = 0.5·(x + 2) - 9
y = 0.5·x + 1 - 9 = 0.5·x - 8
The point of intersection is; 0.5·x - 8 = -2·x - 3
Which indicates x = 2 and y = -7
(x₁ + x₂)/2 = 2
(-2 + x₂)/2 = 2
x₂ = 6
Similarly; (y₁ + y₂)/2 = -7
(-9 + y₂)/2 = -7
y₂ = -5
The coordinate of the point (-2, -9) following a reflection about the line y = -2·x - 3 is (6, -5)
The equation from the perpendicular line to the line of reflection from the point (-5, -8), is; y = 0.5·(x + 5) - 8 = 0.5·x + 2.5 - 8 = 0.5·x - 5.5
y = 0.5·x - 5.5
The point of intersection with y = -2·x - 3 is therefore at the point; 0.5·x - 5.5 = -2·x - 3
x = 1
y = -5
(x₁ + x₂)/2 = 1
(-5 + x₂)/2 = 1
x₂ = 7
Similarly; (y₁ + y₂)/2 = -5
(-8 + y₂)/2 = -5
y₂ = -2
The coordinate of the point (-5, -8) following a reflection about the line y = -2·x - 3 is (7, -2)
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11
Find the value ofr. Do not round your answer.
А
B
19.5 yd
С
40 yd
D
64 yd
24 yd
E
yd
find the value of r
Answer:
would you mind if you break it down more and explain it much more I'm confused when I look at the question
What is the image point of (7,-5)(7,−5) after a translation right 3 units and down 1 unit?
Answer:
The translated image point would then be (10, -6) (10, -6)
Step-by-step explanation:
The image point of (7,-5)(7,−5) after a translation right 3 units and down 1 unit is (4,-6)(4,−6)
What is translation?A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Now the given points are,
(7,-5)(7,−5)
So, when the image points translates right 3 units there is change in x coordinate. Thus,
(7,-5)(7,−5)
= (7-3,-5) (7-3,−5)
= (4,-5)(4,−5)
and, when the image points translates down 1 unit there is change in y coordinate. Thus,
(4,-5)(4,−5)
= (4,-5-1)(4,−5-1)
= (4,-6)(4,−6)
Thus, the image point of (7,-5)(7,−5) after a translation right 3 units and down 1 unit is (4,-6)(4,−6).
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Factor each expression into its simplest form
2x+8
Answer:
2(x+4)
Step-by-step explanation:
common denominator is 2
Answer:
2(x+4)
Step-by-step explanation:
..............
What is the quotient of 6/7and 3/14?
Answer:
4
Step-by-step explanation:
solve for b: -3b-6=18
Answer:
b= -8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
-3b - 6 = 18
+6 +6
-3b = 24
-3b/-3 = 24/-3
b = -8
someone please help me, it’s for my math homework! :)
Evaluate the following expression:42/12 - 85/25 + 117/30
Answer:
4
Step-by-step explanation:
Let's first simplify all terms, then convert them to /10:
42/12 = 7/2 = 35/10
85/25 = 17/5 = 34/10
117/30 = 39/10
Then the final addition is:
(35-34+39)/10 = 40/10 = 4
Riley has decided to become an engineer. Outline the steps she should take in researching her education options.
Answer:
Earn a bachelor’s degree from an ABET-accredited universityEstablish licensure through the NCEES FE examEarn a master’s degree in a sub-discipline of engineeringGain practical experience in the fieldEarn a professional engineering (PE) license in a sub-discipline of engineeringAttain further professional certification or join professional societiesStep-by-step explanation: Hope this helped :)
She should/could obtain a bachelor's degree from a university or pass licensing examinations. She could also get a master's degree in an engineering sub-discipline and work experience in the subject. Last but not least, she might pursue more professional certification or join professional associations.
There are 10 boys and 13 girls in Ms. Kelso’s homeroom. She is going to select one boy and one girl to act as homeroom representatives for student council. How many different pairs of students could Ms. Kelso choose?
10
23
130
230
Answer:
130
Step-by-step explanation:
Answer:
130 (C)
Step-by-step explanation:
simplify the ratio 24 over 36
Answer:
2:3
Step-by-step explanation:
I checked it and it’s right. I hope this helps!
a basketball player shoots 50 times during practice. Score 28 baskets. What is the ratio of your total shots and your scores?
Answer:
total shots to baskets - 50:28 or as a fraction 20/28
Simplified - 25:14 or 25/14
Step-by-step explanation:
Ratios can be written as fractions
If you wanted to do baskets to total shots you would just switch around your numbers and the ratio would become reversed as well.
3y=6x-1 what would the slope of my line be?
HURRY!!!! WHOEVER ANSWERS FIRST AND RIGHT GETS BRAINLIEST!
Answer:
graph -4/1 and y intercept is 1
Step-by-step explanation:
Which of the following expressions have a value of 180 when b = 4?
Select all that apply.
A. 87b−179+957÷87
B. 33b12
C. b2+120
D. 51b−24
E. 11b+187−2,756÷13
Answer: The answer is A and D
Step-by-step explanation: If you go through all the problems, just replace "b" with "(4)" into a calculator. For A and D, they both equaled 180.