To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water.
Which table shows the relationship between the gallons of cleaning solution made and the cups of bleach used?
Answers
Answer:
Option B.
Step-by-step explanation:
Let 'g' represent the number of gallons of cleaning solutions.
Let 'c' represent the number of cups of bleach.
From the question given above, we were told that:
To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water.
This implies that number of gallons (g) of the cleaning solution is directly proportional to the number of cups (c) of the bleach mixed with water i.e
g ∝ c
g = Kc
K is the constant of proportionality.
Next, we shall determine the relationship between g and c as follow
g = 5
c = 3
K =?
g = Kc
5 = K × 3
Divide both side by 3
K = 5/3
g = Kc
K = 5/3
g = 5/3 c
Thus, the relationship between g and c is:
g = 5c / 3
Next, we shall make c the subject of the formula. This is illustrated below:
g = 5c / 3
Cross multiply
3g = 5c
Divide both side by c
c = 3g/5
Next, we shall determine c when g = 10, 15, and 20.
This is illustrated below:
g = 10
c =?
c = 3g/5
c = (3 × 10)/5 = 30/5 = 6
g = 15
c =?
c = 3g/5
c = (3 × 15)/5 = 45/5 = 9
g = 20
c =?
c = 3g/5
c = (3 × 20)/5 = 60/5 = 12
Summary:
Num. of gallon (g) >> Num. of cup (c)
5 >>>>>>>>>>>>>>>> 3
10 >>>>>>>>>>>>>>> 6
15 >>>>>>>>>>>>>>> 9
20 >>>>>>>>>>>>>>> 12
Therefore, option B gives the correct table.
Related Questions
What is the sum of measures of the exterior angles in a 25-gon?
Answers
Answer:
360°
Step-by-step explanation:
The sum of the exterior angles of any polygon = 360°
Ruth went out to eat with friends. She brought a $50 bill. She bought an appetizer for $8.50, an entree for $13.99, and desert for $6.50. She wants to leave a 20% tip for the good service she received. How much is the tip she will leave? Do not round your answer, but keep in mind that the smallest unit in our financial system is a penny which stops in the hundredths place. *
Answers
Answer:
$16.81
Step-by-step explanation:
$50.00 -$8.50 - $13.99 - $6.50 = $21.01
$21.01 * 0.20 = $4.20
$21.01 - $4.20 = $16.81
Write an expression to represent:
Eight less than the product of 2 and a number z.
Answers
The product of 2 and z.
Lin ran ran 2 3/4 miles in 2/5 of an hour. Noah ran 8 2/3 miles in 4/3 of an hour.
1. How far would Lin and Noah run in 1 hour?
2. How long would it take Lin and Noah to run 1 mile at that rate?
3. Who ran faster, Noah or Lin and why?
Answers
Answer:
1. Lin 6 7/8 miles, Noah 6 1/2 miles
2. Lin will take 8 8/11 minutes while Noah will take 9 3/13 minutes
3. Lin ran faster because it took him less amount of time to cover same distance of 1 hour
Step-by-step explanation:
Here, we are told that Lina ran 2 3/4 miles in 2/5 of an hour while Noah ran 8 2/3 miles in 4/3 of an hour.
1. We want to know how far Noah will run in an hour
1 hour is 60 minutes;
So 4/3 of an hour is 4/3 * 60 = 80 minutes
thus;
if he ran 8 2/3 miles in 80 minutes
then he ran x miles in 1 hour(60 minutes)
8 2/3 is same as 26/3 miles
Thus;
26/3 * 60 = 80 * x
x = 26/3 * 60/80 = (26 * 20)/80 = 26/4 = 13/2 = 6 1/2 miles
Lin ran 2 3/4 miles in 2/5 hour (2/5 * 60 = 24 minutes)
2 3/4 miles took 24 minutes
x mile will take 60 minutes
60 * 2 3/4 = 24 * x
60 * 11/4 = 24x
165 = 24x
x = 165/24
x = 6 21/24 = 6 7/8 miles
Lin will run 6 7/8 miles in an hour
2. we want to know how long it will take both of them to run 1 mile
Lin ran 2 3/4 miles in 2/5 of an hour
meaning, he ran 2 3/4 in 2/5 * 60 = 24 minutes
2 3/4 miles was ran in 24 minutes
1 mile will take x minutes
1 * 24 = 2 3/4 * x
24 = 11/4 * x
x = 4 * 24/11 = 96/11 = 8 8/11 minutes
For Noah
6 1/2 miles was ran in 1 hour
1 mile will be ran in x hours
13/2 * x = 60 minutes * 1
x = (2 * 60)/13
x = 120/13
x = 9 3/13 minutes
c. Lin ran faster because he took the lesser amount of time to travel 1 mile
Answer:
1. Lin 6 7/8 miles, Noah 6 1/2 miles
2. Lin will take 8 8/11 minutes while Noah will take 9 3/13 minutes
3. Lin ran faster because it took him less amount of time to cover same distance of 1 hour
Step-by-step explanation:
Step-by-step explanation:
Here, we are told that Lina ran 2 3/4 miles in 2/5 of an hour while Noah ran 8 2/3 miles in 4/3 of an hour.
1. We want to know how far Noah will run in an hour
1 hour is 60 minutes;
So 4/3 of an hour is 4/3 * 60 = 80 minutes
thus;
if he ran 8 2/3 miles in 80 minutes
then he ran x miles in 1 hour(60 minutes)
8 2/3 is same as 26/3 miles
Thus;
26/3 * 60 = 80 * x
x = 26/3 * 60/80 = (26 * 20)/80 = 26/4 = 13/2 = 6 1/2 miles
Lin ran 2 3/4 miles in 2/5 hour (2/5 * 60 = 24 minutes)
2 3/4 miles took 24 minutes
x mile will take 60 minutes
60 * 2 3/4 = 24 * x
60 * 11/4 = 24x
165 = 24x
x = 165/24
x = 6 21/24 = 6 7/8 miles
Lin will run 6 7/8 miles in an hour
2. we want to know how long it will take both of them to run 1 mile
Lin ran 2 3/4 miles in 2/5 of an hour
meaning, he ran 2 3/4 in 2/5 * 60 = 24 minutes
2 3/4 miles was ran in 24 minutes
1 mile will take x minutes
1 * 24 = 2 3/4 * x
24 = 11/4 * x
x = 4 * 24/11 = 96/11 = 8 8/11 minutes
For Noah
6 1/2 miles was ran in 1 hour
1 mile will be ran in x hours
13/2 * x = 60 minutes * 1
x = (2 * 60)/13
x = 120/13
x = 9 3/13 minutes
c. Lin ran faster because he took the lesser amount of time to travel 1 mile
Practice Problems
Find slope(m) and Y-intercept(b)
Make sure to write in standard form, y = mx + b for each
problem
1. y = 7x + 9
2. y=-5x-2
3. y = 3x + 1
Answers
Answer:
1. slope is 7 and y-intercept is 9
2.slope is -5 and y-intercept is -2
3. slope is 3 and y-intercept is 1
Step-by-step explanation:
The standard equation of a line in slope form is;
y=mx + b where m is the slope and b is the y intercept.
In question 1.
y=7x + 9
slope is 7 and y-intercept is 9
In question 2
y= -5x - 2
slope is -5 and y-intercept is -2
In question 3
y= 3x + 1
slope is 3 and y-intercept is 1
A 30-cm ruler broke into two pieces. One piece was 120 mm long. How
long was the other piece? Express your answer in millimeters.
Answers
Answer: 180 mm
Step-by-step explanation:
1 cm = 10 mm
10 cm = 100 mm
30 cm = 300 mm
300 - 120 = 180
Hope this helps!
HELPPP :((( !!!
find the mean and median for the following.
Answers
Median=8
If u need steps then message me here x
Answer:
mean = 6
median = 7
Step-by-step explanation:
mean: add all values and divide by the number of values
median: place all values in ascending order and choose the middle value; if there is an even number of values, the median is the mean of the two middle values.
There are 5 values: 7, 8, 8, 4, 3
a) mean
Add all values and divide by the number of values.
mean = (7 + 8 + 8 + 4 + 3)/5 = 30/5 = 6
mean = 6
b) median
Place values in ascending order.
3, 4, 7, 8, 8
The middle value is 7.
median = 7
(5 + 2) + 7 = 5 + (2 + 7) is an example of which property?
Answers
Answer:
The associative property
Step-by-step explanation:
With this property, you just "associate" the numbers with different numbers.
There are 4 circles and 8 squares. What is the simplest ratio of circles to total shapes?
Answers
Answer:
4 : 12
4/ 12
4 to 12
Step-by-step explanation:
1:3
Its this because u just simplify 4:12 by dividing both numbers by 4
What is the GCF of 28t^2 + 14t?
Answers
Answer:
The GCF would be 14t.
If h(x)=x-7 and g(x)=x ^2, which expression is equivalent to (g•h)(5)
Answers
x^3 ‐ 7x^2
Explanation:
x^2(x-7) = x^3 ‐ 7x^2
Two numbers that are the same distance from 0 on a number line, but in opposite directions, are called opposites. The whole numbers and their opposites make up the set of integers.Opposites combine to make 0. For example, 3 and -3 are opposites.Jacob has saved $50. He spends $15 at the movies. Then, after paying for repairs to his bike, he has $0 remaining. How much did the bike repairs cost?1.What integer represents Jacob’s savings?2.What integer represents the change in Jacob’s savings after he spends money at the movies?3.The number line represents the change in Jacob’s savings after the movies. Use the number line to show Jacob’s change in savings after the bike repairs.4.What integer represents the change in Jacob’s savings due to the bike repairs? What integer represents the cost of the bike repairs?On the Back!5.On a winter’s morning, the temperature was 0°F. The temperature increased during the daytime. At night, the temperature decreased 6°F and returned to 0°F.
Answers
Answer: kindly check explanation
Step-by-step explanation:
Given the following :
Amount saved by Jacob = $50
Amount spent at the movies = $15
Amount left after paying for bike repair = $0
Cost of bike repair :
$50 - $15 = $35
What integer represents Jacob’s savings?
Initial amount before any spending
Jacob's saving = +$50
2.What integer represents the change in Jacob’s savings after he spends money at the movies?
Saved amount - amount spent at the movies
$50 - $15 = $35
No number line is given
If a business receives an invoice for services purchased on account on December 1st for $8,000, how much should the business write a check for to pay the invoice in full on December 8th if the terms are 1/10, n/15?
Answers
Answer:
The amount that should be written on the check is $7920
Step-by-step explanation:
The explanation of the question is given as:
1/10 = 1% discount to be given if paid within 10 days
n/15 = full amount to be paid within 15 days.
From the question, we can see that:
If the check for the invoice is given on December 8th, it is still within the discount time of 10 days.
Discount amount = $8000 × 1%
= $80
$8000 - $80
= $7920
Hence, the amount that should be written on the check is $7920
In 25.5 minutes, Shaun can run 3 miles. How far can he run in 30 minutes?
Answers
Answer:
28.8 miles
Step-by-step explanation:
Answer:
28.8. hdhrhdndndndndhux
The temperature is 8 degrees F. As a cold front moves in, the temperature drops 6 degrees F per hour. What is the temperature at the end of 3 hours
Answers
Answer:
-10 Degrees
Step-by-step explanation:
Probability of Next Candy
Fill in the chart below with the probability of choosing the next candy.
Answers
Answer: 8 just got it correct
Step-by-step explanation:
what graph passes the vertical line test?
Answers
464.69605 rounded to 3 significant figures
Answers
x + 2y = 2 and 6x – 3y = 21 parallel, perpendicular, or neither
Answers
Answer:
perpendicular
Step-by-step explanation:
both lines meet at a 90 degree angle
Write 1.9 as a mixed number and an an improper fraction
Write your answer in simplest form
Answers
Answer:
Mixed number: 1 9/10
Improper fraction: 19/10
A student club started a fundraising effort to support animal rescue organizations. The club sent an information flyer home to the n students in the school. It says, "We welcome donations of any amount, including any change you could spare!" Their goal is to raise T dollars, and to donate to a cat shelter and a dog shelter. * 5
Answers
Answer:
B. 1/4T
Step-by-step explanation:
A student club started a fundraising effort to support animal rescue organizations. The club sent an information flyer home to the n students in the school. It says, "We welcome donations of any amount, including any change you could spare!" Their goal is to raise T dollars, and to donate to a cat shelter and a dog shelter.
What expression, equation, or inequality that describes The dollar amount the club would have if they reached one-fourth of their goal
A. 3/4n × 1/2
B. 1/4T
C. T - 1/4n
D. 1/4n
Their goal is to raise T dollars
The T dollars will be donated to a cat shelter and a dog shelter.
One - fourth = 1/4
Their goal =T
one-fourth of their goal
= 1/4 * T
= 1/4T
The correct answer is B. 1/4T
A 25-foot flag pole casts a shadow of 40 feet. What is the approximate height from the top of the flag pole to the top of the shadow?
~45
~47
~65
Answers
Answer:
47 is the answer
Step-by-step explanation
Answer:
Hey its 47
Step-by-step explanation:
Good morning
The rectangle shown is composed of smaller equally-sized squares. The shaded section has an area of 3/16 square inches. Use a unit rate to determine the area of the larger rectangle.
Answers
Answer:
Area of larger rectangle = 1½ = 1.5 in²
Step-by-step explanation:
The section consists of 3 small squares that has an area = [tex] \frac{3}{16} in^2 [/tex].
Area of 3 small squares = [tex] \frac{3}{16} in^2 [/tex]
Area of 1 small square = [tex] \frac{3}{16} [/tex] ÷ 3
= [tex] \frac{3}{16} * \frac{1}{3} [/tex]
= [tex] \frac{3*1}{16*3} = \frac{1}{16} [/tex]
The larger rectangle has 24 small squares of equal sizes
Area of larger rectangle = area of 1 small square * 24
= [tex] \frac{1}{16} * 24 [/tex]
[tex] = \frac{24}{16} = \frac{3}{2} [/tex]
Area of larger rectangle = 1½ = 1.5 in²
Last month, 349 books were checked out from the school library. This month, 273 books were checked out. Find the Percent of Change from Last Month to This Month.
Answers
Answer:
76
Step-by-step explanation:
Answer:
76 is the answer
What is the solution to the following equation?
−2(4x+3)=5+3x
Answers
Answer:
x = -1
Step-by-step explanation:
Use the graph to determine which one of the three statements is a lie.
1) The average rate of change between (0,4) is positive
2) The average rate of change between (-3,4) is negative
3) The average rate of change between (0,4) is 3/4
Answers
Answer:
2) The average rate of change between (-3,4) is negativeStep-by-step explanation:
The answer options
1) The average rate of change between (0,4) is positive
Correct. The function is increasing in same interval.2) The average rate of change between (-3,4) is negative
Incorrect. The average rate of change is zero in same interval3) The average rate of change between (0,4) is 3/4
Correct. (0-(-3))/(4-0) = 3/4Nana has a water purifier that filters \dfrac13 3 1 start fraction, 1, divided by, 3, end of the contaminants each hour. She used it to purify water that had \dfrac12 2 1 start fraction, 1, divided by, 2, end fraction kilogram of contaminants. Write a function that gives the remaining amount of contaminants in kilograms, C(t)C(t)C, left parenthesis, t, right parenthesis, ttt hours after Nana started purifying the water.
Answers
Answer:
(1/2) * (2/3)^t
Step-by-step explanation:
Nana has a water purifier that filters 1/3 of the contaminants each hour. She used it to purify water that had 1/2 kilogram of contaminants.
Write a function that gives the remaining amount of contaminants in kilograms, C(t), t hours after Nana started purifying the water.
C(t)=
The water purifier will filter 1/3 of the current contaminants each hour.
1/3 ÷ 1/2
= 1/3 × 2/1
= 2/3
This means, it willreduce the contaminant into 2/3 of it current mass
To derive the equation,
Multiply the contaminant with 2/3 every hour
(1/2) * (2/3)^t
Where t = hours
3. A function f(x) has a slope of -and passes through
the point (-3,7). Explain how the graph of f(x)
could be used to find the y-intercept.
Answers
Answer:
Well. this is kinda trivial.
For a function f(x) = y.
The y-intercept is defined as the point where the graph of f(x) intersects the x-axis.
This always happens at x = 0.
So the y-intercept is equal to f(0).
Now, if we have the graph of f(x), you simply can see at what value of y does the graph intersect the x-axis, and that will be the y-intercept.
two thirds plus one fifth
Answers
Answer:
0.866666666666666666666666666666666 or 13/15
Step-by-step explanation:
Convert both numbers to fractions and add them together to get 13/15.
The addition of the two-thirds plus one-fifth is 13/15.
What is the addition?The addition of two or more numbers possesses some important properties.
The list of properties of addition given below will help in predicting the sign of the result obtained in the addition process.
The given expression is;
[tex]\rm \dfrac{2}{3}+\dfrac{1}{5}[/tex]
The addition of the expression is determined in the following steps given below.
[tex]\rm = \dfrac{2}{3}+\dfrac{1}{5}\\\\=\dfrac{2 \times 5+3\times 1}{15}\\\\ =\dfrac{10+3}{15}\\\\=\dfrac{13}{15}[/tex]
Hence, the addition of the two-thirds plus one-fifth is 13/15.
Learn more about addition here;
brainly.com/question/9859817
#SPJ2
Determine the solution to the equation for x
Answers
Answer:
9/5
Step-by-step explanation:
because I know I pass the test