200 gallons of regular gas and 80 gallons of premium gas were sold.
Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).
Now, forming the equation using the given information, to find the amount of each type of gallon.
Equation -
2.10x + 2.90(280 - x) = 652
Performing multiplication with values inside bracket in Left Hand Side
2.10x + 812 - 2.90x = 652
Rewriting the equation -
812 - 652 = 2.90x - 2.10x
Performing subtraction
160 = 0.8x
Rewriting the equation according to x
x = 160÷0.8
Performing division to find the value of x
x = 200
So, 200 gallons of regular gas was sold.
Amount of premium gas sold = 280 - 200
Performing subtraction
Amount of premium gas sold = 80 gallons
Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.
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Bailey starts playing a game on her cell phone with the battery fully charged and plays until the phone battery dies. While playing the game the charge in Bailey's battery decreases by half a percent per minute. Write a function for the percent change in the battery while Bailey is playing the gane
The linear function for the percent change in the battery while Bailey is playing the gane is:
B(t) = 100 - 0.5t, 0 ≤ t ≤ 200.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The intercept is the initial battery, of 100.The slope is of -0.5, as the battery decays by 0.5% each minute.Hence the function is:
B(t) = 100 - 0.5t.
The battery will be of 0, when:
B(t) = 0.
100 - 0.5t = 0.
t = 100/0.5.
t = 200.
Hence the function is:
B(t) = 100 - 0.5t, 0 ≤ t ≤ 200.
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3. (g + h) (×)
4. (g - h ) (×)
5. (f + h) (×)
please solve thankyou!!
can someone solve this?
Answer:
2L+2W
Step-by-step explanation:
U JUST MOVE THE 2 TO THE L AND MOVE THE 2W TO THE OTHER SIDE. I THINK MY ANSWER IS RIGHT BUT MAYBE WAIT FOR ANOTHER PERSON
Confirmed Solution:
[tex]p=2l+2w[/tex]
Hope this helps!
find the slope of the line in the picture
The slope of the line in the picture is 2.8
How to find the slope of the line in the picture?To calculate the slope of the line, we make use of two points on the line
The two points to use are
(0, 0) and (25, 70)
The slope of the line is then calculated as
Slope = (y2 - y1)/(x2 - x1)
So, we have
Slope = (70 -0)/(25 - 0)
Evaluate
Slope = 2.8
Note that the slope can also be regarded as the constant average rates of change or the gradient
Hence, the slope of the line in the picture is 2.8
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What’s the morning time on the clock
A travel agency recorded the travel destinations of 60 South African tourists last month.
Of the 60 tourists, 30 visited Europe, 28 visited the UK, 9 visited America and 12
visited both Europe and the UK. Five tourists did not visit America, Europe or the UK.
(1) Draw a Venn diagram to represent this information.
(2)
(3)
Determine the probability that a tourist, selected at random, visited Europe only.
Determine the probability that a tourist, selected at random, visited America.
Determine the probability that a tourist, selected at random, visited both Europe
and the UK.
(4)
(5)
Determine:
(i) P((not E) or A)
(ii)
P((not A) and UK)
02 The probability that he will
Answer:
to create venn diagram
Step-by-step explanation:
To create an intersecting Venn diagram, draw three circles that overlap in the middle. You'll be able to show which attributes are unique to each circle, which overlap between two, and which are common characteristics of all three groups. Two circles overlapping is a classic venn diagram.
the mass of the combined coins is 75 grams. Each penny has
Stephanie adds pennies, nickels and quarters to a scale until
a mass of 2.5 grams, each nickel has a mass of 5 grams and each quarter has a mass of 5.7 grams.
Create an equation to model this situation, where x is the number of pennies, y is the number of nickels and z is the
that the mass of the combined coins is exactly 75 grams.
number of quarters that Stephanie can put on the scale so
The required equation is 2.5x + 5y + 5.7z = 75.
What is mass?Mass is measured in terms of weight of body. Gram, kilogram, and pounds are some of the standard mass units to measure.
Given that,
Pennies, nickels, and quarters are added to a scale by Stephanie until the combined weight of the coins is 75 grams.
Number of pennies = x
Each pennies has a mass = 2.5 grams
Mass of x pennies = 2.5x grams
Number of nickels = y
Each nickels has a mass = 5 grams
Mass of y nickels = 5y grams
Number of Quarters = z
Each Quarter has a mass = 5.7 grams
Mass of z Quarters = 5.7z grams
Total Mass = Mass of x Pennies + mass of y nickels + mass of z quarters
= 2.5x + 5y + 5.7z grams
Total Mass = 75 grams
Equation both is 2.5x + 5y + 5.7z = 75
The required equation is 2.5x + 5y + 5.7z = 75.
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Eva went to shop and bought 3 apples, 5 peaches, 8 bananas, 1 pineapple and 3 melons. what are the mean and median of her purchase?
If Eva went to a shop and bought 3 apples, 5 peaches, 8 bananas, 1 pineapple, and 3 melons, then the mean and median of her purchase are equal to 4 and 3 respectively.
Mean can be described as the most common value in a group of numbers. The mean of a certain set can be found by the ratio of the sum of the values to the number of values.
Mean = Sum total of the expressions/ Number of expressions
Sum of the values = 3 + 5 + 8 + 1 + 3 = 20
Number of values = 5
Mean = 20 / 5
Mean = 4
Median can be described as the central number in a series of numbers or a dataset.
If we arrange the given dataset in ascending order, that is from smallest to largest, then the median can be found as follows,
1 + 3 + 3 + 5 + 8
As the middle number is 3, therefore the median of the given data set is equal to 3.
Therefore, the mean and median of her purchase are calculated to be 4 and 3 respectively.
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WILL GIVE BRAINLIST TO BEST ANSWER JUST PLEASE HELP!!!!!!
A plumber earns $75 for a repair job, plus an additional $45 per hour he works. On Tuesday, he completed 2 repair jobs and earned a total of at least $465.
Part A: Write an inequality that can be used to determine h, the numbers of hours the plumber worked Tuesday.
Answer:
He worked 7 hours
Step-by-step explanation:
X= Number of jobs, H= Hours worked T= Total money made
firstly we have to arrange this into a formula, which will allow you to insert any a value of one variable and find the other variable
this equation is 75x + 45h = T
from this question we know that he worked 2 jobs and made a total of 456$
Adding these into the equation we get:
(75*2) + 45h = 465
solving to find h by isolating the variable, the final answer will be
h = 7
In this discussion, you will reflect on what you have learned about solving equations.
Discussion Prompt: Sarah and Kayla both solved the problem below. Who do you think solved it correctly? For the person who solved it incorrectly, what mistake do you think was made?
Sarah
5x - 15 - 3x = 10 - (-3x + 20)
2x - 15 = 10 + 3x - 20
2x - 3x - 15 = -10 + 3x - 3x
-1x - 15 = -10
-1x - 15 + 15 = -10 + 15
-1x = 5
x = -5
Kayla
5x - 15 - 3x = 10 - (-3x + 20)
2x - 15 = 10 + 3x - 20
2x + 3x - 15 = -10 + 3x + 3x
5x - 15 = -10
5x - 15 + 15 = -10 + 15
5x = 5
x = 1
Post a brief paragraph responding to the discussion prompt above. Your post should use concepts presented in this module/lesson. Your post must be completed before you can see posts from your classmates.
Discussion Responses
The person that solves the equation correctly is Sarah. It should be noted that the mistake that Kayla made is that she added 2x + 3x rather than subtracting it.
How to illustrate the information?It should be noted that an equation is simply used to illustrate the relationship between two variables.
In this case, the solution to the equation will be:
5x - 15 - 3x = 10 - (-3x + 20)
2x - 15 = 10 + 3x - 20
2x - 3x - 15 = -10 + 3x - 3x
-1x - 15 = -10
-1x - 15 + 15 = -10 + 15
-1x = 5
x = -5
Therefore, the person that solves the equation correctly is Sarah. It should be noted that the mistake that Kayla made is that she added 2x + 3x rather than subtracting it.
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1. The table shows the maximum weight a crane arm can lift at various
distances from its cab.
weight
distance from cab to weight
Construction-Crane Data
Distance from Cab
to Weight (ft)
Weight (lb)
12
24
36
48
cab
60
7,500 3,750 2,500 1,875 1,500
a. Describe the relationship between distance and weight
for the crane.
According to the given statements,
The relationship between Distance and weight is Inversely proportional.
What is term Inversely proportional?If one variable rises, the other will fall; conversely, if one variable falls, the other will rise. These are inversely proportional variables or quantities. In other words, they are said to be inversely proportionate when an increase in one quantity causes a reduction in the other and vice versa.
According to the given values,
Here, distances are given as - (ft) 12, 24, 36, 48, 60
and Weight (Lb) are given as
7500,3750, 2500, 1875, 1500
When distance is small, the weight is high.
Distance ∝ 1/Weight
So, The relationship between distance and Height will be inversely proportional.
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Enlarge the triangle by scale factor 2.
Answer:
Answer in the picture attached
potatoes cost janice $1 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30 per pount.
A . 3 pounds of potatoes
B . 2 pounds of potatoes
A . Janice will purchase potatoes until the value of potatoes is less than the cost of potatoes. Janice has $5.00 to spend on potatoes and the cost of potatoes is $1.00.
By assuming that the First pounce of potatoes is worth $1.50. which is greater than $1.00. If the second pound is worth $1.14, then Janice will purchase these as well, since the value is more than $1.00. If the remaining pounds are worth $0.30 then Janice will not purchase these because the value is less than the cost.
Thus Janice will purchase 3 pounds of potatoes for the Total cost of $3.00
B. Now assume Janica has only $2.00 to spend on potatoes. She will purchase the first pound which is $1.50 and the second pound which is $1.14. She now spends her entire amount of money on potatoes. If she want to purchase she could not do that.
Thus Janice will purchase 2 pounds of potatoes at a total cost of $2.00
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The complete question is:
Potatoes cost Janice $1 per pound, and she has $5.00 that she could possibly spend on potatoes or other items. If she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30 per pound, how many pounds of potatoes will she purchase? How many pounds will she purchase if she has only $2 to spend?
b =x/m(a-x)
Make x the subject of this equation.
Answer:
[tex]x= \dfrac{bma}{bm+1}[/tex]
Explanation:
Given expression:
[tex]\hookrightarrow b = \dfrac{x}{m(a-x)}[/tex]
shift the variables
[tex]\hookrightarrow b m(a-x)= x[/tex]
distribute inside parenthesis
[tex]\hookrightarrow bma-bmx= x[/tex]
collect terms with "x" in one side
[tex]\hookrightarrow -bmx-x= -bma[/tex]
divide both sides by -1
[tex]\hookrightarrow bmx+x= bma[/tex]
factor out common term "x"
[tex]\hookrightarrow x(bm+1)= bma[/tex]
shift the variables making "x" the subject
[tex]\hookrightarrow x= \dfrac{bma}{bm+1}[/tex]
What is the slope of the line that passes through the points (-7, -2) and
(-2,-22)? Write your answer in simplest form.
Answer:
-4
Step-by-step explanation:
Compute the slope of the line through the following points:
p_1 = (-7, -2) and p_2 = (-2, -22)
The slope of the line through (x_1, y_1) and (x_2, y_2) is:
(y_2 - y_1)/(x_2 - x_1)
Substitute (x_1, y_1) = (-7, -2) and (x_2, y_2) = (-2, -22):
= (-22 - -2)/(-2 - -7)
-(-7) = 7:
= (-22 - -2)/(-2 + 7)
-2 + 7 = 5:
= (-22 - -2)/5
-(-2) = 2:
= (-22 + 2)/5
-22 + 2 = -20:
= (-20)/5
The gcd of -20 and 5 is 5, so (-20)/5 = (5 (-4))/(5×1) = 5/5×-4 = -4:
Answer: = -4
I WILL GIVE YOU BRAINLIEST NEED HELP PLEASEE :DD
The coordinates of the pre-image of point F' is (-2, 4)
How to determine the coordinates of the pre-image of point F'?On the given graph, the location of point F' is given as:
F' = (4, -2)
The rule of reflection is given as
Reflection across line y = x
Mathematically, this is represented as
(x, y) = (y, x)
So, we have
F = (-2, 4)
Hence, the coordinates of the pre-image of point F' is (-2, 4)
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cuál es el valor total de 9?
Answer:
(0.98768834,0.15643446)
Step-by-step explanation:
yo creo
Multiply. 6 1/4 x 3 3/5 = 18 3/20 18 17/20 22 1/2 22 1/20
On multiplying two fractional terms [tex]6\frac{1}{4}[/tex] X [tex]3 \frac{3}{5}[/tex] we get [tex]22\frac{1}{2}[/tex] as a result.
multiplication- it is an operation that represent the basic idea hope repeated addition of the same number.
It is used to simplify the task it is used when we need to combine groups of equal size.mixed fraction - it is represented with its quotient and remainder.
it contains a whole number and a proper fraction.To solve above equation firstly solve mixed fraction.
[tex]6\frac{1}{4}[/tex] = 25/4
[tex]3 \frac{3}{5}[/tex] = 18/5
then on multiplying them we get
[tex]6\frac{1}{4}[/tex] X [tex]3 \frac{3}{5}[/tex] = 25/4 X 18/5
= 45/2
=[tex]22\frac{1}{2}[/tex]
[tex]6\frac{1}{4}[/tex] X [tex]3 \frac{3}{5}[/tex] = [tex]22\frac{1}{2}[/tex]
On multiplying two fractional terms [tex]6\frac{1}{4}[/tex] X [tex]3 \frac{3}{5}[/tex] we get [tex]22\frac{1}{2}[/tex] as a result.
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3(2x − 1) < 2(4 + 3x)
Answer:
Step-by-step explanation:
3(2x−1)<2(4+3x)
Step 1: Simplify both sides of the inequality.
6x−3<6x+8
Step 2: Subtract 6x from both sides.
6x−3−6x<6x+8−6x
−3<8
Step 3: Add 3 to both sides.
−3+3<8+3
0<11
any number below 11 is a solution.
-2/3 a +5/6 a -1/6 
The solution is [tex]\frac{9a - 1}{6}[/tex]
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Find the lowest common denominator (LCD), convert each algebraic fraction to an equivalent fraction with the common denominator, and then combine each numerator to add or subtract algebraic fractions with distinct denominators. Reduce if you can.
Use the highest exponent of any common variable factor that has more than one exponent.
Add multiplied terms together to get a single fraction.
[tex]\frac{2a}{3} + \frac{5a}{6} + \frac{-1}{6}\\ \\ = 2(\frac {2a}{3}) + \frac{5a}{6} + \frac{-1}{6}\\\\\\\ = \frac{4a + 5a - 1}{6} \\ \\= \frac{9a - 1}{6}[/tex]
Therefore, the answer is (9a - 1) / 6
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Need help on number 5!
whic is the correct form of the equation a+b+c=d when solved for a?
Answer:
a = d-b-c
Step-by-step explanation:
i think?
Given that m
Please help me with this!
Answer:
where is the probleM?
Step-by-step explanation:
APPLYING THE STA
How might this standard appear on a test?
Use proportional relationships to complete each question.
1) Fill the table. Round to the nearest cent.
Original
Cost
$24
$120
$60
Discount
Percentage
20%
15%
45%
Sale
Price
Sales Tax
Percentage
8.5%
7%
896
Sales Tax
Amount
Total
Cost
Answer:
Step-by-step explanation:
a
a board game spinner is divided into three parts labeled $a$, $b$ and $c$. the probability of the spinner landing on $a$ is $\frac{1}{3}$ and the probability of the spinner landing on $b$ is $\frac{5}{12}$. what is the probability of the spinner landing on $c$? express your answer as a common fraction.
Probability of spinner landing on 'c' is 1/4;
Probability of spinner landing on 'a' = 1/3 = 4/12;
Probability of spinner landing on 'b' = 5/12;
Thus, Probability of spinner landing on 'c' = 1 - (5/12 + 4/12)
= 1 - 9/12
= 3/12
= 1/4;
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C is the midpoint of AD. B is the midpoint of AC BC =4 what is the length of BD
Answer:
================= m
Step-by-step explanation:
uuhhhhhhvvvvbvvggggghgggghhgg
HELP.............................! !
Answer:
It would be 28.69.
Explanation:
4.99 x [tex]5 \frac{3}{4}[/tex] = 28.6925
Because of the kind of number (28.6925), you will have to round up.
To round up the number has to be a 5 or higher. Well, you have a 9 and then a 2. A 2 can't round up a 9, so you just end up discarding the 2 and the 5 at the end of the number.
Henceforth, you are left with 28.69.
-----------------------------------------------
Hope this makes sense and is correct!
God bless! :)
1/6d + 2/3 = 1/4(d - 2)
the Math question is on the image
Answer:
x = 40
Step-by-step explanation:
You want x when y = 16, given that x = 2 when y = 1/25 and x is proportional to the square root of y.
ProportionThe given relation between x and y is ...
x = k√y . . . . . . x is proportional to the root of y
ApplicationThe value of k is found from ...
k = x/√y = 2/√(1/25) = 10
Then for y = 16, we have ...
x = 10·√16 = 10·4
x = 40 . . . . . . . . when y = 16
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Find the slope of the following lines
Explain how you got the answer
From the given graph, the slope of the given line is [tex]m=\frac{-4}{3}[/tex]
Given,
The points
[tex](x_{1},y_{1})=(-2,3)[/tex]
[tex](x_{2},y_{2})=(1,-1)[/tex]
The slope of the line m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substitute the values in the equation
[tex]m=\frac{(-1)-(3)}{1-(-2)} \\m=\frac{-1-3}{1+2}\\ m=\frac{-4}{3}[/tex]
Hence, the slope of the given line is [tex]m=\frac{-4}{3}[/tex]
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