The better deal of the given pair is $31.05/1. The unit rate is $2.07.
What is the better deal?The better deal is the deal that has the lower unit rate. Unit rate is the price per gallon. The unit rate can be determined by dividing the total cost by the total gallons bought.
Division is the operation that is used in mathematics to determine the quotient of two or more numbers. Division entails grouping a number into groups using another number. Other operations used in mathematics are addition, multiplication and subtraction.
Unit rate = total cost / number of gallons
$56 / 25 = $2.24
$31.05 / 15 = $2,07
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Needing some help, been working on this for a while now.
Answer:
x = 15
z = 64
Step-by-step explanation:
Lets make an equation -
(14x - 94) + z = 8x - 4 +z
Both sides are parallel to each other, and therefore the sum is also 180.
Then we solve it -
14x - 8x - 94 + z = -4 + z
Bring the z on the other side to eliminate it.
6x - 94 = - 4
Add 94 on both sides
6x = 90
Divide 6 on both sides and you get x = 15
Substitute x into 8x -4 + z = 180
8*15 - 4 + z = 180
120 - 4 + z = 180
116 + z = 180
Subtract 116 on both sides.
z = 64.
HOPE THIS HELPS!!
CAN U PLSSS HELP ME! I have been stuck on this problem for hours! Pls try to see if u can solve it. This is the problem -
Sean and Emily love making origami. Sean can make a paper crane in 6 minutes, and
Emily can make a paper crane in 8 minutes. One day, they decided to make some paper
cranes together. They started making cranes at the same time, and after a while, they
have 112 total paper cranes. How many of those paper cranes did Sean make?
THANKS A LOT!!
Answer:
Step-by-step explanation:
1. To find the value of x, you'll need to set 14x-94 equal to 8x-4. We do this since the two angels are congruent, and congruent angles are equal to each other:
[tex]14x-94=8x-4[/tex]
You'll then solve for x by isolating the x value.
[tex]14x-8x=94-4[/tex]
[tex]6x=90[/tex]
[tex]x=\frac{90}{6}[/tex]
[tex]x=15[/tex]
2. To find z I would plug in the x value to one of the equations, such as 8x-4, in order to find the measure of that angle:
[tex]8(15)-4\\=116[/tex]
We now know that 14x-94 and 8x-4 are equal to 116. To find z you'll add the angle opposite to it, the blank angle since they are congruent. Now you'll add all the angles together and set the equation equal to 360:
[tex]z+z+116+116=360\\2z+232=360\\2z=(360-232)\\2z=128\\\frac{2z}{2} =\frac{128}{2} \\z=64[/tex]
Your final answers are x=15 and z=64, hope this helps!
75 + 25x = 300 ......................................................................................
The answer is : X = 9
Answer:
9
Step-by-step explanation:
75 + 25x = 300
subtract 75 from both sides:
75 + 25x - 75 = 300 - 75
25x = 225
divide both sides by 25:
25x/25 = 225/25
x = 9
show which of the following polygons are similar, write the similar polygons in order of their corresponding vertices and determine the scale factor of similarity
Answer:
see explanation
Step-by-step explanation:
starting with the polygon on the left at vertex Z ( marked with x ) and going clockwise.
Similarly polygon on right starting with vertex D ( marked with x ) and going clockwise.
ZLXY ≅ DABC
the scale factor of ZLXY → DABC
is the ratio of corresponding sides
scale factor = [tex]\frac{DA}{ZL}[/tex] = [tex]\frac{9}{7.2}[/tex] = [tex]\frac{5}{4}[/tex]
If f(x) = 1/x which equation describes the graphed function? Apex ...
The equation that describes the graphed function [tex]f(x) = \frac{1}{x}[/tex] is option A:[tex]y = (x + 2) - 1.[/tex] This is shown in the graph given below, and transformation is translation.
To mathematically derive this equation, start with the original function [tex]f(x) = \frac{1}{x}[/tex].
The given function [tex]f(x) = \frac{1}{x}[/tex] has a reciprocal relationship between x and y.
To perform a horizontal translation 2 units left, substitute (x + 2) for x. This gives:[tex]f(x + 2) = \frac{1}{x + 2}[/tex].
Next, to achieve a vertical translation 1 unit down, subtract 1 from the function.
Thus, [tex]f(x + 2) - 1 = \frac{1}{x + 2}- 1[/tex].
Simplifying further, combine the terms gives:
[tex]y = (x + 2) - 1.[/tex]
This equation represents the original function :
[tex]f(x) = \frac{1}{x}[/tex]
After a horizontal translation of 2 units left and a vertical translation of 1 unit down.
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Which two situations result in a solution of 0?
Responses
On Tuesday morning, the temperature outside is −5∘F. On Tuesday night, the temperature outside is 5∘F. How much does the temperature change from Tuesday morning to Tuesday night?
On Tuesday morning, the temperature outside is − − 5 ∘ ∘ F. On Tuesday night, the temperature outside is 5 ∘ ∘ F. How much does the temperature change from Tuesday morning to Tuesday night?
On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
On Friday morning, a student earns $ 35 mowing lawns. On Friday night, the student spends the $ 35 while out with friends. How much of the money that the student earns from mowing lawns is left?
A vacationer goes scuba diving and is at a depth of −30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A vacationer goes scuba diving and is at a depth of − − 30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
A student owes a friend $ 7.50 . If the student pays the friend $ 7.50 , how much does the student owe the friend?
The two situations which would result in a solution of 0 include the following:
B. On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
D. A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
For this exercise, the expression which represents the first situation is given by:
Amount of money left = $35 - $35
Amount of money left = 0
For this exercise, the expression which represents the second situation is given by:
Amount of money owed = $7.50 - $7.50
Amount of money owed = 0.
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Question
What numbers are a distance of 23 unit from 12 on a number lineQuestion
What numbers are a distance of 23 unit from 12 on a number line
The number which is at a distance of 23 unit from 12 on a number line is 11.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
Now, we can determine the distance as follows:
Distance = 23 - 12
Distance = 11.
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Which equation represents the line that passes through
the points (2, 0) and (0, 7)?
Answer: [tex]y=-\frac{7}{2}x+7[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{7-0}{0-2}=-\frac{7}{2}[/tex].
So, since the y-intercept is 7, the equation is [tex]y=-\frac{7}{2}x+7[/tex].
Algebraic Expression
a is 7 times less than b.
[tex]7a = b[/tex]
THIS SIMPLY MEANS THAT TO ATTAIN b we have to multiply a by 7.
Question content area top
Part 1
Write the absolute value function as a piecewise-defined function with linear parts.
f(x)=4x+5
The absolute function f(x) = 4x+5 as a piecewise-defined function is:
f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
Given, the absolute function f(x) = 4x+5
The fundamental tenet of piecewise linear regression is that we should construct the regression function in "pieces" if the data exhibit various linear trends over various parts of the data. The components may or may not be joined.
when 4x+5 < 0
4x < -5
x < -5/4
f(x) = -(4x+5) = -4x-5
when 4x+5 ≥ 0
4x ≥ -5
x ≥ -5/4
f(x) = 4x+5
so f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
since, I x I = { -x , x<0
x , x ≥0}
Therefore, we get the required piecewise-defined function with linear parts.
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Need answer now!! Pls help! Will give brainliest to the best/correct answer! 40 points
A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?
A. The line represents a direct variation because -4/3 = 4/3.
B. The line represents a direct variation because it is horizontal.
C. The line does not represent a direct variation because it does not go through the origin.
D. The lines does not represent a direct variation because -4 (3) ≠ 4 (3).
Answer:
Answer: The line does not represent a direct variation because it does not go through the origin.
Figure W is the result of a transformation on Figure V. Which transformation would accomplish this?
Answer:
each point needs to be transformed using (-y,x) for the new coordinate
Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has 120 stamps. Lona joined a stamp club, which sends her 12 new stamps each month. The stamp book holds a maximum of 500 stamps. a. Complete the table at right. b. How many stamps will Lona have in one year from now?zetb c. Write an equation using function notation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by t(n). Month Stamps
0, 120
1 ,132
2
3
4
5
Using a linear function, it is found that:
a. The table is completed as follows: Month 2, Stamps 144; Month 3, Stamps 156; Month 4, Stamps 168; Month 5, Stamps 180.
b. She will have 264 stamps after one year.
c. The function is given by: t(n) = 120 + 12n.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the function in this problem, we have that:
The intercept is of 120, as the initial value is of 120 stamps.The slope is of 12, as 12 stamps are added each month to the collection.Hence the function is given by:
t(n) = 120 + 12n.
To complete the table, we find the numeric values are follows:
t = 2, t(2) = 120 + 12(2) = 144.t = 3, t(3) = 120 + 12(3) = 156.t = 4, t(4) = 120 + 12(4) = 168.t = 5, t(5) = 120 + 12(5) = 180.One year from now is 12 months, hence:
t(12) = 120 + 12(12) = 264.
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Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
The way she can use the number line to model the division is; Maria should start at 0 and then make “bounces” of 4 to the right until landing at 12. She will make 3 bounces of 4 because 12 divided by 4 is 3.
How to Model a Number Line?She is using a number line to model division, 12 ÷ 4 = 3
To carry out a division operation using a number line, follow the steps below:
Select the origin (point 0) as the starting pointIdentify the dividend and the divisorUse the divisor as the gap between 0 and subsequent consecutive numbersCount the number of gaps between 0 and the dividendFor the division operation 12 ÷ 4, Maria should:
Make 0 as the starting point on the number lineIdentify the dividend (12) and the divisor(4)Make the gap between 0 and subsequent numbers to be 4(the divisor)Therefore, the points on the number line will be 0, 4, 8, and 12
Count the number of gaps between these points
That is, 0 to 4, 4 to 8, and 8 to 12.
Since there are three gaps between 0 and 12 on the number line, using a gap difference of 4, then 12 ÷ 4 = 3
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help me I can't solve this question
The constant of proportionality of the given function of the graph would be 3 / 4.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
Let the equation below which is shown in the graph:
y = kx ....(i)
where k is the constant of proportionality.
As per the given graph, take a point x = 4, and y = 3
Substitute the values x = 4, and y = 3 in the equation (i)
3 = k × (4)
4k = 3
k = 3 / 4
Thus, the constant of proportionality of the given function of the graph would be 3 / 4.
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Evaluate:
Eight to the second power.
Answer:
[tex] = 8^{2} \\ = 8 \times 8 \\ = 64[/tex]
ATTACHED IS THE SOLUTION
Write the equation of the line that passes through the given points.
(0, -1) and ( - 13, -4)
We typically write linear equations in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-intercept (the value of y when x=0)Solving the QuestionWe're given:
Line passes through (0, -1) and ( -13, -4)1) Determine the slope (m)
To find the slope, we can use the slope equation:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points through which the line passes
⇒ Plug in the given points:
[tex]m=\dfrac{-1-(-4)}{0-(-13)}\\\\m=\dfrac{-1+4}{0+13}\\\\m=\dfrac{3}{13}[/tex]
Therefore, the slope of the line is [tex]\dfrac{3}{13}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\dfrac{3}{13}x+b[/tex]
1) Determine the y-intercept (b)
In this case, the y-intercept is already given to us.
The y-intercept is the value of y when x=0. Given that the line passes through (0,-1), we know that this is -1.
Plug this into [tex]y=\dfrac{3}{13}x+b[/tex]:
[tex]y=\dfrac{3}{13}x+(-1)\\\\y=\dfrac{3}{13}x-1[/tex]
Answer[tex]y=\dfrac{3}{13}x-1[/tex]
Select the correct answer.
What is the effect on the graph of f(x)
The au
=
when the function is changed to g(x) = |(x - 1)|?
Function transformation: Function transformation is the process of changing one function into another.
The f(x) graph will be shifted 1 unit down in the vertical direction.
How to do this function sum?Function transformation: Function transformation is the process of changing one function into another.
changing a function's form from one to another
Transformational rule
The function will move 'a' units higher when f(x)->f(x)+a is used.
f(x)-> f(x)-a The action is going to be 'a' units down.
The function will be relocated 'a' units left if f(x)->f(x+a).
The function will be relocated 'a' units right if f(x)->f(x-a).
The fundamental job is [tex]f(x)=\frac{1}{x}[/tex]
F(x)-1 is used in place of f(x).
It indicates that the graph of f(x) will shift down by one unit.
A unit down will be added to the vertical translation of the f(x) graph.
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Justin earns $13.9 per hour at the Rite Aid Pharmacy. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 50 hours. What was his gross pay for the week?
Based on the amount earned by Justin per hour, and the overtime work rate, Justin's gross pay for the week is $764.50
How to find the gross pay?First, find the amount that Justin earns from Rite Aid Pharmacy for his regular work:
= Number of hours in regular week x Pay per week
= 40 x 13.9
= $556
The overtime hours was:
= 50 - 40
= 10 hours
The overtime pay is:
= 10 x 13.9 x 1.5
= $208.50
The total gross pay for the week is:
= 556 + 208.50
= $764.50
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What is the quotient of (x³ - 3x² + 5x − 3)÷(x - 1)? x² - 2x - 3
x² + 2x + 7
x² - 3x + 8
x² - 2x + 3
a new test has been developed to determine whether a given student is overstressed. this test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. it is known that 99.5%
0.030844 is the probability that the test results are correct, and that this student is not overstressed.
What is a probability math example?
Probability is the measurement of how likely something is to happen. As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.Given that a particular students test negative for stress negative for stress then probability that the test result are correct and this student is not over stressed.
= 0.5% × 95% / ( 99.5% × 15% ) + ( 0.5% × 95% )
= 0.030844
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The complete question is -
A new test has been developed to determine whether a given student is overstressed. This test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. It is known that 99.5% of all students are overstressed. Given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
c(x) = 0.08x + 9.75
please answer
Step-by-step explanation:
I hope this will be helpful for you.
-3b (2y3 +5y) - 6y3b
Answer:
-15by
Step-by-step explanation:
distribute
rearrange terms
solve the following equation 2x=12
In a particular college class, 60% of the students are female. Of the female students, 75% have long hair. One student is picked randomly in the class. What is the probability that it is a female with long.
The probability that it is a female with long hair is 0.75 .
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.
the likelihood of an occurrence, E is
P(E) = The proportion of positive outcomes to all outcomes.
In probability, an event is said to be independent if it is completely unaffected by the occurrence of any other event, and it is considered to be dependent if it is affected by other occurrences.
Using the literature and formulas mentioned above, we have:
Let F stand for the circumstance that the student is a female and L for the circumstance that the student has long hair.
In this illustration, the probability are as follows:
P(F) = 0.60; P(L) = 0.50
P(F AND L) = 0.45 and P(L|F) = 0.75 as a result.
As a result, there is a 0.75 percent chance that a randomly chosen student has long hair.
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Kareem caught a 4 3/4 pound fish. How much did it weigh in ounces?
Answer:
76 ounces as ( 1 lb = 16 oz ) 4 3/4 * 16 = 76
Step-by-step explanation:
4 3/4 pounds = 76 ounces or 4 3/4 pounds = 2.15456376 kilograms
identify the point that does not appear to fit in the pattern
Answer:
add a picture
Step-by-step explanation:
Mason and his children went into a movie theater and he bought $36.50
worth of candies and pretzels. Each candy costs $4.25 and each pretzel costs
$3.50. He bought 6 more pretzels than candies. Write a system of equations
that could be used to determine the number of candies and the number of
pretzels that Mason bought. Define the variables that you use to write the
system.
Answer:
4.25c + 3.5p = 36.50
c + 6 = p
c = candies and p = pretzels
Step-by-step explanation:
So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50
And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p
Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)
Rachel is making premade 3-inch by 5-inch tile rectangles for her driveway. If it takes her 6 minutes to position each rectangle, how many hours will it take her to create a 2-foot by 4-foot pattern drive? Write your answer as a decimal.
Answer:
Tile a rectangle with unit squares. It is 8 unit squares long and 7 unit squares wide. Each unit square represents one square inch.
Step-by-step explanation:
The time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.
What is a unit rate?A unit rate means a rate for one of something.
It is written as a ratio with a denominator of one.
We have,
A rectangle tile area = 3-inch by 5-inch
Area = 15 inches
Time taken to position 15 inches tile = 6 minutes.
We can write as,
15 inches = 6 minutes _____(1)
We have a 2-foot by 4-foot pattern drive.
Area = 8 feet
We know that,
1 foot = 12 inches
Multiply both sides by 8.
8 feet = 8 x 12 inches
8 feet = 96 inches _______(2)
Now,
From (1) and (2) we get,
15 inches = 6 minutes
Multiply 96/15 on both sides we get,
96/15 x 15 inches = 96/15 x 6 minutes
96 inches = 38.4 minutes
Thus the time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.
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Wile-E-Coyote falls from the top of an 45m cliff while chasing the road runner. How long does it take him to strike the ground below?
Time is considered to be the dimension on which any system evolves.
9.2 seconds will take for him to strike the ground.
How long does it take Wile to strike the ground?Time can be thought of as the dimension in which the evolution of every system occurs.
It can be calculated using the following units: seconds, minutes, hours, days, weeks, months, and years.
Given,
h = 45m
g = -9.8m/s
Solution:
Vi = 0
h = Vi t + 1/2gt^2
Since Vi is 0
2h = gt^2
t^2 = 2h/g
t = [tex]\sqrt{2h/g}[/tex]
[tex]t =\sqrt{2 * -45/-9.8}[/tex]
t = 9.183s
9.2 seconds will take for him to strike the ground.
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how might you use the word average in a situation that does not involve math?
Answer:The mean is commonly referred to as average, but it is not the only kind of average. The mean is often used in research, academics and in sports.
Step-by-step explanation:
There are diffrerent ways to use the word
The average in general is the same as the term average in mathematics.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
The meaning of average, in general, is quite similar to average in maths.
Suppose If we say the average income of a population is five thousand.
This implies that some portion of the population earns more than five thousand and some portion of the population earns below five thousand.
We can also say that the average rate growth of height of a person per year is 5cm this also means that some years the growth is more than 5cm and some years it is less than 5 cm.
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