Given:
Blue car travels [tex]44\dfrac{1}{2}[/tex] miles on [tex]1\dfrac{1}{4}[/tex] gallons of gasoline.
Red car travels [tex]20\dfrac{4}{5}[/tex] miles on [tex]\dfrac{4}{5}[/tex] gallons of gasoline.
To find:
The unit rate for miles per gallon for each car and find which car could travel the greatest distance on one gallon of gasoline.
Solution:
We know that,
[tex]\text{Unit rate}=\dfrac{\text{Total distance covered by the car}}{\text{Number of gallons of gasoline}}[/tex]
Using this formula, the unit rate of blue car is
[tex]\text{Unit rate of blue car}=\dfrac{44\dfrac{1}{2}}{1\dfrac{1}{4}}[/tex]
[tex]\text{Unit rate of blue car}=\dfrac{\dfrac{88+1}{2}}{\dfrac{4+1}{4}}[/tex]
[tex]\text{Unit rate of blue car}=\dfrac{89}{2}\times \dfrac{4}{5}[/tex]
[tex]\text{Unit rate of blue car}=\dfrac{178}{5}[/tex]
[tex]\text{Unit rate of blue car}=35.6[/tex]
Unit rate of red car is
[tex]\text{Unit rate of red car}=\dfrac{20\dfrac{4}{5}}{\dfrac{4}{5}}[/tex]
[tex]\text{Unit rate of red car}=\dfrac{\dfrac{100+4}{5}}{\dfrac{4}{5}}[/tex]
[tex]\text{Unit rate of red car}=\dfrac{104}{5}\times \dfrac{5}{4}[/tex]
[tex]\text{Unit rate of red car}=26[/tex]
Therefore, the unit rate of blue car is 35.6 miles per gallon of gasoline and unit rate of red car is 26 miles per gallon of gasoline.
Since, unit rate of blue car is greater than the red car, therefore blue car travel the greatest distance on one gallon of gasoline.
PLZZ HELP ME AND ONCE AGAIN THANK YOU
Answer:
2nd option
Step-by-step explanation:
the domain is from 0 to infinity
we count 0 because
f(0)=1 (just look in the graph)
so
[tex]x \geq 0[/tex]
which is the 2nd option
–45 • –3 = please i need hep
Answer:
135
Step-by-step explanation:
Can someone explain this problem to me?? After a price reduction of x%, an item has its price increased to its original value. What was the percent of increase? Express your answer as a common fraction in terms of x.
Answer:
[tex]We\ are\ given\ that,\\Percent\ of\ reduction=x_-\\So,\\Let\ the\ percent\ of\ increase\ be\ x_+\\Let\ the\ original\ price\ of\ the\ item\ be\ y\\Let\ the\ price\ after\ the\ decrease\ be\ z\\.\\Hence,\\y-\frac{x_-}{100} =z\\ z+\frac{x_+}{100}=y\\By\ simply\ adding\ the\ equations,\\(y+z)+(- \frac{x_-}{100}+\frac{x_+}{100})=(z+y)\\Hence,\\- \frac{x_-}{100}+\frac{x_+}{100}=0\\Hence,\\ \frac{x_-}{100}=+\frac{x_+}{100}\\Hence,\\x_-=x_+\\[/tex]
[tex]Hence,\ the\ percent\ of\ increase\ is\ same\ as\ the\ percent\ of\ decrease.[/tex]
TWO MULTIPLE CHOICE QUESTIONS PLS HELP
Answer:
sorry i only know the number 2.
so the answer is the first one...
Find two positive numbers such that the sum of the first and twice the second is equal to 124 and whose product is a maximum. For your answer, type in the larger of the two numbers.
Answer:
Answer is in photo
Step-by-step explanation:
Prove that Tan x + Cos x = 1 /Sin x .Cos x
Answer:
tanx + cotx = [tex]\frac{1}{sinxcosx}[/tex]
Step-by-step explanation:
Explanation
Take R.H.S = [tex]\frac{1}{sinxcosx}[/tex]
= [tex]\frac{sin^{2}x+cos^{2}x }{sinxcosx}[/tex]
= [tex]\frac{sin^{2}x }{sinx cosx} + \frac{cos^{2} x}{sinxcosx}[/tex]
= [tex]\frac{sinx}{cosx} + \frac{cosx}{sinx}[/tex]
= tanx + cotx
tanx + cotx = [tex]\frac{1}{sinxcosx}[/tex]
Sorry for the blurry picture I'm in a rush if anyone could help me that would be amazing
Answer:
y=1/2x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or kx
The value of the constant k is equal to the value of the slope m
In this problem we have the point (8,4)
Find the value of k
y/x=k------> substitute the value of x and y
4/8=k
k=1/2
The equation is equal to
y=1/2x
solve the inequality for n 14
Answer:
14n
Step-by-step explanation:
just rearrange the number with the variable
TVs are measured by
their diagonals. If a 60
inch TV has a height of
24 inches, how wide is
the screen?
Answer:
Step-by-step explanation:
Diagonal is 60 inches, height is 24 inches so
60^2 = 24^2 + width^2
6.25 inches
solve 16y² = 36 using the square root property
Answer:
2/3-3/2
Step-by-step explanation:
If g(x) = x2 + 2, find g(3). (2 points)
9
8
11
6
Answer:
The answer is 11
Step-by-step explanation:
so substitute 3 for x, then your equation would be 3^2 + 2
3^2 is 9
9 + 2 = 11
Find the area of the red triangle.
Also explain.
Answer:
The answer is 9
Step-by-step explanation:
So In order to solve this problem, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, add 79 and 10 and subsequently subtracting 72 and 8 to get 9.
Answer:u
Step-by-step explanation:
The air pressure P is inversely proportional to the altitude h. write the related variation equation
Step-by-step explanation:
P * h = k, where k is a real constant.
Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four
students in order to do labs. She has a total of 120 students and 32 total groups are formed.
If i represents the number of three person groups and represents the number of four person groups, then
write a system of equations that models this situation.
Answer:
x + y = 32 (1)
3x + 4y = 120 (2)
x = 8; y = 24
Step-by-step explanation:
Total students = 120
Number of groups = 32
If the number of three person groups = x
Number of four person groups = y
write a system of equations that models this situation
x + y = 32 (1)
3x + 4y = 120 (2)
From (1)
x = 32 - y
Substitute x = 32 - y into (2)
3(32 - y) + 4y = 120
96 - 3y + 4y = 120
- 3y + 4y = 120 - 96
y = 24
Substitute y = 24 into (1)
x + y = 32
x + 24 = 32
x = 32 - 24
x = 8
x = 8; y = 24
A rectangular prism is 12 cm long, 6 cm wideand 5 cm high. What is the volume of the rectangular prism?
Kate walks 5 miles in 2 hours at a steady pace. how far can she walk in 1 hour and 15 minutes? If answered, you get the brain crown thing
Answer:
2.8125 mile
Step-by-step explanation:
hope its right
Which statement describes the rate of change of the following function?
f(x) = -5x - 7
A.
The function has a varying rate of change when x < 7.
B.
The function has a varying rate of change when x < 5.
C.
The function has a constant rate of change, decreasing for all x at a rate of 7.
D.
The function has a constant rate of change, decreasing for all x at a rate of 5.
Given:
The function is
[tex]f(x)=-5x-7[/tex]
To find:
The rate of change of the given function.
Solution:
We have,
[tex]f(x)=-5x-7[/tex] ...(i)
It is a linear function because the degree or power of x in this function is 1.
Slope of a linear function is always constant.
The slope intercept form of a linear function is
[tex]f(x)=mx+b[/tex] ...(ii)
where, m is slope and b is y-intercept.
On comparing (i) and (ii), we get
[tex]m=-5[/tex]
It means, the function has a constant rate of change, decreasing for all x at a rate of 5.
Therefore, the correct option is D.
Javier worked out the following on his math homework: “What equation best represents the relationship between x and y in the graph?" Javier’s answer was y= -4x - 2. Is he correct? If not, explain what he did wrong AND give the correct answer. *
12 points
Answer:yes he is correct
Step-by-step explanation: if you go on a certain site and you put in the equation, you press enter then it will pop up with what you want to do. Press graph, then you can compare the graphs and if it is the same you know it is correct
Find the value of k, if x + 3 is a factor of 3x² + kx + 6. *
I really need help with these two, I'd really appreciate an answer as soon as possible. (Questions in picture below)
Answer:
2.$9.25 3.11
Step-by-step explanation:
For the first question virtually you could just go through each one and determine how they would fit. But what I did for both is determine the change in the first column (5 in #2 3 in #3) Then subtract the second change from the first in the second column (185-138.75 and 132-99) you come up with a rate of change like (46.25 and 33) then using that number dividing by the change from the first column (46.25/5=9.25 and 33/3=11) And to check applying all of that to the other changes.
In △ABC, AB = 13.2m, BC = 6.9m and ∠ACB = 90°. H lies on AC such that ∠BHC = 46°. Find (i) ∠ABH (ii) The length of AH
Answer:
(i) ∠ABH = 14.46⁰
(ii) The length of AH = 4.6 m
Step-by-step explanation:
From the image uploaded;
Consider △ABC;
the length of b is calculated by applying Pythagoras theorem as follows;
b² = c² - a²
b² = (13.2)² - (6.9)²
b² = 126.63
b = √126.63
b = 11.25 m
Also, ∠ABC is calculated as;
[tex]Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o[/tex]
Consider △CBH, ∠CBH is calculated as;
∠CBH = 90⁰ - 46⁰ = 44⁰
(i) ∠ABH will be calculated as;
∠ABH = θ
θ + 44⁰ = ∠ABC
θ + 44⁰ = 58.46⁰
θ = 58.46⁰ - 44⁰
θ = 14.46⁰
Thus, ∠ABH = 14.46⁰
(ii) The length of AH
length HC is calculated as;
[tex]tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m[/tex]
length of AH = CA - HC
x = b - HC
x = 11.25 - 6.66
x = 4.6 m
length of AH = 4.6 m
Suppose that scores on a particular test are normally distributed with a mean of 140 and a standard deviation of 18. What is the minimum score needed to be in the top 5% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.
Answer:
153.16
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score = ???
μ is the population mean = 140
σ is the population standard deviation = 8
Top 5% means the score is in the 95th percentile
The z score of 95th percentile = 1.645
1.645 = x - 140/8
Cross Multiply
1.645 × 8 = x - 140
13.16 = x - 140
x = 13.16 + 140
x = 153.16
Therefore, the minimum score needed to be in the top 5% of the scores on the test is 153.16
Plss answer!!
MERRY Christmas!!!
Critical Question. AAAAA
Answer:
Step-by-step explanation:
abc = 1
We have to prove that,
[tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
We take left hand side of the given equation and solve it,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}[/tex]
Since, abc = 1,
[tex]\frac{1}{c}=ab[/tex] and c = [tex]\frac{1}{ab}[/tex]
By substituting these values in the expression,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}[/tex]
[tex]=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}[/tex]
[tex]=\frac{1+b+ab}{1+b+ab}[/tex]
[tex]=1[/tex]
Which equal to the right hand side of the equation.
Hence, [tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
Somebody help!!! Please!!!
Answer:
y = -1 !!!!!!!!!!! :)))))))))))))
Answer:
y=-1
Step-by-step explanation:
symmetry is where it is the same on both sides, so that would be the line between the top and bottom point and because they are up and down it is a y whereas if it were side to side it would be x. it is on the left side which are negatives and it is one over to the left making it y=-1
If an object on earth weighs 42 lbs, what is its weight on the moon?
Answer:
6.93 lbs.
Step-by-step explanation:
The weight on the moon is approximately 16.5% of what you would weigh on Earth. Using this information, we can say that 16.5% of 42 lbs would equal how much the object would weigh on the moon.
I prefer to convert percentages the decimal way, so let's do it that way. 16.5% is 0.165 as a decimal, so now all we have to do is multiply 0.165 by 42 (since we are saying 16.5% of 42 lbs), and we get 6.93 lbs.
Hope this helps! :)
Ariana has a dimes and y nickels. She has at most 12 coins worth a minimum of
$0.85 combined. Solve this system of inequalities graphically and determine one
possible solution.
9514 1404 393
Answer:
see attached (7 dimes, 5 nickels)
Step-by-step explanation:
The inequalities are plotted in the attachment. The solution shown is ...
(x, y) = (7, 5)
7 dimes and 5 nickels are 12 coins worth $0.90. This is the maximum number of coins, worth more than $0.85.
PLEASE HELP!!!
Which of the following values could x represent in the bar diagram?
ABC or D?
9514 1404 393
Answer:
both C and D are correct
Step-by-step explanation:
The diagram shows that x is the total of $40 and 20% of $40.
Description A would be represented by the difference of $40 and 20% of $40, not the sum.
Description B would be represented by 20% of $40, not the sum of that and $40.
Both descriptions C and D are properly represented in the diagram.
Mrs. Arnold took a survey of the types of pants her students were wearing. She collected the data below. What percent of her students were wearing shorts? Jeans: 14 Shorts: 9 Capris: 2
Answer:
36%
Step-by-step explanation:
Jeans: 14
Shorts: 9
Capris: 2
Total number of students = Number of Jeans + Number of Shorts + Number of Capris
Total number of students = 14 + 9 + 2 = 25
% of students wearing shorts = Number of shorts / Total number of students * 100
% of students wearing shorts = 9 / 25 * 100 = 0.36 * 100 = 36%
A researcher took a poll of people in his state. He asked each person if he or she had any pets (Yes or No) and to state his or her political party affiliation (Republican, Democrat, or Other). If the researcher computed a chi square test of independence using the responses, what would the degrees of freedom value be
Answer:
DF = 2
Step-by-step explanation:
Formula for degree of freedom is;
DF = n - 1
Where n is sample size
In this question, political party affiliation could be Republican, Democrat, or Other. Thus, sample size is 3.
DF = 3 - 1
DF = 2
Thus, degree of freedom value would be 2
Inequ
What is the solution to the inequality -3.x + 7 > 1?
Х
DONE
Answer: x < 2
-3x + 7 > 1
<=> -3x > - 6
<=> x < -6/-3
<=> x < 2
Step-by-step explanation: