The average gas mileage of the cars traded is 15.8 miles per gallon round to the nearest.
Let's assume that the average gas mileage of the cars traded in is x miles per gallon. According to the problem, the average increase in gas mileage for the new car purchased versus the car traded in was 61%. This means that the new car gets 61% more miles per gallon than the car traded in. We can express this relationship mathematically as:
25.4 = x + 0.61x
Simplifying the right-hand side of the equation, we get:
25.4 = 1.61x15.78
Dividing both sides by 1.61, we get:
x = 15.78
Therefore, the average gas mileage of the cars traded in was approximately 15.8 miles per gallon, rounded to the nearest tenth.
To understand this result, we can interpret it as follows: for the first week of the "Cash for Clunkers" program, the average gas mileage of the new cars purchased was 25.4 miles per gallon, which is 61% higher than the average gas mileage of the cars traded in. This suggests that the program was successful in incentivizing people to trade in their old, less fuel-efficient cars for new, more fuel-efficient cars.
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If m<6= 97°, what is m<5
The measure of value of ∠5 is 83°.
Now, It is given that;
Two Lines m and n are parallel with each other and l is the transversal crossing the two given parallel lines.
And, m∠6 = 97°,
Since, Two rays combined into an angle have a single terminal. The point is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Hence, Then by using the property of liner pair angles, we have
⇒ m∠5 + m∠6=180°
(Because they form a linear pair angles.)
⇒ m∠5 + 97 = 180
Subtract 97 both side, we get;
⇒ m∠5 + 97 - 97 = 180 - 97
⇒m∠5 = 180 - 97
⇒m∠5 = 83°.
Therefore, the value of the measure of ∠5 is,
⇒ ∠5 = 83°.
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hat is the domain of the function on the graph?
Answer:
The domain of a function is the set of all possible input values for the function. In this case, the function is a graph, so the domain is the set of all possible x-values that correspond to points on the graph.
To find the domain, we need to consider all of the points on the graph. We can see that the graph extends infinitely to the left and right, so all real numbers are possible input values. Therefore, the domain of the function is all real numbers, or R.
Here is a more formal definition of the domain of a function:
The domain of a function is the set of all real numbers x for which the function f(x) is defined.
In other words, the domain is the set of all input values for which the function produces a valid output value.
Step-by-step explanation:
Please help me answer this urgently. I don’t understand and need a clear explanation.
For the line that passes through the points A(5, 8, -2) and B(-1, 3, 5), find:
a. a vector equation.
b. parametric equations.
c. Symmetric equations
The symmetric equations for the line are:
(36x + 40y - 28z - 100) / 0 = (x-5) / -6 = (y-8) / -5 = (z+2) / 7
To find the parametric equations for the line passing through A(5, 8, -2) and B(-1, 3, 5), we can use the vector equation:
r = A + t(B-A)
where r is the position vector of any point on the line, t is a scalar parameter, and A and B are the given points. Substituting the values, we get:
r = (5, 8, -2) + t((-1)-5, 3-8, 5-(-2))
r = (5, 8, -2) + t(-6, -5, 7)
The parametric equations for the line are:
x = 5 - 6t
y = 8 - 5t
z = -2 + 7t
To find the symmetric equations, we can use the fact that any point on the line is equidistant from points A and B. Thus, the distance from a point (x, y, z) to A must be the same as the distance from the same point to B. Using the distance formula, we get:
√[(x-5)² + (y-8)² + (z+2)²] = √[(x+1)² + (y-3)² + (z-5)²]
Squaring both sides and simplifying, we get:
36x + 40y - 28z - 100 = 0
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Use the following information to answer questions 9 and 10.
Suppose we drop a ball from a height of 10 feet. After each bounce, it returns to a height that is k% of the height from which it last fell. After the 5th bounce, it returns to a height of 9.04 feet. We will ignore things like friction and air resistance so that the terms form a geometric sequence.
9 . Determine k.
97.51%
98.00%
98.83%
99.15%
10. How many bounces does it take until the ball bounces back to a height less than 3 inches (1/4 of a foot)?
163
183
203
223
9. The ball returns to 98.00% of its previous height after each bounce Option B
10. It will take 183 bounce until the ball bounces back to a height less than 3 inches. Option B
How do we solve for k% of previous height?To solve for k% of previous height after each bounce, we say
10×(k/100)⁵ = 9.04
k = [tex](9.04/10)^{1/5}[/tex]×100
k = 98.00
To find out how many bounces it takes for the ball to bounce back to a height less than 3 inches (or 0.25 feet), we use the inequality
10 × (0.961)ⁿ < 0.25
The logarithm of both sides gives
n × log(0.961) < log(0.025)
n > log(0.025) / log(0.961)
n > 182.593
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maya received an 80 dollar gift card for a coffee store. She used it in buying some coffee that cost $8.79 per pound. after buying the coffee she had $44.84 left on her card. How many pounds of coffee did she buy
__________________________________
= 80 - 44.84= 35.16= 35.16 ÷ 8.79= 4 lbsMaya Bought 4 Pounds of Coffee__________________________________
Volume of an open rectangular is 24.3m³.height is 2.7m. what is surface area.
If the volume of an open rectangular object or space is 24.3m³ with a height of 2.7m, the surface area is 9m.
How is the surface area determined?The surface area can be determined by dividing the volume by the height.
This is because the product of the surface area and the height gives the volume.
The surface area is a product of the length and width, while the volume is the product of the length, width, and height.
Volume = 24.3m³
Height = 2.7m
Surface area = 9m (24.3m³ ÷ 2.7)
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PLEASE HELP ME QUICKLY.
Find the average rate of change between the two labeled points.
[The point in between is (3, 72.6).]
Answer: 2/13.86
Step-by-step explanation:
A lines rate of change is equal to it's slope
Slope is rise over run (Y/X)
The point is up 2 on the Y axis and over 13.86 on the X axis
The slope is= 2/13.86
variable:
Hours (h)
10
20
30
40
Cost in dollars (c)
80
110
140
170
The table shows the relationship between hours spent dog sitting and the cost of the services. Write an equation to represent the situation using h and c as your variables.
The solution is it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.
Here,
we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.
C(5) = 25(5) + 75 = 125 + 75 = 200
We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.
Hours Cost
1 $90
2 $130
3 $170
We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.
It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.
It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.
In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.
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complete question:
19) The function C(x) = 25x+75 represents the labor cost (in dollars) for Bob's Auto Repair to replace
your alternator, where x is the number of hours. The table below shows sample labor costs from its main
competitor, Budget Auto Repair. The alternator is estimated to take 5 hours of labor. Which company
would you hire? Explain.
Hours 1,2,3
Cost
$90 $130 $170
Quatre ouvriers mettent 12 jours pour réaliser un travail. Dans les mêmes conditions combien de temps mettraient six ouvriers pour réaliser ce travail ?
How is graphing (5, 0) different from graphing (0, 5)? Explain.
Answer: If the number is placed on the X as in (X,Y) the X value will rise but the Y value will stay the same, but if the number is played on the Y, the Y value will go up, and the X value will stay the same
What is the slope of the line through (-2,-2)(-2,-2)left parenthesis, minus, -2, comma, -2, right parenthesis and (2,-4)(2,−4)left parenthesis, 2, comma, minus, 4, right parenthesis?
Step-by-step explanation:
To find the slope of the line between two points, you can use the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the given coordinates, we have:
m = (-4 - (-2)) / (2 - (-2))
m = (-4 + 2) / (2 + 2)
m = (-2) / (4)
m = -1/2
The slope of the line through the points (-2, -2) and (2, -4) is -1/2.
A higher credit score reduces your fixed costs because you ____.
A. will pay lower interest rates
B. can have more credit cards
C. are able to carry more debt
D. can reduce the amount you need to borrow
A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.
What is a higher credit score?A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.
This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.
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The cup on Sophie's desk holds 4 red pens and 7 black pens. What is the probability of her selecting first a black pen, and then a red one?
Answer:14/165
Step-by-step explanation:
its a fraction i did the same qestion and got it right
30 POINTS! Find the values of x and y
Given that this is an isosceles triangle, then the lengths of the sides opposite the two 45º angles have to be the same length.
For this reason, x = 8.
And since x = 8 and there's only one answer with x=8, the first option must be the answer.
You can calculate the value of y using the Pythagorean Theorem.
[tex]y^2 = 8^2+8^2[/tex]
which will lead you to [tex]y=8\sqrt{2}[/tex].
8 kilometers == meters
Answer: 8000
Step-by-step explanation:
Blank x 2 > 2
8 over 8 or 7 over 8 or 9 over 8
Answer:
dwdaddaw
Step-by-step explanation:
ad plus devide
If s5= -16.3804 and r=9/10,what is a₁?
The first term of GP is a₁ = -4.
Given that,
Sum of five terms of GP = s₅ = -16.3804
Common ratio = 9/10 which is less than 1
Number of terms = n = 5
We know that,
Sum of nth term of GP when common ration is less than 1,
s₅ = a₁(1-[tex]r^{n}[/tex])/(1-r)
Substituting the values,
⇒ -16.3804 = a₁(1-0.9⁵)/(1-0.9)
⇒ a₁ = -16.3804/4.0951
⇒ a₁ = -4
Hence, the value of a₁ is -4.
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Joe earns $25 mowing his neighbor’s lawn each week (w). He is saving his
money to buy a hoverboard that costs $168. Which inequality matches
this situation? (circle your answer)
a) $168-$25 < w b) $25w > $168 c) $25w < $168
"The correct option is (C) $25w < $168." This means that Joe needs to save for at least 7 weeks (since he can't save for a fraction of a week) to afford the hoverboard.
The hoverboard costs $168 and Joe earns $25 each week. To determine if Joe can afford the hoverboard, we need to determine how many weeks he needs to save to reach the cost of the hoverboard.
Let's represent the number of weeks Joe needs to save as "x". Each week, he earns $25, so the total amount he will have after "x" weeks is 25x. In order to buy the hoverboard, he needs to have saved $168. Thus, we can write the inequality:
25x ≥ 168
This inequality represents the fact that the amount of money Joe earns after "x" weeks must be greater than or equal to $168, the cost of the hoverboard, for him to be able to afford it. Simplifying this inequality, we get:
x ≥ 6.72.
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Use the table that shows the recent population, in millions, of the ten largest U.S. cities.
Find the mean absolute deviation. Round to the nearest hundredth.
The mean absolute deviation =________million.
The mean absolute deviation for the data-set in the table is given as follows:
1.52 million.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for the data-set in this problem is given as follows:
(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.
The deviations are given as follows:
|1.5 - 2.54| = 1.04.|3.8 - 2.54| = 1.26.|1.3 - 2.54| = 1.24.|1.6 - 2.54| = 1.06.|2.9 - 2.54| = 0.46.|1.4 - 2.54| = 1.14.|0.9 - 2.54| = 1.64.|2.3 - 2.54| = 0.24.|8.4 - 2.54| = 5.86.|1.3 - 2.54| = 1.24.Hence the mean absolute deviation is given as follows:
(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.
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In 2017 32.2% of college students were minorities. If you took a random group of 500 college students in 2017, then how many of these 500 college students would you expect to be minorities?
The height of a tree in feet over x years is modeled by the function f(x). Determine if each statement is True or False.
The statement is examined using the equation to find that
1. False
2. False
3. True
4. False
How to find the statement is trueThe given equation is
f(x) = 32 / ( 1 + e⁰°⁵ˣ)
Evaluating the first statement by substituting
For x = 3, f(3 ) gives 5.84
For x = 6, f( 6) gives 1.52
5.82 - 1.52 is not equal to 9 ft hence the statement is False
Evaluating the second statement by substituting
when x = 0, the function gives 16 which is against 2 ft hence False
Evaluating the third statement by substituting
For x = 1, f(1) = 12.08 this is less than 16 ft hence a decline hence this is True
fourth statement
The trees maximum height, captured should be 16 ft not 35 ft hence False
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Plants are sold in three different sizes of tray.
A small tray of 10 plants costs £2.50
A medium tray of 40 plants costs £8.40
A large tray of 90 plants costs £12.60
Which size tray of plants is the best value for money?
The size tray of plants which is the best value for money is large tray.
Which size tray of plants is the best value for money?A small tray of 10 plants costs £2.50
Cost per unit = Total cost / number of plants
= £2.50 / 10 plants
= £0.25 per plant
A medium tray of 40 plants costs £8.40
Cost per unit = Total cost / number of plants
= £8.40 / 40 plants
= £0.21 per plant
A large tray of 90 plants costs £12.60
Cost per unit = Total cost / number of plants
= £12.60 / 90 plants
= £0.14 per plant
Hence, the large tray of 90 plants costs £12.60 is the best buy for your money.
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Find all possible values of x.
Using the secant-secant theorem, the possible values of x are x = 6 and x = -10. -10 cannot be a value of x because length cannot be negative.
Secant-secant theorem: Calculating the value of of xFrom the question, we are to determine the value of x in the given diagram.
The Secant-secant theorem states that
"Given two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other segment and its external segment"
Thus,
We can write that
5 × (5 + 7) = x × (x + 4)
Simplifying
5 × 12 = x² + 4x
60 = x² + 4x
x² + 4x - 60 = 0
Solve the quadratic equation
x² + 4x - 60 = 0
x² + 10x - 6x - 60 = 0
x(x + 10) - 6(x + 10) = 0
(x - 6)(x + 10) = 0
x - 6 = 0 or x + 10 = 0
x = 6 or x = -10
Since x cannot be negative,
x = 6
Hence, the value of x is 6
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I REALLY NEED HELP I DONT UNDERSTAND IT!
The area of the pentagon using the composite area formula is 37 in².
What is a pentagon?
A pentagon is one of the many types of polygon having five sides and five angles.
To calculate the area of the pentagon, we use the formula below
Formula:
A = BH/2+LW+bL................... Equation 1From the diagram,
Given:
B = 6 inH = 4 inL = 5 inW = 4 inb = 1 inSubstitute these values into equation 1
A = (4×6/2)+(5×4)+(1×5)A = 12+20+5A = 37 in²Learn more about pentagon here: https://brainly.com/question/29673128
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3.
Carly deposits money into a compound interest account in 2010. The equation P = 600(1.0375)
represents the amount of money in her account, P, after t years.
Determine how much money Carly has in her account in 2047. What was the growth rate?
How long does it take for Carly's account to reach $750? Round answer to the nearest tenth.
The compound interest is solved and the amount in her account in 2047 is given by A = $ 1315.46
Given data ,
To determine how much money Carly has in her account after 37 years, we need to substitute the value of t as 37 into the equation:
P = 600(1.0375)^t
P = 600(1.0375)^37
P ≈ 600(1.0375)^37 ≈ 600(2.19243) ≈ $ 1315.46
Therefore , Carly has approximately $1315.46 in her account after 37 years.
To calculate the growth rate, we need to find the rate of change between the initial and final amounts over the given time period.
Regarding how long it takes for Carly's account to reach $750, we'll assume you mean when the account reaches or exceeds $750. Let's set up the equation and solve for t:
750 = 600(1.0375)^t
Dividing both sides by 600, we get:
1.25 = 1.0375^t
Taking the logarithm of both sides (base 1.0375):
log(1.25) = t * log(1.0375)
t ≈ log(1.25) / log(1.0375) ≈ 8.5 years
Hence , it takes approximately 8.5 years for Carly's account to reach or exceed $750
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choose the greatest number you can mutiply by 30 you can get close to but not go over 150
Answer:
If it can be exactly 150, then 50.
there’s not exactly enough info for me to solve.
2 defective screws out of 100 packs them in boxes of 500 probability of 15 defective screws
The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.
In a scenario where there are 2 defective screws out of 100 packs, each containing 500 screws, we can calculate the probability of obtaining 15 defective screws. Let's assume that each pack is independent of the others.
The probability of a single screw being defective is 2/500, as there are 2 defective screws out of 500 in each pack.
Conversely, the probability of a screw being non-defective is 498/500.
To find the probability of obtaining exactly 15 defective screws, we can use the binomial distribution formula. The probability (P) can be calculated as follows:
P = (100 C 15) * (2/500)^15 * (498/500)^85
The term (100 C 15) represents the number of ways to choose 15 defective screws out of 100 packs.
By plugging these values into the formula and performing the calculations, the probability of obtaining exactly 15 defective screws can be determined. However, I am unable to perform the calculation for you within the given word limit.
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
a. bus
b. car
c. subway
d. train
A type of transportation is LEAST likely to take more than 30 minutes include the following: d. train.
How to interpret the box-and-whisker plots?In order to determine the type of transportation that is least likely to take more than 30 minutes for Conrad to get to an appointment at the other end, we would have to compare the median minute for each data set (type of transportation) that is represented on the box-and-whisker plot shown above.
By critically observing the box-and-whisker plot, we can reasonably infer and logically deduce that a train is the type of transportation that is least likely to take more than 30 minutes because its median minute is the lowest compare to the other data set (type of transportation) that is represented on the box-and-whisker plot shown above.
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What is the volume of the object?
Two rectangular prisms are side by side. The dimensions of the larger rectangular prism are 8 c-m, 6 c-m, and 13 c-m and the dimensions of the smaller rectangular prism are 3 c-m, 4 c-m, and 7 c-m.
A
41cm3
B
526cm3
C
708cm3
D
52,416cm3
The total volume is the one in option C, 708 cubic centimeters.
What is the volume of the object?We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.
Then the volume of the first prism is:
V = 8cm*6cm*13cm = 624 cm³
And the volume of the second prism is:
v' = 3cm*4cm*7cm = 84 cm³
Adding that we will get:
total volume = 624 cm³+ 84 cm³ = 708 cm³
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