The value of Car 1 decreases linearly and can be described by a linear function. Without an exact exponential function for Car 2, we'll assume it may have a slower depreciation rate compared to Car 1. Autumn should consider Car 2 to likely have greater value after 6 years.
Explanation:Part A: Identifying the Type of Function
To determine which type of function best describes the value of each car after a fixed number of years, we must look at the rate at which the car's value decreases. For Car 1, the value decreases by a constant amount each year ($6,000), which suggests a linear function. Conversely, Car 2 does not decrease by the same amount each year, but rather by amounts that seem to be getting progressively larger, hinting at an exponential function.
Part B: Writing the Functions
The linear function for Car 1 can be represented as f(x) = -6,000x + 44,000, since we start at $44,000 and decrease by $6,000 each year. For Car 2, an exponential decay function may fit the data; however, with only three points provided, determining the exact exponential function would require more complex regression analysis which we do not perform here. Assuming the rate of depreciation remains similar, we might estimate the function for Car 2 using a linear approximation for simplicity.
Part C: Future Car Value Comparison
Extending the linear depreciation model for Car 1, its value after 6 years would be f(x) = -6,000(6) + 44,000 = $8,000. A precise prediction for Car 2 after 6 years cannot be determined without an accurate exponential function, but it's apparent that Car 2 depreciates less rapidly than Car 1. Therefore, Autumn would likely find that Car 2 retains more value over 6 years.
Which expression is the greatest common factor (GCF) of the terms of trinomial 12x^7y^9 + 6x^4y^7 - 10x^3y^5
Answer: 2. [tex]\mathbf{2x^3y^5}[/tex]
Step-by-step explanation:
Greatest common factor of any two or more expression is the largest common expression that divides them.The given expression : [tex]12x^7y^9 + 6x^4y^7 - 10x^3y^5[/tex]
Term 1 : [tex]12x^7y^9[/tex]
Term 2 : [tex]6x^4y^7[/tex]
Term 3: [tex]- 10x^3y^5[/tex]
Lowest power of x = 3
Thus , The highest common power of x = [tex]x^3[/tex] (i)
Lowest power of y = 5
The highest common power of y =[tex]y^5[/tex] (ii)
Greatest common factor of 12, 6 , -10= 2 [Because 2 is the largest number that divides all of them] (iii)
From (i) , (ii) , (iii) , we have
Greatest common expression : [tex]2x^3y^5[/tex]
Hence, the correct answer is 2. [tex]\mathbf{2x^3y^5}[/tex]
John's goal is to have more than -7 dollars in his bank account by the end of the month. The variable d is the number of dollars in John's bank account at the end of the month. Write an inequality in terms of d that is true only if John meets his monthly goal.
Answer:
d > - 7
Step-by-step explanation:
Here, d represents the number of dollars in John's bank account at the end of the month.
As per statement,
In John's account,
The balance must be more than -7 dollars,
That is, Number of dollars at the end of each month > - 7 ( '>' is used for more than )
⇒ d > - 7
Which is the required inequality.
Evaluate the line integral where f(x,y,z)=3sin(x)i−(cos(y))j−5xzk and c is given by the vector function r(t)=t5i−t4j+t3kr(t)=t5i−t4j+t3k , 0≤t≤10≤t≤1.
for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value
Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.
A. 30
B. 40
C.60
D. 80
The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.
The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.
Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.How would you use the Fundamental Theorem of Calculus to determine the value(s) of b if the area under the graph g(x)=4x between x=1 and x=b is equal to 240?
The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it be?
A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?
What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?
An apartment has 1026 square feet of carpeting. How much is this in square meters? Use the following conversion: 1 square meter is 10.8 square feet.
HELP PLEASE
Evaluate the expression.
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
v ⋅ w
a) -41
b) <-20, -36, 15>
c) <-28, 18, -35>
d) -9
Answer:
v . w = <-20, -36, 15>
Step-by-step explanation:
r = <7, -3, -7>, v = <4, 6, -5>, w = <-5, -6, -3>
To find the dot product of vectors we multiply the numbers
We need to multiply v and w
vectors is in the form of <x,y,z>
Multiply all the x values
4 times -5= -20
6 times -6 = -36
-5 times -3 = 15
So v . w = <-20, -36, 15>
A basketball player makes 39% of her shots from the free throw line. suppose that each of her shots can be considered independent and that she takes 5 shots. let x = the number of shots that she makes. what is the standard deviation for x?
Answer: 1.09
Step-by-step explanation:
Given : A basketball player makes 39% of her shots from the free throw line.
i.e. Proportion of her shots from the free throw line: p= 0.39
We assume that each of her shots can be considered independent .
She takes 5 shots.
i.e. Number of trials : n= 5
Let x = the number of shots that she makes.
Then , the standard deviation for x will be :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{5(0.39)(1-0.39)}\\\\=\sqrt{1.1895}=1.09064201276\approx1.09064201276\approx1.09[/tex]
Hence, the standard deviation for x= 1.09
Final answer:
The standard deviation for the number of shots made by a basketball player who has a 39% success rate and takes 5 shots is approximately 1.09 shots, calculated using the binomial distribution formula.
Explanation:
To find the standard deviation for the number of shots made by a basketball player who makes 39% of her shots, we use the concept of a binomial distribution.
Given that each shot is independent and that she takes 5 shots, with x representing the number of shots made, we can calculate the standard deviation using the formula for a binomial distribution.
The formula for the standard deviation (σ) in a binomial distribution is σ = √[n × p × (1 - p)], where n is the number of trials (in this case, 5 shots), and p is the success probability per trial (in this case, 0.39 for making a shot).
Plugging in the values, we get σ = √[5 × 0.39 × (1 - 0.39)] = √[5 × 0.39 × 0.61] = √[1.1885] ≈ 1.09 shots.
Therefore, the standard deviation for the number of shots made is approximately 1.09 shots.
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?
Answer: Third graph represents the acceptable weights for the frozen yogurt options.
Step-by-step explanation:
Since we have given that
Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4
After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.
So, it means the weight should be lie between 4 ounces and 7 ounces.
So, it can be written as [4,7].
4≤ x ≤7, here, x is the weight of frozen yogurt.
So, third graph represents the acceptable weights for the frozen yogurt options.
Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero
How many different three digit numbers can be written using digits 1,2,3,4,5 without any repeating digits? Thank you.
We can use the principles of permutation to find out that there are 60 different three-digit numbers that could be formed using the digits 1,2,3,4,5 without repetition.
Explanation:In order to find out how many different three-digit numbers can be formed using the digits 1,2,3,4,5 without repetition, we use the principles of permutation. Firstly, we should determine how many options we have for each digit place in the three-digit number.
There are 5 possible digits for the first place (since none has been used yet).There are 4 remaining digits for the second place.Finally, there are only 3 digits left to fill the third place.We then multiply these options together (5 x 4 x 3) which equals to 60 different three-digit numbers.
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Plastic storage bins are designed so they can be nested. The picture shows how each one fits inside another, leaving only the top part showing. The 4 stacked 10-gallon bins shown here measure 29 inches high. The height of the stack grows at the rate of 4 inches for each added bin. Write an equation in the form y = mx + b to describe the relationship between x, the number of nested bins, and y, the height of the stack.
Find the circumference and the area of a circle with diameter
2ft
The circumference of a circle with diameter 2ft is 2π ft and the area is π ft².
Explanation:To find the circumference of a circle, you can use the formula C = πd, where C is the circumference and d is the diameter. In this case, the diameter is 2ft, so the circumference would be C = π(2) = 2π ft. To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius. Since the radius is half the diameter, the radius would be 2ft/2 = 1ft. Therefore, the area would be A = π(1)² = π ft².
Final answer:
The circumference of a circle with a diameter of 2 feet is approximately 6.28 feet, and the area is approximately 3.14 square feet using the formulas C = πd and A = πr².
Explanation:
To find the circumference and the area of a circle with a diameter of 2 feet, we can use the formulas for circumference and area. The diameter of the circle is given as 2 feet. Therefore, the radius (r) is half of the diameter, which is 1 foot.
The formula for the circumference of a circle is C = πd where C is the circumference, π (pi) is approximately 3.14159, and d is the diameter. Since the diameter (d) is 2 feet, the circumference is:
C = π × 2 feet ≈ 3.14159 × 2 feet ≈ 6.28318 feet
So the circumference is approximately 6.28 feet.
The formula for the area of a circle is A = πr² where A is the area and r is the radius of the circle. Using the radius 1 foot, we find the area as follows:
A = π × (1 foot)² ≈ 3.14159 × 1 foot × 1 foot ≈ 3.14159 square feet
So the area of the circle is approximately 3.14 square feet.
The answers 80kg, 88 divided by 110 then times by 100
The student is completing a two-step mathematical operation to find a percentage by dividing 88 by 110 and then multiplying the result by 100. The '80kg' mention seems to be unrelated. Without more context, it's difficult to relate this to the given references, though they involve calculations and conversions in physics.
Explanation:The student seems to be performing a two-step operation where they are first dividing 88 by 110 and then multiplying it by 100. This is a common way of finding percentages. To get the result first, divide 88 by 110 which equals 0.8. Secondly, multiply 0.8 by 100 to get 80%. The '80kg' seems irrelevant to this operation if no further context is provided, it could be a weight measurement in physics.
In terms of any associations with the provided references, it seems that the question might be related to converting some measurements or calculating kinetic energy ('K'). However, without additional information, it's hard to ascertain the exact nature of the task.
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Write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (3x + 1) / (x + 1)^3(x^2 + 8)^2
Which of the following is not one of the three ways to express ratio A 3/4 B 3:4 C 3 of 4 D 3 to 4
Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?
x = average of next 5 quizzes
4 * 73 = first 4 quizzes
There will be a total of 4 +5 = 9 quizzes
Average of all quizzes = 88 = (4*73+5x)/9
9*88 = 9*(292 +5x)/9
792 = 292 + 5x
500 = 5x
X = 500/5 = 100
Next 5 quizzes need to average 100
The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending? h(t) = 5t + 500 h(t) = 5t – 500 h(t) = –5t + 500 h(t) = –5t – 500
The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?
The data set gives the number of hours it took each of the 10 students in a cooking class to master a particular technique. Which of the numbers below is the best measure of the central tendency of the data? {3, 3, 4, 4, 4, 5, 5, 5, 5, 30}
Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}
answer this plz
14 students are surveyed about the clothes they are wearing.
8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.
How many students are wearing jeans, but not a t-shirt?
2
3
4
5
Answer:
its
Step-by-step explanation:
PLEASE HELP?? EASY 5 POINTS!!! The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
How many solutions to 15x+11=8x
The length of a spring is a linear function of the weight of the object compressing it. For a particular spring, the length decreases by 1.5 inches for every 3 pounds pressing down on it. When 4 pounds are on the spring, the length of the spring is 8 inches long. What is the length of the spring if 15 pounds are pressing down on the spring?
The histogram shows the duration, in minutes, of movies in theaters.
What relationship between the median and mean is shown by the histogram?
A) The mean is less than the median.
B) The median is less than the mean.
C) The mean is equal to the median.
D) The median and mean cannot be compared from a histogram.