Answer: $17,788.20
Step-by-step explanation:
To calculate the monthly payment, we can use the loan formula:
P = (r * A) / (1 - (1 + r)^(-n))
where:
P is the monthly payment
A is the loan amount, which is the sale price of the car ($16,000) in this case
r is the monthly interest rate, which is the annual percentage rate (APR) divided by 12 (4% / 12 = 0.003333...)
n is the total number of payments, which is the number of years of the loan multiplied by 12 (5 years * 12 = 60)
Substituting these values into the formula, we get:
P = (0.003333... * $16,000) / (1 - (1 + 0.003333...)^(-60))
P ≈ $296.47
Therefore, the monthly payment is approximately $296.47, which is within the budget of $300/month.
To calculate the total cost of the car after the loan has been paid in full, we can multiply the monthly payment by the total number of payments (60) and add the original sale price of the car:
Total cost = P * n + A
Total cost = $296.47 * 60 + $16,000
Total cost = $17,788.20
Therefore, the total cost of the car after the loan has been paid in full is approximately $17,788.20.
Pencil boxes cost $15 each. Calculators cost $24 each. Kelly bought a total of 100 pencil boxes and calculators for $2130. How many pencil boxes did she buy?
Answer:
Step-by-step explanation:
Kelly bought a total of 1500 pencil boxes.
4. 6.9B Luke is about to start cooking. He places some butter in a pan and heats up the pan. As the pan heats up, the butter begins to melt. How is the energy moving? The cold is moving from the pan and into the butter The cold is moving from the butter and into the pan The heat is moving from the pan and into the butter The heat is moving from the butter and into the pan
As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.
What is heat transfer?Heat transfer is the transfer of energy from one place to another due to a difference in temperature. Heat transfer can occur through conduction, convection, and radiation. Heat is always transferred from hotter to colder objects and the rate of transfer depends on the temperature difference between the two and the material it is passing through. Heat transfer is essential in many natural and man-made processes.
The energy is moving in two directions. Cold is moving from the pan and into the butter, while the heat is moving from the butter and into the pan. This is known as a heat transfer. Heat transfers occur when two objects at different temperatures come into contact with each other. In this case, the cold pan is coming into contact with the warm butter, causing the heat to move from the butter and into the pan. This heat transfer causes the butter to melt. As the temperature of the pan increases, the heat transfer from the butter to the pan increases, causing the butter to melt faster. Ultimately, this heat transfer is necessary for Luke to prepare his food. Without it, the butter would stay solid and would not cook properly.
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ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Answer:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
Step-by-step explanation:ILL GIVE BRAINLIEST!! Pls answer A
Find the mÁB
104°
126°
B
D
please help me :(
use the Remainder Theorem and synthetic division please
The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 2x⁴ + x² - 10x + 1
Now, We can find all the values as;
At x = - 10;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (- 10) = 2 (- 10)⁴ + (- 10)² - 10 (- 10) + 1
⇒ f (- 10) = 20000 + 100 + 100 + 1
⇒ f (- 10) = 20201
At x = 2;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (2) = 2 (2)⁴ + (2)² - 10 (2) + 1
⇒ f (2) = 32 + 4 - 20 + 1
⇒ f (2) = 17
At x = 3;
⇒ f (x) = 2x⁴ + x² - 10x + 1
⇒ f (3) = 2 (3)⁴ + (3)² - 10 (3) + 1
⇒ f (3) = 162 + 9 - 30 + 1
⇒ f (3) = 143
Thus, The value of the functions are,
⇒ f (- 10) = 20201
⇒ f (2) = 17
⇒ f (3) = 143
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The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy.
A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 2, above 6 to 10 that stops at 6, above 11 to 15 that stops at 2, above 16 to 20 that stops at 5, and above 21 to 25 that stops at 1.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 21. This means that the tide frequently measured around 11 to 15 feet.
The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 21 to 25 feet range.
The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.
The correct statement regarding the histogram is given as follows:
The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
Hence the number of observations of each interval is:
1 to 5: 2 observations.6 to 10: 5 observations.11 to 15: 2 observations.16 to 20: 6 observations.21 to 25: 1 observations.Here are two similarly high bins, hence the distribution can be said to be bimodal, with maximum range given as follows:
25 - 5 = 21 - 1 = 20.
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Answer: its d
Step-by-step explanation:
I need help with choosing the correct answer for the second part of A.) this is a Elementary Statistics homework problem
Jan bought 7 liters of orange juice how many milliters did she buy
Answer:
The answer you're looking for is 7000ml
Step-by-step explanation:
Since there are 1000 millimeters inside a liter we can use the equation
x = 7×1000.
We need to first simplify all terms giving us this equation
x = 7000
With that, we are finished and that's how you do this question.
I hope this was helpful!
In an examination, Julius scored 5 more marks than John who in turn scored 4 marks less than Grace. If the total mark scored by the three students was 150. Find the mark of each student?
Making linear equations for given scores, Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
What is a linear equation, exactly?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable, with the degree of each variable being 1. In other words, a linear equation is an equation of a straight line, which can be expressed in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept of the line. Linear equations are used to model relationships between variables that have a constant rate of change, such as distance traveled over time or cost per item.
Now,
Let's assume that Grace's score is x.
Then, John's score will be x-4.
And, Julius's score will be x-4+5 = x+1.
The sum of their scores is given as 150. So, we can write an equation as:
x + (x-4) + (x+1) = 150
Simplifying the equation, we get:
3x - 3 = 150
Adding 3 to both sides, we get:
3x = 153
Dividing by 3 on both sides, we get:
x = 51
So, Grace's score is x = 51.
John's score is x-4 = 47.
And, Julius's score is x+1 = 52.
Therefore,
Grace scored 51 marks, John scored 47 marks, and Julius scored 52 marks in the examination.
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A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $80,000 saved up for when she goes to college in 15 years, assuming the account earns a 6% return.
Annual deposit: $
We can use the future value formula for an annuity to solve this problem:
FV = PMT * ((1 + r)^n - 1) / r
where:
FV is the future value of the annuity
PMT is the regular payment or deposit
r is the annual interest rate
n is the number of periods (in this case, the number of years)
We want to solve for PMT, so we can rearrange the formula to get:
PMT = FV * r / ((1 + r)^n - 1)
Plugging in the given values, we get:
FV = $80,000
r = 6% = 0.06
n = 15 years
So, the annual deposit required is:
PMT = $80,000 * 0.06 / ((1 + 0.06)^15 - 1) ≈ $3,782.58
Therefore, the man would need to deposit approximately $3,782.58 into the account each year in order to have $80,000 saved up for his granddaughter's college education in 15 years, assuming a 6% return.
A line passes through the point (2, -3) and has a slope of - 4.
Write an equation in slope-intercept form for this line.
A service that repairs air conditioners sells maintenance agreements for $75 a year. The average cost of repairing an air conditioner is $350 and 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair. Find the service’s expected profit.
The service's expected profit is $6,800.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To find the service's expected profit, we need to calculate the total revenue and the total cost, and then subtract the cost from the revenue.
First, let's calculate the total revenue. The service sells maintenance agreements for $75 a year, so for every 100 customers, the revenue will be:
100 customers x $75/customer = $7,500
Now, let's calculate the total cost. We know that 2 in every 100 people who purchase maintenance agreements have air conditioners that need repair, and the average cost of repairing an air conditioner is $350. So for every 100 customers, the cost of repairs will be:
2 customers x $350/customer = $700
Finally, let's calculate the expected profit:
Expected profit = Total revenue - Total cost
Expected profit = $7,500 - $700
Expected profit = $6,800
Hence, the service's expected profit is $6,800.
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pleaseee i need help.
use the Remainder Theorem and synthetic division, please.
Using Remainder Theorem and synthetic division, f(-10) = 191, f(2) = 1, f(3) = 34
What is synthetic division?
A polynomial's coefficients are split one by one in synthetic division.
The split polynomial's zero, which belongs in the box on the far left, has this value.
To use the Remainder Theorem and synthetic division to evaluate f(-10), f(2), and f(3) for the function[tex]f(x)=2x^2+x^2-10x+1[/tex], we can proceed as follows:
First, we need to perform synthetic division using -10, 2, and 3 as the divisors.
1) For f(-10):
The result of the division is 191, so f(-10) = 191.
2) For f(2):
The result of the division is 1, so f(2) = 1.
3) For f(3):
The result of the division is 34, so f(3) = 34.
Therefore, we have:
f(-10) = 191
f(2) = 1
f(3) = 34
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The cost of 3 scarves is $86.25. What is the unit price?
In linear equation, $28.75 is the unit price .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
The cost of 3 scarves is $86.25
then,
the unit price is = $86.25/3 = $28.75
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The scale factor of two similar cylinders is 5:2.
The volume of the smaller cylinder is 28 m3.
What is the volume of the larger cylinder?
Question 8 options:
700 m3
350 m3
70 m3
437.5 m3
175 m3
Using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.
What is the scale factor?When a shape is magnified and each side is multiplied by the same number, this is known as a scale factor.
The scaling factor is this figure. Scale factors are used on maps to accurately depict distances between locations.
With a scale factor of 2, the new shape that results from scaling the old shape is twice as large.
So, get the volume of the larger cylinder as follows:
x/5 = 28/2
2x = 28*5
2x = 140
x = 70m³
Therefore, using the scale factor of 5:2, the volume of the larger cylinder is (C) 70m³.
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Complete question:
The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?
Question 8 options:
A. 700 m3
B. 350 m3
C. 70 m3
D, 437.5 m3
E. 175 m3
Terry takes a 800 mg Tylenol for his headache. Every hour that the Tylenol is in his system, a quarter of the medication dissolves in his body.
1. WRITE a function that models the amount of Tylenol in Terry’s body over time. Use x for hours, and y for the amount of Tylenol, in mg, remaining in the body.
2. When there is less than 100mg of medicine left in the body, it safe to take it again. HOW LONG will it take before Terry can take more medicine?
Therefοre, the sοlutiοn οf the given prοblem οf functiοn cοmes οut tο be Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
What is functiοn?The curriculum fοr mathematics includes a wide range οf tοpics, such as numbers, numbers, and their cοmpοnents, as well as cοnstructiοn, building, and bοth actual and hypοthetical geοgraphic places. A wοrk discusses the relatiοnships between different variables that all wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that, when cοmbined, prοduce specific results fοr each input.
Here,
The functiοn can be written as fοllοws:
=> y = 800 * (0.25)ˣ
where y is the quantity οf Tylenοl still in Terry's system in milligrammes and x is the number οf hοurs since he last tοοk the medicatiοn.
When Terry's bοdy's cοncentratiοn οf Tylenοl gοes belοw 100mg, we need tο find οut hοw lοng it will be befοre he can take mοre medicatiοn.
The expοnential decay fοrmula frοm part 1 can be used tο find a sοlutiοn fοr this:
=> 800 * (0.25)ˣ = 100
by 800, divide bοth sides.
=> (0.25)ˣ = 0.125
Cοnsider the twο sides' lοgarithms:
=> lοg(0.25) * x = lοg (0.125)
tο find x:
=> lοg(0.125) / lοg (0.25)
=> x = 2.4
Terry can easily take anοther 800mg Tylenοl fοr his headache after abοut 2.4 hοurs have passed.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
It is true that the graph contains the point (0, 0).
The following three assertions regarding the function and its graph are true:
The function's graph resembles a parabola.
The graph begins at the bottom.
The point is shown in the graph (0,0).
Explanation:
A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.
The parabola widens downward because the coefficient of x2 is positive (1 in this instance).
When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.
We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).
We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).
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Directions - Evaluate the following exponential function for the x-values in the table. Complete the table with y-values.
y=9x( 3/1 ) x
Some numeric values of the exponential function y = 9(3)^x are given as follows:
x = -2, y = 1.x = -1, y = 3.x = 0, y = 9.x = 1, y = 27.x = 2, y = 81.How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is given as follows:
y = 9(3)^x.
Hence some numeric values of the function are given as follows:
x = -2, y = 1. -> y = 9 x (3)^(-2).x = -1, y = 3. -> y = 9 x (3)^(-1).x = 0, y = 9. -> y = 9 x (3)^(0).x = 1, y = 27. -> y = 9 x (3).x = 2, y = 81. -> y = 9 x (3)^(2).Learn more about the numeric values of a function at brainly.com/question/28367050
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A box contains 8 green marbles and 17 white marbles. If the first marble chosen was a green marble, what is the probability of choosing, without replacement, a white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
Step-by-step explanation:
[tex]\frac{17}{25}[/tex]
Write the ratio as a fraction in lowest terms. 44 minutes to 5 hours
Answer:Let's convert hours to minutes:
Now we have:
44 minutes to 300 minutes
We write the ratio as a fraction:
We can reduce both the numerator and denominator by 4, to get:
The correct answer is:
Step-by-step explanation:
50 Points!!! Write a verbal sentence to represent 5n/n+3=n-8. Show as much work as possible please. Photo attached. (Only looking for answer to 12B)
Answer: Your welcome!
Step-by-step explanation:
5n / (n + 3) = n - 8
5n = n(n + 3) - 8(n + 3)
5n = n^2 + 3n - 8n - 24
n^2 - 5n - 24 = 0
n = 4 or n = -6
The verbal sentence to represent 5n/n+3=n-8 is "When n is 4 or -6, 5n divided by n plus 3 is equal to n minus 8."
A researcher is investigating academic motivation among college students and their siblings. This type of study would be _______
Answer:
This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.
Step-by-step explanation:
A register has 5376 business cards to give out the register gives out an equal number of business cards in 48 days until there are no more business cards live how many business cards does the register give out each day a 111 business cards be 112 business cards C1 130 business cards D1 114 business cards you have to divide 48÷5376
Answer: 112 business cards
Step-by-step explanation:
We will divide the number of business cards by the number of days cards were handed out to see how many cards were handed out per day.
5,376 cards / 48 days = 112 business cards
Find the Rate. (Round to the Nearest Tenth)
Principal = $900
Time = 1 year
Interest = $76.50
Answer:
$ 1,937.50.
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?
If a car travels at an average speed of 68 miles per hour, it takes it 5 hours 15 minutes to travel 357 miles.
What is the average speed?The average speed is the unit rate.
The average speed is computed as the quotient of the total distance and the total time.
Conversely, the time is a function of the division of the total distance by the average speed.
The total distance traveled by the car = 357 miles
The average speed = 68 miles per hour (mph)
The time = Distance/Average speed = 357/68 = 5.25 hours
= 5 hours 15 minutes.
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Pleaseeee yelp meeeeee
Answer:
x ≤ 6.8
Step-by-step explanation:
1.25x + 6.50 ≤ 15
1.25x ≤ 8.5
x ≤ 6.8
So, the answer is x ≤ 6.8
Answer:
Below
Step-by-step explanation:
1.25x + 6.50 <= 15 SUBTRACT 6.50 from both sides of the equation
1.25x ≤ 8.50 DIVIDE both sides by 1.25
x ≤ 6.8
Can someone help me on this?
Answer:
X+15 is the answer..................
(Score for Question 3: of 5 points) 1. a). Find the inverse of the function, f(x) = (x - 2)3 - 3. Please show all work in finding the inverse Answer: b) Now graph the inverse function f-1 (x) using the equation you found as the answer to part a) No computer-generated graphs will be accepted. Remember to clearly indicate at least three (3) points on the graph
The inverse of function is (x + 3)^(1/3) + 2 and the graph is attached below
What is the inverse of the functiona) To find the inverse of the function f(x) = (x - 2)^3 - 3, we can follow these steps:
1. Replace f(x) with y: y = (x - 2)^3 - 3
Solve for x in terms of y:
a. Add 3 to both sides: y + 3 = (x - 2)^3
b. Take the cube root of both sides: (y + 3)^(1/3) = x - 2
c. Add 2 to both sides: x = (y + 3)^(1/3) + 2
Replace x with f^-1(x): f^-1(x) = (x + 3)^(1/3) + 2
b) To graph the inverse function f^-1(x), we can use the equation we found in part a) and plot some points:
When x = 0, f^-1(x) = (0 + 3)^(1/3) + 2 = 3^(1/3) + 2When x = 1, f^-1(x) = (1 + 3)^(1/3) + 2 = 2^(1/3) + 2When x = 3, f^-1(x) = (3 + 3)^(1/3) + 2 = 2 + 2 = 4So we have three points: (0, 3^(1/3) + 2), (1, 2^(1/3) + 2), and (3, 4).
To sketch the graph, we can also note that the function f(x) = (x - 2)^3 - 3 has a vertical asymptote at x = 2 and a local minimum at (2, -3). Therefore, the inverse function f^-1(x) will have a horizontal asymptote at y = 2 and a local maximum at (4, 2).
Combining all of this information, we can sketch the graph of f^-1(x) as shown below:
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Multiply f and 7. Then add 9 in expression
1354.24 rounded to the nearest tenth
what is the exact circumference of a circle with a radius of 17mm (Answer options) 8.5
17
34
68
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=17 \end{cases}\implies C=2\pi (17)\implies C=34\pi[/tex]