The equation of the car can be given as and the price of the car after 8 years is $4445.
What is an exponential function?
A function of the form [tex]a^{x}[/tex] is known as exponential function. In short the function which has an exponent is known as exponential function.
We are given that the value of a new car after 2 years was $11,200. When the car is 6 years old, the value has dropped to $6100.
Let the original price of the car be [tex]P_{0}[/tex]
After two years the price of the car is $11200
Mathematically it can be given as
[tex]11200= P_{0}e^{2x}[/tex]
After 6 years the price of the car is $6100
Mathematically it can be given as
[tex]6100=P_{0}e^{6x}[/tex]
Dividing both equations we get,
[tex]1.83=e^{-4x}[/tex]
Which can also be written as
[tex]e^{4x}=0.54[/tex]
on solving we get,
x=-0.154
Hence the rate at which price of the car is dropping is
[tex]P=P_{0}e^{-0.154t}[/tex]
No we have to find the original price of the car
To do so we substitute t=2 in the equation
we get
11200=[tex]P_0e^{-0.308}[/tex]
On solving we get,
15240=[tex]P_0[/tex]
Now we find the price of the car after 8 years
P=15240·[tex]e^{-1.232}[/tex]
On simplifying we get
P=$4445
Hence the price of the car after 8 years will be $4445
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Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answer:
The answer is D
Step-by-step explanation:
Check to see when the graph is increasing and decreasing from left to right.
It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.
Then, it increases from x = -3 to x = 0 or (-3,0)
Then, it stays constant from x = 0 to x = 2 or (0,2)
Lastly, it decreases from x - 2 to x = 5 or (2,5)
To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)
The only option that fits these conditions is D.
solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
[tex]\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}[/tex]The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
1.2
Step-by-step explanation:
39+(20.4) can u help me with this answer I don't know how to do it
You have the following expression:
39 + (-20.4)
In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:
39 + (-20.4)
= 39 - 20.4
= 18.6
Hence, the simplified expression is 18.6
Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A ands who did Plan
B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B
Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
The number of hour (time) for which workout plan A would last is 0.75 hour. Also, the number of hour (time) for which workout plan B would last is 0.5 hour.
How to calculate the number of hours (time)?In order to solve this word problem, we would assign variables to the number of hours (time) each plan and then translate the word problem into algebraic equation as follows:
Let x be the number of hours (time) for workout plan A.Let y be the number of hours (time) for workout plan B.Translating the word problem into an algebraic equation, we have;
On Friday ⇒ 6x + 5y = 7 ....equation 1.
On Saturday ⇒ 2x + 3y = 3 ....equation 2.
Next, we would solve the simultaneous equation by using elimination method:
3 × (2x + 3y = 3) = 6x + 9y = 9 ........equation 3.
Subtracting equation 1 from equation 3, we have:
6x + 9y = 9
6x + 5y = 7
4y = 2
y = 2/4
y = 1/2
y = 0.5 hour.
For the value of x, we have:
6x + 5y = 7
6x + 5(0.5) = 7
6x + 2.5 = 7
6x = 7 - 2.5
6x = 4.5
x = 4.5/6
x = 0.75 hour.
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Complete Question:
Charmaine the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 6 clients who did Plan A and 5 clients who did Plan B. On Saturday there were 2 clients who did Plan A and 3 who did Plan B Charmaine trained her Friday clients for a total of 7 hours and her Saturday clients for a total of 3 hours. How long does each of the workout plans last?
Can someone help me out (I will give branliest)
Answer: Emma > Amelia > Brandon > Celesle > Damian
Step-by-step explanation:
We convert all the fractions to decimals (2 decimals).
Amelia 4.35 lbs
Brandon [tex]4\frac{1}{3}= \frac{12}{3} +\frac{1}{3} =\frac{13}{3}[/tex] ≈ 4.33 lbs
Celesle 4.2 lbs
Damian √15 ≈ 3.87 lbs
Emma [tex]4\frac{2}{3} =\frac{12}{3} +\frac{2}{3} =\frac{14}{3}[/tex] ≈ 4.67 lbs
4.47 lbs > 4.35 lbs > 4.33 lbs > 4.2 lbs > 3.87 lbs
Emma > Amelia > Brandon > Celesle > Damian
RS = 8y +4, ST = 5y + 7, and RT = 115.What is the value of y?
EXPLANATION:
1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line
2. The correct and most appropriate method is the matching method.
The exercise is as follows:
[tex]\begin{gathered} RS\text{ }=8y+4\text{ } \\ ST=5y\text{ }+7 \\ RS=ST\text{ } \\ 8y+4=5y+7 \\ 8y-5y=7-4 \\ 3y=3 \\ y=\frac{3}{3} \\ \textcolor{#FF7968}{y=1} \\ \text{\textcolor{#FF7968}{the answer is y}}\textcolor{#FF7968}{=1}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{as}\text{\textcolor{#FF7968}{ a whole number or y}}\textcolor{#FF7968}{=\frac{3}{3\text{ }}}\text{\textcolor{#FF7968}{ as a }}\textcolor{#FF7968}{fractional}\text{\textcolor{#FF7968}{ number}} \end{gathered}[/tex]5) Naomi painted 16.5 square feet of a mural at a rate of 2 square feet per hour. Calire painted 7.5 square
feet of the mural at a rate of 4 square feet per hour. If they continue to paint at the same rates, how many
more hours will it take until Naomi and Claire have painted equal areas of the mural?
Answer: 4.5
Step-by-step explanation:
We need to find the amount of time until Calire paints a total of 9 more square feet.
Since the difference in their rates is 2 square feet per hour, it will take 9/2 = 4.5 more hours.
Which of the following statements are not true regarding functions?Check all that apply.A. A function is a relation in which each value of the input variable ispaired with at least one value of the output variable.I B. The vertical line test may be used to determine whether afunction is one-to-one.O C. A sequence is a function whose domain is the set of naturalnumbers.D D. The horizontal line test may be used to determine whether afunction is one-to-one.
Only B is not true, because the vertical line test is to know if a graph is from a function.
Graph the equation after rewriting it in slope-intercept form. 9x+3y=18
The equation of a line in the slope intercept form is expressed as
y = mx + c
The given equation is
9x + 3y = 18
We would rearrange it so that it takes the form of the slope intercept equation shown above.
We would divide both sides of the equation by 3, we have
9x/3 + 3y/3 = 18/3
3x + y = 6
Subtracting 3x from both sides of the equation, we have
3x - 3x + y = 6 - 3x
y = 6 - 3x
The slope intercept form is
y = - 3x + 6
To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have
For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12
For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9
For x = 0, y = 6 - 3(0) = 6 - 0 = 6
For x = 1, y = 6 - 3(1) = 6 - 3 = 3
For x = 2, y = 6 - 3(2) = 6 -6 = 0
The graph is shown below
Describe the end behavior of the graph of the following polynomial function:
We will have the following:
From the polynomial we will have that:
*It falls to the left and rises to the right.
This can be seeing as follows:
Explain how the points A(9,-) and 8(9,3) are related. Use vocabulary words
in your explanation.
Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.
Step-by-step explanation:
Solve the compound inequality. 2x-4 > 8 or 3x-1 < -10
-3 < x < 6
x > 6 or x < -3
x > 2 or x < -3
x < 6 or x < -3
The solution to the compound inequality is x > 6 or x < -3
How to solve compound inequality?An inequality is a mathematical expression that has <, >, ≤ and ≥.
A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
add 4 to both sides of the inequality
2x - 4 + 4 > 8 + 4
2x > 12
divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
add 1 to both sides of the inequality
3x - 1 + 1 < - 10 + 1
3x < - 9
divide both sides by 3
x < -9 / 3
x < -3
Therefore, x > 6 or x < -3
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The solution to the compound inequality will be; x > 6 or x < -3
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.
A compound inequality is defined as an inequality that combines two simple inequalities.
Therefore, solve the compound inequality that will be;
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
Then add 4 to both sides of the inequality so,
2x - 4 + 4 > 8 + 4
2x > 12
Now, divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
Again, add 1 to both sides;
3x - 1 + 1 < - 10 + 1
3x < - 9
Then divide both sides by 3;
x < -9 / 3
x < -3
Therefore, solution to the compound inequality is; x > 6 or x < -3
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The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.
The sphere has a surface area of 482.8064 square meters
How to determine the surface area of the sphere?From the question, the given parameters are:
Diameter, D = 12.4 meters
π = 3.14
The surface area of the sphere is calculated using the following formula
S = 4π(D/2)²
Substitute the given parameters in the above formula
So, we have
S = 4 * 3.14 * (12.4/2)²
Evaluate the exponent
This is represented as
S = 4 * 3.14 * 38.44
Evaluate the product
This is represented as
S = 482.8064
Hence, the surface area of the sphere is 482.8064 square meters
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Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope −1.
Answer: y = -1x + 3
Step-by-step explanation:
Point-Slope form: y - y1 = m(x-x1)
Replace the form with the values provided:
y - 15 = -1(x+12)
Once you get this, you need to get y by itself in order to get it in slope intercept form.
Distribute:
y -15 = -1x - 12
Add -15 to the right side:
y = -1x + 3
25 lbs of potatoes cost $100. How much
would 15 lbs cost?
Round the answer to two decimal digit
Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answer:
Step-by-step explanation:
Which statement about the location of √ 7 on a number line is true?
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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I dont know pls help me
In Close Encounters of a Bear Kind, the statement that represents the author's primary attitude towards John's work is that C. John's work is dangerous.
How to illustrate the information?According to the author, he stated that people don't usually realize that bears
can be very dangerous.
He further stated that they will reap people apart of they e the chance. The narrator gave an example about how he walked out at night and had to run back home for his dear life. This was why he stated that the job of John whom was a photographer was a dangerous one.
In conclusion, the correct option is C.
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Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,1) Midpoint: (-4,-6)
Answer:
(-13, - 6)
Step-by-step explanation:
Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2
(-4,-6) = (9+x)/2, (1+y)/2
9+x= - 4
X= - 13
1+y= - 6
Y= - 7
Ans=
(-13, - 6)
solve the following system of equation graphically on the set of axes below y= x + 5y= -2x -1
To solve graphically this set of equations, we should first draw both lines and see the value of x at which the lines crosses
Both graphs can be drawn as follows
We can see that both graphs intersect at a negative value of x. With a more accurate graph, we can determine that both lines intersect at x=-2.
So the solution for this system of equation is x=-2.
What number is five times the first number. The third number is 100 more than the first number. Of the sound of three numbers is 490, find the numbers
Answer:
The three numbers are:
4.62,
23.1, and
462.2
Step-by-step explanation:
Let X be the "first number."
B = What number is five times the first number: 5X
C = third number is 100 more than the first number: 100X
The sum of all three is 490: X + B + C = 490
----
X + B + C = 490
X + 5X + 100X = 490
106X = 490
X = 4.622
Check:
X = 4.622
B = 5X = 23.11
C = 100X = 462.2
Check:
Sum (4.622 + 23.11 + 462.2) = 490
for anyone that knows how to do this i only need help with these two questions
-4x-1=-y
solve for y
-4y+20+3x=0
solve for y
[tex]-4x-1=-y\\y[/tex]
Flip the equation:
[tex]-y=-4x-1[/tex]
Divide both sides by -1:
[tex]\frac{-y}{-1} =\frac{-4x-1}{-1}[/tex]
[tex]y=4x+1[/tex]
__________________________________________________________
[tex]-4y+20+3x=0\\y[/tex]
Add -3x to both sides of the equation:
[tex]3x-4y+20+-3x=0+-3x\\-4y+20=-3x[/tex]
Add -20 to both sides of the equation:
[tex]-4y+20+-20=-3x+-20\\-4y=-3x-20[/tex]
Divide both sides by -4:
[tex]\frac{-4y}{-4} =\frac{-3x-20}{-4}[/tex]
[tex]y=\frac{3}{4} x+5[/tex]
hemoglobin determinations were made on sixteen animals exposed to ionizing radiation. the following observations were recorded: 15.6, 14.4, 14.8, 13.8, 16.6, 14.0, 17.4, 17.3, 18.6, 16.2, 15.7, 14.7, 16.4, 13.9, 14.8, 17.5. construct a 95 percent confidence interval for population standard deviation?
The required values for a 95 percent confidence interval for population standard deviation are CI₈² = [1.1894, 5.221]
CI₈ = [1.0906, 2.2849]
n = 16, Standard Deviation = 1.4764, Var = 2.1796
X²₀.₀₂₅,₁₅ = 6.26, X²₀.₉₇₅,₁₅ = 27.49
CI₈² = [(15ₓ2.1796/27.48),(15ₓ2.1796/6.26)] = [1.1894, 5.221]
CI₈ = [[tex]\sqrt{15*2.1796/27.48} , \sqrt{15*2.1796/6.26}[/tex]] = [1.0906, 2.2849]
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Bella's mother is 5 less than 4 times her
daughter's age. If her mom is 39 years old, how
old Is Bella?
a lake is stuck with 1,550 young carp. the number of the original fish alive after t years is given by the function P (t)= 1550e^-0.4t, when will there be 440 of the original fish left from to the nearest tenth
so the time needed is 3.1 years
shelly wants to tile a rectangular floor that measures 132 feet by 150 feet using square tiles that are all of the same size, with no overlap and no squares hanging over the edge. what is the measurement of the largest square tiles she can use?
The measurement of the largest square tiles she can use is 6 feet.
Finding all common factors between two numbers and choosing the biggest one yields the highest common factor (HCF). For instance, the numbers 8 and 12 share the elements 1, 2, and 4. Four is the greatest common factor.
Steps for calculating HCF:
Step 1: Write each integer as the sum of its prime factors in step one.
Step 2: List the shared factors between the two numbers.
Step 3: The HCF is the sum of all the common prime factors ( use the lower power of each common factor)
Given,
Measurement of the rectangular floor:
length = 150 feet
breadth = 132 feet
The measurement of the largest square can be calculated by finding the HCF of 132 and 150.
132 = 2*2*3*11
150 = 2*3*5*5
So, HCF (132, 150) = 2*3 = 6.
Hence, the measurement of the largest square tiles she can use is 6 feet.
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6) Bill found a pair of jeans that cost $35.00. If he had a 20%-off coupon, how much would the
jeans cost?
Mr. Stewart wants to cut a board that is 34 inches long into four pieces that are the same length. How long will each
board be after he cuts them?
08.0 inches
8.2 inches
8.4 inches
O 8.5 inches
You and a friend have each randomly draw a card.
There are 52 cards in a deck.
There are 12 face cards in the deck, that is 3 face cards per suit.
The probability of getting at least from two draws is given to be:
[tex]P=P(X=1)+P(X=2)[/tex]Therefore, the probability is calculated using the formula:
[tex]P=\frac{^{12}C_1\times^{40}C_1}{^{52}C_2}+\frac{^{12}C_2}{^{52}C_2}[/tex]Using the combination formula, we have the solution to be:
[tex]\begin{gathered} \Rightarrow\frac{12\times40}{1326}+\frac{66}{1326}=\frac{480}{1326}+\frac{66}{1326} \\ P=\frac{546}{1326} \\ P=\frac{7}{17} \end{gathered}[/tex]The LAST OPTION is correct.