Car 1: It is an exponential function that is given as P = 18,500 (0.9595)ⁿ and the price after 10 years is $12,235.5.
Car 2: It is a linear function that is given as 2000x + 3y = 55500 and the price after 10 years is $11,833.33.
And Yes, there is a significant difference.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Baxter is thinking about buying a car. The table below shows the projected value of two different cars for three years.
Car 1 (value in dollars)
Year 1: 18,500
Year 2: 17,390
Year 3: 16,346.60
Car 2 (value in dollars)
Year 1: 18,500
Year 2: 17,500
Year 3: 16,500
The exponential function describes car 1.
Then the function will be
[tex]\rm P = 18500\times (0.95995)^n[/tex]
The linear function describes car 2.
[tex]\rm y \ - \ 18500 = \dfrac{-2000}{3}(x - 0)\\\\\\3y - 55500 = -2000x\\\\\\2000x +3y = 55500[/tex]
Then the value of the car 1 after 10 years will be
[tex]\rm P = 18500\times (0.95995)^{10}\\\\\\P = \$ \ 12,235.5[/tex]
Then the value of the car 2 after 10 years will be
[tex]\rm 2000 \times 10 +3y = 55500\\\\y = \$ \ 11,833.33[/tex]
Yes, there is a significant difference.
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Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. (5 points) Part B: How much time does Melvin spend swimming every day? Show your work. (3 points) Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning. (2 points)
Answer:
See below
Step-by-step explanation:
Part A:
⇒ Y represents the amount of swimming
⇒ X represents the amount of tennis
Now, creating to equations:
y + 40 = xx + y = 110Part B:
⇒ First equation is substituted for X in the other equation.
Gives us the plug in:
y + 40 + y = 1102y = 70⇒ Y = 35 minutes of swimming
⇒ Adding :
35 + 40 = 75 minutes of swimming per day.
Part C:
No, due to the equation ⇒ 70 + (70 - 40) = 100
Therefore, making this statement impossible.
Susan bought gas for her car,the gas cost 2.79 per gallon susan bought 15.4 gallons,what was the total cost for susans gas
Four friends are sharing 5 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
Answer:
each friend will get 5/4 or 1.25 cups of lemonade
Step-by-step explanation:
5 divide by 4 since there are 4 friends.
so 5/4 of the lemonade will be shared by each friend.
Step-by-step explanation:
each friend would get 1.25 cups each
in a class of 32 students there are 8 girls who played basket ball and 5 boys who did not
(a) 12 boys play basketball
(b) See figure 2 below
==========================================================
Explanation:
Part (a)
You are on the right track so far when you wrote the partial table.
There are 15 girls in the class, and 8 girls that play basketball. That must mean 15-8 = 7 girls do not play basketball.
Focusing on the first row only, we'll have 7 go in the second column and 15 go in the third column. The first row is filled out entirely.
There are 32 students and 15 girls. This means there are 32-15 = 17 boys. We'll write 17 at the end of the second row.
The other missing value of this row is 17-5 = 12 to represent the number of boys who play basketball. This is because of the 5 boys that don't play basketball.
To fill out the missing items in the third row, add the columns straight down.
We have 8+12 = 20 basketball players and 7+5 = 12 people who do not play basketball. Notice how 20+12 = 32 along the bottom row to help confirm the correct values.
Check out figure 1 to see the entire two-way frequency table.
We see that there are 12 boys that play basketball.
------------------------------------------------
Part (b)
The previous part detailed how to set up the two-way frequency table.
For this part, we'll be creating the two-way relative frequency table. The keyword "relative" means that we'll divide each item by the grand total 32.
For instance, in the first row & first column we have 8/32 = 0.25; do the same with the other values. Do not round. The reason for this is because each decimal item is a terminal decimal, meaning the digits stop at some point. If your teacher instructs you to round, then be sure to follow those instructions of course.
Check out figure 2 so you can see the two-way relative frequency table.
A result like 0.25 in the first row & first column tells us that 25% of the class is a girl and plays basketball.
Given the pyramid, calculate the SURFACE AREA and VOLUME. (please help ASAP)
sanjeev ate 1/6 of cake he gave to his frend the remainder 1/5 how much did he keep
Step-by-step explanation:
[tex] = 1 - ( \frac{1}{6} + \frac{1}{5} )[/tex]
[tex] = 1 - ( \frac{5}{30} + \frac{6}{30} )[/tex]
[tex] = 1 - \frac{11}{30} [/tex]
[tex] = \frac{30}{30} - \frac{11}{30} [/tex]
[tex] = \frac{19}{30} [/tex]
So, he keeps [tex] \frac{19}{30}[/tex]
Answer:
Sanjeev kept 19/30 of his cake.
Step-by-step explanation:
So, if Sanjeev ate 1/6 of the cake there will be 5/6 of the cake left over.
He gave 1/5 of this 5/6 to his friend.
He did not give 1/5 of the entire cake, he gave 1/5 of the remainder of his cake, which was 5/6.
To solve this, we must first convert both fractions to the same denominator.
1/5 and 5/6 becomes 6/30 and 25/30
He gave away 6/30 of this 25/30
It is now clear that we must take away how much he gave away from the remainder of the cake.
25/30 subtract 6/30 becomes 19/30
We cannot simplify this.
Therefore, Sanjeev kept 19/30 of his cake.
The polynomial function f(x) = 3x5 – 2x2 7x models the motion of a roller coaster. the roots of the function represent when the roller coaster is at ground level. which answer choice represents all potential values of when the roller coaster is at ground level? begin by factoring x to create a constant term. 0, plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 0, plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7 plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7
The root of the polynomial function f(x) = 3x⁵ - 2x² + 7x is 0
How to determine the roots of the equation?The polynomial function is given as:
f(x) = 3x⁵ - 2x² + 7x
Set the function to 0
3x⁵ - 2x² + 7x = 0
Factor out x
x(3x⁴ - 2x + 7) = 0
Divide both sides by (3x⁴ - 2x + 7)
x = 0
Hence, the root of the equation is 0
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Answer:
B
Step-by-step explanation:
cause math
Kyra is finding the area of the circle. She cuts the circle into equal sectors and arranges them into the shape of a parallelogram.
A circle is cut into 8 equal sections. The sections are arranged into the shape of a parallelogram with a base of 9.42 inches and height of 3 inches.
Which expression represents the approximate area of the circle in square inches?
can i pls get help :(
A circle is a curve sketched out by a point moving in a plane. The area of the circle will be equal to 28.26 in².
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The area of the circle will be approximately equal to the area of the parallelogram. Therefore, the area of the parallelogram can be written as,
[tex]\text{Area of parallelogram} = 9.42 \times 3 = 28.26\rm\ in^2[/tex]
Hence, the area of the circle will be equal to 28.26 in².
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What is the value of y on question 7
The value of y in the given question will be y = -2x + 26.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The value of y will be calculated as:-
Given the equation :-
4y - 2x = 12
y = x / 2 + 12
Now for two perpendicular lines, the product of the intercepts is -1
m₁ x m₂ = -1
So the new intercept will be
m₂ = -1 / m₁ = -1 / 1 / 2 = -2
So new equation will be
y = -2x + c
2 = -2 x 12 + c
c = 26
So the equation will be:-
y = -2x + 26
Therefore the value of y in the given question will be y = -2x + 26.
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Which of the following inequalities matches the graph?
Answer:
6x - y < -3
Step-by-step explanation:
When graphing inequalities:
< or > = dashed line
≤ or ≥ = solid line
< or ≤ = shade below the line
> or ≥ = shade above the line
Create an equation for the line
Choose 2 points on the line:
let (x₁, y₁) = (-1, -3)let (x₂, y₂) = (0, 3)Calculate the slope:
[tex]\sf \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-3)}{0-(-1)}=6[/tex]
Determine the equation for the line using the point-slope formula:
[tex]\implies\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-(-3)=6(x-(-1))[/tex]
[tex]\implies \sf y+3=6(x+1)[/tex]
[tex]\implies \sf y=6x+3[/tex]
As the shading is above the line:
⇒ y > 6x + 3
Compare with answer options
Rearrange each answer option to make y the subject:
Option (a)
-6x + y < 3
⇒ y < 6x + 3
Option (b)
6x + y < 3
⇒ y < -6x + 3
Option (c)
6x - y < -3
⇒ -y < -6x - 3
⇒ y > 6x + 3
Therefore, as option C matches the calculated inequality, the answer is
6x - y < -3
Answer:
6x - y < 3
Step-by-step explanation:
Finding the equation of the inequality :
Slope :
⇒ m = 3 - (-3) / 0 - (-1)
⇒ m = 6/1
⇒ m = 6
Y-intercept :
⇒ (0, 3)
Equation :
⇒ y = 6x + 3
Here :
⇒ Above the origin, so it is greater than ( > )
⇒ y > 6x + 3
⇒ 6x - y < 3
can someone help me with this 10th grade sector problem? This is 10th grade geometry, I will reward brainliest! Also please show your work!
Answer:
841854.7 ft²
Explanation:
[tex]\sf Formula \ for \ area \ of \ sector = \dfrac{\theta}{360 } \ x \ \pi r^2[/tex]
Here given:
θ = 60°radius (r) = 1268 ftHence solve for area of sector:
[Insert values]
[tex]\rightarrow \sf \dfrac{60}{360 } \ x \ \pi (1268)^2[/tex]
[simplify]
[tex]\rightarrow \sf 841854.6778[/tex]
[round to nearest tenth]
[tex]\rightarrow \sf 841854.7[/tex]
Answer:
841,854.7 ft²
Step-by-step explanation:
The area of the sector can be found using the appropriate area formula. The central angle in radians is required.
A = 1/2r²θ . . . . where r is the radius, and θ is the central angle in radians
__
The 60° angle corresponds to 60° × π/180° radians, or π/3 radians. The area of the 60° sector is then ...
A = 1/2(1268 ft)²(π/3) = 803912/3π ft² ≈ 841,854.7 ft²
Devin does not have to plow an area of about 841,854.7 square feet.
__
Additional comment
At 43560 ft² per acre, that's about 19.3 acres.
please please help!!! see attached questions I WILL VENMO YOU ( i’m not sure if the first one is right)
Answer:
Your first answer is correct.
Second question: 300 ft.
Step-by-step explanation:
2nd problem, create a proportion.
[tex]\frac{220}{x}=\frac{305}{416} \\305x = 91520\\\frac{305x}{305}= \frac{91520}{305} \\x=300[/tex]
The radius of a semicircle is 9.1 centimeters. What is the semicircle's perimeter?
Answer:
46.77 cm
Step-by-step explanation:
Perimeter of the semicircle = Circumference + 2r
πr + 2r = r (π + 2)9.1 (3.14 + 2)9.1 (5.14)46.77 cmHelp me with this extremely hard differentiation question , [Scroll] >>
[tex]\huge\frac{d}{dx}[\sum_{n=0}^{∞}[(\frac{(-1) ^ {n}}{(2n+1)!})(\frac{1}{1+e^{x}})^{2n+1}] ][/tex]
Answer:
[tex]f'(x)=\displaystyle -\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
Step-by-step explanation:
Recall the power series [tex]\sin(x)=\displaystyle \sum\limits^\infty_{n=0}(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex].
In this case, [tex]x[/tex] is replaced with [tex]\displaystyle \frac{1}{1+e^x}[/tex], so our power series actually works out to be [tex]\displaystyle \sin\biggr(\frac{1}{1+e^x}\biggr) =\sum\limits^\infty_{n=0}(-1)^n\frac{\bigr(\frac{1}{1+e^x}\bigr)^{2n+1}}{(2n+1)!}[/tex]! Amazing, huh?
Now, we find the derivative of the function by using the chain rule:
[tex]\displaystyle \frac{d}{dx}\sin\biggr(\frac{1}{1+e^x}\biggr)=\frac{d}{dx}\biggr(\frac{1}{1+e^x}\biggr)*\cos\biggr(\frac{1}{1+e^x}\biggr)=-\frac{e^x}{(1+e^x)^2}\cos\biggr(\frac{1}{1+e^x}\biggr)[/tex]
You didn't specify if you just wanted the derivative of the series to be a function or a series, so I'm going to assume you want the function. Let me know if there's more to your problem.
This table shows the relationship between x and y.
Please help and answer has an exponent
A triangle has side lengths of 7 inches, 12 inches, and c inches. Enter values to write an inequality that describes the possible values for c, the length of the third side of the triangle.
Answer:
The inequality is: 5<c<19
Length of third side "c" can have values greater than 5 but less than 19
Solution:
Given that,
Length of two sides of triangle are 7 inches and 12 inches respectively
Let the length of third side be "c"
The Triangle Inequality Theorem, states that, the sum of the lengths of any two sides of a triangle is greater than the length of the third side
So we get a inequality as:
Case 1:
Sum of length of two sides of triangle > length of third side
Rewrite,
Case 2:
Let 12 inches be the length of third side
Sum of sides of length 7 and c > 12
Therefore from case 1 and case 2,
Which can be combined,
Therefore the possible values of "c" are:
"c" can have values greater than 5 but less than 19
Augustus is trying to make chocolate milk. He has made a 10% chocolate milk solution (this means that the solution is 10% chocolate and 90% milk). He has also made a 25% chocolate milk solution. Unfortunately, the 10% solution is too weak, and the 25% solution is way too chocolaty. He has a whole lot of the 10% solution, but he has only 30 gallons of the 25% solution. How many gallons of 10% solution should he add to the 25% solution to make a mixture that is 15% chocolate?
Answer:
60 gallons
Step-by-step explanation:
The amount of 10% solution he should add can be found by writing an equation for the total amount of chocolate in the mix.
__
Let x represent the amount of 10% solution that Augustus needs to add to the 30 gallons of 25% solution. The amount of chocolate in the resulting 15% mix is ...
0.10x +0.25(30) = 0.15(x +30) . . . . gallons of chocolate in the mix
0.10(30) = 0.05x . . . . . . . . subtract 0.10x +0.15(30)
60 = x . . . . . . . . . . . . divide by 0.05
Augustus should add 60 gallons of the 10% solution to make a 15% mixture.
chef johnson used 4 1/2 of flour to make 4 fruitcakes. How many cups of flour are needed for 1 fruitcake
Answer:
1 1/8 cups of flour
Step-by-step explanation:
hi!
If Chef Johnson needs 4 1/2 cups of flour to make 4 fruitcakes and he wants to make one, he has to divide the recipe by 4. 4 1/2 / 4= 1 1/8
Can someone please answer this, ill give you brainliest Would be very appreciated.
[tex]\bf Blue \ Color \ Line : y = x^2[/tex]
If you are going to make it open from downwards. The function should be negative : -(x)²If the graph moves 10 units downwards. : y = (x)² - 10If you are going to move the graph horizontally 2 units left. : y = (x+ 2)²When added all together:
[tex]\bf Black \ color \ Line: y=-\left(x+2\right)^{2}-10[/tex] = Final answer.
In a company, 85% of the workers are women. If 390 people work for the company who aren't women, how many workers are there in all?
Answer:
2210
Step-by-step explanation:
390 =15%
390*3 = 130=5%
130*17=2210
Verify whether x ≤ 3 is the solution to the inequality 7x ≥ 20x - 39.
Answer:
Yes, it is correct.
Step-by-step explanation:
7x≥20x-39
39≥13x
x≤39/13
x≤3
2 x{15 plus[24-(1.5 x2)]}
Answer:
72.
Step-by-step explanation:
2 x{15 plus[24-(1.5 x2)]}
Using PEDMAS:
= 2 x {15 + [24-(3)]}
= 2 x (15 + 21)
= 2 x 36
= 72.
A mouse climbs up a well of 86 meters. It advances 14 meters during the night, but during the day it retreats 2. The mouse will reach the surface on the day:
Step-by-step explanation:
we assume day and night are equally long.
and the mouse will start at night of day 1.
then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).
so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).
with a starting value of 14 (the first night).
so, we are getting an arithmetic sequence
an = an-1 + c
c = 12 in our case.
a1 = 14
a2 = a1 + 12 = 14+12 = 26
a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38
an = a1 + (n-1)×12 = 14 + 12(n-1)
at what n will it reach 86 ?
86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n
84 = 12n
n = 7
so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).
The graph below shows the solution to which system of inequalities?
O A. x< 1 and yz x
B. x< 1 and y>x
C. y≤ 1 and y>x
D. y< 1 and yzx
Answer:
y < 1 and y > x
Step-by-step explanation:
Let's find each equation without any inequalities first.
We have a dotted line at y = 1
Now, a dotted line represents exclusivity, and hence; it should not include the = sign
Therefore, the answer is y < 1 and y > x
Pls help me classify this asap?!!
If (product ) > 20 then (product) - 27 else if (product) < 10, then (product) + 2 else (product) - 6
AnsweB i think
Step-by-step explanation:
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation 23 + 6,2 - 27x= 140 can be used to find x. Height: (x+9) in. Width: (2 - 3) in Length: xin. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer. O The length is 7 inches, the width is 4 inches, and the height is 16 inches. O The length is 5 inches, the width is 2 inches, and the height is 14 inches. O The length is 4 inches, the width is 1 inch, and the height is 13 inches. O The length is 3 inches, the width is O inches, and the height is 12 inches.
For this case we have the following equation for the volume:
[tex]x^3+6x^2-27x=140 < br/ >[/tex]
Rewriting the equation we have:
[tex]x^3+6x^2-27x=140=0 < br/ >[/tex]
We factor the equation to find the roots of the polynomial.
We have then:
[tex](x-5)(x+4)(x+7)=0 < br/ >[/tex]
Then, we discard the negative roots, because the dimensions of the figure must be positive.
We have then that the length is:
[tex]x=5 < br/ >[/tex]
The height is:
[tex]x+9=5+9=14 < br/ >[/tex]
The width is:
[tex]x-3=5-3=2 < br/ >[/tex]
Thus, the dimensions are:
[tex]5*14*2 < br/ >[/tex]
Answer:
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
How to solve for b? Do you need another variable?
Answer:
No there are 180 degrees on a line
Step-by-step explanation:
180
115-
065
65°
PLEASE PLEASE HELP ME
A rhombus is a quadrilateral whose all sides are of equal length. The measure of the ∠QPR is 42°.
What is a Rhombus?A rhombus is a quadrilateral whose all sides are of equal length, and the opposite are parallel to each other.
The diagonals of a rhombus intersect each other at 90°. Therefore, the measure of ∠QTR can be written as,
∠QTR = 90°
(6y+6) = 90°
6y = 90 - 6
6y = 84
y = 14
Also, the diagonals of the rhombus divide the angle into two equal angles, therefore,
∠QPR = ∠SPR
∠QPR = 3y
∠QPR = 3(14)
∠QPR = 42°
Hence, the measure of the ∠QPR is 42°.
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