Answer:
7 yellow cars
Step-by-step explanation:
Tim has 30 cars, so Jill has 30 as well. She has 8+15=23 red and blue cars. This means that there are 7 yellow cars.
n applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points)
The amount provided by each offer after each year depends on the first
salary and the added amount or percentage series.
Part A: Offer A can be represented by a geometric seriesThe salary received after n years is Aₙ = 58,000·1.03⁽ⁿ ⁻¹⁾Part B: Offer B can be represented by an arithmetic seriesThe equation for the salary after n years is Bₙ = 58,000 + (n - 1)×3,000Part C: The offer that will provide a greater income after 5 years is offer B, with an income of $70,000Reasons:
The given parameters of the job offers are;
Starting salary of offer A = $58,000
Amount by which the salary increases for 5 years = 3%
The starting salary offer B = $56,000
Amount by which the salary increases per year = $3,000
Part A: The salary amount received in the first month = $58,000
The salary in the second month, aₙ = 58,000 × (1 + 0.03)
a₂ = 58,000 × (1 + 0.03) = 58,000 × (1.03)
The salary in the third month is given as follows;
a₃ = a₂ × (1.03) = 58,000 × (1.03) × (1.03) = 58,000 × (1.03)²
The salary on the nth month is therefore;
aₙ = 58,000 × (1.03)⁽ⁿ⁻¹⁾
The above formula is in the form of the geometric series formula, which is presented as follows;
aₙ = a·r⁽ⁿ⁻¹⁾
Where;
a = The first term = 58,000
r = The common ratio = 1.03
n = The number of years
Therefore;
Offer A can be represented by an arithmetic series
Part B: The first year salary for offer B = $58,000
The salary on the second year, B₂ = 58,000 + 3,000 = 61,000
Salary on the third year, B₃ = 58,000 + 3000 + 3000 = 58,000 + 2 × 3,000
Therefore;
Salary on the nth year, Bₙ = 58,000 + (n - 1)×3,000
The above equation is in the form of aₙ = a + (n - 1)·d
Where;
a = The first term = 58,000
n = The number of years
d = The common difference = 3,000
Therefore;
Offer B can be represented by an arithmetic series
Part C: The income gained on offer A after 5 years, a₅, is given as follows;
a₅ = 58,000 × (1.03)⁽⁵ ⁻ ¹⁾ = 58,000 × 1.03⁴ ≈ 65,279.51098
The income gained on offer A after 5 years ≈ $65,279.51098
On offer B, we have;
a₅ = 58,000 + (5 - 1) × 3,000 = 70,000
The income gained on offer B after 5 years = $70,000
Therefore;
After 5 years, the income offered by offer B is greater than the income offered by offer A.Learn more about arithmetic and geometric series here:
https://brainly.com/question/2735005
f (x) = 6x + 4. Find the inverse of f(x).
O A. f-1 (2) = 4 - 6x
O B. f-1(x) = 6x - 4
O c. f-(x) =
O D. f-'(x) = 20
2-4
-6
If [tex]f^{-1}(x)[/tex] is the inverse of f(x), then
[tex]f\left(f^{-1}(x)\right) = x[/tex]
By definition of f(x), we have
[tex]f\left(f^{-1}(x)right) = 6f^{-1}(x) + 4 = x[/tex]
Solve for the inverse :
[tex]6f^{-1}(x) + 4 = x[/tex]
[tex]6f^{-1}(x) = x - 4[/tex]
[tex]f^{-1}(x) = \dfrac{x-4}6[/tex]
which makes C the correct choice.
Identify an equation in point-slope form for the line parallel to y = -
2/3x+8 that passes through (4, -5).
A. y-4=(x+5)
B. y+5=2/3 (x-4)
C. y+5 = 3/2(x-4)
D. y-5=-2/3(x + 4)
Anybody can help? (Here's a pfp)
First make a guest check
My Guest check #9
1 donut = $1.29
Donut holes = $4.89
Dozen Donuts = $12
Donut Holes = $4.89
$1.29 + $4.89 + $12 + $4.89 = $23.07
$23.07 * 8% = $24.92 is the 9th check list
My Guest check #10
1 donut = $1.29
1 donut = $1.29
Dozen Donuts = $12
Donut Holes = $4.89
$1.29 + $1.29 + $12 + $4.89 = $19.47
$19.47 * 8% = $21.03 is the 10th check list
If f(x) = -3x2 + 5, find the value of f(4).
=
A. -139
B. -43
C. 53
D. 149
Answer:
B) -43
Step-by-step explanation:
f(x) = -3x²+5
f(4) = -3(4)²+5
f(4) = -3(16)+5
f(4) = -48+5
f(4) = -43
Answer:
B) -43
Step-by-step explanation:
f(x) = -3x²+5
f(4) = -3(4)²+5
f(4) = -3(16)+5
f(4) = -48+5
f(4) = -43
Write an equation in slope-intercept form of the line that passes through (−1, 4) and (0, 2)
[tex]\text{Given that,}\\\\(x_1,y_1) = (-1,4), ~~ (x_2,y_2) =(0,2)\\\\\\\text{Slope,}~ m =\dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{2-4}{0-(-1)} = \dfrac{-2}{0+1} = -2\\\\\text{The equation with given points,}\\\\y-y_1 =m(x-x_1)\\\\\implies y -4 = -2(x+1)\\\\\implies y = -2(x+1)+4\\\\\implies y = -2x -2 +4\\\\\implies y = -2x +2\\\\\text{This is the slope-intercept form(y =mx +b)}[/tex]
find the inverse of f(x)=x^2-3x+2
Answer:
Step-by-step explanation:
y = [tex]\frac{3}{2}[/tex] + [tex]\sqrt{x+\frac{1}{4} }[/tex] and y = [tex]\frac{3}{2}[/tex] - [tex]\sqrt{x+\frac{1}{4} }[/tex]
Answer:
Step-by-step explanation:
f(x) = x² - 3x + 2
y = x² - 3x + 2
solve for x as a function of y
y - 2 = x² - 3x
complete the square by adding the square of half the x¹ coefficient to each side of the equation.
y - 2 + (-1.5)² = x² - 3x + (-1.5)²
y + 0.25 = (x - 1.5)²
[tex]\sqrt{y + 0.25}[/tex] = x - 1.5
x = 1.5 ± [tex]\sqrt{y + 0.25}[/tex]
now swap the x and y variables and revert to function notation
f(x) = 1.5 ± [tex]\sqrt{x + 0.25}[/tex] domain is x ≥ -0.25
each input will have two outputs except where f(-0.25) = 1.5
Prime number after
167, 118, 82, 57, 41, ?
Prime numbers after 167, 118, 82, 57, 41, are:
37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2
Prime numbers are numbers that only have two factors, 1, and themselves.
Apart from these factors, no number can divide them without a remainder.
By observation, the numbers 167, 118, 83, 57, 41, are written in descending order.
This means that the prime number to be chosen will be lesser than 41
Prime numbers lesser than 41 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
Learn more on prime numbers here: https://brainly.com/question/145452
-7(-2 ( 3x+1)+ 4) +9
Answer:
correct answer is explained in the picture attached
In an economics class, 4 students earned an A, 6 earned a B, 5 earned a C, 5 earned a D, and 3 earned an F. If a single student is picked at random, what is the probability that they earned an B or C?
Provide your answer as a simplified fraction.
Answer:
11/23
Step-by-step explanation:
B = 6
C = 5
6+5=11
11/23
m^(2)n+2m^(3) if m=-0.2 and n=-9.6
Hey there!
m^(2)n + 2m^3
= -0.2^(2)(-9.6) + 2(-0.2)^3
= (-0.04)(-9.6) + 2(-0.3)^3
= 0.384 + 2(-0.008)
= 0.384 - 0.016
= 0.368
Therefore, your answer is: 0.368
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]
[tex]\implies\tt{ {m}^{2n} + {2m}^{3} } \\ \\ \implies\tt{ { - 0.02}^{ 2 \times - 9.6} + 2 {( - 0.02)}^{3} } \\ \\ \implies\tt{ - 0.04 \times - 9.6 + 2( - 0.0008)} \\ \\ \implies\tt{0.384 - 0.016} \\ \\ \implies\tt{0.368}[/tex]
what is the value of the 6 in 26,249?
Answer:
what is the value of the 6 in 26,249?
answer:321305
Step-by-step explanation:
Question
You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (3w+4) subscriptions and your friend has sold (5w+1) subscriptions.
a. Write an expression in simplest form that represents the difference between the number of subscriptions your friend has sold and the number you have sold.
b. After 5 weeks, your friend has sold
more subscriptions than you.
Answer:
Your friend sold (5w + 1) subscriptions.
You sold (3w + 4) subscriptions.
The difference between what your friend sold and what you sold is
(5w + 1 ) - (3w + 4)
= 5w + 1 - 3w - 4
= 5w - 3w + 1 - 4
= 2w - 3
Answer: 2w - 3
If it is negative then it means the subscription sold by friend is less than the subscription sold by me and if it is positive then it means the subscription sold by friend is more than the subscription sold by me.
Brainliest plz
Which angle is complementary to <1?
Answer:
I don't know sorry but have a nice time answering this question
pls help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2 dashes to the left
Step-by-step explanation:
just plot a point two dashes to the left
how do i solve for this?
What is the area of a parallelogram with base 40 mm and height 18 mm?
Answer:
720 mm²
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
For the given base and height, the area is ...
A = (40 mm)(18 mm) = 720 mm²
Express as a trinomial.
(x + 6) (2x + 8)
Answer:
2x² + 20x + 48
Step-by-step explanation:
(x+6)(2x+8)
(x)(2x) + (x)(8) + (6)(2x) + (6)(8)
2x² + 8x + 12x + 48
2x² + 20x + 48
Which of the following rational functions is graphed below?
Answer:
Option C
Step-by-step explanation:
According to the graph, there are vertical asymptotes at [tex]x=-3[/tex] and [tex]x=7[/tex]. Therefore, C is correct because -3+3=0 and 7-7=0.
Find the slope of the line passing through the points (3,-1) and (3, -6).
Answer:
Undefined
Step-by-step explanation:
Slope formula:
y2-y1/x2=x1
In (3,-1), 3 is x1 and -1 is y1
In (3, -6), 3 is x2 and -6 is y2
-6-(-1)/3-3
Which is -5/0
And that couldn't happen in a slope
So the answer is undefined
Hope this helps!
Find the value of x .
K
M
(2x – 10) (2x + 40)º
-
N
Answer:
?????????????????????????
Helpppppppppp plsssssss
Answer: You didnt give the 2 equations.
Step-by-step explanation:
The population of a town gradually decreases by about 30
people a year. In 2015, the population was 3,600 people. Write an equation in general form for the population of this town .
Will give brainliest if you answer fast
What is the equation
y=____ x + ____
Fill in the missing number with the graph
Joseph is going to paint the panels of a fence. He is going to use the same repeating pattern for the entire fence. The rule is "orange, yellow, pink, green, purple." If there are 98 panels in the fence, how many will be painted green? Enter your answer in the box.
19 times Answer:
Step-by-step explanation:
The required number of panels that were painted to be green is 19.
Joseph is going to paint the panels of a fence. He is going to use the same repeating pattern for the entire fence. The rule is "orange, yellow, pink, green, purple." If there are 98 panels in the fence, how many will be painted green is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Pattern = "orange, yellow, pink, green, purple."
1 2 3 4 5
Total number of panels = 98
Number of panels that were painted green,
= 98 / 5
= 19 + 3/5
In the 19 pattern, there are 19 panels that is green,
While in the remaining 3 panels consist of orange, yellow, and pink.
Thus, the required number of panels that were painted to be green is 19.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Which equation is correct?
235 × 8 = 200 × 8 + 30 × 8 + 5
235 × 8 = 2,000 × 8 + 300 × 8 + 50 × 8
235 × 8 = 200 + 30 × 8 + 5 × 8
235 × 8 = 200 × 8 + 30 × 8 + 5 × 8
I LOVE YOUUU
The correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
How to determine the correct expression?The product expression is given as:
235 * 8
Express 235 as place values
235 * 8 = (200 + 30 + 5) * 8
Expand the bracket
235 * 8 = 200 * 8 + 30 * 8 + 5 * 8
Hence, the correct expression of 235 * 8 is 200 * 8 + 30 * 8 + 5 * 8
Read more about place values at:
https://brainly.com/question/12386995
Simplify the expression.
7- 5n + n + 5
Lindsay wrote checks from her checking account for $20 and $35. Finally, she deposited $63 into her account. Which number describes the change in the balance of her account?
Answer:
20 and 35 because it says that she wrote a check.
Step-by-step explanation:
A line segment has endpoints (-1, -1) and (-1, 2).
Which vertex would form a triangle that is connected to the endpoints of the line segment?
А.
(-1, 6)
B
(-1, -2)
С
(-1,0)
D
(2,-1)
Answer:
D. (2, - 1)Step-by-step explanation:
Both the given points have x- coordinate of -1.
The first three of the answer options have same -1 as the x-coordinate, this means all three points are on the same line.
It is therefore impossible to have those as vertices of a triangle.
Correct option is D
1/3x+80=1/2x+120 what’s the answer??
Answer:
−240
1/3x+80=1/2x+120