Answer:
C
Step-by-step explanation:
1st year-> 30000
2nd year-> 31800
3rd year ->33708
4th year->35730.48
5th year -> 37874.3088
37874.3088+35730.48+33708+31800+30000= 169112.7888
≈ 169113
The solution is Option C.
The total amount of earnings of Sondra after 5 years is $ 169,113
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the annual salary of Sandra be A = $ 30,000
Now , the percentage increase in salary = 6 %
So , the equation will be
First year :
The increase in first year = annual salary of Sandra + percentage increase in salary x annual salary of Sandra
The increase in first year = 30000 + ( 6/100 ) x 30000
= 30000 + 1800
= $ 31,800
Second year :
The increase in second year = increase in first year + percentage increase in salary x increase in first year
The increase in second year = 31800 + ( 6/100 ) x 31800
= 31800 + 1908
= $ 33,708
Third year :
The increase in third year = increase in second year + percentage increase in salary x increase in second year
The increase in third year = 33708 + ( 6/100 ) x 33708
= 33708 + 2022.48
= $ 35,730.48
Fourth year :
The increase in fourth year = increase in third year + percentage increase in salary x increase in third year
The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48
= 35730.48 + 2143.8288
= $ 37,874.3088
Now , the equation is
The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary
The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088
The total amount earnings of Sondra is = $ 169,112.7888
Therefore , the total amount earnings = $ 169,113
Hence , The total amount of earnings of Sondra after 5 years is $ 169,113
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The following expression represents the profit made by John as he mows lawns: P = 20L
- 100
Which description correctly interprets each part of the expression?
its c because i already did that and got it right
find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6
Answer:
[tex]f(x) = \frac{6}{x^2} -8[/tex] or [tex]f(x) = -\frac{6}{x^2} + 4[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (1,-2)[/tex] --- Point
[tex]\int\limits^6_2 {(1 + 144x^{-6})} \, dx[/tex]
The arc length of a function on interval [a,b]: [tex]\int\limits^b_a {(1 + f'(x^2))} \, dx[/tex]
By comparison:
[tex]f'(x)^2 = 144x^{-6}[/tex]
[tex]f'(x)^2 = \frac{144}{x^6}[/tex]
Take square root of both sides
[tex]f'(x) =\± \sqrt{\frac{144}{x^6}}[/tex]
[tex]f'(x) = \±\frac{12}{x^3}[/tex]
Split:
[tex]f'(x) = \frac{12}{x^3}[/tex] or [tex]f'(x) = -\frac{12}{x^3}[/tex]
To solve fo f(x), we make use of:
[tex]f(x) = \int {f'(x) } \, dx[/tex]
For: [tex]f'(x) = \frac{12}{x^3}[/tex]
[tex]f(x) = \int {\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = \frac{12}{2x^2} + c[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = \frac{6}{1^2} + c[/tex]
[tex]-2 = \frac{6}{1} + c[/tex]
[tex]-2 = 6 + c[/tex]
Make c the subject
[tex]c = -2-6[/tex]
[tex]c = -8[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = \frac{6}{x^2} -8[/tex]
For: [tex]f'(x) = -\frac{12}{x^3}[/tex]
[tex]f(x) = \int {-\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = -\frac{12}{2x^2} + c[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = -\frac{6}{1^2} + c[/tex]
[tex]-2 = -\frac{6}{1} + c[/tex]
[tex]-2 = -6 + c[/tex]
Make c the subject
[tex]c = -2+6[/tex]
[tex]c = 4[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = -\frac{6}{x^2} + 4[/tex]
You can use the formula for finding the arc length on specified interval on x axis.
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
What is the length of the arc of a function f(x) from x = a to x = b?If the function is differentiable in the given interval, then we have:
[tex]s = \int_a^b\sqrt{(1 + (f'(x))^2)}\:dx[/tex]
where s denotes the length of the arc of the given function from x = a to x = b
Using the above formula, as we're already given the arc length, thus,
[tex]\int_a^b\sqrt{(1 + (f'(x))^2)}\:dx = \int_2^6\sqrt{(1 +144x^{-6})}\:dx[/tex]
This gives us
[tex]f'(x) = \pm \sqrt{144x^{-6}} = \pm 12x^{-3}[/tex]
Integrating both sides with respect to x, we get:
[tex]f(x) = \pm \int 12x^{-3}\\\\f(x) = \pm 6x^{-2} + c[/tex]
where c is constant of integration.
Since the curve passes through (1,-2), thus, putting f(x) = -2, x = 1, we get:
[tex]f(x) = \pm 6x^{-2} + c\\-2 = \pm 6 + c\\c = -2 \mp 6 = -8, or ,4[/tex]
c = -8 when we have [tex]f(x) = 6x^{-2} + c[/tex]
c = + 4 when we have [tex]f(x) = -6x^{-2} + c[/tex]
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
Learn more about length of the arc of a curve here:
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What does the enlargement look like and what are the coordinates?
Answer:
(-6, -3) (-3,-3) (-3,-6)
Step-by-step explanation:
Multiple all of the vertices by 1.5.
(-6, -3) (-3,-3) (-3,-6)
Hope I helped!
[enlargment will still be a triangle]
A coordinate plane.
Which statements are true? Check all that apply.
The line that goes through the points (3,7) and (–2,7) is a horizontal line.
The equation x = –8 is a vertical line that goes through the point (–8,3).
The line that goes through the points (0,5) and (0,–7) is a vertical line.
The points on a horizontal line have the same x-coordinate.
Answer:
A , B, and C
Step-by-step explanation:
i just did it
Solve for x and y. Please help, I will mark as brainliest and give many points
Answer:
x=13 y=25
Step-by-step explanation:
Answer:
x = 30°, y = 45°, w = 14√2, v = 7√2Step-by-step explanation:
ΔABC has AB = 2BC, hypotenuse is twice the leg
⇒ x = 30°ΔBCD is isosceles right triangle
⇒ y = 45°ΔMPN is isosceles right triangle (∠M = 45°)
⇒ w = MN = √2PN = 14√2ΔMKP is isosceles right triangle (∠M = 45°)
v= KP = MK = 1/2MN = 1/2(14√2) = 7√2Can someone help please?
Answer:
25 is the correct answer
When all the kids who tried out for the Little league were divided into teams of 16 players, there were exactly 8 teams. How many kids tried out?
Answer:
128
Step-by-step explanation:
16 x 8 = 128
Answer:
128
Step-by-step explanation:
you multiply 16 and 8 because each team has 16 and there are 8 teams so, 16×8=128
what function equation is represented by the graph
f(x) = 4^x+5
f(x) = 3^x+4
f(x) = 3^x+5
f(x) = 4^x+4
Answer:
B
Step-by-step explanation:
We know that when x=0 y=5
B and D are the only ones that meet this criteria
we know that when x=2 y= 13 or so
D no longer works
it has to be B
Tickets to a movie cost $7 for adults and $5 for students . A group of friends purchased 8 tickets for $52, write a system of equations to represent this situation
Looking out for me balcony the angle of elevation to the top of the next building is approximately 22° in the English depression to the bottom of the building approximately 29° if the building is 200 feet away how tall is the building?
I will give brainliest to whoever solves it right. hint its not 80.7 feet
Answer:
Step-by-step explanation:
[tex]\tan22=h_1/200,\ \tan29=h_2/200
h_2+h_1=200(\tan29+\tan22)
H\approx 191.667ft
H\approx 191’ 8”
Mahir ' in ağırlığının feride' nin ağırlağına oranı 9/4 'tür.
Mahir' in ağırlığı 81 kg olduğuna göre feridenin ağırlığı kaç kg'dir? (acil soru)
A scientist wants to predict the number of nitrates in the river. Which sample is better for making this prediction?
Sample A: A random sample of 5 gallons of water from one location in the river
Sample B: A random sample of 5 gallons of water from five different locations in the river
Answer:
Sample B: A random sample of 5 gallons of water from five different locations in the river
Step-by-step explanation:
Manuel is preparing to run in a race. He has developed a training program in which he increases his running distance each day. If he continues to follow the same pattern, what distance will he run on the fifth day.
Day 1 -- 1 mile
Day 2 -- 2 miles
Day 3 -- 4 miles
Day 4 -- 7 miles
A.) 8 miles
B.) 9 miles
C.) 11 miles
D.) 14 miles
Answer:
c
Step-by-step explanation:
c)11 miles
the day and the miles on that day add together to make the miles for the next day so 4+7=11
Question 7
Write the integer that is equivalent to |10|
Answer:
10
Step-by-step explanation:
In the triangle below, the measure of angle A = 52°. Find the measure of angle C.
Answer:
128°
Step-by-step explanation:
180-52=128
What is the zero of the function ?
Answer:
The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
Step-by-step explanation:
6+(9-1)2 divided by 4x (1/2)
Answers:
Here you go, hope this helps
Step-by-step explanation:
6+2x
Find all solutions of the equation in the interval [0, 2π). 2cosθ+ 1= 0
Hello!
[tex]\large\boxed{\frac{2\pi}{3} \text{ and } \frac{4\pi}{3}}[/tex]
2cosФ + 1 = 0
Begin by isolating for cosФ. Subtract both sides by -1:
2cosФ = -1
Divide both sides by 2:
cosФ = -1/2
Using the unit circle, we know that from [0, 2π), values that have a cosine of -1/2 are 2π/3 and 4π/3.
Therefore, the solutions of this equation are:
Ф = 2π/3 and 4π/3
Hello Brainly pleas help
Answer:
can you take a better pick
Step-by-step explanation:
What factor is missing? 24 + 12= ____(8+4)
Answer:
3
Step-by-step explanation:
24 + 12 = ___(8+4)
36 = ___(12)
36/12 = 3
Arrange these in increasing order
Answer:
so least to greatest? 1/4 1/3 1/2
Answer:
1/4, 1/3, 1/2
Step-by-step explanation:
PLZZZZZZZZ HEPL ME TYSM PLZZZZ 40PTS
Answer:
that makes no sense call your teacher for helpy
HELP ME PLSSSSSS Kaitlyn is covering all faces of a tissue box cover shaped like a rectangular prism. The cover has dimensions of 9” x 5” x 3.75”. What is the total area in square inches that she will need to cover?
Answer:
168.75
Step-by-step explanation:
......
Answer:
168.75
Step-by-step explanation:
cos=0.985 rounded to nearest tenth
What is the diameter of a sphere with a volume of 78006 in?
Answer: 53.0
Step-by-step explanation:
Then the diameter equals 53.0122774
The diameter of the sphere is 53.01 inch
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the diameter of the sphere be = d
The radius of the sphere be = r
The volume of the sphere is V = 78006 inch³
The Volume of a Sphere = ( 4/3 ) πr³
Substituting the values in the equation ,we get
( 4/3 ) πr³ = 78006 inch³
Now , Multiply by ( 3 / 4 ) on both sides , we get
πr³ = ( 78006 x 3 ) / 4
= 58504.5 inch³
Divide by π on both sides , we get
r³ = 58504.5 / π
= 18622.56 inch³
Taking cube roots on both sides , we get
r = 26.506 inch
So , the radius of the sphere is r = 26.506 inch
Now , the diameter of the sphere is d = 2 x r
= 2 x 26.506
= 53.01 inch
Hence , The diameter of the sphere is 53.01 inch
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A sign says that the price marked on all music equipment is 30℅ off the original price. you buy an electric guitar for the sale price of $315. How much money did you save
Digital Lesson
Sam does 11 jumping jacks in 8 seconds. If he does the jumping jacks at a constant rate, how many
jumping jacks can he do in 20 seconds?
Answer:
about 28
Step-by-step explanation:
please help me please i really need help please
List the factors in the expression 4r + 5s +8.
PLZ HELP MEEEEE!!!!!
do this for brainliest! :)
Answer:
Question 13 is 27/2 (decimal form, 13.5, Mixed fraction 13 1/2)
Question 14 = 4
Step-by-step explanation:
hope this helped you:)