Answer:
Step-by-step explanation:
Your answer is A.
Anytime you have a variable or something that changes such as the month that is a variable so that means its going to be your x/m in this case
g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025
Answer:
a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000
b) $83,421.88
c) s[n] = 70000·1.05^n -20000
Step-by-step explanation:
a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...
s[0] = 50000 . . . . the recursion relation initial condition
The next year, the salary is multiplied by 1.05 and 1000 is added:
s[1] = 1.05·s[0] +1000
This pattern repeats, so the recursion relation is ...
s[n] = 1.05·s[n-1] +1000
__
c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).
The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...
base salary after n years = 50,000·1.05^n
The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:
sum = a1(r^n -1)/(r -1) . . . . . (see note below)
sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)
So, the total salary after n years is ...
s[n] = 50000·1.05^n + 20000(1.05^n -1)
The exponential terms can be combined, so we have the explicit formula ...
s[n] = 70000·1.05^n -20000
__
b) The year 2025 is 8 years after 2017, so we want to find s[8].
s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000
= 103,421.88 -20000 = 83,421.88
In 2025, the employee's salary will be $83,421.88.
_____
Note on the sum of the add-ons
A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....
The sum of such a geometric sequence has the formula
Sn = a1·(r^n -1)/(r -1)
Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as
Sn = 20000·(1.05^n -1).
help and i ill give brainliest
Answer:
11
Step-by-step explanation:
f(16) = 7 + 16/4
= 7 + 4
= 11
How many 10-bit strings have weight 1?
How many 10-bit strings have weight 5?
How many 10-bit strings have weight 9?
Answer:
ok so it will be 16-bit
Step-by-step explanation:
Describe a way to make the arithmetic problem 45% x 680 mentally
Answer:
306.
Step-by-step explanation:
Firstly, we are aware 100% of 680 is obviously 680,
Next, we know half of a 100% is 50% therefore half of 680 is 340.
Then, we know 45% is 5% less than 50%
To find 5% of a number mentally, divide it by 10 as 100÷5=20
680÷20=34
Lastly 50% subtracted by 5%: 340-34=306.
Now we know, 45% of 680 is 306.
Hope this helps.
Hope this helps.Please mark BRAINLIEST.
Angles 4 & 8 are an example of which type of angle? *
O Alternate Exterior
O Alternate Interior
O Corresponding
O Vertical
Answer:
Corresponding
Step-by-step explanation:
They are on the same side which makes them corresponding angles
what is the value of 17-2(5-3)
Answer:
13
Step-by-step explanation:
17-10+6
7+6=13
hope it helps
Find the gradient of the line Joining the points p(-2,6) and Q(3,-2)
Answer:
[tex] - \frac{8}{5} [/tex]
Step-by-step explanation:
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
(x₁, y₁) is the 1st coordinate while (x₂, y₂) is the 2nd coordinate.
Gradient of the line
[tex] = \frac{6 - ( - 2)}{ - 2 - 3} [/tex]
[tex] = \frac{6 + 2}{ - 5} [/tex]
[tex] = - \frac{8}{5} [/tex]
-3-(-5)What is the answer to this equation
Answer:
2Step-by-step explanation:
[tex] - 3 - ( - 5) \\ - 3 + 5 \\ 2 \\ [/tex]
ALGEBRA question 100 POINTS. Easy
Answer: (-4x)^2 (6x^5) » (-4)^2 (x^2) (6x^5) » (16)(x^2)(6x^5) » (96)[x^(2+5)] » 96x^7
Step-by-step explanation:
Answer: (-4x)^2 (6x^5) » (-4)^2 (x^2) (6x^5) » (16)(x^2)(6x^5) » (96)[x^(2+5)] » 96x^7
Step-by-step explanation: I am sure of my answer
2x=20−2
Value of x!!!
Answer:
[tex]\sf\longmapsto \: x = 9[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: 2x = 20 - 2[/tex]
[tex]\sf\longmapsto \: 2x = 18[/tex]
[tex]\sf\longmapsto \: x = \frac{18}{2} [/tex]
[tex]\sf\longmapsto \: x = 9[/tex]
Hello there! :)
2x=20-2
2x=18
Divide both sides by 2 to isolate x:
x=9
Hope this helps!
#HaveAnAmazingDay
[tex]GraceRosalia[/tex]
Plz help me
Determine whether the following sets form subspaces of R^3:
(a) {(x1,x2,x3)^T |x1+x3=1}
(b) {(x1,x2,x3)^T |x1=x2=x3}
Answer:
a.
Step-by-step explanation:
hope it's helpful
brainliest me pls
(7x)(2xy) how do I rewrite that as a sum
CE TASK
V.
3
The carpenter spent 7/8 of his money on bags of sand for the sandbox. He spent 1/2 of the rest
of his money on some packs of bunting flags to decorate thesandbox and had $19.90 left How much money did the carpenter start with? Draw a bar model to show your work
Determine how much money did the carpenter start with
The total money with the carpenter is $318.4
Given:
let
x = total money with the carpenter
Bags of sand = 7/8 of x
= 7/8x
Money remaining = x - 7/8x
= (8x-7x) / 8
= 1/8x
Bags of bunting bags = 1/2 of 1/8x
= 1/2 × 1/8x
= 1/16x
Money left = $19.90
Total money = bags of sand + bag of bunting flag + money left
x = 7/8x + 1/16x + 19.90
x = (14x + x) / 16 + 19.90
x = 15/16x + 19.90
x - 15/16x = 19.90
16x - 15x / 16 = 19.90
x/16 = 19.90
divide both sides by 1/16
x = 19.90 ÷ 1/16
= 19.90 × 16/1
= 318.4
Therefore, the total money with the carpenter is $318.4
Read more:
https://brainly.com/question/7852538
In the equation x² + 64 = 16x, the roots are ____.
Answer:
square roots are x, 8, 4x
Step-by-step explanation:
x^2 square root is x
64 square root is 8
16x square root is 4x
Which equation matches the graph?
Answer:
Option C): f(x) = 3x - 4.
Step-by-step Explanation:
What is a Linear Function in Slope-intercept Form?A linear function in slope-intercept form is given by f(x) = mx + b where:
"m" represents the slope, which is the measure of steepness and orientation of a nonvertical line. "b" represents the y-coordinate of the y-intercept, (0, b). The y-intercept is the point on the graph where the line intersects the y-axis. It is also the point where the x-coordinate equals to zero.How to solve for the slope?We can solve for the slope by using the following formula:
[tex]\displaystyle\mathsf{Slope\:(m)\:=\:\frac{Rise}{Run}\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)}[/tex]
Choose two points from the graph and substitute their values into the slope formula.
(x₁, y₁) = (2, 2)(x₂, y₂) = (0,-4)[tex]\displaystyle\mathsf{Slope\:(m)\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)\:=\:\Bigg(\frac{2-(-4)}{2-0}\Bigg)\:=\:\Bigg(\frac{2+4}{2}\Bigg)\:=\:\frac{6}{2}\:\:=\:3}[/tex]
Therefore, the slope of the line is 3.
How to find the y-intercept (b)?As defined in the previous section of this post, the y-intercept (0, b) is the point on the graph where it crosses the y-axis. We can see that the line intersects the y-axis at point (0, -4). This means that the value of our y-intercept, b, is -4.
Finding the y-intercept algebraically.Alternatively, we can solve for the y-intercept (b) by choosing a point on the graph and substitute its values into the slope-intercept form.
We will use and substitute the values of (x₁, y₁) and the slope into the function to solve for b.
(x₁, y₁) = (2, 2)Slope (m ) = 3f(x) = mx + b
⇒ 2 = 3(2) + b
⇒ 2 = 6 + b
⇒ 2 - 6 = 6 - 6 + b
⇒ -4 = 0 + b
⇒ - 4 = b
Hence, the value of the y-intercept is: b = 4.
Final Answer:Based from our calculations, we can infer that the linear function that matches the graph is Option C: f(x) = 3x - 4.
__________________________Keywords:Linear functions
Linear equations
Slope-intercept form
_______________________________
Learn more about Linear Functions here: https://brainly.com/question/26351470
Learn more about Point-slope form here: https://brainly.com/question/26681302
Answer:
f(x)=3x-4
Step-by-step explanation:
The question is in the screenshot!!
find reason and statements
Answer:
Missing reason/statements:
R1, R2, R3 - GivenS4. ∠1 ≅ ∠3R4. Transitive propertyR5. Definition of congruenceS6. m∠1 = 120°R6. SubstitutionWhat is the length of ef in the right triangle below?
Answer: A
Step-by-step explanation:
Using pythagoras;
[tex]25 = \sqrt{7^{2}+ x^{2} }\\25^{2}=7^{2} +x^{2} \\625 = 49 +x^{2} \\576 = x^{2} \\x = 24[/tex]
Please give me a brainliest answer
Answer:
24Step-by-step explanation:
The Pythagoras theorem formula states that in a right triangle ABC, the square of the hypotenuse is equal to the sum of the square of the other two legs. If AB, BC, and AC are the sides of the triangle, then: BC2 = AB2 + AC2. While if a, b, and c are the sides of the triangle, then c2 = a2 + b2.
√(25²-7²) =
√(625-49)=
√576=
24
Complete the table of values for y=x2-x-5.
Answer:
when -2 , y = 1
when 0, y = -5
when 2, y = -3
when 3, y = 1
when 4, y = 7
Hhhhhhhhhhhhhhhhjjjjjj
Answer:
8.75 per hour
Step-by-step explanation:
Since it is a linear function we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 370-20)/(40-0)
=350/40
= 8.75
Trong 300 người bệnh chỉ dùng thuốc A có 55% người khỏi; trong 240 người bệnh chỉ dùng thuốc B có 50% người khỏi. Với mức ý nghĩa 5% có thể nói thuốc A hiệu quả hơn thuốc B không?
vâng vì phụ nữ là những người tán gẫu
without using a calculator or mathematical table sove 187²-87²
A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answer:
2 in 16
Step-by-step explanation:
what is 4/5 divided by 2/3 simplest
Answer:
1 1/5
Step-by-step explanation:
4/5 ÷ 2/3
4/5 × 3/2
12/10
6/5
1 1/5
(5x+5)-2x
No scam.....
Answer:
=3x+5
Step-by-step explanation:
Let's simplify step-by-step.
5x+5−2x
=5x+5+−2x
Combine Like Terms:
=5x+5+−2x
=(5x+−2x)+(5)
=3x+5
Answer:
=3x+5
Answer:
[tex]\boxed{\boxed{\sf 3x+5 }}[/tex]
Step-by-step explanation:
[tex]\sf (5x+5)-2x[/tex]
[tex]\sf \left(a\right)=a[/tex]
⇒ First step is to get rid of expression parentheses:
[tex]\longmapsto[/tex] [tex]\sf 5x+5-2x[/tex]
⇒ Now, we need to combine like terms:
[tex]\longmapsto[/tex] [tex]\sf (5x-2x)[/tex] [tex](5)[/tex]
[tex]\longmapsto[/tex] [tex]\sf 3x+5[/tex]
__________________________________
In the month of September, all of the Kroger grocery stores in Nashville sold 429,382 eggs. In that same month, all of the Kroger grocery stores in Memphis sold 283,054 eggs. How many eggs did the Nashville and Memphis Kroger grocery stores sell all together in the month of September? Use 2 strategies to show how you found out how many eggs Kroger sold in September.
Answer:
712436 eggs were sold together
Step-by-step explanation:
429,382 + 283,054 = 712436
******Please help me please help me help please help*****
9514 1404 393
Answer:
(c) y = 36·5
Step-by-step explanation:
If x represents the number of chocolates, the given formula ...
y = kx
with the values k = 36 and x = 5 inputted will look like ...
y = 36·5
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies k^2+2k-3>0
Step-by-step explanation:
For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,
b^2 - 4ac must be positive.
b^2 - 4ac > 0
(k - 3)^2 - 4(3 - 2k) > 0
k^2 - 6k + 9 - 12 + 8k > 0
k^2 + 2k - 3 > 0
To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
How to prove the expressionTo have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;
Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.
In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0
Learn about quadratic equations at: https://brainly.com/question/1214333
#SPJ3
Given the relation shown in the table below :
Answer:
domain: -7, -1, 0, 1
Range: -1, 0, 1, 2, 7
Step-by-step explanation:
I don't know the drop-down menu choices so I can't answer that one for you sorry :(
But I hope this helps :)
Helppppppppppppp please
Answer:
1.45 x 10^2
Step-by-step explanation:
In scientific notation, you get the number down to 1 digit before the decimal place and all the rest after it, then multiply by 10 raised to a power in order to get it back to the original. An easy way to do it is to count the number of times you moved the decimal and remember which direction you did it. The number is the power (in this case 2) and the direction tells you if it's positive or negative (in this case it was to the left, so it's positive two.)
In simpler terms, slide the decimal to the right two places and make it 1.45, then multiply it by 10^2 (which is 100) to make it equal to 145. This leaves you with 1.45 x 10^2.