Using an exponential function, it is found that the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year is given by:
[tex]P = 100\% \times [(1 .03)^t - 1][/tex]
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.As a percentage, the increase is modeled by:
[tex]P = 100\% \times [(1 + r)^t - 1][/tex]
In this problem, the growth rate is of r = 0.03, hence:
[tex]P = 100\% \times [(1 + 0.03)^t - 1][/tex]
[tex]P = 100\% \times [(1 .03)^t - 1][/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
find X
15x and 8x-2
i will give brainliest
Answer:
x = 4
Step-by-step explanation:
15x + 8x -2 = 90
23x - 2 = 90
23x = 90+2
23x = 92
92/23 = 4
check answer:
4 x 15 = 60
4 x 8 = 32
32-2=30
60+30=90
Answer:x=4
Step-by-step explanation: we know,
90 + 8x-2+15x=180
90+23x-2=180
88+23x=180
23x=180-88
x=92/23
x=4
Line segment EF is graphed on the coordinate plane below?
What is the length of EF? Record your answer to the nearest tenth of a unit.
The population of village was 5000. The male population decreased by 20% and female population increased by 30 % make in change in total population. Find the male and female population of the village in the beginning.
Answer:
Step-by-step explanation:
I need help. I will give 15 points for the answer.
Answer:
a) because all the angles of both of the triangle of equal and help by angle angle similarity criteria we can say that ∆ABCis similar to ∆PQRb) since ∆ABC~ ∆PQR[tex] \frac{ab}{ac} = \frac{pq}{pr} [/tex][tex] \frac{6}{ac } = \frac{18}{27} \\ ac = \frac{6 \times 27}{18 } \\ ac = 9cm[/tex]Hope it helps you<3Korey and lan are arguing about how to find the perimeter of a rectangle. Korey says you should add the length and the width and then multiply the sum by 2. Ian says you should double both length and width and then add them together who is correct
Answer:
They are both right
Step-by-step explanation:
This is because you can do it either way.
For example, if you had a rectangle with the side length 10 and a width 5,
-Korey: you could add them to get 15 and them double them to get 30
or
-Ian: double both (5*2=10 and 10*2=20) and then add and 10+20 = 30
So they are the same
Factorise x2 + 5x - 84
(x - 7)(x + 12)
Answer:
[tex] {x}^{2} + 5x - 84 \\ {x}^{2} + 12x - 7x - 84 \\ x(x + 12) - 7(x + 12) \\ (x - 7)(x + 12)[/tex]
As the height of the cylinder increases, its volume decreases.
Which is the independent variable?
height or volume
Answer:
height is independent
Step-by-step explanation:
as you change the height, the volume changes accordingly.
what is this equation 6x-4y=18 and -x-6y=7
Step-by-step explanation:
here you have answer.....
There is a $500 prize to share among them. Ms. Cardillo’s class brought in 3,107 pop can tabs. Ms. Camming’s class collectected 1,097 pop can tabs. Mr. Lucas’ class brought in 2,347 pop can tabs. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of pop can tabs that they collected?
Can someone help me with this please
Answer:
medium: 16large: 18Step-by-step explanation:
Using the variable definitions shown, the two given relations are ...
11 +x +y = 45 . . . . . . 45 total orders
x = y -2 . . . . . . . . . . 2 fewer medium orders than large
__
Using the second equation, we can substitute for x in the first equation to solve this system:
11 +(y -2) +y = 45
2y = 36 . . . . . . . . . . collect terms and subtract 9 from both sides
y = 18 . . . . . . . . . . . divide both sides by 2
x = 18 -2 = 16 . . . . use the second equation to find the value of x
16 people ordered medium, and 18 people ordered large coffees.
4(n+6)+3n is greater than or equal to 3n-4
Answer:
7n+24 is greater than that 3n-4
Step-by-step explanation:
First Distributive Property
4(n+6)+3n
Combine like terms
4n +24+3n
7n+ 24
Explanation
7n+24 is greater than that 3n-4
If we multiply three consecutive integers and then add the middle number to the result, the answer is always the middle number cubed.
5 × 6 × 7 + 6 = 216 = 63
10 × 11 × 12 + 11 = 1331 = 113
15 × 16 × 17 + 16 = 4096 = 163
Use what you have learned in this lesson to write a third-degree polynomial expression in factored form and standard form that represents this pattern. Show that the factored form is equivalent to the expression written in standard form. Substitute three different values for the variable to prove this pattern works for other numbers.
Step-by-step explanation:
Let use have a interger,n
Thus three consectice intergers can be represented by
[tex]n[/tex]
[tex]n + 1[/tex]
[tex]n + 2[/tex]
Multiply, and we get
[tex]n(n + 1)(n + 2)[/tex]
[tex]n( {n}^{2} + 3n + 2)[/tex]
[tex]n {}^{3} + 3 {n}^{2} + 2n[/tex]
Then add the middle number, n+1.
[tex] {n}^{3} + 3n {}^{2} + 3n + 1[/tex]
We must prove that the middle number cubed = the equation.
Using the binomial theroem,
[tex](n + 1) {}^{3} = {n}^{3} + 3( {n}^{2} 1 {}^{1} ) + 3n( {1}^{2} ) + 1 {}^{3} [/tex]
[tex](n + 1 ){}^{3} = {n}^{3} + 3 {n}^{2} + 3n + 1[/tex]
So this is indeed true.
You can do the subsitue variables for n to prove it.
There is a rectangle. The long side is 8.2cm the short side is 3.6cm. Find the area. (Include units)
Answer:
29.52cm sqauared
Step-by-step explanation:
length x width = area of rectangle
Answer: 29.52cm2
Step-by-step explanation:
8.2 times 3.6=...
in a all-area track meet 271 sprinters enter a 200-meter dash competition. the track has 7 lanes so only 7 sprinters can compete at a time. at the end of each race, the six non-winners are eliminated, and the winner will compete again in later race. How many races are needed to determine the champion sprinter?
The number of races needed to determine the champion sprinter = 39 races.
Calculation of number of racesThe number of sprinters = 271
The number of sprinters per race= 7
The area to be covered for each race = 200m
For every race covered, a champion is selected and the rest is eliminated.
Therefore, to determine the remaining champion from 271 sprinters,
271/ 7 = 38.7
Which is approximately 39 races.
Learn more about meter here:
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HELP I GIVE BRAINYEST The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A=8x -10^\circ}∠A=8x−10
∘
start color #11accd, angle, A, equals, 8, x, minus, 10, degrees, end color #11accd \qquad \green{\angle B=3x + 90^\circ}∠B=3x+90
∘
start color #28ae7b, angle, B, equals, 3, x, plus, 90, degrees, end color #28ae7b
Answer:
B = 150
Step-by-step explanation:
Since angles A and B are opposite interior angles, they are congruent.
8x - 10 = 3x + 90
8x - 3x = 90 + 10
5x = 100
x = 20
Now that we have the value of x, we have to solve for angle B.
B = 3x + 90
B = 3*20 + 90
B = 60 + 90
B = 150
Answer: the right answer on khan academy is 150° (with PROOF)
What is the name of the platonic solid below
Answer:
the other person is wrong
Step-by-step explanation:
I looked it up and its HEXAHEDRON
Tetrahedron is a pyramid
What is the equation of the line of best fit that Pat drew?
OA.
y = -51 + 3
OB.
y = -5.7 + 7
O C.
Y =
* + 3
-Br
y = -x + 7
OD.
Answer:
B) y = -5x + 7
Step-by-step explanation:
Pick 2 points on the line: (10, 5) and (15, 4)
slope = change in y ÷ change in x = (15 - 10) ÷ (4 - 5) = -5
from inspection, the y-intercept is (0, 7)
Therefore, using slope-intercept formula: y = mx + b
(where m is the slope and b is the y-intercept)
y = -5x + 7
Write 5y^3 without exponents.
Answer:
can be written as without exponent.
Given:
To find:
Write the given expression without exponent.
Solution:
Formula to be used:
Step 1:
Write the expanded form of given expression.
Step 2:
simplify
or
125×y×y×y without exponent.
Answer:
5 × y × y × y
Step-by-step explanation:
5y³ ( only y is being cubed with 5 a multiplier ) , so
= 5 × y × y × y
Hay algo que, aunque te pertenezca, la gente siempre lo utiliza más que tú. ¿Qué es?
Answer:
Respuesta: tu nombre (Answer: your name)
Step-by-step explanation:
What is the equation of a line with slope -3 through the point (3, 5)?
Answer:
y = -3x + 5
Step-by-step explanation:
Problem shown on the picture
Step-by-step explanation:
please answer those Questions Mathematics
in the diagram below, the value of y must be
Answer:
y = 45°
Step-by-step explanation:
4 sides = 360°
(2y+1)° + y° + 112° + 112° = 360°
2y + y = 360 - 112 - 112 - 1
3y = 135
y = 135÷3
= 45°
Please help will give most Brainly
What does the random variable for a binomial experiment of n trials measure?.
Answer:
What does the random variable for a binomial experiment of n trials measure? The random variable measures the number of successes out of n trials. ... A binomial experiment requires that the probability of success be the same for each trial. In an experiment, there are n independent trials.
Step-by-step explanation:
what are the domain and range of f(x)=2(x-8)-10
Answer:
Domain: All real numbers
Range: f(x) ≥ - 10
Step-by-step explanation:
I had the same test. Completed it and got it right.
Sorry for the lack of explanation, I can't put it into words at the moment.
Please help I will give Brainliest.
Answer:
$21,600
Step-by-step explanation:
h(x) = 5000 · (1.08)^4
5000 · 4.32
h(x)= 21,600
Answer:
$6802.44
Step-by-step explanation:
We will replace x with 4.
h(4) = 5000 · (1.08)^4
Use a calculator from here if you don't want stress.
1.08 x 1.08 x 1.08 x 1.08 = 1.36048896
1.36048896 x 5000 = 6802.4448
Since we are looking at the cost, we will approximate to the nearest hundredth.
6802.4448 ≈ 6802.44
The cost is $6802.44.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer: A
Step-by-step explanation:
Divide top and bottom by 4
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The simplest form of the fraction is simply finding a common number to divide both the numerator and denominator by.
4/8 , we can divide both sides by 4 since it's possible to do so.
[tex]\frac{4/4}{8/4}[/tex]
[[tex]\frac{1}{2}[/tex]]
A. is the simplest form
please help I will give brainlyest
Answer:
See below.
Step-by-step explanation:
The answer is D. M and O are congruent, but that is not an option, so the focus goes towards M and N. M and N are similar, but are not congruent.
-hope it helps
Answer:
M and N are similar but not congruent.
Step-by-step explanation:
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!!
Answer:
m∠3 = 55°
Step-by-step explanation:
m∠1 = m∠4 (parallel lines with same angle)
m∠2 = m∠3 (parallel lines with same angle)
apply whole angle measure equals to 360°
11x -7 + 5x - 5 + 11x -7 + 5x - 5 = 360
32x -24° = 360°
32x = 384°
x = 12°
Therefore
m∠3 = 5x - 5
m∠3 = 5(12) - 5
m∠3 = 55°
[tex]\\ \tt\hookrightarrow 11x-7+5x-5=180[/tex]
[tex]\\ \tt\hookrightarrow 16x-12=180[/tex]
[tex]\\ \tt\hookrightarrow 16x=192[/tex]
[tex]\\ \tt\hookrightarrow x=12[/tex]
<3=<2=5(12)-5=60-5=55°someone can help me for all the question ?
Answer:
1. 5
2. 3 adult tickets; 2 child tickets
3. See below
Step-by-step explanation:
1.
2 adult tickets cost 2 × $12 = $24
Subtract $24 from $64:
$64 - $24 = $40
Divide $40 by $8:
$40 ÷ $8 = 5
Answer: 5 child tickets
2.
x = number of adult tickets
y = number of child tickets
The total number of tickets is 5, so the first equation is:
x + y = 5
The cost of x adult tickets is 12x. The cost of y child tickets is 8y. The total cost is 12x + 8y. We are told the total cost is $52. The second equation is:
12x + 8y = 52
The system of equation is:
x + y = 5
12x + 8y = 52
Let's solve it by substitution.
Solve the first equation for x.
x = 5 - y
Now we substitute x in the second equation by 5 - y.
12(5 - y) + 8y = 52
Distribute:
60 - 12y + 8y = 52
Combine like terms on the left side:
-4y + 60 = 52
Subtract 60 from both sides:
-4y = -8
Divide both sides by 4.
y = 2
Substitute y = 2 in the first original equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
Answer: 3 adult tickets; 2 child tickets
3.
The customer's claim is incorrect. His sum is $71. 71 is an odd number. Since all ticket prices are even numbers, it is impossible to add only even numbers and get an odd sum. A sum of several amounts of 12 and several amounts of 8 can never equal 71.
We can also show his claim is false using a system of equations.
x + y = 7
12x + 8y = 71
Use substitution.
x = 7 - y
12(7 - y) + 8y = 71
84 - 12y + 8y = 71
84 - 4y = 71
-4y = -13
y = 3.25
This means 3.25 child tickets. The problem states that tickets can be purchased only in whole numbers, so 3.25 tickets cannot be purchased, so the customer's claim is false.