Therefore, the minimum score required for the scholarship 652
We are told in the question that:
A university plans to award scholarships to students whose scores are in the top 30%.
The top 30% means
100 - 30% = 70%
This means the student must be in the 93rd percentile
We solve using the z-score formula.
z = (x-μ)/σ, where
x is the raw score?
μ is the population mean = 496
σ is the population standard deviation = 109
Z score for 93rd percentile = 1.476
1.476 = x - 491/109
Cross Multiply
1.476 × 109 = x - 491
160.884 = x - 491
x = 160.884 + 491
x = 651.884
Approximately to the nearest whole number = 652
Therefore, the minimum score required for the scholarship 652
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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
0 , x<0
f(x) = ((x^2)/4) , 0 <= x <= 2
1 , 2<= x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X %u2264 1)
(b) P(0.5 %u2264 X %u2264 1)
(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)
(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).
Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:
[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]
To use the cdf to obtain the following.P(X ≤ 1)
So, the probability distribution function is the derivative of the cumulative distribution function.
∴ f(x) = d/dx(F(x))
Also, from the cdf, we know that:
[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]
f(x) = 1 when x ≥ 2.
Using the above conditions, we have to calculate the following:
(a) P(X ≤ 1)
Here, P(X ≤ 1) = F(1).
When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]
Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]
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Jaya spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7300 feet. Jaya initially measures an angle of elevation of 16^∘ to the plane at point A. At some later time, she measures an angle of elevation of 28^∘ to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest tenth of a foot if necessary
The distance the plane traveled from point A with measures an angle of elevation of 16°, to point B with measures an angle of elevation of 28°, is equals to the 11,728.6feet.
Jaya spots an airplane on radar that is currently approaching in a straight line start from point O in above figure, and that will fly directly overhead.
Altitude that plane maintain,h = 7300 feet
Initially, measure an angle of elevation to the plane at point A = 16°
Measure an angle of elevation to the plane at point B = 28°
Now, Let the distance between point A and point B be equal to 'x feet' and distance between point B and point C ( base) be equal to 'y feet'. So, distance between point A to point C = (x + y ) feet. We have to calculate the distance the plane traveled from point A to point B, i.e., x feet. See the above figure carefully, we see in right angled triangle BOC, tan 28° = 7300/y --(1)
In right angled triangle AOC,
tan 16° = 7300/(x + y) --(2)
Cross multiplication in equation (2)
=> tan 16° ( x + y ) = 7300
=> x + y = 7300/tan 16° --(3)
from equation (1), y = 7300/tan 28°
=> y = 7300/0.5317 = 13,729.55
so, x = 7300/tan 16° - y = 7300/0.287 - 13,729.55
= 25,458.12 - 13,729.55
= 11,728.58 ~ 11,728.6
Hence, required distance is 11,728.6feet.
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If two points on a line are A(4, 6) and B(8, −8), the rise is __________, and the run is __________, so the slope of the line is __________.
a particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. with the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx
The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.
The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.
Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
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Find an equation of the line with gradient 4 and that passes through the point
(-5, -5)
Answer:
y = 4x + 15
Step-by-step explanation:
Using 'y=mx+c' form,
Since m = 4,
y = 4x + c
Substituting (-5, -5) into the above equation:
-5 = -20 + c
c = 15
Hence,
y = 4x + 15
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At dominos, each pizza is cut into 8 slices. Chris ate 5 slices from a pizza with a diameter of 20inch pizza, what is the area of the slices Chris ate?
Answer: The area of each slice of pizza can be calculated by finding the area of the whole pizza and dividing it by the number of slices.
The radius of the pizza is half of the diameter, so the radius is 20/2 = 10 inches.
The area of the whole pizza can be calculated using the formula for the area of a circle:
Area = π × radius^2
Area = π × 10^2
Area = 100π square inches
Since there are 8 slices, each slice has an area of:
100π square inches / 8 = 12.5π square inches
Therefore, the area of the 5 slices that Chris ate is:
5 × 12.5π square inches = 62.5π square inches
This is approximately equal to 196.35 square inches, when rounded to two decimal places.
Step-by-step explanation:
problem i need help now
Answer:
Step-by-step explanation: 55 i think
Answer:
2%?
Step-by-step explanation:
PLEASE HELP!!!! DUE TOMORROW AND GRADED!!!! I WILL GIVE BRAINLIEST
Answer:
f(-3) = 6
Step-by-step explanation:
You want the value of f(-3) given a graph of f(x).
Reading a graphTo find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.
The attachment shows this process, and that the value of f(-3) is 6.
__
Additional comment
Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.
The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.
Find the discriminant of $3x^2 + \left(3 + \frac 13\right)x + \frac 13$.
The discriminant, D of the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex] when calculated is 64/9
How to determine the discriminant of the equationThe quadratic equation is given as
[tex]3x\² + 3 \frac 13x + \frac 13[/tex]
The discriminant of a quadratic equation of the form ax² + bx +c = 0 is given by the expression b² - 4ac
In this case, we have the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex], which can be written in the standard form as
[tex]3x\² + \frac {10}3x + \frac 13[/tex]
Comparing with the standard form ax² + bx + c = 0,
we have a = 3, b = 10/3 and c = 1/3
The discriminant of this quadratic equation is therefore:
D = b² - 4ac
[tex]D = (\frac{10}{3})\² - 4 \cdot 3 \cdot \frac{1}{3}[/tex]
D = 64/9
Hence, the discriminant of [tex]3x\² + 3 \frac 13x + \frac 13[/tex] is 64/9
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The graph of y = 4sin(x + 3) - 2 is obtained by shifting the graph of y = 4sin x - 2 horizontally 3 units to the right.
True of false
Step-by-step explanation:
False, it is 3 units to the left
For any function,
[tex]f(x)[/tex]
the function transformation of
[tex]f(x - h)[/tex]
implies a transformation h units to the left
If h is the positive, this implies a transformation to the right
If h is negative, this implies a transformation to the left.
Here's since
[tex](x + 3[/tex]
can be written as
[tex](x - ( - 3))[/tex]
Our h is negative, therefore we move 3 units to the left
4.02 Lesson check ! (1)
1. The sequence is an arithmetic sequence with a common difference of d = -200.
2. The sequence is not an arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
For item 1, each term is the previous term subtracted by 200, hence the sequence is in fact an arithmetic sequence with a common difference of -200.
For item 2, the difference between consecutive terms is difference, hence the sequence is not an arithmetic sequence.
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I heed a lot of help Guys
Answer: The graph is translated to the left 9 units
Step-by-step explanation:
When the thing is negative it will move to the right it will be positive. When it's negative it will move to the left than it will be negative.
At a coffee shop, the first 100 customers'
orders were as follows.
Hot
Cold
Small Medium Large
5
48
22
8
12
5
Find the probability a customer ordered a hot
drink, given that they ordered a small.
P(B|A) =
P(AnB)
P(A)
Round to the nearest hundredth.
P(hot | small) = [?]
Enter
The probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.
The Bayes theorem is what?A mathematical technique called the Bayes theorem enables us to revise our views or probability regarding an occurrence in light of fresh data or evidence. It has the name of the reverend Thomas Bayes, a statistician and philosopher active in the 18th century. According to the Bayes theorem, the likelihood of an event A given that an event B has already happened is equal to the likelihood of an event B given that an event A has already occurred, multiplied by the prior likelihood of an event A, divided by the previous likelihood of an event B.
The Baye's Theorem is given as:
P(B|A) = P(A|B) × P(B) / P(A)
Here,
P(A) is the probability that a customer ordered a small drink = 0.22.
P(B) is the probability that a customer ordered a hot drink, regardless of whether it was small or medium or large = 0.05.
P(A|B) is the probability that a customer ordered a small drink, given that they ordered a hot drink = 0.2.
Substitute the value we have:
P(B|A) = P(A|B) × P(B) / P(A) = (0.2 × 0.05) / 0.22 ≈ 0.045
Therefore, the probability that a customer ordered a hot drink, given that they ordered a small, is approximately 0.045.
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Unit 10: circles
Homework 8
#2, 4, 6, and & 8
The measures in the circles are calculated as:
2. FD = 22; 4. US = 58
6. MN = 11; 8. YZ = 34
What is the Intersecting Chords Theorem?The Intersecting Chords Theorem states that when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
2. 12(3x - 5) = 15(8) [based on the Intersecting Chords Theorem]
36x - 60 = 120
36x = 120 + 60
36x = 180
x = 5
FD = 3x - 5 + 12 = 3(5) - 5 + 12
FD = 22
4. 30(3x + 1) = 42(x + 11) [based on the Intersecting Chords Theorem]
90x + 30 = 42x + 462
90x - 42x = -30 + 462
48x = 432
x = 9
US = 3x + 1 + 30 = 3(9) + 1 + 30 = 58
6. (2x - 7 + 9)(9) = (8 + 10)(10) [based on the intersecting secants theorem]
18x + 18 = 180
18x = 180 - 18
18x = 162
x = 9
MN = 2x - 7 = 2(9) - 7
MN = 11
8. (2x + 12 + 6)(6) = (x + 3 + 10)(10) [based on the intersecting secants theorem]
12x + 108 = 10x + 130
12x - 10x = -108 + 130
2x = 22
x = 11
YZ = 2x + 12 = 2(11) + 12
YZ = 34
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One x-intercept for a parabola is at the point
(1,0). Use the factor method to find the other
x-intercept for the parabola defined by this
equation:
y = 2x² + 8x - 10
Separate the values with a comma.
Enter the correct answer.
Roy, Sydney, Mila, Taniya invested money on a project. Roy invested twice as Sydney. Mila invested twice as Roy. Taniya invested half as Mila. If the total profit of the project is $27,000. What percentage of profit Mila should receive?
Mila should receive 44.44% of the profit.
What is equations?An equation is a statement that asserts the equality of two expressions, typically with one or more variables. Equations are used to represent relationships between different quantities, such as the relationship between the length and width of a rectangle or the relationship between the time and distance traveled by an object.
What is profit?Profit is the financial gain that is earned by a business or an individual after all expenses and costs have been subtracted from revenue or income. It is the difference between the amount earned from sales or services and the costs incurred to produce or provide those goods or services.
In the given question,
Let's begin by determining the amount of money each person invested in the project.
Let Sydney's investment be x.
Roy's investment is twice Sydney's, so Roy invested 2x.
Mila's investment is twice Roy's, so Mila invested 2(2x) = 4x.
Taniya's investment is half of Mila's, so Taniya invested 0.5(4x) = 2x.
The total amount invested is x + 2x + 4x + 2x = 9x.
Now, we need to find the percentage of profit Mila should receive. Since the profit is shared in proportion to the amount invested, Mila should receive a fraction of the profit equal to her investment divided by the total investment.
Mila's share = (Mila's investment) / (Total investment) x (Total profit)
Mila's share = (4x / 9x) x 27000
Mila's share = 12000
So Mila should receive $12,000 of the profit. To find the percentage of profit Mila should receive, we can divide her share by the total profit and multiply by 100:
Percentage of profit Mila should receive = (Mila's share / Total profit) x 100%
Percentage of profit Mila should receive = (12,000 / 27,000) x 100%
Percentage of profit Mila should receive = 44.44%
Therefore, Mila should receive 44.44% of the profit.
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The statement say a contractor contracted to supply water to three Altein ring road has decided to investigate the financial impact that the monthly installments, salaries and the price of fuel had to his business per month. The contractor will use one of his water tankers to conduct an investigation. The contractor was supplying water to the Altien village 5 km ring road construction site where the road had to be paved using the paving bricks. The paving of the road has started in January 2022 and ran for 10 months.
Questions
1.1 write down the loan term of the truck in years
1.2 determine the monthly repayments that were made towards the water tanker including the insurance cover amount
1.3 the contractor had already made half of the monthly installments towards the truck in June 2022. Determine the total amount of money that was owed to the finance excluding the insurance in June 2022
1.4 give an explanation on the significance of including an insurance cover when a contractor purchases the water tanker
Therefore , the solution of the given problem of unitary method comes out to be in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.
What is an unitary method?The task can be completed by multiplying the data gathered using this type of nanosection along with two variable individuals who utilized the unilateral strategy. In essence, this signifies that perhaps the designated entity is defined or the colour of both mass production is skipped whenever a wanted item occurs. For forty pens, a variable charge of Inr ($1.01) could have been required.
Here,
1.1. The statement omits details about the truck's loan term. Therefore, without more details, we are unable to respond to this query.
1.2. Assume that the truck's loan period is n years and that the contractor borrowed P dollars at an annual interest rate of r to buy the water tanker.
M is calculated as (r * P * (1 + r)n) / ((1 + r)n - 1)
5 years + 60 months Equals n
r = 5% / 12 = 0.004166667 (weekly interest rate) (monthly interest rate)
P = $100,000
=> M = (0.004166667 * $100,000 * (1 + 0.004166667)^60) / ((1 + 0.004166667)^60 - 1)
≈> $1,870.24
As a result, the total monthly payments made for the water tanker, including the insurance protection, came to about $1,870.24.
1.3
(Total Amount Borrowed - Amount Paid) / 2
=> ($100,000 - $1,870.24 * 6) / 2 = $47,259.52 is the sum that is owed.
Therefore, in June 2022, the total amount due to the finance, exclusive of the insurance, was roughly $47,259.52.
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Find the unit rate for each, then tell which is the least expensive brand.
Bugsy-B: $9.99 for 64 ounces, How many dollars per ounce?
Tazi-D: $2.25 for 16 ounces, how many dollars per ounce?
Answer: Tazi-D
Bugsy-B: 0.16 per ounce
Tazi-D: 0.14 per ounce
Step-by-step explanation:
divide the $ by the ounce for both.
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
The slope of the linear function that represents the cost of plan B is $0.17.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Since Plan B has the same monthly base charge as plan A, we can logically deduce that the data points (0, 14.45) and (45, 22.10) lie on the linear function.
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (22.10 - 14.45)/(45 - 0)
Slope (m) = $0.17
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Complete Question:
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table. Monthly Charge for Plan A Minutes used, x Monthly charge ($), y 0 14.45 3 14.84 6 15.23 9 15.62 12 16.01 Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
What does 100-20-20-30-30+20+30+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+20+10=.
100-30-30-20-20=0. 20+30=50. 50+5+1+1+1+1+1=60. 60+1+1+1+1+1+1+1+1+1+1=70.
70+20=90. 90+10=100. So 100 is our answer.
Answer: this equals 100
Step-by-step explanation:
What is the coordinate for G(3,-2) after it is reflected across the x-axis?
(2,3)
(-2,3)
(3,2)
(-3,-3)
Answer:The coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2).
What do you mean by reflection of coordinates?
A reflection on the coordinate plane is a type of transformation. It takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image.
Given is a point (-3, 2) reflected across the y - axis.
Now, when any given coordinate is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.
As given, the coordinates of the point are - P(-3, 2)
Now, after reflection across the y - axis, the new coordinates of the image of this point will be -
x' = - (- 3) = 3
y' = y = 2
P'(3, 2)
Therefore, the coordinates of the resulting point after the reflection across the y - axis will be P'(3, 2)
Answer:
3,2
Step-by-step explanation: Just took the test
PLS HELP ASAP
!!!!!!!!!
Answer:
3x³- 8x² + 2x +3
Step-by-step explanation:
All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.
3x³-3x²-5x²+5x-3x+3=
3x³-8x²+2x+3
Arthur can paint a wall in 45 minutes alone. Cheyenne can paint a wall in 1 hour alone. One
room has 4 walls. How many minutes will it take them to paint 3 rooms together?
The time needed to paint 3 rooms together is given as follows:
308.4 minutes.
How to obtain the time needed?The time needed is obtained applying the proportions in the context of the problem.
First we use the together rate, which is the sum of each separate rate, for the time needed to paint a single wall, hence:
1/x = 1/45 + 1/60
1/x = 7/180
7x = 180
x = 180/7
x = 25.7 minutes per wall.
The number of walls in 3 rooms is given as follows:
3 x 4 = 12 walls.
Thus the time needed to paint the 3 rooms is given as follows:
25.7 x 12 = 308.4 minutes.
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A family is traveling a total distance of 532 miles. If the family travels at an average speed of 57 miles per hour, which equation represents the number of miles remaining, m, after h hours?
m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.
The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.
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Write the ratio in its simplest form: 2m: 8cm : 40mm
The simplest form of the ratio 2m : 8cm : 40mm is
50mm : 2mm : 1mm
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter
2m = 2× 1000mm = 2000mm
8cm = 8 × 10 = 80mm
40mm = 40mm
therefore the ratio will be in form of
2000mm : 80mm ; 40mm
divide through by 10
200mm : 8mm : 4mm
divide through by 4
50mm : 2mm : 1mm
therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm
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A pair of parallel lines is cut by a transversal.
A pair of parallel lines is shown cut by a transversal. Angle A is located in the upper left exterior next to the transversal, and angle B is located in the bottom right exterior corner of the transversal.
If m∠A = (5x − 4)° and m∠B = (8x − 28)°, what is the value of x?
Answer:
8 degrees
Step-by-step explanation:
Given in the picture, hope it helps.
You rent an apartment that costs $1200 per month during the first year, but the rent is set to go up 11% per year. What would be the rent of the apartment during the 8th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 8th year would be approximately $2491.4.
To calculate the rent of the apartment during the 8th year, we need to apply the 11% increase per year for a total of 7 years (from the 2nd to the 8th year). Here's the calculation:
Rent for the 2nd year:
$1200 + (11% of $1200) = $1200 + ($132) = $1332
Rent for the 3rd year:
$1332 + (11% of $1332) = $1332 + ($146.52) = $1478.52
Rent for the 4th year:
$1478.52 + (11% of $1478.52) = $1478.52 + ($162.64) = $1641.16
Rent for the 5th year:
$1641.16 + (11% of $1641.16) = $1641.16 + ($180.53) = $1821.69
Rent for the 6th year:
$1821.69 + (11% of $1821.69) = $1821.69 + ($200.39) = $2022.08
Rent for the 7th year:
$2022.08 + (11% of $2022.08) = $2022.08 + ($222.43) = $2244.51
Rent for the 8th year:
$2244.51 + (11% of $2244.51) = $2244.51 + ($246.90) = $2491.41
Therefore, the rent of the apartment during the 8th year would be approximately $2491.4.
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How many degrees is the sum of the measures of the interior angles of a regular polygon with 18 sides?
there are 6 pure spectral colors: red,blue,orange,yellow,green and violet,Bees can only see 2/3 of these colors.how many of the pure spectral colors can bees see?
Answer:
Step-by-step explanation:
2/3*6
6*6
12
24f(x)=−x2+1 g(x)=x
Exer. 21-34: Find (a) (f∘g)(x) and the domain of f∘g and (b) (g∘f)(x) and the domain of g∘f.
(a) (f∘g)(x) and the domain of f∘g are defined for real numbers and (b) (g∘f)(x) and the domain of g∘f is defined for real numbers.
The given functions are:f(x) = −x² + 1g(x) = x
Exer. 21-34: To Find
(a) (f ∘ g)(x) and the domain of f ∘ g and (b) (g ∘ f)(x) and the domain of g ∘ f.(a) (f ∘ g)(x) and the domain of f ∘ gTo find the composite of the two functions, substitute the value of g(x) into f(x). Now, (f ∘ g)(x) is given by:f(g(x)) = f(x) = f(x) = f(x) = -x² + 1. The domain of (f ∘ g)(x): Since g(x) is defined for all real numbers, the domain of (f ∘ g)(x) is also defined for all real numbers.
(b) (g ∘ f)(x) and the domain of g ∘ f
To find the composite of the two functions, substitute the value of f(x) with g(x). Now, (g ∘ f)(x) is given by:g(f(x)) = g(-x² + 1) = -x² + 1
The domain of (g ∘ f)(x): The domain of f(x) is defined for all real numbers. However, the domain of g(x) is also defined for all real numbers. Therefore, the domain of (g ∘ f)(x) is defined for all real numbers.
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