Answer:
Step-by-step explanation:
To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.
First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:
PV = PMT x [(1 - (1 / (1 + r)n)) / r]
where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.
In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:
PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06
Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:
PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)
where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.
In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:
PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97
So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:
R153,094.97 - R141,798.06 = R11,296.91
So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.
A student wants to investigate the chemical changes that a piece of wood undergoes when it is burned. He believes wood that burns for 15 minutes will weigh less than unburned wood. Design a laboratory experiment that would allow the student to test his predictions, using appropriate equipment and technology. Be sure to consider safety requirements in your answer.
Answer:
Experimental Procedure:
Materials:
Piece of wood
Electronic balance
Bunsen burner
Heat-resistant mat
Stopwatch or timer
Safety goggles
Lab coat
Safety Precautions:
Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.
Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.
Use the Bunsen burner only under adult supervision.
Be cautious when handling hot objects, and allow them to cool before touching.
Procedure:
Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.
Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.
Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).
After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.
Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.
Calculate the difference between the initial and final mass of the wood, and record it in the table.
Repeat steps 1-6 three times to obtain three sets of data.
Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.
Conclusion:
If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.
Jaylen estimates the side of the square to be 8.5 inches long. The actual length of the side of the square is 8.3 inches long. What is the percent error of the area of the two squares?
Answer:
4.88%
Step-by-step explanation:
All sides of a square are equal
let x = length of a side
Area = x·x = x²
Estimated area = (8.5)² = 72.25 in²
Actual area = (8.3)² = 68.89 in²
percent error = (actual area - estimated area) / (estimated area) x 100
% error = (68.89 - 72.25) / (68.89) x 100 = -4.88% the negative sign means the estimate was higher than the actual.
Find d/dx (cos(x) + e^5x) using derivative rules.
O-sin(x) +5e^5x
O-sin(x) + 5xe^(5x-1)
O-sin(x) +e^5x
None of the answers listed is correct.
O sin(x) +e^5x
Answer:
1st one.-sin(X)+5e^5x
a) Construct a probability distribution
b) Graph the probability distribution using a histogram and describe its shape
c) Find the probability that a randomly selected student is less than 20 years old.
d) Find the probability that a randomly selected student's age is more than 18 years
old but no more than 21 years old.
LOOK AT SCREENSHOT FOR FULL QUESTION
The probability that a randomly selected student's age is more than 18 years old but no more than 21 years old is 0.57.
What is a continuous random variable's probability?
Continuous random variables are defined as having an infinite number of possible values. A continuous random variable hence has no probability of having an accurate value.
a) In order to create a probability distribution, all potential values of the random variable must be listed along with the related probabilities. We may get the relative frequency (or probability) for each value of the random variable from the above frequency distribution:
Age Frequency Probability
16 3 0.03
17 5 0.05
18 10 0.10
19 15 0.15
20 20 0.20
21 22 0.22
22 17 0.17
Total 92 1.00
b) We can use a histogram to see the probability distribution. The likelihood is represented by the vertical axis, while the age is represented by the horizontal axis. The height of each bar in the histogram should represent the likelihood for that age, with bars for each age value.
With a peak at age 20, the distribution's shape looks to be roughly symmetrical.
c) To get the likelihood that a student chosen at random is under 20 years old, we must add the probabilities for the ages 16, 17, 18, and 19:
P(age < 20) = P(age = 16) + P(age = 17) + P(age = 18) + P(age = 19)
= 0.03+0.05+0.10+0.15
= 0.33
Consequently, there is a 0.33 percent chance that a randomly chosen student is under 20 years old.
d) To determine the likelihood that a randomly chosen student is older than 18 but not older than 21, we must add the probabilities for the ages 19, 20, and 21:
P(18 < age ≤ 21) = P(age = 19) + P(age = 20) + P(age = 21)
= 0.15 + 0.20 + 0.22
= 0.57
As a result, there is a 0.57 percent chance that a randomly chosen student will be older than 18 but not older than 21.
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f(x) = 2x - 1 g(x) = 7x + 8 find (gof) (x)
Answer:
(gof)(x) = 14x + 1
Step-by-step explanation:
We can think of (gof)(x) as g(f(x)). Writing it in this form shows that we must start with the inner function and work our way to the outer function.
Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.
f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1
Now, this output becomes the input for g(x):
g(2x-1) = 7(2x - 1) + 8
14x -7 + 8
(gof)(x) = 14x + 1
State any excluded values of a domain and identify the type of break in the graph at the value of x
f(x)=x+7/x-2
Answer:
The excluded value in the domain is x = 2 because the denominator of the rational function becomes zero at this value of x, which results in division by zero.
At x = 2, there is a vertical asymptote, which means that the graph of the function approaches positive or negative infinity as x approaches 2 from either side.
58 points please urgent super urgent
4x=16
what is x
Answer:4? Think
Step-by-step explanation:
What is the volume of this cone?
The volume of the cone is 2119. 5 cubic centimeters
How to determine the volume of the coneThe formula used for calculating the volume of a cone is expressed as;
V = πr² h/3
Given that the parameters are namely;
V is the volume of the cone.π takes the constant value of 3.14h is the height of the cone.r is the radius of the cone.Now, substitute the values, we have;
Volume , V = 3.14 × 15² × 9/3
Divide the values, we have;
Volume = 3.14 × 225 × 3
Multiply the values, we get;
Volume, V = 2119. 5 cubic centimeters
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Find the ratio of the perimeter of △ABC to the perimeter of △XYZ.
The ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:
1/3.
What is the perimeter of a triangle?The perimeter of a triangle is the total length of its three sides. To find the perimeter of a triangle, you need to add up the lengths of all three sides.
The ratio between the side lengths of triangle ABC and triangle XYZ is given as follows:
5/15 = 1/3.
The perimeter of a triangle is measured in units, as area the side lengths, hence they have the same ratio, and thus the ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:
1/3.
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The perimeter of a rectangular garden is 30 ft. The length is 3 ft more than the width. Find the length and the width of the garden.
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
in our case
length = width + 3
and
2×length + 2×width = 30
using the first equation in the second :
2×(width + 3) + 2×width = 30
width + 3 + width = 15
2×width + 3 = 15
2×width = 12
width = 12/2 = 6 ft
length = width + 3 = 6 + 3 = 9 ft
20 points!! please help!!
To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.
What is area?Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure
Area of rectangle = length x width
= 20 ft x 8 ft
= 160 sq. ft
Area of triangle = 1/2 xbase xheight
= 1/2 x 8 ft x 10 ft
= 40 sq. ft
To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).
Using the Pythagorean theorem, we have:
12² = 10² + b²
144 = 100 + b²
44 = b²
b = √44
b ≈ 6.63 ft
Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:
Area of total figure = area of rectangle + area of triangle
= 160 sq. ft + 40 sq. ft
= 200 sq. ft
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I will mark you brainiest!
What is the value of x in the figure below
A) 4.5
B) 10
C) 5
D) None of the choices are correct
Answer:
I will not show you the process it is easy the answer is 4.5 or 6 ≈
2 1/4-6/7=
2 5/12-blank=2/3
7 1/12-5 3/8=
blank+7/10=2 9/20
To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:
9/4 - 24/28
= 63/28 - 24/28
= 39/28
Therefore, 2 1/4 - 6/7 = 39/28.
To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:
2 5/12 = (2*12 + 5)/12 = 29/12
Then we can subtract 2/3 from both sides:
2 5/12 - 2/3 = blank
To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:
29/12 - 8/12
= 21/12
= 7/4
Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.
To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:
7 1/12 = (712 + 1)/12 = 85/12
5 3/8 = (58 + 3)/8 = 43/8
Then we can subtract:
85/12 - 43/8
= 85/12 - (433)/(83)
= 85/12 - 129/24
= 5/24
Therefore, 7 1/12 - 5 3/8 = 5/24.
To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:
2 9/20 = (2*20 + 9)/20 = 49/20
Then we can subtract 7/10 from both sides:
blank + 7/10 - 7/10 = 49/20 - 7/10
Simplifying the right side:
49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4
Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:
blank = 7/4
Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.
Use the quadratic formula to solve the equation 2 - 5x-9=0
The answer is x = 5±√61/2, I really hope this helps (:
1 The table below shows the cost of an attorney as a function of the number o
hours worked.
A C=355h
3 C= _—_h+355°
Number of
Hours, h
1
255
4
7
8
Based on the table, which function models this situation?
Total Cost, C
с
$355
$1120
$1885
$2140
D
C=255h+100
C=765h-410
All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.
What does a function look like in math?A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".
The following function represents this circumstance:
C = -195h + 550
The first two data points can be used to create two equations:
355 = -195(1) + C
1120 = -195(3) + C
When we solve for C in each equation, we obtain:
C = 550
C = 550 + 585 = 1135
We can try utilising the first and third data points as the second equation doesn't quite match the third data point:
355 = -195(1) + C
1885 = -195(4) + C
Solving for C in each equation, we get:
C = 550
C = 550 + 975
= 1525
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the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
An Olympic swimming pool is 25 meters wide. How many decimeters
wide is an Olympic swimming pool?
Answer: 2.5 dm
Step-by-step explanation:
Divide 25.0 by 10
= 2.5
examine each equation and determine if it represents a
linear or nonlinear function. Explain your reasoning please.
7 y = ²³/x+7
8 y = x³ + 2
Using function concepts, we have that:1. Non-linear2.B)x y0 11 22 53 103. Linear4.: Linear: Linear: Non-Linear: Linear5. LinearIn a linear function, the rate of change is constant.A linear function is also of the first degree.Item 1:From -3 to -1, the rate of change is of From -1 to 1, the rate of change is of .Different rates of change, so non-linear.Item 2:At function b, from 0 to 1, the rate of change is of 1, from 1 to 2 of 3, different rates of change, so non-linear.Item 3:Highest degree of x is 1, so first degree, and thus linear.Item 4:The only non-linear is , which is of the second degree. is a constant function, with a rate of change of 0, so linear.The last function is written as:Highest degree of x is 1, so also linear.Item 5:In all cases, the rate of change is constant, so linear.
Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Select three options. x + 15 + 35 = 155 35 x + 15 = 155 35 x = 155 minus 15 It will take 8 months to pay off the debt. It will take 4 months to pay off the debt.
Answer: 3. 35x + 15 = 155
Step-by-step explanation:
35 x 4 = 140
140 + 15 = 155
It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
mentum
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Mar 10
11:
Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
Lmkkkk helppppppppppp
Answer:
1.986 x 10 to the tenth power
Step-by-step explanation:
Find a number between 100 and 200 which is also equal to a square number
multiplied by a prime number.
Answer:
162, 147 etc.
Step-by-step explanation:
we have to find
[tex]N = k^2 \cdot p[/tex]
we can iterate k = 1 to 10 to check all possible solutions,
[tex]N = 9^2 \cdot 2[/tex]
[tex]N = 7^2 \cdot 3[/tex]
N = 162, 147 etc.
Hopefully this answer helped you!!
48805 rounded to the nearest thousand
Answer: 49,000
48805 is greater than 48500, so it rounds to 49,000
during last nights basketball game the number of points scored by the hornets was triple the number of points scored by the raiders the raiders scored 6 points how many points did the hornets score?
2
9
12
18?
Answer:
18
Step-by-step explanation:
siz times three is eighteen
ASAP ASAP!!!!
[tex] {1}^{3 } [/tex]
1³=??
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below.
Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]
where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.
After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
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Complete question
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
Which relationships describe angles 1 and 2? Select each correct answer. O complementary angles O adjacent angles O vertical angles O supplementary angles
Answer:2
Step-by-step explanation:Because the 2 is closest to the middle line
Answer:
relationship describes angles 1 and 2 is supplementary angles. From the given figure
it is concluded that
the relation ship between angle 1 and 2 is supplementary angles
because its is linear pair
and forms a line
therefore , the angles are supplementary angles
hence , relationship describes angles 1 and 2 is supplementary angle
Step-by-step explanation: Hope this helps !! Mark me brainliest!! :))
A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nall
Number
of Nails
67
18
10
Abundance
(%)
[7]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
Med Nail % Abund.
Enter
According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.
Explain medium?Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.
To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:
Total number of nails = 67 + 18 + 10 = 95
Next, we can calculate the percent abundance of the medium nails using the formula:
Percent abundance = (number of medium nails / total number of nails) x 100%
Using the values from of the table as inputs, we obtain:
Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%
As a result, the sample's average percentage of medium nails is roughly 18.95%.
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Whats the the sum of x and 2
The sum of x and 2 is equal to x + 2.
What is value?Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.
This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.
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HELPPPPPP PLEASE PLEASEEEEEE
Determine a function type that
could represent the values in the
table.
x f(x)
0 −18
1 −15
2 −12
3 −9
4 −6
◻ linear
◻ quadratic
◻ exponential
Answer: Linear
Step-by-step explanation:
Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3
f(2) - f(1) = -12 - (-15) = 3
f(3) - f(2) = -9 - (-12) = 3
f(4) - f(3) = -6 - (-9) = 3
Since the differences are constant and equal to 3, this confirms that the function is linear.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation:
y = mx + bwhere m is the slope and b is the y-intercept.
We can use the first two points (0, -18) and (1, -15) to find the slope:
m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3
Now we can use the slope and one of the points to find the y-intercept:
y = mx + b
-18 = 3(0) + b
b = -18
Therefore, the equation of the linear function is:
f(x) = 3x - 18
So the function type that could represent the values in the table is linear.