Answer:
We can use trigonometry to find AB.
First, we can use the fact that the sum of the angles in a triangle is 180° to find angle A:
A + B + C = 180°
A + 90° + 30° = 180°
A = 60°
Now, we can use the sine function to find AB:
sin A = opposite/hypotenuse
sin 60° = AB/96
AB = 96 * sin 60°
AB = 96 * √3/2
AB = 48√3
Therefore, AB is approximately 83.14 cm (rounded to two decimal places).
Select the correct answer.
Which variable is likely to be linked to both of the variables mentioned in this statement?
There is a strong positive correlation between shoe size and reading score.
A.state in which the student lives
B.height of the student's parents
C.age of the student
D.the student's eye color
Answer:
B
Step-by-step explanation:
Pretty sure this is B. The height of your parents is the clearest way to determine how tall someone you'll be, and usually, your shoe size depends on your height. You can see this in real life. Shaq has huge feet because he's a huge guy.
A makes no sense. C might, but this will only apply to really small children. And D makes no sense either. So B is the best choice.
Answer:
C. age of the student is likely to be the answer
The bowling average of the players in the Capital Three bowling tournament is 158 with variance of 121. If Dr. Baker bowls an average of 169 during the tournament. Compute the appropriate statistic.
What proportion of bowlers performed better than Dr. Baker?
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
How to find the proportionStandard deviation (σ) = √(variance) = √(121) = 11
Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:
z = (X - μ) / σ
z = (169 - 158) / 11
z = 11 / 11
z = 1
Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.
The area to the left (or the cumulative probability) is approximately 0.8413
1 - 0.8413 = 0.1587
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
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Find the surface area of the rectangular prism. 2 m 5 m 2 m
A vending machines coin box contains nickels dimes and quarters. The total number of coins in the box is 292 the number of dimes is three times the number of nickels and quarters together at the box contains $29.95. find the number of nickels dimes and quarters that it contains.
There are 32 quarters, 225 dimes, and 53 nickels in the vending machine.
Let's denote the number of nickels by N, the number of dimes by D, and the number of quarters by Q.
From the first sentence, we know that:
N + D + Q = 292 (total number of coins)
From the second sentence, we know that:
D = 3(N + Q) (the number of dimes is three times the number of nickels and quarters together)
From the third sentence, we know that:
0.05N + 0.1D + 0.25Q = 29.95 (total value of the coins is $29.95)
Now we can substitute the second equation into the third equation to get:
0.05N + 0.1(3(N + Q)) + 0.25Q = 29.95
0.05N + 0.3N + 0.1Q + 0.25Q = 29.95
0.35N + 0.35Q = 29.95
N + Q = 85
We can now substitute this last equation into the first equation to get:
N + D + Q = 292
N + D + 85 = 292
N + D = 207
We can substitute the second equation into this last equation to get:
N + 3(N + Q) = 207
4N + 3Q = 207
We can now solve the system of equations consisting of the last two equations we derived:
N + Q = 85
4N + 3Q = 207
Multiplying the first equation by 4 and subtracting it from the second equation:
4N + 3Q - 4(N + Q) = 207 - 4*85
-N = -53
N = 53
Substituting this value into the equation N + Q = 85:
53 + Q = 85
Q = 32
Finally, we can use the equation D = 3(N + Q) from earlier to find the value of D:
D = 3(N + Q)
D = 3(53 + 32)
D = 225
Therefore, the vending machine contains 53 nickels, 225 dimes, and 32 quarters.
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PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
Therefore , the solution of the given problem of probability comes out to be z-score from a typical normal distribution.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The formula for the standard error of the mean (SEM), which is as follows:
=> SEM = the standard deviation / √(sample size).
We can enter these numbers into the SEM calculation to determine the SEM given that the standard deviation of the tariff rates is $1200 and the sample size is 400:
=> SEM=$1200/√(400)
=> $1200/20 =$60
It is possible to calculate the z-score for a $80 departure from the mean with a $60 SEM as follows:
=> z = (80 - 0) / $60 = 1.3333
Now that we have the probability corresponding to the z-score of 1.3333,
we can look up the cumulative distribution function (CDF) of the standard normal distribution using a z-table or a statistical calculator.
The CDF depicts the likelihood that a random variable will occur is less than or equal to a certain z-score from a typical normal distribution.
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Find the value of x. Then find the area of the triangle.
Step-by-step explanation:
first of all, remember, the sum of all angles in a triangle is always 180°.
now, we see that both bottom angles are 45°.
that means
180 = 45 + 45 + top-angle
90° = top-angle
aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).
via Pythagoras
c² = a² + b²
where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.
in our case both legs are 7×sqrt(2) units long.
so,
baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =
= 98 + 98 = 196
baseline = sqrt(196) = 14 units
x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.
so, one side of the baseline from x is 14/2 = 7 units.
and now Pythagoras for that sub-triangle :
(7×sqrt(2))² = 7² + x²
98 = 49 + x²
49 = x²
x = sqrt(49) = 7 units
the area of the triangle is
baseline × height / 2
in our case
14 × 7 / 2 = 7×7 = 49 units²
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.
Employee Before After
1 8 7
2 7 3
3 8 2
4 8 4
5 6 5
6 7 10
7 6 4
8 8 9
At the 0.050 significance level, can he conclude that the number of absences has declined?
a. Compute the test statistic.
b. Compute the p-value.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073.
How to solve the question?
To determine whether the fitness program has had a significant effect on reducing employee absenteeism, we need to conduct a hypothesis test.
Null hypothesis: The average number of absences before and after the fitness program are the same.
Alternative hypothesis: The average number of absences after the fitness program is less than before the program.
To test this hypothesis, we can use a one-tailed paired t-test with a significance level of 0.05. We will calculate the difference between the number of absences before and after the program for each employee, and then compute the mean and standard deviation of the differences. The t-test statistic will then be calculated as the mean difference divided by the standard deviation of the differences, multiplied by the square root of the sample size.
Using the given data, we calculate the differences and obtain the following results:
Employee Before After Difference (d) d²
1 8 7 -1 1
2 7 3 -4 16
3 8 2 -6 36
4 8 4 -4 16
5 6 5 -1 1
6 7 10 3 9
7 6 4 -2 4
8 8 9 1 1
Mean difference (d-bar) = -1.25
Standard deviation of differences (s) = 3.27
Sample size (n) = 8
The t-test statistic can now be calculated as:
t = (d-bar / (s / √(n))) = (-1.25 / (3.27 / √(8))) = -1.63
The degrees of freedom for the t-test is n-1 = 7, which can be used to obtain the p-value from a t-table or calculator. Using a one-tailed test with a significance level of 0.05 and 7 degrees of freedom, the critical t-value is -1.895.
Since our calculated t-value (-1.63) is greater than the critical t-value (-1.895), we fail to reject the null hypothesis. In other words, we do not have sufficient evidence to conclude that the fitness program has resulted in a significant reduction in employee absenteeism.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073. Since this p-value is greater than the significance level, we again fail to reject the null hypothesis.
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What is the greatest common factor of the polynomial below?
12x²9x
OA. 4x
OB. 3x
OC. 4x²
OD. 3x²
The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.
How to Find the Greatest Common Factor of a Polynomial?The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.
To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:
12x²9x = 3x(4x)3(3x) = 3x(4x3)
So the GCF of 12x²9x is 3x.
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Drag each value to the correct location on the equation. Not all values will be used. Convert radians to degrees. 4 /9
4[tex]\pi[/tex]/9 radians equals 80 degrees.
How will you convert radians into degrees?To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.
We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.
So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:
[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]
On simplifying we get,
720 / 9 = 80 degrees
As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.
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Complete question:
attach in the image form
Find the area of the circle. Round to the nearest square meter.
A. 63 m2
B. 314 m2
C. 897 m2
D. 1,257 m2
Answer:
B. 314 m²
Step-by-step explanation:
Area of circle = π · r²
r = 10 m
π = 3.14
Let's solve
3.14 x 10² = 314 m²
So, the area of the circle is B. 314 m²
If HI=square root 20, classify this triangle by sides. *
10
6
8
b
6
in
4
3₂2
(4
H
scalene
isosceles
3 4
O equilateral
none
I
5
6
7
G
8 9
10
According to the information provided, HI = 20, the triangle can be categorised by sides that are as follows:
what is a sequence?A collection of numbers or "terms" is called a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.I have a code that tells me where to look for words in a sequence. A collection of objects in a peculiar order is called a sequence (or event) in mathematics. . It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
We need further details regarding the triangle's side lengths in order to identify whether the cylinder is scalene, isosceles, etc equilateral. The cylinder with HI = 20 appears to have no relationship to the sides with lengths values 10, 6, & 8.
Given that the material after "b" contains symbols and numerals that do not make sense together, it can be incomplete or improperly structured. If you would kindly submit a thorough and correctly formatted inquiry, I would be pleased to assist you with sorting the triangle according to its sides or to offer any other information you might require.
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Given the following table of scores, calculate the indicated locator and percentile.
Do not round your results.
Here are the answers to the above questions:
Locator for the 52nd percentile, L52: 6.7252nd percentile, P52: 61.4Percentage of scores above the 52nd percentile: approximately 48%What is the explanation for the above response?To calculate the locator and percentile, we need to first arrange the scores in ascending order:
6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49
a) To calculate the locator for the 52nd percentile, we use the following formula:
Lp = (p/100) * (N + 1)
where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.
For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:
L52 = (52/100) * (13 + 1) = 6.72
Therefore, the locator for the 52nd percentile is 6.72.
b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:
P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50
P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50
P52 = 38 + 0.48 * 50
P52 = 61.4
Therefore, the 52nd percentile is approximately 61.4.
c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:
100 - 52 = 48
Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.
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Which table shows a proportional relationship between x and y?
Responses
x 1 2 3 4
y 4 10 12 16x 1 2 3 4 y 4 10 12 16 ,
x 2.5 3 5 6
y 5 6 10 15x 2.5 3 5 6 y 5 6 10 15 ,
x 7 14 28 35
y 1 2 4 5x 7 14 28 35 y 1 2 4 5 ,
x 1 3 4 7
y 2 5 8 14
(PLS HURRY I NEED TO GET THIS DONE)
(65 POINTS FOR THE RIGHT ANSWER)
The proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
Explain about the proportional relationship:A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.
This implies that the ratio between both always remains the same and that as x increases, y increases, and as x drops, y decreases.The proportional connection equation's graph is a line that passes directly through the origin.From the given options, consider the table:
x 7 14 28 35
y 1 2 4 5
As per proportional relationship.:
y=kx
k = y/x (must be same in all cases)
k = 1/7
k = 14/2 = 1/7
k = 4/28 = 1/7
k = 5/35 = 1/7
As all the k value for the given values of x and y are found equal.
Thus, the proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
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What is the volume of the triangular prism
below?5 cm 3 cm 4 cm 3 cm pls show work
The volume of the triangular prism as shown in the attached image is 30 cm³.
Showing the working for volume of triangular prismTo find the volume of a triangular prism, we need to multiply the area of the triangular base by the height of the prism.
The area of the triangular base can be found using the formula:
Area = (1/2) × base × height
In this case, the base is 5 cm and the height is 4 cm, so the area of the triangular base is:
Area = (1/2) × 5 cm × 4 cm = 10 cm²
The height of the prism is 3 cm.
Therefore, the volume of the triangular prism is:
Volume = Area of triangular base × height
= 10 cm² × 3 cm
= 30 cm³
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15th term of 2, 10, 18, 26, 34
Step-by-step explanation:
a1 = 2
a2 = 10
d = a2 - a1 = 10 - 2 = 8
a15 = a + 14d = 2 + 14(8) = 2 + 112 = 114
Answer:
2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114
Step-by-step explanation:
all you do is add 8 each time
HELP! A paper airplane is thrown from the top of a treehouse. The paper airplane flies 16 feet through the air and lands in a sandbox that is 9 feet from the base of the tree that the treehouse is in.
What is the angle of depression that the paper airplane is flying down at?
Explain your process
The angle of depression that the paper airplane is flying down at 55. 78 degrees
How to determine the valueNote that the different trigonometric identities in mathematics are;
sinetangentcotangentsecantcosecantcosineThese identities also have their ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent//hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Using the cosine identity
Adjacent = 9 feet
Hypotenuse = 16 feet
Substitute the values
cos θ = 9/ 16
divide the values
cos θ = 0. 5625
θ = 55. 78 degrees
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Answer:
55.8° (nearest tenth)
Step-by-step explanation:
The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).
To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.
Substitute these values into the cosine ratio and solve for θ:
[tex]\cos (\theta)=\dfrac{9}{16}[/tex]
[tex]\theta=\cos^{-1}\left(\dfrac{9}{16}\right)[/tex]
[tex]\theta=55.7711336...^{\circ}[/tex]
[tex]\theta=55.8^{\circ}\; \sf (nearest \; tenth)[/tex]
Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).
Write an equation that you can use to solve for x.
Three lines intersect at the same point. Two of the lines intersect at a 90 degree angle. The third line divides one of the right angles into two adjacent angles. One of the adjacent angles is labeled 63 degrees and the other adjacent angle is labeled x degrees
Answer:
Ok so we know it has to equal=180 right?
90+90=180
180/4
45
WRITE THIS IN SYSTEM OF EQUATIONS FROM CONTEX
Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
The system of equations defined is:
x = 2y
x*0.05 + y*0.10 = 1.40
How to write the system of equations?First we need to define the variables:
x = number of nickels
y = number of dimes.
Now we can find the equations, we know that he has twice as many nickels as dimes, then:
x = 2y
We also know that Tristan has $1.40 then we can write:
x*0.05 + y*0.10 = 1.40
So the system of equations is:
x = 2y
x*0.05 + y*0.10 = 1.40
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Does anybody know this? I am a bit confused and please answer it right cause if you don't know it don't bother
The number of different passwords, considering 2 digits and 2 letters, is given as follows:
A. 6,760,000.
B. 3,276,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The password is composed by:
Four digits.Two letters.With repetition, we have that:
Each of the four digits have 10 possible outcomes.Each of the two letters have 26 possible outcomes.Hence the number of passwords is given as follows:
10^4 x 26² = 6,760,000.
Without repetition, we have that:
Digits: 10, 9, 8 and 7 outcomes.Letters: 26 and then 25 outcomes.Hence the number of passwords is given as follows:
10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.
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What inequality matches this graph?
A} x > -5
B} x ≥ -5
C} x < -5
D} x ≥-5
According to the given condition. The inequality that matches this graph is option B) x ≥ -5.
What is an inequality equation?An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
According to the given information:The inequality that matches this graph is option B, "x ≥ -5". The graph represents a solid dot at x = -5 and a shaded region to the right of x = -5, including x = -5. This means that x can take on any value greater than or equal to -5, so the inequality can be written as x ≥ -5.
Therefore, According to the given condition. The inequality that matches this graph is option B) x ≥ -5.
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It is equally probable that the pointer on the spinner
shown will land on any one of the eight regions,
numbered 1 through 8. If the pointer lands on
a borderline, spin again. Find the probability that the
pointer will stop on an even number or a number less
than six
Answer: the answer is 4
Step-by-step explanation: good luck
An amusement park has three roller coasters, the "Falcon Flyer placed at (50, 300), the "Sprinter" placed at (400, 550), and the "Air Rider" placed at (800, 250). All measurements are in meters. You are at a point half way between the "Falcon Flyer" and the "Sprinter", see a long line, and decide to take a shortcut to the "Air Rider". How far will you walk on this shortcut if it follows a straight path? Round your answer to the nearest meter
Answer: 601 meters
Step-by-step explanation:
First, let's find the midpoint between the "Falcon Flyer" and the "Sprinter".
The x-coordinate of the midpoint is (50 + 400)/2 = 225.
The y-coordinate of the midpoint is (300 + 550)/2 = 425.
So the midpoint is (225, 425).
Now we need to find the distance between the midpoint and the "Air Rider". Using the distance formula:
d = sqrt[(800 - 225)^2 + (250 - 425)^2]
d = sqrt[(575)^2 + (-175)^2]
d = sqrt[330625 + 30625]
d = sqrt(361250)
d ≈ 601.041
So the distance you will walk on this shortcut is approximately 601 meters.
What strategy could you use to figure out when Beau is likely to win 500 trophies
Answer:
I would say probability.
calculate the side of a square with a perimeter 84cm
Answer:
441cm^2
Step-by-step explanation:
84 divided by 4 is 21
21cm*21cm is 441cm^2
Hey can you please help me because I don’t understand this question
The area of the shaded region is 88π square inches.
What is the area of the circle?To find the area of the shaded region, we need to subtract the area of the inner circle (with a radius of 9 inches) from the area of the outer circle (with a radius of 13 inches).
The area of a circle is given by the formula A = πr^2, where r is the radius.
Area of outer circle = π * (13²) = 169π square inches
Area of inner circle = π * (9²) = 81π square inches
Area of shaded region = Area of outer circle - Area of inner circle
= 169π - 81π
= 88π square inches
So, the area of the shaded region is 88π square inches.
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See text below
A ring-shaped region is shown below. Its inner radius is 9 in, and its outer radius is 13 in.
9 in
13 in
Find the area of the shaded region.
Use 3.14 for π. Do not round your answer.
2
in2
X
G
Solve 3/8 + n = 7/8
giving away 10 points for this
jalen drew a rectangle with a perimeter of 20 inches. the smaller side measured 3 inches. jalen said the longer side of the rectangle had to be 7 inches. is jalen correct?
Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(3 + 7)
20 = 2(10)
20 = 20 (True).
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Suppose you wish to borrow $400 for five weeks and the amount of interest you must pay is $25 per $100 borrowed. What is the APR at which you are borrowing money?
If we borrowed amount of $400 for 5 weeks, then the APR at which the money is borrowed is 260.71%.
First, we calculate the total interest paid for borrowing $400 for five weeks.
The interest rate is $25 per $100 borrowed, so for $400 borrowed, the interest paid is : $25 × 4 = $100,
So, the total amount that needs to be paid-back is $400 (the original borrowed amount) plus $100 (the interest paid) = $500,
Next, we can use the APR formula to calculate, which is
⇒ APR = (Interest Paid/Amount Borrowed)/(Number of days) × 365 × 100,
In this case, the total interest paid is $100 and the total amount borrowed is $400, and
The number of days amount is borrowed is = 5×7 = 35 days,
Substituting the values,
We get,
⇒ APR = (100/400)/35 ×365 × 100 ≈ 260.71%
Therefore, the APR at which the money is being borrowed is 260.71%.
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1) Find the APR for a $2400, two-year, add-on interest loan, that had a finance charge of $288.
2)) Suppose you have a loan for 4 years, with monthly payments of $185, and an APR of 9.0% (original finance charge of $1426). If you decide to pay it off in 3 years rather than 4 years, find the unearned interest.
3) Find the monthly payment necessary to amortize a $80,000 mortgage at 6% annual interest for 25 years.
1. the APR for this loan is 6%.
2. the unearned interest is $118.83.
3. the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.
How do we calculate?APR = (finance charge / loan amount) / number of years * 100%
In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2
APR = (288 / 2400) / 2 * 100%
APR = 0.06 * 100%
APR = 6%
b.
Number of payments = 4 years * 12 months/year = 48
If the loan is paid off in 3 years instead of 4 years, the number of payments made is:
Number of payments made = 3 years * 12 months/year = 36
Substituting these values into the formula, we get:
Unearned interest = (1426 / 48) * (48 - 36)
Unearned interest = $118.83
3.
To find the monthly payment necessary to amortize a mortgage, we need to use the formula:
M = P * (r / (1 - (1 + r)^(-n)))
where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).
In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):
Monthly interest rate = 6% / 12 = 0.005
To find the total number of payments, we multiply the number of years by 12:
Number of payments = 25 years * 12 months/year = 300
Substituting these values into the formula, we get:
M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))
M ≈ $506.69
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Miss Johnson's guests were to arrive at 6:15 P.M., but because of a bad storm they were 2/5 of an hour late. What time did they arrive for dinner?
the guests arrived for dinner at 6:39 P.M.which is solved by according to given question.
How to solve the question?
To solve this problem, we need to first convert the fraction of an hour that Miss Johnson's guests were late into minutes. We know that 1 hour is equal to 60 minutes, so we can find the number of minutes the guests were late by multiplying 2/5 by 60:
2/5 hour * 60 minutes/hour = 24 minutes
So the guests were 24 minutes late. To find out what time they arrived, we need to add 24 minutes to the original arrival time of 6:15 P.M.:
6:15 P.M. + 24 minutes = 6:39 P.M.
Therefore, the guests arrived for dinner at 6:39 P.M.
It's important to note that fractions can often be confusing when dealing with time calculations. In this case, we converted the fraction of an hour to minutes to make the calculation easier. Additionally, it's always a good idea to double-check your work to ensure that your answer makes sense in the context of the problem.
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