Part A: The monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.
Part B: The monthly amount payable by Victor is $276.17.
What is interest?Interest is defined as the amount of money paid for the use of someone else's money.
Part A:
Given that the amount P is $6500, interest rate R is 13% and time period T is 15 months. The yearly time period is given as,
[tex]T = \dfrac {15}{12}[/tex]
[tex]T = 1.25 \;\rm Years[/tex]
The interest is calculated as given below.
[tex]I = P\times\dfrac {R}{100}\times T[/tex]
[tex]I = 6500 \times \dfrac {13}{100} \times 1.25[/tex]
[tex]I =\$ 1056.25[/tex]
The total amount after 15 months is given as,
A = P + I
A = $6500 + $1056.25
A = $7556.25
This is the amount of 15 months. The amount of one month is calculated as given below.
Monthly Amount = [tex]\dfrac {\$7556.25}{15}[/tex]
Monthly Amount = $503.75
Hence we can conclude that the monthly amount payable by Victoria is $503.75. Option B shows the monthly payment made by Victoria.
Part B:
Given that the amount P is $6800, interest rate R is 13.5% and time period T is 3 years.
The total amount after 3 years is given as,
[tex]A = P (1 + \dfrac {R}{100})^T[/tex]
[tex]A = 6800 (1 + \dfrac {13.5}{100})^3[/tex]
[tex]A = 6800 \times 1.4621[/tex]
[tex]A = \$ 9942.28[/tex]
This is the amount of 3 years or for 36 months. The amount of one month is calculated as given below.
Monthly Amount = [tex]\dfrac {\$9942.28}{36}[/tex]
Monthly Amount = $276.17
Hence we can conclude that the monthly amount payable by Victor is $276.17.
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calculate the area of the lawn covered by an oscillating sprinkler that sprays water in a half circle with a radius of 10ft
Find the sum of the first 30 terms of the sequence. a_(n)=4n+1
bonnie had 6 bags of 6 gel pens. she wanted to give the same number of gel pens to 9 friends. how many gel pens did each friend get?
An American car company has designed a new high fuel efficiency vehicle that is rated at 55 miles per gallon. The company plans to export the car to Europe and must advertise the fuel efficiency in SI units. What is the fuel usage rate in kilometers per liter?
are you able to classify polygons by their sides and angles
Polygons can be classified by their sides and angles using formulas and definitions like regular polygons with equal sides and angles.
Polygons can be classified by their sides and angles. A regular polygon has equal sides and equal angles, such as an equilateral triangle or a square. The sum of interior angles in any polygon can be calculated using the formula 180 * (n - 2) degrees where n is the number of sides.
5(×-4)+3×-9×=6-(2×+5)+8×
ANSWER FAST 20 PTS
What is the measure of T?
ABCD RSTU
125°
110°
100°
60°
Answer:
100
Step-by-step explanation:
Camilla’s class played soccer for 2/3 hour. She played for 3/5 of the game. How much time did Camilla play? A 5/10 hour, B 6/15 hour, C 5/8 hour, D 6/8 hour. Will chose A as the correct answer. How did he get that answer?
Solution:
we are given that
Camilla’s class played soccer for 2/3 hour.
She played for 3/5 of the game.
we have been asked to find
How much time did Camilla play?
Here we are given total time of play for the whole class and camilla played part of that time so we will just multiply the total play time with the fraction of time that camilla played. That will give the actual play time of camilla.
So camila played for [tex]=\frac{2}{3}*\frac{3}{5} =\frac{6}{15}Hr[/tex]
Hence camilla played for 6/15 Hr.
Hence the correct option ois B.
What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?
A.157.95 cubic units
B.351.351 cubic units
C.124.605 cubic units
D.113.49 cubic units
Which is the next term in this pattern ?
January, February, April, July,___
-August
-November
-October
-December
14m+m+17m−9m if m=30
Answer:
690
Step-by-step explanation:
Put 30 where m is in the expression and do the arithmetic. Or, simpify the expression first, then do the same.
14·30 +30 +17·30 -9·30 = 420 +30 +510 -270 = 690
Simplifying first, you have ...
14m +m +17m -9m = m(14 +1 +17 -9) = 23m
23·30 = 690
To solve the equation 14m + m + 17m - 9m when m=30, substitute the value of m in the equation and follow order or operations. The result is 960.
Explanation:To solve for the given problem involving the variable m, simply substitute the value of m into the equation. The equation given is 14m + m + 17m - 9m. Substituting 30 for m in the equation gives us: 14(30) + 30 + 17(30) - 9(30). To solve this, use the order of operations principle, which states that multiplication and division should be performed before addition and subtraction.
First, perform the multiplication: 420 + 30 + 510 - 270. Next, add and subtract from left to right: 960. Thus, if m = 30, then 14m + m + 17m - 9m = 960.
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What is the solution to the system of equations graphed below
Answer:
Option C is correct
(1, 5)
Step-by-step explanation:
A system of equations contains two or more than two linear equations that divide two or more unknowns.
To find a solution for the system of equations,
we must find a value from the graph that is true for all equations in the given system.
We know that:
If the graphs of the equations intersect,
then there is one solution that is true for both equations.
Given the graph.
There are two lines
Equation of Blue line : y = -x+6
Equation of Red line = y = 2x+3
Since, the graph of two lines y = -x+6 and y = 2x+3 intersects which means there is one solution that satisfies the both equation.
Therefore, the solution to the system of equations graphed is, (1, 5)
Noah’s taxable income is $27,156. He is filing as married filing jointly, and he has already paid $3260 in federal taxes. What will he receive or pay after he figures his taxes for the year?
Final answer:
To determine what Noah will receive or pay after figuring his taxes for the year, we need to calculate his tax liability. According to the 2020 tax brackets, a married couple filing jointly with a taxable income of $27,156 falls into the 12% tax bracket. Since Noah has already paid $3,260 in federal taxes, he has overpaid his taxes and will receive a refund of $1.28.
Explanation:
To determine what Noah will receive or pay after figuring his taxes for the year, we need to calculate his tax liability.
First, we need to determine his taxable income after considering his filing status. As he is filing as married filing jointly, we can check the tax brackets for that status.
According to the 2020 tax brackets, a married couple filing jointly with a taxable income of $27,156 falls into the 12% tax bracket. To calculate the tax liability, we multiply the taxable income by the tax rate, which gives us $27,156 * 0.12 = $3,258.72.
Since Noah has already paid $3,260 in federal taxes, he has paid more than his tax liability for the year. In this case, he will receive a tax refund equal to the difference between his tax liability and the amount he has already paid, so the amount he will receive is $3,258.72 - $3,260 = $-1.28.
Therefore, Noah will receive a tax refund of $1.28 after figuring his taxes for the year.
The heights of fully grown English oak (also known as Brown oak) trees are normally distributed with a mean of 95 feet and a standard deviation of 10 feet. What proportion of fully grown English oak trees are taller than 110 feet?
Final answer:
Using the z-score calculation and the standard normal distribution, approximately 6.68% of fully grown English oak trees are taller than 110 feet.
Explanation:
To find the proportion of fully grown English oak trees taller than 110 feet, given that the heights are normally distributed with a mean of 95 feet and a standard deviation of 10 feet, we first calculate the z-score for a height of 110 feet. The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value of interest (110 feet), μ is the mean (95 feet), and σ is the standard deviation (10 feet).
By substituting the given values: z = (110 - 95) / 10 = 1.5. This z-score represents the number of standard deviations 110 feet is above the mean. To find the proportion of trees taller than 110 feet, we consult the standard normal distribution table or use a calculator that provides the area to the right of the z-score, which corresponds to the proportion we seek.
The standard normal distribution table or a calculator shows that the proportion of the area under the curve to the right of a z-score of 1.5 is approximately 0.0668.
Thus, about 6.68% of fully grown English oak trees are taller than 110 feet.
How can I solve this please:
Solve for q: (4q - 6n)/(3m) = f
General Idea:
Solving for a variable means getting that variable by itself by UNDOING whatever is done to it. We need to perform reverse operation to UNDO.
Applying the concept:
[tex] \frac{4q-6n}{3m}=f\\ \\ To \; undo \; 3m\; in\; the \; denominator \; 3m, \; MULTIPLY \; 3m\; on\; both\; sides [/tex]
[tex] 3m \times \frac{4q-6n}{3m}=f \times 3m\\ \\ 4q-6n=3mf\\Add \; 6n \; both\; sides\\ \\ 4q-6n+6n=3mf+6n\\ Combine \; like\; terms\\ \\ 4q=3mf+6n\\Divide \; 4\; on\; both\; sides\\ \\ \frac{4q}{4} =\frac{3mf+6n}{4} \\ Simplify\; fraction\; in\; left\; sides\\ \\ q=\frac{3mf+6n}{4} [/tex]
Conclusion:
[tex] Solving \; the \; equation \; \frac{4q-6n}{3m}=f \; for q, \; we get...\\ \\q=\frac{3mf+6n}{4} [/tex]
Help with this math question
The given inequality is:
|-8x+24| \leq 16
This inequality can be divided in two parts as:
a) -16 \leq -8x +24
b) -8x + 24 \leq 16
Solving part a:
-16 \leq -8x+24 \\ \\ -40 \leq -8x \\ \\ 5 \geq x \\ or \\ x \leq 5
Solving part b:
-8x+24 \leq 16 \\ \\ -8x \leq -8 \\ \\ x \geq 1
Therefore, the solution to the given inequality is x \leq 5 and x \geq 1. Combining both the ranges we get the solution: 1 \leq x \leq 5.
In interval notation, this solution can be expressed as [1,5
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A basketball player makes 40% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 3 shots. let x = the number of shots that he makes. what is the probability that he makes 2 shots or less?
Using the binomial distribution, it is found that there is a 0.936 = 93.6% probability that he makes 2 shots or less.
-------------------
For each throw, there are only two possible outcomes. Either the player makes it, or he misses it. The probability of making a throw is independent of any other throw, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this question:
The player makes 40% of the shots, thus [tex]p = 0.4[/tex]3 shots, thus [tex]n = 3[/tex]The probability of making 2 or less is the probability that he does not make all of them, that is:
[tex]P(X < 3) = 1 - P(X = 3)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.4)^{3}.(0.6)^{0} = 0.064[/tex]
[tex]P(X < 3) = 1 - P(X = 3) = 1 - 0.064 = 0.936[/tex]
0.936 = 93.6% probability that he makes 2 shots or less.
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Evie buys a coat that is marked down by 30% from the original price. After the markdown, the sale price of Evie's coat is $56.00. What was the original price of the coat before the markdown?
A.$72.80
B.$80.00
C.$86.00
D.$95.20
write the equation of the line with the following chracteristics
perpendicular to y=1/2x+3 through (9,1)
Please help and explain questions 20-22
Using fermat's little theorem, find the least positive residue of $2^{1000000}$ modulo 17.
By applying Fermat's Little Theorem, we can find the least positive residue of [tex]2^{1000000[/tex] modulo 17. Using the repeated squaring method, we calculate that [tex]2^{16[/tex] is congruent to 1 modulo 17. Therefore, [tex]2^{1000000[/tex] is also congruent to 1 modulo 17.
Fermat's Little Theorem states that if p is a prime number and a is any positive integer that is not divisible by p, then a raised to the power of p-1 is congruent to 1 modulo p. In this case, we need to find the least positive residue of 2 raised to the power of 1000000 modulo 17.
First, we need to find the value of 2 raised to the power of 16 modulo 17, since 17 is a prime number. Using the repeated squaring method, we can calculate:
[tex]2^2[/tex] = 4 (mod 17)
[tex]2^4[/tex] = [tex](2^2)^2[/tex] = [tex]4^2[/tex] = 16 (mod 17)
[tex]2^8[/tex] = [tex](2^4)^2[/tex] = [tex]16^2[/tex] = 1 (mod 17)
[tex]2^{16[/tex] = [tex](2^8)^2[/tex] = [tex]1^2[/tex] = 1 (mod 17)
Now, we can find the value of [tex]2^{1000000[/tex] modulo 17 using the fact that [tex]2^{16[/tex] is congruent to 1 modulo 17:
[tex]2^{1000000[/tex] = [tex](2^{16})^{62500[/tex] x [tex]2^0[/tex] = [tex]1^{62500[/tex] x 1 = 1 (mod 17)
Therefore, the least positive residue of [tex]2^{1000000[/tex] modulo 17 is 1.
Over the past month, a hairstylist has had 49 female clients and 21 male clients. What is the ratio of male clients to female clients for this hairstylist?
The ratio of male clients to female clients for the hairstylist is 21:49, which simplifies to 3:7 after dividing both numbers by the GCD of 7.
The question asks to find the ratio of male clients to female clients for a hairstylist. In this scenario, the hairstylist has had 49 female clients and 21 male clients. To find the ratio of male to female clients, we compare the number of male clients to the number of female clients.
The ratio is expressed as male clients : female clients. Thus, the ratio of male clients to female clients is:
21 male clients : 49 female clients
To simplify the ratio, we find the greatest common divisor (GCD) of 21 and 49, which is 7. Dividing both numbers by 7, we get:
3 male clients : 7 female clients
What is the area of this triangle? A=bh2
A 24 in²
B 30 in²
C 48 in²
D 96 in²
Answer:
a 24
Step-by-step explanation:
How many elements are in the set {A,B,C}?
Answer:
There are 3 elements in the set.
Step-by-step explanation:
Given set,
{A, B, C}
∵ Set is the collection of defined distinct objects,
These objects are called elements of the set,
We have given a set in which A, B, C are present thus they must be distinct,
So, by the above definition,
The given set has three elements.
If a particular utility burned 5.40 million tons of coal that was 2.00% sulfur by weight, how many tons of sulfur dioxide was emitted?
Luke and Christopher go to the movie theater and purchase refreshments for their friends.
Luke spends a total of $41.00 on 3 drinks and 10 bags of popcorn.
Christopher spends a total of $11.00 on 2 drinks and 2 bags of popcorn.
Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
In a bag of 25 m&ms, each piece is equally likely to be red, green, orange, blue, or brown, independent of the color of any other piece. find the the pmf of r, the number of red pieces. what is the probability a bag has no red m&ms?
To find the probability mass function (pmf) of the number of red M&Ms in a bag, use the binomial distribution formula. The probability a bag has no red M&Ms is calculated by raising (4/5) to the 25th power, as per the binomial distribution with a success probability of 1/5 and 25 trials.
Explanation:The question involves finding the probability mass function (pmf) of the number of red M&Ms in a bag of 25 M&Ms where each M&M has an equal chance of being one of five colors.
To determine the pmf of the number of red M&Ms, which we'll call r, we can use the binomial distribution, since each M&M is an independent Bernoulli trial with two outcomes (red or not red), and each M&M has the same probability of being red.
The probability of getting a red M&M is 1/5, so the pmf of r for k red M&Ms in a bag of 25 is given by P(r=k) = (25 choose k) × (1/5)^k × (4/5)^(25-k).
To find the probability that a bag has no red M&Ms, we set k to 0 in the pmf formula: P(r=0) = (25 choose 0) × (1/5)⁰ × (4/5)²⁵. This simplifies to (4/5)²⁵, since any number to the zero power is 1 and (25 choose 0) is also 1.
Is the figure on the right congruent to the sample figure? Explain.
Write a function rule that gives the total cost c(p) Of p pounds of sugar if each pound costs $.59.
What is the measure of JK?