At Southside Middle School, 20% of the students play an instrument. There are 305 students. How many students play an instrument ??.
Answers
Answer:
6.557377049 but if simplified put either 6.5 or 6.6
Step-by-step explanation:
20 divided by 305 is 0.065. 0.065 times 100 is 6.5 or 6.6. Hope you pass.
Related Questions
Solve the system of equations 3x = 84 - 2y 9x = 8y - 24
Answers
Answer:
\(3x = 84 - 2y - - - (i) \\ 9x = 8y - 24 - - - - (ii) \\ from \: (ii) \\ 3(3x) = 8y - 24 \\ but \: from \: (i) \: \: 3x = 84 - 2y \\ hence \: put \: (i) \: in \: (ii) \\ 3(84 - 2y) = 8y - 24 \\ 252 - 6y = 8y - 24 \\ 276 = 14y \\ y = \frac{138}{7} \\ x = \frac{104}{7} \)
Consider the surface 1' = 332 + 22 — 10?. Find an equation of the tangent plane to the surface at the point [—T,
8, —fi]_ Find a 1fitter equation of the normal line to the surface at {—T, 8, —E} r[t} =I I.
Answers
The specific values for [-T, 8, -E] and evaluate the gradient vector to get the final equations of the tangent plane and normal line.
To find the equation of the tangent plane to the surface 1' = 332 + 22 — 10? at the point [-T, 8, -E], we can use the gradient vector. The gradient vector is a vector that points in the direction of the steepest slope on the surface at a given point. The equation of the tangent plane can be written as:
1' = f(-T, 8, -E) + ∇f(-T, 8, -E) · (x + T, y - 8, z + E)
where f(-T, 8, -E) is the value of the surface at the point [-T, 8, -E] and ∇f(-T, 8, -E) is the gradient vector at that point.
To find the gradient vector, we need to calculate the partial derivatives of the surface function with respect to x, y, and z, and evaluate them at the given point. Once we have the gradient vector, we can substitute it into the equation of the tangent plane.
For the equation of the normal line to the surface at the point [-T, 8, -E], we can use the parametric form of a line. The parametric equation of a line can be written as:
r(t) = [-T, 8, -E] + t∇f(-T, 8, -E)
where r(t) represents the position vector of a point on the line and t is a parameter.
Remember to plug in the specific values for [-T, 8, -E] and evaluate the gradient vector to get the final equations of the tangent plane and normal line.
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a number is stored in cell a1. write an excel formula that will square this number.
Answers
The value of an excel formula that will square this number is,
⇒ N²
We have to given that;
A number is stored in cell a1.
Hence, We can formulate;
Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.
And, We also get;
To display the square of the value in cell A1 into cell B1,
We can type = A1² into cell B1.
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Solve for all values of x by factoring.
x2 + 10x + 8 = x
Answers
Answer:
x=-1,x=-8 can't factor it
Step-by-step explanation:
Step-by-step explanation:
x = -1 , x = -8
Hope its help u
Derive expressions for the means and variances of the following linear combinations in terms of the means and covariances of the random variables X1, X2, and X3. (a) X1 - 2X2 (b) X1 + 2X2 - 3 (C) 3X1 - 4X2 if X1 and X, are independent (So, 012 = 0).
Answers
Means and Variances of Linear Combinations:
(a) X1 - 2X2
Mean: μa = μ1 - 2μ2
Variance: σa2 = σ12 + 4σ22 + 4σ122
(b) X1 + 2X2 - 3
Mean: μb = μ1 + 2μ2 - 3
Variance: σb2 = σ12 + 4σ22 + 4σ122
(c) 3X1 - 4X2
Mean: μc = 3μ1 - 4μ2
Variance: σc2 = 9σ12 + 16σ22
In the case that X1 and X2 are independent, then σ122 = 0, so:
(a) X1 - 2X2
Mean: μa = μ1 - 2μ2
Variance: σa2 = σ12 + 4σ22
(b) X1 + 2X2 - 3
Mean: μb = μ1 + 2μ2 - 3
Variance: σb2 = σ12 + 4σ22
(c) 3X1 - 4X2
Mean: μc = 3μ1 - 4μ2
Variance: σc2 = 9σ12 + 16σ22
All events are independent. Find the probability in question.
1. P (B) = , P (A and B) = 2 find P (A)
81/2000
2. P (A)=, P (A and B)=, find P (B) =
3/25
3. P (B) = 0.25, P (A and B) = 0.1, find P (A) =
2.5
4. P (A) = 0.3, P (A and B) = 0.075, find P (B) =
=
4
Answers
The probabilities of the independent events are as given as follows:
P (A) = 9/20P (B) = 3/4P (A) = 0.4P (B) = 0.25What are the probabilities?Since all the events are independent events, the probabilities are calculated as follows:
P (B) = 3/10, P (A and B) = 27/200; find P (A)
P (A) = P (A and B) / P (B)
P (A) = (27/200) / (3/10)
P (A) = 9/20
2. P (A)= 2/5, P (A and B)= 3/10, find P (B)
P (B) = (3/10) / (2/5)
P (B) = 3/4
3. P (B) = 0.25, P (A and B) = 0.1, find P (A)
P (A) = 0.1/0.25
P (A) = 0.4
4. P (A) = 0.3, P (A and B) = 0.075, find P (B)
P (B) = 0.075/0.3
P (B) = 0.25
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escribir una funcion cuadratica f cuyos ceros sean -13 y -2 por favor ayudaaa
Answers
Answer:
x²+15x+26
Step-by-step explanation:
zeros are x=-13, x=-2
x=-13 then x+13=0
x=-2 then x+2=0
(x+13) (x+2)
x²+15x+26
y=ax²+bx+c
the census bureau reports that 27% of california residents were born outside the united states. (a) suppose that you randomly choose 4 californians. what is the probability that exactly 1 of the chosen californians were born outside the u.s.?
Answers
The probability that exactly 1 of the chosen Californians were born outside the US when 4 Californians are chosen randomly where 27% of California residents were born outside the united states is 0.42.
This is a case of Binomial distribution where there is 0.27 probability a resident of California were born outside US and 0.73 probability they were born inside the US.
In this case of Binomial distribution, the total number of successful trial(n) is the number of Californian residents chosen that is n = 4. Probability that exactly 1 of the chosen resident is
P = 4C1 × (0.27)¹ × (0.73)⁽⁴⁻¹⁾
= 4!/ ((4-1)! × 1!) × 0.27 × 0.73³
= 4 × 0.27 × 0.389017
= 0.42013836
≈ 0.42
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Find the surface area of the figure below 6m 8m 8m
Answers
Answer:
160
Step-by-step explanation:
Place the decimal point in the quotient. Divide as with whole numbers. Divide until there is no remainder. 32/1 876.80
Answers
Answer:
2190
Step-by-step explanation:
876×80÷32 the working is Uploaded. It was divided without a remainder.
Describe how to simplify the expression . Divide the bases and then add the exponents. Keep the base the same and then add the exponents. Multiply the bases and then subtract the exponents. Keep the base the same and then subtract the exponents.
Answers
Option 4 is the correct option. Keep the base the same and then subtract the exponents. The simplified value of the expression is 3 ^ -2. This can be obtained by using Quotient of Power Property.
Which is the correct option?Quotient of Power Property: To divide powers with same base, subtract the exponents. that is , \(\frac{a^{x}}{a^{y}}=a^{x-y}\)For example: 8^3/8^5 = 8^(3 - 5) = 8^ -2Here in this question it is given that,
⇒ (3^-6)/(3^-4)
By using the Quotient of Power Property, we can find the simplified value of the expression.
Since the bases are equal we can subtract the exponents of the numbers.
Here the common base is 3 and -6 and -4 are the exponents of the numbers.
Now by subtracting the exponents we get,
⇒ (3^-6)/(3^-4)
= 3^ [-6 - (-4)]
= 3 ^ [-6 + 4]
= 3 ^ -2
Hence option 4 is the correct option. Keep the base the same and then subtract the exponents. The simplified value of the expression is 3 ^ -2.
Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Describe how to simplify the expression (3^-6)/(3^-4).
Option 1: Divide the bases and then add the exponents.
Option 2: Keep the base the same and then add the exponents.
Option 3: Multiply the bases and then subtract the exponents.
Option 4: Keep the base the same and then subtract the exponents.
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6) What is the value of x in the figure shown below? (8x) 140° A. 130 C. B. 22.5 D.. 5
Answers
Notice that the angles of 140° and (8x)° are supplementary angles, since they make an angle of 180°. Then:
\(8x+140=180\)Solve for x:
\(\begin{gathered} \Rightarrow8x=180-140 \\ \Rightarrow8x=40 \\ \Rightarrow x=\frac{40}{8} \\ \Rightarrow x=5 \end{gathered}\)Therefore, the value of x is:
\(5\)find the average rate of change for the function over the given interval. f(t) = 4t2 − 5, [3, 3.1]
Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.
left endpoint:
right endpoint:
Answers
We can conclude that the function f(t) is increasing at a varying rate over the interval [3, 3.1], and the average rate of change of 17.9 is a representation of this changing rate over the interval.
We are given the function f(t) = 4t^2 - 5 and the interval [3, 3.1]. We can find the average rate of change of f(t) over this interval using the formula:
average rate of change = [f(3.1) - f(3)] / [3.1 - 3]
First, we calculate f(3) and f(3.1):
f(3) = 4(3)^2 - 5 = 31
f(3.1) = 4(3.1)^2 - 5 = 36.59
Substituting these values into the formula, we get:
average rate of change = [36.59 - 31] / [3.1 - 3] = 17.9
So the average rate of change of f(t) over the interval [3, 3.1] is 17.9.
To compare this average rate of change with the instantaneous rates of change at the endpoints of the interval, we can calculate the derivatives of f(t) at t = 3 and t = 3.1:
f'(t) = 8t
f'(3) = 8(3) = 24
f'(3.1) = 8(3.1) = 24.8
The instantaneous rate of change of f(t) at t = 3 is 24, which is less than the average rate of change over the interval. This means that the function is increasing at a slower rate at t = 3 than it is over the interval [3, 3.1].
The instantaneous rate of change of f(t) at t = 3.1 is 24.8, which is greater than the average rate of change over the interval. This means that the function is increasing at a faster rate at t = 3.1 than it is over the interval [3, 3.1].
Therefore, we can conclude that the function f(t) is increasing at a varying rate over the interval [3, 3.1], and the average rate of change of 17.9 is a representation of this changing rate over the interval.
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a cylinder has a volume of 803.84in cubed what is the height
Answers
Answer:
Divide the volume by the product of the length and width to calculate the height of a rectangular object. For this example, the rectangular object has a length of 20, a width of 10 and a volume of 6,000. The product of 20 and 10 is 200, and 6,000 divided by 200 results in 30. The height of the object is 30.
Step-by-step explanation:
lol i dont know if this is correct
An advertising company is purchasing a new industrial-sized color printer. The company has been approved for a $75,000 loan at two different
banks. The terms of each loan are:
Offer 1: 4.99% annual simple interest, with a total account balance of $91,529.38 after a 53-month term
Offer 2: 3.5% annual interest compounded monthly for a 62-month term
Assuming no payments are made, what is the difference in the account balances at the end of the loan terms. Round your answer to the nearest
penny.
O $1,624.49
$1,686.87
$1,894.02
O $2,207.67
Answers
The difference in the account balances at the end of the loan terms is given as follows:
$1,686.87.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the offer 2 are given as follows:
P = 75000, r = 0.035, n = 12, t = 62/12.
Hence the balance of the offer 2 is given as follows:
B = 75000 x (1 + 0.035/12)^(12 x 62/12)
B = $89,842.51.
The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:
91529.38 - 89842.51 = $1,686.87.
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Exercises 15 and 16 concern arbitrary matrices A, B, and C for which the indicated sums and products are defined. Mark each statement True or False. Justify each answer.15. a. If A and B are 2 x 2 with columns ay.az, and bI, ba. respectively, then AB = a,b ab].b. Each column ofAB is a linear combination of the columns of B using weights from the corresponding column of A.c. AB+ AC = A(B+C)d. AT + BT = (A + B)"c. The transpose of a product of matrices equals the product of their transposes in the same order.
Answers
a. True. The product of two 2 x 2 matrices A and B is given by the formula AB = [a1*b1 + a2*b3, a1*b2 + a2*b4; a3*b1 + a4*b3, a3*b2 + a4*b4], where a1, a2, a3, and a4 are the elements of A and b1, b2, b3, and b4 are the elements of B.
In this case, the columns of A are ay and az, and the columns of B are bI and ba. So, the product AB is given by [ay*bI + az*ba, ay*ba + az*bb], which is equivalent to [a,b ab].
b. True. Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A. This is because the elements of each column of AB are obtained by multiplying the elements of the corresponding column of A with the elements of the corresponding row of B and summing the products.
c. True. The sum of two matrices is obtained by adding the corresponding elements of the matrices.
So, AB+ AC = [a1*b1 + a2*b3 + a1*c1 + a2*c3, a1*b2 + a2*b4 + a1*c2 + a2*c4; a3*b1 + a4*b3 + a3*c1 + a4*c3, a3*b2 + a4*b4 + a3*c2 + a4*c4] = [a1*(b1+c1) + a2*(b3+c3), a1*(b2+c2) + a2*(b4+c4); a3*(b1+c1) + a4*(b3+c3), a3*(b2+c2) + a4*(b4+c4)] = A(B+C).
d. True. The transpose of a matrix is obtained by flipping the matrix along its main diagonal. So, AT + BT = [a1, a3; a2, a4] + [b1, b3; b2, b4] = [a1+b1, a3+b3; a2+b2, a4+b4] = (A + B)T.
e. False. The transpose of a product of matrices equals the product of their transposes in the reverse order. So, if A and B are two matrices, then (AB)T = BT*AT.
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4÷2=
12÷2=
6÷3=
45÷9 =
Answers
Answer:
4÷2=2
12÷2=6
6÷3=3
45÷9 =5
Step-by-step explanation:
problem solving an archeologist finds part of a circular plate. what was the diameter of the plate to the nearest tenth of an inch?a part of a circular plate is drawn. two chords of length 7 inches each are bisected perpendicularly by two segments passing through the center. the length of each segment is 6 inches.
Answers
The diameter of the circular plate is 16.3 inches (rounded to the nearest tenth of an inch).
The given figure can be visualized as a circle with two perpendicular chords of length 7 inches each.
The chords are bisected perpendicularly by two segments passing through the center, each of length 6 inches.
Now, we have to find the diameter of the circular plate.
To find the diameter, we have to draw a perpendicular line to the center from one of the endpoints of a chord.
This will give us a right triangle with one side as 3 inches (half of the length of the chord) and the hypotenuse as the radius of the circle.
Using Pythagoras theorem, we get:
r² = 3² + 6² = 45r = √45 = 3√5 inches
Since the radius is 3√5 inches, the diameter is 6√5 inches.
To get the value of the diameter to the nearest tenth of an inch, we substitute 3.16 for √5.
Therefore, the diameter of the circular plate is:
Diameter = 6(3.16) = 18.96 inches ≈ 16.3 inches (rounded to the nearest tenth of an inch).
Thus, the diameter of the circular plate is 16.3 inches (rounded to the nearest tenth of an inch).
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Can someone help me with this
Answers
The quantity of possible outcomes is known as probability.All events that could possibly occur.
What are examples and probability? The quantity of possible outcomes is known as probability.All events that could possibly occur.For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail).P(heads) = 12 is the formula.Three main categories of probability are as follows:Possibility theory.Probabilistic experimentation.Probability based on axioms.There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.To learn more about probability refer
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The drama club is selling tickets to their play to raise money for the ticket sells for $9. The auditorium can hold no more than 110 people. The drama club must make a minimum of $720 from show's expenses. Each student ticket sells for $4 and each adult ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine two possible solutions.
Answers
A system of inequalities to model this situation is 4x + 9y ≥ 720 and x + y ≤ 110.
The two possible solutions are (80, 40) and (100, 20).
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the number of student tickets sold and the number of adult tickets sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent number of student tickets sold.Let the variable y represent number of adult tickets sold.Since each student ticket was sold for $4 and each adult ticket sales to cover the show's costs sells for $9 in order to make a minimum of $720 from show's expenses, a linear equation which can be used to model the situation is given by;
4x + 9y ≥ 720
Additionally, the auditorium can hold no more than 110 people;
x + y ≤ 110
Next, we would use an online graphing calculator to plot the above system of linear equations in order to determine its solution as shown in the graph attached below.
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What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
A.
y = 3x + 4
B.
y = 3x − 14
C.
y = 3x − 4
D.
y = 3x + 12
Answers
Answer:
A. y = 3x + 4
Step-by-step explanation:
got it correct!
Jocelyn owns a small business selling used books. She knows that in the last week 51
customers paid cash, 63 customers used a debit card, and 25 customers used a credit
card.
Based on these results, express the probability that the next customer will pay with
cash or a debit card as a percent to the nearest whole number?
Answers
Answer:
82%
Step-by-step explanation:
Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a "slow" time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?
Answers
The indicated critical value, z0.05, can be found by referring to a standard normal distribution table.
In statistics, critical values are used in hypothesis testing and confidence interval calculations. They represent the threshold beyond which a test statistic or interval estimate would be considered statistically significant.
To find the indicated critical value, z0.05, we need to refer to a standard normal distribution table or use a statistical software. The value z0.05 corresponds to the point on the standard normal distribution that accumulates 5% of the total area to the left of it. In other words, it represents the value for which the cumulative probability is 0.05.
By consulting a standard normal distribution table or using a statistical software, we can find that the value of z0.05 is approximately -1.645 (rounded to three decimal places). This means that 5% of the area under the standard normal curve lies to the left of -1.645.
Therefore, the indicated critical value, z0.05, is approximately -1.645.
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Line ET is tangent to circle A at T, and the measure of arc TG is 46. What is the measure ofO 136O 44O 90OO 67
Answers
Line ET is tangent to circle A at T, and the measure of arc TG is 46 and the measure of O is 67°.
Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent crosses it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line. A line that touches a circle just once is said to be tangent to it. A point tangent to circle can only have one tangent. The intersection of the tangent and the circle is known as the point of tangency.
Now, \(\angle {TEG} =\)180-90-23=67°
as line TE is tangent to circle and it is perpendicular to line NT.
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Important help asap.
Answers
Answer: y = 5x
Step-by-step explanation:
(check to make sure it matches the graph)
y = 5(0) = 0
y = 5(2) = 10
y = 5(4) = 20
y = 5(6) = 30
y = 5(20) = 100 dollars
Use the scenario below to ansuer questions 9-11. Raymond purchased a new tractor for his wheat farm. He estimates that the tractor will depreciate in value by about 8.5% per year as shown in the table below. AGE OF TRACTOR IN YEARS X o 1 VALUE OF TRACTOR (U.S. DOLLARS) f(x) 165,000 151,000 138,140 126,400 115,660 105,830 9. 2 What will be the estimated value of the tractor when it is 6 years old? 6 3 4 5 200000 У 180000 10. The graph shows the function f(x) = 165000(0.915) where f(x) is the value of Raymond's tractor after x years. What does poini (10, 67873) represent in the situation? 160000 165,000(0.915) 140000 120000 100000 Value of Teactor (collars) 800001 (10.87873) 60000 11. Using the function equation and a graphing utility, in how many years will the tractor be worth less than $50,000? 40000 20000 0 0 -2 2 16. 12 14 after 13 years 8 10 Time (years) -20000
Answers
Given:
\(f(x)=165000(0.915)^x\)Find-: what does point (10,67873) represent.
Sol:
\(f(x)=165000(0.915)^x\)Where,
\(\begin{gathered} f(x)=\text{ The value of random tractor } \\ \\ x=\text{ year} \end{gathered}\)At point.
\((10,67873)\)Point (10, 67873) represents after the 10-year value of the random tractor is 67873.
Check value for x = 10 year.
\(\begin{gathered} f(x)=165000(0.915)^x \\ \\ f(10)=165000(0.915)^{10} \\ \\ f(10)=67873 \end{gathered}\)Find the value of h(-67) for the function below.
h(x) = -49x − 125
A.
-3,408
B.
3,158
C.
3,283
D.
-1.18
Answers
Answer:
B. 3,158
Step-by-step explanation:
h(x) = -49x − 125
Let x = -67
h(-67) = -49(-67) − 125
=3283-125
= 3158
Answer:
Answer B
Step-by-step explanation:
To find the value of h(-67) for the function h(x) = -49x - 125,
we substitute -67 for x in the function and evaluate it.
h ( - 67 ) = - 49 ( - 67 ) - 125
Now we can simplify the expression:
h ( -67 ) = 3283 - 125
h ( -67 ) = 3158
+2 ( 4n - 1 ) + ( 3a - 5) =
20 POINTS!!
Answers
Step-by-step explanation:
I see I did the question yesterday and I thought I wrote it down in my love my note but honestly I didn't so you may have to download app called mathematics or something like that they just automatically tell you the Answer sorry I couldn't help
3a + 8n−7
12. A helicopter is equipped with cameras to monitor forest fires. The figure below
represents a moment in time at which the helicopter is flying at an altitude of 850
meters directly above the forest floor. At that moment, the angle of depression from
helicopter to the fire is 25°. (note that the figure is not drawn to scale)
25
850 m
What is the distance from the helicopter to the fire? Round the answer to the
nearest tenth of a meter.
O 2011.3 m
0937.9 m
O 770.4 m
O 359.2 m
Answers
Answer: 937.9
Step-by-step explanation: 850/cos(25)=937.9
Find the effective rate of interest corresponding to a nominal rate of 3.5% per year compounded annually, semiannually, quarterly and monthly. (Round your answers to two decimal places.) (a) annually (b) semiannually (c) quarterly (d) monthly
Answers
The effective rates of interest corresponding to a nominal rate of 3.5% per year compounded annually, semiannually, quarterly, and monthly are (a) Annually: 3.50%, (b) Semiannually: 3.52%, (c) Quarterly: 3.52%, (d) Monthly: 3.53%
To find the effective rate of interest corresponding to a nominal rate compounded at different intervals, we can use the formula:
Effective Rate = (1 + (Nominal Rate / m))^m - 1
where:
Effective Rate is the rate of interest earned or charged over a specific time period.
Nominal Rate is the stated interest rate.
m is the number of compounding periods per year.
(a) Annually:
For compounding annually, the effective rate can be calculated as:
Effective Rate = (1 + (0.035 / 1))^1 - 1 = 0.035 = 3.50%
(b) Semiannually:
For compounding semiannually, the effective rate can be calculated as:
Effective Rate = (1 + (0.035 / 2))^2 - 1 = 0.035175 = 3.52%
(c) Quarterly:
For compounding quarterly, the effective rate can be calculated as:
Effective Rate = (1 + (0.035 / 4))^4 - 1 = 0.035235 = 3.52%
(d) Monthly:
For compounding monthly, the effective rate can be calculated as:
Effective Rate = (1 + (0.035 / 12))^12 - 1 = 0.035310 = 3.53%
Therefore, the effective rates of interest corresponding to a nominal rate of 3.5% per year compounded annually, semiannually, quarterly, and monthly are as follows:
(a) Annually: 3.50%
(b) Semiannually: 3.52%
(c) Quarterly: 3.52%
(d) Monthly: 3.53%
These effective rates reflect the actual interest earned or charged over a specific time period, taking into account the compounding frequency. It is important to note that as the compounding frequency increases, the effective rate will approach the nominal rate.
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