Translate the following into an expression m% of n

The amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

The amount to which $800 will grow under each of these conditions is as follows:a) 8% compounded annually for 9 years

When compounded annually for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years

Compounded annually = n = 1 Amount = $1,447.91 (rounded to the nearest cent)

b) 8% compounded semiannually for 9 years Compounded semiannually for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded semiannually = n = 2 Amount = $1,471.16 (rounded to the nearest cent)

c)  8% compounded quarterly for 9 years Compounded quarterly for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded quarterly = n = 4 Amount = $1,491.03 (rounded to the nearest cent)

d) 8% compounded monthly for 9 years Compounded monthly for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded monthly = n = 12 Amount = $1,505.91 (rounded to the nearest cent)

e) 8% compounded daily for 9 years Compounded daily for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded daily = n = 365Amount = $1,511.74 (rounded to the nearest cent)

The observed pattern of FVs (future values) occurs due to compounding. Compounding is the process of earning interest not only on the principal amount invested but also on the interest earned from the principal. This results in an increase in the interest earned and the future value of the investment. The more frequent the compounding, the higher the future value of the investment. Hence, the amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

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The expressions (3√-5 + 2)(4√-12 - 1) and (4i - 3)² have values of -24√5 - 2 + 16i√3 - 3i√5 and  -7 - 24i respectively.

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

In the first expression;

(3√-5 + 2)(4√-12 - 1) will give us -24√5 - 2 + 16i√3 - 3i√5

In the second expression, we have (4i - 3)² which will give us -7 - 24i

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The amount you will have saved after 4 years with a monthly savings is B. $15,587.88.

To calculate the amount you will have saved after 4 years with a monthly savings of $300 and an annual interest rate of 4% APR, we can use the formula for compound interest.

First, we need to convert the APR to a monthly interest rate by dividing it by 12. So the monthly interest rate is (4% / 12) = 0.3333%.

Next, we calculate the future value of the savings using the formula:

Future Value = P(1 + r)^n - 1 / r

where P is the monthly savings amount, r is the monthly interest rate, and n is the number of months.

Plugging in the values:

Future Value = 300(1 + 0.003333)^48 - 1 / 0.003333

Calculating this expression, we get approximately $15,587.88.

Therefore, The correct answer is B. $15,587.88.

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Answer: The sum of 58.887 + 92.234 is 151.121

Step-by-step explanation:

In this kind of decimal number, the summation can be done by adding numbers from the right-hand side. For example, we have two numbers, one is 58.887 and the other is 92.234. In these numbers, the right-hand side of both numbers is 7 and 4. Respectively, we have to add them up.

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Answer:

10^12

Step-by-step explanation:

Answer:

it should be 251, if i did it correct lol

Step-by-step explanation:

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Moon Software Inc. must issue approximately 3,927 OID bonds to raise $3,000,000.

The par bonds have a coupon rate of 10% and a par value of $1,000. To raise $3,000,000, Moon Software Inc. needs to issue 3,000 par bonds since $3,000,000 divided by $1,000 equals 3,000.

The OID bonds have a semiannual coupon rate of 7.75% and a par value of $1,000. Since these bonds need to provide investors with the same effective yield as the par bonds, they must be offered at a discount. To calculate the number of OID bonds required, we need to determine the discount needed to match the effective yield of the par bonds.

The effective yield of the par bonds is 10%. The OID bonds have a coupon rate of 7.75%, so the discount needed to match the effective yield is 10% - 7.75% = 2.25%.

To raise $3,000,000 with OID bonds, we divide the amount by the discount rate: $3,000,000 / 2.25% = $133,333,333.33.

Since each OID bond has a par value of $1,000, we divide the total amount by $1,000: $133,333,333.33 / $1,000 = approximately 133,333.33 bonds.

Since we need a whole number of bonds, we round up to the nearest whole number, which gives us 133,334 bonds.

Therefore, Moon Software Inc. must issue approximately 133,334 OID bonds to raise $3,000,000.

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Answer:

subtracting 1 from 3 is the correct answer of this question

The first step in simplifying the expression is subtracting 1 from 3.

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Step 1:

12 = [ (3 – 1) + 4] x 6  [ subtracting 1 from 3 ]

Step 2:

12 = [ 2 + 4 ] x 6 [ adding 2 and 4 ]

Step 3:

12 = 6 x 6 [ multiplying 6 and 6 ]

Step 3:

12 = 12

Thus,

The first step is subtracting 1 from 3.

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To find the percent of the total area under the standard normal curve between the z-scores of 0.65 and 1.4, we need to calculate the area between these two values.

Using a standard normal distribution table or a calculator, we can find the area corresponding to z = 0.65 and z = 1.4. Subtracting the smaller area from the larger area will give us the area between the two z-scores.

By subtracting the area corresponding to z = 0.65 from the area corresponding to z = 1.4, we find that the percent of the total area between z = 0.65 and z = 1.4 is approximately 24%. (Round to the nearest integer.)

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Answer:

10 \(\geq\) s*0.25 + a*0.75

Step-by-step explanation:

Assign variable for each game

s = number of Skeeball games

a = number of Air hockey games

Then write out what you know...

1. Total cost of Skeeball = s*0.25

2. Total cost of Air hockey = a*(3*0.25) -> a*0.75

So the inequality would be...

10 \(\geq\) s*0.25 + a*0.75

Answer:

complementary angles are sum up to 180°

68.8+x=180°

68.8 complementary angle is 111.2

Answer:

Step-by-step explanation:

The gradient is the same term as the slope.

We have the line with the slope of 4 and passing through the point (3, 7).

Use the point - slope form and substitute the coordinates to get:

Answer:

I can answer the type of angle: Acute

Step-by-step explanation:

It's less than 90 degrees, so it's \(acute.\)

Answer: D

Step-by-step explanation:

Quotient means division

The vertex form of the function is f(x) = -2(x-4)^2 + 2

The standard vertex form of a function is expressed according to the expression;

f(x) = a(x-h)^2+k

where

a is a constant = -2

(h, k) is the vertex = (4, 2)

Substitute

f(x) = -2(x-4))^2+2

f(x) = -2(x-4)^2 + 2

Hence the vertex form of the function is f(x) = -2(x-4)^2 + 2

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Answer:

Dan would have 9 jellybeans.

Step-by-step explanation:

Since Jane has 4 more, all we have to do is subtract 4 from 13 to get the answer, 9.

The area of the parallelogram is not 9 square centimeters because a parallelogram not always a square.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The area of parallelogram is 9 square centimeters.

Now,

We know that;

A parallelogram not always a square.

And, The area of parallelogram is 9 square centimeters is possible when the parallelogram is a square.

Thus, The area of the parallelogram is not 9 square centimeters because a parallelogram not always a square.

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Answer:

\(y = 10 \times - 1 = \)

\( \times - 1 = - 10\)

y=

\( - 10\)

Yes, this is true.

A normal distribution with a mean of 0 and a standard deviation of 1 is often denoted as N(0, 1) or n(0, 1). This distribution is also known as the standard normal distribution. It is a symmetric bell-shaped distribution where the majority of the data falls within approximately three standard deviations from the mean.

The standard normal distribution, denoted as N(0, 1) or n(0, 1), is a specific type of normal distribution that has a mean of 0 and a standard deviation of 1. It is often used as a benchmark for comparing and standardizing data in statistical analysis.

The shape of the standard normal distribution is symmetric and bell-shaped. It follows the familiar "bell curve" pattern, where the data is concentrated around the mean and gradually tails off towards the extremes. The total area under the curve is equal to 1, representing the entire probability space.

The standard deviation of 1 indicates the spread or variability of the data. In a standard normal distribution, about 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations.

The standard normal distribution is widely used in statistical calculations and hypothesis testing. It serves as a reference distribution for many statistical methods, such as z-tests and z-scores. By converting data from other normal distributions into standard units using z-scores, researchers can compare and analyze data from different distributions on a common scale.

The standard normal distribution also has specific properties that make it mathematically tractable. The cumulative distribution function (CDF) of the standard normal distribution, often denoted as Φ(z), gives the probability that a standard normal random variable is less than or equal to a given value z. This CDF is tabulated in standard statistical tables or can be calculated using mathematical functions.

Overall, the standard normal distribution is a fundamental concept in statistics, providing a reference distribution for comparing and analyzing data and serving as a basis for many statistical techniques and calculations.

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Answer:

127°

Step-by-step explanation:

I remember a teacher gave me a solution to solve these types of questions.

choose only one corner and draw lines from that Corner to the rest of the corners to form triangles.

for example, in this question, I choose 120°. 1 line to 125°, 1 to 133°, one to 112°. you can't draw any straight lines to the rest of the corners.

now you have 4 triangles. and the sum of the angles of each triangle, is 180°. so, the sum of the angles of this Irregular hexagon is 4×180=720°.

now:

112+133+120+100+128+x=720

593+x=720

x=720-593

x=127°

i know it seems a little complicated, but if you read it carefully, you'll probably understand.if anything is unclear, ask freely.

The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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There are polynomials that satisfy the condition p = p^2, and W is not empty. Hence, statement D is correct answer,

To analyze the set W, which consists of all 1st degree polynomials (or less) such that p = p^2, we will consider each statement and determine its validity.

Statement A: W is closed under scalar multiplication.

For a set to be closed under scalar multiplication, multiplying any element of the set by a scalar should result in another element of the set. In this case, let's consider a polynomial p = ax + b, where a and b are constants.

To test the closure under scalar multiplication, we need to multiply p by a scalar k:

kp = k(ax + b) = kax + kb

Notice that kp is still a 1st degree polynomial (or less) because the highest power of x in the resulting polynomial is 1. Therefore, W is closed under scalar multiplication. This makes statement A true.

Statement B: W doesn't contain the zero vector.

The zero vector in this case would be the polynomial p = 0. However, if we substitute p = 0 into the equation p = p^2, we get:

0 = 0^2

This equation is true for all values of x, indicating that the zero vector (p = 0) satisfies the condition p = p^2. Therefore, W does contain the zero vector. Hence, statement B is false.

Statement C: W is NOT closed under addition.

For a set to be closed under addition, the sum of any two elements in the set should also be an element of the set. In this case, let's consider two polynomials p1 = a1x + b1 and p2 = a2x + b2, where a1, a2, b1, and b2 are constants.

If we add p1 and p2:

p1 + p2 = (a1x + b1) + (a2x + b2) = (a1 + a2)x + (b1 + b2)

The resulting polynomial is still a 1st degree polynomial (or less) because the highest power of x in the sum is 1. Therefore, W is closed under addition. Thus, statement C is false.

Statement D: W is empty.

To determine if W is empty, we need to find if there are any polynomials that satisfy the condition p = p^2.

Let's consider a general 1st degree polynomial p = ax + b:

p = ax + b

p^2 = (ax + b)^2 = a^2x^2 + 2abx + b^2

To satisfy the condition p = p^2, we need to equate the coefficients of corresponding powers of x:

a = a^2

2ab = 0

b = b^2

From the first equation, we have two possible solutions: a = 0 or a = 1.

If a = 0, then b can be any real number, and we have polynomials of the form p = b. These polynomials satisfy the condition p = p^2.

If a = 1, then we have the polynomial p = x + b. Substituting this into the equation p = p^2:

x + b = (x + b)^2

x + b = x^2 + 2bx + b^2

Equating the coefficients, we get:

1 = 1

2b = 0

b = b^2

The first equation is true for all x, and the second equation gives us b = 0 or b = 1.

Therefore, there are polynomials that satisfy the condition p = p^2, and W is not empty. Hence, statement D is correct option.

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Answer:

nah i said D first

\

Step-by-step explanation:

The no. of ways in which the doctor visits her patients during morning rounds = 5!

That means we can only find the number of ways if we n+1 factorial the number of rounds. In this case, the factorial is 1x2x3x4x5= 120

The product of all positive integers less than or equal to n in mathematics is known as the factorial of a non-negative integer, indicated by the symbol n! Additionally, the factorial of n is equal to the sum of n and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

In addition to highlighting the connections between variables, it also enables the isolation and individual analysis of the impacts of changing a single variable. The primary drawback is how challenging it is to explore with more than two parameters or several levels.

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Digby Corporation's retained earnings for the midyear on July 31st were $15.959 million.

The retained earnings refer to the portion of the company's accumulated profits that have not been distributed to common stockholders.

We can compute the retained earnings are the difference between the total assets and total liabilities and common stock since common stock plus retained earnings are equal to stockholders' equity.

Digby Corporation

Midyear ended July 31st

Cash of $2.010 million

Total Assets = $43.091 million

Total Liabilities of $25.862 million

Total Common Stock of $1.270 million

Total liabilities and common stock = $27.132 million ($25.862 + $1.270)

Total Assets = $43.091 million

Less total liabilities and common stock $27.132 million

Retained earnings = $15.959 million ($43.091 - $27.132)

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Answer:

The answer is 6 (:

Step-by-step explanation:

88-4=84

8+6=14

84 divied by 14= 6

hope this helps! <3

Answer:

work = force × distance

Therefore,

work = 3200N × 16m

= 51200J

So,

Power = Work done/ time taken

Therefore,

Power = 51200/30

= 1706.6 ~ 1707W

Hope it helps!

There were 870 downloads of the standard version and 220 downloads of the high-quality version.

Let's denote the number of downloads of the standard version as 'x' and the number of downloads of the high-quality version as 'y'.

From the given information, we know that the size of the standard version is 2.8 megabytes (mb) and the size of the high-quality version is 4.9 mb.

We also know that yesterday there were a total of 1090 downloads of the song, resulting in a total download size of 3514 mb.

Based on the given information, we can set up a system of equations:

Equation 1: x + y = 1090 (since the total number of downloads is 1090)

Equation 2: 2.8x + 4.9y = 3514 (since the total download size is 3514 mb)

To solve this system of equations, we can use any method such as substitution or elimination.

Let's use the substitution method:

From Equation 1, we can express x in terms of y:

x = 1090 - y

Substituting this value of x into Equation 2, we have:

2.8(1090 - y) + 4.9y = 3514

Expanding the equation:

3052 - 2.8y + 4.9y = 3514

Combining like terms:

2.1y = 462

Dividing both sides by 2.1:

y = 220

Now we have the number of downloads of the high-quality version (y). To find the number of downloads of the standard version (x), we can substitute the value of y back into Equation 1:

x + 220 = 1090

x = 1090 - 220

x = 870

Therefore, there were 870 downloads of the standard version and 220 downloads of the high-quality version.

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