Evaluate this expression.
3^-2

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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Using technology,  the difference between the arithmetic average ROR and the weighted average ROR is 0.52%

The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values ​​and the number of observations involved in this sum.

Given An investment portfolio

Since arithmetic average ROR:

The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:

ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4

arithmetic average ROR=6.20%

total amount invested=$3200+$1750+$1235+$2,300

total amount invested=$8,485

weighted average:

ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)

weighted average:

ROR=5.68%

difference=6.20%-5.68%

difference=0.52%

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Answer: it’s 1.1%

Step-by-step explanation: just got it right on the test

Answer:

82

Step-by-step explanation:

Answer:

the answer is B) 24.

Step-by-step explanation:

To find the lateral surface area of the triangular prism, we need to find the perimeter of the base and then multiply it by the height of the prism.

Looking at the net, we can see that the base is a triangle with sides of length 3 cm, 4 cm, and 5 cm. So the perimeter of the base is:

3 cm + 4 cm + 5 cm = 12 cm

The height of the prism is given as 2 cm. Therefore, the lateral surface area is:

12 cm x 2 cm = 24 cm²

So the answer is B) 24.

IF THIS HELPED, CAN YOU PLEASE GIVE 5⭐? thank you

Answer:

3.34.

Step-by-step explanation:

4.2 * 0.2 + 2.5

= 0.84 + 2.5

= 3.34.

Answer:

3.34

Step-by-step explanation:

the product is 4.2×0.2=0.84

add is 2.5 + 0.84=3.34

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

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The probablity of rolling a 5 is 1/9.

The probablity of rolling doubles is 1/6.

The probablity that Randa rolles either 5 or doubles on her next turn can be determined as,

Thus, 5/18 is the required solution.

The capacity of the trophy that us 30 cm high is 0.4286 liter

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

7 cm height cup holds 100 ml. Therefore:

7 cm = 100 ml

For a 30 cm height trophy:

30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml

1000 ml = 1 l

428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter

The capacity of the trophy is 0.4286 liter

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Answer:

\(x > 60\)

Step-by-step explanation:

\(x-30 > 30\)
\(x > 60\) (add 30 onto both sides of the inequality)

Answer:

(f - g)(x) = 2x² - 3x - 8

Step-by-step explanation:

Since , (f - g)(x) = f(x) - g(x)

Then

(f - g)(x) = (2x² - 5) - (3x + 3)

            = 2x² - 5 - 3x - 3

            = 2x² - 3x - 5 - 3

            = 2x² - 3x - 8

Answer: A

Step-by-step explanation: c shifts the graph up or down.

Answer:

this answer was 10 times

Answer:

907.5

Step-by-step explanation:

Formula to find the area of a circle: πr²

πr² = 3.14 x 17²

     = 3.14 x 289

     = 907.46

     ≈ 907.5

Hope this helps :)

Answer:B and D

Step-by-step explanation:

Answer: The answer is D: This is not a binomial experiment, because the number of trails is not fixed.

Step-by-step explanation: I took the test and chose the answer A and it was incorrect. The correct answer is D. I took the test on Ap3x.

Hope this helps

Answer:

70.69

Step-by-step explanation:

Area = \(\pi r (r + \sqrt{h^2+r^2} )\)

Area = \(\pi (2.5) (2.5 + \sqrt{(6)^2+(2.5)^2} )\)

Area = 70.68583471

Area = 70.69

Answer:

can someone explain more about the problem

is confusing.

Step-by-step explanation:

The area of largest square is 169.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle.

Given that the two legs of the right triangles are 5 cm and 12 cm.

Then to find the hypotenuse value we can use the Pythagoras theorem,

(hypotenuse)² = (perpendicular)²+ (base)²

(hypotenuse)² = (12)²+ (5)²

(hypotenuse)² = 144+ 25

(hypotenuse)² = 169

(hypotenuse) = 13

Now, right triangle and square share one side that is hypotenuse = 13.

side of square = 13

Area of square is Square of side.

Area of square = (side)²

Area of square = (13)²

Area of square = 169

Therefore the area of largest square is 169.

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The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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(i) one full tanker would be able to supply 5 colonies?

(ii) The tanker supplied 155.51 m³ of water in all

The volume of a cylinder can be calculated using the formula:

V = πr²h

where r and h are the radius and height of the cylinder

Thus, volume of tanker = π * 1² *70 = 70π m³

The volume of a cuboid can be calculated using the formula:

V = Length (L) × Width (W) × Height (W)

volume of cuboidal water tank = 7 * 2 * 3 = 42m³

The volume of sphere can be calculated using the formula:

V = 4/3 πr³

where is the radius of the sphere

r = 42/2 = 21 cm = 0.21 m

volume of spherical clay pots = 4/3 * π * 0.21³ = 0.012348π cm³

(i) Number of colonies = Volume of tanker/Volume of cuboidal tank

Number of colonies = 70π/42 = 5 colonies

(ii) Quantity of water = (3 * Volume of cuboidal tank) + (400 * volume of matkas)

Quantity of water = (3 * 42) + (400 * 0.012348π)

Quantity of water = 126 + 29.51

Quantity of water = 155.51 m³

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Answer:

it's the first one... I think

Answer:

third one

I'm assuming does 2's are squared symbols.

Step-by-step explanation:

It's the third one because

sin^2 x sec^2 x

sin^2 x (1/cos^2 x) by reciprocal identity

sin^2 x/cos^2 x by multiplicative identity prop

tan^2 x by quotient identity

The first one wouldn't work because plugging in pi/4 gives 1+1=1 which isn't true.

The second one doesn't work because plugging in pi/4 gives 2+2=1 which isn't true.

The last equation doesn't make sense at all. There is no variable on the left and on the right there is an extra variable.

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer:

the product of 2a+3b-c and2a+3b-c is(2a+3b-c)²

Answer:

b they are both solution

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

I think it's 27

because length is 3 times its width

Answer:

a<-11

Step-by-step explanation: