In the formula


A(t) = Pert for continuously compound interest, the letters P, r, and t stand for ---Select--- percent interest prime rate amount after t years principal number of years , ---Select--- interest rate per year rate of return investment amount investment per year interest rate per day , and ---Select--- number of months number of days number of time periods number of years number of times interest is compounded per year , respectively, and A(t) stands for ---Select--- amount of principal amount after t days amount of interest earned after t years amount of interest earned in year t amount after t years. So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $. (Round your answer to the nearest cent. )

Answers

Answer 1

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for Principal, rate of interest, and time respectively, and A(t) stands for Amount after t amount of time.  If $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $225.5.

The formula for Compound Interest at a continuous period of time is denoted by [tex]A(t) = Pe^{rt}[/tex]

where the Principal amount is multiplied by the exponential value of the interest rate and time passed.

Hence we are given here

P = $200, r = 4% = 0.04, and the amount to be calculated for t = 3 years

Hence we will find the amount by replacing these values to get

A(3) = 200 × e⁰°⁰⁴ ˣ ³

= $200 × e⁰°¹²

= $225.499

rounding it off to the nearest cent gives us

$225.5

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Correct Question

In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for ______ , _______ , and __________ respectively, and A(t) stands for _______ .

So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $__________. (Round your answer to the nearest cent.)


Related Questions

Zachary says that the equation 0 = (x – 4)(x – c) has one unique real number solution. What must be the value of c for his statement to be true?

c = 4

Answers

Answer:

c=4

Step-by-step explanation:

as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0

8 pound of peanuts cost 24 dollars. 6 pounds of walnuts cost half as much. Which is more expensive and by how much.

Answers

Answer:

Step-by-step explanation:

The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:

Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound

The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):

Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound

Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).

In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.

[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]

Answers

The value of the fraction is 3/-2

What is a fraction?

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractions

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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10-2 skills practice simplifying radical expressions square root of 5 over 3

Answers

Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

Let AX = B be a consistent linear system with 12 equations and 8 variables. If the solution of the system contains 3 free variables, then what is the rank of the coefficient matrix A?

Answers

The rank of the coefficient matrix A is 5.

How to determined the matrix?

Since the system AX = B is consistent and has 12 equations and 8 variables, the rank of the coefficient matrix A must be less than or equal to 8 (the number of variables).

If the solution of the system contains 3 free variables, it means that the dimension of the null-space of A is 3. By the rank-nullity theorem,

we know that the dimension of the null-space of A plus the rank of A is equal to the number of columns of A (which is 8 in this case).

Therefore, we have:

rank(A) + dim(null(A)) = 8

rank(A) + 3 = 8

rank(A) = 5

So, the rank of the coefficient matrix A is 5.

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A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 112 seconds at a speed of 0.8 feet per second.
She then travels directly up for 120 seconds at a speed of 0.6 feet per second.

After this 232-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.5 feet per second? If necessary, round your answer to the nearest tenth of a second.

Answers

The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.

How to calculate the amount of time

To calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.

1. 112 seconds × 0.8 feet per second = 89.6 feet

2. 120 seconds × 0.6 feet per second = 72 feet

The distance from sea level is now: 89.6 feet - 72 feet

= 17.6 feet

The time, in seconds, that it will  take for the scientist to travel back to sea level at 3.5 feet per second will be:

17.6 feet ÷  3.5 feet per second

5.0 seconds to the nearest tenth.

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If KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, what is the scale factor of figure KLMN to figure PQRS?

Answers

The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.

To find the scale factor of figure KLMN to figure PQRS, given KN = 3 cm, MN = 7 cm, RS = 14 cm, and PS = 6 cm, follow these steps:

1. First, find the length of a side in figure KLMN. We can use KN since it's given: KN = 3 cm.
2. Next, find the corresponding side length in figure PQRS. Since KN corresponds to PS, we have: PS = 6 cm.
3. Now, find the scale factor by dividing the length of the side in figure PQRS by the length of the corresponding side in figure KLMN: scale factor = PS/KN = 6 cm / 3 cm.

The scale factor of figure KLMN to figure PQRS is 6 cm / 3 cm = 2.

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Jen is filling bags with M&Ms. She has 5 1/2 cups of M&Ms. She needs 1 1/4 cups of M&Ms to fill each bag. How many bags can Jen fill completely?

Answers

Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.

First, we need to find the total number of cups of M&Ms Jen has

5 1/2 cups = 11/2 cups

Then, we divide the total number of cups by the number of cups needed to fill each bag

(11/2 cups) ÷ (1 1/4 cups/bag)

To divide by a fraction, we can multiply by its reciprocal

(11/2 cups) x (4/5 cups/bag)

= 44/10 cups

Simplifying, we get

= 4 2/10 cups

= 4 1/5 cups

So, Jen can fill 4 bags completely.

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Mathswatch Question:


Liam is a tyre fitter.


It takes him 124 minutes to fit 4 tyres to a lorry.


a) How long would it take him to fit 6 tyres to a lorry. ?


b) If he works for 93 minutes, how many tyres can he fit?


Working out for question a:


a) 124×6÷4=186(minutes)


Correct answer for question a is 186.


Correct answer for question b is 3

Answers

To answer question a, we use the formula:

time taken = (number of tyres to fit x time taken to fit one tyre) / number of tyres fitted at once

In this case, Liam takes 124 minutes to fit 4 tyres to a lorry. To find out how long it would take him to fit 6 tyres, we plug in the values:

time taken = (6 x 124) / 4
time taken = 186 minutes

So it would take Liam 186 minutes to fit 6 tyres to a lorry.

For question b, we know that Liam takes 124 minutes to fit 4 tyres, so he takes 31 minutes to fit 1 tyre. If he works for 93 minutes, we can find out how many tyres he can fit:

number of tyres = time taken / time taken to fit one tyre
number of tyres = 93 / 31
number of tyres = 3

So Liam can fit 3 tyres in 93 minutes.

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The total cost C(x) (in dollars) incurred by Aloha Company in manufacturing x surfboards a day is given by the following function.
C(x) = −10x2 + 500x + 110 where (0 ≤ x ≤ 15)
(a)
Find C '(x).
C '(x) = (b)
What is the rate of change of the total cost (in dollars) when the level of production is 7 surfboards a day?
$ per surfboard

Answers

(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.

The given function is: C(x) = -10x^2 + 500x + 110

To find the derivative, we will apply the power rule:

C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)

For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500

(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.

To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360

The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.

Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard

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Farmer jones raises only pigs and geese. he wants to raise at most 16 animals. he wants no more
than 12 geese. he spends $5 to raise a pig and $2 to raise a goose and has 550 available to spend. if he
makes a profit of s4 per pig and s8 per goose, how many of each does he need to raise in order to
maximize his profits?
write the objective function. let a represent the number of pigs and y represent the number of geese.

Answers

The profit per pig is $4 and the profit per goose is $8.

How can the farmer raise at most 16 animals in order to maximize his profits?

Let's start by defining the variables:

a = number of pigs Farmer Jones raises

y = number of geese Farmer Jones raises

The problem tells us that he wants to raise at most 16 animals, so we can write:

a + y ≤ 16

It also tells us that he wants no more than 12 geese, so we can write:

y ≤ 12

We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:

5a + 2y ≤ 550

Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:

Profit = 4a + 8y

To summarize, the linear programming model for this problem is:

Maximize: Profit = 4a + 8y

Subject to:

a + y ≤ 16

y ≤ 12

5a + 2y ≤ 550

where a and y are non-negative integers.

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What is the max/min of the quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7)? Is it a maximum or a minimum? Show your workor explain your reasoning. ​

Answers

The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.

To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:

f(x) = 0.5(x² - 4x - 21)

f(x) = 0.5x² - 2x - 10.5

The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.

To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:

x = -(-2)/2(0.5) = 2

So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:

f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11

Therefore, the minimum value of the function is -11.

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Sofia owns a small business selling ice cream. She knows that in the last week 56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.



Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form

Answers

The probability that the next customer will pay with a credit card is 9/40.

To find the probability that the next customer will pay with a credit card, we need to determine the total number of customers and then calculate the fraction of those who used a credit card.

Step 1: Find the total number of customers.
56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Total customers = 56 + 6 + 18 = 80 customers

Step 2: Calculate the probability of a customer using a credit card.
Number of customers who used a credit card = 18
Total number of customers = 80


Probability = (Number of customers who used a credit card) / (Total number of customers)
Probability = 18 / 80

Step 3: Simplify the fraction.


Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 80 is 2.
18 ÷ 2 = 9
80 ÷ 2 = 40

Simplified fraction: 9/40

So, the probability that the next customer will pay with a credit card is 9/40.

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Let f(x) = 4x^3 – 3x^2 – 18x +5. (a) Find the critical numbers of f. (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. (c) Find the local minimum value(s) and focal maximum value(s) of f, if any.
(d) Find the open interval(s) where f is concave upward and the open interval(s) where f is concave downward e) Find the inflection points of the graph of f, if any

Answers

(a) The critical numbers happen when x = 3 or x = -1/2

(b) f is decreasing on (-∞, -1/2), increasing on (-1/2, 3), and increasing on (3, ∞).

(c) f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.

(d) f is concave downward on (-∞, 1/4) and concave upward on (1/4, ∞).

(e) The inflection point of f is at x = 1/4.

(a) To find the critical numbers of f, we need to find the values of x where the derivative of f equals zero or does not exist.

f'(x) = 12x² - 6x - 18 = 6(2x² - x - 3) = 6(x - 3)(2x + 1)

Setting f'(x) equal to zero, we get:

6(x - 3)(2x + 1) = 0

x = 3 or x = -1/2

These are the critical numbers of f.

(b) To find the intervals where f is increasing and decreasing, we need to examine the sign of the derivative f'(x) in the intervals determined by the critical numbers.

When x < -1/2, f'(x) < 0, so f is decreasing on the interval (-∞, -1/2).

When -1/2 < x < 3, f'(x) > 0, so f is increasing on the interval (-1/2, 3).

When x > 3, f'(x) > 0, so f is increasing on the interval (3, ∞).

(c) To find the local minimum and maximum values of f, we need to examine the critical numbers and the end points of the intervals.

f(3) = 4(3)³ - 3(3)² - 18(3) + 5 = -22

f(-1/2) = 4(-1/2)³ - 3(-1/2)² - 18(-1/2) + 5 = 25.5

Thus, f has a local minimum value of -22 at x = 3, and a local maximum value of 25.5 at x = -1/2.

(d) To find the intervals where f is concave upward and concave downward, we need to examine the sign of the second derivative f''(x).

f''(x) = 24x - 6 = 6(4x - 1)

When x < 1/4, f''(x) < 0, so f is concave downward on the interval (-∞, 1/4).

1/4 < x, f''(x) > 0, so f is concave upward on the interval (1/4, ∞).

(e) To find the inflection points of f, we need to examine the points where the concavity changes.

The concavity changes at x = 1/4, which is the only inflection point o

Solve for w.
65=170-w

Answers

W = 105
170-65 = 105 that's how W is 105

Y’all pls help this is due

Answers

the answer would be 4.7

Answer: 4.7KL

Step-by-step explanation:

KL=DAL/100

KL=470/100

KL=4.7

the line is parallel to the graph of y=-1/2x-1 and contains the point (-4, 5)

Answers

The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.

What is the equation of the parallel line?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the graph

y = (-1/2)x - 1

The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.

Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:

y - y1 = m(x - x1)

y - 5 = (-1/2)(x - (-4))

y - 5 = (-1/2)x - 2

y = (-1/2)x + 3

Therefore, the equation of the parallel line is y = (-1/2)x + 3.

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If f(x) = 3x² - 3, find x = 2

Answers

Answer:

The answer is 9

Step-by-step explanation:

When x = 2,

f(2) = 3×2^2-3

f(2) = 3×4-3

f(2) = 12-3

f(2)= 9

Use the rules to find derivatives of the functions at the specified values.
f(x) = 4x^3 at x = 2
f(2) = _____

Answers

The value of the function f(x) at x = 2 is 48.

The question asks us to find the value of the function f(x) = 4[tex]x^3[/tex] at x = 2 and its derivative f'(x) at x = 2.

The value of the function f(x) at x = 2, we simply plug in x = 2 into the function and evaluate:

f(2) = 4[tex](2)^3[/tex] = 4(8) = 32

Therefore,

The value of the function f(x) at x = 2 is 32, which we can write as f(2) = 32.

To find the derivative of the function f(x) at x = 2, we first need to find the general formula for the derivative of f(x), which we can do using the power rule for derivatives.

The power rule states that

To find the derivative of f(x) at x = 2, we simply plug in x = 2 into the formula for f'(x) that we just found:

f'(2) = [tex]12(2)^2[/tex] = 48

Therefore,

The derivative of the function f(x) at x = 2 is 48, which we can write as f'(2) = 48To find the derivative of the function

f'(x) = 12[tex]x^2[/tex]

To find the value of f(2), we can simply plug in x = 2 into the original function:

f(2) = 4[tex](2)^3[/tex] = 32

To find the value of f'(2), we can plug in x = 2 into the derivative we just found:

f'(2) = 12[tex](2)^2[/tex] = 48

Therefore,

f(2) = 32 and f'(2) = 48.

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made bracelets with string and beads. she used xx centimeters of string to make 77 bracelets. she used 17.817.8 centimeters of string for each bracelet. how much string did she use in all? write an equation and use it to solve this problem.enter the correct answers in the boxes.show hints

Answers

Total string used = Number of bracelets × String used per bracelet

Total string used = 77 × 17.8 = 1370.6 cm

How much string did she use in total?

Let's denote the total amount of string used as "T". We know that the girl used xx centimeters of string to make 77 bracelets, and each bracelet required 17.8 centimeters of string.

To find the total string used, we can set up the following equation:

T = 77 * 17.8

Simplifying the equation, we have:

T = 1369.6

Therefore, the girl used a total of 1369.6 centimeters of string to make all the bracelets.

In conclusion, the equation T = 77 * 17.8 can be used to determine the total amount of string used, and the solution to the equation is T = 1369.6 centimeters.

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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.

Answers

1. To assign each volunteer either the real drink or the placebo, we can use the following method:

- Assign the first five volunteers (Abby, Barry, Callie, Dion, and Ernie) to the first five digits in the list (6, 9, 4, 2, 9).
- If the digit is even, assign the volunteer the real drink; if it is odd, assign the volunteer the placebo.
- Repeat this process for the remaining volunteers (Falco, Garrett, Hallie, Indigo, and Jaylene) using the next five digits in the list (8, 6, 1, 4, 0).

Here is the assignment:

Volunteer | Real or Placebo
----------|----------------
Abby | Real
Barry | Real
Callie | Placebo
Dion | Real
Ernie | Placebo
Falco | Real
Garrett | Real
Hallie | Real
Indigo | Placebo
Jaylene | Placebo


2. To select the 20 houses in each division, we can use the following method:

- Assign each house in the subdivision a number from 01 to 100.
- Use a random number generator to generate 20 random numbers between 01 and 100.
- Visit the houses corresponding to the 20 numbers generated.

Repeat this process for each subdivision.

3. One way to simulate the average number of children required to have two girls is to use the following method:

- Assign a value of 0 to a counter variable.
- Repeat the following steps until two girls are born:
- Use a random number generator to generate a number between 0 and 1.
- If the number is less than 0.5, add 1 to the counter variable (representing a boy); otherwise, add 2 to the counter variable (representing a girl).
- Record the value of the counter variable.
- Repeat this process a large number of times (e.g., 10,000).
- Calculate the average value of the counter variable across all simulations. This will give an estimate of the average number of children required to have two girls.

x An investor puts $4,500 into a life insurance policy that pays 8.0% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 8 years?​ HELP PLEASE

Answers

The amount of accumulated interest the investor can expect in 8 years is $2,880.

How to find the accumulated interest ?

To calculate the accumulated interest on the life insurance policy, we can use the simple interest formula:

I = P x r x t

In this case, the principal amount invested is $4,500, the annual interest rate is 8.0% (or 0.08 as a decimal), and the time period is 8 years. Therefore:

I = 4,500 x 0.08 x 8

I = $2,880

Therefore, the investor can expect to earn $2,880 in accumulated interest at the end of 8 years.

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I’m confused as to what the solution is if I follow the first step

Answers

Answer:

x = 4, y = 1, z = 5

Step-by-step explanation:

z + x =9....(3) we can say it's x + z = 9

x - z = - 1

x + z = 9

______ -

- 2z= - 10

z = 10/2

z = 5

if z + x = 9

5 + x = 9

x = 9 - 5

x = 4

if x + y = 5

4 + y = 5

y = 5 - 4

y = 1

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The answer to this math problem please.

Answers

Answer:

C) 6

Step-by-step explanation:

n=6

6( 6 + 1) + 3 =45

36 + 6 + 3 = 45

36 + 9 = 45

Frank needs to find the area enclosed by the figure. The figure is made by


attaching semicircles to each side of a 54-m-by-54-m square. Frank says the area


is 1,662. 12 m2. Find the area enclosed by the figure. Use 3. 14 for it. What error


might Frank have made?


The area enclosed by the figure is


m2


(Round to the nearest hundredth as needed. )

Answers

To find the area enclosed by the figure, we first need to find the area of  the square and the  area of each semicircle.

The area of the square is simply the length of one of its sides squared, which is:

54 m x 54 m = 2,916 m²

The area of each semicircle is half the area of a full circle with the same radius as the side of the square. The radius of each semicircle is 54 m/2 = 27 m.

The area of each semicircle is:

1/2 x π x 27 m² = 1/2 x 3.14 x 27 m x 27 m ≈ 1,442.31 m²

Since there are four semicircles, the total area of the semicircles is:

4 x 1,442.31 m² = 5,769.24 m²

Therefore, the total area enclosed by the figure is:

2,916 m² + 5,769.24 m² ≈ 8,685.24 m²

Frank's answer of 1,662.12 m² is significantly less than the actual area. He may have made the mistake of only calculating the area of one of the semicircles instead of all four, or he may have forgotten to include the area of the square.

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100 points Please help asap!

Answers

The solution of the system of equations is given by the ordered pair (-2, 2).

Based on the table, a x-value that is a solution to the equation is -2.

The solution to the equations are (-6, 3) and (-4, -5).

An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).

How to graphically solve this system of equations?

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

8x - 4y = -24    ......equation 1.

4x - 12y = -32  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).

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Max has eight circular chips that are all the same size and shape in a bag.



(3 chips are square, and 5 are stars)



Max reaches into the bag and removes one circular chip. What is the theoretical probability that the circular chip has a star on it? Write your answer as a fraction, decimal, and percent

Answers

The probability of drawing a star-shaped chip is 5/8.

The theoretical probability of drawing a star-shaped circular chip from the bag is 5/8 or 0.625 or 62.5%. Out of the total of eight circular chips, five are stars, and three are squares.

Therefore, the probability of drawing a star-shaped chip is the ratio of the number of star-shaped chips to the total number of chips in the bag, which is 5/8.

To understand this conceptually, we can think of probability as a fraction where the numerator is the number of favorable outcomes (in this case, drawing a star-shaped chip) and the denominator is the total number of possible outcomes (all the circular chips in the bag).

Thus, the theoretical probability of drawing a star-shaped chip is 5/8 because there are five star-shaped chips out of the total eight circular chips in the bag.

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It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. If it takes them 15 hours when they work together, how long would it take the apprentice alone?

Answers



Let's assume that the experienced plumber can complete the job in x hours.

According to the problem, the apprentice takes four times as long as the experienced plumber to complete the job. Therefore, the apprentice can complete the same job in 4x hours.

If they work together, they can complete the job in 15 hours. Therefore, we can write the following equation based on their combined work rate:

1/x + 1/4x = 1/15

Multiplying both sides by the common denominator of 60x gives:

60 + 15 = 4x

75 = 4x

x = 75/4

x = 18.75

Therefore, the experienced plumber can complete the job in 18.75 hours.

Using the relationship that the apprentice takes four times as long as the experienced plumber to complete the job, we can find the time it takes for the apprentice to complete the job alone:

4x = 4(18.75) = 75

Therefore, the apprentice would take 75 hours to complete the job alone.

a pet store has 115 fish and each tank can hold six fish how many tanks do you nedd

Answers

Answer:

20 tanks

Step-by-step explanation:

if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:

115/6 = 19.1666666667

Now we round up bc we cant leave any fish out right?

So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.

Check this by multiplying the tanks and fish in every tank:

20 x 6 = 120

Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D

Answer: 20 is the correct option.

Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.

We are to find the number of tanks that the store need.

We will be using the UNITARY method to solve the given problem.

Number of tanks needed to store 6 fishes = 1.

So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]

Therefore, number of tanks needed to store 115 fishes is given by

[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.

Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.

Thus, the store needs 20 tanks for 115 fishes.

Hope this helps :)

21. if you have the raw scores of two individuals on a norm-referenced test, which of the following is important in terms of making meaning of those scores? a. measures of central tendency (mean, median, mode) b. the relative positions of the scores to the rest of the group c. whether higher scores are better than lower scores d. how an individual feels about his or her score e. all of these are important.\

Answers

The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.

A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.

These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.

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