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A student has grades​ 84, 91,​ 78, and 74. He will have one more test. If they are all weighted​ equally, what must he earn in order to average at least an 83 for the​ course, so he can earn a​ B?

Enter his minimum test grade. ___

Answers

Answer 1

Answer:

88

Step-by-step explanation:


Related Questions

A manufacturer must monitor the temperature at which the cakes are baked. The manufacturer liked to see any evidence that mean temperature is above 200 F. To test, we collected 100 data. What test to do?

Answers

Conduct a one-sample t-test to determine if the mean temperature of the cakes is statistically significantly above 200 F.

To test whether the mean temperature of the cakes is above 200 F, a one-sample t-test is suitable. In this case, the manufacturer has collected 100 data points, which allows for an adequate sample size. The one-sample t-test compares the sample mean to a hypothetical mean (in this case, 200 F) and determines if there is enough evidence to suggest that the true population mean is significantly different.

By performing this test, the manufacturer can assess whether the baking process consistently produces cakes with a mean temperature above the desired threshold. The results of the t-test will provide statistical evidence to support decision-making regarding the baking temperature.

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help me solve this problem please

help me solve this problem please

Answers

The answer is A 16. To solve, subtract 41 from both sides of the equation to get z=16.

Answer:

It's either 16 or -16

Step-by-step explanation:

Subtract 41 and 57 and you get one of those two.

My bet is 16 due to you not being able to have a negative amount of bills in your wallet in real life.

.-4(8 -c) - (3c + 7)

Answers

Answer:

c-39 is the answer

Step-by-step explanation:

multiply the numbers that are in bracket

-4(8-c)-(3c+7)

the answer will be this

-32+4c-3c-7

ARRANGE IN LIKE TERM

-32-7+4c-3c

c-39 is the answer

Hope it is helpful for you

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!!20 points and Brainliest please help!!!

Which of the following could be factored by grouping?

A) ab + ad - ac + ae
B) ac + ad + bc - bd
C) ab + cd – ab + cd
D) ac + ad + bc + bd

!!20 points and Brainliest please help!!!Which of the following could be factored by grouping?A) ab +

Answers

D) ac + ad + bc + bd

Hope it helps :)

Answer:

D) ac + ad + bc + bd

Step-by-step explanation:

what are two ways to build 3x-(-4)​

Answers

Answer:

3x + 4

or

3x + (4)

Step-by-step explanation:

You can shape that problem into many more but these are just 2 examples.

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What is the special angle pair relationship between the two

What is the special angle pair relationship between the two

Answers

Answer: Alternate exterior angles

Step-by-step explanation:

The Stock Market Alexander is a stockbroker. He earns 14​% commission each week. Last​ week, he sold ​$7,100 worth of stocks. How much did he make last week in​ commission? If he averages that same amount each​ week, how much did he make in commission in​ 2011?

Answers

The amount he earned last week in commission is $994.

The commission he earned in 2011 is $51,688

What is the commission?

The commission earned is a fraction of the total sales of stocks.

Commission earned = amount of sales x percentage commission

14% x $7,100

= 14/100 x $7,100

= 0.14 x $7,100

= $994

Amount she earned in commission in a year = number of weeks in a year x commission earned per week

= $994 x 52 = $51,688

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ay you should help me with this tyty

ay you should help me with this tyty

Answers

Answer:

C. \(m=20\), \(n=10\)

Step-by-step explanation:

Since the triangle is a special 30°-60°-90° triangle, the hypotenuse is twice the size of the shortest leg. The long leg is \(\sqrt{3}\) of the short leg.

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. (Source:www.ets.org). A graduate school requires that students score above 160 to be admitted.
What proportion of combined GRE scores can be expected to be over 160?
What proportion of combined GRE scores can be expected to be under 160?
What proportion of combined GRE scores can be expected to be between 155 and 160?
What is the probability that a randomly selected student will score over 145 points?
What is the probability that a randomly selected student will score less than 150 points?
What is the percentile rank of a student who earns a quantitative GRE score of 142?

Answers

The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students’ scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8.A graduate school requires that students score above 160 to be admitted.

Proportion of combined GRE scores can be expected to be over 160:We are given that the mean is 150 and the standard deviation is 8.8. We have to calculate the proportion of combined GRE scores that can be expected to be over 160.The standardized score is calculated as:z = (x - μ) / σwhere x = 160, μ = 150, and σ = 8.8Then we have:z = (160 - 150) / 8.8z = 1.136The area under the standard normal distribution curve to the right of 1.136 is 0.127. This means that 12.7% of combined GRE scores can be expected to be over 160.Proportion of combined GRE scores can be expected to be under 160:To calculate the proportion of combined GRE scores that can be expected to be under 160, we can subtract the proportion that is over 160 from the total proportion, which is 1.

So, the proportion of combined GRE scores that can be expected to be under 160 is:1 - 0.127 = 0.873This means that 87.3% of combined GRE scores can be expected to be under 160.Proportion of combined GRE scores can be expected to be between 155 and 160:We can use the same formula to calculate the proportion of combined GRE scores that can be expected to be between 155 and 160. First, we need to calculate the standardized scores for 155 and 160.z1 = (155 - 150) / 8.8z1 = 0.568z2 = (160 - 150) / 8.8z2 = 1.136Then, we need to find the area under the standard normal distribution curve between these two standardized scores.Using a standard normal distribution table or calculator, we find that the area between z = 0.568 and z = 1.136 is 0.155.

Therefore, the proportion of combined GRE scores that can be expected to be between 155 and 160 is 0.155. This means that 15.5% of combined GRE scores can be expected to be between 155 and 160.What is the probability that a randomly selected student will score over 145 points?We are given that the mean is 150 and the standard deviation is 8.8. We have to calculate the probability that a randomly selected student will score over 145 points.The standardized score is calculated as:z = (x - μ) / σwhere x = 145, μ = 150, and σ = 8.8Then we have:z = (145 - 150) / 8.8z = -0.568The area under the standard normal distribution curve to the right of -0.568 is 0.715. This means that the probability that a randomly selected student will score over 145 points is 0.715.

In summary, we can expect that 12.7% of combined GRE scores will be over 160, and 87.3% of combined GRE scores will be under 160. The proportion of combined GRE scores that can be expected to be between 155 and 160 is 15.5%. A randomly selected student has a probability of 0.715 of scoring over 145 points and a probability of 0.5 of scoring less than 150 points. Finally, a student who earns a quantitative GRE score of 142 has a percentile rank of 18.2%. These calculations are based on the normal distribution of GRE scores with a mean of 150 and a standard deviation of 8.8.

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Comparing two algorithms.

Say we have two different algorithms with respective runtimes of f(n) and g(n). Given the following cases, prove whether or not f(n) = ϴ(g(n)) is true in each case. Show your work but with the crucial steps only. P.S. sqrt(n) means the square-root of n, aka n^(½).

Case

f(n)

g(n)

A

log(n^200)

log(n^2)

B

sqrt(n)

log(n)

C

3^n

5^n

D

sin(n)+3

cos(n)+1

Answers

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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PLEASE HELP ME EASY 8TH GRADE MATH!!!!

PLEASE HELP ME EASY 8TH GRADE MATH!!!!

Answers

Answer: The probability is 3 out of 20

Step-by-step explanation:

Which relation is a function?

Which relation is a function?

Answers

Answer: The answer C the one in the botton the one that has the arrow Up

Step-by-step explanation:

two numbers are respectively 20% and 50% more than the third number. what % is the first number of the second?​

Answers

The first number 20% greater than the third number.

The second number is 50% MORE than the third number.

Let the third number be 100.

According to the question,

First number =120

Second number =150

Percentage of the first of the second number

120/150 x 100 = 80%

The correct answer is 80%

515 to 103 markup percentage rate

Answers

The mark up percentage gained by the shopkeeper is 400%.

What is termed as the markup percentage rate?The markup percentage is the difference between how an item costs this same seller and what the customer pays. The greater the markup, as a percentage of a cost, the greater the profit.The markup percentage of a product is the ratio of its gross profit to its cost.It is most useful for companies that sell physical goods in industries in which prices are linked to the cost of acquiring more.The percentage of markup varies by industry as well as product. Other than discovering a price that did work for both your company and your customers, there is no golden rule.

For the given question.

The cost of the item is $103.

The customer pays is $515.

The mark up percentage is -

mark up percentage = 515 - 103 / 103

mark up percentage = 4 × 100%

mark up percentage = 400 %.

Thus, the mark up percentage gained by the shopkeeper is 400%.

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State the explicit formula for the sequence below and find the 8th term.
-4, 16, -64, 256,...
O an = -4(4)n-1; n = 8 is-262,144
O an = -4(-4)-1; n = 8 is 65,536
O an = 4(4)n-1; n = 8 is 65,536
O a = 4(-4)n-1; n = 8 is 261,144
6.25 pts
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Answers

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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When you solve using the quadratic formula and you get to
\( {b}^{2} \)
and b is negative... do you end up with a negative or positive number?​

Answers

Answer:

\( \boxed{if \: b= - 2 : {b}^{2} = { (- 2)}^{2} = 4}\)

Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

Answers

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.

To find the order of matrix:

We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.Dimension is assigned to the provided matrix: 6 × 5This means the given matrix contains six rows and five columns.As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.

To prove:

In other words, the inner products of the dimensions should be equal.That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.The dimensions of the matrix are given by, row × column.

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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Matrix a is a 6 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

A particular variety of bamboo grows for
4
months out of the year at a rate of
3
inches per day. The rest of the year, the bamboo is dormant and does not grow.

A graph of the growth for a
12
-month period is shown.



What is the domain of the function that models this phenomenon?

Answers

Using function concepts, it is found that the domain of the function that model this phenomenon is [0, 12].

The domain of a function is the set that contains all possible input values.

In this problem, the function is the height of the bamboo according to the month of the year, hence, the input is the month of the year, which has values between 0 and 12, and thus, the domain of the function that model this phenomenon is [0, 12].

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Someone please help me I’ll give out brainliest please dont answer if you don’t know

Someone please help me Ill give out brainliest please dont answer if you dont know

Answers

Answer:

\(3x-1\)

Step-by-step explanation:

\(3+2(x-2)+x=3+2x-2.2+x=(2x+x)+(3-4)\\=3x-1\)

Answer:

3x-1

Step-by-step explanation:

trust me i know

Ruby has a monthly salary of $1,800 and also earns 6% commission on her sales. If Ruby had $37,000 in sales last month, what were her total earnings for the month? a. $1,908 b. $2,220 c. $2,328 d. $4,020 Please select the best answer from the choices provided A B C D.

Answers

Ruby's total earning for the month will be $4,020.

It is given that -

Ruby's monthly salary =$1,800

Ruby's  commission on sales= 6%

Ruby's last month sales= $37000

What will be the total earnings of Ruby ?

Ruby's monthly salary =$1,800

Ruby's  commission on sales= 6%

Ruby's last month sales= $37000

Amount Ruby earned as a commission = \(\dfrac{37000\times6}{100}\) =  $2220

Ruby's total earning will be = Salary + commission

                                               = 1800+2220

                                                = $4020

Hence Ruby's total earning for the month will be $4,020.

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What condition has no solution?

Answers

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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3. At an exhibition, the ratio of the number of men to the number of women was 10:3. Halfway through the exhibition, 110 men left and the number of men was 5/12 of the total number of people who remained behind. How many women were there at the exhibition? ​

Answers

Answer:

Step-by-step explanation:

Let's assume the initial number of men at the exhibition is 10x, and the initial number of women is 3x.

After 110 men left, the number of men remaining is 10x - 110.

The total number of people remaining is (10x - 110) + (3x) = 13x - 110.

According to the given information, the number of men remaining (10x - 110) is 5/12 of the total number of people remaining (13x - 110). We can write this as an equation:

10x - 110 = (5/12)(13x - 110)

To solve this equation, we can start by simplifying both sides:

10x - 110 = (65/12)x - (55/6)

To get rid of the fractions, we can multiply both sides of the equation by 12:

12(10x - 110) = 65x - 110(2)

120x - 1320 = 65x - 220

Next, we can bring the x terms to one side and the constant terms to the other side:

120x - 65x = 1320 - 220

55x = 1100

Dividing both sides by 55, we find:

x = 20

Now, we can substitute the value of x back into the initial expressions to find the number of men and women:

Number of men = 10x = 10(20) = 200

Number of women = 3x = 3(20) = 60

Therefore, there were 60 women at the exhibition

Hope this answer your question

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Fill in the blank to complete the following sentence
the two roots a+ square root of b and a- square root of b are called ___radical

Answers

Answer:

conjugate

Step-by-step explanation:

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HELP ME PLEASEE



Given that 4, 5x and 16 are the first three terms of geometric progression

Find:
(1)
the possible values of x,

(2)
the sum of the first ten terms if all the terms are positive.

Answers

Answers:

x = -8/5 or x = 8/5

Sum of the first ten terms where all terms are positive = 4092

========================================================

Explanation:

r = common ratio

first term = 4second term = (first term)*(common ratio) = 4rthird term = (second term)*(common ratio) = (4r)*r = 4r^2

The first three terms are: 4, 4r, 4r^2

We're given that the sequence is: 4, 5x, 16

Therefore, we have these two equations

5x = 4r4r^2 = 16

Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.

-----------------

To find the sum of the first n terms, we use this geometric series formula

Sn = a*(1 - r^n)/(1 - r)

We have

a = 4 = first termr = 2, since we want all the terms to be positiven = 10 = number of terms to sum up

So,

Sn = a*(1 - r^n)/(1 - r)

S10 = 4*(1 - 2^10)/(1 - 2)

S10 = 4*(1 - 1024)/(-1)

S10 = 4*(-1023)/(-1)

S10 = 4092

Machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour. if both machines work together, how much time will it take them to make a total of 1000 widgets?

Answers

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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Find the product using the correct number of significant digits.
0.025 x 4.07 =

Answers

Answer: 0.10175

Step-by-step explanation:

First, bring the decimal points to the right for both numbers, to be a total of 5 decimal points to the right. Then, with the numbers 25 and 407, multiply them, and we get 10175. Then, we must bring the 5 decimal points back, and we end up with 0.10175.

Answer: 0.10

Step-by-step explanation:

on time4llearning

F=9/5C + 32 solve for C

Answers

\(F=\frac{9}{5}C+32\)

To solve for C let us do these steps

1. Put the term of C on one side and the other terms on the other side

Subtract 32 from both sides to move the term 32 to the other side

\(\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}\)

2. Make the coefficient of C = 1

Divide both sides by 9/5

\(\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}\)

You can Multiply the bracket (F- 32) by 5/9

\(C=\frac{5}{9}F-\frac{160}{9}\)

after allowing 10% discount on the Marked price of an article is and then 15% vat is charge its price become Rs 16720 how much amount was given as discount ​

Answers

Answer:

let marked prize=mp

discount=10%

sp=mp-d%ofmp=mp(1-10/100)=0.9mp

vat=15%

sp with vat=sp+vat%of sp=sp(1+15/100)=1.15sp=1.15×0.9mp=1.035mp

sp with vat=1.035mp16720=1.035mpmp=16720/1.035=16154.589discount amount=d%of mp=10%×16154.589=rs1615.458

What is the key point and asymptote in logbase13 X = Y, and how do you find it

Answers

The key point in the equation log base 13 X = Y is that it represents the logarithmic relationship between the base 13 logarithm of X and the variable Y. The asymptote in this equation is the line Y = 0, which represents the limit or boundary as Y approaches negative or positive infinity.

To find the key point, we need to rearrange the equation to isolate X. Taking the exponentiation of both sides with base 13, we get X = 13^Y. This means that for any given value of Y, X is equal to 13 raised to the power of Y.

To find the asymptote, we can consider the behavior of the equation as Y approaches negative or positive infinity.

As Y approaches negative infinity, the value of X will approach zero, since 13 raised to a very large negative power becomes very small.

As Y approaches positive infinity, the value of X will increase without bound, as 13 raised to a very large positive power becomes very large.

In summary, the key point in the equation log base 13 X = Y is that X is equal to 13 raised to the power of Y. The asymptote is the line Y = 0, representing the limit or boundary as Y approaches negative or positive infinity.

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You are considering investing in a security that will pay you $3,000 in 34 years. a. If the appropriate discount rate is 8 percent, what is the present value of this investment? b. Assume these investments sell for $773 in return for which you receive $3,000 in 34 years. What is the rate of return investors earn on this investment if they buy it for $773? a. If the appropriate discount rate is 8 percent, the present value of this investment is $ 219.13. (Round to the nearest cent.) b. The rate of return investors can earn on this investment if they buy it for $773 is %. (Round to two decimal places.)

Answers

In this scenario, we are considering an investment that will pay $3,000 in 34 years. We are given an appropriate discount rate of 8 percent. To determine the present value of this investment, we can use the present value formula. Additionally, we are provided with the information that the investment is being sold for $773, and we need to calculate the rate of return investors will earn on this investment.

a. Present value of the investment:

To calculate the present value of the investment, we use the present value formula:

Present Value = Future Value / (1 + Discount Rate)^n,

where Future Value is $3,000, the Discount Rate is 8 percent (0.08), and n is the number of years, which is 34 in this case.

Present Value = $3,000 / (1 + 0.08)^34 = $219.13

Therefore, the present value of the investment, considering an 8 percent discount rate, is $219.13.

b. Rate of return on the investment:

The rate of return on an investment is calculated using the formula:

Rate of Return = (Future Value - Purchase Price) / Purchase Price * 100,

where Future Value is $3,000 and the Purchase Price is $773.

Rate of Return = ($3,000 - $773) / $773 * 100 ≈ 288.46%

Therefore, the rate of return investors can earn on this investment, if they buy it for $773, is approximately 288.46%.

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If nobody answers me imma just die Cause I know Im nothing cause nobody will help Simplify 3272234518 Work Needed I WILLL GIVEE BRAINLIESTTTT "When demand conditions are the same in all countries,the Rybczynski andStolper-Samuelson theorems can be used to prove the Hecksher-Ohlintheorem. Explain.Why must demand conditions be the same? kyle spent all of his allocated budget on video games and comic books. to maximize his utility, kyle should have purchased an important factor that prevented the ancient greek city-states from uniting to form a single nation was the FITB . a) Estimate the value of 50.75 x 0.18 Mackenzie scott donated $84. 5 million to which organization, the largest individual donation received in its history?. Determine whether the table of values below represents a linear function. If it represents a linear function, write the function. If it does not represent a linear function, explain why not. Write a scientific explanation to describe where earthquakes and volcanoes most commonly occur and their relation to plate boundaries . Someone pls help!! Worth a lot of points soby. tes yo & Write 1 seriously 2 weekly 3 nearby 4 rarely 5 completely a sentence Date Page each for the following adverbs Rewrite the following passage in the Passive. 21. Somebody has stolen a bus from outside the school. Some children saw the thief. The police are searching for the bus now. They will use the childrens descriptions to catch the thief Let V be a finite-dimensional vector space and let \mathcal{B}=\left\{\alpha_{1}, \dots, \alpha_{n}\right\}B={ 1, n } be a basis for V. Let (\quad | \quad)() be an inner product on V. If c_{1}, \dots, c_{n}c 1,,c nare any n scalars, show that there is exactly one vector \alpha in V such that \left(\boldsymbol{\alpha} | \boldsymbol{\alpha}_{i}\right)=c_{i}, j=1, \ldots, n( )=c ij=1,,n. Which advancement in metalwork was important during the Shang dynasty? Steel was turned into sharp swords. Bronze was used for multiple purposes. Gold was turned into valuable jewelry for trade. Iron was used to make cooking pots and weapons. expenses 12 EBITDA 13 Depreciation and amorization 14 EBIT 15 Interest expense 16 Pretax income 17 Income taxes 18 Net income 19 Shares outstanding 20 EPS 21 22 Exhibit 2. Lagorge Systems, Inc Balance Sheet 23 in millions) 24 2017 25 Current Assets 26 Cash and equivalents 210.00 $ 27 Receivables $ 474.00 $ 28 Inventories 5 520.00 $ 29 Total current assets 1,204.00 $ 30 31 Noncurrent Assets 32 Property, plant, and equipment 2,501.00 $ 33 Less. Accumulated depreciation 604005 34 Net property, plant, and equipment 1,897.00 $ 35 Other noncurrent assets 100005 36 Total noncurrent assets 199700 37 Total assets 3,201 005 38 39 Current Liabilities 2018 248.00 513.00 564.00 1,325.00 2,850.00 784.00 2,066.00 100 00 2.166.00 3.491.00 For many European countries, the end of WWI was the beginning of Insert commas in the following sentences:1. When all is said and done a lot more is said than done. 2. If you mark your suitcase with colored tape it will be easier to find at the baggage counter. 3. Feeling brave and silly at the same time Anita volunteered to go onstage and help the magician.4. As the bride smiled and strolled past me down the aisle I saw a bead of sweat roll from her own forehead down her cheek.5. Remembering my own wedding I knew she wasn't sweating from the heat. 6. The dance aided by members of the chorus hobbled across the state toward the wings.7. Mr. and Mrs. Anderson who were married on the Fourth of July named their first child "Freedom."8. All trees even the most gigantic are only 1 percent living tissue; the rest is deadwood.9. The repairman unaware of the grease on his shoes left a black trail from our front door to the washing machine.10. John Adams and Thomas Jefferson the second and third presidents of the United States died on the same day in 1826. In a museum gift shop, a miniature dinosaur, the Acrocanthosaurus, is22.8 centimeters long and 15.9 centimeters tall. The package says that theactual dinosaur was approximately 9 meters long. How tall was thedinosaur?A. 2.10 metersB. 6.28 metersC. 12.91 metersD. 13.80 metersAB 4. Imagine that your six-year-old cousin asked you this question: "How can a cat video showup on my tablet? Is it magic?" How would you explain the process of data transmission ina way simple enough for a young child to understand?