I have 2 questions

Transform the equation.
Stretch y=5x by a factor of 3
What is the transformed equation?

Transform the equation.
Shift y=5√x+5 horizontally, 5 units to the right and a stretch by a factor of 4
What is the transformed equation?

I Have 2 Questions Transform The Equation.Stretch Y=5x By A Factor Of 3 What Is The Transformed Equation?Transform

Answers

Answer 1

Answer:

1. I assume that stretching vertically by factor of 2 means that every point on the transformed curve is twice as far from the x axis as the original curve.

Imagine that you have plotted y=5x.  you want to change the y scale so that each point on the original curve is two times as high.  For example, one point on the original curve is (1,5).  This point must be relocated to (1,10).  Similarly, the point (2,10) on the original curve must be relocated to (2,20).

You can see that these relocations are accomplished if we transform the function to y=2(5x)=10x.

Step-by-step explanation:

hope this helps! even though it's just the first one...


Related Questions

Can somebody please help me with this question I am completely confused I am giving lots of points and more if it is correct.

Can somebody please help me with this question I am completely confused I am giving lots of points and

Answers

Answer:

1. Country = 160, Pop= 135

2. Country = 170, Pop = 155

3. Country = 180, Pop = 175

4. Country = 190, Pop = 195

5. Country = 200, Pop = 215

6. Country = 210, Pop = 235

7. Country = 220, Pop = 255

8. Country = 230, Pop = 275

9. Country = 240, Pop = 295

10. Country = 259, Pop = 315

Step-by-step explanation:

Replace the x in the equations with the week number then solve the equation

Question 12
Write an equation of a line that passes through (8,5) and (11, 14).

Answers

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{14})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{8}}} \implies \cfrac{14 -5}{11 -8} \implies \cfrac{ 9 }{ 3 }\implies 3\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{3}(x-\stackrel{x_1}{8}) \\\\\\ y-5=3x-24\implies y=3x-19\)

Answer:

So to write this as an equation follow the steps:

1.First you take y delta divided by x delta. This means that you but in the coordinates, take them minus eachother then divided by eachother. Let me show you with maths for better understanding:

Now you have k in y=kx+m ( the equation has different letters depening on where you are from but I think you understand).

So know we just use simple algebra bu putting in the coordinates in the equation. So for this example im going to use the coordinates x= 8 and y=5

so we get:

Question 12Write an equation of a line that passes through (8,5) and (11, 14).

Suppose 14% of the listeners of a radio station listen to it while they are at work. What is the approximate standard deviation of the sampling distribution of the proportion for the sample of size 85?

Answers

To calculate the approximate standard deviation of the sampling distribution of the proportion for a sample size of 85, we can use the formula:

Standard Deviation (σ) = √[(p * (1 - p)) / n]

where:
p is the proportion of listeners (14% or 0.14 in decimal form),
1 - p is the complement of the proportion,
n is the sample size.

Substituting the values into the formula:

σ = √[(0.14 * (1 - 0.14)) / 85]

Calculating this expression gives us the approximate standard deviation of the sampling distribution of the proportion for the given sample size.

Please what is the answer?

Please what is the answer?

Answers

Answer: scale to measure the weight

Step-by-step explanation:

how many times can 82 go into 401

Answers

Answer:

4.89 times

Step-by-step explanation:

I hope this helps :)

Answer:

82 can go into 401 four times.

Step-by-step explanation:

82 multiplied by 4 is 328, and if you add another 82, the number would be greater than 401, so the answer is 4 times.

Need the answer asap
Pls answer it correctly

Need the answer asap Pls answer it correctly

Answers

Answer:

I will be your human calculator! top to bottom!

1. (+1)     5. (+28)  9. (+8)

2. (+4)    6. (+3)   10. (-5)

3. (+14)   7. (+24) 11. (+6)

4. (-3)      8. (-3)     12. (+1)!    Good Luck!

a number is stored in cell a1. write an excel formula that will square this number.

Answers

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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Sundeep works as a technician at an oil change service station. He is paid $18.75/h for a 40h
week and time-and-a-half for overtime work. If he worked 49.5h last week, what were
Sundeep’s gross earnings

Answers

Answer:

5,000.15

Step-by-step explanation:

The approximate distance of the moon from Earth iS 4 X 105 km and the average approximate distance from the Earth to Venus is 4 X 10 km. How
much farther is Venus from Earth than the moon?

Answers

Answer:

The average approximate distance from the Earth to Venus is 4 x 10^7 km, which is 4 x 10^7 - 4 x 10^5 = <<410^7-410^5=4*10^5>>4 x 10^5 km farther than the distance of the moon from Earth. Answer: 4 x 10^5



What is the sum of the geometric series 2+4+8+ . . . . . ..+64?

(A) 30

(B) 62

(C) 126

(D) 252

Answers

The answer is (C) 126.

The sum of a geometric series can be found using the formula: S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term (a) is 2, the common ratio (r) is 2 (since each term is double the previous term), and the number of terms (n) can be found by noticing that 64 is equal to 2^6.

Substituting these values into the formula, we get: S = 2 * (1 - 2^6) / (1 - 2)

Simplifying further, we have: S = 2 * (1 - 64) / (-1)

S = 2 * (-63) / (-1)

S = 126

Therefore, the sum of the geometric series 2+4+8+...+64 is 126.

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The sum of the geometric series 2 + 4 + 8 + ... + 64 is 126. Hence, the answer is (C) 126.

The provided series is a geometric series with a common ratio of 2.

To determine the sum of the series, we can use the formula for the sum of a geometric series:

\(\[S = \frac{a \cdot (1 - r^n)}{1 - r}\]\)

where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio,

and n is the number of terms.

In this case, the first term (a) is 2, the common ratio (r) is 2, and the number of terms (n) can be determined by finding the exponent that makes 64 the last term. Since 2 raised to the power of 6 (2⁶) equals 64, there are 6 terms in the series.

Using the formula, we can calculate the sum of the series:

\(\[S = \frac{{2 \cdot (1 - 2^6)}}{{1 - 2}}\)

\(= \frac{{2 \cdot (1 - 64)}}{{1 - 2}}\)

\(= \frac{{2 \cdot (-63)}}{{-1}}\)

= 2 * 63

= 126

Therefore, the correct answer is (C) 126.

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A line has gradient 5.
M and N are two points on this line.
M is the point (x, 8) and N is the point (k, 23).
Find an expression for x in terms of k.

Pls help it’s emergency!!

Answers

Answer:

x = k - 3

Step-by-step explanation:

Given parameters:

  Gradient of the line = 5;

Coordinates; M(x, 8)

                       N(k, 23)

Solution:

If we use the expression for finding the slope of the line, we can solve this problem;

     Slope  = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

    where

    x₁ = x    y₁ = 8

    x₂ = k    y₂ = 23

Input the parameters:

       5  = \(\frac{23 - 8}{k -x }\)

          15 = 5(k - x)

           3= k- x

           k - x = 3

 Express x in terms of k;

          -x = 3 - k

Multiply through by -1;

          x = -3 + k

          x = k - 3

How many points are needed to define a plane?

Answers

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

in 2007 in the united states there were approximately 480 cars for every 1,000 people. the total number of cars in the united states in 2007 was closest to

Answers

Nearly 150,000,000 cars were registered in the US as a whole in 2007. China, India, and the United States are the three nations with the largest populations on earth.

Average lifespan and child mortality rate are indeed the two key metrics that most accurately reflect a citizenry's standard of living.

The population of the globe is projected to reach about 10 billion people in 2050. Africa and Asia will see the most expansion in population if indeed the patterns in demographic persist.

Cultural practices, governmental regulations, and monetary support, as well as female employment prospects as well as education levels, all have an impact on the overall birthrate of a community.

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Help please!
Complete the table to make a proportional relationship between weight and price.

Help please!Complete the table to make a proportional relationship between weight and price.

Answers

Answer:

17.50

Step-by-step explanation:

1: 3.50 dollars

multiply by 5 on eahc side

5 : 17.50

The complete table to make a proportional relationship between weight and price is 17.50.

You start with an equation: 1 * 3.50 dollars

You want to multiply both sides of the equation by 5.

So, you have:

1 * 3.50 dollars = 5 * 3.50 dollars

On the left side, when you multiply 1 by 3.50 dollars, you get 3.50 dollars.

On the right side, when you multiply 5 by 3.50 dollars, you get 17.50 dollars.

So, the result of multiplying both sides by 5 is:

3.50 dollars = 17.50 dollars

This shows that if you have 1 item costing 3.50 dollars and you want to buy 5 of those items, the total cost would be 17.50 dollars.

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20 points
Algebra 1
First person to solve it correctly with work gets Brainly! :-) GL

20 pointsAlgebra 1First person to solve it correctly with work gets Brainly! :-) GL

Answers

Answer:

x = -3

Step-by-step explanation:

Step 1: Take log of both sides.

\(log(4^x)=log(2^x^-^3)\) \(x*(log(4)) = (x-3)*(log(2))\) \(x = (\frac{log(2)}{log(4)}) * (x-3)\) \(x = 0.5 * (x-3)\)

Step 2: Simplify.

\(x = (0.5)(x) + (0.5)(-3)\) \(x = 0.5x - 1.5\)

Step 3: Subtract 0.5x from both sides.

\(x - 0.5x = 0.5x - 1.5 - 0.5x\) \(0.5x = -1.5\)

Step 4: Divide both sides by 0.5.

\(\frac{0.5x}{0.5} = \frac{-1.5}{0.5}\) \(x = -3\)

Step 5: Check if solution is correct.

\(4^-^3 = 2^-^3^-^3\) \(\frac{1}{64} = 2^-^6\) \(\frac{1}{64}=\frac{1}{64}\)

Therefore, x = -3.

Q3. Solve the system of equations using 3 iterations of Gauss Seidel method. Start with x= 0.8,=y=0.4,z=−0.45. 6x+y+z=6
x+8y+2z=4
3x+2y+10z=−1

Answers

After three iterations using the Gauss-Seidel method, the approximate values for x, y, and z are x ≈ 0.799, y ≈ 0.445, and z ≈ -0.445.

To solve the system of equations using the Gauss-Seidel method with three iterations, we start with initial values x = 0.8, y = 0.4, and z = -0.45. The system of equations is:

6x + y + z = 6

x + 8y + 2z = 4

3x + 2y + 10z = -1

Iteration 1:

Using the initial values, we can solve the first equation for x:

x = (6 - y - z) / 6

Substituting this value of x into the second equation, we get:

(6 - y - z) / 6 + 8y + 2z = 4

Simplifying:

6 - y - z + 48y + 12z = 24

47y + 11z = 18

Similarly, substituting the initial values into the third equation, we have:

3(0.8) + 2(0.4) + 10(-0.45) = -1

2.4 + 0.8 - 4.5 = -1

-1.3 = -1

Iteration 2:

Using the updated values, we can solve the first equation for x:

x = (6 - y - z) / 6

Substituting this value of x into the second equation, we get:

(6 - y - z) / 6 + 8y + 2z = 4

Simplifying:

6 - y - z + 48y + 12z = 24

47y + 11z = 18

Substituting the updated values into the third equation, we have:

3(0.795) + 2(0.445) + 10(-0.445) = -1

2.385 + 0.89 - 4.45 = -1

-1.175 = -1

Iteration 3:

Using the updated values, we can solve the first equation for x:

x = (6 - y - z) / 6

Substituting this value of x into the second equation, we get:

(6 - y - z) / 6 + 8y + 2z = 4

Simplifying:

6 - y - z + 48y + 12z = 24

47y + 11z = 18

Substituting the updated values into the third equation, we have:

3(0.799) + 2(0.445) + 10(-0.445) = -1

2.397 + 0.89 - 4.45 = -1

-1.163 = -1

After three iterations, the values for x, y, and z are approximately x = 0.799, y = 0.445, and z = -0.445.

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1 2 2 4 3 9 4 16 what is the range of the function please help

Answers

Answer:

Step-by-step explanation:

x            y

1            2

2           4

3           9

4           16

This sounds like a quadratic equation of f(x)=x^2, thus, the range is:

R(x): (-∞,+∞)If the function only has these points, then the range is:R(x): [2]∪[4]∪[9]∪[16]

tan51 degrees = x/14.8. Solve for x. Round to the nearest hundredth.

Answers

Answer:

x ≈ 18.28

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

tan51° = x/14.8

Step 2: Solve for x

Multiply 14.8 on both sides:                    14.8tan51° = xEvaluate:                                                  18.2765 = xRewrite:                                                    x = 18.2765Round:                                                      x ≈ 18.28

Yvonne ran 3/8 of the race stopping for water. She wants to stop for water one more time before finishing the race. List two ways Yvonne can do this

Answers

Yvonne stops for water after 6/8 on the race for one more time.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Yvonne ran 3/8 of the race stopping for water.

This means,

After every 3/8 Yvonne stopped for water.

Now,

Total distance = 1

Distance remaining after one stop.

= 1 - 3/8

= 5/8

And,

Another stop will be after 3/8.

This means,

Distance remains after the second stop.

= 5/8 - 3/8

= 2/8

Now,

1 - 2/8

= 6/8

The second stop is after 6/8 of the race.

Thus,

Yvonne stops for water after 6/8 on the race for one more time.

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Write the equation of the line in fully simplified slope-intercept form.

Write the equation of the line in fully simplified slope-intercept form.

Answers

Answer:

\(y=-\frac{1}{4} x-6\)

Step-by-step explanation:

The slope-intercept form is \(y=mx+c\), where m is the slope of the line and c is where the line crosses the \(y\)-axis.

To calculate \(m\) we can use the formula \(m = \frac{dy}{dx}\) where \(dy\) is the difference in \(y\) between two points and \(dx\) is the difference between \(x\).

Information we can get from the graph given: \(c=-6\). Since \(c\) is the point at which the line crosses the \(y\)-axis.

To find \(m\) let's get two points from the graph.

Point 1: \((4,-7)\)

Point 2: \((8,-8)\)

Now use the equation \(m = \frac{dy}{dx}\).

\(m = \frac{-7 - (-8)}{4-8} = -\frac{1}{4}\).

Now we have \(m\) and \(c\), let's put them back into the general equation.

\(y=-\frac{1}{4} x-6\)

I GIVE BRAINLIST ON ALL MY QUESTIONS !!!!


Which of the
following is an inequality represented by this graph ?

I GIVE BRAINLIST ON ALL MY QUESTIONS !!!!Which of the following is an inequality represented by this

Answers

The answer is c, i am 100% percent sure it is correct

Answer:

y > - 1/3 x + 1

Step-by-step explanation:

?

Mrs. Merton has decided to set up a pie making business. To set herself up in business she must purchase equipment totalling $200, plus each pie that she makes costs her 25 cents. She is planning to sell her pies for $1. 50 each. If x denotes the number of pies that are made, what is the total revenue at breakeven?

Answers

Answer:

$240

Step-by-step explanation:

Breakeven is the revenue with no profit or loss. The money spent is same as money made.

Money spent is200 + 025xMoney made is1.5xSince these are same, the number of pies is200 + 0.25x = 1.5x1.5x - 0.25x = 2001.25x = 200x = 200/1.25x = 160The revenue is200 + 0.25*160 = 200 + 40 = 240

what is the simplified expression of 4(-w+8)

Answers

Answer:

-4w + 32

Step-by-step explanation:

4 (-w + 8)

= (-4 × w) + (4 × 8)

= -4w + 32

Hope it helps :)

Please mark my answer as the brainliest

Answer:

-4w + 32

Step-by-step explanation:

4 (-w + 8)

= (-4 × w) + (4 × 8)

= -4w + 32

Explain how using systems of equations might help you find a better deal on renting a car.

Answers

Answer:

See explanation

Step-by-step explanation:

Using systems of equations will help you find a better deal on renting a car.

Let's use these two equations as an example.

Company A. y=50x+120 where 120 is how much it costs to rent the vehicle and 50 is the rate per day. If you use company A, you will pay $50+$120= $170 for the first day, $220 for two days, etc...

Company B. y=40x+150 where 150 is how much it costs to rent the vehicle and 40 is the rate per day. If you use company B, you will pay $40+$150= $190 for the first day, $230 for two days, etc...

Now you have to take this into consideration - how long you're renting the vehicle for.

If you rent a car for two days, it'll cost $220 with Company A and $230 with Company BIf you rent a car for three days, it'll cost $270 with Company A and $270 with Company B.If you rent a car for four days, it'll cost $320 with Company A and $310 with Company B.

As you can see, at first Company A seems to have the better deal because of its low cost to rent a car, but it has a higher fee per day. Company B had a higher cost to rent a car initially, but the driver will pay a lower fee a day. Using Company A is beneficial for those who desire to rent a car for less than three days and Company B would be cheaper for those renting more than three days.

By using system of equation, you can determine the better deal according to the length of rental by comparing the initial cost and daily rental fee.

4. For data at the interval level, you cannot calculate meaningful differences between data entries.

Answers

For data at the interval​ level, we cannot calculate meaningful differences between data entries. The statement is false.

Interval:

The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.

The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.

Data at the ordinal level can be qualitative or quantitative.  A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries."

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4s4 17s2 14s 2 = (2s3 3s2-4s 1)(x)

Answers

The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

Plot G(8,-6) , H(2,-6) , J(7,4) , and K(7,10) in a coordinate plane. Are GH and JK congruent?

Answers

Answer:

Yes GH ≅JK

Step-by-step explanation:

The line GH and JK are congruent because they measures are equal.

JK line is vertical so the x-coordinate is constant and the difference in y is 10-4 = 6 and

GH line is horizontal so the y-coordinate is constant and the difference in x is 8-2 = 6

Plot G(8,-6) , H(2,-6) , J(7,4) , and K(7,10) in a coordinate plane. Are GH and JK congruent?

4. What are the Z-scores for the following Confidence Interval levels? Remember, you MUST account for both tails of the curve, positive and negative, when identifying each. That means you will need to do a little math to obtain the correct z-value. 3 Points 68%= 85% = 99% =

Answers

In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Solve system elimination
7x-5y=10
-6x-4y=8
11 point a given

Answers

*Answer:

X=0   Y=-2

Step-by-step explanation:

4*(7X-5Y)-5*(-6X-4Y)=4*10-5*8

28X-20Y+30X+20Y=0

58X=0

X=0

-5Y=10

Y=-2

Mai and Noah also solved the equation, but some of their steps have errors. Fid the incorrect step in each solution and explain why it is incorrect.

Answers

Answer:

what equation

Step-by-step explanation:

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Samantha, a high school teacher, wants to spend more time with her childrenand is looking for a part-time job in her field. What would be a good careeralternative for her?A. TutorB. Administrative assistantC. Pet groomerD. Restaurant managerNo link please loukas is the ceo of a company that makes laundry detergent. even in this very competitive market, loukas acts with ________ to take actions that benefit the interests of society as well as the organization. I DONT KNOW LOL PLS HELO AGAIN FOR MY TEST.. I am trying to score a good score but I understand nothing Your mother takes you to your grandparents house for dinner. She drives 30 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives for another 30 minutes at a constant speed of 80 miles per hour. How far did you and your mom travel altogether? .vfncjhfbntbdnfkurbtncivt mckcudv dmdj Someone pls help???????????????????????? 01:47:40How has the development of technology positively affected our wellness?A It has provided entertainment in which people are less active.B. It has increased the quality and availability of treatments.C. It has increased the amount of advertising on the Internet.D. Some technology has led to an increase in pollution.Please select the best answer from the choices provided. Which does not describe cognitive developmental theory as understood by multicultural education advocates?a) Learning must be meaningful.b) Learning is limited to basic academic skills in reading, writing and computing.c) Learning comes from the interaction of the mind and experience.d) Learning is a process of meaning making. i had 6 cupcakes two days ago, and 9 yesterday. help me continue this pattern. thank you. What is the solution for -10 < x - 9?x > -19x < -1x < -19x > -1 How did Johannes Gutenberg MOST influence history?*Right answers only 6Yellow78YellowNick decided to exercise for1 hour on Mondays, hour onWednesdays, and hour onFridays.Green1012Blue14How many total hours willNick exercise if he sticks tothis schedule for 4 weeks?15Red1618OrangeIH192021Yellow If you deposit $300 in an account with a 6% interest rate, how much will be in your account after 1 year? $ If you leave this money in the account, how much will be in your account after 2 years? Mr. reams mixes 12 cups of paint in a large bowl. he uses the paint to fill 40 small dishes with 2 fluid ounces of paint each. how many cups of paint does mr. teams have left in the bowl? Yo _____ a las once y media Which figure from Russian history does Napoleon most likely represent?Lenin, who led the rebellion against the tsar in the name of communismMarx, who outlined a new social philosophy in the Communist ManifestoStalin, who built a dictatorship under the guise of communismTrotsky, who was ultimately banished from the Communist Party 3(47)=27How do I solve this so i have a question, I've been making edits and animation, but while working any of you guys have tricks? (App i use for editing: kinemaster) If an auditor conducts an audit of financial statements in accordance with applicable auditing standards, which of the following will the auditor most likely detect?a. Misposting of recorded transactionsb. Unrecorded transactionsc. Forgeryd. Collusive fraud Student life did a survey of students in which they asked about voting in the most recent student election. The results were: Part-time Student Full-time Student Row Total Voted 15 20 35 Did not vote 25 30 55 Column Total 40 50 90 If a student is selected at random from this group of 90 students, find the probability that: a) the student voted in the most recent election. b) the student voted in the most recent election, given the student is part-time. c) the student voted in the most recent election and the student is part-time. d) Are the events student voted and student is part-time independent? Explain.