PLS HELP WHO EVER ANSWERD FIRST WILL GET THE BRAINLIEST PLS

Leo is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of items she sells. Suppose that x and y are related by the equation y=32x+1900.


What is Leo's total pay if she doesn’t sell any items?

A. $19


B. $3,200


C. $32


D. $1,900

Explain your work pls

Answers

Answer 1

By using Linear equation, it can be calculated that

Leo's total pay if she doesn’t sell any items = $1900

Option D is correct.

What is linear equation?

At first it is important to know about  equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let y represent Leo's total pay (in dollars).

Let x represent the number of items she sells

x and y are related by the equation y=32x+1900.

If Leo does not sell any item, x = 0

y = 32 \(\times\) 0  +1900

y = $1900

Leo's total pay if she doesn’t sell any items = $1900

Option D is correct.

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Related Questions

Please say whether they are equivalent or not

Answers

Answer:

Nothing is here. You may need to reupload question.

Please help i cant get this

Please help i cant get this

Answers

Answer:

0.264

Step-by-step explanation:

Answer:

3 11/14 is your fraction answer

Step-by-step explanation:

Alfonso has a $10 bill. At the grocery store, he buys a loaf of whole wheat bread for $1.99 and 9 bananas. He gets $5.13 in change. What is the price of one banana?
A. $0.32


B. $0.54


C. $0.89


D. $2.88

Answers

10.00-1.99= 8.01
8.01-5.13= 2.88
2.88/9=0.32

One banana is $0.32

If Alfonso has a $10 bill. At the grocery store, he buys a loaf of whole wheat bread for $1.99 and 9 bananas. He gets $5.13 in change. The price of one banana is $0.32

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

Alfonso has a $10 bill.

At the grocery store, he buys a loaf of whole wheat bread for $1.99 and 9 bananas

So $10.00-$1.99= $8.01

We need to find price of one banana.

He gets $5.13 in change.

$8.01-$5.13=$2.88

He used $2.88 to buy nine bananas

The price of each banana we will calculate by dividing $2.88 by 9.

$2.88/9=$0.32

The price of each banana is $0.32, Option A is correct.

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If angle 2 equals (2x+5)degrees and angle 3 equals 85 degrees, what is the value of x?

If angle 2 equals (2x+5)degrees and angle 3 equals 85 degrees, what is the value of x?

Answers

Answer:

x=40

Step-by-step explanation:

2x+5=85

2x+5-5=85-5

2x=80

\frac{2x}{2}=\frac{80}{2}

x=40

The value of x for the given expression in angles will be 40. The correct option is B.

What are supplementary angles?

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet. The supplementary angles are defined as when the sum of the angles is equal to 180 degrees.

Given that ∠2 equals (2x+5)degrees and ∠3 equals 85 degrees. The value of x will be calculated by using the supplementary property of angles.

2x+5=85

2x+5-5=85-5

2x=80

x=40

Therefore, the value of x for the given expression in angles will be 40. The correct option is B.

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1in represents 10 miles. How many miles would 4 inches represent?

Answers

Answer:

the 40 miles would the 4 inches represent

Step-by-step explanation:

The computation of the number of miles represent by 4 inches is shown below:

Given that

1 inches represent 10 miles

So for 4 inches

It represent

= 4 × 10 miles

= 40 miles

hence, the 40 miles would the 4 inches represent

Business solutions's second-quarter 2020 fixed budget performance report for its computer furniture operations follows. the $163,700 budgeted expenses include $110,700 in variable expenses for desks and $18,000 in variable expenses for chairs, as well as $35,000 fixed expenses. the actual expenses include $36,200 fixed expenses. list fixed and variable expenses separately. fixed budget actual results variances desk sales (in units) 135 141 chair sales (in units) 60 68 desk sales $ 174,150 $ 180,480 $ 6,330 f chair sales 30,000 35,020 5,020 f total expenses 163,700 172,640 8,940 u income from operations $ 40,450 $ 42,860 $ 2,410 f prepare a flexible budget performance report that shows any variances between budgeted results and actual results.

Answers

The flexible budget performance report is as follows:

Fixed expenses:

Budgeted: $35,000

Actual: $36,200

Variance: $1,200 unfavorable

Variable expenses:

Budgeted: $128,700

Actual: $136,440

Variance: $7,740 unfavorable

Total expenses:

Budgeted: $163,700

Actual: $172,640

Variance: $8,940 unfavorable

Income from operations:

Budgeted: $40,450

Actual: $42,860

Variance: $2,410 favorable

To prepare a flexible budget performance report that shows the variances between the budgeted results and actual results, we need to calculate the flexible budget and compare it to the actual results.

Fixed Expenses:

Budgeted fixed expenses: $35,000

Actual fixed expenses: $36,200

Fixed expenses variance: $36,200 - $35,000 = $1,200 unfavorable

Variable Expenses for Desks:

Budgeted variable expenses for desks: $110,700

Actual desk sales units: 141

Budgeted variable expense per desk: $110,700 / 135 units = $820 per desk

Flexible budget for desk variable expenses: 141 units * $820 per desk = $115,620

Variable Expenses for Chairs:

Budgeted variable expenses for chairs: $18,000

Actual chair sales units: 68

Budgeted variable expense per chair: $18,000 / 60 units = $300 per chair

Flexible budget for chair variable expenses: 68 units * $300 per chair = $20,400

Now, let's calculate the total flexible budget and the variances:

Total flexible budget: Fixed expenses + Variable expenses = $36,200 + ($115,620 + $20,400) = $172,220

Total expenses variance: Actual expenses - Total flexible budget = $172,640 - $172,220 = $420 unfavorable

Income from operations variance: Actual income - Budgeted income = $42,860 - $40,450 = $2,410 favorable

The report highlights the variances between the budgeted results and the actual results, providing insights into the company's performance in the second quarter of 2020.

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The bacteria population in a small pond is decreasing because of pesticides. Each month, the
population of bacteria decreases. Initially, there were 60,000 bacteria in the pond. Fill in the
blanks for the table and the equation. Please do not use commas.

The bacteria population in a small pond is decreasing because of pesticides. Each month, thepopulation

Answers

The number of bacteria after 3 months is 7500.

The equation is y = 60,000 x \(0.5^3\).

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

Number of bacteria initially = 60,000

After one month,

The number of bacteria = 30,000

This means,

60,000 - 30,000 = 30,000

The percentage decreased.

= 30,000 / 60,000 x 100

= 1/2 x 100

= 50%

Now,

The equation for the number of bacteria after x months.

y = 60,000 x \(0.5^x\)

For x = 3,

y = 60,000 x \(0.5^3\)

y = 60,000 x 0.125

y = 7500

Thus,

The number of bacteria after 3 months is 7500.

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How far does a turtle travel in five minutes

Answers

Answer:

A turtle travels about 90 feet

Because if a turtle can travel 450 feet within 25 minutes, then dividing 25 by 450 is 18 feet per minute, but if you multiply 5 minute x 18 feet, you get 90 feet in all.

So, a turtle can travel 450 feet per 25 minutes,

18 feet per minute, and

90 feet per 5 minutes

Hope this helps and I hope it is right, I used my skill thinking to solve this. So, please let me know if it did help and you do get it.

At the baby next checkup the baby weighed 11 pounds and four ounces how many ounces did the baby gain since the appointment mentioned in the first probloem

Answers

If at the previous appointment the baby weighed 10 pounds and 8 ounces, then the baby has gained 12 ounces since the last appointment.

To calculate this, we need to subtract the weight at the previous appointment from the weight at the current appointment:

11 pounds and 4 ounces - 10 pounds and 8 ounces = 12 ounces

So the baby has gained 12 ounces since the last appointment. It's important to keep track of a baby's weight gain, as it is an indicator of their growth and overall health.

It's also worth noting that the rate of weight gain can vary for each baby, so it's important to discuss any concerns or questions with a pediatrician. Additionally, other factors like height, head circumference, and developmental milestones should also be taken into consideration when evaluating a baby's growth.

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(a) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.
a(t) = 19t i + et j + e−t k, v(0) = k, r(0) = j + k
(b) Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.
a(t) = 8t i + sin t j + cos 2t k, v(0) = i, r(0) = j
r(t) =

Answers

(a)  The position vector of a particle that has the given acceleration and the specified initial velocity and position is

r(t) = 3.17\(t^3\) i + \(e^t\) j + \(e^-t\) k + kt - jt

(b) The position vector of a particle that has the given acceleration and the specified initial velocity and position is

r(t) = 1.33\(t^3\) i + sin t j - 0.25cos 2t k + ti + j

(a) To find the position vector, we need to integrate the acceleration twice with respect to time. First, we integrate the acceleration to get the velocity:

v(t) = ∫ a(t) dt = 9.5\(t^2\) i + \(e^t\) j - \(e^{-t\) k + C1

where C1 is the constant of integration. We can find C1 using the initial velocity:

v(0) = k = 0i + \(e^0\) j - \(e^0\) k + C1

C1 = k - j

So the velocity is:

v(t) = 9.5\(t^2\) i + \(e^t\) j - \(e^{-t\) k + k - j

Next, we integrate the velocity to get the position:

r(t) = ∫ v(t) dt = 3.17\(t^3\) i + \(e^t\) j + \(e^{-t\) k + kt - jt + C2

where C2 is the constant of integration. We can find C2 using the initial position:

r(0) = j + k = 0i + j + k + C2

C2 = 0

So the position vector is:

r(t) = 3.17\(t^3\) i + \(e^t\) j + \(e^-t\) k + kt - jt

(b) Following the same method, we integrate the acceleration to get the velocity:

v(t) = ∫ a(t) dt = 4\(t^2\) i - cos t j + 0.5sin 2t k + C1

where C1 is the constant of integration. We can find C1 using the initial velocity:

v(0) = i = 0i - cos 0 j + 0.5sin 0 k + C1

C1 = i

So the velocity is:

v(t) = 4\(t^2\) i - cos t j + 0.5sin 2t k + i

Next, we integrate the velocity to get the position:

r(t) = ∫ v(t) dt = 1.33\(t^3\) i + sin t j - 0.25cos 2t k + ti + C2

where C2 is the constant of integration. We can find C2 using the initial position:

r(0) = j = 0i + j + 0k + C2

C2 = j

So the position vector is:

r(t) = 1.33\(t^3\) i + sin t j - 0.25cos 2t k + ti + j

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25=125^k find the value of k​

Answers

Answer:

2/3

Step-by-step explanation:

25=125^k

5^2=5^3k

2=3k

k=2/3

The value of k is k = 2/3.

What is an exponent?

The number of times a number is multiplied by itself is referred to as an exponent.

Given that, \(25 = 125^k\).

Follow the steps to find the value of k:

\(25 = 125^k\\\\5^2=(5^3)^k\\\\5^2=5^{3k}\)

Since the base of the exponents is the same, it follows:

2 = 3k

k = 2/3

Hence, the value of k is k = 2/3.

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Rosa earns $120 per week tutoring math. Each week, she puts 36$ from her paycheck in a bank account to save for college. Find the amount Rosa saves out of $100.

Answers

Answer:

30

Step-by-step explanation:

You can do 36*100=3600 and do 3600/120. This is a very simple way to get 30 out of 100

Answer: $30

Step-by-step explanation: If she saves $36 when she earns $120, then she saves *amount =36/120 ×100

Amount saved with $100 earning is $30

which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.

Answers

The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


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. a closet contains n pairs of shoes. if 2r shoes are chosen at random (with 2r < n), what is the probability that there will be (a) no complete pair, (b) exactly one complete pair, (c) exactly two complete pairs among them?

Answers

Answer:

Step-by-step explanation:

Solve this equation:
3x^2y^2-y^7+x^4
When
x=-2
y=1​

Answers

Answer:

27

Step-by-step explanation:

Given:

x = - 2, y = 1

Find the value of the expression:

3x²y² - y⁷ + x⁴ =3(-2)²(1)² - 1⁷ + (-2)⁴ =12 - 1 + 16 =27
3x²y²-y⁷+x⁴3(-2)²(1)²-(1)⁷+(-2)⁴3(4)-1+1612+1527

HELP ASAP I MARK BRAINLIEST

HELP ASAP I MARK BRAINLIEST

Answers

I think it’s choice b

During conventional Pavlovian conditioning, the conditional stimulus is repeatedly presented just before the Group of answer choices conditional response. unconditional stimulus. other conditional stimulus. operant response. classical stimulus.

Answers

During conventional Pavlovian conditioning, the conditional stimulus is repeatedly presented just before the unconditional stimulus.

In Pavlovian conditioning, the conditional stimulus (CS) and the unconditional stimulus (US) play crucial roles in shaping the learning process. The CS refers to a neutral stimulus that, through repeated pairing with the US, comes to evoke a conditioned response (CR) similar to the response elicited by the US. The US, on the other hand, is a stimulus that elicits an unconditioned response (UR) naturally and without prior learning. In the context of conventional Pavlovian conditioning, the CS is repeatedly presented just before the US. This temporal association allows the CS to become a reliable predictor of the US, leading to the formation of an association between the two stimuli. As a result, the CS acquires the ability to elicit a CR that resembles the UR evoked by the US. This process is often referred to as classical conditioning or associative learning, where the CS serves as a signal for the upcoming US and triggers the conditioned response.

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What is the area of the parallelogram ABCD

What is the area of the parallelogram ABCD

Answers

Answer:

16 square units

Step-by-step explanation:

hope that helps

Jeremy rides his bike at a rate of 12 miles per hour. The table below
represents the number of hours and miles Kevin rides. Assume both bikers
ride at a constant rate.

Jeremy rides his bike at a rate of 12 miles per hour. The table belowrepresents the number of hours and

Answers

Answer:

A) Jeremy has the greater speed.  

B) y = 23x

C)  See graph

D) The slope is 23.  This means that Lauren can travel 23 miles in 1 hour.

Step-by-step explanation:

Part A:

Kevin's rate is 11.5 miles per hour.

Take two points, I used (2,23) and (4,46) to find the rate for Kevin.

Find the change in y over the change in x.  The y values are 46 and 23.  The x values are 4 and 2.  You find the change by subtracting

\(\frac{46-23}{4-2}\) = \(\frac{23}{2}\) = 11.5

Part B:

If Kevin's rate is 11.5, then Lauren's rate is 23

Part C:

See graph

 Part D :  

  The slope for C is 23.  This means that Lauren can ride 23 miles in one hour.

Helping in the name of Jesus.                                                                                      

Jeremy rides his bike at a rate of 12 miles per hour. The table belowrepresents the number of hours and

5+5x2=? heh i "ToTaLlY" dont know this

Answers

Answer:

15

Step-by-step explanation:

if r(t) = (4t, 3tยฒ, 4tยณ) , find r'(t), T(1), r''(t), and r'(t) ร r ''(t).

Answers

The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.

We are given the vector-valued function r(t) = (4t, 3t², 4t³).

To find r'(t), we need to take the derivative of each component of r(t) with respect to t:

r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)

r'(t) = (4, 6t, 12t²)

To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):

r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)

| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14

T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)

To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:

r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)

r''(t) = (0, 6, 24t)

Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):

r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)

r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)

r'(t) ร r''(t) = 144t³

Therefore, we have:

r'(t) = (4, 6t, 12t²)

T(1) = (2/7, 3/7, 6/7)

r''(t) = (0, 6, 24t)

r'(t) ร r''(t) = 144t³

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What interest payment is exceeded by only 18% of the bank's Visa cardholders?

Answers

The interest payment exceeded by only 18% of the bank's Visa cardholders refers to the 82nd percentile of the interest payment distribution among Visa cardholders.

To determine the interest payment that is exceeded by only 18% of the bank's Visa cardholders, we need to look at the percentile of the interest payment distribution. Percentiles represent the percentage of values that fall below a certain value.

In this case, we are interested in the 82nd percentile, which means that 82% of the interest payments are below this value, and only 18% of the payments exceed it. The interest payment exceeded by only 18% of the cardholders can be considered as the threshold or cutoff point separating the top 18% from the rest of the distribution.

To find the specific interest payment corresponding to the 82nd percentile, we would need access to the data or a statistical analysis of the interest payment distribution among the bank's Visa cardholders. By identifying the 82nd percentile value, we can determine the interest payment that is exceeded by only 18% of the cardholders.

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we would associate the term inferential statistics with which task?

Answers

Inferential statistics involves using sample data to make inferences, predictions, or generalizations about a larger population, providing valuable insights and conclusions based on statistical analysis.

The term "inferential statistics" is associated with the task of making inferences or drawing conclusions about a population based on sample data.

In other words, it involves using sample data to make generalizations or predictions about a larger population.

Inferential statistics is concerned with analyzing and interpreting data in a way that allows us to make inferences about the population from which the data is collected.

It goes beyond simply describing the sample and aims to make broader statements or predictions about the population as a whole.

This branch of statistics utilizes various techniques and methodologies to draw conclusions from the sample data, such as hypothesis testing, confidence intervals, and regression analysis.

These techniques involve making assumptions about the underlying population and using statistical tools to estimate parameters, test hypotheses, or predict outcomes.

The goal of inferential statistics is to provide insights into the larger population based on a representative sample.

It allows researchers and analysts to generalize their findings beyond the specific sample and make informed decisions or predictions about the population as a whole.

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Toby has five coins. Three of the coins add up to 30p. Three of the coins add up to 40p. All the coins add up to 50p. List Tony's coins in ascending order of value.

Answers

Tony's coins in ascending order of value will be 5p, 10p, and 15p.

How to depict the information?

Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.

In this case, 5p + 10p + 15p = 30p

10p + 15p + 15p = 40p

5p + 5p + 10p + 15p + 15p = 50p

Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.

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Answer:

5p, 5p, 10p, 10p, 20p

Step-by-step explanation:

5p, 5p, 10p, 10p, 20p,

Nolan says the relationship in the table is not proportional because the point (0, 0) does not appear in the table.

Which is the best way to explain to Nolan why he is incorrect?
A. A graph made from the table will be increasing, so it is proportional.
B. Not all proportional relationships contain (0, 0), so it could be proportional.
C. The points on the graph will have even y-coordinates, so it is proportional.
D. Even though (0, 0) is not in the table, the graph is a line through (0, 0), so it is proportional.

Answers

Answer: D. Even though (0, 0) is not in the table, the graph is a line through (0, 0), so it is proportional.

Step-by-step explanation:

The table is not included but this should be the correct answer.

Linear relationships which are proportional will have to pass through the origin which is (0,0). This does not mean that on the table, the points (0,0) have to be there.

Even if it does not explicitly appear in the table, so long as the line passes the origin, it is to be considered a proportional relationship. The (0,0) might not appear on the table because only a few points the line passed through were listed but if when the line is plotted, the line goes through (0,0), it is proportional.

Answer:

D

Step-by-step explanation:

True or false: (log x)2 = 2logx. Explain your thinking.

Answers

False
Well we can’t put 2 log x it’s opposite it’s 2 x log

Please help, I will give brainliest to whoever helps!

Please help, I will give brainliest to whoever helps!

Answers

Answer:

I'm sorry i cant see the photo its very wierd

Step-by-step explanation:

What is simple linear regression? Give an intuitive definition and illustrate with a graph. Label residuals and explain how they are used in the construction of the regression line.

Answers

Simple linear regression is a statistical technique used to model the relationship between two variables by fitting a straight line to the data. It provides a way to predict or estimate the value of one variable (dependent variable) based on the value of another variable (independent variable).

In simple linear regression, the relationship between the independent variable (x) and the dependent variable (y) is represented by a straight line. The goal is to find the best-fitting line that minimizes the differences between the observed values of the dependent variable and the predicted values from the regression line.

A graph illustrating simple linear regression includes the scatterplot of the data points, the regression line, and the residuals. The scatterplot shows the individual data points with the independent variable on the x-axis and the dependent variable on the y-axis. The regression line is the line that best fits the data, minimizing the sum of the squared residuals.

Residuals are the vertical distances between the observed data points and the regression line. They represent the differences or errors between the actual values and the predicted values. By examining the residuals, we can assess how well the regression line fits the data. If the residuals are randomly scattered around zero, it suggests that the linear regression model is appropriate. If there is a pattern or systematic deviation in the residuals, it indicates that the model may not be capturing the underlying relationship accurately.

The regression line is constructed by minimizing the sum of the squared residuals, which is known as the least squares method. This ensures that the line represents the best linear approximation of the relationship between the variables.

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M is the midpoint of RS. R has the coordinates (-12, 4), and M has coordinates (1, -2). What are the coordinates of S?​

Answers

If the point R has the coordinates (-12, 4) and point M has coordinates (1,-2)  then the coordinates of point S are (14 , -8) .

The midpoint (x,y) of the line segment having the endpoints as (a,b) and (c,d) can be calculated by using the formula :

(x,y) = \((\frac{a+c}{2} ,\frac{b+d}{2} )\) ;

The end points of the line segment RS are R (-12, 4) and S(x,y) ,

the point M is the mid point and the coordinate is M (1, -2) .

So , the coordinate of point S are represented as :

(1,-2) = \((\frac{-12+x}{2},\frac{4+y}{2} )\);

Simplifying both the equations ,

we get ;

2 = -12 + x       and     -4 = 4 + y  

x = 12 + 2      and      y = -4 - 4

x = 14       and      y = -8   .

Therefore , the coordinate of S is (14,-8) .

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A research scholar wants to know how many times per hour a certain strand of virus reproduces. He wants to construct the 90%
confidence interval with a maximum error of 0.16
reproductions per hour. Assuming that the mean is 6.2
reproductions and the variance is known to be 5.29
, what is the minimum sample size required for the estimate? Round your answer up to the next integer.

Answers

The minimum sample size required for the estimate, considering the z-distribution, is given as follows:

560.

What is a z-distribution confidence interval?

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

\(\overline{x}\) is the sample mean.z is the critical value.n is the sample size.\(\sigma\) is the standard deviation for the population.

The margin of error is modeled as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The parameters for this problem are given as follows:

\(M = 0.16, \sigma = \sqrt{5.29} = 2.3, z = 1.645\)

Hence the sample size is obtained as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(0.16 = 1.645\frac{2.3}{\sqrt{n}}\)

\(0.16\sqrt{n} = 1.645 \times 2.3\)

\(\sqrt{n} = \frac{1.645 \times 2.3}{0.16}\)

\((\sqrt{n})^2 = \left(\frac{1.645 \times 2.3}{0.16}\right)\)

n = 560. (rounded up).

More can be learned about the z-distribution at https://brainly.com/question/25890103

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