Please awnser asap I will brainlist

To find three points on the circle defined by the equation (x+67)2+(y+4)2=494(x+76​)2+(y+4)2=449​, we can manipulate the equation to extract the center and radius information.

Expanding the equation, we have:

x2+127x+3649+y2+8y+16=494x2+712​x+4936​+y2+8y+16=449​

Combining like terms, we get:

x2+y2+127x+8y+1149=0x2+y2+712​x+8y+4911​=0

Comparing this equation to the standard form of a circle, (x−a)2+(y−b)2=r2(x−a)2+(y−b)2=r2, we can identify the center (a,b)(a,b) as −67,−4−76​,−4 and the radius rr as 7227​.

Now we can find three points on the circle by substituting different angles into the equation. For example:

   At 00 degrees: (−6/7+72),−4(−6/7+27​),−4 or (11/14,−4)(11/14,−4)

   At 9090 degrees: −6/7,−4+72−6/7,−4+27​ or −6/7,1/2−6/7,1/2

   At 180180 degrees: (−6/7−72),−4(−6/7−27​),−4 or (−55/14,−4)(−55/14,−4)

Therefore, three points on the circle are (11/14,−4)(11/14,−4), (−6/7,1/2)(−6/7,1/2), and (−55/14,−4)(−55/14,−4).

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The average speed in miles per minute during the interval of 30 and 40 is -1.5 miles per minute

From the question, we have the following parameters that can be used in our computation:

The graph

During the interval of 30 and 40, we have

Distances = 15 and 0

So, we have

Average speed = (15 - 0)/(30 - 40)

Evaluate

Average speed = -1.5

Hence, the average speed in miles per minute is -1.5

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The notation of the transformation of the polygons is (x, y) = (x - 9, y + 2)

From the question, we have the following parameters that can be used in our computation:

The polygons 1 and 2

In the graph, we can see that

using the above as a guide, we have the following:

(x, y) = (x - 9, y + 2)

This means that the transformation of the polygons is (x, y) = (x - 9, y + 2)

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

Yes; TSU ~ PJM

Step-by-step explanation:

Because the angle in between the sides are the same, we can see if each corresponding side is proportional to each other. If they are, then they are similar. (This is SAS similarity theorem)

First we can divide 10 by 15 and see if 14 divided by 21 is the same:

10/15 = 0.6666....

14/21 = 0.6666....

Yes, the two triangles are similar

Answer:

Δ STU  [tex]\bold{\sim}[/tex]  ΔPJM similar

Step-by-step explanation:

Similar triangles are two or more triangles that have the same shape, but their sides are in proportion. In other words, if you divide the length of any side of one triangle by the corresponding side of another triangle, you will get the same number.

For Question:

In Δ STU and ΔPJM

TS:US =10:14=5:7

PJ: JM=15:21= 5:7

Since the length of any side of one triangle is by the corresponding side of another triangle, you will get the same number.

Therefore,

Δ STU  [tex]\bold{\sim}[/tex]  ΔPJM is similar.

Hence Proved:

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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Answer:1 11/12

Step-by-step explanation:

State the null and alternative hypotheses.

c. H0: µ = 0, Ha: µ > 3

The null hypothesis (H0) states that the population mean rating is equal to 3, while the alternative hypothesis (Ha) suggests that the population mean rating is greater than 3.

Specify the rejection region for α = 0.01. Reject H0 if

a. z > 2.33

The rejection region for a one-tailed test with a significance level of 0.01 (α) is in the upper tail of the distribution. In this case, we reject the null hypothesis if the test statistic (z-score) is greater than 2.33.

Calculate the test statistic

c. 0.44

To calculate the test statistic, we use the formula:

z = (sample mean - population mean) / (sample standard deviation / √n)

Plugging in the given values, we get:

z = (3.31 - 3) / (0.70 / √172) ≈ 0.44

What is your conclusion?

b. Fail to Reject H0

Since the calculated test statistic (0.44) does not exceed the critical value (2.33) in the rejection region, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the average rating is significantly greater than 3 in the population.

Obtain the lower bound of a 99% confidence interval for the mean rating.

d. 3.17

To obtain the lower bound of a 99% confidence interval, we subtract the margin of error from the sample mean. The margin of error can be calculated by multiplying the critical value (obtained from the z-table for a 99% confidence level) with the standard error (sample standard deviation divided by the square root of the sample size).

The lower bound is given by:

3.31 - (2.33 * (0.70 / √172)) ≈ 3.17

Obtain the upper bound of a 99% confidence interval for the mean rating.

c. 3.44

To obtain the upper bound of a 99% confidence interval, we add the margin of error to the sample mean. Using the same calculation as above, the upper bound is given by:

3.31 + (2.33 * (0.70 / √172)) ≈ 3.44

What assumption(s) do you need to make in order to answer the above questions?

b. The population distribution is assumed to be normal.

To perform hypothesis testing and construct confidence intervals, it is typically assumed that the population distribution is approximately normal. Additionally, assumptions such as random sampling and independence of observations are generally made.

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Step-by-step explanation:

I am going to assume that = sign should be the ≅.

For the Statements :

1. AB=DC

AB ll DC

2. Line AC is the transversal of AB and CD

3. Angle BAC ≅ Angle DCA

4. Angle BCA ≅ Angle DAC

5. Line AC=Line AC

6. Triangle ABC ≅ Triangle CDA

For the Reasons:

1. Given

2. Definition of a transversal

3. Alternate Interior Angles

4. Alternate Interior Angles

5. Reflexive Property

6. ASA

Answer:

We cannot determine if the triangles are similar.

Step-by-step explanation:

The diagram shows two triangles, ΔABC and ΔDEF.

The tick marks on the sides of the triangles show that two corresponding sides are congruent:

In similar triangles:

As the diagram does not include any information about the interior angles or the length of the third side, we cannot determine if the triangles are similar.

To prove the triangles are similar by SAS similarity, we would need the measure of the included angles (angles B and E).

To prove the triangles are similar by SSS similarity, we would need the measure of the third side.

To prove the triangles are similar by AA similarity, we would need the measures of two corresponding angles.

The instantaneous rate of change of f(x)=4-2 [tex]x^{2}[/tex] at x=0.5 is −2. This means that at that specific point, the function is changing at a rate of -2 units per unit change in x.

The instantaneous rate of change of a function at a specific point can be found by taking the derivative of the function and evaluating it at that point. In this case, we have the function f(x)=4-2 [tex]x^{2}[/tex] and we want to find the instantaneous rate of change at x=0.5.

To find the derivative of f(x), we apply the power rule for differentiation. Taking the derivative of each term, the derivative of 4 is 0, and the derivative of −2[tex]x^{2}[/tex] is −4x. Therefore, the derivative of f(x) is  (x)=−4x.

Now, to find the instantaneous rate of change at x=0.5, we substitute

x=0.5 into the derivative function. f′(0.5)=−4(0.5)=−2.

This means that the function is changing at a rate of -2 units per unit change in x.

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Answer:

The least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.

Step-by-step explanation:

To find the least number that should be subtracted from 1456 to make a perfect square with formula, we need to use the formula for the square of a number.

(n + a)squared = nsquared + 2nas + asquared

In our case, since we want to find the least number to be subtracted, we need to make the result of the formula 2nas + asquared negative (so the difference is a perfect square)

2nas + asquared < 0

Let's try for some values of n:

1456 - n = aperfect square

1456 - 5^2 = (1456 - 25)^2 = 1431^2

1456 - 7^2 = (1456 - 49)^2 = 1407^2

1456 - 9^2 = (1456 - 81)^2 = 1375^2

Since 1375^2 is the smallest of the squares calculated so far, we can conclude that the smallest number that should be subtracted from 1456 to make a perfect square formula with a perfect square result is 1456 - 9^2 == 1456 - 81 == 9^2 == 81

So in this case, the least number that should be subtracted from 1456 to make a perfect square with formula is 9^2, which is equal to 81.

Therefore, for a double batch of 2,000 lbs of flour in mixer 1, you would need 8,000 lbs of water.

To determine the amount of water needed for a double batch of 2,000 pounds (lbs) of flour in mixer 1, we need to consider the ratio of water to flour.

Typically, when making a batch, there is a specific ratio of water to flour. Let's assume the ratio is 1:2, meaning for every 1 pound of flour, we need 2 pounds of water.

For a double batch, we need to multiply the amount of flour by 2:

2,000 lbs of flour × 2 = 4,000 lbs of flour.

Using the ratio, we multiply the amount of flour by the ratio:

4,000 lbs of flour × 2 lbs of water per 1 lb of flour = 8,000 lbs of water.

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Answer:

  (b)  x + 6

Step-by-step explanation:

You want the rule for the x-coordinate when the transformation is a right shift of 6 units.

A point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.

The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:

  x ⇒ x+6 . . . . . . the x-coordinate transformation rule

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Avoidable costs are costs that can be eliminated if the activity that caused them is discontinued. The examples are listed.

Direct materials: Direct materials are the materials that go into a product and can be easily traced to it. For example, the wood used to make a table is a direct material. If a company decides to stop making tables, it can avoid the cost of buying wood.

Direct labor: Direct labor is the labor that is directly involved in making a product. For example, the wages paid to the workers who assemble a car are direct labor. If a company decides to stop making cars, it can avoid the cost of paying direct labor.

Variable overhead: Variable overhead is the overhead costs that vary with the number of units produced. For example, the cost of electricity used to power a factory is a variable overhead cost. If a company decides to stop producing a product, it can avoid the variable overhead costs associated with that product.

Sunk costs: Sunk costs are costs that have already been incurred and cannot be recovered. For example, the cost of research and development for a new product is a sunk cost. If the company decides not to launch the product, it cannot recover the cost of research and development.

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The valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.

Let's solve each inequality step by step:

1. Two less than a number (x) is no more than 5:

The inequality is given as x - 2 ≤ 5. Adding 2 to both sides, we get x ≤ 7. This means that any number less than or equal to 7 satisfies the inequality.

2. Seven subtracted from 4 times a number (x) is more than 13:

The inequality is given as 4x - 7 > 13. Adding 7 to both sides, we get 4x > 20. Dividing both sides by 4, we obtain x > 5. So any number greater than 5 satisfies the inequality.

3. The sum of two times a number (x) and -2 is at least 8:

The inequality is given as 2x - 2 ≥ 8. Adding 2 to both sides, we get 2x ≥ 10. Dividing both sides by 2, we have x ≥ 5. So any number greater than or equal to 5 satisfies the inequality.

4. Four added to 3 times a number (x) is less than 19:

The inequality is given as 3x + 4 < 19. Subtracting 4 from both sides, we get 3x < 15. Dividing both sides by 3, we obtain x < 5. So any number less than 5 satisfies the inequality.

Based on the above solutions, the valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. These numbers can be represented on a number line graph by marking the appropriate points and shading the corresponding regions.

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The situation in which you would add 9 is c) 9 more than a number.

Addition is one of the four basic mathematical operations, including subtraction, multiplication, and division.

Mathematical operations involve the use of mathematical operands on variables, numbers, constants, and values to create algebraic expressions, equations, and functions.

Various Cases:

a) decrease of 9: What is required here is the subtraction of 9 and not addition.

b) descend 9 feet: When an object or person descends 9 feet, the measurement calls for a subtraction operation.

c) 9 more than a number: Addition operation is required to make a number to become 9 more than it was previously.

d) product of a number and 9: The product of a number and 9 involves multiplication and will not make add 9 to the number.

Thus, the addition of 9 is required in case c).

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a) decrease of 9

b) descend 9 feet

c) 9 more than a number

d) product of a number and 9

Answer:

Don has 75 marbles to sell,  Mark has 24 marbles to sell

Step-by-step explanation:

Don has three more than three times the number of marbles Mark has

Now this information can be put into equation form

(In this equation, D = Don and M = Mark)

Equation:

D = 3M + 3

The total number of marbles is 99

This represented as an equation is:

D + M = 99

Now, with both of these equations, it is now a system of equations. Now you must solve the system of equations.

Substitute the value of D from the first equation into the second equation

(3M + 3) + M = 99

4M + 3 = 99

4M = 99 - 3

4M = 96

M = 96/4

M = 24

Now you can substitute the value of M back into the first equation to find the value of D

D = 3(24) + 3

D = 72 + 3

D = 75

This shows that Don has 75 marbles to sell, and Mark has 24.

The solution above is graphed correctly in the last option choice is x > -6

We have been given the equation 2x + 3> -9

In order to graph the solution, we must find the value of x

2x + 3 > -9

Subtract three from both sides

-9 - 3 = -12

2x > -12

Divide both sides by 2

x > -6

Examine the inequality symbol to figure out how to graph the solution. If the sign is "greater than," graph the line to the left. If it was "less than," you would draw a straight line.

We have the "greater than" symbol in our issue, which implies we will graph our line to the right, and since we start our line at -6, we know the last choice is the correct solution.

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The following question may be like this:

Which graph shows the solution set for 2x+3>-9.

Using concentration-volume relationship, 30 ml of potassium chloride should be added to the IV solution.

To calculate the amount of potassium chloride to be added to the IV, we need to consider the concentration of the potassium chloride ampoules and the desired final concentration in the IV solution.

Given:

Physician's order: Add 60mEq of potassium chloride to 1000ml D5W

Potassium chloride concentration in ampoules: 40 mEq per 20 ml

Desired final concentration: Not specified

To determine the amount of potassium chloride to be added, we can set up a proportion based on the mEq (milliequivalents) of potassium chloride:

This is done using concentration-volume relationship

40 mEq / 20 ml = 60 mEq / x ml

Cross-multiplying, we have:

40 mEq * x ml = 60 mEq * 20 ml

Simplifying:

40x = 1200

Dividing both sides by 40:

x = 30 ml

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Answer: $2.21

Step-by-step explanation:

To calculate the cost per pound of mushrooms, we need to use the yield factor given in the question. The yield factor tells us the percentage of the total weight of the mushrooms that can be used for cooking or sale. Here, the yield factor is 90%, which means that 90% of the weight of the mushrooms can be used. Let's begin with the calculation:

First, we need to find out how much of the weight of the mushrooms is usable: 90% of 15 pounds = 0.9 x 15 = 13.5 pounds

Now, we can find out the cost per pound of the mushrooms:

Cost per pound = Total cost / Total usable weight

Total cost = $29.85

Total usable weight = 13.5 pounds

Therefore, the cost per pound of mushrooms = $29.85 / 13.5 pounds ≈ $2.21 per pound

Therefore, the cost per pound of mushrooms is $2.21 per pound.

Answer:

3.36643191324

-1.36643191324

Step-by-step explanation:

subtract 23 from both sides so that everything is on one side

5x²-10x-23=0

you can't factor this, so you need to use the quadratic formula:

(-b±√(b²-4*a*c))/2a

in our case, a= 5 b= -10 and c = -23

(-(-10)±√(10²-4*5*(-23)))/(2*5)

(10±√(100+460))/10

(10±√560)/10

we solve this twice. once where ± is + and again where ± is -

(10+√560)/10 = 3.36643191324

(10-√560)/10= -1.36643191324

Answer:

The interval from -12 to -7

The interval from 6 to 12.

Step-by-step explanation:

The equation is log(x + 9) + log(x 9) = log[(x + 9)(x 9)]. = log(x² − 81)

Here is the equation:

log(x² - 81) = 0.47712

This can be expressed in exponential form:

x² - 81 = 10^(0.47712)

x² = 81 + 3.02343

x² = 84.02343

x ≈ ± 9.1658

The answers are therefore x -9.1658 and x 9.1658.

These intervals are where these solutions occur:

The answer, x -9.1658, can be found in the range from -12 to -7.

- The answer x = 9.1658 is found in the range of 6 to 12.

The appropriate choices are:

- The range between -7 and -12; - The range between 6 and 12.

The complete factorization of the polynomial x³+2x²+x+2 is(x-1)(x+1)(x+2).

To factorize the polynomial x³+2x²+x+2 completely, one may use the rational root theorem, and synthetic division method.

Therefore, first we list the factors of 2 and divide it by the factors of 1 as the leading coefficient:Factors of 2 = ±1, ±2Factors of 1 = ±1Therefore, the possible rational roots for the given polynomial equation are± 1, ±2From the given polynomial, x³+2x²+x+2,

we can easily see that there is no remainder when divided by (x-1). Hence, (x-1) is a factor of the polynomial and we can use synthetic division to factorize the polynomial.x³+2x²+x+2 = (x-1)(x²+3x+2)Now we can use the quadratic formula or factoring to find the remaining factors. We get,x²+3x+2 = (x+1)(x+2).

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To prepare a July 31 Balance Sheet for Academic Learning Services, you would need access to the financial statements and records provided in the class, as well as the information from Practical Exercise

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Answer/Step-by-step explanation:

A cook has 6 onions that have a total mass of 900 grams and 8 apples that have a total mass of 1 kilogram. All onions are the same size, and all apples are the same size. Which has the greater mass, an onion or an apple? Explain.

1. Underline the question you need to answer.

See above

2. What units are used in the problem?

The units used are grams and kilograms.

3. What should you do before comparing the masses?

Before comparing masses you should make sure that the apples and onions unit's are both the same.

4. How many kilograms is 900 grams?

0.9 kilograms

---

This is solved by creating a proportion:

Proportion is a mathematical comparison between two ratios (or fractions) and are equal to each other.

We know that 1 kilogram = 1000 grams

You can remember this by the fact that the prefix kilo = 1000

Your proportion would be set up as:

1 kilogram/ 1000 grams = x kilograms/ 900 grams

we can multiply 900 grams on both sides to isolate x (get x by itself)

900 grams * 1 kilogram/ 1000 grams = 900 grams * x kilograms/ 900 grams

simplified it would look like:

900 kg/1000 = x kg

x = 0.9 kg

So 0.9 kilograms is equal to 900 grams.

---

5. How many grams is 1 kilograms?

There are 1000 grams in 1 kilograms.

6. What do you need to do find the mass of 1 onion and 1 apple? Explain.

To find the mass of one onion you must divide the total mass of onions (900 grams) by 6, and you get that one onion is equal to 150 grams. To find the mass of one apple you can first convert its total mass (1 k) to grams, which equals 1000 grams. Now you can take its total mass in grams and divide it by 8. You get that one apple is equal to 125 grams.

Which has the greater mass, an onion or an apple? Explain

An onion has a greater mass than the apple because one onion has mass of 150 grams, which is greater than one apple's mass of 125 grams.

(1) The full payment required on January 22 to reduce the balance on the invoice to zero is $136,294.57.

(2)The full payment required on October 19 to reduce the balance on the invoice to zero is $98,482.75.

(3)The full payment required on April 3 to reduce the balance on the invoice to zero is $48,190.38.

The calculation of the full payment required takes into account the terms specified on the invoice. In the first scenario, the invoice terms are 2/10, n/30, which means that a 2% discount can be applied if payment is made within 10 days, otherwise, the full payment is due within 30 days.

Therefore, the full payment is calculated as the invoice amount minus the discount. Similarly, for the second scenario, the invoice terms are 3/10, 2/20, 1/30, and n/50, which involve multiple discounts based on different payment dates.

The full payment is determined by applying the applicable discounts. Finally, in the third scenario, the invoice terms are ROG (Receipt of Goods), and the full payment is due by April 15. Hence, the full payment required on the specified date is calculated.

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It will cost $1080 to paint all the interior surfaces of the pool.

6. & 7. The triangles have sides of 8, 8, and 10 cm, and an area of 24 square cm. The remaining areas are 18 and 12 square cm, respectively.

Triangle with Sides 8, 8, and 10 cm: First, we must calculate the area of the whole triangle, which has sides of 8, 8, and 10 cm. Using the Heron's formula, we can find the area of a triangle given the lengths of its sides: A = √(s(s - a)(s - b)(s - c)), where s = (a + b + c)/2 is the semi perimeter of the triangle.

A = √(13(13 - 8)(13 - 8)(13 - 10)) = √(13(5)(5)(3)) = √(2925) = 15√(65) ≈ 59.17 square cm. Next, we can calculate the areas of the shaded regions as follows: Area of Shaded Region 1 = Area of Whole Triangle - Area of Small Triangle Area of Shaded Region 1 = 15√(65) - 18 = 15√(65) - 6√(65) = 9√(65) ≈ 27.94 square cm.

Area of Shaded Region 2 = Area of Whole Triangle - Area of Large Triangle Area of Shaded Region 2 = 15√(65) - 24 = 3√(65) ≈ 7.74 square cm.7.

A swimming pool has the dimensions 8 m (length), 6 m (width), and 1.5 m (depth). The total area to be painted is the sum of the areas of the floor, the ceiling, and the walls of the pool. Since the pool is rectangular in shape, we can break it down into six different parts: the top and bottom surfaces, and the four vertical surfaces.

Let's begin by calculating the area of the floor, which has dimensions of 8 m by 6 m:Area of Floor = length x width = 8 x 6 = 48 square meters.

Next, we can calculate the area of the ceiling, which has the same dimensions as the floor: Area of Ceiling = length x width = 48 square meters. Since the pool has a depth of 1.5 m, the total height of the vertical surfaces is 1.5 x 2 = 3 m (since there are two vertical surfaces on each side of the pool).

Thus, the total area of the four vertical surfaces is given by: Area of Walls = perimeter x height = 2(length + width) x height = 2(8 + 6) x 3 = 84 square meters.

Finally, we can calculate the total area to be painted by adding up the area of the floor, ceiling, and walls: Total Area = Area of Floor + Area of Ceiling + Area of Walls Total Area = 48 + 48 + 84 = 180 square meters.

The cost of paint is given as $6 per square meter, so we can calculate the total cost of painting the pool as follows: Cost = Total Area x Cost per Square Meter Cost = 180 x $6 = $1080. Therefore, it will cost $1080 to paint all the interior surfaces of the pool.

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When r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

The expression [3r-15] represents an algebraic expression that depends on the value of r. The condition given is that r is less than 5. To evaluate this expression, we substitute the value of r into the expression and simplify it.

Given that r is less than 5, let's substitute r = 4 into the expression:

[3(4) - 15]

= [12 - 15]

= -3

Therefore, when r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

It's important to note that this answer is specific to the given condition that r is less than 5. If the condition changes or if r is greater than or equal to 5, the result of the expression may be different.

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Answer: 1000

Step-by-step explanation:

If one person can pick up a plate every 10 seconds, then the rate of picking up plates can be represented as 1 plate/10 seconds.

When two people are picking up plates, the rate doubles, so it becomes 2 plates/10 seconds or 1 plate/5 seconds.

To find how long it will take for 200 people to pick up plates, we need to use the formula:

time = amount ÷ rate

Plugging in the values, we get:

time = 200 plates ÷ (1 plate/5 seconds)

time = 200 plates × 5 seconds/plate

time = 1000 seconds

Therefore, it will take 1000 seconds for 200 people to pick up plates at a faster rate.

I hope that this answer has helped you!