tarting in the 1970s, medical technology allowed babies with very low birth weight (vlbw, less than 1500 grams, or about 3.3 pounds) to survive without major handicaps. it was noticed that these children nonetheless had difficulties in school and as adults. a long study has followed 242 randomly selected vlbw babies to age 20 years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight.49 (a) is this an experiment or an observational study? why? (b) at age 20, 179 of the vlbw group and 193 of the control group had graduated from high school. is the graduation rate among the vlbw group significantly lower than for the normal-birth-weight controls? give appropriate statistical evidence to justify your answer. ap3.33 a nuclear power plant

The ordered pair (z, 11) is not a solution of the inequality.

Explain inequality

An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.

According to the given information

To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:

2z < 15

2(11) < 15

22 < 15 (this is false)

Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.

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The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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Segment CP is tangent to circle C at point B.

How to prove that the line is tangent to a circle?

Draw circle C with center at point A and radius AD = CD = DE.

Draw point P outside the circle C.

Draw segment AP and extend it to intersect the circle at point B.

Draw segment BD.

Draw segment CP.

Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.

Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).

Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).

Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.

Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.

Therefore, segment CP is tangent to circle C at point B.

Hence, the proof is complete.

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The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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Answer:

negative

y=-x

y=-2x+6

y=(-1/2)x+1

y=-5x+20

undefined

x=4

x=-3

zero slope

y=2

y=-100

Therefore , the solution of the given problem of fraction comes out to be the previous week's rainfall total was 7/4 inches.

Any combination of sections of the same size can be used to represent the whole. Quantity is described as "a portion" under a particular measurement in Standard English. 8, 3/4. Fractions are included in wholes. These act as the ratio divisor, which is a pair of integers in mathematical words. Here are a couple of examples showing how to change straightforward halves into entire numbers.

Here,

Let's refer to the amount of rain that fell the previous week as x inches.

The information provided indicates that it rained 2 1/2 inches on Wednesday, which is 3/4 of an inch more than the quantity that fell the previous week. This knowledge can be expressed as an equation:

=> 2 1/2 = x + 3/4

=> 2 1/2 - 3/4 = x

=> 2 1/2 = 5/2

=> 3/4 = 3/4

=> 5/2 - 3/4 = x

In this instance, 2 and 4 have a common denominator of 4, which is 4. So, using 4 as the common denominator, we can rewrite the fractions as follows:

=> 5/2 - 3/4 = x

=> (5/2) × (2/2) - 3/4 = x

=> 10/4 - 3/4 = x

=> 7/4 = x

Therefore, the previous week's rainfall total was 7/4 inches.

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Answer: We can use a proportion to estimate the total number of fur seal pups in Rookery A. Let x be the total number of fur seal pups in Rookery A. Then we have:

6269/x = 221/1100

Cross-multiplying, we get:

221x = 6269 * 1100

Dividing both sides by 221, we get:

x = 6269 * 1100 / 221

Simplifying, we get:

x = 31,245.25

Rounding to the nearest whole number, we get:

x ≈ 31,245

Therefore, the estimated total number of fur seal pups in Rookery A is 31,245.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x²-3x - 10 = 0

x² -5x + 2x - 10 = 0

(x² -5x)+ (2x - 10) = 0

x(x - 5) +2(x - 5) = 0

(x + 2) (x - 5) = 0

x +2 = 0

x = -2

OR

x -5 = 0

x = 5

hence ans is, (1) {5,-2}

Two consecutive integers in algebraic language would be 7 and 8

Let's call the first integer "X" then the next consecutive integer would be "x+1".

so if the sum of the two integers is 15, we can write the following expression.

x + (x+1) = 15

Solving for x  we get  
2x + 1 = 15
2x =14
x = 7

Hence, the two consecutive integers in this case are 7 and 8.

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Translation:

Two consecutive integers in algebraic language

Without specific data from the survey, I cannot provide the exact average length of time a person lived in the slums. I can be found by collecting data and finding average.

In general, surveys can be used to gather information on a population's characteristics and experiences, including their life expectancy. If the survey conducted in the slums of Nairobi included questions about life expectancy or mortality rates, the average lifespan of the individuals surveyed could be calculated using the data collected. It's important to note that the average lifespan in the slums may differ from that of other areas in Nairobi or other regions of the world.
Based on the information provided, Dr. Salon mentioned a survey conducted in the slums of Nairobi. To determine how long the average person lived in the slums, we would follow these steps:

1. Collect the data: The survey would gather information about the length of time people lived in the slums.
2. Calculate the average: Add up the total number of years all respondents lived in the slums and divide by the total number of respondents.

Without specific data from the survey, can't provide the exact average length of time a person lived in the slums. Please provide more information or refer back to Dr. Salon's lecture for the results of the survey.

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The answer is 24. To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Numbers are often used to measure and compare objects, and they can be used to solve problems and make predictions.

8 1/2% is equal to 0.04.

To calculate the number of poetry books for children, multiply 0.04 by 600.

0.04 x 600 = 24

To find the number of poetry books for children, the decimal equivalent of 8 1/2% needs to be multiplied by the total number of poetry books.

In conclusion, 8 1/2% of 600 poetry books is equal to 24 books.

To calculate this, 8 1/2% needs to be converted to a decimal by dividing it by 100.

Then, the decimal needs to be multiplied by the total number of poetry books. This will give the answer, which can be rounded down if necessary.

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Answer:

13.416407865

Step-by-step explanation:

You wouldn't use soh cah toa

There is no angle given. Instead you should do 6²+12²=180

And then you would square root 180=13.416407865

Therefore the answer is 13.416407865

1) The equation (x + 6)² + (y + 4)² = 36 represents a circle centered at the point (-6, -4) with a radius of 6. Therefore, the signal is located at the point (-6, -4).

2) The range of the signal refers to the maximum distance that the signal can travel before it becomes too weak to be detected. In this case, the range of the signal is equal to the radius of the circle, which is 6. This means that any point on the circle (x + 6)² + (y + 4)² = 36 is 6 units away from the signal located at (-6, -4).

To visualize this, imagine the signal as a point source located at (-6, -4), and the range of the signal as a circle centered at the signal with a radius of 6. Any point on this circle represents the farthest distance that the signal can reach and still be detected.

In summary, the signal is located at (-6, -4) and its range is 6 units, as represented by the circle (x + 6)² + (y + 4)² = 36.

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Answer:

[tex]y = \frac{1}{3} x + 3[/tex]

Step-by-step explanation:

Start at the point (-3, 2). Go up 1 unit, then right 3 units, to the point (0, 3). The slope of the line is 1/3, and the y-intercept is 3, so we have

[tex] y = \frac{1}{3} x + 3[/tex]

The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.

We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.

The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.

Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.

The probability that the first job is finished before 10:01 is given by:

P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935

Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:

P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693

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Answer: 39°

Step-by-step explanation:

In an isosceles triangle, two sides are of equal length, and the angles opposite these equal sides are also equal. Let's call these two equal angles x. Given that one angle measures 102°, we can find the possible measures for the other two angles.

The sum of the interior angles of a triangle is always 180°. So, we have:

x + x + 102° = 180°

2x = 180° - 102°

2x = 78°

x = 39°

Therefore, the other two angles in the isosceles triangle are both 39°.

Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.

Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour

Answer: Let's say we want to find out how many red Skittles we need to add to the bag to have the same ratio of red Skittles as in the original bag.

Suppose the original bag contains x red Skittles. Then, the ratio of red Skittles to the total number of Skittles in the bag is x/100.

Let's say we add y red Skittles to the bag, so the total number of red Skittles in the bag becomes x + y. The total number of Skittles in the bag becomes 100 + y, since we only added red Skittles.

For the ratio of red Skittles to be the same as in the original bag, we need:

(x + y) / (100 + y) = x / 100

Cross-multiplying, we get:

100(x + y) = x(100 + y)

Simplifying and rearranging, we get:

y = 100x / (100 - x)

So, we need to add 100x / (100 - x) red Skittles to the bag to have the same ratio of red Skittles as in the original bag. For example, if the original bag has 20 red Skittles, we need to add:

y = 100(20) / (100 - 20) = 25

So, we need to add 25 red Skittles to the bag to have the same ratio of red Skittles as in the original bag.

Step-by-step explanation:

Nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
Without knowing the travel times of the two nurses, it is not possible to determine the differences in their travel times for a random day.

Assuming that each trip from the nursing pod to a room and back is approximately 50 feet and each trip to the central medical supply, break room, and linen supply is approximately 100 feet, nurse Susan Jones would walk a total of:
- 7 trips to each of the 12 rooms = 7 x 12 x 2 x 50 feet = 8,400 feet
- 20 trips to the central medical supply = 20 x 2 x 100 feet = 4,000 feet
- 6 trips to the break room = 6 x 2 x 100 feet = 1,200 feet
- 12 trips to the pod linen supply = 12 x 2 x 100 feet = 2,400 feet
Therefore, nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.

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Nurse Susan Jones would walk nearly 34.4 miles during her shift.

Assuming that Nurse Susan Jones walks an average of 0.2 miles per round trip, she would walk approximately 34.4 miles during her shift (7 trips x 12 rooms x 2 round trips x 0.2 miles per round trip + 20 trips x 2 round trips x 0.2 miles per round trip + 6 trips x 2 round trips x 0.2 miles per round trip + 12 trips x 2 round trips x 0.2 miles per round trip).

Unfortunately, there is not enough information provided to calculate the differences in travel times between two nurses on a random day. It would depend on factors such as the number and location of rooms each nurse is responsible for, the location of the medical supply and break room, and any additional tasks or responsibilities each nurse has during their shift.

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The probability that the sample mean would be less than 100.9 months is approximately 0.9600.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as a normal distribution with a mean of 97 months (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

The standard deviation of the sampling distribution can be calculated as follows

σ/√n = √(169)/√59 = 2.065

Therefore, the z-score corresponding to a sample mean of 100.9 months is

z = (100.9 - 97) / 2.065 = 1.75

Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score less than 1.75 is approximately 0.9599.

Therefore, the probability that the sample mean would be less than 100.9 months is approximately 0.9599.

Rounding this to four decimal places, we get

P(x < 100.9) ≈ 0.9600

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Answer:

Step-by-step explanation:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

When comparing the data from the two locations, the measure of center that should be used to determine which location typically has the cooler temperature is the median.

In Sunny Town, the histogram shows that the shaded bars are skewed to the right, indicating that the distribution is positively skewed. This means that there are a few high temperatures that pull the mean towards the higher end.

However, the median, which represents the middle value when the data is arranged in ascending order, is less affected by extreme values and is a better measure of the center for skewed distributions.In Desert Landing, the histogram shows a symmetric distribution, with the shaded bars evenly distributed around the center.

In this case, both the mean and median can be considered reliable measures of the center.Therefore, to determine which location typically has the cooler temperature, we should use the median.

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Answer: a and d

Step-by-step explanation:

1 pear = 3 slices

5 pears = 15 slices

5x3=15

OR

5/1/3=15

Equation A and Equation D are the two equations that Kylie can use to solve the problem.

This is a simple mathematics problem.

Kylie has five pears. She cuts each of her pears into thirds, i.e., three slices of each pear.

So, now Kylie will do the same for each pear she has:

Total Slices with Kylie = 5 x 3

Total Slices with Kylie = 15

Equation D can also be used to define the situation of Kylie. Total pears with her are five and each pear is divided into thirds, i.e., 1/3

Total Slices with Kylie = 5 ÷ 1/3

Total Slices with Kylie = 15

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The total amount of interest paid over the life of the loan is $1863.45.

The present value of the loan.

Since there are 12 months in a year, and the loan has n-years, there are 12n monthly payments.

Let's use the formula for the present value of an annuity due:

[tex]PV = PMT \times ((1 - (1 + r) ^(-n)) / r) \times (1 + r)[/tex]

PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

Substituting the given values, we get:

[tex]PV = \$800 \times ((1 - (1 + 0.12/12) ^(-12n)) / (0.12/12)) \times (1 + 0.12/12)[/tex]

[tex]PV = \$800 \times ((1 - (1.01)^(-12n)) / 0.01) \times 1.01[/tex]

[tex]PV = \$800 \times ((1 - 1.01^(-12n)) / 0.01) \times 1.01[/tex]

[tex]PV = \$800 \times ((1 - 0.887^(-n)) / 0.01) \times 1.01[/tex]

The formula for the interest paid in any given month of an annuity due:

[tex]I = PV \times r \times (1 + r) ^(m - 1)[/tex]

I is the interest paid in the 45th month, PV is the present value of the loan, r is the monthly interest rate, and m is the month.

Substituting the given values for the 45th month, we get:

[tex]\$424.45 = PV \times 0.01 \times (1 + 0.01 )^(45 - 1)[/tex]

[tex]\$424.45 = PV \times 0.01 \times (1.01)^4^4[/tex]

[tex]PV = \$424.45 / (0.01 \times (1.01)^4^4)[/tex]

PV =[tex]\$75799.45[/tex]

Now that we know the present value of the loan, we can calculate the total amount of interest paid over the life of the loan.

Let's use the formula for the total interest paid in an annuity due:

[tex]Total interest = (PMT \times n \times (n + 1) / 2) - PV[/tex]

Substituting the given values, we get:

Total interest = [tex](\$800 \times 12n \times (12n + 1) / 2) - \$75799.45[/tex]

Total interest = [tex]\$9600n^2 + \$4800n - \$75799.45[/tex]

We can solve for n by using the fact that the interest paid in the 45th month is $424.45:

[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1 + 0.01)^(45 - 1)[/tex]

[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1.01)^4^4[/tex]

n = 4.5

Substituting n = 4.5 into the formula for total interest, we get:

Total interest =[tex]\$9600 \times (4.5)^2 + \$4800 \times 4.5 - \$75799.45[/tex]

Total interest = $1863.45

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The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.

Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.

Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:

Density = Mass/Volume

Substituting the given values, we get:

Density = 6 grams/12 cm³

Density = 0.5 grams/cm³

Therefore, the density of the sample is 0.5 grams/cm³.

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The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).

The given function is y = 3x² + 2.

The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.

Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.

The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).

Since the minimum value of the function is 2, the range of the function is [2, ∞).

Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

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The surface area of this solid would be; 127.

To Find the surface area of the composite solid, we have;

Sides (a) area

4 * 3 = 12

12 * 2 = 24

Now Sides (b) area

7 * 3 = 21

21 * 3 = 63

Then Face (c) area

3 * 4 / 2 = 6

6 * 2 = 12

Base area

4 * 7 = 28

Total surface area

To calculate the total surface area we have to add the value of each face :

28 + 12 + 63 + 24 = 127

Thus, the surface area of this solid is 127.

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The cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x). Also the inequality equation is 160 - 4x -2[tex]x^{2}[/tex]  [tex]\geq[/tex] 130 to maintain minimum revenue of $130 after rising price by x number of times by $1 as 2 customers leave on average per hour.

Let x represents the number of $1 increases in the cost of the buffet.

Noah manages a buffet at a local restaurant and charges  $10 for the buffet.

On average, 16 customers choose the buffet as their meal every hour.

That is, the average revenue from 16 customers is = $(10*16)= $160

After surveying Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour.

That is, as cost of buffet for every hour rises by $x from $10 we get, $ (10+x) , and the average number of customers who select the buffet will decrease by 2 per hour.

The new average number of customers per hour after rise in cost of buffet by $x is (16 -2x).

This implies, the revenue earned now is = $(16- 2x)(10 + x) = $(160 + 16x - 20x -2[tex]x^{2}[/tex] ) = $ (160 - 4x -2[tex]x^{2}[/tex] )

The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Thus, after the increase in price by $x per hour , the inequality equation that helps Noah to pick best pricing decisions will be ,

160 - 4x -2[tex]x^{2}[/tex]  [tex]\geq[/tex] 130

Here, cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x).

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the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:

x = r cos(θ)

y = r sin(θ)

Substituting the given values, we get:

x = 6 cos(-π/3) = 6 × (1/2) = 3

y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3

Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

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