Tommy wants to use his 5.89 m long ladder against a wall, as shown below. The instructions state that the angle between his ladder and the ground should be in the range 74° to 77°. Calculate the maximum distance that the base of his ladder should be placed from the wall. Give your answer in metres to 2 d.p.​

it's always a good idea to double-check the recipe before measuring out the ingredients. Additionally, it's important to use accurate measuring tools, such as measuring cups and spoons, to ensure that the dip turns out as intended.

How to calculate the problem?

Pepperoni dip is a popular party dip made with cream cheese, sour cream, mayonnaise, and chopped pepperoni. The exact measurements for the ingredients can vary depending on the recipe and the desired consistency and taste. However, a typical recipe might call for:

8 oz cream cheese, softened

1/2 cup sour cream

1/2 cup mayonnaise

1 cup chopped pepperoni

To convert these measurements to improper fractions, we can use the fact that 1 cup is equivalent to 8 fluid ounces. Therefore, the measurements in improper fractions are:

8/1 (or simply 8) ounces of cream cheese

1/2 cup = 4 fluid ounces of sour cream

1/2 cup = 4 fluid ounces of mayonnaise

1 cup = 8 fluid ounces of chopped pepperoni

It's worth noting that some recipes may use different measurements or units, such as teaspoons or tablespoons, so it's always a good idea to double-check the recipe before measuring out the ingredients. Additionally, it's important to use accurate measuring tools, such as measuring cups and spoons, to ensure that the dip turns out as intended.

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Your complete question is :-What are the measurements for the ingredients in pepperoni dip? Use improper fractions when needed.

the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

In cοmputer science and mathematics, a graph is a cοllectiοn οf vertices (alsο knοwn as nοdes οr pοints) cοnnected by edges (alsο knοwn as links οr lines).

I can help yοu graph the functiοn y=-2sin(-3x) οver the interval [0, 2π].

Tο start, let's analyze the functiοn. The negative sign in frοnt οf the sine functiοn means that the graph will be reflected acrοss the x-axis. The 2 in frοnt οf the sine functiοn means that the amplitude οf the graph will be 2 units.

The argument οf the sine functiοn is -3x, which means that the periοd οf the graph will be 2π/3. This means that the graph will cοmplete 3 full οscillatiοns οver the interval [0, 2π].

Using this infοrmatiοn, we can sketch the graph as fοllοws:

At x=0, the sine functiοn is 0, sο the graph starts at the x-axis at y=0.

As x increases, the sine functiοn οscillates between -1 and 1, sο the graph οscillates between -2 and 2. Since the argument οf the sine functiοn is -3x, the graph cοmpletes οne full οscillatiοn fοr every 2π/3 increase in x.

At x=2π/3, the graph cοmpletes οne full οscillatiοn and returns tο the x-axis at y=0.

As x cοntinues tο increase, the graph repeats the same pattern every 2π/3 units οf x, until it cοmpletes 3 full οscillatiοns at x=2π.

Therefοre, the graph οf y=-2sin(-3x) οver the interval [0, 2π] will lοοk like a wave that οscillates 3 times between y=-2 and y=2, with a periοd οf 2π/3. The graph will start at the x-axis at y=0 and be reflected acrοss the x-axis.

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The unit price of the red ribbon is $0.88 per meter.

What is rate ?

A rate is a measure of the speed of something in relation to another quantity or measurement. It is a ratio that expresses how much of one quantity occurs in a given amount of another quantity. In other words, it is a comparison of two different measurements.

To find the unit price of the red ribbon, we need to divide the total cost by the number of units (in this case, meters) in the roll:

Unit price =  cost / Number of units

In this case, the total cost is $7.92 and the number of units is 9 meters. So, we have:

Unit price = $7.92 / 9 meters

Using a calculator or by performing long division, we can simplify this expression to find the unit price:

Unit price = $0.88 per meter

Therefore, the unit price of the red ribbon is $0.88 per meter.

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The exact volume of the cone is 168π cubic feet and the approximated volume is 528 cubic feet

To find the volume of a cone, we can use the formula:

V = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

Since the diameter of the base is 12 feet, the radius is half of that, or 6 feet.

Using the given height of 14 feet, we can plug in the values into the formula:

V = (1/3)π(6²)(14)

V = (1/3)π(36)(14)

V = (1/3)π(504)

V = 168π

Therefore, the exact volume of the cone is 168π cubic feet.

If we want to approximate the value using 3.14 for π, we can use a calculator to get:

V ≈ 168 * 22/7

V ≈ 528

Therefore, the approximated volume of the cone is 528 cubic feet

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The measure of angle P = 67.38, calculated the trigonometric function value, we get the same answer.

We have all sides of the triangle, so we can calculate the trigonometric function value of angle P :

sin P = 12/13 ≈ 0.9231

Since △PQR is a right-angled triangle, we can use the cosine or sine or tan rule to find the ∠P

1) Sine

sin ∠P = opposite/ hypotenuse = 12/13

∠P = sin −1 (12/13) = 67.38

(2) Cosine

cos ∠P = adjacent/ hypotenuse = 5/13

∠P = cos−1 (5/13) = 67.38

(3) tan

tan ∠P = opposite/ adjacent = 12/5

∠P = tan−1 (12/5) = 67.38

Hence, as you can see that whichever rule is being used, the answer will always be the exact same.

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Median is the appropriate measure of centre to identify which coffee shop normally sells the most coffee per hour, and the findings reveal that Wide Awake is the coffee shop that typically sells the most coffee per hour.

We must contrast the central tendency measures of the two datasets to identify which coffee shop normally sells the most coffee per hour. The mean and the median are our two available measurements of central tendency.

By adding up all the values and dividing by the total number of values, the mean—the average value of the data—is determined. When values are ordered in order, the median is the middle value in the dataset.

When we compute the mean and median for both coffee shops, we obtain:

Mean = (1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5 + 9.5 + 3 + 5) / 12 = 6.125 gallons of coffee ground

Average: 5 gallons

Mean = (2.5 + 10 + 4 + 18 + 4 + 3 + 6.5 + 15 + 5 + 2.5) / 10 = 6.5 gallons while wide awake.

4.5 gallons is the median.

We can see from the figures above that the mean values for both coffee shops are nearly equal, with Coffee Ground's mean being slightly lower at approximately 5 gallons compared to Wide Awake's mean at about 6.5 gallons. Yet, the median value for Wide Awake is 4.5 gallons as opposed to 5 gallons for Coffee Ground.

When there are outliers in the data or when the distribution is skewed, the median is a better indicator of central tendency to utilize. Given that the datasets are tiny and contain outliers, the median is a more appropriate measurement in this situation. We can infer from the median numbers that Wide Awake normally sells the most coffee each hour.

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The value of the function f at t = 7, will be 11.

a function is a relationship between two sets of numbers or values, where each input value from the domain produces exactly one output value from the range. This relationship can be represented by a graph, an equation, or a table.

For example, the equation f(x) = 2x is a function that takes an input value x, multiplies it by 2, and produces an output value in the range. If we input x = 3 into this function, we get f(3) = 2

The function is given as,

f = 2t – 3

At t = 7, the value of the function f will be.

f = 2 x 7 – 3

f = 14 – 3

f = 11

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The complete question is;

Find the output, f, when the input, t, is 7. f = 2t - 3

Answer: 240,000= .6x and/or 400,000

Step-by-step explanation:

If 240,000 is 60% of our answer, we can write the equation as...

240,000= .6x

In order to find the answer, (I am unsure if you need it) we would divide both sides by .6.

This would leave us with 400,000.

The new coordinates for the function g(x) at the point (1,6) are (1,5).

What is coordinates ?

Coordinates are a set of values that specify the position of a point or an object in space. They are used to locate points in a plane or in three-dimensional space. In the plane, a point can be located using two coordinates, called the x-coordinate and the y-coordinate. In three-dimensional space, a point can be located using three coordinates, called the x-coordinate, y-coordinate, and z-coordinate.

The coordinates of a point are typically written as an ordered pair (x, y) in the plane, or as an ordered triplet (x, y, z) in three-dimensional space. The x-coordinate represents the position of the point along the horizontal axis, the y-coordinate represents the position of the point along the vertical axis, and the z-coordinate represents the position of the point along the third axis, which is usually perpendicular to the x- and y-axes.

To find the new coordinates for the function g(x) given that the point (1,6) is on the graph of y = f(x), we can substitute x = 1 and y = 6 into the equation for g(x) and simplify:

g(x) = 2f(1/3(x-1)) + 5

g(1) = 2f(1/3(1-1)) + 5

g(1) = 2f(0) + 5

g(1) = 2f(0) + 5(1)

g(1) = 2f(0) + 5

Since the point (1,6) is on the graph of y = f(x), we know that f(1) = 6. To find f(0), we can use the fact that the function passes through the origin (0,0) because:

g(1) = 2f(0) + 5

g(0) = 2f(-1/3) + 5

Since the point (1,6) is on the graph of y = f(x), we can use it to find the value of f(1/3) as follows:

(1,6) is on the graph of y = f(x)

so f(1) = 6

and 1/3(1-1) = 0

This means that the point (1/3, f(1/3)) is on the graph of y = f(x). Therefore, we can use the transformation in g(x) to find the new y-coordinate for g(1) as follows:

g(1) = 2f(1/3(1-1)) + 5

g(1) = 2f(0) + 5

g(1) = 2(0) + 5

g(1) = 5

Therefore, the new coordinates for the function g(x) at the point (1,6) are (1,5).

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El ángulo -3π / 4 está en el tercer cuadrante del plano cartesiano.

it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit amount at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

To solve this problem, we can start by finding the monthly difference in their deposits:

Muhammad: $59/month

Connor: $66/month

Since Muhammad's monthly deposit is lower than Connor's, we need to find out how many months it will take for Muhammad's balance to catch up to and surpass Connor's. We can set up an equation to represent this situation:

$158 + $59x = $74 + $66x

where x is the number of months elapsed.

We can simplify and solve for x:

$158 + $59x - $74 - $66x = 0

$84 - $7x = 0

$7x = $84

x = 12

Therefore, it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit money at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

the complete question is :

Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 in his bank account and deposits $66 per month into his account. If Muhammad and Connor continue to deposit money into their accounts at the same rate, how long will it take for Muhammad's account balance to surpass Connor's?

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The greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

To calculate the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters, we need to divide the width of the paper by the width of each wristband, and then divide the length of the paper by the length of each wristband, and then multiply the two numbers together. The result will be the greatest number of wristbands that can be made from the paper.

Using the dimensions given in the question, and assuming that each wristband measures 1.5 centimeters by 22 centimeters (which is a typical size for a wristband), we can calculate the number of wristbands as follows:

Width of paper = 18 centimeters

Width of each wristband = 1.5 centimeters

Number of wristbands in width = (18 / 1.5) = 12

Length of paper = 85 centimeters

Length of each wristband = 22 centimeters

Number of wristbands in length = (85 / 22) ≈ 3.86 (round down to 3)

Total number of wristbands = (12 x 3) = 36

Therefore, the greatest number of wristbands that can be made from a rectangular piece of paper that measures 18 centimeters by 85 centimeters is 36.

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A statement about the seeds in the remaining packets is best supported by this information include the following: B. Between 50 and 100 seeds will sprout.

Based on the information provided about the packets of tomato seeds, we can logically deduce the following parameters;

Number of packets of tomato seeds = 6 packets.

Number of seeds in each packet = 24 seeds.

Next, we would determine the total number of seeds in six (6) packet by multiplying the number of packets of tomato seeds by the number of seeds in each packet as follows;

Total number of seeds = 6 × 24

Total number of seeds = 144 seeds.

Since 15 seeds sprouted in one packet of 24 seeds, the ratio can be calculated as follows;

Ratio = 15 : 24

Sprouted seeds = 144 × 15/24

Sprouted seeds = 90 seeds.

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Complete Question:

Mari bought 6 packets of tomato seeds. Each packet contained 24 seeds. She planted 1 packet of the seeds, and 15 seeds sprouted.

Which statement about the seeds in the remaining packets is best supported by this information?

No more than 50 seeds will sprout.

Between 50 and 100 seeds will sprout.

At least 100 but no more than 120 seeds will sprout.

All 120 seeds will sprout.

Answer:

120°

Step-by-step explanation:

The sum of the measurement of the interior angles of a parallelogram is 360

t +  2t + t + 2t = 360  Combine like terms

6t = 360  Divide both sides by 6

[tex]\frac{6t}{6}[/tex] = [tex]\frac{360}{6}[/tex]

t = 60

If t = 60, then 2t = 120

Helping in the name of Jesus.

According to the question the equation has been solved by using Pythagorean. The left-hand side of the identity simplifies to [tex]cos^2(x)[/tex]

The Pythagorean Theorem can be used to find the correct angled triangle's missing length. The triangle contains three sides: the hypotenuse, this same opposite, which will always be the longest, and the adjacent side, which really doesn't touch the hypotenuse. The Pythagorean equation is: [tex]a^2+b^2=c^2.[/tex]

We can start by using the reciprocal identity for cosecant:

[tex]cos(x) = 1/sin(x)[/tex]

Then, we substitute this into the left-hand side of the identity:

[tex]sin(x)(csc(x) - sin(x)) = sin(x)(1/sin(x) - sin(x))\\= sin(x)/sin(x) - sin^2(x)\\= 1 - sin^2(x)[/tex]

Using the Pythagorean identity for sine and cosine, we know that:

[tex]1 - sin^2(x) = cos^2(x)[/tex]

Thus, the left-hand side of the identity simplifies to [tex]cos^2(x)[/tex], which is equal to the right-hand side of the identity.

Therefore, the identity is verified.

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The initial population of the bacteria culture is 200 bacteria.

The initial population of the bacteria culture can be determined using the equation for exponential growth: P(t)=P0(1+rt), where P(t) is the population after time t, P0 is the initial population, and r is the relative growth rate.

In this case, after 2 hours, the population is 600 and after 8 hours the population is 75,000. Plugging in the values, we get P0 = 600/(1+2*r), or P0 = 600/3. Thus, the initial population of the bacteria culture is 600/3 = 200 bacteria.

Exponential growth is a function of time and rate of growth. It is often used to model population growth or decay, such as in this case. The equation for exponential growth states that the population at any time is equal to the initial population multiplied by the rate of growth at each unit of time.

In this case, the rate of growth (r) is constant over the time period, so the population can be determined by putting in the values for P(t) and P0 and solving for r. Then, using the same equation, the initial population (P0) can be determined.

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Answer:

x ∈ (0,75; +∞) and x∈ (1; +∞)

Step-by-step explanation:

1) 3 - 4x < 0

-4x < -3 / : (-4)

x > 0,75

x ∈ (0,75; +∞)

2) 2x - 4 > -2

2x > -2 + 4

2x > 2 / : 2

x > 1

x∈ (1; +∞)

value of variable x in the circle is 4unit.

A circle is a two-dimensional form that may be described as a collection of points that are equally spaced out from the centre.

The area of a circle is also an important property, and is given by the formula A = πr^2, where r is the radius. The circle is used in many fields, including mathematics, science, engineering, and art, and is often used to represent concepts such as unity, wholeness, and infinity.

Circles are found in many natural and man-made objects, such as wheels, clocks, planets, and bubbles. They are also used in various applications, such as in navigation, architecture, and computer graphics.

AE=8

CE=12

DE=x

BE=6x

As we know that

AE×CE=DE×BE

8×12=x×6x

96=6x²

x²=16

x=4

Hence, value of variable x in the circle is 4unit.

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The probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes, assuming a population standard deviation of 1.5 minutes and using the Central Limit Theorem, is approximately 0.881 or 88.1%.

Since we have a sample size of 50, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean. We know that the population standard deviation is 1.5 minutes. Therefore, the standard error of the mean is:

SE = σ/sqrt(n) = 1.5/sqrt(50) ≈ 0.212

To find the probability that the mean time spent reading is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean (which is not given, but we can assume is equal to the sample mean of 25), and SE is the standard error of the mean calculated above.

So, for the lower bound of 24.7 minutes:

z = (24.7 - 25) / 0.212 ≈ -1.42

And for the upper bound of 25.5 minutes:

z = (25.5 - 25) / 0.212 ≈ 2.36

We can then use a standard normal distribution table or calculator to find the probability that z is between -1.42 and 2.36, which represents the probability that the sample mean is between 24.7 and 25.5 minutes:

P(-1.42 < z < 2.36) ≈ 0.881

Therefore, the probability is 0.881 or 88.1%.

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The true equations from the given trig. expressions can expressed as;|

From trigonometery tabel the value of the given angles are:

Cos 37 = 0.7986

Sin 53 = 0.7986

Tan 37 = -0.840

Tan 53 =  -0.431

sin 37=-0.644

cos 53 = -0.918

sin37 = -0.644

Sin (90 – θ) = Cos θ

Then we can now be testing the options one after the other by equatiing the terms in right hand side to the one in the left hand sides after doind this we can see that the foirst and the last options are true statement

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Answer:

80

Step-by-step explanation:

edge 2023

We assume the intensity function is

[tex]f(x) = 50,000(0.975^x) . . . . x[/tex]

Use 200 for x and do the arithmetic.

A 99% confidence interval for the difference in mean wait times for ambulance and self-transported patients is  (0.15, 3.33) minutes. Since the interval includes 0, we cannot conclude that the difference in mean wait times is statistically significant at a 99% level of confidence.

To estimate the difference between the mean wait times for ambulance-transported patients and self-transported patients, we can use the two-sample t-interval for the difference in means, assuming equal variances:

[tex]$\bar{x}_1 - \bar{x}2 \pm t{\alpha/2, n_1 + n_2 - 2} \times \sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_2}}$[/tex]

[tex]$\bar{x}1$ and $\bar{x}2$[/tex]where are the sample means, [tex]$s_p$[/tex] is the pooled standard deviation, [tex]$n_1$[/tex] and [tex]$n_2$[/tex] are the sample sizes, and[tex]$t{\alpha/2, n_1 + n_2 - 2}$[/tex] is the critical value from the t-distribution with[tex]$n_1 + n_2 - 2$[/tex] degrees of freedom.

Substituting the given values, we get:

[tex]$\bar{x}_1 - \bar{x}_2 \pm 2.626 \times \sqrt{\frac{8.30^2}{77}+\frac{5.16^2}{73}}$$\implies 6.04 - 4.30 \pm 2.626 \times \sqrt{\frac{8.30^2}{77}+\frac{5.16^2}{73}}$[/tex]

[tex]$\implies 1.74 \pm 1.59$[/tex]

Thus, the 99% confidence interval for the difference between the mean wait times is (0.15, 3.33) minutes.

To determine whether the difference in mean wait times is statistically significant based on the confidence interval, we need to check if the interval contains zero. Since the interval does not contain zero, we can conclude that the difference in mean wait times between ambulance-transported patients and self-transported patients is statistically significant at the 99% confidence level.

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--The given question is incomplete, the complete question is given

"Patients with heart-attack symptoms arrive at an emergency room either by ambulance or self- transportation provided by themselves, family, or friends. When a patient arrives at the emergency room, the time of arrival is recorded. The time when the patient's diagnostic treatment begins is also recorded An administrator of a large hospital wanted to determine whether the mean wait time time between arrival and diagnostic treatment) for patients with heart-attack symptoms differs according to the mode of transportation. A random sample of 150 patients with heart-attack symptoms who had reported to the emergency room was selected. For each patient, the mode of transportation and wait time were recorded. Summary statistics for each mode of transportation are shown in the table below. Mode of Transportation Sample Size Mean Wait Time Standard Deviation (in minutes) of Wait Times (in minutes) 6.04 4.30 8.30 5.16 Ambulance Self 77 73 (a) Use a 99 percent confidence interval to estimate the difference between the mean wait times for ambulance-transported patients and self-transported patients at this emergency room. You may assume that conditions for inference are met. (b) Based only on this confidence interval, do you think the difference in mean wait times is statis- tically significant? Justify your answer."--

The outer perimeter of the composite figure is calculated to the nearest hundredth as: 55.70 feet.

The outer perimeter of the composite figure that is shown below which consist of a semicircle and a triangle, can be calculated using the formula below:

Perimeter = 1/2(2πr) + 2(s), where:

s = slant height of the triangle = 20 ft

r = radius of the semicircle = 10/2 = 5 ft

Substitute the values:

Perimeter = 1/2 * (2 * 3.14 * 5) + 2(20)

Perimeter = 55.70 feet

Thus, rounding to the nearest hundredth, the perimeter is calculated as: 55.70 feet.

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For Snowman A:

The initial height of Snowman A is 28 inches, and it decreases by 4 inches per hour. So, the equation for the height of Snowman A in terms of t hours after sunrise is:

A = 28 - 4t

For Snowman B:

The initial height of Snowman B is 46 inches, and it decreases by 7 inches per hour. So, the equation for the height of Snowman B in terms of t hours after sunrise is:

B = 46 - 7t

To find when both snowmen have an equal height, we need to set A and B equal to each other and solve for t:

28 - 4t = 46 - 7t

3t = 18

t = 6

Therefore, both snowmen will have an equal height of 16 inches after 6 hours.

52,437 rounded to the nearest thousand is 53,000.

When we round a number to the nearest thousand, we want to find the closest multiple of 1,000 to the given number. To do this, we need to look at the digit in the hundreds place, which is the third digit from the right in the number.

In the case of 52,437, the digit in the hundreds place is 4. If this digit were less than 5, we would round down to the nearest thousand, but since it is 5 or greater, we need to round up. When we round up, we increase the value of the digit in the thousands place by 1 and replace all the digits after that with zeros.

In this case, the digit in the thousands place is 2, so we need to increase it to 3. The digits after the thousands place are already zeros, so we don't need to change them. Therefore, when we round 52,437 to the nearest thousand, we get:

52,437 rounded to the nearest thousand = 53,000

So 52,437 rounded to the nearest thousand is 53,000.

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Answer: C

Step-by-step explanation:

Area of Square = [tex]l^2[/tex]
Area of Rectangle = [tex]lw[/tex]

Square A = [tex]l^2[/tex]

6 = [tex]l^2[/tex]

[tex]l[/tex] = 2.449

Rectangle B = [tex]lw[/tex]

5 = 2.449 x [tex]w[/tex]

[tex]w[/tex] = 2.0008

For Square C, [tex]l[/tex] = [tex]w[/tex]

Square C = [tex]l^2[/tex]

Square C = 2.0008²

Square C = [tex]\frac{25}{6}[/tex] OR 4.166

If the coefficient of x in the objective function is less than the ratio of the coefficient of x in one of the constraint equations to the coefficient of the corresponding decision variable, then increasing the coefficient of x in the objective function will not change the optimal solution.

To determine the maximum amount that the coefficient of x in the objective function can be increased. Let's assume that this ratio is r.

If the current coefficient of x in the objective function is less than r, then the optimal solution will not change if the coefficient of x is increased by any amount.

If the current coefficient of x in the objective function is equal to r, then the optimal solution will not change if the coefficient of x is increased by any amount that does not violate the constraint equation with the smallest ratio.

If the current coefficient of x in the objective function is greater than r, then the optimal solution will change if the coefficient of x is increased by an amount that is greater than or equal to the difference between the current coefficient of x and r.

Therefore, the maximum amount that the coefficient of x in the objective function can be increased without changing the optimal solution depends on the ratio of the coefficient of x to the coefficient of the corresponding decision variable in the constraint equations.

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