The graph of p = 400 and the graph of p = 50s – 200 intersect at the point (12,400). If the equation p = 50s – 200 represents the profit, p, based on s sales, what does the intersection best represent?

a. When the sales are 400, the profit is 12.
b. When the sales are 12, the profit is 400.
c. The profit is always 400.
d. The sales are always 12.

Based on the passage you provided, it seems like you are being asked to apply principles of logic and construct a truth table based on the premises and conclusion presented in the passage. To accomplish this, you need to follow the three steps outlined:

Step 1: Break the premises into several statements (usually denoted by p, q, r, etc.)

From the passage, we can identify the following statements:

- Statement 1: Water is fundamental for life and the environment.

- Statement 2: Water crisis is one of the most important challenges of the 21st century.

- Statement 3: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- Statement 4: If all public services collaborate to address the water scarcity problem, then the governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- Statement 5: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- Statement 6: Therefore, there is no efficient collaboration among various public sectors to address the water shortage problem.

Step 2: Express the premises and conclusion symbolically.

Using the statements identified above, we can symbolically represent them as follows:

- p: Water is fundamental for life and the environment.

- q: Water crisis is one of the most important challenges of the 21st century.

- r: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- s: All public services collaborate to address the water scarcity problem.

- t: Governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- u: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- v: There is no efficient collaboration among various public sectors to address the water shortage problem.

Step 3: Construct a truth table.

To construct a truth table, assign truth values (T or F) to each statement and evaluate the truth value of the conclusion based on the truth values of the premises

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Answer:

2.20

Step-by-step explanation:

First, change 42° to radian

42/180 * π = 0.733 rad

The length of the arc = 3 * 0.733 = 2.20

The required measure of the arc RT is given as 2.512 units.

Given that,
In circle S with m RST = 42 and

RS = 3 units,

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Arc = radius  × angle
Arc = 3 × 42 × π/180

The length of the arc = 2.512

Thus, the required measure of the arc ET is given as 2.512 units.

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The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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answer:

tell us why the other gardens are needed

Answer:

negative 10

Step-by-step explanation:

Based on the data collected from the 75 randomly selected students at CSUF, the average amount of sleep they obtained on a typical night was 6.9 hours, with a standard deviation of 1.482 hours. This means that the majority of students at CSUF are sleeping between 5.4 and 8.4 hours per night, as 68% of the data falls within one standard deviation of the mean.

To answer the question of whether the average amount of sleep is less than the recommended eight hours, we need to look at the lower end of the range. The data shows that 6.9 hours is significantly less than the recommended eight hours of sleep per night. This indicates that the average amount of sleep obtained by CSUF students is less than the recommended amount.

To estimate the average amount of sleep for all CSUF students, we can use the data collected from the 75 students and calculate a confidence interval. This interval will give us a range of values that we can be confident contains the true average amount of sleep for all CSUF students.

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Based upon this information, the value of the test statistic is 0.23.

The term "test statistic" refers to a quantity obtained from the sample and used in statistical hypothesis testing.

The sample proportion, or ratio of the sample size to the number of "yes" responses (23), would be the test statistic in this situation (100). The sample proportion is computed in the following manner:

The test statistic is p = 23/100, or 0.23.

So, 0.23 is the test statistic. The percentage of dog owners that routinely feed their dogs Woof Chow dog food is represented by this sample estimate.

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Answer:

240

Step-by-step explanation:

5.5 x 20 = 110

6.4  x 20 = 130

110 + 130 = 240

Answer:

240 centimeters squared

Answer: its 236

Step-by-step explan

After rounding the given numbers to 2 significant numbers we get:

a. 27.8

b. £2798

c. 6.91 m

Given, Round the following numbers to 2 significant figures:

Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value.

The act of simplifying a number so that its value remains near to what it was is known as rounding. The outcome of rounding off a number is less precise but simpler to utilize. The place value of a number's digits is taken into account while rounding it.

a) 27.834

Round off to 2 significant numbers.

= 27.8

b) £2798.01

Round off to 2 significant numbers.

=  £2798

c) 6.909 m

Round off to 2 significant numbers.

while rounding off we see that the nearest number is 91 so,

= 6.91

Hence we get the desired results.

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Answer:

Option D can be your answer

The true statement about geometric figure is

One plane can be drawn so it contains all three points.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a two-dimensional analogue that can incorporate three dimensions of space, a line, and a point.

We have three points R, S and T.

So, there are infinitely many planes that pass through the line that contains the three points if the three points are colinear.

There is a plane that contains our three points if we have three separate points in 3-space.

So, For the three points R, S, and T, the third assertion is accurate.

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Answer:

above sea level

Step-by-step explanation:

Between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. The statement that indicates between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. This is option B.

In microeconomics, the long-run average cost (LRAC) is a method of showing the average expense per unit for a given level of production input. It is the cost of producing goods per unit using a specified number of inputs, such as labor and capital.

Long-run average cost is the average cost per unit of production after the company has adapted its production scale fully. As a result, the term "long-run" denotes a period in which all of the firm's inputs are variable.

The cost structure's shape is represented by the long-run average cost curve. The curve is determined by dividing the cost of producing goods by the number of goods produced. It aids in identifying the production rate at which a firm may generate the most output at the lowest cost.The long-run average cost curve depicts how the average cost of production varies with scale.

The curve might be downward-sloping, indicating economies of scale, flat, implying constant returns to scale, or upward-sloping, indicating diseconomies of scale, based on the company's production methods.

Hence, the answer is B.

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Answer:

\(a_{66}\) = 653

Explanation:

General formula: \(a_{n}\) = (\(a_{1}\) + ((term) - 1) · (common difference)

\(a_{66}\) = 3 + (66 - 1) · (10)

\(a_{66}\) = 653

The area under the standard normal curve between z=â1.16 and z=â0.03 is 0.3663.

To find the area under the standard normal curve between z = -1.16 and z = -0.03, we will use the following steps:

1. Look up the z-values in the standard normal distribution table (or use a calculator or online tool that provides the corresponding probability values).
2. Subtract the probability value for z = -1.16 from the probability value for z = -0.03.
3. Round your answer to four decimal places.

Step 1: Look up the z-values in the standard normal distribution table.
- For z = -1.16, the corresponding probability value is 0.1230.
- For z = -0.03, the corresponding probability value is 0.4893.

Step 2: Subtract the probability values.
Area = P(-0.03) - P(-1.16) = 0.4893 - 0.1230

Step 3: Round the answer to four decimal places.
Area = 0.3663

So, the area under the standard normal curve between z = -1.16 and z = -0.03 is approximately 0.3663.

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Answer:

A.2 Hours.

B.2 Inches.

Step-by-step explanation:

Its easy,

A. 8 inches = 4 hours, 4 inches = .... hours

4 inches = 8 ÷ 2

Hours: 4 hours ÷ 2 = 2 hours

B. 8 inches = 4 hours, .... inches = 1 hour

1 hour = 4 ÷ 4

Inches: 8 inches ÷ 4 = 2 inches.

To answer this question the first step is to find the volume of each of the cylindrical cups.

The volume of a cylinder is given by the following equation:

Where V is the volume, r is the radius and h is the height.

Find the radius of each of the cups by dividing their diameters by 2:

Calculate the volume of each of the cups using the given values:

It means that the blue cup has a volume of 32pi cubic inches and the green cup has a volume of 128pi cubic inches.

To find how many cupfuls of water will it take for him to empty his sink using each cup, divide the volume of the sink by each of the volumes of the cups:

It will take 21.88 (22) blue cups for him to empty the sink.

It will take 5.47 (6) green cups for him to empty the sink.

Therefore , the solution of the given problem of equation comes out to be circle's radius is three and a half units, and its center is at the coordinates (2, 3).

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization yields b + 7, as opposed to another algorithm that divides 12 into two components and can assess data from y + 7, which creates y + 7.

Here,

A circle's standard form solution is:

=> (x - h))² +  (y - k))²  = r)²

.To reformat the circle equation provided in standard form:

=> 7x)²  - 28x + 7y)²  + 42y = 35

=> 7(x)²  - 4x) + 7y)²  + 42y = 35

=> 7(x)²  - 4x + 4) + 7y)²  + 42y = 35 + 28

=> 7(x - 2))²  + 7y)²  + 42y = 63

=> 7(x - 2))² + 7(y)²  + 6y) = 63

=> 7(x - 2))²  + 7(y)²  + 6y + 9) = 63 + 63

=> 7(x - 2))²  + 7(y + 3))²  = 126

=> (x - 2)² + (y + 3))²  = 18

So, (x - 2)2 + (y + 3)2 = 18 is the equation of this circle in standard notation.

The circle's radius is three and a half units, and its center is at the coordinates (2, 3).

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The mean e(t) is 48.393 and the standard deviation sd(t) is approximately 2.850.

To determine the mean e(t) and standard deviation Sd(t) of the relay team's total time in the medley event, we need to calculate the weighted average and standard deviation of each swimmer's time.

The mean e(t) is calculated by adding up the product of each swimmer's time and the corresponding weight (number of strokes) and dividing it by the total weight.

\(e(t) = (49.39 * 2 + 55.67 * 1 + 48.76 * 3 + 45.8 * 4) / (2 + 1 + 3 + 4)\)

Calculating this expression, we get:

\(e(t) = (98.78 + 55.67 + 146.28 + 183.2) / 10\)

\(e(t) = 483.93 / 10\)
\(e(t) = 48.393\)

So, the mean e(t) is 48.393.

To calculate the standard deviation sd(t), we need to find the weighted variance and then take its square root.

First, we calculate the weighted variance by summing up the products of each swimmer's squared time difference from the mean and the corresponding weight, and dividing it by the total weight.

variance(t) = \([(2 * (49.39 - 48.393)^2) + (1 * (55.67 - 48.393)^2) + (3 * (48.76 - 48.393)^2) + (4 * (45.8 - 48.393)^2)] / (2 + 1 + 3 + 4)\)

Calculating this expression, we get:

variance(t) =\([2 * (0.997)^2 + 1 * (7.277)^2 + 3 * (0.367)^2 + 4 * (-2.593)^2] / 10\)
variance(t) =\([2 * 0.994 + 1 * 52.94 + 3 * 0.135 + 4 * 6.713] / 10\)
variance(t) =\((1.988 + 52.94 + 0.405 + 26.852) / 10\)

variance(t) =\(81.185 / 10\)

variance(t) = \(8.119\)

Finally, taking the square root of the variance gives us the standard deviation sd(t):

\(sd(t) = √8.119\)

\(sd(t) ≈ 2.850\)

So, the standard deviation sd(t) is approximately 2.850.

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The required number in scientific notation is 3.937×\(10^{-8}\) inch.

Option (2) is correct.

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. Scientific Notation is the expression of a number n in the form a∗10b. where a is an integer such that 1≤|a|<10. and b is an integer too.

Given:

one nanometer is about 0.00000003937 of an inch.

According to given question we have

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

one nanometer = 0.00000003937 of an inch.

one nanometer = 3.937×\(10^{-8}\) inch.

Therefore, the required number in scientific notation is 3.937×\(10^{-8}\) inch.

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Apply Pythagorean theorem

The market demand curve for tea is downward sloping. The price elasticity of demand is 4, indicating elastic demand.

To derive the market demand curve for tea, we need to calculate the total quantity demanded at different prices by summing the individual quantities demanded by MBA students.

At a price of BHD 0.200, the total quantity demanded is 2 cups * 75 students = 150 cups. At a price of BHD 0.300, the total quantity demanded is 1 cup * 75 students = 75 cups. The market demand curve for tea for MBA students is a downward-sloping line connecting these two points.

To find the price elasticity of demand, we use the formula: Price elasticity = (% change in quantity demanded) / (% change in price). For the individual demand curve, the price elasticity can be calculated as (1/2) / (0.1/0.2) = 4.

For the market demand curve, the price elasticity is the average of the individual elasticities, which is also 4. This indicates that the demand for tea by MBA students is relatively elastic, meaning that a small change in price will result in a relatively large change in the quantity demanded.

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Answer:

Explanation:

Given the line:

3x - 2y = 1

The boat travels at  18 miles per hour.

What is speed?

Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.

The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.

Given:  A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.

From the above information we can write,

Let, u is the boat speed in still water, then

\(\frac{30}{u-3} = \frac{42}{u+3}\)

Taking cross multiplication,

30(u + 3) = 42(u - 3)

Solving,

30u + 90 = 42u - 126

42u - 30u -126 -90 = 0

12u = 216

u = 18

Therefore, the speed of boat in still water is, 18 miles per hour.

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