Suppose that the demand x (in units) for a product is x = 28,000 - 200p, where p dollars is the market price per unit. Then, the consumer expenditure for the product is E = px = 28,000p - 200p². For what market price will expenditure be greatest?

Answer:

c < - 4

Step-by-step explanation:

- 4c - 1 > 15 ( add 1 to both sides )

- 4c > 16

Divide both sides by - 4 , reversing the symbol as a result of dividing by a negative quantity.

c < - 4

Answer:

1.20548  Or 1.21

Step-by-step explanation:

Hope this helps!

Answer: 440 Days = 1.2054 Years = 1 Year, 2 Months and 2 Weeks

Step-by-step explanation: hope this helps a little!!!

Answer:

both numbers are positive so it would be in the top right quadrant so you would start on the right horizontal line, at zero then go over three boxes then go up six for that box. hope that helps :))

Answer:

See long explanation & picture below.

Step-by-step explanation:

See the picture below.

To graph do this:

y = x + 3

Start by graphing the y-intercept.

The y-intercept of y = mx + b is b, so here it is 3.

3 is a point on the y-axis, so its coordinates are (0, 3).

Now you use the slope to get other points.

The slope is m in y = mx + b.

In y = x + 3, it is as if you have y = 1x + 3, so the slope, m = 1.

The slope = 1

slope = rise/run

rise is up and down.

run is left and right

A slope of 1 is the same as a slope of 1/1.

That is a rise of 1 and a run of 1.

You start at the y-intercept, and your next point is 1 unit up and 1 unit to the right. See the other points in red up and to the right of (0, 3).

Then you draw a red line passing through all the red points and you extend it in both directions.

You have graphed the equation y = x + 3

To graph y = 4x - 6, use the same method.

The y-intercept is -6, so you plot a point on the y-axis at y = -6 in purple.

The slope is 4. 4 is the same as 4/1, so go 4 up and 1 right to get the next point. You can get a few points on the line this way.

Connect the purple points with a purple line and extend it in both directions.

You have now graphed y = 4x - 6

The intersection of the two lines is shown with a big green dot.

That is the solution of the system of equations.

The solution of the system of equations is the point of intersection of the two lines. You already knew it was (3, 6), and you were correct.

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Answer:

90

Step-by-step explanation:

Step-by-step explanation:

The fraction is 4/10 * 2/9 = 4/45.

Answer:

The probability is 4/45

Step-by-step explanation:

We know the chances of a blue marble is 4/10 so thats a first

The chances of a green marble WITHOUT the blue marble being put back is 2/9

So you multiply the two fractions

2/9*4/10

you’ll get 8/90 or simplified

4/45

Answer:

43.2

Step-by-step explanation:

40/100 * 108

4/100*108

43.2

Answer: y=-3x/4 -1/4

Step-by-step explanation:

y=mx+b

-1=-3/4 * 1 +b

-1=-3/4 + b

(-1=-3/4 + b)*4

-4=-3+4b

4b=-1

b=-1/4

y=-3x/4 -1/4

The variance of the scores in a sample tends to be less than or equal to the variability of the scores in the population from which the sample was obtained.

When we take a sample from a population, it is expected that the variability within the sample will be somewhat representative of the variability in the population. However, due to the random nature of sampling, there is a chance that extreme scores or outliers in the population may not be fully captured in the sample, resulting in slightly reduced variability. Therefore, the sample variance typically provides an estimate that is close to the population variance but is generally smaller due to the potential sampling variability.

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So the amount of water needed to fill the aquarium is approximately 1.87 gallons. This is our final answer, rounded to the nearest tenth.

To calculate the amount of water needed to fill the aquarium, we first need to find the volume of the tank. To do this, we can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height
Plugging in the measurements given in the problem, we get:
Volume = 2 feet x 0.5 feet x 1.5 feet
Volume = 0.75 cubic feet
Next, we need to convert cubic feet to gallons. There are 7.48 gallons in one cubic foot, so we can multiply the volume by 7.48 to get the amount of water in gallons:
0.75 cubic feet x 7.48 gallons/cubic foot = 5.61 gallons
However, we need to subtract the amount of space taken up by the gravel and the water that won't be filled to the top of the tank. The layer of gravel takes up 3 inches at the bottom of the tank, which is 0.25 feet. To find the volume of the gravel, we can use the same formula:
Volume = length x width x height
Volume = 2 feet x 0.5 feet x 0.25 feet
Volume = 0.25 cubic feet
We also need to subtract the volume of water that won't be filled to the top. The tank will be filled to a height of 1.25 feet (1.5 feet - 0.25 feet for the gravel), but we need to leave a 3-inch gap at the top. This gap is 0.25 feet, so we can find the volume of the unfilled space:
Volume = length x width x height
Volume = 2 feet x 0.5 feet x 0.25 feet
Volume = 0.25 cubic feet
Now we can subtract the volume of the gravel and unfilled space from the total volume of the tank:
Total volume - volume of gravel - volume of unfilled space = volume of water
0.75 cubic feet - 0.25 cubic feet - 0.25 cubic feet = 0.25 cubic feet
Finally, we can convert this to gallons:
0.25 cubic feet x 7.48 gallons/cubic foot = 1.87 gallons

So the amount of water needed to fill the aquarium is approximately 1.87 gallons. This is our final answer, rounded to the nearest tenth.

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Answer:

0.1

Step-by-step explanation:

Answer:

x=20; vertical angles theorem

Step-by-step explanation:

hi! we can use the vertical angles theorem for this. vertical angles are congruent to each other, meaning they are the same amount of degrees. so, we can set 2x+10 and 50 equal to each other.

2x+10=50

2x=40

x=20

x=20 because of the vertical angles theorem.

The center of the circle will be (2, -5) and the radius of the circle will be 1 unit.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The equation is given below.

x² - 4x + y² + 10y = -28​

Then the center and the radius of the circle will be

x² - 4x + 4 + y² + 10y + 25 = -28​ + 4 + 25

               (x - 2)² + (x + 5)² = 1²

Thus, the center and the radius of the circle will be (2, -5) and 1 unit respectively.

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Using relations in a right triangle, we have that:

1 - a) x = 54.28º.

1 - b) y = 57.794º.

1 - c) z = 31.056º.

2) The angle is of 62.8º.

3) The angle is of x = 53.017º.

4) The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

5) The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

The relations in a right triangle are given as follows:

For item 1a, we have that the sides, hence:

tan x = 8.9/6.4

x = arctan(8.9/6.4)

x = 54.28º.

For item 1b, we have the adjacent side and the hypotenuse, hence:

cos y = 9.7/18.2

y = cos^-1 (9.7/18.2)

y = 57.794º.

For item 1c, we have the opposite side and the hypotenuse, hence:

sin z = 6.5/12.6

z = sin^-1(6.5/12.6)

z = 31.056º.

For item 2, we have the sides, given at the graph at the end of the answer, hence:

tan x = 7.2/3.7

x = tan^-1(7.2/3.7)

x = 62.8º.

The angle is of 62.8º.

For item 3, first we find the hypotenuse of the bottom triangle, by the Pythagorean Theorem, as follows:

h² = 7.9² + 18.6²

h = sqrt(7.9² + 18.6²)

h = 20.21.

Then:

sin x = 20.21/25.3

x = sin^-1(20.21/25.3)

x = 53.017º.

For item 4, we have the adjacent side and the hypotenuse, hence:

cos(x) = 3/3.2

x = cos^-1 (3/3.2)

x = 20.364º.

The angle x is of 20.364º, which is greater than 17º, hence she can use the smooth tiles.

For item 5, we have the opposite side and the hypotenuse, hence:

sin y = 1.8/2.9

y = sin^-1 (1.8/2.9)

y = 38.37º.

The angle y is of 38.37º, which is greater than 35º, hence he can go down the slide.

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The value of x for the given triangle using cosine law will be 11.61°.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle,

By cosine law,

cos2x = (50² + 29² - 26²)/(2 × 50 × 29)

cos2x = 2665/2900

2x = 23.22°

x = 11.61°

Hence "The value of x for the given triangle using cosine law will be 11.61°".

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The answer is A because x-1 means moving left 1 on the x axis. As well, y+4 means moving 4 up on the y axis.

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

                                        Subtracting Integers

Subtract +9 - +4 =

Add The Opposite +9 + -4 =

Result +5

Answer:

x = 6

Step-by-step explanation:

Vertical angels are always equal, there fore angle A = angle B.

If angle A = angle B, and

angle A = 3x - 9 and angle B = x + 3, then

3x - 9 = x + 3

Now you can solve this like a regular inequality

Start by subtracting x by it's self then 3x to get both variables on one side.

2x - 9 = 3

Now you can add 9 to it's self and to 3 on the other side.

2x = 12

Finally, divide 2 by it's self and 12.

x = 6

The true statement is (b) Xavier used 15 oz of pineapple to with 24 oz of orange juice

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

The graph that represents the ratio of orange juice to pineapple juice

The graph passes through the origin

So, we have

slope = 16/10

Evaluate

slope = 1.6

When pineapple juice is 15, we have

orange = 15 * 1.6

orange = 24

Hence, the true statement is b

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The probability of any one undergraduate being selected in a random sample of 2550 undergraduates from a population of 25500 can be calculated using the formula:

Probability = Number of individuals in the sample / Total population

In this case, the probability would be:

Probability = 2550 / 25500 = 0.1 or 10%

Therefore, the probability of any one undergraduate being included in the random sample is 10%. This means that for every 10 undergraduates in the population, only one would be included in the sample. It is important to note that this probability assumes a truly random sampling process with no bias or influencing factors affecting the selection of individuals.

In conclusion, the probability of any undergraduate being in a random sample of 2550 undergraduates selected from a population of 25500 is 10%. This information can be useful in determining the representativeness of the sample and making inferences about the larger population based on the characteristics of the sample.

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10. 600 increased by 44% is = 864

11. The amount, when reduced by 60%, equals $2100.

12. Johnny's hourly rate before the raise was approximately $18.33.

13. The population of Enfield five years ago was approximately 65,674.

14. The amount of Susan's sales was approximately $25,333.33.

A percent is a way of expressing a fraction or a proportion out of 100. It is represented by the symbol "%". The term "percent" comes from the Latin word "per centum," which means "per hundred." Percentages are commonly used to describe relative quantities, proportions, or rates of change.

10. To find the increase of 44% on 600, we can calculate:

Increase = 600 * 44%

= 600 * 0.44

= 264

Therefore, 600 increased by 44% is 600 + 264 = 864.

11. Let's assume the amount we need to find is X. We can set up the equation as follows:

X - 60% of X = 840

X - 0.6X = 840

0.4X = 840

X = 840 / 0.4

X = 2100

12. Let's assume Johnny's hourly rate before the raise is X. We can set up the equation as follows:

X + 5.25% of X = $19.28

X + 0.0525X = $19.28

1.0525X = $19.28

X = $19.28 / 1.0525

X ≈ $18.33 (rounded to the nearest cent)

13. Let's assume the population of Enfield five years ago was X. We can set up the equation as follows:

X + 36% of X = 89,244

X + 0.36X = 89,244

1.36X = 89,244

X = 89,244 / 1.36

X ≈ 65,674 (rounded to the nearest whole number)

14. Let's assume the amount of Susan's sales is X. We can set up the equation as follows:

X * 15% = $3800

0.15X = $3800

X = $3800 / 0.15

X = $25,333.33 (rounded to the nearest cent)

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Using sigma notation, the given series is Σ (-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2) {for n = 1, 2, 3, ...}.

The series is:

1/3 - 2/4 + 3/5 - 4/6 + 5/7 - 6/8

We are to write this series using sigma notation and show all work.

The first numerator is 1, the second numerator is 2 (negative), the third numerator is 3, and so on. We can see a pattern where the numerator follows the index variable.

Since the signs alternate between addition and subtraction, we can introduce (-1)⁽ⁿ ⁺ ¹⁾ to ensure the correct sign for each term. Putting everything together, we can write the given expression using sigma notation:

Observe that each term is in the form of:

(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2) {for n = 1, 2, 3, ...}

So, we can write each term as (-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2) and then we can add up the terms using sigma notation.

Let's do it one step at a time.

Term 1: n = 1(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

               = (-1)⁽¹ ⁺ ¹⁾ × 1/(1+2)

               = (1/3)

Term 2: n = 2(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

                = (-1)⁽ⁿ ⁺ ¹⁾ × 2/(2+2)

                = (-2/4)

                = (-1/2)

Term 3: n = 3(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

                = (-1)⁽³ ⁺ ¹⁾ × 3/(3+2)

                = (3/5)

Term 4: n = 4(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

                = (-1)⁽⁴ ⁺ ¹⁾ × 4/(4+2)

                = (-4/6)

                = (-2/3)

Term 5: n = 5(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

                = (-1)⁽⁵ ⁺ ¹⁾ × 5/(5+2)

                = (5/7)

Term 6: n = 6(-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2)

                = (-1)⁽⁶ ⁺ ¹⁾ × 6/(6+2)

                = (-6/8)

                = (-3/4)

Now, we can write the series using sigma notation as follows:

Σ (-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2) {for n = 1, 2, 3, ...}

Therefore, using sigma notation, the given series is:

Σ (-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2) {for n = 1, 2, 3, ...} and each term is in the form of (-1)⁽ⁿ ⁺ ¹⁾ × n/(n+2).

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A total of 55.86 minutes have gone by since Greg started his run on the treadmill.

If Greg has completed 57% of his run, it means he has 43% of his run remaining.

To find out how many minutes have gone by, we can use proportions.

Let's say x is the total number of minutes Greg needs to complete his run:

x = 57% * 98 minutes

Evaluate

x =  minutes

Therefore, approximately 55.86 minutes have gone by since Greg started his run on the treadmill.

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Answer:

18s+369>573

Step-by-step explanation:

Answer:

if it a worksheet search the question online and the answer key comes up

Step-by-step explanation:

Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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Answer:

Answer is (1,3,5,6,7,9)