This problem is similar to one from your textbook. Assume that a certain product has the demand function given by 9 = 1000e -0.02p (a) Write revenue, R, as a function of price. R(p) = !!! (b) Find the marginal revenue. R' (p) = !!! (c) Find the revenue and marginal revenue when the price is $5. Revenue (Rounded to nearest cent) = Marginal Revenue (Rounded to two decimal places) =

The correct option a. sugar in a serving, is to be plotted on the horizontal X-axis.

In response to the query, yes or no, depending on how much sugar is in a dish of cereal.

As amount of fat depends on the amount of sugar in a serving.

Sugar in a serving should therefore be displayed as an independent variable on the horizontal X-axis.

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The cost for each garage is modeled with linear equations, by graphing them, we will see that Garage A is cheaper for 10 hours.

First, we know that Garage A charges a fixed fee of $10, plus $2 per hour, then if you rent it for x hours, the total cost is given by the linear equation:

A(x) = $2*x + $10.

For Garage B, the fixed cost is $4, and there is an extra of $3 per hour, so the total cost after x hours is:

B(x) = $3*x + $4

The graph of the two linear equations can be seen below. The green line corresponds to A(x) and the blue line corresponds to G(x).

There we can see that for x = 10, the blue line is above the green one, so Garage B will have a greater cost, then the correct answer is that for 10 hours Garage A is cheaper.

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Answer:

yes

Step-by-step explanation:

Answer:To solve for q in the equation -18 + -3q = -63, we need to get q by itself on one side of the equation. We can do this by adding 18 to both sides of the equation:

-18 + -3q + 18 = -63 + 18

Simplifying, we get:

-3q = -45

Then, we can divide both sides of the equation by -3 to solve for q:

(-3q) / -3 = -45 / -3

Simplifying, we get:

q = 15

Therefore, the solution for q is 15.

Step-by-step explanation:

Answer:

0.049.

Step-by-step explanation:

The number after the 9 is 4 so 9 remains.

Answer:

\( \frac {1}{3}x - 5 \)

Step-by-step explanation:

Let the unknown number be x.

Translating the word problem into an algebraic expression, we have;

\( \frac {1}{3}x - 5 \)

Or

\( \frac {x}{3} - 5 \)

Simplifying further, we have;

\( \frac {x}{3} = 5 \)

Cross-multiplying, we have;

x = 15

Therefore, the above algebraic expression is five less a third of a number.

The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).

{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}

In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.

{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.

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Answer:

Only statement second is correct about the distribution.

Step-by-step explanation:

The stem plot data given to us is;

1 | 9

2 | 5

3 | 4   6   8   8

4 | 0   3   6   7   7

5 | 0   0   1    2

As it is given in the question that 1 | 9 = 19 sit-ups, so the data value are;

19, 25, 34, 36, 38, 38, 40, 43, 46, 47, 47, 50, 50, 51, 52

(a) The first statement that there is one outlier in the distribution is false as there are two outliers in the data (19 and 25) as they are very far from the rest of the data.

(b) The statement that the distribution is skewed left is correct because the tail of the distribution is towards the left.

(c) The statement that the center is around 47 is false as the center or mean of the data is 43 because the middle most data value is 43.

(d) The statement that the distribution is bimodal is false as there are is three modes in the data (38, 47 and 50), so the given distribution is trimodal.

Answer

it is the first one

explanation

I got it right

Answer:

4-8

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

I changed 4/12 to a fraction then simplified it

4/12=1/3

one gold fish ate their food for every 3 they fed

The missing parts of the statements using trigonometric ratios are respectively:

trigonometric ratio

0.6428

x feet

90 feet

45 ft

30°

The angle of depression is simply the same as the angle of declination as both are formed below the horizontal axis with a downward slope.

Thus, if the surveyor knows the angle of declination, then he can use trigonometric ratio to get the length X in the diagram.

The trigonometric ratio to be used is cosine since we have the hypotenuse and want to find the adjacent side. Thus;

The cosine of a 50° angle is 0.6428

This cosine represents when the length x feet is divided by 90 feet.

Now, if the angle of declination changed to 60°, the cosine would be 0.5 and the new length x will be 90 * 0.5 = 45 ft.

The angle of inclination will be 30°

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Conditions that had to be met in order to use the formula for the standard deviation of given sample proportion is np ≥ 10 and n(1-p) ≥ 10.

Therefore the answer is d. np ≥ 10 and n(1-p) ≥ 10.

To use the formula for the standard deviation of a sample proportion, we need to make sure that the sample size is large enough and that the number of successes (np) and failures (n(1-p)) in the sample are both at least 10.

In this case, we are given a sample size of 240 and a proportion of 0.054 who have been exposed to the virus. Thus, np = 240 x 0.054 = 12.96 and n(1-p) = 240 x 0.946 = 227.04. Both np and n(1-p) are greater than 10, so the conditions are met, and we can use the formula for the standard deviation of p:

sp = √[(p(1-p))/n]

= √[(0.03 x 0.97)/240]

≈ 0.019

Therefore, the standard deviation of the sample proportion is approximately 0.019.

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--The question is incomplete, answering to the question below--

"A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p = the proportion of residents who have been exposed in a random sample of 240. Which of the following conditions had to be met in order for us to use the formula for the standard deviation sp of p?

a. The population distribution is approximately Normal

b. n >= 30

c. n < 0.10 N

d. np >= 10 and n(1 -p) >= 10

e. √(np (1 - p)) >= 10"

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

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

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Step-by-step explanation:

8/15

Answer: \(\chi^2\) test statistic.

Step-by-step explanation:

The chi-square (\(\chi^2\)  ) test is a non-parametric statistical test(also known as Goodness of fit test) which is used to determine if a distribution of observed frequencies differs from the expected frequencies.

Chi-square statistic uses either nominal (categorical) or ordinal level data.

Hence, When determining how well an observed set of frequencies fits an expected set of frequencies, the test statistic is \(\chi^2\) test statistic.

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

Answer:

D: 141 KG

Step-by-step explanation:

7.05 x 20 = 141

Just multiply the mass of the object by however many objects there are if they all weigh the same.

Answer:

4.75 megabytes per second

Step-by-step explanation:

500-25 = 475

475 / 100 = 4.75

The volume of the given figure above would be = 4,095 yards³.

To calculate the volume of the given figure, it is first divided into two giving rise to a rectangular prism and a trapezoidal prism.

The volume of a rectangular prism= length×width×height

where;

length= 30yrds

width= 9 yards

height= 7 yards

volume= 30×9×7 = 1,890yards³

The volume of a trapezoidal prism= ½(a+b)×h×l

where;

a= 19yd

b= 30yd

h= 10yd

l= 9 yd

volume= ½(19+30)×10×9

= 49×5×9

= 2,205yards³

Therefore, the total volume of the figure would be ;

= 1,890+2,205

= 4,095 yards³

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Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

36 is a whole number.

Answer:

The number 3.6 is a rational number.

All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be

Answer:

Test statistic

|Z| = 2.105632 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

There is  difference exist between the drug group and placebo group

Step-by-step explanation:

Step(i):-

Given each group was made up of 150 Hulks. 78 of them reported an improvement from the placebo group.

first sample proportion

                  \(p^{-} _{1} = \frac{78}{150} = 0.52\)

Second sample proportion

                \(p^{-} _{2} = \frac{96}{150} = 0.64\)

a)  Null Hypothesis : H₀ : There is no difference exist between the drug group and placebo group

H₀ : p₁ = p₂

Alternative Hypothesis : H₁ : There is  difference exist between the drug group and placebo group

H₀ : p₁ ≠ p₂

b)

Step(ii):-

\(Z = \frac{p_{1} -p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } }) }\)

 where

            \(P = \frac{n_{1} p^{-} _{1} + n_{2} p^{-} _{2} }{n_{1}+n_{2} }\)

           \(P = \frac{150 X 0.52+ 150 X 0.64}{150+150 }\)

          P = 0.58

         Q = 1- P = 1- 0.58 = 0.42

  \(Z = \frac{p_{1} -p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } }) }\)

 \(Z = \frac{0.52 -0.64}{\sqrt{0.58 X 0.42(\frac{1}{150 } +\frac{1}{150 } }) }\)

Z =   -2.105632

|Z| = |-2.105632| = 2.105632

Level of significance = 0.05

Z₀.₀₅ = 1.96

Final answer:-

|Z| = 2.105632 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

There is  difference exist between the drug group and placebo group

Answer:

orange 9,87

Step-by-step explanation:

Answer:

y = x³ - 3x² + 4x - 12

Step-by-step explanation:

We are told that the polynomial intercept is 3 degree and has it's intercepts at 2, 2 and 3.

Now, at y - intercept, y = 0m

Thus, the polynomial is;. (x - 2)(x - 2)(x - 3) = 0.

This gives;

(x² - 4x + 4)(x - 3) = 0

This gives;

x³ - 12x + 4x - 3x² + 12x - 12 = 0

x³ - 3x² + 4x - 12 = 0

Answer:

2(1 - x)

Step-by-step explanation:

Twice the difference of 1 and a number

a number = x

The difference of 1 and a number is expressed as :

1 - x

Twice this difference, means the difference of (1-x) multiplied by 2

2 * (1 - x) = 2(1 - x)

Answer:

2% I think, I don't know, 4%‽

On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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Answer:

Step-by-step explanation:

In as much as I might give a warning on not to doubt oneself, I also need to put out what one should take note of when solving quadratic problems.

Using the general formula, it's of utmost importance to not mix the variables together. Remember, making "a", "b" and "b", "a" will lead to an entirely different answer, which is most likely wrong anyway.

It's important to take note of the signs too. Remember, the formula say,

-b ± √(b² - 4ac) / 2a

The first b is negative, and that means a negative value will turn positive there. These are very trivial steps, but they can also make or mar our efforts in getting the correct answer

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.