The demand d for a company’s product at cost x is predicted by the function d(x) = 500 – 2x. The price p in dollars that the company can charge for the product is given by p(x) = x + 5. Use the formula Revenue = price × demand to find the revenue function for the product.

Using Altitude/leg Theorem. The solution for x are:

No.3: x = 12 units

No. 4: x = 8√3 units

The altitude theorem states that the altitude of the right triangle can be found by taking the square root of the product of the two segments of the hypotenuse that are created when the altitude is drawn.

In mathematical notation, if we have a right triangle with legs a and b, and hypotenuse c, and if h is the length of the altitude drawn from the right angle to the hypotenuse, then we have:

h² = ab

or

h = √(ab)

No. 3

Using the altitude theorem:

x = √(16*9)

x = 12 units

The Leg Rule states that the length of each leg of a right triangle can be found by taking the square root of the product of the hypotenuse and the adjacent segment on that leg.

In mathematical notation, if we have a right triangle with legs a and b, and hypotenuse c, then we have:

a² = bc or a = √(bc) and

b² = ac or b = √(ac)

No. 4

hypotenuse = 12 + 4 = 16

x = √(16 * 12)

x = 8√3 units

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Answer:

96 in³

Step-by-step explanation:

Volume = 2(BHD) / 2

The 2s cancel out

Volume = 3(8)4

Volume = 96

The length of QT is given as follows:

b. 12.

A bisection means that the larger angle is divided into two smaller angles of equal measure, and the side lengths of relative to the angle are equal.

The bisection segment for this problem is given as follows:

RT.

Hence the congruent segments are:

QT and TS = 12.

Thus the length of QT is given as follows:

QT = 12.

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Step-by-step explanation:

7x − 3 = 25

Add 3 to both sides.

7x = 28

Divide both sides by 7.

x = 4

Answer:

I think is add 3 from both sides

Step-by-step explanation:

7x-3=25

25+3=28

7x=28

x=4

Answer:

Step-by-step explanation:

4/4

8/6

4/6

Answer:

He computes the mean as $1,022.

Step-by-step explanation:

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

Answer:

C . 2y-x= -6

Step-by-step explanation:

A system of linear equations can have no solution, a unique solution or infinitely many solution.

We say two linear equations has infinitely many solutions when the result is true.

To determine if a system has infinitely many solutions, the coefficient of their respective variables (x and y) would be equal. Also the constant of both equations would be equal.

Given that x - 2y = 6

The coefficient of x is 1, coefficient of y is -2 and constant is 6. The equation with the same attributes is:

C . 2y-x= -6

2y - x = -6

multiply through by -1

x - 2y = 6

It is same as the above

Adding both x - 2y = 6 and 2y-x= -6 gives 0 = 0

The probability that the mean sulfate content of 9 randomly selected water samples is below 7 mg/L is approximately 0.1587 or 15.87%.

What is probability  ?

Probability is a measure of the likelihood of an event occurring. It is a mathematical concept used to quantify uncertainty and make predictions about the outcome of uncertain events. The probability of an event is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be expressed as a fraction, decimal, or percentage.

We can use the central limit theorem to approximate the sampling distribution of the mean sulfate content. Since the sample size (n = 9) is greater than 30 and the population standard deviation is known, the central limit theorem applies.

The standard error of the mean can be calculated as:

SE = σ / sqrt(n) = 1.5 / sqrt(9) = 0.5

where σ is the population standard deviation and n is the sample size.

The z-score for a sample mean of 7 mg/L can be calculated as:

z = (7 - 7.5) / 0.5 = -1

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than -1, which is approximately 0.1587.

Therefore, the probability that the mean sulfate content of 9 randomly selected water samples is below 7 mg/L is approximately 0.1587 or 15.87%.

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Answer:

The answer is the second option

Step-by-step explanation:

Kevin's kick can be considered the best among the four.

To determine the most impressive kick, we can compare the distances and heights achieved by each player.

Andre's kick reached a maximum height of 17 yards and landed 48 yards away from the goal.

Juana's kick followed the path y = -x + 14 - 24, where y represents the height of the ball in yards and x represents the horizontal distance from the goal line. From the graph, we can estimate that her kick landed about 38 yards from the goal and reached a maximum height of 14 yards.

Kevin's kick is shown in the graph, indicating that it landed approximately 19 yards from the goal and had a peak height of 20 yards.

Emiko's kick reached a maximum height of 18 yards and landed approximately 20 yards from the goal.

Considering these measurements, Kevin's kick stands out. It traveled the farthest, landing closest to the goal line, and it achieved the highest height, reaching 20 yards. Consequently, Kevin's kick can be considered the best among the four.

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Answer:

$28.08

Step-by-step explanation:

$33.17 - $12.82 = $20.35

75% of $20.35 = $15.26

$15.26 + $12.82 = $28.08

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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(a) The probability mass function of X will be P(X=n) = 5/(6n)

(b) E[X] =1.2

(c) Probability [ Alice win] will be =0.5

(d) The value of expected winnings will be 4.25

(a) Let 'p' represent the probability of getting the same number on both the dices on a roll of pair of die

And (1-p) = probability of not getting the same number on both the dices on a roll of pair of die

Sample space for the same number appearing on both the dices on a roll of pair of die = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

As there are a total of 36 outcomes on a roll of pair of dice,

p = 6/36 = 1/6

Let the events be defined as:

Dn : Both Alice and Bob roll the same number on the nth roll

Wn : The game is finished in the nth roll (i.e. Alice and Bob roll different numbers (as the numbers are different, one will be larger))

Then,P(W) = P(W) , n = 1,2,3,4....infinity

Wn takes place when event D takes place in the first (n-1) rolls and Event W takes place in the nth roll

\($\mathrm{P}(\mathrm{W})=\sum P\left(W_n\right), \mathrm{n}=1,2,3,4 \ldots .$\). infinity

And, W_n takes place when

Event D takes place in the first (n-1) rolls and event W takes place in the \($n^{\text {th }}$\) roll

\(P\left(W_n\right)=P\left(D_1\right)^* P\left(D_2\right)^* P\left(D_3\right) \ldots . .{ }^* P\left(D_{n-1}\right) P\left(W_n\right)P\left(D_n\right)\\=(p)P\left(W_n\right)\\=(1-p)\)

Implies

\($$\begin{aligned}& \left.P\left(W_n\right)=(p)^{n-1}\right)^*(1-p) \\& =\left((1 / 6)^{n-1}\right)^*(1-(1 / 6)) \\& =\left((1 / 6)^{n-1}\right)^*(5 / 6) \\& =5 /\left(6^n\right)\end{aligned}$$\)

(b)

\($$\begin{aligned}& \mathrm{E}[\mathrm{X}]=\sum n * P(X=n), \mathrm{n}=1,2,3,4 \ldots . . \text { infinity } \\& =\sum n * \frac{5}{6^n} \\& =5 * \sum n * \frac{1}{6^n}\end{aligned}$$\)

If \($\mathrm{S}=\sum n * \frac{1}{6^n}$\)

Then S is a sum of infinite aritho-geometric series of the form

\($$\sum_{k=1}^{\mathrm{inf}} k * r^k \text {, }$$\)

The sum of which is given as \($S=\frac{r}{(1-r)^2}$\) for 0 < r < 1

Here, r=(1 / 6)

\(\Rightarrow & S=\frac{\frac{1}{6}}{\left(\frac{5}{6}\right)^2} \\& =\frac{6}{25}\)

E[X] = (5) x (6/25) = (6/5)= 1.2

(c) Since the dies are fair, and the outcomes are independent, the probability of each player winning is equal

Therefore,

P(Alice WIn) = P(Bob WIn) = 0.5

(d) If X represent the round in which the game ends, then the probability of us winning in that round

P(W|X=n) = 0.5*P(X=n)

= (0.5)*(5/(6n))

P(W|X=1) = (0.5)*(5/(61)) = (5/12)

P(W|X=2,3,4...) = 0.5 - P(W|X=1) = (1/2) - (5/12) = (1/12)

Leth the variable W represent the winnings

(W|X=1) = 10

(W|X=2,3,4...) = 1

E[W] = P(W|X=1)*(W|X=1) + P(W|X=2,3,4...)*(W|X=2,3,4...)

= (10 x (5/12)) + (1 x (1/12))

= (50/12) + (1/12)= (51/12)= 4.25

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Answer:

1/ x21 y12

Step-by-step explanation:

The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

840

Step-by-step explanation:

You can divide by 5 and get 168

840/6 = 140

840/21 = 40

Answer:

The largest 3 digit number divisible by 5, 6, & 21 is 840.

Answer:

30%

Step-by-step explanation:

did it

Answer:

f(6) = 12

Step-by-step explanation:

We are given the following function:

\(f(x) = x^2 - 5x + 6\)

Evaluate the function f(6).

This is \(f(x)\) when \(x = 6\). So

\(f(6) = 6^2 - 5(6) + 6 = 36 - 30 + 6 = 12\)

f(6) = 12 is the answer.

Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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Plan 1:

Initial (fixed) fee: $60

Variable fee: $0.50 per mile

Plan 2:

Initial (fixed) fee: $0

Variable fee: $0.70 per mile

If we call x to the number of miles driven by Tony, then the cost of Plan 1 is:

P1 = 60 + 0.5x

The cost of Plan 2 is:

P2 = 0.7x

It's required to find the number of miles Tony should drive for both plans to cost the same, that is:

60 + 0.5x = 0.7x

Subtracting 0.5x:

60 = 0.7x - 0.5x

Operating:

60 = 0.2x

Dividing by 0.2:

x = 60 / 0.2

x = 300

Tony should drive 300 miles for both plans to cost the same.

Under that condition, both plans cost the same. Plan 1 cost:

P1 = 60 + 0.5*300

P1 = 60 + 150

P1 = $210

Plan 2 cost:

P2 = 0.7*300

P2 = $210

Both costs are equal

Answer:

neither

Step-by-step explanation:

parallel lines will have the same number next to the x

perpendicular lines will have the negative reciprocal number next to the x

(for example 2 and -1/2 are negative reciprocals)

y−4=3(x+5)

parenthesis first

y−4=3x+15

y=3x+19

y+3= −13(x+1)

y+3= −13x−13

y= −13x−16

3x and −13x are neither the same nor negative reciprocals of each other so

the answer is neither

Answer:

t = 25

Step-by-step explanation:

T is 25 because you take 1 away from the t+1 side and add the 1 to the 24 side.

Answer:

9

Step-by-step explanation:

when multiplying exponets with the same base we add the exponets

-4+6

2

3^2

and now to simplify

3*3

9

hopes this helps

Answer:

2/5

Step-by-step explanation:

Answer:

a is the right anser

Step-by-step explanation:

The average rate of change from day 2 to day 10 is given by the slope of the line m =

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The number of houses sold on day 2 is P

The number of houses sold on day 10 is Q

Let the first point be P ( 2 , 8 )

Let the second point be Q ( 10 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 2 - 8 ) / ( 10 - 2 )

Slope m = -6/8

m = -3/4

Therefore , the number of houses sold between day 2 and 10 is -3/4 houses per day

Hence , the slope is m = -3/4 houses per day

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The complete question is attached below :

The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day 10

Answer:

hvcr;vg;ie

Step-by-step explanation: