PLEASE HELP!
The profit P (in dollars) made by a cinema from selling x bags of popcorn can be molded by P=2.36x-(x^2/25000)-3500, 0<=x<=50,000.

a) On what intervals is P increasing and decreasing?

b) How many bags of popcorn must the cinema sell in order to maximize profit and what is the maximum profit per bag?

Answer:

c

Step-by-step explanation:

c

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.

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Answer:

5=y-intercept

Step-by-step explanation:

the y intercept point is when y has a number but x is 0 so we see what is y (f(x)) and it is 5

The equivalent ratios are 8: 6 and 12:9.    

Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.  

Here we have 4:3

To find equivalent ratios, we can multiply both terms by the same number.

Multiplying by 2

=> 4 × 2 : 3 × 2

=> 8 : 6

Multiplying by 3

=> 4 × 3 : 3 × 3

=> 12: 9

Therefore,

The equivalent ratios are 8: 6 and 12:9.    

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Complete Question

What is the equivalent ratio for 4: 3

\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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Answer:

\(B' = (-96,-24)\)

Step-by-step explanation:

Given

\(A(0,6)\)

\(B(-8,-2)\)

\(C(8,-2)\)

Required

Determine the coordinates of B' if dilated by a scale factor of 12

The new coordinates of a dilated coordinates can be calculated using the following formula;

New Coordinates = Old Coordinates * Scale Factor

So;

\(B' = B * 12\)

Substitute (-8,-2) for B

\(B' = (-8,-2) * 12\)

Open Bracket

\(B' = (-8 * 12,-2 * 12)\)

\(B' = (-96,-24)\)

Hence the coordinates of B' is \(B' = (-96,-24)\)

Answer:

Bit late but the answer is (-4,-1)

Step-by-step explanation:

Took the test in k12

Answer:

Radius = 25.5 units

Diameter = 51 units

Step-by-step explanation:

r = radius of circle

d = Diameter of circle

  = \(2r\)

Circumference of circle = \(2\pi r\)

Substitute the provided value of the circumference:

                               \(51\pi = 2\pi r\)

r is to be isolated and made the subject of the formula:

                                 \(r = \frac{51\pi}{2\pi}\)

\(\pi\) in the numerator and denominator cancel each other outcompletely:

                                 \(r = \frac{51}{2}\)

                          ∴r = radius of circle = 25.5 units

This also means that:

\(d = 2r\)

\(d = 2(25.5)\)

∴d = Diameter of the circle = 51 units

Answer:

Step-by-step explanation:

Answer:

B would be 72 using a^2+b^2=c^2

Step-by-step explanation:

30^2 + x =78^2

in other words

900 + x =6084

6084-900= 5184

The square root of 5184 is 72

Answer:

50%

Step-by-step explanation:

Answer:

  a) 1.2 seconds

  b) 50 bpm

Step-by-step explanation:

The period is the value of t that makes the angle be 2π:

  5πt/3 = 2π

  t = 3(2π)/(5π) = 6/5

The period of the function is 6/5 = 1.2 seconds.

__

The number of beats per minute is ...

  (1 beat)/(1.2 s) × (60 s)/(1 min) = 60/1.2 beats/min = 50 beats/min

It will take 12 hours for 15 men to do same job.

How to determine this?

When amount of hour ∝ 1/number of men

When H represent Hour

And M represent the number of men

k to represent the constant

H = k/M as it is inversely proportional

It takes 10 men 18 hours to repair a road

18 = k/10

k = 18 × 10

k = 180

How long will it take 15 men?

When k = 180

H = k/M

H = 180/15

H = 12 hours

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We can solve this problem using two equations, one quadratic, and one linear, such as the graphs have no point in common, that is, both graphs have no common points or intersections between them. Therefore, we can use the following equations:

1. Quadratic equation: we can have one equation shifted to the right 2 units:

2. Now, we can use a line equation so that it does not pass through the quadratic equation. Since most of the quadratic equation is in the first quadrant, we can use a line with a negative slope. We can use the x-intercept equal to (-2, 0), and (0, -2). For this, we can find the slope for this line:

x1 = -2

y1 = 0

x2 = 0

y2 = -2

Applying the point-slope form of the line, we have:

Then, we have that the system of equation is:

If we graph both equations, we have the following graph:

Since we can see that both graphs will never intersect each other, we can conclude that this system does not have solutions in the Real set of numbers.

The linear equation is:

The quadratic equation is:

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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Answer:

- 6

Step-by-step explanation:

Rate of change over the interval 1 ≤ x ≤3 is given by
\(\dfrac{f(3) - f(1)}{3-1} \\\\= \dfrac{66- 78}{2}\\ \\= \dfrac{-12}{2}\\\\= -6\)

We can see from the table that the function value drops by 6 for every 1 unit increase in x

The true statement about the sampling distributions is: Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4.

Thus, option (C) is correct.

According to the Central Limit Theorem, for a large enough sample size, the sampling distribution of the sample mean tends to follow a normal distribution, regardless of the shape of the population distribution.

Therefore, both sampling distributions of size 4 and size 50 will be normal.

Moreover, the mean of the sampling distribution of the sample mean will be equal to the population mean.

Since the population mean is given as 26.8 years, the mean for both size 4 and size 50 will be 26.8 years.

Thus, option (C) is correct.

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Answer:

$367.5

Step-by-step explanation:

$350 × 0.05% = $17.5

$350 + $17.5 = $367.5

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

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there is no solution here. i checked, trust me.

The System of Equation have No Solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

6x - 12y = 15................(1)

2x - 4y = 6...........(2)

Now, Multiply equation (2) by 3 we get

6x - 12y = 15

6x - 12y = 18

____________

           0 = -3

also, 6/2 = -12/ (-4) ≠ 15/6 which is parallel lines.

So, the equation have No solution.

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A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Frequency :

The frequency of a particular data is the number of times the particular data value occurs. We represent the value of frequency as f.

Relative frequency :

Relative frequency is the fraction or proportion times an answer occurs in the data set.

Relative frequency can be written in decimal, fraction and percent.

To find the relative frequency, divide the frequency by the total number of data values.

Cumulative frequency :

Cumulative frequency is the collection of all previous frequencies together.

Cumulative frequency is also called frequency of non-exceedance.

There are two types of Cumulative Frequency Curves (or Ogives) :

1. More than type Cumulative Frequency Curve.

2. Less than type Cumulative Frequency Curve.

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Answer:

4/15

Step-by-step explanation:

The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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ANSWER

======

The graph is increasing from left to right.

======

EXPLANATION

======

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y. The slope indicates the rate of change in y per unit change in x. The y-intercept indicates the y-value when the x-value is

Answer:

Step-by-step explanation:

The angles in matching corners are called Corresponding Angles.

The Corresponding Angles Theorem: If a transversal cuts two parallel lines, their corresponding angles are congruent

Correct answer choice is C.

The missing reason is corresponding angles theorem.

Corresponding angles are angles that have the same relative position or measurement in two similar figures. They are formed when two lines, parallel or not, are intersected by a transversal.

Given that, lines a and b are parallel and line c is a transversal.

We need to prove ∠2 is supplementary to ∠8.

The proof:-

1. a || b, c is a transv.          1. given

2. ∠6 ≅ ∠2                          2. corresponding angles theorem

3. m∠6 = m∠2                     3. def. of congruent

4. ∠6 is supp. to ∠8            4. def. of linear pair

5. ∠2 is supp. to ∠8            5. congruent supplements theorem

Hence the missing reason is corresponding angles theorem.

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The distance are

a. 42.42

b. 15. 52

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52

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We can see that there are a total of 3 games that fall into the 51-57 category (games 1, 5, and 8). Therefore, the answer to the question is D. 3 games were in the 51-57 category. The correct option is D.

To solve this problem, we need to first determine which category each game falls into based on the given categories.
Game 1: 51 points - falls into the 51-57 category
Game 2: 70 points - falls into the 72 or more category
Game 3: 63 points - falls into the 58-64 category
Game 4: 59 points - falls into the 58-64 category
Game 5: 56 points - falls into the 51-57 category
Game 6: 75 points - falls into the 72 or more category
Game 7: 60 points - falls into the 58-64 category
Game 8: 55 points - falls into the 51-57 category
Game 9: 67 points - falls into the 65-71 category
Game 10: 64 points - falls into the 58-64 category
Now, we can see that there are a total of 3 games that fall into the 51-57 category (games 1, 5, and 8). Therefore, the answer to the question is D. 3 games were in the 51-57 category.
It's important to note that categorizing the data in this way is helpful for analyzing trends and patterns in the team's scoring over time, but it does not provide a complete picture of the team's performance in each game.

It's also worth considering other factors such as the team's opponents, the location of the game, and any injuries or other circumstances that may have affected the outcome.

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Answer:

Cube 1 = 30 cubic

Cube 2 = 48 cubic

Cube 3 = 72 cubic

Step-by-step explanation:

Cube 1 = 5x2x3

Cube 2 = 6x2x4

Cube 3 = 8x3x3

Radius of the circumscribed circle of triangle XYZ = 12.08

XY = 24

XZ = 22

JQ  =5

From the diagram we are given, we can see that; XJ = JY

Thus; XJ = JY = XY/2

XJ = JY = 22/2 = 11

Since we know JQ and XJ, let us consider triangle XJQ.

Using Pythagoras theorem;

(XQ)² = (XJ)² + (JQ)²

(XQ)² = 11² + 5²

(XQ)² = 146

XQ = √146

XQ = 12.08

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