For a certain company, the cost function for producing x items is C(x)=40x+100 and the revenue function for selling x items is R(x)=−0.5(x−110)^2+6,050 . The maximum capacity of the company is 130 items.
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!

Answers to some of the questions are given below so that you can check your work.
1.Assuming that the company sells all that it produces, what is the profit function? P(x)=
2.What is the domain of P(x) ? Hint: Does calculating P(x) make sense when x=−10 or x=1,000 ?
3.The company can choose to produce either 70 or 80 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 70 items =
Profit when producing 80 items =
4.Can you explain, from our model, why the company makes less profit when producing 10 more units?

The number of servings that can be obtained from the can is 3 3/4.

An equation is a formula that links two statements and uses the equals sign (=) to indicate that the statements are equivalent. A mathematical statement proving the equality of two algebraic expressions is called an equation. For instance, the equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14. The relationship between the two sentences that appear on opposing sides of a letter is expressed mathematically. The single variable and the symbol are typically the same. Like 2x - 4 Equals 2, for example.

To find the number of servings that can be obtained from the can, we need to divide the total weight of vegetables in the can by the weight of one serving:

Number of servings = (15/16) ÷ (1/4)

= (15/16) × (4/1)

= 60/16

= 15/4

Therefore, the number of servings that can be obtained from the can is 15/4.

None of the answer choices match this result exactly, but we can simplify 15/4 to 3 3/4, which is answer choice D.

So the answer is D. 3 3/4.

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The area of the shaded region of the composite figure is 389 square units.

A geometric shape made up of two or more simpler shapes is known as a composite figure. You must divide a composite figure into simpler shapes and then add up each shape's unique regions to determine the composite figure's area.

The methods you can take to determine a composite figure's area are as follows: Slice up the composite figure into more basic forms. You can separate the composite figure into its component parts, for instance, if it is made up of a rectangle and a triangle.

Calculate the area of each shape separately.

The total area of the composite figure can be calculated by adding the areas of all the simpler shapes.

The shaded region can be divided into a rectangle and a triangle.

The area of the rectangle with l = 19 and w = 17 is:

Area = length x width = 17 x 19 = 323 square units

Now, the dimensions of the triangle are:

base = 17 - 6 = 11

height = 31 - 19 = 12

Thus,

Area = (base x height) / 2 = (11 x 12) / 2 = 66 square units

Now, the total area of the shaded portion is:

Area = 323 + 66 = 389 square units.

Hence, the area of the shaded region of the composite figure is 389 square units.

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Answer:

A) f(-1) = 3

B) Vertex: (1;9)

C) y = 6

Step-by-step explanation:

Given:

[tex] f(x) = - {x}^{2} + 2x + 6[/tex]

a = -1, b = 2, c = 6

A) Replace the x with -1 in this function:

[tex]f( - 1) = - ({ - 1})^{2} + 2 \times ( - 1) + 6 = - 1 - 2 + 6 = 3[/tex]

.

B) First, let's find x vertex and then replace x with its vertex value in the given function to find y vertex:

[tex]x(vertex) = \frac{ - b}{2a} = \frac{ - 2}{2 \times ( - 1)} = \frac{ - 2}{ - 2} = 1[/tex]

[tex]y(vertex) = {1}^{2} + 2 \times 1 + 6 = 9[/tex]

Vertex: (1;9)

.

C) The parabola will cross the y-axis when x is zero (replace x with 0 in the given function):

[tex] - {0}^{2} + 2 \times 0 + 6 = 0 + 0 + 6 = 6[/tex]

y = 6

Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.

To find the annual amount, you first need to know the frequency of the payment. If the payment is made monthly, you need to multiply the monthly payment by 12 to get the annual amount. If the payment is made weekly, you need to multiply the weekly payment by 52 (the number of weeks in a year) to get the annual amount.

If the payment is irregular or occurs at different intervals, you can add up the total amount received over the course of the year and use that as the annual amount.

by the question.

To calculate the balance of Account 1 after 4.8 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

where:

A = the final amount

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

Plugging in the values given in the problem, we have:

[tex]A = 8100(1 + 0.047/365)^{(365*4.8)}[/tex]

[tex]A=8100(1+0.00128)\\A=8100(1.00128)\\A=8,110.43[/tex]

[tex]A \approx8,110.43[/tex]

Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.

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Answer:

26

Step-by-step explanation:

10 + 15

Answer:

Step-by-step explanation:

yes you would. they are very strict with food stamps or EBT card they will still ask for the 3 months for  so put in your 3 months and you should be fine.

Answer:

-7.225 according to a calculator.

The ascending order of the fraction is 70/11, 51/8, 62/7, 85/9.

Ascending order is a method of arranging numbers from smallest value to largest value.

For example, arranging , 3,1,2,5,6,8,4 in ascending order, we start from the least, which is 1 and ends with the greatest which is 8 i.e 1,2,3,4,5,6,8

To actually know the least and the greatest we will have find the value of each fraction.

62/7 = 8.86

51/8 = 6.38

85/9 = 9.44

70/11 = 6.36

Therefore , with the values found the arrangement from least to the greatest is

70/11, 51/8, 62/7, 85/9

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Joel needs to practice for another 9/4 hours or 2 1/4 hours to meet his goal.

To solve the problem, we need to add up the number of hours Joel has practiced so far and subtract it from his goal of 4 1/2 hours per week.

First, we need to convert the mixed numbers to improper fractions:

Next, we add the fractions:

3/2 + 5/4 + 4/4 = 6/4 + 5/4 + 4/4 = 15/4

So far, Joel has practiced for 15/4 hours this week.

To find out how many more hours he needs to practice to meet his goal, we subtract 15/4 from 4 1/2:

4 1/2 - 15/4

We need to make the denominators the same by finding a common denominator of 4:

4 2/2 - 15/4 = 9/4

Therefore, Joel needs to practice for another 9/4 hours or 2 1/4 hours to meet his goal.

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Answer:

Randy makes 45 cents more than he did when he started.

Step-by-step explanation:

If Randy makes $234 for a 40 hour week, that means he makes $5.85 an hour. You can find how much he makes currently by dividing the total amount he earned by the amount of hours worked.

[tex]234/40=5.85[/tex]

He initially earned $5.40 an hour and he now earns $5.85. By subtracting his final earnings by his initial earnings it gives you the amount his earning increased by.

[tex]final= $5.85initial= 5.40[/tex]

[tex]5.85-5.40=0.45[/tex]

He makes 45 cents more than he did when he started.

Since m_MN = m_AB, we can conclude that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

Triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is usually considered the simplest type of polygon. Triangles are distinguished by their sides, angles, and whether or not they are equilateral, isosceles, or scalene. The sides of a triangle are always connected, and the angles of a triangle always add up to 180°.

Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of a triangle. Then the point M, which is the midpoint of the side AB, coordinates M(x1 + x2 / 2, y1 + y2 / 2). Similarly, the point N, which is the midpoint of the side AC, has coordinates N(x1 + x3 / 2, y1 + y3 / 2).

The slope of the segment MN is given by:
m_MN = (y1 + y3 / 2 - (y1 + y2 / 2)) / (x1 + x3 / 2 - (x1 + x2 / 2))

The slope of the segment AB is given by:
m_AB = (y2 - y1) / (x2 - x1)

Substituting the coordinates for M and N into the equation for m_MN, we get:
m_MN = (y1 + y3 / 2 - (y1 + y2 / 2)) / (x1 + x3 / 2 - (x1 + x2 / 2))
= (y3 - y2) / (x3 - x2)

Substituting the coordinates for A and B into the equation for m_AB, we get:
m_AB = (y2 - y1) / (x2 - x1)
= (y3 - y2) / (x3 - x2)

Since m_MN = m_AB, we can conclude that the segment joining the midpoints of two sides of a triangle is parallel to the third side.

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After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.

A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.

A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.

6 is tο 40% as X is tο 100%

Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2[/tex]

Answer:

- 14c - 5

Step-by-step explanation:

5(- c- c - 1) - 4c ← distribute parenthesis by 5

= - 5c  - 5c - 5 - 4c ← collect like terms

= - 14c - 5

Answer:

yes, because the results are unlikely to occur by chance

Step-by-step explanation:

1/1000 is converted to 10% as a decimal. That's like saying for everyone 1000 people, at least one of the can be this "random chance". The smaller the general population is, the higher the affect this percentage has on that group. If the population is lower, than there might be more of a chance that it'll occur but also because there's a smaller population, there's less variety.

The coordinates of the images after the translation are E'(-4,-1), F'(-3,-4), and G'(2,-1).

To translate a point 2 units down, we subtract 2 from its y-coordinate.

For point E(-4,1), the image E' will have coordinates (-4,1-2) = (-4,-1).

For point F(-3,-2), the image F' will have coordinates (-3,-2-2) = (-3,-4).

For point G(2,1), the image G' will have coordinates (2,1-2) = (2,-1).

Therefore, the coordinates of the images after the translation are E'(-4,-1), F'(-3,-4), and G'(2,-1).

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Answer:

  √(25+12√2) ≈ 6.48

Step-by-step explanation:

You want the length of the longest side, labeled x, in the obtuse triangle with sides of lengths 3 and 4 and angle 135° between.

The law of cosines tells you ...

  c² = a² +b² -2ab·cos(C)

Using this here, we have a=4, b=3, C=135°:

  x² = 4² +3² -2·4·3·cos(135°)

  x² = 25 -24(-√2/2) = 25 +12√2

  x = √(25 +12√2) ≈ 6.48

Mariah fοrmulate the equatiοn as 150= 2B+3T

And Chris fοrmulate the equatiοn as T = 50-2/3B

A assertiοn that twο expressiοns are equal is knοwn as an equatiοn. Twο things are equal, accοrding tο an equatiοn.

Given,

A grοcer will spend $150 οn beans and tοmatοes cοmbined. Beans cοst $2 per pοund and tοmatοes cοst $3 per pοund.

Here B be a number οf pοunds οf beans and T the cοrrespοnding number οf pοunds οf tοmatοes the grοcer cοuld buy.

Sο we can write

2B + 3T= 150…….(1)

Mariah says she has a simple equatiοn but it's nοt in the fοrm B= (sοme expressiοn) οr T= (sοme expressiοn)

Sο the equatiοn we can write in the fοrm οf cοst

150= 2B+3T

Chris tries tο fοrmulate an equatiοn in the fοrm οf T

2B + 3T= 150

Or, 3T= 150-2B

Or, T = 50-2/3B

Equatiοn that is fοrmed by Mariah is 150= 2B+3T

Chris fοrmulate the equatiοn as T = 50-2/3B

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Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer:

here is ur answer....OPTION "D"

Step-by-step explanation:

Therefore, the researcher can conclude that SAM-e has a significant effect on the moods of Alzheimer's patients.

Given:

[tex]n = 30, \bar{X} = 26.2, \mu = 28.1, S = 2.97, \alpha = 0.01[/tex]

Hypothesis:

[tex]ANSWER: D. H0: \muSAM-e = 28.1; Ha: \muSAM-e \neq 28.1[/tex]

Degrees of Freedom = n-1 = 30-1 = 29

The critical t scores are:

[tex]t\alpha/2, n-1= t0.01/2, 30-1 = \pm 2.7564[/tex]

The estimated standard error is: [tex]S/\sqrt{n} = 2.97/\sqrt{30} = 0.5422[/tex]

Test statistic:

[tex]t = \frac{\bar{X} - \mu }{S/\sqrt{n}} = \frac{26.2 - 28.1}{2.97/\sqrt{30}} = -3.50[/tex]

[tex]|t| > t\alpha/2, n-1 , i.e 3.50 > 2.7564, Reject H0 at 1% level of significance.[/tex]

The t-statistic lies in the critical region. Therefore, the null hypothesis is Rejected

Therefore, the researcher can conclude that SAM-e has a significant effect on the moods of Alzheimer's patients.

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To find on what interval the temperature is positive, we need to find the values of x for which f(x) is greater than zero.

The function f(x) is defined as:

f(x) = -3|x - 4.7| + 2

Since the absolute value of any real number is always non-negative, we can see that f(x) will be positive only if the expression inside the absolute value bars is less than 2/3. So, we can set:

-3|x - 4.7| + 2 > 0

Solving for |x - 4.7|, we get:

|x - 4.7| < 2/3

This means that x must be within 2/3 units of 4.7. So, the interval on which the temperature is positive is:

4.7 - 2/3 < x < 4.7 + 2/3

Simplifying, we get:

4.0333 < x < 5.3667

Therefore, the temperature is positive on the interval (4.0333, 5.3667).

Sequence from least interest amount to greatest amount is

investment of $400 at 3% for 6 years

investment of $400 at 14% for 2 years

investment of $300 at 14% for 6 years

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any accumulated interest from previous periods. It is a linear function of time and is calculated by multiplying the principal amount, the interest rate, and the time period. The formula for simple interest is:

I = P × r × t

To calculate the simple interest earned on an investment of $400 at 3% for 6 years, we can use the formula:

I = P × r × t

Plugging in the given values, we get:

I = 400 × 0.03× 6

I = 72

Therefore, the simple interest earned on an investment of $400 at 3% for 6 years is $72.

To calculate the simple interest earned on an investment of $300 at 14% for 6 years, we can use the formula:

I = P ×r× t

Plugging in the given values, we get:

I = 300×0.14× 6

I = 252

Therefore, the simple interest earned on an investment of $300 at 14% for 6 years is $252.

To calculate the simple interest earned on an investment of $400 at 14% for 2 years, we can use the formula:

I = P ×r ×t

Plugging in the given values, we get:

I = 400 ×0.14 × 2

I = 112

Therefore, the simple interest earned on an investment of $400 at 14% for 2 years is $112.

Hence, sequence from least interest amount to greatest amount is

investment of $400 at 3% for 6 years

investment of $400 at 14% for 2 years

investment of $300 at 14% for 6 years

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Let x be the number of kilograms of apples in the fruit salad.

Then, the number of kilograms of oranges is (2/3)x, because the ratio of apples to oranges is 3:2.

The total weight of fruit salad is 3 kgs, so we can write an equation:

x + (2/3)x = 3

Simplifying and solving for x, we get:

(5/3)x = 3

x = (3*3)/5

x = 1.8

Therefore, there are 1.8 kg of apples and (2/3)*1.8 =

Answer: B

Step-by-step explanation:

The volume of the cylindrical water tank can be calculated as:

Volume = π x radius^2 x height

We know that the tank holds 1,200 liquid gallons, which is equivalent to:

1,200 / 7.48 = 160.43 cubic feet

We also know that the radius of the tank is 2.4 feet. Substituting these values into the formula, we get:

160.43 = 3.14 x 2.4^2 x height

Solving for height, we get:

height = 160.43 / (3.14 x 2.4^2) = 8.9 feet (approx.)

Therefore, the approximate height of the water tank is 8.9 feet (b).

Answer:

its B, 8.9, trust me, I got it right on the test

Step-by-step explanation:

Answer: True

Step-by-step explanation:

12-2=10

11-1=10

Answer:

True

Step-by-step explanation:

12-2 equals to 10

11-1 also equals to 10

Therefore, 12-2=11-1 is true

Answer: $x^2+y^2=9$

Step-by-step explanation:

A circle is the locus of points such that its distance from its center is constant. In our case, we have that the center of the circle is the origin, while the radius is 3. Thus, by the Pythagorean Theorem, the equation of the circle is $x^2+y^2=3^2=9$.

Answer: D- Multiply the first fraction by 2/2 and the second fraction by 3/3

Step-by-step explanation:

A) You never find the common numerator only denominator

B) Not logical

C) You would have to compare the fractions first

D) 2/9 * 2/2 = 4/18

5/6 * 3/3 = 15/18

5/6 is greater. This is the best way to compare the fractions, and so, Answer Choice (D) is the best option.

Answer:

B

Step-by-step explanation:

Every 2 balloons you buy the price goes up by 6.4 so for every 1 balloon, the price goes up by 3.2 since 6.4/2=3.2