A company makes a profit of $50 per software program and $35 per video game. The company can produce at most 200 software programs and at most 300 video games per week. Total production cannot exceed 425 items per week. How many items of each kind should be produced per week in order to maximize the profit?

IDENTIFY VARIABLES, STATE OBJECTIVE FUNCTION, AND STATE THE CONSTRAINTS.

Answer:

x=-2/3

Step-by-step explanation:

2+3x-4=6x

2-4=6x-3x

-2=3x

x=-2/3

Answer:

-1000

Step-by-step explanation:

(5r)^3 for r = -2

(5 x +2)^3 =

(-10)^3 =

-1000

Answer:

The correct answer is D.  54 ÷ 18 = c

Step-by-step explanation:

Let's review the information given to us to answer the question correctly:

Number of cookies Mrs. Myles has to give to the students = 54

Number of students in Mrs. Myles class = 18

2. Write a number sentence using the variable c to represent the number of cookies each student gets.

c = Number of cookies Mrs. Myles has to give to the students/Number of students in Mrs. Myles class

Replacing with the real values, we have:

c = 54/18

The correct answer is D.  54 ÷ 18 = c

Answer:

[tex]\large\boxed{4\sqrt3}[/tex]

Step-by-step explanation:

[tex]\text{A geometric mean of}\ a\ \text{and}\ b:\\\\\sqrt{ab}\\\\\text{We have}\ a=4,\ b=12.\\\\\text{Substitute:}\\\\\sqrt{4\cdot12}=\sqrt{48}=\sqrt{16\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{16}\cdot\sqrt3=4\sqrt3[/tex]

Answer:

a = 10 cm

Step-by-step explanation:

Area of triangle, A = 51 cm²

base, b = 10.2 cm

Let height of triangle be a cm

Formula:-

[tex]A=\dfrac{1}{2}\times a\times b[/tex]

[tex]51=\dfrac{1}{2}\times a\times 10.2[/tex]

[tex]a=\dfrac{51\times 2}{10.2}[/tex]

[tex]a=10[/tex]

hence, the missing length is 10 cm

Answer:

88

Step-by-step explanation:

first multiply 7×8 #2 take that answer then multiply by 11

Answer:

616

Step-by-step explanation:

Answer:

i think that it's c

Step-by-step explanation:

The speed in feet per second is 247.5

The parachutist will fall 4950 feet during 20 seconds.

Step-by-step explanation:

Given,

Speed during free fall = 75 meters per second

It is given that,

1 meter = 3.3 feet

75 meter = 75*3.3 = 247.5 feet

Therefore;

Speed during free fall in feet = 247.5 feet per second

Now,

1 second = 247.5 feet

20 seconds = 247.5*20 = 4950 feet

Fall during 20 seconds = 4950 feet

The parachutist will fall 4950 feet during 20 seconds.

Keywords: multiplication

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The parachutist's speed in freefall, converted to feet per second, is 247.5 feet per second. In 20 seconds of free-fall, the parachutist would fall a total of 4950 feet.

The parachutist's speed in free-fall is given as 75 meters per second. We know that 1 meter is equivalent to approximately 3.3 feet. So, to convert the speed from meters per second to feet per second, we multiply the speed in meters per second by 3.3. This gives us a speed of 75 * 3.3 = 247.5 feet per second.

Then, to find out how many feet the parachutist will fall during 20 seconds of free fall, we multiply the speed in feet per second by the time in seconds, which results in 247.5 * 20 = 4950 feet.

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Answer:

Step-by-step explanation:

As per the given image, the co-ordinates are, P(-4, -3), Q(-2, -3), R(5, 4) and S(3, 4).

Since, the scale factor is 2 and centered at the origin, we need to multiply the co-ordinates with 2 in order to get the co-ordinates of the figure after dilation.

Hence, the co-ordinates will be

P = (-8, -6)

Q = (-4, -6)

R = (10, 8)

S = (6, 8).

Answer:

x=8/7

Step-by-step explanation:

2/3=x/4+x/3

3x/12+4x/12=8/12

7x/12=8/12

x=(8/12)/(7/12)

x=(8/12)(12/7)

x=8/7

Answer:

48...

Step-by-step explanation:

12(4) equals 48oz

48oz= 3lb

Answer:

no

but 79 is as much smaller than

7900100

by 100001.2658

Step-by-step explanation:

that means that 7900100 is as much as 79 of 100001.2658.

I hope dis will help

Answer:

They have to drive  [tex]20\frac{1}{4}[/tex] miles more

Step-by-step explanation:

Given:

Total Distance of the road trip = [tex]32 \frac{3}{4}[/tex] miles

Distance  travelled already = [tex]12 \frac{1}{2}[/tex] miles.

To Find:

How much farther do they have to drive = ?

Solution:

The distance they have to travel farther = Total distance - distance  travelled

The distance they have to travel farther =  [tex]32 \frac{3}{4} - 12 \frac{1}{2}[/tex]

=>[tex]\frac{128 + 3}{4} - \frac{24 +1}{2}[/tex]

=>[tex]\frac{131}{4} - \frac{25}{2}[/tex]

=>[tex]\frac{131- 50}{4}[/tex]

=>[tex]\frac{81}{4}[/tex]

=>[tex]20\frac{1}{4}[/tex]

The area of the rectangle is 2000 square inches.

Given that the length of a rectangle is five times its width, if the perimeter of the rectangle is 120 inch, the following calculation must be performed to find its area:

Therefore, the area of the rectangle is 2000 square inches.

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The width of the rectangle is 10 inches and the length is 50 inches. The area of the rectangle is 500 square inches.

Let's denote the width of the rectangle as w. Since the length of the rectangle is five times its width, we can write the length as 5w. The formula for the perimeter of a rectangle is P = 2(l + w), so we can set up the equation 120 = 2(5w + w). Solving this equation, we find that the width is 10 inches and the length is 50 inches.

To find the area of the rectangle, we use the formula A = l * w. Plugging in the values for length and width, we get A = 50 * 10 = 500 square inches. Therefore, the area of the rectangle is 500 square inches.

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Answer:

therefore the left over board is 0.216[tex]a^{2}[/tex] where 'a' is length of a side of the black poster board.

Step-by-step explanation:

i) Sasha cuts 4 identical circles from a square piece of black poster.

ii) let each side of the square piece be a.

iii) let us divide the square piece into four equal square parts from which the four identical circles will be cut

iv) therefore the side of each smaller square will be [tex]\frac{a}{2}[/tex].

v) therefore the diameter of each identical circle will be [tex]\frac{a}{2}[/tex]

vi) therefore the radius if each of the four identical circles will be [tex]\frac{1}{2} \times \frac{a}{2} = \frac{a}{4}[/tex]

vii) the area of each of the four identical circles will be = [tex]\pi \times (\frac{a}{4} )^{2} = 3.14 \times (\frac{a}{4}) ^{2} = \frac{3.14a^{2}}{16} = 0.196a^{2}[/tex]

vii) the area of each of the four smaller squares = [tex]\frac{a}{2} \times \frac{a}{2} = \frac{a^{2} }{4} = 0.25a^{2}[/tex]

viii) therefore the area left over from each of the four smaller squares

= 0.25[tex]a^{2}[/tex] - [tex]0.196a^{2}[/tex] = 0.054[tex]a^{2}[/tex]

ix) therefore the left over board is given by 4 [tex]\times[/tex] 0.054[tex]a^{2}[/tex] = 0.216[tex]a^{2}[/tex] where a is length of a side of the black poster board.

Answer:

30/10 and 5/11

Step-by-step explanation:

Answers:

A. True

B. True

C. True

D. False

E. True

In short, only answer choice D is false. Everything else is true.

=================================

Explanations:

A. The ordering of FGH and LMN is important. This is because F and L pair up as the first letters of the triple letter sequences, so do G and M as the second letters. Segment FG pairs up with LM because we're talking about the first two letters of both sequences. At the same time, FH and LN pair up because they are composed of the first and third letters of FGH and LMN respectively. Due to the triangles being similar, we can say FG/LM = FH/LN, ie we have a proportion.

------------------

B. Segment LN is proportional to FH, as explained back in part A. For example, FH could be 10 times longer than LN, making FH = 10*LN. Once the scale factor is set, you must use it for the other pairs of sides as well.

------------------

C. Similar triangles have corresponding angles that are congruent. This means F = L, G = M and H = N. Dividing the measure of F over the measure of L leads to 1 (regardless of what the angles happen to be) due to the rule x/x = 1, where x is nonzero. The same thing happens with dividing the measures of angle G over angle M. We get 1 on both sides after simplifying this given equation, so it is a true equation.

-----------------

D. Similar triangles are not congruent, so their corresponding side lengths are not congruent either.

-----------------

E. As explained back in part C, the corresponding angles are congruent because we know the triangles to be similar. The ordering of the letters matter. Angles H and N are the third letters of FGH and LMN respectively, which is why they pair up and are congruent.

The correct options are A, B, C and E.

It is given that,

Explanation:

The triangles FGH and LMN are similar, so their corresponding angles are congruent and corresponding sides are proportional.

[tex]\dfrac{FG}{LM}=\dfrac{FH}{LN}[/tex]

It means option A is correct.

[tex]FH\sim LN[/tex]

It means option B is correct.

Using the definition of similarity,

[tex]\angle F\cong \angle L,\angle G\cong \angle M,\angle H\cong \angle N[/tex]

[tex]\dfrac{m\angle F}{m\angle L}=\dfrac{m\angle G}{m\angle M}=1[/tex]

It means option C is correct.

Corresponding sides are similar, not congruent. So, the statement [tex]GH\cong MN[/tex] is false.

It means option D is incorrect.

[tex]\angle H\cong \angle N[/tex]

It means option E is correct.

Thus, the correct options are A, B, C and E.

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Answer:

The number of adult ticket sold is [tex]12[/tex]

The number of child ticket sold is [tex]38[/tex]

Step-by-step explanation:

Given cost of adult tickets are $[tex]8[/tex], and cost of child tickets are $[tex]4[/tex]

Let the number of adult ticket sold is [tex]x[/tex]

Also, the number of child ticket sold is  [tex]y[/tex]

We can write two equation from given information.

[tex]x+y=50\ Equation\ (1)\\8x+4y=248\ Equation(2)[/tex]

Now, plug [tex]x=50-y[/tex] in [tex]Equation(2)[/tex] we get,

[tex]8(50-y)+4y=248\\400-8y+4y=248\\-4y+400=248\\-4y=248-400\\-4y=-152\\y=\frac{-152}{-4}\\y=38[/tex]

Now, from [tex]Equation(1)[/tex]

[tex]x+y=50\\x+38=50\\x=50-38\\x=12[/tex]

So, The number of adult ticket sold is [tex]12[/tex]. And the number of child ticket sold is [tex]38[/tex]

Answer:

15 crickets; 20 ladybugs

C = G + 10

L= C+5

Step-by-step explanation:

Crickets = C

Ladybugs = L

Grasshoppers = G

We know he found 5 grasshoppers, so:

C = G + 10  --> because he found 10 more crickets than grasshoppers

if we plug in 5 for G (grasshoppers), we can solve for C (crickets):

C= 5+10

15 Crickets

Now that we know he found 15 crickets we can make our second equation:

L= C+5  --> because he found 5 more ladybugs than crickets

if we plug in 15 C (crickets), we can solve for L (ladybugs):

L= 15+5

20 Ladybugs

If Jeff found 5 grasshoppers, the given information leads to two equations showing that he found 15 crickets and 20 ladybugs.

Based on the information given, you can form two equations according to the number of insects Jeff found.

If Jeff found 5 grasshoppers, you can substitute 5 for G in the first equation, which will give you the number of crickets: 5 = C - 10, gives C = 15.

Then, you can substitute C = 15 into the second equation to find the number of ladybugs: 15 = L - 5, gives L = 20.

So, Jeff found 15 crickets and 20 ladybugs.

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Answer:

B. 3n-7

Step-by-step explanation:

The words seven less than means that seven will be subtracted. 3 times a number means that 3 is being multiplied by an unknown value or variable. Thats how you get 3n - 7

Answer:

8^2 x 3.14 x 6

Step-by-step explanation:

0.0023419203747073‬ but i think you mean 5124 by 12 and that is 427

Question:

Let p: x = 4 Let q: y = −2 Which represents "If x = 4, then y = −2”? p ∨ q p ∧ q p → q p ↔ q

Answer:

Option c: p → q

Explanation:

Option a: p ∨ q

p ∨ q means that either p is true or q is true or both are true.

Hence, Option a is not the correct answer.

Option b: p ∧ q

p ∧ q means that both p and q are true.

Hence, Option b is not the correct answer.

Option c: p → q

p → q means that if p is true, then q is also true.

Hence, Option c is the correct answer.

Option d: p ↔ q

p ↔ q means that if p is true, then q is true. If q is true, then p is true.

Hence, Option d is not the correct answer.

Thus, p → q is the correct option.

Answer:

it has only one solution

Step-by-step explanation:

The total number of flyers each girl will label is represented by the expression 200 + 4f. The number of earrings Rhonda has is represented by the expression 0.5x + 15. The amount of money Gina has is represented by the expression 2x + 50.

To find the total number of flyers each girl will label, we can set up an equation. Let f represent the number of additional flyers each girl will label. Since they have already labeled 200 flyers and are sharing the work evenly, each girl will label the same number of flyers. So, we can set up the equation: 200 + 4f = total number of flyers

To simplify this expression, we can combine like terms. The simplified expression representing the total number of flyers each girl will label is 200 + 4f.

For the second question, let x represent the number of earrings that Sharon has. Because Marilyn has half as many earrings as Sharon, Marilyn has 0.5x earrings. Rhonda has 15 more earrings than Marilyn, so she has 0.5x + 15 earrings. Therefore, the algebraic expression representing the number of earrings Rhonda has is 0.5x + 15.

For the third question, let x represent the amount of money Sam has in savings. Since Hector saved twice as much money as Sam, Hector has 2x in savings. Ted saved $100 more than Hector, so Ted has 2x + 100 in savings. Gina saved $50 less than Ted, so Gina has 2x + 100 - 50 in savings. Therefore, the algebraic expression representing the amount of money Gina has is 2x + 50.

Answer:

Mr. Duke received 1.65% percent of the agency's fee.

Step-by-step explanation:

Given:

Mr. Duke worked for a real-estate Agency.

He sold a house for $225,000. The agency’s fee for the sale was 3% of the sale price.

Mr. Duke received $3712.50 of the agency’s fee as his commission.

Now, to find the percent of the agency's fee Mr.Duke receive.

Mr. Duke sold house = $225,000.

Mr.Duke received = $3712.50.

So, to get the percent of agency's fee Mr. Duke receive:

[tex]\frac{3712.50}{225000} \times 100[/tex]

[tex]=0.0165\times 100[/tex]

[tex]=1.65\%.[/tex]

Therefore, Mr. Duke received 1.65% percent of the agency's fee.

Final answer:

To find the value of x in the equation 1.54x + 6.814 = 8.2, isolate x by subtracting 6.814 from both sides and then dividing by 1.54, which results in x = 0.9.

Explanation:

The question asks for the value of x in the equation 1.54x + 6.814 = 8.2. To solve for x, follow these steps:

Subtract 6.814 from both sides of the equation to isolate the term with x on one side: 1.54x + 6.814 - 6.814 = 8.2 - 6.814, which simplifies to 1.54x = 1.386.

Divide both sides of the equation by 1.54 to solve for x: x = 1.386 / 1.54.

Calculating the division gives x = 0.9.

The value of x in the equation 1.54x + 6.814 = 8.2 is 0.9.

Answer: $34

Step-by-step explanation:

Basically just 29+7

=34

Answer:

9

Step-by-step explanation:

the total ration is 8

the number of women = (3/8) x 24

                                     = 9

To find the number of women on the committee, we calculated the value of each part of the ratio as the total number of people divided by the sum of the parts of the ratio (24/8). Multiplying the number of women's parts in the ratio (3) by the number of people per part (3) gives us 9 women on the committee.

The subject of this question is Mathematics, specifically it deals with the topic of ratios and proportion within the high school curriculum. To determine the number of women on the First-Year College Experience Committee, we use the given ratio of men to women, which is 5:3, and the total number of people on the committee, which is 24. To solve the problem, we need to find out how many 'parts' of the ratio add up to the total. In this case, 5 parts for men plus 3 parts for women equals 8 parts in total.

Each part is worth 24 (total members) divided by 8 (total parts), giving us 3 people per part. Since the ratio represents 3 parts for women, we multiply the number of people per part by the number of parts for women: 3 parts times 3 people per part equals 9 people. Therefore, there are 9 women on the committee.