A company produces two products, A and B. At
least 30 units of product A and at least 10 units of
product B must be produced. The maximum
number of units that can be produced per day is
80. Product A yields a profit of $15 and product B
yields a profit of $8. Let a = the number of units of
product A and b = the number of units of product
B.
What objective function can be used to maximize
the profit?
P=
DONE✔
a+
b

Answer:-₍1,3₎

Step-by-step explanation:

To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:

$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$

$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$

Adding the equations, we get:

$10x + 15y - 9x - 15y = 20 - 21$

Simplifying, we get:

$x = -1$

Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:

$2(-1) + 3y = 4$

Solving for $y$, we get:

$y = 2$

Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:

$3(-1) + 5(2) = 7$

$10(-1) + 15(2) = 20$

Both equations are true, so our solution is correct.

The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.

We can rewrite this equation as:

1 - sin² x = sin²x

Solving for sin x, we get:

sin x = ±✓(1/2)

Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:

sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.

sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.

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The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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14 students excel in all three subjects.

Let's use the Principle of Inclusion-Exclusion to solve this problem.

Let A be the set of students excelling in Arts, B be the set of students excelling in Science, and C be the set of students excelling in Mathematics.

|A| = 24, |B| = 16, |C| = 13

|A ∩ B| = 16, |B ∩ C| = 13, |A ∩ C| = 12

Let x be the number of students who excel in all three subjects.

|A ∩ B ∩ C| = x

We are given that 2 students excel in none of the subjects.

So, |A ∪ B ∪ C| = 52 - 2 = 50

Using the Principle of Inclusion-Exclusion:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|

Substituting the given values, we get:

50 = 24 + 16 + 13 - 16 - 13 - 12 + x

Solving for x, we get:

50 = 24 - 12 + x

x = 38 - 24

x = 14

So, 14 students excel in all three subjects.

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Answer:

(10, -10)

Step-by-step explanation:

This are the farest the graph can go unless you want (100,-100)

Change the values from negative to positive and positive to negative to get the most farest results

Answer: D

Step-by-step explanation:

I graphed so you can see.  Count how far each are away.

(5,8) is 12 away

(-7,-5) is 13 away

So you answer is D

Or

You can also think of it as, for, (5, 8)  only the x changed so you only moved in the x direction.  subtract the numbers 5-(-7)=12

For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13

Answer:

Casey's monthly payment is $150.
Anita's monthly payment is $230.

Step-by-step explanation:

Part A:

The system of equations that describes this situation is:

a + c = Total monthly bill

a = c + 80

where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.

Part B:

To solve the system, we can substitute the second equation into the first equation and get:

(c + 80) + c = Total monthly bill

Simplifying this equation, we get:

2c + 80 = Total monthly bill

We also know that over the course of 4 months, their combined bills are $1,520. So we can write:

4(Total monthly bill) = 1520

Substituting the equation for Total monthly bill from the previous step, we get:

4(2c + 80) = 1520

Simplifying this equation, we get:

8c + 320 = 1520

Subtracting 320 from both sides, we get:

8c = 1200

Dividing both sides by 8, we get:

c = 150

So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:

a = c + 80

a = 150 + 80

a = 230

Therefore, Anita's monthly payment is $230.

The most appropriate measure of variability to use in this case is the IQR (Interquartile Range) of 13.

The reason for this is that the data appears to be skewed towards the higher values, with more donations in the higher range (from 40 to 59 dollars) and fewer in the lower range (from 10 to 39 dollars).

Using the range (which is the difference between the highest and lowest values) would not accurately represent the variability of the data, as it would be heavily influenced by the outliers. On the other hand, the IQR, which is the range of the middle 50% of the data, is a more robust measure of variability that is not influenced by outliers. Therefore, the IQR of 13 is the most appropriate measure of variability to use in this case.

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Answer:

Area = ½* height(a+b)

Where;

a=4units

b=8units

h=6units

Therefore Area= ½*6(4+8)

= ½*6*12

=36sq.un

Answer:

24sq²

Step-by-step explanation:

Area = ( b1 + b2) x h

          ---------------------

                     2

Area =   (8 + 4) x 6

          ---------------------

                     2

Area =     (12) x 6

          ---------------------

                     2

A = 72/2

A = 36

A = 1/2 * b * h

A = (1/2) * 4 * 6

A = (1/2) * 24

A = 12

36 - 12 = 24sq²

I hope this helps!

If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).

To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.

First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.

tan θ = -3/5

tan²θ = 9/25

sec²θ = tan²θ + 1 = 34/25

cos²θ = 1/sec²θ = 25/34

cos θ = √(25/34) = 5/√(34)

Now, we can use the Pythagorean identity to find sin θ:

sin²θ + cos²θ = 1

sin²θ = 1 - cos²θ

sin²θ = 1 - 25/34

sin²θ = 9/34

sin θ = √(9/34) = 3/√(34)

In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.

Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.

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James pays back approximately 82.33% of the total loan in interest over the 20-year period.

To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.

Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately

= 4.25% / 12

= 0.35% (4.25% annual rate divided by 12 months).

The monthly payment of $915.00 is comprised of both principal and interest.

In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.

To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months

20 years x 12 months/year = 240 months

and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.

To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:

$123,500 ÷ $150,000 x 100 ≈ 82.33%

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Answer:

exponential graph

Step-by-step explanation:

it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted

Answer:

See graph

Step-by-step explanation:

The graph of any function can be identified by making an x-y table.

Choose some values for x (often -2, -1, 0, 1, 2)

f(-2) = - 2^(-2) = - 1/4

f(-1) =  - 2^(-1) = - 1/2

f(-0) =  - 2^(-0) = - 1

f(1) =  - 2^(1) = - 2

f(2) =  - 2^(2) = - 4

The inequality in standard form that will represent the maximum number of cans of apple juice and cans of pineapple juice Stewart can use would be = 240ounce = 10a + 18p.

The total quantity of fruit punch that would be used for the birthday = 240 ounce.

The quantity of juice each can holds for apple juice,a, = 10 ounces.

The quantity of juice each can hold for pineapple juice,p,= 18 ounces.

Therefore the best expression in standard form would be = 240ounce = 10a + 18p.

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The probability that the team wins the debate is 0.6475

P(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)

= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)

= 0.6475

Therefore, the probability that the team wins the debate is 0.6475.

In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:

Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.

Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.

Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.

If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.

Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.

Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.

Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.

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Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".

Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.

No, Michael is not correct.

Translating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.

In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.

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As indicated by the question, the company's prices have been declining. As a result, a sharp increase is not anticipated, nor is a significant change in the following 30 days.

a public market where business stock and its derivatives can be traded at a set price on a regulated exchange. This means that there is little chance of a big shift in the stock price during the next 30 days.

Look at the query to comprehend the printing company's pricing pattern. The price of this printing company's shares has decreased, according tothe inquiry. It has fallen steadily over time.

Investors shouldn't anticipate a sudden increase in the price of this company's shares because the question doesn't indicate one. However, 30 days is a relatively small period of time to indicate any movement in the stock's price.

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Answer:

Step-by-step explanation:

2x2x2 = 2^3

2^3 = 8

2^x + 4 = 8

so x= 2

Answer:

B

Step-by-step explanation:

not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa

Answer:

Step-by-step explanation:

The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).

To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:

0.3 * sqrt(100) = 3

So the margin of error in terms of the number of vehicles is ±3.

Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.

So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.

Answer:  6

Step-by-step explanation:

you just get those numbers and times them 3 times 2 is 6

Answer:

A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.

B. Yes, it is possible. By the Triangle Inequality Theorem:

15 + 15 > 20, and 20 + 15 > 15

Over a given period of time, Seth sold more water bottles than Hayden.

To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.

We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:

Average daily sales rate for Seth = (10+20+30+40)/4 = 25

The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.

Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.

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The cost per highlighter is approximately $1.

To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;

80h + 20p = 120 (day 1)

120h + 40p = 200 (day 2)

We can simplify these equations by dividing both sides by 20;

4h + p = 6 (day 1)

6h + 2p = 10 (day 2)

Now we can use the first equation to solve for p in terms of h;

p = 6 - 4h

Substitute this expression for p into second equation;

6h + 2(6 - 4h) = 10

Simplify and solve for h;

6h + 12 - 8h = 10

-2h = -2

h = 1

Therefore, the cost per highlighter is $1.

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Answer:

The two numbers are 494 and 504

Step-by-step explanation:

Let x = one of the numbers

Let y = the other number

x + y = 998

x - y = 10   or x = y + 10

Substitute y + 10 for x in the first equation and solve for y

x + y = 998

y + 10 + y = 998  Subtract 10 from both sides

y + y = 988  Combine like terms

2y = 988  Divide both sides by 2

y = 494

One of the numbers is 494.

x = y + 10  Substitute 494 for y

x = 494 + 10

x = 504

The other number is 504.

Check:

x + y = 998

504 + 494 = 998

998 = 998 checks

x - y = 10

504 - 494 = 10

10 = 10 checks

Helping in the name of Jesus.

Answer:

option c) x=-6

Step-by-step explanation:

-15x = 90

= x = 90/-15

= x = (-6)

The side length x of the given right angle triangle is: 14.97

When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.

According to the Pythagoras Theorem, the following equation can be written as:

x² = 18² - 10²

x = √224

x = 14.97

Thus, that is the missing length of the given right triangle

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The percentage increase in the number of water bottles from February to April is 19%.

A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.

Therefore,

Therefore,

Number of water bottles in march = 4100 + 7% of 4100

Number of water bottles in march =4100 + 7 / 100 × 4100

Number of water bottles in march = 4100 + 287

Number of water bottles in march =  4387

Hence,

Number of water bottles manufactured in April = 4387 + 500 = 4887

Therefore,

percentage increase from February to April = 4887 - 4100 / 4100 × 100

percentage increase from February to April = 787 / 4100 × 100

percentage increase from February to April = 78700 / 4100

percentage increase from February to April = 19.1951219512

percentage increase from February to April = 19%

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the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,

In the given question,

Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.

From the problem, we know that:

The first mechanic worked for 20 hours, so he charged 20x dollars.

The second mechanic worked for 15 hours, so he charged 15y dollars.

Together, they charged a total of $2600, so we have:

20x + 15y = 2600

The sum of the two rates was $155 per hour, so we have:

x + y = 155

We can use these two equations to solve for x and y. First, we can rewrite the second equation as:

y = 155 - x

Then, we can substitute this expression for y into the first equation:

20x + 15(155 - x) = 2600

Simplifying and solving for x, we get:

20x + 2325 - 15x = 2600

5x = 275

x = 55

Now that we know x, we can use the second equation to find y:

y = 155 - x = 155 - 55 = 100

Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.

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