A small company manufactures two products: A and B. Each product requires three operations: assembly, finishing and testing. Product A requires 1 hour of assembly, 3 hours of finishing, and 1 hour of testing. Product B requires 3 hours of assembly, 1 hour of finishing, and 1 hour of testing. The total work-hours available per week in the assembly division is 60, in finishing is 60, and in testing is 24. Each item of product A has a profit of $50, and each item of Product B has a profit of $75. How many of each should be made to maximize profit?

The system of equations is -x + y = 4 and -2x + y = 0

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system

The above is represented in the (a) part of this solution

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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Answer:

6.3151

Step-by-step explanation:

461 ÷ 73 = 6.31506

it gets rounded to the 4th decimal place of to 6.3151

To find out how many boxes are needed to pack 939 souvenir paperweights, we divide the total number of paperweights by the number of paperweights that can fit in each box.

Total number of paperweights = 939

Number of paperweights per box = 11

To calculate the number of boxes needed, we divide the total number of paperweights by the number of paperweights per box:

Number of boxes needed = Total number of paperweights / Number of paperweights per box

Number of boxes needed = 939 / 11

Performing the division:

Number of boxes needed ≈ 85.36

Since we cannot have a fraction of a box, we round up to the nearest whole number:

Number of boxes needed = 86

Therefore, 86 boxes will be needed to pack 939 souvenir paperweights.

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Answer:

16:48 or 16 to 48 or 16 / 48

Step-by-step explanation:

Answer:

16:48

Step-by-step explanation:

16 is the total amount of students who want lemonade.
You add 16 with 32 to get 48 students in total.
So the ratio is 16:48.

n = - 3

How is the given equation  \(5^{n} =\frac{1}{125}\)   solved to find n ?

Converting the fraction to negative exponential form,

\(5^{n} ={125}^{-1} \\\\5^{n} ={(5^{3})}^{-1} \\\\\text{We know } (a^{n} )^{m} =a^{nm} \\\\\text{Applying this exponent power rule in the above expression},\\\\5^{n} = 5^{-3} \\\\\text{As the corresponding exponents are equal}\\\\n= -3\)

What are laws of exponents?

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Answer: 36, 64, 225

Step-by-step explanation:

6^2 is 6 multiplied by 6. Same goes for any number. 467^2 is 467x467.

I hope you found my answer helpful! If you have any other questions you can ask me :) If you ended up finding it helpful give it a thanks! Maybe even a brainliest if you feel like it ;D

Answer:

It occurs 18 times.

Step-by-step explanation:

The simplification of the addition of two or more fraction with unlike denominator is:

Convert the denominator with like terms and then add the numerators.

Method of simplification of addition of fraction with unlike denominator is:

Therefore, to simplify unlike fractions find least common multiple and add the like fractions.

The given question is incomplete, I answer the question in general according to my knowledge:

Simplification of adding fractions with unlike denominators with  example?

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Answer:

n = 10

Step-by-step explanation:

let the number be n , then

45 - 3n = n + 5 ( subtract n from both sides )

45 - 4n = 5 ( subtract 45 from both sides )

- 4n = - 40 ( divide both sides by - 4 )

n = 10

The cost of book has to be less than or equal to 26.39.

The amount of money Elena can buy has to be less than or equal to $30. Thus, the inequality sign to be used is the less than or equal to sign.

(1 + tax)cost of books + cost of bus fare ≤ value of the gift

1.08c + 1.5 ≤ 30

In order to determine the maximum cost of books, take the following steps:

Combine similar terms

1.08c  ≤ 30 - 1.5

Add similar terms together

1.08c  ≤ 28.50

Divide both sides of the equation by 1.08

c  ≤ 28.50 / 1.08

c  ≤ 26.39

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Answer:

6

Step-by-step explanation:

\(\tan 60^{\circ}~\text{equals y coordinate divided by x coordinate, where }(x,y) = \left(\dfrac 12, \dfrac{\sqrt 3}2 \right)\)

\(\tan 60^{\circ}\\\\= \dfrac yx \\\\\\=\dfrac{\sin 60^\circ}{\cos 60^\circ}\\\\\\=\dfrac{\tfrac{\sqrt 3}2}{\tfrac 12}\\\\\\=\dfrac{\sqrt 3}2 \times 2\\\\\\=\sqrt 3\)

This rule is enough

Now

Here A=60°

Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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14

Step-by-step explanation:

Her brother is 9 and she is 14.

say she is 14, 14+2=16 a perfect square.

14-10=4 which is the square root of 16.

So she is 14 and her brother is 9.

(He is a perfect square too, by the way.)

Elements in set A is 7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then,Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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According to the given information in the question the element in set A is  7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then, Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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Parker should build the playhouse with a height of 1.59 meters, which is equivalent to 159 centimeters.

Parker is planning to build a playhouse for his sister. The scaled model below gives the reduced measures for width and height. The width of the playhouse is 22 centimeters and the height is 10 centimeters. Not drawn to scale The yard space is large enough to have a playhouse that has a width of 3.5 meters.

If Parker wants to keep the playhouse in proportion to the model, he should use the following cross multiplication of the proportion to find the height: `3.5/22 = 3.5x/h`.

First, the given proportions should be simplified. We will cross-multiply the given proportions:`22h = 3.5 × 10``22h = 35

`Divide both sides by 22 to solve for h:`h = 35/22

`The final answer is `h = 1.59 meters`. Parker should build the playhouse with a height of 1.59 meters, which is equivalent to 159 centimeters.

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Please find attached photograph for your answer

The x-component of A is Ax = 25.7 units and the y-component of A is Ay = 21.3 units (both rounded to one decimal place).

Given: Vector A has a magnitude of 33.5 units and it points in a direction 320° counterclockwise from the positive x-axis.

Solution:We can start by finding the x-component and y-component of vector A.

So, we can use the following formulas:

Ax = A cos θ

Ay = A sin θ

where A is the magnitude of the vector and θ is the angle that it makes with the positive x-axis.

The given angle is 320° counterclockwise from the positive x-axis.

So, the angle made by vector A with positive x-axis is

360° – 320° = 40°.

Now, we can substitute the values in the formulas:

A = 33.5 units

θ = 40°

Ax = 33.5 cos 40°

Ay = 33.5 sin 40°

Ax = 25.7 units (rounded to one decimal place)

Ay = 21.3 units (rounded to one decimal place)

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the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Answer:

88 inches

Step-by-step explanation:

Divide the shape into 2 shapes and add all side lengths.

20+8+8+16+12+24=88

Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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Answer:

A is 6 and B is 4

Step-by-step explanation:

hope it helped!!!

Answer:

Jane is 11 1/4 years old.

Step-by-step explanation:

Subtract all of the numbers given.

\(13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}\).

To subtract this, we need to find a common denominator.

A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.

The new expression will look like this:

\(13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}\).

Now we can subtract.

\(13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}\)

Reduce the answer.

\(11\frac{3}{12}=11\frac{1}{4}\)

In decimal form 11.25

Hope this helps!

If not, I am sorry.

The required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

Given that,
Make two separate investments for a total of $4000. The percent return on Charles Schwab & co. At the end of the year was 5% and the percent return on Merill lynch was 7%. The combined return on both funds was $256.

here,
let x be the invested amount on Charles Schwab & co and y be the invested amount on Merrill lynch.
According to the question,
x + y = 4000
x = 4000 - y   - - - - - (1)
And
0.05x +0.07y = 256 - - - - (2)
From equation 1 and 2
x=1200 and y=2800

Thus, the required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

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Answer: {4,3,0,-4}

Step-by-step explanation:

The range is the set of all the values of y

Range {4,3,0,-4}

The correlation between variables x and y is 0.50 . The true option is option (c) .

that's the regression coefficient is positive for given bivariata.

Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The

sample correlation coefficient r quantifies the strength of the relationship.

Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.

Here:

Pearson's correlation coefficient is denoted by "r" and is

r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)

We have given that correlation between x and y is 0.50.

cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2

=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)

Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.

Symbolically it can be expressed as:

bₓᵧ= r σ ₓ /σ ᵧ

where x and y are correlated

σ ₓ --> standard deviation of X

σᵧ ---> standard deviation of y

We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.

Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.

Hence, Regression cofficient is positive.

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Step-by-step explanation:

first u gotta make the solutions on the other side a negative then keep the positive so now you've gotten rid of the lines so now I gotta solve both 4x-3<7 and 4x-3<-7 then solve liek you regular would with moving the 3 to the other side

4x<10 and 4x<-4 then divide both of them by the number itself to get x by itself

Answer:

A) E

B) Shape A and E

(i think)

Answer:

Adjacent angles

Step-by-step explanation: