Mathematics College

A manufacturer of ski clothing makes ski pants and ski jackets. The profit on a pair of ski pants is $3 and on a jacket is $2. Both pants and jackets require the work of sewing operators and cutters. There are 60 minutes of sewing operator time and 48 minutes of cutter time available. It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket. Cutters take 4 minutes on pants and 8 minutes on a jacket. The manufacturer wants to make a minimum of 4 ski pants and 2 ski jackets, Let x represent the number of ski pants. Let y represent the number of ski jackets.

Answers

Answer 1

For the sewing operator:

[tex]8x\text{ + 4y }\leq\text{ 60}[/tex]

For cutter:

[tex]4x\text{ + 8y }\leq48[/tex]

The two above equation is solve to obtain the graph

The solution of the graph is where the two lines meet

The coordinate is (10, 4), at the this point the maximum profit is made

So 10 ski pants and 4 ski jackets is made to get maximum profit

The profit made is given by

P = 3x + 2y

x =10 , y = 4

P = 3(10) + 2(4)

P = 30 + 8 = $38

Related Questions

the sequence has 100 term and the listing of number were as follow x, 7, 11, 15.......... 399 find the value of x

Answers

Answer:

x = 3

Step-by-step explanation:

Given the sequence x, 7, 11, 15, ... 399, where 399 is the 100th term, you want to know the first term, x.

Arithmetic sequence

The differences of the first few terms are ...

11 -7 = 4

15 -11 = 4

This suggests an arithmetic sequence with a common difference of 4.

The first term, x, will be 4 less than the second term:

x +4 = 7

x = 7 -4 = 3

The value of x is 3.

Check

The n-th term of an arithmetic sequence with first term a1 = 3 and common difference d = 4 is ...

an = a1 +d(n -1)

an = 3 +4(n -1) = 4n -1

Then the 100th term is ...

a100 = 4(100) -1 = 399 . . . . consistent with the given information

An architect designs a house that is 10 m wide. The rafters holding up the roof are equal length and meet at an angle of 65°. The rafters extend 0.4 m beyond the supporting wall. How long are the rafters?

Answers

The length of the rafter when the architect design a house is 12.778m.

How to calculate the length?

The information illustrates that the architect designs a house that is 10 m wide and that the rafters holding up the roof are equal length and meet at an angle of 65°.

The rafters extend 0.4 m beyond the supporting wall. Then, the length will be:

cos65° = BC / AC

cos 65° = (5 + 0.4)/x

cos 65° = 5.4/x

x = 5.4 / 0.4226

x = 12.778m

The length is 12.778m

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The cafeteria prepares 80 meals a day for students if 3/8 of the meals are vegetarian, how many meals are are not vegetarian?

Answers

Meal prepared a day = 80 meals

Vegetarian meals will be

[tex]\text{vegetarian}=\frac{3}{8}\times80=\frac{240}{8}=30[/tex]

Non vegetarian meals = 80 - 30 = 50 meals

Complete the instructions to move from one point to another along the line
y = 2/3x + 1

___ ___ unit(s), then right 9 units.

Answers

Answer:

Step-by-step explanation:

the equation is written in slope intercept form

y= mx + b with m= slope and b= y-intercept

so in your equation

y=2/3x + 1,

the slope is 2/3 and the y-intercept is (0,1)

slope is also known as rise/run

so to move from one point to another, starting at (0,1) (since you know that point is on the line) you would move up 2 units and to the left 3 units.

hope this helped!

Can you please help me out with a question

Answers

Answer:

P = 80 units

Explanation:

Let's label some points in the triangle as:

Since the sides of the triangles are tangent to the circumference, we can write the following relationships:

XC = YC

AZ = AY

BX = ZB

So, the length of the missing side XC is equal to:

XC = YC = 14

On the other hand, the length of AB is the sum of the length of AZ and ZB, so we can calculate ZB as:

AB = AZ + ZB

26 = AY + ZB

26 = 18 + ZB

26 - 18 = ZB

8 = ZB

Because AZ and AY have the same length.

Finally, the measure of BX is equal to:

BX = ZB

BX = 8

Therefore, the perimeter of the triangle is:

Perimeter = AY + YC + AZ + ZB + BX + XC

Perimeter = 18 + 14 + 18 + 8 + 8 + 14

Perimeter = 80

So, the answer is 80 units.

Sebastian bought cookies from his sister's scout troop. He bought 4 boxes of shortbread cookies and 3 boxes of peanut butter cookies. There are 20 shortbread cookies in each box but only 18 peanut butter cookies in each box. How many cookies did Sebastian buy in all?

Answers

Sebastian buy 134 cookies.

Given,

He bought 4 boxes of shortbread cookies

and, 3 boxes of peanut butter cookies.

There are 20 shortbread cookies in each box.

but only 18 peanut butter cookies in each box.

To find the how many cookies did Sebastian buy in all?

Now, According to the question:

Formulate the above conditions:

18 x 3 + 20 x 4

Calculate the product or quotient

54 + 20 x 4

54 + 80

= 134

Hence, Sebastian buy 134 cookies.

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ERROR ANALYSIS In Exercise 30, describe and correct the error in finding the inverse of the functionf(x)=1/7x^2, x>=0y=1/7x^2x=1/7y^27x=y^2+-√7x=y

Answers

Given the function

[tex]\begin{gathered} f(x)=\frac{1}{7}x^2 \\ x\ge0 \end{gathered}[/tex]

To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

[tex]y=\frac{1}{7}x^2[/tex]

Step 2: Swap the variables:

[tex]x=\frac{1}{7}y^2[/tex]

Step 3: Solve for y:

[tex]y=\pm\sqrt[]{7x}[/tex]

But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

[tex]f^{-1}(x)=\sqrt[]{7x}[/tex]

Sophie records the total number of cans of cat food she uses after different numbers of days. She wants to know if the number of cans of cat food she uses is proportional to the number of days. After 3 days – 6 cans After 4 days - 8 cans After 9 days – 18 cans 1. Complete the table # of Days (x) 3 4 (fill in the questions marks) # of Cans (y) 6 8 18 # of Days (x) # of Cans (y) = 2 3 2 2 8-2 4 니 2. Is the number of cans of cat food used proportional to the number of days? Explain. 3. How many cans of cat food will Sophie use after 12 days?

Answers

The number of cans is proportional to the number of days, because each day it uses 2 c

Please help I am so bad at geometry

Answers

X = 31

Step by Step:

1) 2x+5=67
-5 -5
2) 2x=62
3) (2/2)x=(62/2)
4) x = 31

A store sells cat food in 4-pound bags. The cat food cost 2 dollars per pound.

Answers

Here is the completed table:

Number of bags purchased Total weight Total Cost

1 4 8

2 8 16

3 12 24

4 16 32

5 20 40

What is the total weight and the total cost?

One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.

Weight of 1 bag of cat food = 4

Weight of 2 bags of cat food = 4 x 2 = 8

Weight of 3 bags of cat food = 4 x 3 = 12

Weight of 4 bags of cat food = 4 x 4 = 16

Weight of 5 bags of cat food = 4 x 5 = 20

The cost of cat food is $2 per pound.

Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound

Cost of 1 bag of cat food = 1 x 4 x 2 = 8

Cost of 2 bags of cat food = 2 x 4 x 2 = 16

Cost of 3 bags of cat food = 3 x 4 x 2 = 24

Cost of 4 bags of cat food = 4 x 4 x 2 = 32

Cost of 5 bags of cat food = 5 x 4 x 2 = 40

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Gerard compares the offers at two different banks to decide where he should open a savings account. A. Draw a representation to show how much would be in the first savings account if Gerard's initial deposit were d dollars.

Answers

Explanations:

Given the following parameters

An initial deposit of Gerard is "d" dollars

For the savings with 5% interest, the interest on "d" dollars will be expressed as;

[tex]\begin{gathered} \text{Interest = 5\% of d} \\ \text{Interest = 0.05d} \end{gathered}[/tex]

Get the total savings plus interest in the first account

[tex]\begin{gathered} \text{Balance}=\text{Initial deposit + Interest} \\ \text{Balance=d+0.05d} \\ \text{Balance=1.05d} \end{gathered}[/tex]

Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the interest will be added to the first deposit, hence;

[tex]\text{Balance=(d+100)dollars}[/tex]

In Tabulated form:

Dm³ + n = rwhat does D equal?

Answers

[tex]Dm^3+n=r[/tex][tex]Dm^3=r-n[/tex][tex]D^{}=\frac{r-n}{m^3}[/tex]

joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles assuming she runs at the same pace how far can she run in 40 minutes? round to the nearest hundredth how far can she run in m minutes

Answers

In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles the distance she can she run in 40 minutes is 4.31 miles.

How can the number of miles be calculated?

This can be solved by the cross multiplication using the rate that given in the question.

We were told that joeita took 58 minutes of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is

58 minutes = 6.25 miles

40 minutes = X miles

Let X be the number of miles she want to cover in 40 minutes

we ca cross multiply the expression above as :

( 40 minutes * 6.25 miles ) = (58 minutes * X miles)

the X = 4.31 miles

Answers

[tex]\begin{gathered} 24\text{ students in total took an algebra test} \\ 18\text{ students passed the test} \\ \text{The percentage of students that passed is calculated as;} \\ \frac{Number\text{ that passed}}{Total\text{ number of students}}\times100 \\ \text{Percentage pass=}\frac{18}{24}\times100 \\ \text{Percentage pass=}\frac{1800}{24} \\ \text{Percentage pass=75} \end{gathered}[/tex]

The answer is 75%

. Suppose that in this process, 20% of the available raw sugar is changed to a refined sugar every 5 hrs. If a process begins with 1,000 pounds of raw sugar, write an exponential equation for the amount A of raw sugar (in pounds) t hrs after the process begins.

Answers

The exponential equation which represents the amount of raw sugar t hours after the process begins is; A = 1,000 (0.8)^(t/5).

Which equation represents the amount of raw sugar left t hours after the process begins?

It follows from the task content that the amount of raw sugar left after the process begins is to be determined according to the information given.

Since, 20% of the available raw sugar is changed to a refined sugar every 5 hrs, it follows that only 80% of the raw sugar is left after each successive time interval period.

Hence, the exponential model of the situation is such that;

A = 1,000(0.8)^(t/5).

Where t = number of hours after the process begins.

Therefore, the required equation is; A = 1,000(0.8)^(t/5).

Answers

Answer:

Step-by-step explanation:

None

What is the value of x?

4x=5x-12

Enter your answer in the box.

X=

Answers

Answer:

Step-by-step explanation:

First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.

Now we have this:

4x - 5x = -12.

Simplify:

-x = -12.

We need positive x, so divide both sides by -1.

x = 12.

Hope this helps! :)

The two triangles in the figure below are similar triangles. Solve for x.128846O 810O not enough information

Answers

Solution

step 1

Explain similarity

Both triangles are similar therefore the ratio of their corresponding sides must be equal.

Step2

State the corresponding sides

[tex]\frac{12}{x}=\frac{8}{4}[/tex]

Step 3

Find x

[tex]\begin{gathered} 8x\text{ = 12}\times4 \\ x\text{ =}\frac{48}{8} \\ x=6 \end{gathered}[/tex]

Hence option A

Emily and Andy each go to a hardware store to buy a wire. the table shows the relationship between the cost and the length of wire. Part A: Emily needs 24 ft of wire. how much will she spend on wire.Part B: Andy needs 13 yards of wire. how much will he spend on wire

Answers

Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

From the given graph choose one option

The length of the wire = 120 inches

The cost of 120 inches of wire = $6

Cost of 1 inch of wire = 6/120

= $0.05

Part A

The length of the wire = 24 feet

Convert the feet to inches

24 feet = 288 inches

The cost of 288 inches of wire = 0.05×288

= $14.4

Part B

The length of the wire = 13 yards

Convert the yards to inches

13 yards = 468 inches

The cost of 468 inches of wire = 0.05×468

= $23.4

Hence,

Part A

If Emily needs 24 feet of wire, then she has to spend $14.4

Part B

If Andy needs 13 yards of wire, then he has to spend $23.4

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Using standard normal table if the area is 0.125 what would the probability be ?

Answers

The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.

Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.

usBelow, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female3463TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%

Answers

[tex]\text{probability}=\frac{\text{ number of favorable cases}}{\text{ total number of }cases}[/tex]

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

[tex]\text{ P(}female|junior\text{)=}\frac{P(female\cap junior)}{P(junior)}[/tex]

The probability that a student is female and junior is:

[tex]P(female\cap junior)=\frac{6}{30}=\frac{1}{5}[/tex]

The probability that a student is a junior is:

[tex]P(junior)=\frac{2+6}{30}=\frac{8}{30}=\frac{4}{15}[/tex]

Finally, The probability that a student is female given that it is a junior is:

[tex]P(female|junior)=\frac{\frac{1}{5}}{\frac{4}{15}}=\frac{1}{5}\cdot\frac{15}{4}=\frac{3}{4}=0.75\text{ or 75\%}[/tex]

An architect is designing a gazebo which base is a regular dodecagon. At what angle should he cut to frame the base?

Answers

Answer:

Explanation:

Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.

So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;

[tex]\begin{gathered} \frac{360^{\circ}}{12}=30^{\circ}\text{ (degre}e\text{ per corner)} \\ \frac{30^{\circ}}{2}=15^{\circ\text{ }}(angle\text{ to be cut)} \end{gathered}[/tex]

The angle that the architect should cut to frame the base is 15 degrees

Write and solve an equation. Do not forget to label your variable or your units

Answers

Mr. Thompson weighs 260 pounds and he loses 4 pounds each month.

The equation will be :

w = 260 - 4m

where w is the weight after m months

when w = 220 pounds, the number of months will be :

220 = 260 - 4m

4m = 260 - 220

4m = 40

m = 40/4

m = 10

The answer is 10 months

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?A)21B)24C)20D)19

Answers

SOLUTION:

Step 1:

In this question, we are given the following:

The following two right triangles are similar.If side DE = 45, side HI = 36, and side DF = 30, what is the length of side HJ?

Step 2:

The details of the solution are as follows:

Since side DE = 45, side HI = 36, and side DF = 30.

Then, the length of side HJ =

[tex]\begin{gathered} Using\text{ Similar triangles, we have that:} \\ \frac{DF}{DE}=\frac{HJ}{HI} \\ Then,\text{ we have that:} \\ \frac{30}{45}=\frac{HJ}{36} \\ cross-multiply,\text{ we have that:} \\ 30\text{ x 36 = 45 x HJ} \\ Divide\text{ both sides by 45, we have that:} \end{gathered}[/tex][tex]HJ=\frac{30\text{ x 36}}{45}[/tex]

[tex]HJ\text{ = }\frac{1080}{45}[/tex][tex]HJ\text{ = 24 \lparen OPTION B \rparen}[/tex]

A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.

Answers

Answer:

75?

Step-by-step explanation:

Answer:

Step-by-step explanation:

3 divided by 5

0.6x125

y= 3x - 5 y= -6x + 4

Answers

The given system of equation:

y = 3x - 5 (1)

y = -6x + 4 (2)

We can solve the system of equation by using elimination method :

Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Subtract the equation (1) & (2)

[tex]\begin{gathered} y-y=3x-5-(-6x+4) \\ 0=3x-5+6x-4 \\ 0=9x-9 \\ 9x=9 \\ x=\frac{9}{9} \\ x=1 \end{gathered}[/tex]

So, we get x = 1

Substitute the value of x in the equation (1)

[tex]\begin{gathered} y=3x-5 \\ y=3(1)-5 \\ y=3-5 \\ y=(-2) \end{gathered}[/tex]

y = (-2)

So, the solution of the system of equations are : (x,y) = (1,-2)

Answer: (x,y) = (1,-2)

help me please......

Answers

There is the required value would be 6 in the box.

What is the Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

If you are in the partition XY in the ratio 3 to 4 from point X to point Y

To determine multiply the length of XY.

XY = 14 units then 3/7 of 14

= 3/7 × 14

Apply the multiplication operation,

= 42/7

Apply the division operation,

= 6

Hence, the required value would be 6 in the box.

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A simple random sample of 5 months of sales data provided the following information:

Month: 1 2 3 4 5

Units Sold: 97 110 89 97 92

a. Develop a point estimate of the population mean number of units sold per month.

b. Develop a point estimate of the population standard deviation (to decimals).

Answers

Using it's concepts, the point estimates for the population are given as follows:

a) Mean: 97 units sold per month.

b) Standard deviation: 16.06 units sold per month.

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of observations in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality(number of observations) of the data-set.

In the context of this problem, the 5 observations are given as follows:

97, 110, 89, 97, 92.

Hence the mean is given by:

M = (97 + 110 + 89 + 97 + 92)/5 = 97.

Considering the mean of 97 found above, the standard deviation is given as follows:

[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]

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In a survey, 10 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $49 and standard deviation of $2. Find the margin of error at a 80% confidence level.

Give your answer to two decimal places

Answers

Given the data that we have here where the number of people in the survey is 10, s = 2 and mean = 49, the margin of error is given as 0.76

How to solve for the margin of error

The margin of error can be used to provide the data that has to do with the amount of sampling error that would be in a given data statistic.

We would have to calculate the amount of error using the data that we have below.

We have the following values

number n = 10

mean u = 49

standard deviation sd = 2

The level of confidence c i = 80% = 0.80

we have to find the critical value

degree of freedom = 1 - 0.80

= 0.20

zα/2

= 0.20 / 2 = 0.10

= 1.383

The margin of error

= zα / 2 * s / √n

= 1.383 * 2/√10

= 1.383 x 2 / 3.623

= 1.383 x 0.552028

= 0.7634

The calculated margin of error is given as 0.7634

Answers

in this problem we have a vertical line

The equation of a vertical line is equal to the x-coordinate of the point that passes through it

in this case

the equation of the line is

x=-1

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