Find a linear function that models the cost, C, to produce x toys given the rate of change and initial output value. The cost to produce plastic toys increases by 90 cents per toy produced. The fixed cost is 40 dollars. C(x) = dollars Write a linear model for the amount of usable fabric sheeting, F, manufactured in t minutes given the rate of change and initial output value. Fabric sheeting is manufactured on a loom at 7.25 square feet per minute. The first five square feet of the fabric is unusable. F(t) = ft^2 is the amount of usable fabric sheeting manufactured in t minutes.

Answers

Answer 1

Answer:

C(x) = $40 + 0.9x

F(t) = 7.25t - 5

Step-by-step explanation:

Given that :

C(x) = Cost model to produce x toys

Fixed cost of production = $40

Rate of change = 90 cent per toy produced.

A linear model will take the form :

F(x) = bx + c ;

Where ; b = rate of change or slope ; c = intercept or initial value

Therefore, a linear cost model will be :

Cost model to produce x toys = fixed cost + (rate of change * number of toys)

C(x) = $40 + 0.9x

2.)

F(t) = amount of usable factory sheets manufactured in t minutes :

Rate of production = 7.25 ft² / minute

Number of unusable fabric sheeting = 5 ft²

The function, F(t) :

F(t) = 7.25t - 5


Related Questions

Số táo của An, Bình, Chi là như nhau. An cho đi 17 quả , Chi cho đi 19 quả thì lúc này số táo của Chi gấp 5 lần tổng số táo còn lại của An và Bình. Hỏi lúc đầu mỗi bạn có bao nhiêu quả táo? ( Giải bài toán trên bằng phương trình hoặc hệ phương trình )

Answers

Answer:

So, the initial number of apples is 7.

Step-by-step explanation:

The number of apples of An, Binh, and Chi are the same. An gave away 17 apples, Chi gave away 19 apples, so now Chi's apples are 5 times higher than the total remaining apples of An and Binh. How many apples did each of you have at first? (Solve the above problem by equation or system of equations)

Let the initial numbers of apples is a.

An gave 17 apples

Chi gave 19 apples

So,

x - 19 = 5 (x - 17 + x)

x - 19 = 5 (2x - 17)

x - 19 = 10 x - 85

9 x = 66

x = 7

a set of date consists of 225 observations. the lowest value of the data set is 2,403; the highest is

Answers

Answer:

8 classes

Step-by-step explanation:

Given

[tex]Least = 2403[/tex]

[tex]Highest = 11998[/tex]

[tex]n = 225[/tex]

Required

The number of class

To calculate the number of class, the following must be true

[tex]2^k > n[/tex]

Where k is the number of classes

So, we have:

[tex]2^k > 225[/tex]

Take logarithm of both sides

[tex]\log(2^k) > \log(225)[/tex]

Apply law of logarithm

[tex]k\log(2) > \log(225)[/tex]

Divide both sides by log(2)

[tex]k > \frac{\log(225)}{\log(2)}[/tex]

[tex]k > 7.8[/tex]

Round up to get the least number of classes

[tex]k = 8[/tex]

Identify the percent, amount, and base in this problem.
What percent of 80 is 40?

Answers

Answer:

50

Step-by-step explanation:

40: 80x100 =100 =(40x100): 80 =100): 80 =4000: 80 = 50

The percentage of the number 80 is 40 will be 50%.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The percentage is given as,

P = [(80 - 40) / 80] x 100

P = (40 / 80) x 100

P = 0.50 x 100

P = 50%

The percentage of the number 80 is 40 will be 50%.

More about the percentage link is given below.

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what is the sum of the geometric series 4∑ t=1 6t-1​

Answers

Answer:

Hello friend kya in snap and p to Trisha

Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.

Answers

Answer:

A. false B. true C. false D. true

Whope you all like this answer

AC if TC = 20q + 10q^2?

Answers

Answer:

AC = (20+ 10q)

Step-by-step explanation:

Given that,

Total cost, TC = 20q + 10q²

We need to find AC i.e. average cost.

It can be solved as follows :

[tex]AC=\dfrac{TC}{q}\\\\AC=\dfrac{20q + 10q^2}{q}\\\\AC=\dfrac{q(20+ 10q)}{q}\\\\AC={(20+ 10q)}[/tex]

So, the value of AC is (20+ 10q).

Is the distance a baseball travels in the air after being hit a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

Answers

Answer: a continuous random​ variable

Step-by-step explanation:

Can you count the distance it traveled? You can't, so it couldn't be discrete because you can count discrete variables.

Can you measure the distance it traveled? You sure can, that makes it a continuous random variable.

Do you know the exact distance it's going to travel? You won't, therefore it's a random variable since you don't know the value beforehand.

if 18 : 6 = x : 3 then what is 5 + 3x

Answers

Answer:

32

Step-by-step explanation:

18 : 6 = 3

therefore, x : 3 has to equal 3.

X : 3 = 3

X = 3 × 3

X = 9

To verify:

18 : 6 = 9 : 3

3 = 3

It's true that X = 9, so now just replace the X with 9 in the next equation

5 + 3(9) = 32

Answer:

32

Step-by-step explanation:

18 :  6 = x : 3

Product of means  =  Product of extremes

6 * x = 3*18

     x = [tex]\frac{3*18}{6}[/tex]

     x = 3*3

x = 9

Now plugin x = 9 in the expression

5 + 3x = 5 + 3*9

          = 5 + 27

          = 32

A.For a group of individuals, the random variable x denotes the number of credit cards per individual with the following distribution. x: 0 1 2 3 4 5 P(x): .27 .28 .20 .15 .08 .02 a. find the mean, variance and standard deviation of x b. find the probability that a randomly selected individual holds at least 1 card.

Answers

Answer:

1.55

2.66

1.631

Step-by-step explanation:

Given :

x: 0 1 2 3 4 5

P(x): .27 .28 .20 .15 .08 .02

The expected mean, E(X) = Σ(x*p(x))

E(X) = (0*0.27)+(1*0.28)+(2*0.20)+(3*0.15)+(4*0.08)+(5*0.02)

E(X) = 1.55

The expected variance :

Σx²*p(x) - E(X)

(0^2*0.27)+(1^2*0.28)+(2^2*0.20)+(3^2*0.15)+(4^2*0.08)+(5^2*0.02) - 1.55

4.21 - 1.55 = 2.66

The standard deviation :

√variance = √2.66 = 1.631

by what number should 2/9 be divided to obtain 8/3​

Answers

Answer:

[tex] \frac{1}{12} [/tex]

Step-by-step explanation:

[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]

So, if you divide 2/9 by 1/12, you'll get 8/3

Answered by GAUTHMATH

From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)​

Answers

Answer:

the answer is 32.8in.

Step-by-step explanation:

(sin 22)/42 = (sin 24)/x

x = 45.60

sin 46 = x/45.60

x = 32.80

32.8in.

hope it helped :)

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Find the standard normal area for each of the following (Round your answers to 4 decimal places.): Standard normal area a.P(1.26 < Z < 2.16) b.P(2.05 < Z < 3.05) c.P(-2.05 < Z < 2.05) d.P(Z > .55)

Answers

Answer:

The correct answer is:

(a) 0.0884

(b) 0.0190

(c) 0.9596

(d) 0.2921

Step-by-step explanation:

(a)

= [tex]P(1.26<Z<2.16)[/tex]

= [tex]P(Z<2.16)-P(Z<1.26)[/tex]

= [tex]0.9846-0.8962[/tex]

= [tex]0.0884[/tex]

(b)

= [tex]P(2.05<Z<3.05)[/tex]

= [tex]P(Z<3.05)-P(Z<2.05)[/tex]

= [tex]0.9989-0.9798[/tex]

= [tex]0.0190[/tex]

(c)

= [tex]P(-2.05<Z<2.05)[/tex]

= [tex]P(Z<2.05)-P(Z<-2.05)[/tex]

= [tex]0.9798-0.0202[/tex]

= [tex]0.9596[/tex]

(d)

= [tex]P(Z>0.55)[/tex]

= [tex]1-P(Z<0.55)[/tex]

= [tex]1-0.7088[/tex]

= [tex]0.2912[/tex]

convert 23/4 into mixed number

Answers

5 3/4 is the mixed number

Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Answers

Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

A cyclist rides at an average speed of 25 miles per hour. If she wants to bike 195 km, how long (in hours) must she ride

Answers

1km = 0.621371miles

195 km= ?

cross multiplication

= 121.167 miles

25 miles= 1hour

121.167miles = ?hours

121.167=25x

divide by 25x both sides

=4.84 hours

approx 5hours

She must ride for 5 hours if she wants to bike 195 km.

What is Average speed?

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Given that cyclist rides at an average speed of 25 miles per hour.

Since 1 km = 0.621371 miles

So 195 km = 121.167 miles

The speed of the cyclist (s)  = 24 miles per hour.

Distance covered by the rider = 195 km

Distance covered by the rider (d) = 121.167 miles

By using the formula,  time taken by a body, we calculate the time,

⇒ t = d/s

Substitute the value of d and s in above the equation

⇒ t = 121.167/ 24

Apply the division operation,

⇒ t = 5

Hence, she must ride for 5 hours if she wants to bike 195 km.

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what is the product of ten and the sum of two and a number is five times the number

Answers

My answer is 60
Product means the result of a multiplication problem or more.
Sum is addition
So , 10+2=12•5=60

Convert 0.53 hectograms to centigrams.
53 centigrams
0.000053 centigrams
530 centigrams
5,3000 centigrams

Answers

Answer:

As for metric prefixes, "hecto" means hundred and "centi" means hundredth.  

So, converting .53 hectograms to centigrams requires multiplying it by 10,000.

So, .53 hectograms * 10,000 equals 5,300 centigrams.

Source http://www.1728.org/convprfx.htm

Step-by-step explanation:

CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars. You take a simple random sample of 56 auto insurance policies. Find the probability that a single randomly selected value is less than 995 dollars. P(X < 995)

Answers

Answer:

P(X < 995) = 0.4761

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

CNBC recently reported that the mean annual cost of auto insurance is 1013 dollars. Assume the standard deviation is 284 dollars.

This means that [tex]\mu = 1013, \sigma = 284[/tex]

Find the probability that a single randomly selected value is less than 995 dollars.

This is the p-value of Z when X = 995. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{995 - 1013}{284}[/tex]

[tex]Z = -0.06[/tex]

[tex]Z = -0.06[/tex] has a p-value of 0.4761. So

P(X < 995) = 0.4761

(6^2)^4 simplify the expression

Answers

Answer:

36

Step-by-step explanation:

(6^2)^4

(6)^2+4

6^6

36

simplify the expression : (6²)⁴= (36)⁴= 1679616

Or

[tex]{6}^{2 \times 8} = 1679616[/tex]

Which of the following statements must be true about this diagram? Check all
that apply.
4 3
1
1
N
A. The degree measure of 23 equals the sum of the degree
measures of 21 and 22.
B. m23 is greater than m 2
C. The degree measure of 24 equals the sum of the degree
measures of 22 and 23.
D. m 4 is greater than m_2.
E. m24 is greater than m 1.
F. The degree measure of 24 equals the sum of the degree measures
of 21 and 22.

Answers

Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

HELP PLS ASAP!

The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function &
Substitute a numerical value for k into the function equation.

Answers

Step-by-step explanation:

The horizontal stretch or compression for a function f(x) is given by  g = f(bx) where b is a constant. If b> 0 then the graph of a function is compressed.

As it is given in the question that the function is transformed by a compression factor of 3.

Given function

The value of k will be 3 if the function is transformed by a compression factor of 3

if A={1,2,3,4,5},B={4,5,6,7} and C={2,3,4}find (A-B)-C​

Answers

Answer:

(A - B) - C = { 1 , 4 , 6 , 7 }

Step-by-step explanation:

A = { 1 , 2 , 3 , 4 , 5 }

B = { 4 , 5 , 6 , 7 }

A - B = { 1 , 2, 3 ,6 , 7 }

C = { 2 , 3 , 4 }

(A - B) - C = { 1 , 4 , 6 , 7 }

PLEASE EMERGENCY!!!!
Which of the following statements is FALSE?

Answers

Answer:

Third one.

BO is not 7.8 cm

Step-by-step explanation:

identify the system by type

Answers

Answer:

Inconsistent system

Step-by-step explanation:

Given

The attached graph

Required

The type of system

When two lines are parallel, it means they have the same slope and as such, the system has no solution.

Equations with the same slope are:

[tex]y = 2x + 6[/tex]

[tex]y = 2x- 8[/tex]

Both have a slope of 2

Such system are referred to inconsistent system.

Hence, (c) is correct.

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. text({)1, 1/4, 1/16, 1/64, 1/256, ... text(})

Answers

Answer:

[tex]T_n = \frac{1}{4^{n-1}}[/tex]

Step-by-step explanation:

Given

[tex]({)1, 1/4, 1/16, 1/64, 1/256, ... (})[/tex]

Required

The general term

The given sequence is geometric.

So first, we calculate the common ratio (r)

[tex]r = T_2/T_1[/tex]

So, we have:

[tex]r = 1/4 \div 1[/tex]

[tex]r = 1/4[/tex]

The function is then calculated using:

[tex]T_n =T_1 * r^{n-1}[/tex]

This gives

[tex]T_n =1 * 1/4^{n-1}[/tex]

[tex]T_n = \frac{1}{4^{n-1}}[/tex]

7/3a - 8/5 +4/15a
Simplified

Answers

Answer:

13/5a - 8/5

Step-by-step explanation:

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

The simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,7/3a - 8/5 +4/15a.

We have to simplify the expression.

We have to apply the arithmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

=7/3a - 8/5 +4/15a

= 35/15a + 4/15a - 8/5

= 39/15a - 8/5

= 13/5a - 8/5

Thus, the simplified form of the given expression, "7/3a - 8/5 +4/15a" will be 13/5a - 8/5.

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Which of the following is not true?

Answers

Answer:

C. m<c = 140°

Step-by-step explanation:

Let's analyse each of the given options:

A. m<a = 140° is TRUE

Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.

B. m<b = 140° is TRUE.

Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.

C. m<c = 140° is NOT TRUE.

Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.

D. m<d = 140° is TRUE.

Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.

Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.

Answers

Answer:

[tex](a)\ Area = 13.0695[/tex]

[tex](b)\ Area = 26.139[/tex]

Step-by-step explanation:

Given

The attached image

Solving (a): The area (one side up)

This is calculated as:

Area= Area of semicircle + Area of rectangle

So, we have:

[tex]Area = \pi r^2 + l *w[/tex]

Where:

[tex]l,w =2,3[/tex] --- the rectangle dimension

[tex]d = 3[/tex] --- the diameter of the semicircle

So, we have:

[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]

[tex]Area = \pi * 2.25 + 6[/tex]

[tex]Area = 2.25\pi + 6[/tex]

[tex]Area = 2.25*3.142 + 6[/tex]

[tex]Area = 13.0695[/tex]

Solving (b): Area when both leaves are up.

Simply multiply the area in (a) by 2

[tex]Area = 2 * 13.0695[/tex]

[tex]Area = 26.139[/tex]


The farmer is buying fence panels.
He needs a total length of 200 m of fence panels.
Each fence panel is 2.5 m in length.
Work out how many fence panels the farmer will need to buy?

Answers

Answer:

80 panels

Step-by-step explanation

Simplify the following expression.

3^{0}

Answers

Answer:

Anything to the power of zero (with the exception of zero itself) is equal to one.

So 3⁰ = 1

3^{0} = 1. You apply the exponent rule. And there's your answer.
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None of the above What stanza structure is for Annabel Lee by Edgar Allan Poe Please help me with this question. every action produces an equal and opposite -- ---------- when one object exterts a force on another object,the second object pushes back with the same amount of--------- someone knows the answer Multiply 3x (2x - 1) A cup of mass 0.4 kg with its base radius of 4 cm is kept on a table. Calculate the pressure exerted by the cup on the table. Who says the following and why?"What is life but a series of inspired follies? The difficulty is to find them to do. Never lose a chance: it doesn't comeevery day."A. Pickering is displaying his famous wit.B. Higgins is convincing himself to take the Liza project onC. Mrs. Pearce is sarcastically trying to make Higgins reconsider taking Liza in.D. Mrs. Higgins is making excuses for Henry's behavior. Stoichiometry - Chemistry algo de La historia de los productos tecnologicos Assume that processor refers to an object that provides a void method named process that takes no arguments. As it happens, the process method may throw one of several exceptions. Write some code that invokes the process method provided by the object associated with processor and arrange matters so that your code causes any exception thrown by process to be ignored. Hint: use the catch (Exception ex) and do nothing under the catch clause. X and Y are independent random variables. X has mean 100 and standard deviation 12. Y has mean 30 and standard deviation 9. What are the mean and standard deviation of (XY)? need ASAP. Use point-slope form to write the equation of the line in slope-intercept form that passes through the points (0, -5) and (-3, 4).Slope formula: m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFractionPoint-slope form: y y1 = m(x x1)Slope-intercept form: y = mx + bChoose the equation of the line.y = 3x 13y = 3x 5y = 3x + 5y = Negative one-third x + 13 You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?$550 in 4%, $450 in 6%$300 in 4%, $700 in 6%$700 in 4%, $300 in 6%$150 in 4%, $850 in 6% Find the measure of the third angle of a triangle if the measures of the other two angles are given.31.8 and 89.8 Find two positive numbers whose difference is 3 and whose product is 1638.