A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the
marginal cost, in cents, per card. Find the total cost of producing 900 cards, disregarding any fixed costs.
C'(x) = -0.05x + 77, for x S 1000
The total cost is
cents

Answers

Answer 1

Answer:

49,050cents

Step-by-step explanation:

Given the expression for calculating the marginal cost per card of producing x note cards expressed as

C'(x) = -0.05x + 77

On intergrating the marginal cost, we will get the total cost

C(x) =  -0.05x²/2 + 77x

Substitute x = 900 into the resulting expression

C(900) =  -0.05(900)²/2 + 77(900)

C(900) = -20,250+69,300

C(900) = 49,050

Hence the total costs in cents is 49,050cents


Related Questions

2/3y = 1/4 what does y equal?

Answers

Answer:

Step-by-step explanation:

2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3

Which of the following is the differnce of two squares

Answers

C the answer is c! Hope I’m rigth

the point (-2,5) is reflected across the y-axis. which of these is the ordered pair of the image

Answers

Answer:(2,5)

Step-by-step explanation:   watch this video

https://youtu.be/l78P2Xi68-k

An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?

Answers

Answer:

It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Step-by-step explanation:

Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:

1/5 + 1/4 = X

0.20 + 0.25 = X

0.45 = X

9/20 = X

9 = 60

2 = X

120/9 = X

13,333 = X

Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!

For the graph below, which of the following is a possible function for h?


A) h(x) = 4-x



B) h(x) = 2x



C) h(x) = 5x



D) h(x) = 3x

Answers

9514 1404 393

Answer:

  C)  h(x) = 5^x

Step-by-step explanation:

h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...

  h(x) = 5^x

_____

The general form of an exponential function is ...

  f(x) = (initial value) · (growth factor)^x

I need help understanding how to get the answer.

Answers

Answer:

-157.87

Step-by-step explanation:

1) the rules are:

[tex]log_a(bc)=log_ab+log_ac;[/tex]

and

[tex]log_ab^c=c*log_ab.[/tex]

2) according to the rules above:

[tex]log_7(yz^8)=log_7y+8log_7z=-6.19-8*18.96=-157.87.[/tex]

If two marbles are selected in succession with replacement, find the probability that both marble is blue.

Answers

Answer:

1 / 9

Step-by-step explanation:

Choosing with replacement means that the first draw from the lot is replaced before another is picked '.

Number of Blue marbles = 2

Number of red marbles = 4

Total number of marbles = (2 + 4) = 6

Probability = required outcome / Total possible outcomes

1st draw :

Probability of picking blue = 2 / 6 = 1 /3

2nd draw :

Probability of picking blue = 2 / 6 = 1/3

P(1st draw) * P(2nd draw)

1/3 * 1/3 = 1/9

The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1

Answers

9514 1404 393

Answer:

  (b)  -1

Step-by-step explanation:

The graph shows the difference between the two expressions is zero at x=-1.

__

Additional comment

For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.

Answer:

The answer is b: -1

Step-by-step explanation:

good luck!

A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the shorts are at its maximum height of 16 meters at a and it’s minimum height of 2 meters at s.

Determine the equation of the sinusoidal function that describes the height of the shorts in terms of time.

Determine the height of the shorts exactly t=10 minutes, to the nearest tenth of a meter

Answers

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

Question: The likely missing parameters in the question are;

The time at which the shorts are at the maximum height, t₁ = 10 seconds

The time at which the shorts are at the minimum height, t₂ = 25 seconds

The general form of a sinusoidal function is A·sin(B(x - h)) + k

Where;

A = The amplitude

The period, T = 2·π/B

The horizontal shift = h

The vertical shift = k

The parent equation of the sine function = sin(x)

We find the values of the variables, A, B, h, and k as follows;

The given parameters of the sinusoidal function are;

The maximum height = 16 meters at time t₁ = 10 seconds

The minimum height = 2 meters at time t₂ = 25 seconds

The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)

∴ T = 2 × (25 - 10) = 30

The amplitude, A = (Maximum height- Minimum height)/2

∴ A = (16 m - 2 m)/2 = 7 m

The amplitude of the motion, A = 7 meters

T = 2·π/B

∴ B = 2·π/T

T = 30 seconds

∴ B = 2·π/30 = π/15

B = π/15

At t = 10, y = Maximum

Therefore;

sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2

Plugging in B = π/15, and t = 10, gives;

((π/15)·(10 - h)) = π/2

10 - h = (π/2) × (15/π) = 7.5

h = 10 - 7.5 = 2.5

h = 2.5

The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A

Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7

The given minimum value = 2

The vertical shift, k = 2 - (-7) = 9

Therefore, k = 9

Therefore;

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

More can be learned about sinusoidal functions on Brainly here;

https://brainly.com/question/14850029

!!!!Please Answer Please!!!!

ASAP!!!!!!

!!!!!!!!!!!!!

Answers

Answer:

False

Step-by-step explanation:

well i think that the answer from my calculations

Which function describes this graph? (CHECK PHOTO FOR GRAPH)

A. y = x^2 + 7x+10
B. y = (x-2)(x-5)
C. y = (x + 5)(x-3)
D.y = x^2+5x+12

Answers

Answer:

Option A. y = x² + 7x + 10

Step-by-step explanation:

We'll begin calculating the roots of the equation from the graph.

The roots of the equation on the graph is where the curve passes through the x-axis.

The curve passes through the x-axis at –5 and –2

Next, we shall determine the equation. This can be obtained as follow:

x = –5 or x = –2

x + 5 = 0 or x + 2 = 0

(x + 5)(x + 2) = 0

Expand

x(x + 2) + 5(x + 2) = 0

x² + 2x + 5x + 10 = 0

x² + 7x + 10 = 0

y = x² + 7x + 10

Thus, the function that describes the graph is y = x² + 7x + 10

While out for a run, two joggers with an average age of 55 are joined by a group of three more joggers with an average age of m. if the average age of the group of five joggers is 45, which of the following must be true about the average age of the group of 3 joggers?

a) m=31
b) m>43
c) m<31
d) 31 < m < 43

Answers

Answer:

they have it on calculator soup

Step-by-step explanation:

Answer:

D. 31<m<43

Step-by-step explanation:

45 x 5 = 225 which is the age of the 5 joggers altogether.

55 x 2 = 110 which is the age of the 2 joggers together.

3m + 110 = 225 then solve for m so,

3m = 115

m = 38.3333

so hence, m is greater than 31 but less than 43.

answer: D

What is the value of x in the triangle? 45, 45, x

Answers

Answer:

90

Step-by-step explanation:

it its a 45 45 90 triangle

Graph the inequality.
7 <= y - 2x < 12

Answers

Answer:

X(-12,-7)

Step-by-step explanation:

This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.

An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?

PLEASE HELP

Answers

Answer:

8

Step-by-step explanation:

As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8

What is the measure of F?
G
65
10
H H
10
A. Cannot be determined
B. 55
C. 75
D65

Answers

Answer:

D. 65°

Step-by-step explanation:

It is so because the triangle is isosceles, two identical sides and two equal angles.

According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20

Answers

Answer:

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.

This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]

Sample of 30:

This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]

What is the probability that the sample mean will be between $7.75 and $8.20?

This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.

X = 8.2

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

By the Central Limit Theorem

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

[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = 2.63[/tex]

[tex]Z = 2.63[/tex] has a p-value of 0.9957

X = 7.75

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

[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = -2.3[/tex]

[tex]Z = -2.3[/tex] has a p-value of 0.0107.

0.9957 - 0.0157 = 0.985

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

Solve the equation by completing the square.

0 = 4x2 − 72x

Answers

Answer:

B

Step-by-step explanation:

Given

4x² - 72x = 0 ← factor out 4 from each term

4(x² - 18x) = 0

To complete the square

add/subtract (half the coefficient of the x- term)² to x² - 18x

4(x² + 2(- 9)x + 81 - 81) = 0

4(x - 9)² - 4(81) = 0

4(x - 9)² - 324 = 0 ( add 324 to both sides )

4(x - 9)² = 324 ( divide both sides by 4 )

(x - 9)² = 81 ( take the square root of both sides )

x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )

x = 9 ± 9

Then

x = 9 - 9 = 0

x = 9 + 9 = 18

Answer:0,18

Step-by-step explanation:

its right

(4-1) + (6 + 5) = help plz

Answers

The right answer is D!

Prove the following identities : i) tan a + cot a = cosec a sec a​

Answers

Step-by-step explanation:

[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]

[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]

[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]

Question :

tan alpha + cot Alpha = cosec alpha. sec alpha

Required solution :

Here we would be considering L.H.S. and solving.

Identities as we know that,

[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]

By using the identities we gets,

[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]

Now, here we would be using the identity of square relations.

[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]

By using the identity we gets,

[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]

[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]

Hence proved..!!

1. Write a variable expression that matches the following situation: Marguerite wants to put a garland around her garden. If the length of the garden is 50 meters and the width of the garden is 2 more than the length, what is the perimeter of the garden?​

Answers

Answer:

3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m

Step-by-step explanation:

that is the answer i think

Below are the heights (in inches) of students in a third-grade class. Find the median height. 39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Answers

Given:

The heights (in inches) of students in a third-grade class are:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

To find:

The median height.

Solution:

The given data set is:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Arrange the data set in ascending order.

37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53

Here, the number of observations is 16. So, the median of the given data set is:

[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]

[tex]Median=\dfrac{47+48}{2}[/tex]

[tex]Median=\dfrac{95}{2}[/tex]

[tex]Median=47.5[/tex]

Therefore, the median height of the students is 47.5 inches.

40% of what number is 16.6?

Answers

Answer: 41.5

hope this helps!

What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)

Answers

Answer: A (x+1)(x+2)(x+5)

Step-by-step explanation:

Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т

Answers

9514 1404 393

Answer:

  x = 7

  y = 5

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

For a=-j and b=7,

  (-j)^-7 = 1/(-j)^7   ⇒   x = 7

For a=k and b=-5,

  k^-5 = 1/k^5   ⇒   y = 5

Pleas help me in this question Find R

Answers

Answer:

R = 25.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos R = adj side / hyp

cos R = 9/10

Taking the inverse cos of each side

cos ^-1 ( cos R) = cos^ -1 ( 9/10)

R=25.84193

Rounding to the nearest tenth

R = 25.8

Answer:

[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]

Step-by-step explanation:

We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:

sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent

We are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).

The side TR (9) is adjacent or next to angle R. The side SR (10) is the hypotenuse because it is opposite the right angle.

We have the adjacent side and the hypotenuse, so we will use the cosine function.

[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]

[tex]cos R = \frac {9}{10}[/tex]

Since we are solving for an angle, we must take the inverse cosine of both sides.

[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R= 25.84193276[/tex]

If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.

[tex]R \approx 25.8 \textdegree[/tex]

The measure of angle R is approximately 25.8 degrees and choice D is correct.

X+34>55

Solve the inequality and enter your solution as an inequality comparing the variable to a number

Answers

Answer:

x > 21

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

x + 34 > 55

Step 2: Solve for x

[Subtraction Property of Equality] Subtract 34 on both sides:                      x > 21

Which side of the polygon is exactly 6 units long?

Answers

Answer:

AB is correct as It is the shorter parallel line

as the line measures 6 units.

Step-by-step explanation:

The polygon is a trapezoid / (trapezium Eng/Europe)

We see the given coordinates  (2, 6) - (-4, 6) = x-6 y 0 = x = 6units

as x always is shown as x - 6  as  x= 6

We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6

y = 0  x = 6 = 6 units as its horizontal line.

when y is 6-6 = 0 then we know the line is horizontal for y = 0.

The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.

When looking at diagonal lines we still group the x's and y's and make the fraction whole.

When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.

Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X

Answers

Given:

The logarithmic equation is:

[tex]\log 970=x[/tex]

To find:

The exponential equations that is equivalent to the given logarithmic equation.

Solution:

Property of logarithm:

If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]

We know that the base log is always 10 if it is not mentioned.

If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]

We have,

[tex]\log 970=x[/tex]

Here, base is 10 and the value of a is 970. By using the properties of exponents, we get

[tex]970=10^x[/tex]

Interchange the sides, we get

[tex]10^x=970[/tex]

Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].

Note: It should be "=" instead of "-" in option B.

Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places

Answers

Answer:

"0.250" is the appropriate answer.

Step-by-step explanation:

Given:

New car sample,

= 1453

Preferred foreign,

= 363

Now,

The amount of new automobile purchasers preferring foreign cars will be approximated as:

= [tex]\frac{363}{1453}[/tex]

= [tex]0.250[/tex]

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