A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics processing unit). The manufacture found that the marginal cost C to produce x GPUs can be found using the equation C = 0.04x² – 5x + 600. If the marginal cost were $569, how many GPUs were produced?

I think it’s f(x+k) = f(x) + k correct if I’m wrong

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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Answer:

jeez i need more help than you do and nobody answers my question :(

Step-by-step explanation:

Answer:

960 would be correct becasue it says it in the problem.

Answer:

The probability that you are able to guess ten or more correct answers is P(x≥10) = 0.0026

Step-by-step explanation:

The question is incomplete:

You take a multiple choice test that you are not prepared for, so you have to guess on all twenty questions. The probability that you guess correctly on any given question is 20% (since there are five choices on each question). What is the probability that you are able to guess ten or more correct answers?

This can be modeled by a binomial random variable, with sample size n=20 and probabillity of success p=0.2.

The probability of guessing k answers right can be calculated as:

\(P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{20}{k}\cdot0.2^k\cdot0.8^{20-k}\)

We have to calculate the probabiltiy that 10 or more answers are correctly answered guessing: P(x≥10)

\(P(x\geq10)=\sum_{k=10}^{20}P(x=k)\)

\(P(x=10)=\dbinom{20}{10}\cdot0.2^{10}\cdot0.8^{10}=184756\cdot0.0000001\cdot0.1074=0.0020\\\\\\P(x=11)=\dbinom{20}{11}\cdot0.2^{11}\cdot0.8^{9}=167960\cdot0.00000002\cdot0.1342=0.0005\\\\\\P(x=12)=\dbinom{20}{12}\cdot0.2^{12}\cdot0.8^{8}=125970\cdot0\cdot0.1678=0.0001\\\\\\P(x=13)=\dbinom{20}{13}\cdot0.2^{13}\cdot0.8^{7}=77520\cdot0.000000001\cdot0.2097=0.0000\\\\\\P(x\geq14)=0.0000\)

\(P(x\geq10)=0.0020+0.0005+0.0001=0.0026\)

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Answer:

(3,12)

Step-by-step explanation:

y = 3x + 3

y = 6x -6

x = 3

y = 12

= (3,12)

Answer:

All you have to do, is find an x that if used in both equations, both equal the same y.

3 x 3 + 3 = 12

6 x 3 - 6 = 12

So, the only thing here is (3, 12)

Step-by-step explanation:

It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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29 years from now, the father will be 49 years old.

Let's start by setting up the given information:

Currently, the father is 20 years old, and the son is 5 years old.

In 10 years, the father will be twice as old as the son.

The father is currently four times as old as the son.

Determine the age of the father and son in 10 years:

In 10 years, the father's age will be 20 + 10 = 30 years.

In 10 years, the son's age will be 5 + 10 = 15 years.

Write equations based on the given information:

The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.

The father's current age is four times the son's current age: 20 = 4 × 5.

Solve the equations:

From the second equation, we find that the son's current age is 5 years.

Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).

Simplifying further, we have: 30 = 2 × 15, which is true.

Determine the current age of the son in 29 years:

The son's current age is 5 years.

Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.

Determine the current age of the father in 29 years:

The father's current age is 20 years.

Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.

Therefore, 29 years from now, the father will be 49 years old.

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In a equation in the form:

The maximum or minimum value is the value of the function when x is:

_________________________________

For the given function:

Answer:

Step-by-step explanation:

Correct choice is C or orange tile

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

We have,

To determine the angle created by the bottom of the ramp and the ground, we can use the trigonometric function of sine.

In the given triangle, the height is 6 ft and the base is 16 ft.

The angle we want to find is opposite the height (let's call it θ).

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

sin(θ) = opposite/hypotenuse

sin(θ) = 6/16

sin(θ) = 0.375

To find the angle θ, we can take the inverse sine (also known as arcsine) of 0.375:

θ = arcsin(0.375)

θ ≈ 22.62°

To meet safety regulations, the angle should be no more than 18°. Therefore, the contractor needs to lower the ramp by:

22.62° - 18° ≈ 4.62°

Thus,

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

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Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

The first step is to find the probability for each of the events, which are pick up a gold marble, pick up a silver marble and pick up a black marble:

Now, multiply each of the probabilities by its corresponding reward and find the sum of them to find the expected value:

The expected value is -$0.11.

Answer:

Step-by-step explanation

Initial amount = $85

Final amount = $110

percentage error = ((Final amount - Initial amount)*100)/Final amount

= (25*100)/110

=22.7272

=22.7 (to the nearest tenth of a percent, which is 1 decimal place)

The solution is 22.7 %

The percentage error in the estimation of donations at the pet store by Jenny is 22.7 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the percentage error be represented as A

Now , the value of A is

The estimated donation amount by Jenny = $ 85

The actual donation amount collected by Jenny = $ 110

Now , the percentage error in the estimation of Jenny A is calculated by the equation ,

Percentage error in the estimation of Jenny A = ( ( | estimated donation amount - actual donation amount collected by Jenny ) | / actual donation amount collected by Jenny ) ) x 100

Substituting the values in the equation , we get

Percentage error in the estimation of Jenny A = ( | 85 - 110 | / 110 ) x 100

On simplifying the equation , we get

Percentage error in the estimation of Jenny A = ( 25/110 ) x 100

Percentage error in the estimation of Jenny A = 2500 / 110

Percentage error in the estimation of Jenny A = 22.72 %

Therefore , the value of A is 22.7 %

Hence , the percentage error in the estimation is 22.7 %

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Answer:   \(\dfrac{7}{1,337,220}=5.2\times 10^{-6}\)

Step-by-step explanation:

Order does not matter so it is a Combination.

There are 14 men and we are going to choose 12 --> ₁₄C₁₂

There are 27 people and we are going to choose 12  --> ₂₇C₁₂

\(\dfrac{_{14}C_{12}}{_{27}C_{12}}\rightarrow\dfrac{14!}{(14-12)!}\div \dfrac{27!}{(27-12)!}=\large\boxed{\dfrac{7}{1,337,220}}\)

Probabilities are used to determine the chances of an event

The probability of selecting 12 males is: \(\frac{7}{1337220}\)

The parameters are given as:

\(n = 24\) --- sample size

\(Male = 14\)

\(Female = 13\)

\(r = 12\) ---- number of jury pool

The number of ways of selecting 12 members of the jury, from a total of 27 is:

\(^nC_r = \frac{n!}{(n - r)!r!}\)

So, we have:

\(^{27}C_{12} = \frac{27!}{(27 - 12)!12!}\)

\(^{27}C_{12} = \frac{27!}{15! \times 12!}\)

\(^{27}C_{12} = 17383860\)

The number of ways of selecting 12 members of the jury, from a total of 14 male is:

\(^nC_r = \frac{n!}{(n - r)!r!}\)

So, we have:

\(^{14}C_{12} = \frac{14!}{(14 - 12)!12!}\)

\(^{14}C_{12} = \frac{14!}{2! \times 12!}\)

\(^{14}C_{12} = 91\)

So, the probability of selecting 12 males is:

\(Pr = \frac{^{14}C_{12}}{^{27}C_{12}}\)

\(Pr = \frac{91}{17383860}\)

Simplify

\(Pr = \frac{91/13}{17383860/13}\)

\(Pr = \frac{7}{1337220}\)

Hence, the required probability is: \(\frac{7}{1337220}\)

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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Answer:

alternate interior angles are congruent

Answer:

omg that's so hard im still in 8th grade ;-;

Answer:

540 pages

Step-by-step explanation:

100 pages = 50 mins

??? pages = 270 mins (converted 4hrs 30 mins to minutes)

Now you could cross multiply to find what the number of pages are:

100 pages x 270  mins = 50 mins x ??? pages

27000 = 50 mins x ??? pages

27000/50 = ??? pages

540 = ??? pages

So there are 540 pages in his favourite book.

Answer:

j=7

Step-by-step explanation:

10=2j-4                          add 4 on both sides

10+4=2j                        

14=2j                                divide by 2 on both sides

7=j

Answer:

Step-by-step explanation:

\(7- \sqrt[3]{2-x} =12\)

we have to just keep in mind to do the same operation to both sides of the equal sign

\(7-7- \sqrt[3]{2-x} =12-7\) ; subtract 7 from both sides

\(- \sqrt[3]{2-x} = 5\) ; multiply both sides by -1

\(\sqrt[3]{2-x} = -5\) ; raise both sides to the power 3

2-x = (-5)³

2-x = -125 ; subtract 2 from both sides

-x = -125-2

-x =-127; multiply both sides by -1

x= 127

the total area of the pie is 237

Answer:

I am assuming you mean the smallest decimal so it is 4.125

Step-by-step explanation:

you said quick so

Answer: 4.25

Step-by-step explanation: if you make all of these into a whole number the biggest number comes out to be 20 and its 4.25

In the  word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.

Let  S = number of small pizzas delivered

Let M = number of medium pizzas delivered

Let L = number of large pizzas delivered

We'll start by solving equation 1 for one variable and substituting it into the other equations.

S + M + L = 12

We can rewrite this equation as -

S = 12 - M - L

Now, substitute this value of S in equations 2 and 3 -

4S + 10M + 15L = 109

4(12 - M - L) + 10M + 15L = 109

48 - 4M - 4L + 10M + 15L = 109

6M + 11L = 61

2S + 4M + 13L = 81

2(12 - M - L) + 4M + 13L = 81

24 - 2M - 2L + 4M + 13L = 81

2M + 11L = 57

Now we have a system of two equations with two variables -

6M + 11L = 61 ...(4)

2M + 11L = 57 ...(5)

Subtract  equation   (5)from equation (4) -

(6M +   11L) - (2M +11L) = 61 - 57

4M = 4

M = 1

Substitute the value of M into equation (5) -

2(1) + 11L = 57

2 + 11L = 57

11L = 55

L = 5

Now substitute the values of M and L into equation (1) -

S + 1 + 5 = 12

S + 6 = 12

S = 6 - 6

S = 0

Therefore, the solution is -

S = 0 (no small pizzas)

M = 1 (1 medium pizza)

L = 5 (5 large pizzas)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?

Answer:

ME = 3.64

Step-by-step explanation:

Given:

Sample size, n = 21

Sample mean, X' = 95

Standard deviation \( \sigma \) = 8.

Confidence interval = 95%

Significance level \( \alpha\) = 0.05

Required:

Find margin of error

To find the margin of error, use the formula below:

\( M.E = \frac{\sigma}{\sqrt{n}} * t_\alpha_/_2; _d_f \)

Where,

\( t_\alpha_/_2 = 0.05/2 = 0.025\)

degree of freedom, df = n - 1 = 21 - 1 = 20

Therefore,

\( M.E = \frac{8}{\sqrt{21}} * t_0_._0_2_5; _2_0 \)

Using the table at 95% Confidence interval, we have:

\( = \frac{8}{\sqrt{21}} * 2.086 \)

\( = 3.6416 \)

Rounding to 2 decimal places,

ME = 3.64