HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!

HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!

Answers

Answer 1

Answer:

the x intercept is -2,0 and the y intercept is 0,3

Step-by-step explanation:

I used desmos graphing calculator and wrote in your equation and look at the y line to find the y intercept and the x line to find the x intercept

Answer 2

Step-by-step explanation:

the x-intercept is -2 and the y-intercept is 3


Related Questions

all of the following increase the width of a confidence interval except a. decreased sample size b. increased sample size c. increased confidence level d. increased variation

Answers

The width of a confidence interval increase except increased sample size , the correct option is (b) .

In the question,

it is asked that which option will decrease the width of a confidence interval ,

we know that the ,

the decrease in sample size increases the width of the confidence interval , and

the increased confidence interval also leads to increase in width of confidence interval , and

the increase in variation also leads to increase in the width of the confidence interval .

So , the only option that decreases the width of the confidence interval is increased sample size

that is increase in sample sizes causes smaller confidence interval.

Therefore , the correct option is (b) .

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A rectangle kitchen floor measures 7’ x 16 hey stove on the floor has a rectangular base measuring 3’ x 4’ in a refrigerator covers a rectangular area of the floor measuring 4’ x 5’ how many square feet of tile will be needed to cover the kitchen floor not counting the area use by the stove and the refrigerator

Answers

Answer:
You will need 80 square feet of tile to cover the kitchen floor, leaving out the area used by the stove and refrigerator.

Step-by-step explanation:

Step 1: Calculate the area of the kitchen floor: 7' x 16' = 112 square feet.

Step 2: Calculate the area of the stove: 3' x 4' = 12 square feet.

Step 3: Calculate the area of the refrigerator: 4' x 5' = 20 square feet.

Step 4: Subtract the areas of the stove and refrigerator from the total area of the kitchen floor: 112 - 12 - 20 = 80 square feet.

Identify the slope, and y -intercepts and graph the linear equation.
4. y=1-3
5. 5x +3y = 15
6. y = 3

Answers

The slope, and the y-intercepts are

Slope = 0, y-intercept = -2Slope = -5/3, y-intercept = 5Slope = 0, y-intercept = 3

How to determine the slope and the intercept of the equations

A linear equation can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the above as a guide, we have the following:

Slope of (4) = 0 and the y-intercept is -2Slope of (5) = -5/4 and the y-intercept is 5Slope of (6) = 0 and the y-intercept is 3

See attachment for the graph

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Identify the slope, and y -intercepts and graph the linear equation.4. y=1-35. 5x +3y = 156. y = 3

solve for x……………………..

solve for x..

Answers

Step-by-step explanation:

6+x-2=2x-1

4+x=2x-1

2x-x=4+1

X=5

a pollster decides to poll every 10th person that comes out of a store. this alternative to random sampling is called

Answers

The alternative to random sampling is called as systematic sampling which is accepted by a pollster to poll every 10th person that comes out of a store.

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).

This method will provide you with a representative sample that can be used to make generalizations about the population if the order of the population is random or random-appearing (for example, alphabetical).

Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out.

Similar to basic random sampling, systematic sampling can be used with a list of the complete population. Contrary to basic random sampling, one can still utilize this technique if you don't have access to a list of the population beforehand.

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Chris earns $65.00 a week delivering flowers for a local florist. In addition, he is paid $0.15 per mile for the use of his car. One week he traveled 156 miles making deliveries. How much was he paid that week?

Answers

Answer:

88.4

Step-by-step explanation:

156 times 0.15 is 23.40

23.5+65 = 88.4

pls vote me brainliest

please help me with this question and I will give you brainlist!

please help me with this question and I will give you brainlist!

Answers

Answer:

6.3 ft

Step-by-step explanation:

To find:-

The height of shadow casted by the tree.

Answer:-

We are here given that 40ft tree casts a shadow of 12foot . We are interested in finding out the height of the shadow casted by a 21ft tree .

Here we can use Unitary Method to find out the height of the shadow as ,

A 40ft tree casts a shadow of 12ft .

A 1ft tree would cast a shadow of 12/40ft .

A 21 ft tree would cast a shadow of 12/40*21 = 6.3 ft

Hence the height of shadow casted by a 21ft tree is 6.3ft .

Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?

A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.

Answers

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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What two numbers round to 9.4 when rounded to the nearest tenth?

Answers

The answer is going to be 9

HELP ME PLEASE!!!! Image attached of the work

HELP ME PLEASE!!!! Image attached of the work

Answers

The probability we want to find is P = 0.27, or 27% in percent form.

How to find the probability?

Here we just need to take the quotient between the number of people 40 or older that finished high school and the total of people of that age group.

We can see that the total in that age group is:

T = 3041 + 5355 = 8396

And the ones that finished only highschool are:

N = 745 + 1523 = 2,268

Then the probability is:

P = 2,268/8,396 = 0.27

P = 0.27

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what distance does the tip of the minute hand on a clock travel in 11 minutes if the minute hand is 23 cm long?

Answers

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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The Metzgers want to seed theirbackyard. The seed they selectcovers 375 m² per box. Howmany boxes of seed will theyneed to buy? Use the yarddiagram. Round any portionof a box to the next box?

The Metzgers want to seed theirbackyard. The seed they selectcovers 375 m per box. Howmany boxes of seed

Answers

Seeding the backyard

In order to find how many boxed they need, first they need to know the area they will have to cover:

In order to find it, we have find the total area of the rectangle and take off the area of the House and the area of the shed:

We know that all those areas are rectangles, their area are found multiplying their sides lenght:

House area = 5m x 16m = 80m²

Shed area = 3m x 3m = 9m²

Since the lateral side of the total area is

5m + 16m + 5m = 26m, then

Total area = 26m x 50m = 1300m²

Then, the area they need to cover is

total area - house area - shed area = 1300m² - 9m² - 80m²

= 1211m²

Since the seed they select covers 375 m² per box, in order to find how many boxes they need, we just need to divide the area they are going to cover with this number:

1211m² ÷ 375 m² = 3.229

We round it to 4 boxes as indicated.

Answer: they need to buy 4 boxes of seeds

The Metzgers want to seed theirbackyard. The seed they selectcovers 375 m per box. Howmany boxes of seed
The Metzgers want to seed theirbackyard. The seed they selectcovers 375 m per box. Howmany boxes of seed

If the length of a rectangle is 16 cm and breadth is 7 cm, the area in square centimetres will be

Answers

Answer:

the answer is 112 mate hope u got ur answer

it would be 112 cm2 hope this helps

the times to complete an obstacle course is normally distributed with mean (μ) 73 seconds and standard deviation (σ) 9 seconds. what is the probability using the empirical rule that a randomly selected finishing time is less than 100 seconds? provide the final answer as a percent rounded to two decimal places.

Answers

68.18% is the right answer

28 is what percent of 507

Answers

Answer:

5.52%

Step-by-step explanation:

Answer:

5.5226824458%

Step-by-step explanation:

If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, how many minutes will it take the machine to fill 240 bottles?

Answers

If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, Then the machine will take approximately 18 minutes to fill 240 bottles.

Constant rate is a rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Given that machine take 3 minutes to fill 40 bottles

So for 1 minute the machine fill \(\frac{40}{3}\) = 13.3333 bottles.

That is in 1 minute the machine fill approximately 14 bottles.

So the machine take a time to fill 240 bottles is \(\frac{240}{14} = 18.461\).

Thus the machine take approximately 18 minutes to fill 240 bottles.

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please HELPPPPPPPPPPPPP

please HELPPPPPPPPPPPPP

Answers

25.13274122.

....................

A club is forming a committee to plan its annual Holiday Dance. One person will serve as Chair of the committee, another will be Vice-Chair and there will be two other members. Is this an example of a combination or permutation?

Answers

A club is forming a committee to plan its annual Holiday Dance. One person will serve as Chair of the committee, another will be Vice-Chair and there will be two other members.  this is an example of a combination

Combining is a way of calculating the total score for an event, regardless of the order of the scores. To calculate the combination, use the formula nCr = n! /r! * (n - r)!, where n is the total number of items and r is the number of items selected at one time.

The combination is a mathematical technique that determines the number of possible arrangements within a collection of items, regardless of the order of selection.

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Leanette and ruthe breed poodles as a hobby. They sold half of the puppies and half a puppy from the latest litter to the local pet shop. Then they sold half of the puppies that were left in the litter and half a puppy to the poodle palace. Then they decided to give the one remaining puppy to their friend Grace. How many puppies were originally in the litter

Answers

Initially, there were average nine puppies in the litter, but they sold four and a half of them (4.5), one of them (0.5), and one puppy was given away (1).

9 puppies equals 4.5 puppies sold, 0.5 puppies sold, 1 puppy given away, for a total of 6 puppies. Initially, there were nine puppies in the litter, but they sold four and a half of them (4.5), one of them (0.5), and one puppy was given away (1). Thus, a total of 6 puppies have been bought, sold, or given away. Leanette and Ruthe kept the remaining 3 puppies. They made the decision to sell the neighbourhood pet store 4.5 puppies and half a puppy, and then they sold the Poodle Palace the remaining 4.5 puppies and half a dog. They ultimately made the choice to give their buddy Grace the one surviving puppy. As a result of giving away all 9 puppies, they were left with no puppies from the litter.  Here's an illustration of how Leanette and Ruthe could use the puppies in the litter for both their own and other people's good.

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express each statement in logic using the variables: p: it is windy. q: it is cold. r: it is raining. (a) it is windy and cold. (b) it is windy but not cold. (c) it is not true that it is windy or cold. (d) it is raining and it is windy or cold. (e) it is raining and windy or it is cold. (f) it is raining and windy but it is not cold.

Answers

The given statements can be expressed as

a) \($p \land q$\).

b) \($p \land\neg q$\)

c) \($\neg(p \lor q)$\)

d) \($p \land (q \lor r)$\)

e) \($r \land (p \lor q)$\)

f)   \($r \land (p \land \neg q)$\)

What is a logical expression?

A statement that can be true or false is referred to as a logical expression Depending on the values of p and q, it can be true or false. This is distinct from a mathematical expression, which represents a true statement.

The given statements are

p: it is windy.

q: it is cold.

r: it is raining.

Now

a) it is windy and cold

   This statement can be expressed as - \($p \land q$\).

(b) it is windy but not cold.

     This statement can be expressed as - \($p \land\neg q$\)

(c) it is not true that it is windy or cold. - \($\neg(p \lor q)$\)

(d) it is raining and it is windy or cold.  - \($p \land (q \lor r)$\)

(e) it is raining and windy or it is cold. \($r \land (p \lor q)$\)

(f) it is raining and windy but it is not cold. \($r \land (p \land \neg q)$\)

Hence, the given statements can be expressed as

a) \($p \land q$\).

b) \($p \land\neg q$\)

c) \($\neg(p \lor q)$\)

d) \($p \land (q \lor r)$\)

e) \($r \land (p \lor q)$\)

f)    \($r \land (p \land \neg q)$\)

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Find the area of the figure above.

Find the area of the figure above.

Answers

Answer:

84

Step-by-step explanation:

You do problems like these by finding the area of each shape individually and then adding them together. I first found the area of the rectangle by multiplying 6 in. by 11 in. to get 66 in.^2. I then found the area of the triangle by multiplying length of the base of the triangle which is the same as the short side of the rectangle at 6 in. by the 6 in. height and dividing it by 1/2. This gets 18 and 66+18=84


(3) Determine the convergence of the series ∑[infinity]
n=1
n!
2−n.
(4) Determine the values of a parameter afor which the series
converge. ∑[infinity]
n=1
an
n3 .

Answers

(3) The ratio takes a look at, the series diverges. (4) The series converges for all values of a such that\($$-1 \leq a < 1$$.\)

(3) To decide the convergence of the series\($$\sum_{n=1}^{\infty} \frac{n!}{2^n}$$\), we will use the ratio test. The ratio of consecutive terms \($$\left|\frac{a_{n+1}}{a_n}\right| = \frac{(n+1)!}{2^{n+1}} \cdot \frac{2^n}{n!} = \frac{n+1}{2}$$\)

The restriction of this ratio as n is going to infinity is\($$\lim_{n \to \infty} \frac{n+1}{2} = \infty > 1$$\)

Therefore, via the ratio take a look at, the series diverges.

(4) To decide the values of a parameter for which the collection\($$\sum_{n=1}^{\infty} \frac{a^n}{n^3}$$\) converges, we also can use the ratio test. The ratio of consecutive terms is\($$\left|\frac{a_{n+1}}{a_n}\right| = \frac{a^{n+1}}{(n+1)^3} \cdot \frac{n^3}{a^n} = a \cdot \frac{n^3}{(n+1)^3}$$\)

The limit of this ratio as n is going to infinity is\($$\lim_{n \to \infty} a*\cdot \frac{n^3}{(n+1)^3}$$\)

Therefore, through the ratio check, the series converges to 1, the ratio check is uncertain and we need to use any other check. In this situation, we can use the contrast test.

If a=1, then the series will become\($$\sum_{n=1}^{\infty} \frac{1}{n^3}$$\)which converge by way of the p-series test. If a= -1, then the series turns into\($$\sum_{n=1}^{\infty} (-1)^n \frac{1}{n^3}$$\)which converges via the alternating collection test. Therefore, the series converges for all values of a such that\($$-1 \leq a < 1$$.\)

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Which statements accurately describe the function f(x) = 3 (squareroot 18) ^x ? Select three options. A. The domain is all real numbers. B. The range is y > 3. C. The initial value is 3. D. The initial value is 9. D. The simplified base is 3 square root 2​

Which statements accurately describe the function f(x) = 3 (squareroot 18) ^x ? Select three options.

Answers

Answer:

The domain is all real number

Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house

Can you show the math as far as formulas go?

Answers

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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t-models, part II Using the t tables, software, or a calculator, estimate
a) the critical value of t for a 95% confidence interval with df = 7.
b) the critical value of t for a 99% confidence interval with df = 102.

Answers

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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A car traveled 3⁄4 mile in one minute at constant speed. What was the speed of the car in miles per hour?

Answers

Answer:

45 mph

Step-by-step explanation:

3/4x60=45

There are 45 rows of tomato plants in the hydroponics farm at O'Brien's Farms Each row has 14 plants. 2/3 of the plants have sprouted. How many sprouted plants does O'Brien's have?

Answers

Answer: 420 sprouted plants

Step-by-step explanation:

First find the total number of tomato plants in the farm.

= Number of rows * No. of plants per row

= 45 * 14

= 630 plants

2/3 of them have sprouted so the number of sprouted plants is:

= 2/3 * 630

= 420 sprouted plants

A recent Fox News Poll asked a random sample of 900 adults nationwide the following question: "Do you believe in God?". At the same time CNN posted the same question on their website as a "Quick Vote" question where anyone who wants to can cast their vote. Here's the result of both surveys:
Yes No Sample Size
CNN Quick Vote 52% 48% 7362
Fox News Poll 92% 8% 900
a) As you can see, the results of the 2 polls are quite different. Which survey gives a better estimate of the percentage of all US adults who would say they believe in God?
CNN Quick Vote survey because it has more people.
Fox News Survey because Fox claims to be fair and balanced.
The Fox News Survey because the people were randomly drawn from adults nation-wide.

Answers

The Fox News Survey gives a better estimate of the percentage of all US adults who would say they believe in God.

The Fox News Survey gives a better estimate of the percentage of all US adults who would say they believe in God. This is because it was conducted using a random sample of 900 adults nationwide, which helps to reduce biases and ensure that the sample represents the population as accurately as possible. On the other hand, the CNN Quick Vote survey relied on self-selected participants who chose to cast their vote online, which can introduce selection bias and may not be representative of the entire population. Therefore, the results of the Fox News Survey are likely to be more accurate and reliable.

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4) A computer is randomly generating 4 digit numbers by randomly selecting a digit for each place value. The value of the number generated must be 3000 or more. (So, for instance, 1,588 is not a number that can be generated.) a) How many different 4 digit numbers can generated if repeated digits are allowed? b) How many different 4 digit numbers can be generated if repeated digits are NOT allowed? Now, (for parts c,d and e) let us always assume that repeated digits are NOT allowed(still must be 3000 or more) : c) How many different 4 digit numbers can be generated that have all even digits? d) How many different 4 digits numbers can be generated that will end with the digit 8? e) What is the probability that a randomly generated 4 digit number will have all even digits?

Answers

a) The number of different 4-digit numbers that can be generated with repeated digits allowed is 10,000.

b) The number of different 4-digit numbers that can be generated without repeated digits is 4,536.

c) The number of different 4-digit numbers that have all even digits is 256.

d) The number of different 4-digit numbers that end with the digit 8 is 700.

e) The probability of randomly generating a 4-digit number with all even digits is approximately 5.65%.

a) If repeated digits are allowed, there are 10 options for each digit (0-9), so the total number of different 4-digit numbers that can be generated is 10^4 = 10,000.

b) If repeated digits are not allowed, the first digit can be chosen from 1-9 (excluding 0) since the number must be 3000 or more. The second digit can be chosen from 0-9 (excluding the digit already chosen for the first digit), giving 9 options. Similarly, the third digit has 8 options, and the fourth digit has 7 options. Therefore, the total number of different 4-digit numbers without repeated digits is 9 * 9 * 8 * 7 = 4,536.

c) To generate a 4-digit number with all even digits, the first digit can be chosen from the set {2, 4, 6, 8}, giving 4 options. The second, third, and fourth digits can also be chosen from the set {2, 4, 6, 8}, each with 4 options. Therefore, the total number of different 4-digit numbers with all even digits is 4 * 4 * 4 * 4 = 256.

d) To generate a 4-digit number that ends with the digit 8, the first digit can be chosen from the set {3, 4, 5, 6, 7, 8, 9}, giving 7 options. The second and third digits can be chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, each with 10 options. The last digit is fixed as 8. Therefore, the total number of different 4-digit numbers ending with 8 is 7 * 10 * 10 * 1 = 700.

e) The probability of randomly generating a 4-digit number with all even digits can be calculated by dividing the number of favorable outcomes (256) by the total number of possible outcomes (4,536). Therefore, the probability is 256 / 4,536 ≈ 0.0565, or approximately 5.65%.

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1) If total costs for a product are given by C(x) = 1760 + 8x + 0.6x2 and total revenues are given by R(x) = 100x -0.4x2, find the break-even points. =
2) If total costs for a commodity are given by C(x) = 900 +25x and total revenues are given by R(x) = 100x - x2, find the break-even points. 3) Find the maximum revenue and maximum profit for the functions described in Problem #2.

Answers

a) The break-even points for the given cost and revenue functions are approximately x = 16.526 and x = 6.474.

b) The break-even points for the given cost and revenue functions are approximately x = 12.225 and x = 62.775.

c) The maximum profit for the given cost and revenue functions is approximately $843.75.

a) To find the break-even points, we need to determine the values of x where the total costs (C(x)) equal the total revenues (R(x)). We set C(x) = R(x) and solve for x:

C(x) = R(x)

1760 + 8x + 0.6x² = 100x - 0.4x²

Combining like terms and rearranging the equation, we get:

1x² - 92x + 1760 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 16.526

x ≈ 6.474

b) Similarly, we set C(x) = R(x) and solve for x:

900 + 25x = 100x - x²

Rearranging the equation, we get:

x² - 75x + 900 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 12.225

x ≈ 62.775

c) To find the maximum revenue, we need to determine the vertex of the revenue function R(x) = 100x - x². The x-coordinate of the vertex is given by x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -1 and b = 100. Plugging in the values, we get:

x = -100 / (2 * -1) = 50

Substituting this value back into the revenue function, we find:

R(50) = 100(50) - (50)² = 5000 - 2500 = 2500

Therefore, the maximum revenue for the given cost and revenue functions is $2500.

To find the maximum profit, we need to subtract the total costs from the total revenues. Given that the cost function is C(x) = 900 + 25x, the profit function is P(x) = R(x) - C(x). Substituting the revenue and cost functions, we have:

P(x) = (100x - x²) - (900 + 25x)

P(x) = -x² + 75x - 900

To find the maximum profit, we need to determine the vertex of the profit function. Using the same formula as before, we find:

x = -75 / (2 * -1) = 37.5

Substituting this value back into the profit function, we find:

P(37.5) = -(37.5)² + 75(37.5) - 900 ≈ 843.75

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