For the function, locate any absolute extreme points over the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.) h(x) = x3 – 5x2 - 6x, -2 sxs 10 absolute maximum (x, y) = -.519,1.627 x absolute minimum (x, y) = ( 3.852, – 40.146)

Answers

Answer 1

For the function that is locate any absolute extreme points over the given interval  h (x) - x 3 - 5x2 - 6x, 10 a we get absolute maximum for x and y  (-0.380, 0.488) (10, 350) and  absolute minimum for x and y (-2, -22) and (4.38, -52.924)

Both critical point lies in domain -2 [tex]\leq[/tex] n [tex]\leq[/tex] 10. We know that h (n) is not define at both side of interval end point so n = -2 and n = 10 are critical point,

The critical point are point where f(n) is defined and its derivative is zero or undefined.

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For The Function, Locate Any Absolute Extreme Points Over The Given Interval. (Round Your Answers To
For The Function, Locate Any Absolute Extreme Points Over The Given Interval. (Round Your Answers To
For The Function, Locate Any Absolute Extreme Points Over The Given Interval. (Round Your Answers To
For The Function, Locate Any Absolute Extreme Points Over The Given Interval. (Round Your Answers To

Related Questions

The bottom of a swimming pool is 12 feet below the surface of the water.

What is the pool's depth in feet?

Enter your answer as an integer.

If it is negative, enter it like this: -42

Answers

Answer:12 feet

Step-by-step explanation:

in a survey about a new cleaning product, 75% of respondents report they would buy the product again. the margin of error for the survey is 5%. based on the margin of error, what percentage range reflects the population's true response?

Answers

Answer:80% - 70%

Step-by-step explanation:

If the margin for the error is 5% im guessing that means 5% backwards or forwards so i believe that my answer is correct

ps if im right brainliest please

The percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.

Given, a margin of error of 5%, we can determine the range that reflects the population's true response.

To find the range, we consider the maximum and minimum values within the margin of error.

Maximum Value: 75% + 5% = 80%

Minimum Value: 75% - 5% = 70%

Therefore, the percentage range that reflects the population's true response, considering the margin of error, is from 70% to 80%.

This means that we can be 95% confident that the actual percentage of people who would buy the product again lies within this range.

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Nth for the leaner sequence 22,18,14,10,6

Answers

The nth term of the sequence is aₙ = 26 - 4n.

How to find the nth term of a sequence?

A sequence is defined as an arrangement of numbers in a particular order.

The sequence is an arithmetic sequence. Therefore, the nth term of the sequence can be found as follows:

aₙ = a + (n - 1)d

where

a = firs termd = common differencen = number of term

Therefore,

a = 22

d = 18 - 22 = -4

n = number of terms

Hence,

aₙ = 22 + (n - 1)-4

aₙ = 22  - 4n + 4

aₙ = 22 + 4 - 4n

aₙ = 26 - 4n

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the manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8. what is the probability of type ii error at the 5% significance level?

Answers

The probability of type ii error at the 5% significance level is 49.5%

Probability:

In statistics, the number of possible way of occurring an particular event is referred as probability.

Given,

The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8.

Here we need to find the probability of type ii error at the 5% significance level.

While we looking into the give question, we have identified the following,

Semi skilled worker hourly wages = $9

Number of samples = 100

sample mean = $8

Standard deviation = $2

Hypotheses

H₀ : μ = 9

H₁ : μ ≠ 9

Significance level = 5%

Therefore, the type II error is calculated as,

=> P [(100 - 9/(2/√100)) ≥ (9 - 8)/(2/√100))] = 1 - 5

When we simplify this one then we get, the probability as 49.5%.

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Hellloooo helpppp meeee

Answers

70 + 60 + 8x + 2 = 180

132+8x= 180

8x= 180-132

8x=48

x= 6

plug in x

8(6)+2 = 50

Answer:

x = 6

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

To find the value of x, we can use the following equation:

70 + 60 + 8x + 2 = 180

Add like terms

132 + 8x = 180

Subtract 132 from both sides

8x = 48

divide both side by 8

x = 6

Help me out please thank you
answers:
-3/4
-4/3
4\3
3/4

Answers

Answer:

Slope: -4/3

y-intercept: -9

Step-by-step explanation:

hope it helps!

A circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answers

Multistep problem alert! Step 1: the area of the circle with radius 2cm is pi x r^2. So, 3.14159x2^2 = 3.14159x4 = 12.5663 sq cm; Step 2: the area of the rectangle is lw (length times width), or 11x7=77 sq cm; Step 3: find the difference of 77 and 12.5663 by subtracting. (64.4337sq cm is the area of the rectangle not covered by the circle); Step 4: round 64.4337 to the nearest hundredth=64.43 sq cm. So, the area of the shaded region, which I assume is the rectangle area not covered by the circle is 64.43 sq cm. Peace!

At top speed, cheetahs can run 80 miles per hour. How fast would that be in meters/second?

Answers

Answer:

The top speed of a cheetah is around 69 to 75 mph. However, the cat can only sprint a short distance of around 0.28 miles. A cheetah is about 2.7 times faster than the fastest human runner. A cheetah accelerates very quickly, allowing it to overtake prey at close range. The fastest cheetah on record is Sarah. Sarah lives at the Cinncinati Zoo in Ohio.

Step-by-step explanation:

Answer:

35.7632

Step-by-step explanation:

multiply the value in miles per hour by the conversion factor '0.44704'.=35.7632 meters per second

a spinner has six equal parts labeled from 1 to 6. the spinner is spun twice. what is the probability of getting a 3 twice in a row?

Answers

The probability of getting 3 twice in a row is 1/36

A spinner has 6 equal parts labeled from 1 to 6.

The spinner is spun twice.
First time what is the conditions {1,2,3,4,5,6}

Second time choices are

{1,1} {1,2} {1,3} {1,4} {1,5} {1,6}

{2,1} {2,2} {2,3} {2,4} {2,5} {2,6}

{3,1} {3,2} {3,3} {3,4} {3,5} {3,6}

{4,1} {4,2} {4,3} {4,4} {4,5} {4,6}

{5,1} {5,2} {5,3} {5,4} {5,5} {5,6}

{6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

So we have total 6*6 = 36 choices

{3,3} comes only 1 times.

We know the formula for probability:

Probability(Event) = Favorable Outcomes/Total Outcomes.

Favorable Outcomes = 1.

Total Outcomes=36.

So the probability of getting a 3 twice in a row is 1/36.

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what is the probability of getting either a spade or an ace when drawing a single card from a deck of 52​ cards?

Answers

When drawing one card from a deck of 52 cards, the probability of obtaining either a spade or an ace are 4/13.

Given,

Number of cards in a deck = 52

Number of spades = 13

Number of aces = 4

Number of ace of spade = 1

We have to find the probability of getting either a spade or an ace when drawing a single card from the deck;

Here,

Probability of either a spade or an ace :

P(spade or ace) = P(spade U ace)

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

Now,

Probability = required outcome / Total possible outcomes

P(spade) = 13 / 52

P(ace) = 4 / 52

P(spade n ace) = 1 / 52

Then,

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

= 13/52 + 4/52 - 1/52

= 16 / 52 = 4 /13

That is,

The probability of getting either a spade or an ace when drawing a single card from a deck of 52 cards is 4/13

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Do you prefer taking tests on paper or online? a college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68. 4 with a standard deviation of 12. 1. Those who took the test online had an average score of 71. 3 with a standard deviation of 14. 2. Can you conclude that the mean scores differ between online and paper tests? find the p-value and state a conclusion

Answers

As per the given standard deviation, the mean scores difference between online and paper tests is 2.9 and the p value of the test is 0.2999

Standard deviation:

In statistics, standard deviation is a quantity expressing by how much the members of a group differ from the mean value for the group.

Given,

A college instructor gave identical tests to two randomly sampled groups of 45 students. One group took the test on paper and the other took it online. Those who took the test on paper had an average score of 68.4 with a standard deviation of 12.1. Those who took the test online had an average score of 71.3 with a standard deviation of 14.2.

Here we need to find the mean scores difference between online and paper tests and the p value of the test.

While we looking into the given question we have identified the following values,

Test on paper:

Average score = 68.4

Standard deviation = 12.1

Online test

Average score = 71.3

Standard deviation = 14.2

Total number of students = 45

So, the difference between the mean scores differ between online and paper tests is calculated as,

=> 71.3 - 68.4 = 2.9

And the p -  value is 0.2999.

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a student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000. if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean, what would you set your confidence interval lower and upper bounds to be?

Answers

As per the given standard deviation, the confidence interval is 495.84, upper bound is $65,495.8 and the lower bound is $64,504.2

Confidence interval

Confidence interval means a range of values, bounded above and below the statistic's mean, that likely would contain an unknown population parameter.

Given,

A student at another business school surveys 100 of 1000 graduates from last year and asks about their salaries. the researcher finds that the average income is $65, 000, with a standard deviation of $8000.

Here we need to find the confidence interval lower and upper bounds if you wanted to be 95% sure that the real mean of all 1000 students is within a range of the sample mean.

While we looking into the given question, we have identified the following values,

standard deviation = $8,000

Average income = $65,000

Sample size = 1000

Confidence level = 95%

Then the value of confidence interval is calculated by the formula,

Then we get the value of

Lower bound = 64504.2

Upper bound = 65495.8

Confidence interval (±) = 495.84

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Classify each number according to its value. 2.1 × 10-4 9.2 × 10-4 3.4 × 10-5 2.1 × 10-3 2.8 × 10-7 8.3 × 10-5 7.2 × 10-5

Answers

According to the information, the numbers are classified as follows: Greater than 8.2 x 104 = None; between 8.2 x 10⁴ and 8.2 x 10⁻⁶ : 2.1 x 10⁻⁴, 9.2 x 10⁻⁴, 3.4 x 10⁻⁵, 2.1 x 10⁻³, 8.3 x 10⁻⁵, 7.2 x 10⁻⁵; and less than 8.2 x 10⁻⁵: 2.8 x 10⁻⁷.

How to find the classification of numbers?

To find the classification of numbers we must know how scientific notation works and know how to classify these numbers. According to its scientific notation, if we want to classify numbers greater than 8.2 x 10⁴ we must take the following into account:

All numbers with a power greater than 10⁴ would be greater than 8.2. Therefore, none of the options would be greater than this number.

In the second case, to find the numbers that are between 8.2 x 10⁴ and 8.2 x 10⁻⁶ we must look at the same element, that is, the numbers that have a power less than 10⁴ and greater than 10⁶ would be in the range of this exercise. So the numbers in this range would be:

2.1 x 10⁻⁴9.2 x 10⁻⁴3.4 x 10⁻⁵2.1 x 10⁻³8.3 x 10⁻⁵7.2 x 10⁻⁵

In the third case, to identify the numbers that are less than 8.2 x 10⁻⁵ we must take into account the same element. If power is less than 10⁻⁵, they would classify in this interval. So the values that classify are:

8.2 x 10⁻⁷

Note: This question is incomplete because there is some information missing. Here is the complete information:

Greater than 8.2 x 104

Between 8.2 x 104

and 8.2 x 10-6

Less than 8.2 x 10-5

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a research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 60,139.7 and 3505.42 kilometers. can you conclude, using ????

Answers

There is no sufficient evidence to indicate the true standard deviation is less than 4000.

What is the standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

  = (15 * 13823970.16) / (16000000)

  = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

            = 0.3946

0.1 < P-value <0.5

Hence, there is no sufficient evidence to indicate the true standard deviation is less than 4000.

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Plot the points (2, -1) and (7,-1) and find the slope.​

Answers

Answer:

slope = 0

Step-by-step explanation:

Slope =

[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]

X1=2 X2=7

Y1=-1 Y2=-1

hence

[tex] \frac{ - 1 - ( - 1)}{7 - 2} [/tex]

[tex] \frac{ - 1 + 1}{7 - 2} [/tex]

[tex] \frac{0}{5} [/tex]

[tex]slope = 0[/tex]

11.30 fcat scores and poverty. in the state of florida, elemen- tary school performance is based on the average score obtained by students on a standardized exam called the florida comprehensive assessment test (fcat). an analysis of the link between fcat scores and sociodemo- graphic factors was published in the journal of educational and behavioral statistics (spring 2004). data on average math and reading fcat scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 florida elementary schools are listed in the table on p. 629.

Answers

Math: s=11.2996s=11.2996, Reading: s=14.4128s=14.4128 for the performance in the elementary school of Florida.

What is meant by statistics?

The study of data collection, analysis, presentation, and interpretation is known as statistics. Much of the early push for the subject of statistics came from government needs on census in addition to data on a range of economic operations. The current requirement to convert vast volumes of data accessible in many applied disciplines into valuable information has driven both theoretical and practical breakthroughs in statistics.

The facts and statistics that are gathered, standardized, and condensed for presentation and interpretation are known as data. The two types of data are quantitative and qualitative, respectively. Quantitative data quantify how much or how many of something exists, whereas qualitative data offer labels or names for groups of similar objects.

How to solve?

We need to determine whether the math core or the reading score better predicts the percentage of students below the poverty level.

The standard error s=11.2996s=11.2996 for the math scores is less than the standard error s=14.4128s=14.4128 for the reading scores, thus the math scores will result in better prediction.

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A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.

Answers

6000FT, is the shortest length of fence that the rancher can use.

What is unitary method ?

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Let the rectangular field's length be x.

rectangle field width = y

square feet of a rectangular field's area

Because length is always positive, it is always positive.

Once more, discriminate with respect to x

replace x=1500

Therefore, at x=1 500, fencing is minimal.

Change x to 1 500.

the rectangular field is 1500 feet long.

rectangle field's width is 1000 feet.

Replace the values

shortest used fence length =6000ft

Hence, 6000FT, is the shortest length of fence that the rancher can use.

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how many (non-congruent) isosceles triangles exist which have a perimeter of $10$ and integer side lengths?

Answers

As per the Pythagoras theorem, there are totally 4 triangles possible.

Pythagoras theorem:

In geometry, Pythagoras theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

Given,

Here we need to find how many (non-congruent) isosceles triangles exist which have a perimeter of 10 and integer side lengths.

As per the Pythagoras theorem, we know that the sum of two sides should be greater than the third.

And here we have the isosceles triangles, then the value of two side of the triangle is equal.

Here the perimeter of the triangle is 10.

Then the values must be the sum of 10,

=> 2, 6, 2

=> 1, 1, 8

=> 3, 3, 4

=> 4, 4, 2

These are the possible combinations.

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B is the midpoint of AC. D is the midpoint of CE. DE=5 and AE=18. What is the length of BD?
please help

Answers

Using the concept of midpoint of a line segment, the length of BD is 9 units

Midpoint of a Line Segment

A midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points. Given any two points, say A and C, the midpoint is a point B which is located halfway between points A and C. Therefore, to calculate the midpoint, we can simply measure the length of the line segment and divide by 2.

In the question given;

AE = 18, DE = 5

But D is the midpoint of CE

CE = 2DE

CE = 2 * 5 = 10

The line CE IS 10

But AE is the total length of the line segment and it equals 18

AE = AC + CE

AC = AE - CE

AC = 18 - 10

AC = 8

If AC = 8, BC = 1/2(AC)

BC = 1/2 (8)

BC = 4

The line BD = BC + CD

BE = 4 + 5 = 9

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What is the solution to the inequality below? 5−10≥−3+14​

Answers

Answer:

5≥17

Step-by-step explanation:

Mrs. Smith had 5/6 of a sack of garden soil for
plants. She used 2/3 of it for planting 6 pots
How much garden soil did she use?

Answers

Answer:

1/6

Step-by-step explanation:

convert them both to the same denominator (bottom number)

2/3 is 4/6

5/6-4/6 is 1/6

suppose a random variable has population mean 141 and population standard deviation 8.85. what is the standard error of the sample mean of a sample of 43 observations? (round to 2 decimal places.)

Answers

The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).

As given in the question,

Population mean of the random variable 'μ' = 141

Standard deviation 'σ' = 8.85

Sample size 'N' = 43 observations

Standard error of the sample mean

= σ / √N

= 8.85 / √43

= 8.85 / 6.56

= 1.349

= 1.35 (round to 2 decimal places )

Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.

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If each quadrilateral below is a rectangle find the missing measure in #4

Answers

The missing measures of the angles are as follows:

m∠BCD = 90°m∠ABD = 16°m∠CBE = 74°m∠ADE = 74°m∠AEB = 148°m∠DEA = 32°

How to determine the measures of the angles?

The figure that completes the question is added as an attachment

From the figure of the rectangle, we have:

m∠BDC = 16°

A rectangle has four (4) interior angles that are 90 degrees each.

This means that

m∠ADE = 90 - 16

m∠ADE = 74°

Also, we have:

m∠ABD = m∠BDC = 16° by the alternate interior angles

By the complementary angle, we have:

m∠CBE = 90 - 16 = 74°

By the alternate interior angles, we have

m∠ADE = m∠CBE = 74°

Solving further, we have the following equations:

m∠AEB = 180 - 2(16)

m∠AEB = 148°

m∠DEA = 180 - m∠AEB

m∠DEA = 180 - 148

m∠DEA = 32°

Hence, the measure of the angle DEA is 32 degrees

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ghghghghghghghghghghghghghghghgh circle.

Answers

Answer:

yass

queen

Step-by-step explanation:

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Add 0.75 and 0.18. How many tenths are in the sum?

Answers

Answer:

Step-by-step explanation:

EXPLANATIONDETAIL STEPSforward

Based on the given conditions, formulate::

Calculate : :

Thanks (77)

Answer: 2 or 100 tenths

Step-by-step explanation:

0.75 + 0.18

You need to do it in the vertical way yo make it easier here i will show you.

 0.75

+ 0.18

______

   0.93

YOU MUST ALIGN THE DECIMALS TO GET IT RIGHT

Dear Math Students, I have to divide 5 cups in half for a recipe. Here's what I did: 5÷1/2= 5 x 2/1 =10 I know I did the division correctly, but my answer should be less than 5, not more. Can you explain my mistake and help me fix it? Your friend, Puzzled Penguin​

Answers

Answer: your first step was right5

Step-by-step explanation:

5/2 =2.5

find the area (in cm2) of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.

Answers

The area of the largest rectangle that can be inscribed in the right triangle is calculated to be 6 cm^2

As we know that for a rectangle of width W and length L the area is given as;

A = L × W

Now let's say that L is along the 8 cm side and W is along the 3 cm side, let's find a relation between these two.

When we inscribe the rectangle in the larger triangle the quotient between the catheti of the right triangle must be equal to the quotient of the catheti of the right triangle that is generated.

Therefore that new triangle will have legs equal to the;

8cm - L and W.

Then we have that:

8cm - L / W = 8 cm / 3 cm

L = 8 cm - 8/3 × W

Now we can write L in terms of W so that we can replace that in the area equation to get

A = (8cm - (8/3)×W)×W = 8cm×W - (8/3)×W^2

This is the equation we have to maximize, also this is a quadratic polynomial of negative leading coefficient, which means that the maximum is at the vertex.

As we know the vertex of the general quadratic polynomial;

a × x^2 + b × x + c

is at:

x = -b / 2a

Then, in this scenario, the vertex is at;

W = (-8 cm) / (2 × 8/3) = 1.5 cm

Then the length is given by:

L =  8cm - (8/3) × 1.5cm = 4 cm

Therefore the area of the largest rectangle that can be inscribed in the given right triangle is;

A = 1.5 cm × 4 cm = 6 cm^2

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g how many ways are there to choose the exec board so that there is at least one masters student and one phd student? (for any of the 4 positions)

Answers

The board has a total of 78960006 options from which to select at least one master's and one PhD candidate.

Given,

Total number of students = 8000

Number of Phd students = 5000

Number of masters students = 3000

Number of members in Student Government Executive Board = 4

We have to find the number of ways to choose the exec board so that there is at least one masters student and one Phd student;

Here,

There are 3,000 different ways to have one Master student on the board.

After choosing a masters student, there are 5,000 different methods to have a PhD student on the board.

The number of possible ways to choose the final two members = 7998!/(7998 - 2)!

That is,

5,000 3,000 + 7998!/(7998 - 2) = 78960006 

Therefore, 

78960006 is the total number of ways the board can choose at least one masters and one PhD.

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beth wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. how large of a sample must she have to get a margin of error less than 0.03?

Answers

The size of the sample that she would have to get a margin of error less than 0.03 is 752

How to solve for the sample size

We have the margin of error E = 0.03

The confidence interval C I = 90 percent

p = 1 - p = 0.5

z α / 2 = 1.645

The formula for the sample size is given as

(z α / 2 / E)² * p * (1 - p)

(1.645 /  0.03)² * 0.5 * 0.5

= 54.833² * 0.5 *0.5

= 752

Hence n is given as 752. The size of the sample would have to be 752.

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from a group of 7 men and 6 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if (a) 2 of the men refuse to serve together?

Answers

There are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Here, n is the total objects available and r is the number of object need to choose from n objects.

Consider no man refuses to serve together. Now, number of ways in which 4 men and 3 women committee can be formed from a group of 7 men and 6 woman.

[tex]^7C_4\times\ ^6C_3[/tex]

Now, consider a goup in which the two persons who do not want to serve togather are togather. Consider these person as a single person. Now, we need to choose 3 men (two individual men and one group of 2 men will make 4 men in the group) from 6 men (7 converts into 6 because group of two person is considerd as 1.).

[tex]\ ^6C_3\times\ ^6C_3[/tex]

Now, subtract [tex]\ ^6C_3\times\ ^6C_3[/tex] from [tex]^7C_4\times\ ^6C_3[/tex] to get the actual answer.

[tex]^7C_4\times\ ^6C_3-\ ^6C_3\times\ ^6C_3\\=\frac{7!}{4!3!}\times \frac{6!}{3!3!}-\frac{6!}{3!3!}\times\frac{6!}{3!3!}\\=35\times20-20\times20\\=20\times15\\=300[/tex]

Hence, there are 300 number of ways in which committee can be formed. It can be solved by the fomula of combination.

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