If sample data come from a population that is not normally distributed, which
sample size would be large enough for the sampling distribution to
approximate a normal distribution?
A. 8
O B. 28
C. 18
D. 58

Answer:

m∠A = 139°

Step-by-step explanation:

First we must know that

Supplementary angles equal to 180 degree.

Since we know that supplementary angles equal to 180 degree we can solve now:

Putting m ∠A and m ∠ B together and put the = 180

( 7x - 15 ) + ( 2x - 3 ) = 180

Now solving for x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Hence,  Angle A will have a measure of 7x - 15 which means  7 ×  22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

139 + 31= 180

[RevyBreeze]

Supplementary angles have sum 180°

m<A

Answer:

Step-by-step explanation:

tanx + cotx = secx / sinx

take left hand side

=tanx + cotx

=sinx/cosx + cosx/sinx

=sinx*sinx+cosx*cosx/sinx*cosx

=sin^2x + cos^2x/sinx*cosx

=1/sinx*cosx

=1/cosx * 1/sinx

=secx/sinx

at second last step i changed multiplication sign into divide sign and write the reciprocal of 1/sinx which is sinx.

Answer:

D or B

Step-by-step explanation:

sorry if its wrong

Product is multiplication.

The opposite of 4 is -4

3 x -4 = -12

Answer: -12

By using the concept of interest, we can calculate the year in which the tuition will reach $10,000 as 2027

Interest is the extra money you pay for borrowing money or for an investment, and it accumulates over time.

In this case, the interest rate is 3%, so the total tuition increases by 3% each year. To calculate the year in which tuition will reach $10,000, we will need to use the following formula:

Interest = (principal × rate × time) / 100.

The principal is $8,000, the rate is 3%, and the time is the number of years it takes for the tuition to reach $10,000. Thus, the equation becomes:

Interest = (8000 × 0.03 × time) / 100.

We can solve for time by multiplying both sides of the equation by 100 and dividing by 240. This gives us the following result:

Time = ($10,000 - $8,000) / (0.03 × $8,000) = 4.17 years.

Therefore, the tuition will reach $10,000 in

(2023 + 4.17) = 2027

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ANSWER

EXPLANATION

To find the number of committees of six people that can be selected from nine people, we apply Combination:

Therefore, we have:

Hence, there are 84 different ways of selecting.

The standard deviation of the given data set, {12, 12, 12, 12, 12, 12, 12}, is zero. This is because the deviation of every value from the mean is zero. Therefore, the standard deviation of the given data set is zero.

In statistics, the standard deviation (SD) is a measure of how much the data is spread out from the mean, or how much the data deviates from the average value. It is calculated by finding the square root of the variance.Variance (σ2) is a measurement of the degree to which a set of data deviates from the mean. In other words, variance is a measure of how much the data is spread out. It is defined as the average of the squared differences from the mean.The formula for calculating the variance is

:σ2 = Σ(x - μ)2/N

where Σ represents the sum, x is the value of the observation,

μ is the mean of the observations, and

N is the total number of observations.

The standard deviation formula is the square root of the variance.

Therefore,σ = √σ2 = √Σ(x - μ)2/N

The given data set is {12, 12, 12, 12, 12, 12, 12}.

The mean of this data set is:(12+12+12+12+12+12+12) / 7 = 12

The deviation of every value from the mean is zero. Therefore, the variance of the given data set is zero. The standard deviation formula is the square root of the variance. Therefore, the standard deviation of the given data set is zero.

The standard deviation of the given data set, {12, 12, 12, 12, 12, 12, 12}, is zero.

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The exponential growth of three sections is given below.

Exponential growth means whose growth more rapid in proportion.

An exponential function is of the form , where b is a positive number not equal to 1.

The value of b determines whether tha function is an exponential growth or an exponential decay.

An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.

Given the function= y 4(5/6)^x

B= 5/6 < 1

Therefore, the function  is an exponential decay.

Given the function

Therefore, the function  is an exponential growth.

Therefore, the function  is an exponential growth is y= 129(1.63)^x is an exponential growth.

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Answer:

The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

Step-by-step explanation:

Refer the attached figure

We will use equation calculator to find the equation of given plot

\(y = 483.36 \times e^0.0264x\)

We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.

x values are years

y values are population

For 1940, \(x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2\)

For 1997, \(x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64\)

For 2005,\(x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74\)

Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.

The average change in value each year is given by -

a = (C - 5)/(x - y)

The rate of change is defined as the change in the magnitude of one value with respect to other value.

Given is C as the current value and 5 is the starting value.

Assume that the value is [C] in year [x] and the value was 5 in year [y], then the average change in value each year =

a = (C - 5)/(x - y)

Therefore, the average change in value each year is given by -

a = (C - 5)/(x - y)

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If the null hypothesis is true in a chi-squared test, then we expect the test statistic to be approximately equal to its expected value.

In a chi-squared test, the null hypothesis is the statement that there is no significant association between two variables. If the null hypothesis is true, then we expect the test statistic to be approximately equal to its expected value. The expected value is calculated using the degrees of freedom and the expected frequency of each category in the contingency table.

The chi-squared test statistic is calculated by subtracting the observed frequency from the expected frequency for each category and then squaring the result. These squared differences are then summed across all categories to calculate the chi-squared test statistic.

If the null hypothesis is true, we expect the test statistic to be close to its expected value. This is because when the null hypothesis is true, the observed frequencies should be close to the expected frequencies. Therefore, the squared differences should be small, resulting in a small test statistic.

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Answer:

522,761 baseballs

Step-by-step explanation:

Number of baseball bats produced over the last 2 years = 357, 945

Number of little league baseballs produced over the last 2 years = 490,867

Number of major league baseballs produced over the last 2 years = 389,839

Total number of baseballs produced over the period = 490,867 + 389,839

                                                                                         = 880,706

Number of baseballs manufactured more than bats = 880,706 - 357945

                                                                                      = 522,761

There are 522,761 baseballs produced more than bats during the 2 years.

Answer:

y-4=-2/5(x+5)

Step-by-step explanation:

Points slip form is y-y₁=m(x-x₁)

Since you have a graph we can see the line goes down 2 and over 5. Since the slope is going downwards it is a negative slope. This mean m=-2/5. Then pick any point on the line ( I chose (-5,4)) and plug it in for y₁ and x₁.

Answer:

( 4, 5 ) -( 5, 6 ) =7,15

Step-by-step explanation:

Answer:

V(t) = 26,000 - 15t

Step-by-step explanation:

Given the following :

Initial approximate volume of water = 26 billion ounces

Yearly consumption = 150 million ounces

Let V = volume remaining

Linear equation to model decreasing supply of water.

Volume left = Initial volume - consumption

Consumption = 150 million per year

Consumption after t years = 150 million * t

Volume left = 26,000,000,000 - 150,000,000t

V = 26,000,000,000 - 150,000,000t

Divide by 1,000,000

V(t) = 26,000 - 15t

Answer:

Step-by-step explanation:

GIVEN:

To find the missing number in the proportion, you have to isolate it the term of x from one side of the equation.

\(\sf{\dfrac{8}{7}=\dfrac{x}{21} }\)

First, thing you do is switch sides.

\(\sf{\dfrac{x}{21}=\dfrac{8}{7} }\)

Multiply by 21 from both sides.

\(\Longrightarrow: \sf{\dfrac{21x}{21}=\dfrac{8*21}{7} }\)

Solve.

Multiply the numbers from left to right.

Use the order of operations.

PEMDAS stands for:

\(\Longrightarrow: \sf{\dfrac{8*21}{7}=\dfrac{168}{7}=24 }\)

\(\Longrightarrow: \boxed{\sf{x=24}}\)

I hope this helps. Let me know if you have any questions.

a. i. There are 27,040,000 different passwords are possible if repetition of digits and letters is allowed and passwords are not case sensitive  (so 123AB is the same as 123aB)

ii. There will be 99,532,800  different passwords are possible if repetition of digits and letters is not allowed and the passwords are case-sensitive

b. i. The probability that all 4 randomly selected students were math majors is  0.520

ii. There are 4,725 different pairs of math majors that could be chosen for the committee.

a. i) There are 10 choices for each of the first 3 digits, and 26 choices for each of the last 2 letters. Since the password is not case sensitive, we can choose either uppercase or lowercase letters, so there are 26 + 26 = 52 choices in total for each letter. Therefore, the total number of different passwords is:

10 x 10 x 10 x 52 x 52 = 27,040,000

ii) There are 10 choices for the first digit, 9 choices for the second digit (since we can't repeat the first digit), 8 choices for the third digit (since we can't repeat the first two digits), and 52 choices for the first letter. For the second letter, there are 51 choices left (since we can't repeat the first letter), but we need to distinguish between uppercase and lowercase letters, so there are 52 x 51 = 2,652 choices for the two letters in total. Therefore, the total number of different passwords is:

10 x 9 x 8 x 52 x 2,652 = 99,532,800

b) i) The total number of ways to select a 4-student committee from 20 students is:

20 choose 4 = 4,845

The number of ways to select a committee consisting of 4 math majors is:

10 choose 4 = 2,520

Therefore, the probability that all 4 randomly selected students were math majors is:

2,520 / 4,845 = 0.520

ii) The number of ways to select a 4-student committee with exactly two math majors is:

(10 choose 2) x (10 choose 2) x (15 choose 0) = 4,725

(We choose 2 math majors from 10, and 2 non-math majors from 15, since there are 5 biology majors and 5 music majors to choose from.)

Therefore, there are 4,725 different pairs of math majors that could be chosen for the committee.

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Answer:

n = 17-13

Step-by-step explanation:

n+13=17

Subtract 13 from each side

n+13-13 = 17-13

n = 17-13

Answer:

25

Step-by-step explanation:

\(3^2+4^2=9+16=25\)

Answer:

The one you have is right. Happy holidays too! :D

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

The Xs are the same!

Answer:

25 s

Step-by-step explanation:

700/112=6.25

6.25*4=25

Answer:

28 s (the fourth option)

Hope it helps.

Step-by-step explanation:

The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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Answer:

leg = 1

hypotenuse = √2 or 1.41

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Constants are any numbers that don't change.

2x + 3y + 6

Since "6" is the only number here, that is the only constant.

Best of Luck!

Answer:

6

Step-by-step explanation:

Assumptions: For the purpose of this exercise, let's assume that we are analyzing defects in a manufacturing process. We will invent data for five different categories of defects and their corresponding frequencies. the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

a. Based on the invented data, the histogram analysis reveals the following distribution of defects and their frequencies:

Category A: 50 defects

Category B: 30 defects

Category C: 20 defects

Category D: 15 defects

Category E: 10 defects

To identify the top 20% of the category of defects contributing to 80% of the total volume, we calculate the cumulative frequency. Starting with the category with the highest frequency, we add up the frequencies until we reach 80% of the total. In this case, Category A contributes the highest frequency, and its cumulative frequency is 50. The total number of defects is 125 (50 + 30 + 20 + 15 + 10). By calculating the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

b. Performing a Root Cause Analysis for the Top Contributing Factor (Category A) using the 5-Why method or Fishbone diagram helps determine the underlying causes. We identify potential factors such as equipment malfunction, operator error, insufficient training, or process variability. By asking "why" repeatedly, we dig deeper into each cause to uncover the root cause.

c. Based on the analysis, we develop a corrective action plan and preventive action plan. For example:

Corrective Action Plan: Assign qualified technicians to regularly inspect and maintain the equipment, conduct additional training for operators to enhance their skills, and implement process control measures to reduce variability.

Preventive Action Plan: Establish a preventive maintenance schedule for equipment, implement a comprehensive training program for all operators, and conduct regular process audits to identify and address potential issues proactively.

The corrective and preventive action plans should clearly define the tasks, responsibilities, and timelines. The maintenance department may be responsible for equipment maintenance, the training department for operator training, and the quality department for process audits. Regular monitoring and evaluation of the action plans should be conducted to ensure effectiveness and make any necessary adjustments.

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Answer:

B. The slope of g(x) is less than the slope of f(x)

Step-by-step explanation:

The slope of f(x) is 2/1 or just 2 and the slope of g(x) is 1/2, less than f(x).

Answer:

B.

Step-by-step explanation:

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer:

$58,000

Step-by-step explanation:

Total money that Mariana will generate:

Savings = $7,000

One-time grant = $1,000

Annual academic scholarship = $6,000

study program = $10,000/year

Study program for 4 years = $40,000

Total = $7,000 +  $1,000 + $6,000 + $40,000

Total = $54,000

Total money that Mariana will generate for her 4 years = $54,000

Cost of fee at Texas A&M per year =  $28,000

Cost of fee at Texas A&M for 4 years =  4*$28,000 = $112,000

Amount Mariana will have to borrow to attend Texas = $112,000 - $54,000

Amount Mariana will have to borrow to attend Texas = $58,000

Hence Mariana will have to borrow $58,000 in student loan to attend Texas A&M for 4 years