1) What is the role of probability in statistics?
2) How can we use probabilities to identify values that are significantly low and significantly high? to get credit you must provide an example of each and that example has not been given by any other student.

The equation of the fitted regression line for the given data {(1, 2), (2, 4), (3, 5), (4, 7)} is y = 1.5x + 0.5, calculated using least-squares method.

To find the equation of the regression line, we can use the least-squares method. This method aims to minimize the sum of the squared differences between the actual data points and the predicted values on the line. In this case, we want to find a line of the form y = mx + b, where m represents the slope and b represents the y-intercept.

To calculate the slope (m) and y-intercept (b), we can use the following formulas:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

b = (Σy - mΣx) / n

where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x values, Σy is the sum of y values, and Σ(x^2) is the sum of squared x values.

Using these formulas and the given data, we can calculate the slope and y-intercept as follows:

Σx = 1 + 2 + 3 + 4 = 10

Σy = 2 + 4 + 5 + 7 = 18

Σxy = (1 * 2) + (2 * 4) + (3 * 5) + (4 * 7) = 2 + 8 + 15 + 28 = 53

Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) = 1 + 4 + 9 + 16 = 30

n = 4

Now, let's substitute these values into the slope formula:

m = (4 * 53 - 10 * 18) / (4 * 30 - 10^2)

m = (212 - 180) / (120 - 100)

m = 32 / 20

m = 1.6

Next, we can substitute the calculated slope and the sum values into the y-intercept formula:

b = (18 - 1.6 * 10) / 4

b = (18 - 16) / 4

b = 2 / 4

b = 0.5

Therefore, the equation of the fitted regression line is y = 1.5x + 0.5.

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Answer:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

Answer: 35.7%

Step-by-step explanation:

First find out the total number of all coupons in the box.

= 75 + 125 + 150

= 350 drink coupons

There are 125 medium coupons so the probability that the first customer will pick a medium one is:

= Number of medium coupons / Number of total coupons

= 125 / 350

= 35.7%

Answer:

2 of the 3 answers in picture

Step-by-step explanation:

Answer:

The answers are 2, 3, and 1 only

Step-by-step explanation:

This is the correct answer for plato users

Answer: yeah you got it

Step-by-step explanation:

8,700*

12/100=1044/y         Equation

1044 x 100= 104,400       Cross multiply

104,400÷12=8700            Divide quotient by pecentage out of 100 (12)

The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

Let's expand the expression:

(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)

Using the distributive property, we have:

= 3pi - 7pi^2 - 3qi + 7qi^2

Since i^2 is equal to -1, we can substitute -1 for i^2:

= 3pi - 7p - 3qi - 7q

Now, equating the imaginary part to 58i:

-7p - 7q = 58

Dividing both sides by -7:

p + q = -8

From the given options, only p = 3 and q = -7 satisfy this equation:

3 + (-7) = -4

Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

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Answer:

a) slope is 7

b) slope is positive, so Increasing

c) y-intercept is -3

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Only values that satisfy y > 3x + 1 are solutions.

Only values that satisfy y < 3x – 3 are solutions.

Values that satisfy either y > 3x + 1 or y < 3x – 3  are solutions.

There are no solutions.                                                               Edge 2022

Answer: no

Step-by-step explanation:

plug in (3,10) to y=2x+3

10=2(3)+3

10=6+3

10[tex]\neq[/tex]9

Answer:

IQR=13 im pretty sure

Step-by-step explanation:

The measure interquartile range is 13 option (B) IQR= 13 is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have a box plot, and the data from a survey of ages of people taking an exercise class was skewed to the left.

We know on the left side skewed has more data on the right and on the left side, there are fewer data.

From the dot plot, the end point is not given, so we are assuming the end point is 58.

IQR = 58 - 45 = 13

Thus, the measure interquartile range is 13 option (B) IQR= 13 is correct.

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Answer:

0.029g

Step-by-step explanation:

Answer:

The difference after 5 years is 772.57

Answer:

7

Step-by-step explanation:

Answer: 7

Because 9-2=7

Step-by-step explanation:

please forgive me if I have done something wrong there I am in a hurry I have to go ccooking. if there's something wrong there you can tell me I check it out when I come back good luck.

Answer:

1. 4310.3

2.1809.6

3. 2414.7

4. 230.9

5. 767.8

6. 70.3

7.1143.4

8.125.7

9. 1382.0

10. 158.5

Step-by-step explanation:

Answer:

Closing costs are fees paid at the closing of a real estate transaction. Typically home owners will pay between 2 to 5 percent of the purchase price of their home in closing fees. So, if your home cost $150,000, you might pay between $3,000-$7,000 in closing costs.

Someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.

Employee Contribution:

The employee paid 4.15% of their gross wages towards social security. So, to calculate the employee's contribution:

Employee Contribution = (4.15/100) * Gross Wages

For someone earning $47,000 a year:

Employee Contribution = (4.15/100) * $47,000

                           = (0.0415) * $47,000

                           = $1,950.50

The employee will pay $1,950.50 towards social security.

Employer Contribution:

The employer paid 6.3% of the employee's gross wages towards social security. So, to calculate the employer's contribution:

Employer Contribution = (6.3/100) * Gross Wages

For someone earning $47,000 a year:

Employer Contribution = (6.3/100) * $47,000

                           = (0.063) * $47,000

                           = $2,961.00

The employer will pay $2,961.00 towards social security.

Total Social Security Contribution:

To find the total social security contribution, we add the employee and employer contributions:

Total Contribution = Employee Contribution + Employer Contribution

Total Contribution = $1,950.50 + $2,961.00

                         = $4,911.50

Therefore, someone earning $47,000 a year will pay a total of $4,911.50 towards social security out of their gross wages.

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Answer:

It's the one right under the first one

Answer:

x = 2, y = - 25

Step-by-step explanation:

(1)

note that 36 = 6² , then

[tex]6^{x}[/tex] = 6²

Since bases on both sides are equal then equate the exponents

x = 2

------------------------------------------

(2)

Using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

note that 25 = 5² , then

[tex]25^{11+3y}[/tex] = [tex](5^2)^{11+3y}[/tex] = [tex]5^{22+6y}[/tex]

Then

[tex]5^{5y-3}[/tex] = [tex]5^{22+6y}[/tex]

Since bases on both sides are equal then equate the exponents

22 + 6y = 5y - 3 ( subtract 5y from both sides )

22 + y = - 3 ( subtract 22 from both sides )

y = - 25

The 90% confidence interval for the mean number of calories is 155.3 to 158.4

From the question, we have the following parameters that can be used in our computation:

The dataset

The mean is calculated as

x = sum/count

So, we have

x = (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139 + 175 + 148 + 152 + 111 + 141 + 153 + 190 + 157 + 131 + 149 + 135 + 132) / 20

x = 156.85

Calculate the margin of error using

E = t * σ/√n

Where t = 1.729 i.e. the critical value

So, we have

E = 1.729 * 4/√20

Evaluate

E = 1.55

The confidence interval is then calculated as

CI = x ± E

So, we have

CI = 156.85 ± 1.55

Evaluate

CI = 155.3 to 158.4

Hence, the 90% confidence interval for the mean number of calories is 155.3 to 158.4

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Answer:

35%

Step-by-step explanation:

100% - 35% = 65%

Janice spends 35% swimming

And spends 65% jogging

The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.

A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.

In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.

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30 fl oz for $3.55

if we make them each 10 fl oz then here are the costs:

$1.18 (originally 30 fl oz)

$1.20 (originally 50 fl oz)

(a) The probability that a randomly selected student from the three wards has the virus is 24%.

(b) The probability that a randomly selected student from the hospital who has the virus is in Ward C is approximately 24.5%

a) The probability that a randomly selected student from the three wards has the virus is: (10% of 35) + (15% of 70) + (20% of 50) = 3.5 + 10.5 + 10 = 24%.Thus, the probability that a randomly selected student from the three wards has the virus is 24%.

b) If a randomly selected student from the hospital has the virus, the probability that they are in Ward C is given by Bayes' theorem. The formula for Bayes' theorem is:P(A|B) = P(B|A) x P(A) / P(B)where:P(A|B) is the probability of event A occurring given that event B has occurred. In this case, A is the event that the student is in Ward C and B is the event that the student has the virus.P(B|A) is the probability of event B occurring given that event A has occurred. In this case, it is the proportion of patients in Ward C who have the virus, which is 20%.P(A) is the probability of event A occurring. In this case, it is the proportion of all patients in the hospital who are in Ward C, which is 50 / (35 + 70 + 50) = 0.2941.P(B) is the probability of event B occurring. In this case, it is the probability of a randomly selected student having the virus, which is 24%.Thus, the probability that a randomly selected student from the hospital who has the virus is in Ward C is:P(A|B) = 0.2 x 0.2941 / 0.24 ≈ 0.245 or 24.5%.Hence, the probability that a randomly selected student from the hospital who has the virus is in Ward C is approximately 24.5%.

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A randomly selected student from the hospital has the virus, the probability that they are in Ward C is 0.2.

The solution to the given problem is explained as follows:

(a) What is the probability that a randomly selected student from these three wards has the virus.

The total number of students in the three wards is:

35 + 70 + 50 = 155 students.

Thus, the probability that a randomly selected student from these three wards has the virus is given by:

P(Probab-1550) = P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(C ∩ A) + P(A ∩ B ∩ C)

WhereP(A) = probability of selecting a student from ward A and

having the virus = 0.1,

P(B) = probability of selecting a student from ward B and

having the virus = 0.15,

P(C) = probability of selecting a student from ward C and

having the virus = 0.2,

P(A ∩ B) = probability of selecting a student from both wards A and B and having the virus.

P(B ∩ C) = probability of selecting a student from both wards B and C and having the virus.

P(C ∩ A) = probability of selecting a student from both wards C and A and having the virus.

P(A ∩ B ∩ C) = probability of selecting a student from all three wards and having the virus = 0.

From the given information:•

Ward A has 35 patients, 10 percent of whom have the virus,•

Ward B has 70 patients, 15 percent of whom have the virus,•

Ward C has 50 patients, 20 percent of whom have the virus

,Thus,P(A) = 35 × 0.1 / 100 = 0.035,

P(B) = 70 × 0.15 / 100 = 0.105,

P(C) = 50 × 0.2 / 100 = 0.10,

And,P(A ∩ B) = 0.035 × 0.105

= 0.00367,P(B ∩ C)

= 0.105 × 0.1 = 0.0105,

P(C ∩ A) = 0.1 × 0.035 = 0.0035,

P(Probab-1550) = 0.035 + 0.105 + 0.1 - 0.00367 - 0.0105 - 0.0035 + 0

= 0.22333

So, the probability that a randomly selected student from these three wards has the virus is 0.22333.

(b) If a randomly selected student from the hospital has the virus, what is the probability that they are in Ward C?

The probability that a randomly selected student from the hospital has the virus is

P(Probab-1550) = 0.22333.

From Bayes’ theorem,

P(C | Probab-1550) = P(Probab-1550 | C) × P(C) / P(Probab-1550)

where,P(C | Probab-1550) is the probability that a randomly selected student from Ward C has the virus,

P(Probab-1550 | C) is the probability that a student from Ward C has the virus,

P(C) is the probability of selecting a student from Ward C.P(Probab-1550 | C) = 0.2

= probability of selecting a student from Ward C and having the virus,

P(C) = 50 / 155 = probability of selecting a student from Ward C,

Therefore,P(C | Probab-1550) = 0.2 × 0.22333 / 0.22333

= 0.2

Thus, if a randomly selected student from the hospital has the virus, the probability that they are in Ward C is 0.2.

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Answer:

2 2/5=5/5+5/5+2/5=12/5

3 3/4= [(3•4)+3]/4=15/4

(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=

48/75 kilometers in 1 minute

Step-by-step explanation:

How that this helps! :)

Have a great rest of your day/night!

The Z-score for an athlete with a time of 9 seconds is -0.5. Approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score.

To create the 1-2-3 curve, we can use the mean (µ) and standard deviation (σ) to mark the values on the curve. The 1-2-3 curve represents the standard deviations away from the mean.

1-2-3 Curve:

1st Standard Deviation: Mean ± σ

2nd Standard Deviation: Mean ± 2σ

3rd Standard Deviation: Mean ± 3σ

We have that the mean (µ) is 10 seconds and the standard deviation (σ) is 2 seconds, we can mark the 1-2-3 curve as follows:

1st Standard Deviation: 8 to 12 seconds

2nd Standard Deviation: 6 to 14 seconds

3rd Standard Deviation: 4 to 16 seconds

If an athlete has a time of 9 seconds (x), we can calculate their Z-score using the formula: Z = (x - µ) / σ.

Z-score: (9 - 10) / 2 = -0.5

Placing the Z-score of -0.5 on the curve, we find that it falls between the mean and the first standard deviation (8 to 12 seconds).

To determine the percentage of the team below the athlete and above the athlete, we can use the Z-table. Looking up the Z-score of -0.5 in the table, we find that the area below the Z-score is 0.3085. This means that approximately 30.85% of the team's times were below the athlete's time of 9 seconds.

To compute the area above the Z-score, we subtract the area below from 1: 1 - 0.3085 = 0.6915. This indicates that approximately 69.15% of the team's times were above the athlete's time of 9 seconds.

Therefore, approximately 30.85% of the team was below the athlete, and approximately 69.15% of the team was above the athlete based on the Z-score of -0.5.

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The sets given are not bases for the vector space of solutions to the differential equation. A property of invertible matrices is explained. If a set of vectors is linearly independent and spans a subspace, then adding another vector to the set maintains linear independence. The statement about nullity and column space is false.

a) None of the sets Si, S2, S3, Su, or Ss is a basis for the vector space S of solutions to the given differential equation.

b) Let A be the matrix associated with the linear transformation defined by the differential equation. If S is an invertible matrix such that SAS⁻¹ = B, where B is another matrix, and v is an eigenvector of A corresponding to the eigenvalue λ, then S⁻¹v is an eigenvector of B corresponding to the eigenvalue λ.

c) Suppose {v₁, v₂, v₃} is a linearly independent set of vectors in a vector space V. If va spans the subspace span{v₁, v₂}, then {v₁, v₂, v₃} is also a linearly independent set.

d) FALSE. If A is a 13 x 4 matrix with nullity(A) = 0, it means that the matrix has no nontrivial solutions to the homogeneous system Ax = 0. This implies that the columns of A are linearly independent, but it does not guarantee that colspace(A) = ℝⁿ. The column space of A could still be a proper subspace of ℝⁿ.

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The probability that the average of 35 randomly selected numbers will be more than 7.77 is approximately 0.2157.

a. The distribution of X is uniform, meaning each number from 4 to 11 has an equal probability of being selected. The probability of selecting any specific number is 1/8 since there are 8 numbers in the range.

b. If the computer randomly picks 35 numbers, the distribution of the selection can be approximated by a normal distribution. This is known as the Central Limit Theorem. The mean of the distribution will still be the same as in part a, which is (4 + 11) / 2 = 7.5. The standard deviation of the distribution can be calculated using the formula:

Standard deviation = (b - a) / √(12)

where a and b are the lower and upper bounds of the range, respectively. In this case, a = 4 and b = 11.

Standard deviation = (11 - 4) / √(12) ≈ 1.6794

Therefore, the distribution of the selection of 35 numbers can be approximated by a normal distribution with a mean of 7.5 and a standard deviation of 1.6794.

c. To find the probability that the average of 35 numbers will be more than 7.77, we need to calculate the z-score and then use the standard normal distribution table.

z-score = (7.77 - 7.5) / (1.6794 / √35) ≈ 0.7832

Using the standard normal distribution table or a calculator, we can find the probability associated with the z-score of 0.7832. Let's assume it is P(Z > 0.7832).

The probability that the average of 35 numbers will be more than 7.77 can be calculated as:

P(Z > 0.7832) = 1 - P(Z < 0.7832)

Referencing the standard normal distribution table or using a calculator, we find the probability to be approximately 0.2157.

Therefore, the probability that the average of 35 numbers will be more than 7.77 is approximately 0.2157 (rounded to 4 decimal places).

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Answer:

c.126

Step-by-step explanation:

180-54=126