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Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-5, -2) and point (8, -3) rounded to the nearest tenth?


10.3 units


12.6 units


1 unit


13 units

Answers

Answer 1

Answer:

13 units

Step-by-step explanation:

Im doin this in class to so i got you

the equation would be d=(8-(-5))2-(-3-(-2))2

Next solve in the parenthesis 13 power of 2 +-1 power of 2

Then do the powers 169+1

d=170

Then you square 170 which is 13.03840481

That simplifies to 13

yayyyy


Related Questions

A sociologist surveyed 300 people about their level of anxiety on a scale of 1 to 100. Unfortunately, the person inputting the data into the computer accidentally transposed six of the numbers causing the statistics to have errors.What type of error is this?1. Sampling error 2. Non sampling error

Answers

Answer:

non sampling error

Step-by-step explanation:

Sampling error in a statistical analysis arising from the unrepresentativeness of the  sample taken.

Non Sampling error is a term used in statistics that refers to an error that occurs during data collection, causing the data to differ from the true values.

Answer:

sampling error

Step-by-step explanation:

One day the appliance store offers a $50 discount on all purchases over $300. The store also has a sale with 15% off of all refrigerators. The 15% discount is applied after the $50 discount. What is the price, in dollars, of a $435 dollar refrigerator after both discounts? Answer the problem. Explain how you would solve the problem (list the steps you would take).

Answers

Answer:

$327.25

Step-by-step explanation:

$435 - $50 = 385

15% = 15/100 = 0.15

$385 * 0.15 = 57.75

$385 - $57.75 = $327.25

The price, in dollars, of a $435 dollar refrigerator after both discounts is $327.25.

The calculation is as follows:

= $435 - $50

= 385

Since there is 15% discount

So here we have to do 15% discount of $385

i.e.

= $385 - 15% of $385

= $385 - $57.75

= $327.25

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An NHL hockey player has 59 goals so far in season what are the possible numbers of additional goals the player can score to make or break the NHL record of 92 goals in a season

Answers

Answer:

53 by the fact NFL players use a for wheeler u Dan je e eka a f wjd r

Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?

Answers

Answer: 15

Step-by-step explanation:

Answer:

he have to kep cutting them until he find out he answer

Step-by-step explanation:

PLLLZ HELP Find Sn if a1 = 20, d = –10, and n = 25.

–2500

–2750

2500

–5000

Answers

Option A: [tex]-2500[/tex] is the value of [tex]S_{25[/tex]

Explanation:

It is given that the first term is [tex]a_1=20[/tex]

The common difference is [tex]d=-10[/tex]

We need to determine the sum of 25 terms.

The sum of  terms of an arithmetic series can be determined using the formula, [tex]S_n=\frac{n[2a_1+(n-1)d]}{2}[/tex]

Substituting [tex]n=25[/tex] , [tex]a_1=20[/tex] and [tex]d=-10[/tex]

Thus, we have,

[tex]S_{25}=\frac{25[2(20)+(25-1)(-10)]}{2}[/tex]

Simplifying the values, we get,

[tex]S_{25}=\frac{25[40+(24)(-10)]}{2}[/tex]

[tex]S_{25}=\frac{25[40-240]}{2}[/tex]

Subtracting the terms within the bracket, we get,

[tex]S_{25}=\frac{25[-200]}{2}[/tex]

Multiplying the terms in the numerator, we have,

[tex]S_{25}=\frac{-5000}{2}[/tex]

Dividing, we get,

[tex]S_{25}=-2500[/tex]

Thus, the sum of the 25 terms is [tex]-2500[/tex]

Therefore, Option A is the correct answer.

Answer:

-2500 answer

Step-by-step explanation:

A consumer organization inspecting new cars found that many had appearance defects. While none had more than 3 defects, 7% had three, 11% had two, and 21% had one defect. Find the expected number of appearance defects in a new car, and the standard deviation.

Answers

Answer:

E(X) = 0.64

Sd(X) = 0.933

Step-by-step explanation:

3(0.07) + 2(0.11) + 1(0.21)

E(X²) = 3²(0.07) + 2²(0.11) + 1²(0.21)

= 1.28

Var(X) = 1.28 - 0.64² = 0.8704

Sd = 0.933

Fran is limited to watching television less than 12.6 hours per week. She has already watched 4.2 hours, and each show is 0.7 of an hour long. 0.7x + 4.2 < 12.6 How many more shows can Fran watch this week?

Answers

Answer: the number of hpurs that Fran can watch this week is lesser than 12

Step-by-step explanation:

Let x represent the number of hours of television that Fran can watch in a week.

Fran is limited to watching television less than 12.6 hours per week. She has already watched 4.2 hours, and each show is 0.7 of an hour long. The inequality representing the situation is expressed as

0.7x + 4.2 < 12.6

0.7x + 4.2 < 12.6 - 4.2

0.7x < 8.4

x < 8.4/0.7

x < 12

Answer:

12

Step-by-step explanation:

Fran has wached 4.2 hours of tv out of 12.6, if the equasion is curect that means that she has wached 6 shows already.

From here there is two ways to do his one is to look at how meny shows she can watch in 12.6 hours and subtract how meny shows she has wached from it  and then convert back to desimals.

The other way to do this( the better way) is to do 12.6-4.2=8.4 then do 8.4 / .7 and you would get 12

Determine whether the statement is sometimes, always, or never true.

If ax + b - 4 = b and a doesn't = 0 then x = 4/a

sometimes
always
not enough information provided
never

Answers

Answer:

  always true

Step-by-step explanation:

Adding 4-b to both sides of the equation gives ...

  ax = 4

Then dividing by "a" gives ...

  x = 4/a

This is always true when a≠0.

PLEASE HELP WILL MARK 1ST RIGHT ANSWER AS BRAINIEST!!!
In triangle $ABC$, the measure of angle $A$ is $x$ degrees, the measure of angle $B$ is $2x$ degrees and the measure of angle $C$ is $5x$ degrees. What is the value of $x$? Express your answer as a decimal to the nearest tenth.

Answers

Answer:

22.5

Step-by-step explanation:

All of the angles inside the triangle equals 180. Therefore, the equation is x+2x+5x=180. Then, you solve for x. The final equation should look like 8x=180 And that is how we get 22.5

Answer:

22.5

Step-by-step explanation:

The sum of the interior angles in a triangle is 180 degrees, so we have the equation $x+2x+5x=180$, so $x=\boxed{22.5}$.

Chelsea collects sand dollars.The number she has collected is greater than 400 and less than 460.The number in hundreds place is one less than the number in the tens place.The number in the ones place is two more than the number in the tens place.How many sand dollars has Chelsea collected?

Answers

Answer:

457 sand dollars

Step-by-step explanation:

Let the number=x

The number she has collected is greater than 400 and less than 460

400<x<460

The number in hundreds place is one less than the number in the tens place.

The number in the Hundreds place is 4. Since it is one less, our number for now will be of the form 45* where * is the ones digit.

Also, the number in the ones place is two more than the number in the tens place.

The number in the tens place is 5. If it is two more than 5, the number in the ones place is 7.

Therefore Chelsea has collected 457 sand dollars

Brainliest + 20 points to whoever helps!!!

Under which circumstances should you use a two-population z test?
a. The standard deviation is unknown.
b. The sample size is less than 30.
c. The population is slightly skewed and n > 40.
d. The standard deviation is known and n > 30.

Answers

Answer:

D. The standard deviation is known and n > 30.

Step-by-step explanation:

Your sample size is greater than 30.Data points should be away from each other.Your data should be commonly categorized. Your data should be randomly picked from a population. Each item should have an equal chance of being selected. The sample sizes should be equal.
Final answer:

A two-population z test should be used when the standard deviation is known and the sample size is greater than 30.

Explanation:

The circumstances under which you should use a two-population z test are:

The standard deviation is known and the sample size is greater than 30.

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A landscaping company charges a $10 fee to make a house call plus an hourly rats for labor. If the total bill for a job that takes two hours comes to $61.00 write an equation that can be used to solve for the hourly labor rate

Answers

Answer:

61 divided by 10 and that should even out how many hours they worked

Step-by-step explanation:

Answer: the equation that can be used to solve for the hourly labor rate is

2x + 10 = 61

Step-by-step explanation:

Let x represent the amount charged by the landscaping company per hour of labour.

The landscaping company charges a $10 fee to make a house call plus an hourly rate for labor. This means that the total charge for y hours is

xy + 10

If the total bill for a job that takes two hours comes to $61.00, the equation that can be used to solve for the hourly labor rate would be

2x + 10 = 61

Plz help

The volume of the rectangular prism is 60x3 + 145x2 + 70x. Factor to find the possible expressions for length, width and height of the prism.



4x(5x + 7)(3x + 2)



x(2x + 7)(10x + 1)



5x(4x + 7)(3x + 2)



5x(7x + 4)(3x + 2)

Answers

Option C: [tex]5 x(4 x+7)(3 x+2)[/tex] is the possible expressions for length, width and height of the prism.

Explanation:

The volume of the rectangular prism is [tex]60 x^{3}+145 x^{2}+70 x[/tex]

To determine the length, width and height of the rectangular prism, let us factor the expression.

Thus, factoring 5x from the expression, we have,

[tex]5 x\left(12 x^{2}+29 x+14\right)[/tex]

Let us break the expression [tex]12 x^{2}+29 x+14[/tex] into two groups, we get,

[tex]5x[\left(12 x^{2}+8 x\right)+(21 x+14)][/tex]

Factoring 4x from the term [tex]12 x^{2}+8 x[/tex] , we get,

[tex]5x[4 x(3 x+2)+(21x+14)][/tex]

Similarly, factoring 7x from the term [tex]21 x+14[/tex] , we get,

[tex]5x[4 x(3 x+2)+7(3x+2)][/tex]

Now, let us factor out [tex]3x+2[/tex], we get,

[tex]5 x(4 x+7)(3 x+2)[/tex]

Hence, the possible expressions for length, width and height of the prism is [tex]5 x(4 x+7)(3 x+2)[/tex]

Therefore, Option C is the correct answer.

Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage ofthe total variation that can be explained by the linear relationship between the two variables. r = 0.885 (x = weight of male, y = waist size of male)

Answers

Answer:

Step-by-step explanation:

The coefficient of determination = [tex]r^{2} = 0.885^{2}[/tex] = 0.7832

It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.

If the risk-free rate is 7 percent, the expected return on the market is 10 percent, and the expected return on Security J is 13 percent, what is the beta of Security J

Answers

Answer:

0.02 or 2% = Beta

Step-by-step explanation:

Given that,

Risk-free rate = 7 percent

Expected return on the market = 10 percent

Expected return on Security J = 13 percent

Therefore, the beta of Security J is calculated as follows;

Expected return on Security J = Risk-free rate + Beta (Expected return on the market - Risk-free rate)

13 percent = 7 percent + Beta (10 percent - 7 percent)

0.13 - 0.07 = 0.03 Beta

0.06 = 0.03 Beta

0.06 ÷ 0.03 = Beta

0.02 or 2% = Beta

Chris wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has
120
feet of fencing available. Find the dimensions that will enclose the maximum area.

The fence parallel to the house is ___
feet, the fence perpendicular to the house is ____
feet and the area of the yard is ____
square feet.

Answers

Answer:

parallel: 60 ftperpendicular: 30 ftarea: 1800 ft^2

Step-by-step explanation:

Let x represent the length of fence parallel to the house. Then the length perpendicular is ...

  y = (120 -x)/2

The area of the yard is the product of these dimensions, so is ...

  A = xy = x(120-x)/2

This is the equation of a parabola that opens downward and has zeros at x=0 and x=120. The maximum (vertex) is on the line of symmetry, halfway between these zeros, at x=60.

The fence parallel to the house is 60 feet.

The fence perpendicular to the house is (120-60)/2 = 30 feet.

The area of the yard is (60 ft)(30 ft) = 1800 ft^2.

What is the area of the largest circular fire that can be made in this fire pit? Use 3.14 for π. Round to the nearest square inch.
!no absurd answers, please! : (

Answers

Area of the largest circle fit in the fire pit is 4069.44 square inches.

Solution:

Length of the rectangular pit = 7 feet

Width of the rectangular pit = 6 feet

The diameter of a largest circle inscribed in a rectangle is equal to the smaller side of the rectangle.

Diameter of the largest circle = 6 feet

Radius of the largest circle = 3 feet

Area of the circle = πr²

                             = 3.14 × 3²

Area of the circle = 28.26 square feet

Let us convert square feet into square inches.

1 square feet = 144 square inches

28.26 square feet = 28.26 × 144

                              = 4069.44 square inches

Area of the largest circle fit in the fire pit is 4069.44 square inches.

Given f(x)= x+1 and g(x)=√x+2 determine the following. Write each answer using interval notation.
Determine the Domain of g(f(x))
Domain:

Answers

Answer:

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

Domain = [-1,∞)

Step-by-step explanation:

Given f(x) = x+1 and g(x) = √x + 2

g(f(x)) is a composite function.

g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]

To find the domain of composite function we must get both domains right (the composed function and the first function used).

The domain of f(x) is all the real numbers.

The domain of g(f(x)) is the values of x provide that the square root is greater than or equal zero

So, x+1 ≥ 0

∴ x ≥ -1

So, the domain = [-1,∞)

Final answer:

The domain of the composite function g(f(x)) is x ≥ -2.

Explanation:

The domain of a function is the set of all possible input values for which the function is defined. To determine the domain of the composite function g(f(x)), we need to consider two things:

The domain of the inner function f(x)The domain of the outer function g(x)

In this case, the domain of f(x) is all real numbers because there are no restrictions on the input values for f(x) = x + 1.

However, the domain of g(x) = √(x + 2) is limited by the requirement that the radicand (the expression inside the square root) must be greater than or equal to zero. So, x + 2 ≥ 0.

Solving this inequality, we get x ≥ -2.

Therefore, the domain of g(f(x)) is x ≥ -2, which can be written in interval notation as (-∞, -2] or [-2, ∞).

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Vera claimed the solution set on the number line represents the inequality Negative 78.9999 greater-than-or-equal-to x. A number line going from negative 82 to negative 78. A closed circle is at negative 79. Everything to the left of the circle is shaded. Which error did Vera make? Vera wrote the inequality with the variable on the left side of the relation symbol. Vera wrote a relation symbol that does not represent the direction of the ray. Vera selected an inequality that does not include –79 in its solution set. Vera used the wrong number in her inequality.

Answers

Answer:

Vera used the wrong number in her inequality.

Step-by-step explanation:

Inequalities are graphed to present a clearer picture of their behavior

To graph an inequality, the following are required steps

(1) Locate the indicated number on the other side of the  inequality sign variable x in the inequality equation (in this case we have 78.9999 ≥ x)

(2) Draw a number line and place an open or shaded circle around around the number specified in the inequality equation depending on whether the variable is also equal to the number

(3) Shade the possible numbers of the variable

In this case Vera used 78.999 in the equation and 79 on the graph

Answer:

Vera used the wrong number in her inequality.

Step-by-step explanation:

Vera graphed the inequality -78.9999 ≥ x. However, she plotted the point at -79, not -78.9999. Thus, we can tell the answer is Vera used the wrong number in her inequality.

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If a student places in the 99th percentile on an exam, she performed better than 99% of all students who completed the exam. Her performance is similar to a statement based on a __________.

Answers

Answer:

Cumulative frequency distribution

Step-by-step explanation:

Cumulative frequency distribution is a form of a frequency distribution that represents the sum of a class and all classes below it. Remember that frequency distribution is an overview of all distinct values (or classes of values) and their respective number of occurrences.

Final answer:

Placing in the 99th percentile means a student did better than 99% of test takers, akin to scoring beyond the second standard deviation, a high achievement.

Explanation:

If a student places in the 99th percentile on an exam, this indicates that her performance was better than 99% of all students who completed the exam. Her achievement is akin to being beyond the second standard deviation in the context of a normal distribution, showing an exceptional score. In the given context, this means she likely scored higher than what is considered the range for the majority of her peers.

Being in the 90th percentile would indicate that 90 percent of test scores were at or below that mark, a clear demonstration of high achievement compared to peers. In educational measurement, the choice between absolute rating and relative ranking can greatly affect the evaluation of student performance. With relative ranking, a student's performance is compared against that of their peers, such as being in the top 10% as opposed to achieving a specific score percentage, which would be an absolute rating.

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows...... 4; 7; -1; 1; 0; 5; -2; 2; -1; 6; 5; -3
What is the mean change score? (Round your answer to two decimal places.)
What is the standard deviation for this population? (Round your answer to two decimal places.)
What is the median change score? (Round your answer to one decimal place.)
Find the change score that is 2.2 standard deviations below the mean. (Round your answer to one decimal place.)

Answers

Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{23}{12} = 1.92[/tex]

b) standard deviation for this population

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.

Sum of squares of differences = 126.92

[tex]\sigma = \sqrt{\frac{126.92}{12}} = 3.25[/tex]

c) median change score

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

[tex]\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5[/tex]

d) change score that is 2.2 standard deviations below the mean.

[tex]x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23[/tex]

Francisco's game involves a bag of 3 green, 2 yellow, 4 red, and 3 black marbles. Andrew wants to increase the likelihood of selecting a yellow marble. How can the game be modified to make drawing a yellow marble more likely? Select all that apply.XAndrew should add more green marbles to the bag.-Andrew should add more yellow marbles to the bag.-Andrew should remove from the bag 1 green, 1 black, and 2 red marbles.XAndrew should add more black marbles to the bag-Andrew should triple the number of yellow marbles in the bag.

Answers

To increase the likelihood of selecting a yellow marble Andrew should:

-Add more yellow marbles to the bag

-Remove from the bag 1 green, 1 black, and 2 red marbles

-Triple the number of yellow marbles in the bag

Answer:

B,C,E

Step-by-step explanation:

just did it

please help ! i got through half the problem - i just can't figure out how to split the $2 to jay and kay. giving out brainliest !!

Jay, Kay, and Lee are hiking. Lee forgot to bring water. Jay brought 2 gallons of water and Kay brought 1.75 gallons of water. The three of them agree to divide all the water equally among them. Lee gives $2 for the water he receives, which Jay and Kay agree to divide fairly between the two of them. How much money should Jay receive?

Answers

Answer:

The answer to your question is Jay will receive $1.07 and Kay will receive $0.93.

Step-by-step explanation:

Data

Jay brought 2 gallons

Kay brought 1.75 gallons

Money = $2

Process

1.- Calculate the total amount of water

Water = 2 + 1.75

          = 3.75 gallons

2.- Calculate the money Jay will receive using proportions

               3.75 gallons ---------------- $2.00

               2      gallons  ---------------  x

               x = (2 x 2) / 3.75

               x = 4/3.75

               x = $1.07

3.- Calculate the money Kay will receive using proportions

               3.75 gallons ----------------$2.00

               1.75 gallons   --------------- x

               x = (1.75 x 2.00) / 3.75

               x = 3.5/3.75

               x = $0.93

In the test of hypothesis H 0 : μ = 100 vs Ha: μ ≠ 100, a sample of size 250 yields the standardizedtest statistic z = 1.47. Find the p-value for the test and state your conclusion at α = 0.10

Answers

Answer:

The p-value of the test is 0.1416.

The null hypothesis was not rejected concluding that μ = 100.

Step-by-step explanation:

The hypothesis is defined as:

H₀: μ = 100 vs. Hₐ: μ ≠ 100

The test is a two-tailed test.

The test statistic value is z = 1.47.

The significance level of the test is α = 0.10.

The p-value is computed as follows:

[tex]p-value=2\times P(Z<-1.47)=2\times0.0708=0.1416[/tex]

Decision rule:

If the p-value of the test is less than the significance level 0.10, then the null hypothesis is rejected and vice-versa.

The p-value = 0.1416 > α = 0.10.

The p-value is more than the significance level.

The null hypothesis was not rejected.

Conclusion:

The mean value is not different than 100.

Final answer:

To find the p-value for the test, calculate the area under the standard normal curve more extreme than the observed test statistic. The p-value is 0.1416, and we fail to reject the null hypothesis at α = 0.10.

Explanation:

To find the p-value for the test, we need to calculate the area under the standard normal curve that is more extreme than the observed test statistic. In this case, the test statistic is z = 1.47. Since it is a two-tailed test, we need to find the probability in both tails.

First, we find the area to the right of 1.47 by subtracting the cumulative probability from the mean to 1.47 from 1: P(Z > 1.47) = 1 - P(Z < 1.47) = 1 - 0.9292 = 0.0708.

Next, we double this probability to get the total p-value for both tails: p-value = 2 * 0.0708 = 0.1416. Since the p-value (0.1416) is greater than the significance level (α = 0.10), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the population mean is not equal to 100.

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In a sample of n = 6 scores, the smallest score is X = 3, the largest score is X = 10, and the mean is M = 6. If the largest score is changed from X = 10 to X = 22, then what is the value of the new mean?

Answers

Answer:

8

Step-by-step explanation:

Given that in a sample of n = 6 scores, the smallest score is X = 3, the largest score is X = 10

Mean = 6

Since mean = 6 we get sum of all the 6 scores = [tex]6(6) = 36[/tex]

Now  II part says 10 is changed to 20

i.e. original sum = 36

Changed value  = 10

Adjusted value =26

Add: new value  =22

New sum            =48

So we have sum = 48

New mean= [tex]\frac{48}{6} =8[/tex]

(This can also be done using the formula

old mean + positive change in one score/6)

Final Answer:

The new mean after changing the largest score from 10 to 22 is 8.

Explanation:

To solve this problem, we will follow these steps:
1. Calculate the total sum of all scores using the original mean.
2. Subtract the original largest score from the total sum.
3. Add the new largest score to the total sum to get the new total sum.
4. Calculate the new mean by dividing the new total sum by the sample size.

Let's go through these steps one by one:
Step 1: Calculate the original total sum of scores.
Given that the mean (M) is 6 for a sample size (n) of 6:
Total sum of scores (original) = Mean × Sample size = M × n = 6 × 6 = 36

Step 2: Subtract the original largest score from the total sum.
Original total sum = 36 (from Step 1)
Original largest score = 10
Total sum after removing the original largest score = 36 - 10 = 26

Step 3: Add the new largest score to the total sum to get the new total sum.
Total sum after removing the original largest score = 26 (from Step 2)
New largest score = 22
New total sum of scores = 26 + 22 = 48

Step 4: Calculate the new mean.
New total sum of scores = 48 (from Step 3)
Sample size (n) = 6
New mean = New total sum of scores ÷ Sample size = 48 ÷ 6 = 8

Therefore, the new mean after changing the largest score from 10 to 22 is 8.

Find a1, d, and the Explicit Rule for this arithmetic sequence: -3, 4, 11, 18, 25, ...
1.)a1 =-3, d=-7, an = -7n - 3
2.)a1 =-3, d = 7, an = 7n - 10
3.)21 = -3, d =-7, an = -7n - 10
4.)a1 = -3, d = 7, an = 7n - 3​

Answers

Answer:

2

Step-by-step explanation:

Answer: 2.)a1 =-3, d = 7, an = 7n - 10

Step-by-step explanation:

In an arithmetic sequence, consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a1 = - 3

d = 4 - - 3 = 11 - 4 = 18 - 11 = 25 - 18 = 7

Therefore, the Explicit Rule for this arithmetic sequence is

an = - 3 + 7(n - 1)

an = - 3 + 7n - 7

an = 7n - 7 - 3

an = 7n - 10

a. I have five coins in my pocket – four are fair, and the other is weighted to have a 70% chance of coming up heads. I pull one out at random and flip it three times. What is the conditional probability that I get four heads given I pulled out the weighted coin?

Answers

Answer:

The conditional probability that I get four heads given I pulled out the weighted coin = 0.2401

Step-by-step explanation:

Probability of getting 4 heads from 4 trials for a fair coin = 0.5⁴

But given that it is the weighted coin that is pulled out,

The probability of getting 4 heads from 4 trials = 0.7⁴ = 0 2401

Solve each problem.
(8 +5i) + (6 - 7i)

Answers

Answer:

2(7-i)

Step-by-step explanation:

(8 +5i) + (6 - 7i)

Opening each bracket

8 +5i +6 -7I

8 +6 +5i-7i

14-2i

2(7-i)

Answer:

14 - 2 i

Step-by-step explanation:(8 + (5 * i)) + (6 - (7 * i)) =

A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the semicircle. What are the dimensions of the rectangle with maximum​ area?

Answers

Answer:

L = 2*√2

w = √2

Step-by-step explanation:

Given:

A rectangle is constructed with its base on the diameter of a semicircle with radius 2 and with its two other vertices on the semicircle.

Find:

What are the dimensions of the rectangle with maximum​ area?

Solution:

- Let the length and width of the rectangle be L and w respectively.

- We know that Length L lie on the diameter base. So , L < 4 and the width w is less than 2 . w < 2.

- Using the Pythagorean Theorem, we relate the L with w using the radius r = 2 of the semicircle.

                           r^2 = (L/2)^2 + (w)^2

                           sqrt (4 - w^2 ) = L / 2

                           L = 2*sqrt (4 - w^2 )           L < 4 , w < 2

- The relation derived above is the constraint equation and the function is Area A which is function of both L and w as follows:

                          A ( L , w ) = L*w

- We substitute the constraint into our function A:

                          A ( w ) = 2*w*sqrt (4 - w^2 )

- Now we will find the critical points for width w for which A'(w) = 0

                         A'(w) = 2*sqrt (4 - w^2 ) - 2*w^2 / sqrt (4 - w^2 )  

                         0 = [2*sqrt (4 - w^2 )*sqrt (4 - w^2 )   - 2*w^2] / sqrt (4 - w^2 )  

                         0 = 2*(4 - w^2 )   - 2*w^2

                         0 = -4*w^2 + 8

                         8/4 = w^2

                         w = + sqrt ( 2 )   ..... 0 < w < 2

- From constraint equation we have:

                          L = 2*sqrt (4 - 2 )

                          L = 2*sqrt(2)

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.048.0 and 53.053.0 minutes. Find the probability that a given class period runs between 50.550.5 and 51.7551.75 minutes.

Answers

Answer:

Probability = 0.241

Step-by-step explanation:

We can find the probability that a given class period runs through the given time recognizing that a uniform probability distribution is mostly a rectangle with an area equal to 1.

Therefore,

Probability = 51.7551 - 50.550/53.053 - 48.0480 = 1.2057/5.005

= 0.241

Answer:

The probability of selecting a class that runs between 50.550.5 and 51.7551.75 minutes is 0.24

Step-by-step explanation:

A uniform distribution is a flat distribution that has the same probability density for every number. The area under the graph of the distribution must be 1. Since this distribution runs from 48.048.0 to 53.053.0  minutes,

it has a range of 5.005 (53.053.0 - 48.048.0).

The density must be 1/5.005 ≅ 0.2, so that 5.005*0.2 ≅ 1.0.

 

To find the probability of being between two numbers multiply the range between the numbers by the probability density.

range:51.7551.75 - 50.550.5 ≅ 1.2

1.2*0.2 = 0.24

P(50.550.5 < x < 51.7551.75) = 0.24

The probability of selecting a class that runs between 50.550.5 and 51.7551.75 minutes is 0.24

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