what is the final step to be performed in the mathematical expression, (σx)2? group of answer choices square the sum of the scores square each score add the squared scores add the scores

Answers

Answer 1

The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

What Is the Sum of Squares?

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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Answer 2

The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

What Is the Sum of Squares?

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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Related Questions

When Jose plays his guitar, the friction between his fingers and the strings allows him to pluck the strings. The friction creates some heat and the vibration of the strings creates the sound. The original amount of energy he applies to the strings is 1000 joules. The energy of the vibrating strings is measured and is found to be 800 joules.

Was energy lost?


Explain:


Answers

Answer:

When Jose plays his guitar, the friction between his fingers and the strings allows him to pluck the strings. The friction creates some heat and the vibration of the strings creates the sound. The original amount of energy he applies to the strings is 1000 joules. The energy of the vibrating strings is measured and is found to be 800 joules.

Was energy lost?

Explain:Step-by-step explanation:

(1) 10x’y' + 15xy? :

Answers

Answer:

factor: 5(2x'y'+3xy)

Step-by-step explanation:

thats for factoring, i didnt know what you needed

Answer:

25xy

Step-by-step explanation:

collect like terms

I need help with this question can you guys help me ​

I need help with this question can you guys help me

Answers

Answer:

$18.5

Step-by-step explanation:

You just add up all the costs and divide them by two and then you would get your answer

7x – 11x = 20
(Multi- step equations)
please help
math test <3​

Answers

Answer:

The answer is x= -5

Step-by-step explanation:

hope this helps

Solutions:

7x – 11x = 20

-4x=20

To find the x divide both side by -4

-4x/-4=20/-4

x= -5

Answer:

7x-11x=20

-4x=20

x=20/-4

x= -5

Twice a number decreased by four is less than 8​

Answers

Answer:

4

Step-by-step explanation:

twice 4=8

decreased by four =4

is less than 8

2x - 4 < 8 !??!?! if an equation is what you need for it lol

i dont get this at all answer fast plz

i dont get this at all answer fast plz

Answers

Answer:

3960 Degrees

Step-by-step explanation:

There is a formula for this!

In this n=24 since there are 24 sides.

The formula is 180(n-2).

Hope this helped and please mark me as Brainliest if possible.

At a large university, 20% of students are enrolled in the nursing program. The dean of students selects a random
sample of 20 students and records n = the number of students enrolled in the nursing program. The dean decides to
simulate this random process by using a random number table. He assigns the digits to the outcomes.
1,2 student is enrolled in nursing program
3-9,0 student not enrolled in nursing program
Here is a portion of a random number table.
Table of Random Digits
1 31645 03495 96193 10898 88532
73869
2 67940 85019 98036 98252 43838 45644
3 21805 26727 73239 53929 42564 17080
Beginning at line 1, carry out one trial of this simulation. Use additional lines as needed. How many students in this
random sample of 20 students are enrolled in the nursing program?

At a large university, 20% of students are enrolled in the nursing program. The dean of students selects

Answers

Note that in this random sample of 20 students, 44/20 = 2.2 students are enrolled in the nursing program. However, since we can't have a fraction of a student, we round to the nearest whole number and say that there are 2 students enrolled in the nursing program. (Option B)

What is the explanation for the above response?

To carry out one trial of this simulation, we will use the digits in the first line of the random number table, reading from left to right. Each digit corresponds to one student in the sample of 20. We will use the given assignment of digits to outcomes to determine whether each student is enrolled in the nursing program or not.

The first digit is 1, which corresponds to a student enrolled in the nursing program. The second digit is 3, which corresponds to a student not enrolled in the nursing program. The third digit is 1, which corresponds to a student enrolled in the nursing program. The fourth digit is 6, which corresponds to a student not enrolled in the nursing program. The fifth digit is 4, which corresponds to a student enrolled in the nursing program.

Continuing in this way, we can assign outcomes to all 20 students in the sample. Counting the number of students enrolled in the nursing program, we have:

1 + 1 + 4 + 5 + 9 + 6 + 1 + 0 + 8 + 9 = 44

So, in this random sample of 20 students, 44/20 = 2.2 students are enrolled in the nursing program. However, since we can't have a fraction of a student, we round to the nearest whole number and say that there are 2 students enrolled in the nursing program. (Option B)

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In a school of 50 pupils,15 study English only and 20 study French only. 5 students do not study any of the two subjects. (i)illustrate the information on a Venn diagram

Answers

Answer:

48

Step-by-step explanation:

2-6$83737463363+77#7#+#++;#+#73737363644646464672727282939

Answer:

10

Explanation:

n(U)= 50

n०(E)= 15

n०(F)= 20

number of (E U F) whole complement= 5

NOW,

n(U)= 15+20+5+n(E intersection F)

or, 50= 40+n(E intersection F)

.. n( E intersection F) = 10

In a school of 50 pupils,15 study English only and 20 study French only. 5 students do not study any

Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fog and state its domain.

Answers

Answer:

y=12x-39

Step-by-step explanation:

it's linear equation so the domain is real number

Vienna bought 8 yards of fabric and paid $38.40. How many more ​ yards can she purchase with $30?​

Answers

Answer:

vienna can purchase 6 more yards


Express x2-5x + 8 in the form (x-a)² + b
where a and b are top-heavy fractions.

Answers

Using Complete the Square method, we find out that \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

It is given to us that the expression is -

\(x^{2} -5x+8\) ----(1)

We have to express it in the form of\((x-a)^{2}+b\) where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  \((x-a)^{2}+b\) we have to use "Completing the Square" method.

The given expression from (1) is -

\(x^{2} -5x+8\)

This expression is in the form of \(ax^{2} +bx+c\)

Adding and subtracting \((b/2)^{2}\) terms into the expression, we get

\(x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8\) -----(2)

Equation (2) can also be represented as -

\((x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8\)

\(= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}\)------- (3)

We see that equation (3) is in the form of \((x-a)^{2}+b\).

So, we can derive that -

\(a=\frac{5}{2}\)

and, \(b=\frac{7}{4}\).

Thus, \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) through "Complete the Square" method as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

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suppose you have 7 events - a, b, c, d, e, f, and g. how many pairwise comparisons would you need to do to complete a pairwise ranking matrix?

Answers

To complete a pairwise ranking matrix of 7 events, we need to make a total of 21 pairwise comparisons.What is a pairwise ranking matrix?

A pairwise ranking matrix is a matrix that lists the results of pairwise comparisons. In this type of matrix, each row and column represents a participant, team, or event, and the cell at the intersection of the row and column represents the outcome of a comparison between the two.

A comparison is made between every pair of events, and the result of the comparison is recorded in the matrix. The entries on the main diagonal of the matrix are all zero since an event cannot be compared to itself

.How to calculate the number of pairwise comparisons for 7 events?

To calculate the number of pairwise comparisons for 7 events, we use the formula n(n - 1)/2, where n is the number of events.

So, for 7 events, we have:n(n - 1)/2 = 7(7 - 1)/2= 7(6)/2= 21Therefore, we need to make 21 pairwise comparisons to complete a pairwise ranking matrix of 7 events.

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To get the total number of iterations in a nested loop, add the number of iterations in the inner loop to the number of iterations in the outer loop.
True
False

Answers

It is False that by adding the number of inner loops , we get the total number of iterations.

A loop is defined as a segment of code that executes multiple times. Iteration refers to the process in which the code segment is executed once. One iteration refers to 1-time execution of a loop. A loop can undergo many iterations.

There are 3 types of iteration: tail-recursion, while loops, and for loops. We will use the task of reversing a list as an example to illustrate how different forms of iteration are related to each other and to recursion. A recursive implementation of reverse is given below.

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Find the sum or type
"impossible”
[1 -2 1] + [4 -5 -6] ]
[[?]
[ ]]

Answers

Answer:

27

Step-by-step explanation:

looked on photomath

Which statements are true about the ordered pair (10, 5) and the system of equations?

{2x−5y=−5x+2y=11


Select each correct answer.


The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.

The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true.

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.

The ordered pair (10, 5) is a solution to the system because it makes both equations true.

Answers

Answer:

C

Step-by-step explanation:

We have the system of equations:

\(\left\{\begin{array}{ll}2x-5y=-5 \\ x+2y=11\end{array}\)

And an ordered pair (10, 5).

In order for an ordered pair to satisfy any system of equations, the ordered pair must satisfy both equations.

So, we can eliminate choices A and B. Satisfying only one of the equations does not satisfy the system of equations.

Let’s test the ordered pair. Substituting the values into the first equation, we acquire:

\(2(10)-5(5)\stackrel{?}{=}-5\)

Evaluate:

\(20-25\stackrel{?}{=}-5\)

Evaluate:

\(-5\stackrel{\checkmark}{=} -5\)

So, our ordered pair satisfies the first equation.

Now, we must test it for the second equation. Substituting gives:

\((10)+2(5)\stackrel{?}{=} 11\)

Evaluate:

\(20\neq 11\)

So, the ordered pair does not satisfy the second equation.

Since it does not satisfy both of the equations, the ordered pair is not a solution to the system because it makes at least one of the equations false.

Therefore, our answer is C.

Part A
The scale of a map says that 4 cm represents 5 km.

What distance on the map (in centimeters) represents an actual distance of 4 kilometers? 3.2 cm (dont answer this i already got it)

Part B
What is the actual number of kilometers that is represented by 5 centimeters on the map? __ km

Answers

The required distance on the map (in centimeters) represents an actual distance of 4 kilometers is a) 3.2 cm and the actual number of kilometers that is represented by 5 centimeters on the map is b) 6.25 km.

What is distance?

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

The scale of a map says that 4 cm represents 5 km.

According to given question we have

a.

So, (4 km)/(5 km) = 0.8

4 km is 0.8 of 5 km, so in the map it is 0.8 of 4 cm.

4 kilometers

=0.8 ×4 cm

= 3.2 cm

b.

So, (5 cm)/(4 cm) = 1.25

5 cm is 1.25 times 4 cm, so it represents 1.25 × 5 km.

5 centimeters

=1.25 × 5 km

= 6.25 km

Therefore, the required distance on the map (in centimeters) represents an actual distance of 4 kilometers is a) 3.2 cm and the actual number of kilometers that is represented by 5 centimeters on the map is b) 6.25 km.

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Idk how to do this I need help

Idk how to do this I need help

Answers

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the3 given angles and equate to 180

x + 6 + 3x - 2 + 7x = 180, that is

11x + 4 = 180 ( subtract 4 from both sides )

11x = 176 ( divide both sides by 11 )

x = 16

Thus

∠ V = x + 6 = 16 + 6 = 22°

∠ W = 3x - 2 = 3(16) - 2 = 48 - 2 = 46°

∠ X = 7x = 7(16) = 112°

I need help
Solving this problem

I need helpSolving this problem

Answers

The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

I need helpSolving this problem

an information technology company claims that a certain model of laptops have mean battery capacity of 5 hours. a consumer report firm wants to show that the actual mean is smaller than the company claims. what should be the null and alternative hypotheses?

Answers

The null and alternative hypotheses are-

Null hypothesis H₀; μ ≤ 9Alternative hypothesis Hₐ: μ > 9Explain the formulation of Hypotheses?

The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.

This alternative hypothesis is a statement that contradicts the null and is the assertion that a sample research seeks to demonstrate. This null hypothesis can be accepted that represents the declaration of equality, the generally accepted presumption about the population.The intended relationship between the variables must be stated first. In order for researchers to determine whether such a hypothesis is true or untrue, it must also be able to be tested and falsified. Third, it must be consistent the with corpus of information already in existence. Last but not least, it should be said as briefly and simply as possible.

A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.

For this assertion, we form:

Null hypothesis H₀; μ ≤ 9

Alternative hypothesis Hₐ: μ > 9

The assertion is represented by the alternative hypothesis in this right-tailed test.

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TIMING THE CAR

"I was walking along the road at three and a half miles an hour," said Mr. Pipkins, "when the car dashed past me and only missed me by a few inches."
"Do you know at what speed it was going?" asked his friend.
"Well, from the moment it passed me to its disappearance round a corner took twenty-seven steps and walking on reached that corner with one hundred and thirty-five steps more."
"Then, assuming that you walked, and the car ran, each at a uniform rate, we can easily work out the speed.

What was the speed?
Explain your method.

Answers

We can define the speed as the quotient between the distance moved, and the time it takes to move that distance, so we have:

speed = Distance/Time.

Now we can rewrite this as:

Distance = Speed*Time.

We will find that the speed of the car was 21 mi/h.

Here the information given is:

Mr. Pipkins speed is: S = 3.5 mi/h

The car needed 27 "steps" to reach the corner.

Mr. Pipkins needed 27 + 135 = 162 "steps" to reach the same corner.

Because the number of steps is related to time and distance, the ratio between the number of steps should be the same as the ratio between the speeds:

162/27 = 6

(Pipkins needed 6 tomes more steps than the car, so the car moves 6 times faster than Pipkins)

This means that the speed of the car is 6 times larger than the speed of Mr. Pipkins.

Then the speed of the car is:

S' = 6*(3.5 mi/h) = 21 mi/h.

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Which expression is equivalent 4/5 - 1/3?

Answers

Answer:

7/15

Step-by-step explanation:

Well 4/5 - 1/3 = 12 / 15 - 5 / 15 which is equal to 7/15, but there aren't any expressions in your question.

Answer:

7/15

Step-by-step explanation:

4/5 - 1/3 = 12 / 15 - 5 / 15 = 7/15

I need answers for this question

I need answers for this question

Answers

The inequality 3 ≤ x - 2 simplifies to x ≥ 5. This means x can take any value greater than or equal to 5. Therefore, option (E) with a number line from positive 5 to positive 10 is correct.

Given: 3 \(\leq\) x - 2

We need to work out which number line below shows the values that x can take. In order to solve the inequality, we will add 2 to both sides. 3+2 \(\leq\) x - 2+2 5 \(\leq\) x

Now the inequality is in form x \(\geq\) 5. This means that x can take any value greater than or equal to 5. So, the number line going from positive 5 to positive 10 shows the values that x can take.

Therefore, the correct option is (E) A number line going from positive 5 to positive 10.  We added 2 to both sides of the given inequality, which gives us 5 \(\leq\) x. It shows that x can take any value greater than or equal to 5.

Hence, option E is correct.

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Trent and Vivian go to the basketball court at the park for 45 minutes after school to practice shooting free throws. Each person shoots for an equal amount of time, while the other person rebounds the ball. How long does each person shoot free throws? Write your answer as a proper fraction or mixed number.

Answers

Answer:

22¹/₂ minutes

Step-by-step explanation:

If Trent and Vivian go to the basketball court at the park for 45 minutes after school to practice shooting free throws, the total time it takes for the both of them to shoot free throws is 45 minutes.

Let the amount of time Trent and Vivian shoot the free throws be t₁ and t₂ respectively.

Since they both throw at equal times, t₁ = t₂ = t.

Now t₁ + t₂ = 45 the total time it takes to shoot the free throws.

Since, t₁ = t₂ = t.

t₁ + t₂ = 45

substituting t into the equation, we have

t + t = 45

adding the t's, we have

2t = 45

dividing both sides by 2, we have

t = 45/2

t = 22¹/₂ minutes

So, it takes each person 22¹/₂ minutes to shoot free throws.

Answer:

22 1/2 minutes

Step-by-step explanation:

45 divided by two =22 1/2

Hope this helps :)

T Write a rational function r(x) such that r(2) is undefined, lim r(x) = 1, and x-2 lim r(x) = = 8. x 3 r(x) -

Answers

This rational function satisfies the conditions that r(2) is undefined, lim r(x) = 1 as x approaches infinity, and lim r(x) = 8 as x approaches 3.

We want to find a rational function r(x) that satisfies the given conditions as follows:

r(2) is undefined

lim r(x) = 1

lim r(x) = = 8.

x 3

First, let's focus on r(2) being undefined.

A rational function is undefined where its denominator is equal to zero.

So we need to make the denominator of r(x) (x - a), where a is a number, equal to zero at x = 2.

Let's set (x - 2) equal to zero and solve for x as follows: x - 2 = 0x = 2

We see that x = 2 satisfies the requirement that r(2) is undefined.

Now let's make sure that r(x) approaches 1 as x approaches infinity. To make the numerator approach 1 and the denominator approach infinity, we can make the degree of the numerator 0 and the degree of the denominator 1, such that the numerator is a constant and the denominator is a linear function of x.

For example, let's set the numerator to 1 and the denominator to x - 3.

Now let's check that lim r(x) = 1 as x approaches infinity.

We can do this by dividing the numerator and denominator of r(x) by the highest power of x in the denominator, which is x, as follows:

r(x) = 1 / (x / (x - 3)) = (1 / x) / ((x - 3) / x)

As x approaches infinity, the numerator approaches zero, and the denominator approaches 1.

Therefore, lim r(x) = 0/1 = 0 as x approaches infinity.

Next, we need to find a value of x for which lim r(x) = 8.

Let's set the denominator of r(x) equal to x - 3, since we want to approach 8 as x approaches 3.

To make the numerator approach 8, we need to multiply it by (x - 3) / (x - 3).

So let's set the numerator of r(x) equal to 8(x - 3).

Then: r(x) = 8(x - 3) / (x - 3) = 8as x approaches 3, the denominator approaches zero, and the numerator approaches 8. Therefore, lim r(x) = 8 as x approaches 3.

Finally, we can combine the three conditions we found to get:

r(x) = 8(x - 3) / ((x - 2)(x - 3))

This rational function satisfies the conditions that r(2) is undefined, lim r(x) = 1 as x approaches infinity, and lim r(x) = 8 as x approaches 3.

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Final answer:

The function r(x) = (x-3)/(x-2) meets all the specified conditions: it is undefined at x = 2, the limit of the function as x approaches any number other than 2 is 1, and the limit as x approaches 3 of (x-2)r(x) equals 8.

Explanation:

A suitable function that meets all the specified conditions would be r(x) = (x-3)/(x-2).

Let's analyze why this function meets the conditions:

r(2) is undefined because when we substitute x = 2 into our function, the denominator becomes zero, which makes the function undefined.The limit of r(x) as x approaches any value other than 2 is 1. This is because if you simplify the function, the higher degree terms cancel each other out, leaving you with 1.The limit as x approaches 3 of (x-2)r(x) = 8. If you plug x = 3 into (x-2)r(x), you would get 8, confirming the third condition.

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why in models such as logistic regression we need to estimate the marginal effects of each independent variable in order to understand how a change in one independent variable affects our dependent variable.

Answers

In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.

What is linear regression?

According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.

For linear regression

Y=a + bx + error

If we neglect error

then Y=a + bx.

If x increases by 1

then Y = a +b(x+1) which implies

Y=a + bx + b.

So Y increases by its slope.

Hence their is an increase in the slope in y.

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The sum of two consecutive numbers is -73. Find the value of the greater number.

Answers

Answer:

-37, -36

Step-by-step explanation:

the sum is -73

the numbers are consecutive so they must both be negative

73 /2 = 36.5  so the numbers are

-36 + -37 = -73

Answer:

-36

Step-by-step explanation:

All we need to do is this equation:

x+(x+1)=number

So, x+x+1=-73

2x+1=-73

 -1       -1

2x=-74

/2    /2

x=-37

we can check this by adding -37+-36=-73 because -37 would be the lesser number.

Watch out, because that is the lesser number. -36 would be greater.

So -36.

9(x-11)=9

Solve this with step by step explanation

Answers

Answer:

x=12

Step-by-step explanation:

given: 9(x-11)=9

Distribution: 9x-99=9

Simplify:(common denominator is 9) x-11=1

x=12

Step-by-step explanation:

multiply the 9 in the brackets, so the equation will be 9x-99=9.

next move -99 to the other side and change its sign

making the equation 9x=108

now diveide both sides by 9 to leave x alone.

x=12 is the final answer;)

Two events, E1 and E2, are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment?

Answers

P(E1) + P(E2) - P(E1 ∩ E2) is the probability that at least one of the two events occurs in any trial of the experiment.

The correct answer is D. P(E1) + P(E2) - P(E1 ∩ E2).

The probability that at least one of two events occurs can be calculated using the principle of inclusion-exclusion.

The formula for this is:

P(E1 or E2) = P(E1) + P(E2) - P(E1 and E2)

Where:

P(E1) is the probability of event E1 occurring.

P(E2) is the probability of event E2 occurring.

P(E1 and E2) is the probability of both events E1 and E2 occurring simultaneously.

This formula represents the probability that at least one of the two events (E1 or E2) occurs in any trial of the experiment.

It's derived using the principle of inclusion-exclusion.

P(E1) represents the probability of event E1 occurring.

P(E2) represents the probability of event E2 occurring.

P(E1 ∩ E2) represents the probability of both events E1 and E2 occurring simultaneously.

By adding the probabilities of each individual event and then subtracting the probability of their intersection, you're accounting for the possibility of double-counting the intersection when adding the probabilities of the individual events.

So, the formula accurately captures the probability of at least one of the two events occurring.

Hence, P(E1) + P(E2) - P(E1 ∩ E2) is the probability that at least one of the two events occurs in any trial of the experiment.

The correct answer is D. P(E1) + P(E2) - P(E1 ∩ E2).

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complete question:

Two events, E1 and E2, are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment?

A.

P(E1) + P(E2) − 2P(E1 ∩ E2)

B.

P(E1) + P(E2) + P(E1 ∩ E2)

C.

P(E1) − P(E2) − P(E1 ∩ E2)

D.

P(E1) + P(E2) − P(E1 ∩ E2)

nominal decisions can be broken into which two distinct categories?

Answers

Answer:

Nominal decisions can be broken into two distinct categories: dichotomous decisions and polychotomous decisions.

A sinking fund is established to discharge a debt of $20,000 in 15 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 5%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

Answers

Answer:

the amount of each deposit is $45,555

Step-by-step explanation:

The computation of the each deposit is shown below:

Given that

Future value be $20,000

Time period = 15 × 2 = 30

And, the rate = 5% ÷ 2 = 2.5%

Now the formula is as follows

= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1

= ($20,000 × 2.5) ÷ (1 + 0.025)^30 - 1

= $50,000 ÷ 1.0975675791

= $45,555

Hence, the amount of each deposit is $45,555

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