Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
∠2 and ∠8

The annual depreciation rate is $163.33.

Depreciation rate is calculated using the formula

Annual Depreciation Rate =(Total Depreciable Cost)/(time)    ..where time is in years.

In the given Question

The original cost of item = $500

Cost of item after 3 years = $10

Total Depreciable Cost = (original cost of item) -(Cost of item after 3 years)

=500-10

=$490

So,

Annual Depreciation Amount = (Total Depreciable Cost)/(time)

Annual Depreciation Amount =490/3=163.33

Hence, the item cost would depreciate $163.33 per year.

which means every year the amount will depreciate by $163.33

Therefore, the annual depreciation rate is $163.33 .

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Answer:

see explanation

Step-by-step explanation:

a bit more info is needed so this may be wrong.

so first you add up the x values which is 12x+8x+x=21x

then you can see we have a problem, we dont know the x value so the answer would be 21x +3

but we can go a bit further to get an answer as 3(7x+1)

this is also known as factorisation.

so ans: 3(7x+1)

For the data set 3, 6, 4, 13, 3, 7, 5, 13, 3, 7, 5, 15, 3, 8, 5, 27, 4, 8, 6, 6, 4, 11, the outliers are 3, 3, 3, 3, 15, and 27.

In statistics, outlier refers to the data point from a given data set that differs significantly from the other data points.

One way to determine the outlier in a given data set is to calculate the interquartile range.

1. Arrange the data set in ascending or descending order.

3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27

2. Divide the data set into two sets and find the median.

{3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6} , {6, 6, 7, 7, 8, 8, 11, 13, 13, 15, 27}

Q1 median = 4

Q3 median = 8

3. Solve for the IQR.

IQR = Q3 - Q1

IQR = 8 - 4

IQR = 4

4. Determine the outlier if

high outlier ≥ Q3 + (1.5 x IQR) = 8 + (1.5 x 4) = 14

high outlier ≥ 14

low outlier ≤ Q1 − (1.5 x IQR) = 4 - (1.5 x 4) = 3

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The missing term of the sequence is - 4.9.

Here the sequence is -4.6, __, -5.2....

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the sequence is in an arithmetic sequence, as there is a common difference between them.

The nth term of the sequence has a formula

[tex]a_{n}[/tex] = a + (n - 1) d

Here we know the 3rd term of the sequence so that we can find the common difference between them

[tex]a_{3}[/tex] = -4.6 +(3-1)d

-5.2 = -4.6 + 2d

0.6 = 2d

d = 0.3

So here the common difference is 0.3.

Now we have to find the 2nd term of the sequence,

[tex]a_{2}[/tex] = -4.6 + ( 2-1) 0.3

   = -4.6 + 0.3

   = - 4.9

Therefore the second term of the sequence is -4.9.

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The equivalent expression by distributing the sign outside the parentheses: -(-8.2w+10) −(−8.2w+10) will be 16.4w - 20.

It should be noted that bwsed on the information given, the expression is illustrated as:

-(-8.2w+10) −(−8.2w+10)

The signs should be taken into consideration. This will be:

-(-8.2w+10) −(−8.2w+10)

= 8.2w - 10 + 8.2w - 10

= 16.4w - 20

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It is a geometric sequence since it has a common ratio. The next two terms are -80, 160

Let a sequence be:

          a(1), a(2), a(3), a(4), a(5), ...

To determine whether the sequence is an arithmetic sequence, or a geometric sequence, or neither, we need to check how its consecutive terms relate to each other.

The given sequence is:

-5,10,-20,40, . . .

a(2) - a(1) = 10 - (-5) = 15

a(4) - a(3) = 40 - (-20) = 60

So they don't have a common difference.

a(4)/a(3) = 40/(-20) = -2

a(3)/a(2) = -20/(10) = -2

a(2)/a(1) = 10/(-5) = -2

So they have a common ratio, i.e. r = -2.

Therefore, we can conclude that -5,10,-20,40, . . is a geometric sequence.

In a geometric sequence, the next term is equal to the previous term times the ratio.

We already have: -5,10,-20,40, ...

Hence:

Next term after 40 = 40 . (-2) = -80

Next term after -80 = -80 . (-2) = 160

Thus, the next two terms are -80, 160

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Distance between the pair of points W(2,0) and X(8,6) is equal to

8.5 units(nearest tenth).

As given in the question,

Given points are  W(2,0) and X(8,6)

Distance between the pairs of points = [tex]\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2} }[/tex]

                                                          = [tex]\sqrt{(6-0)^{2}+(8-2)^{2} }[/tex]

                                                          = [tex]\sqrt{36 +36}[/tex]

                                                          =[tex]\sqrt{72}[/tex]

                                                          = [tex]8.5[/tex] units (nearest tenth)

                                                                                                                                                    Therefore, distance between the pair of points W(2,0) and X(8,6) is equal to 8.5 units (nearest tenth).

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The absolute value inequality to represent this situation is |d - 50| <= 5

The given parameters are

Margin = 5 feet

Depth = 50 feet

The absolute value inequality to represent this situation is

|d - Depth| <= Margin

So, we have:

|d - 50| <= 5

Hence, the absolute value inequality to represent this situation is |d - 50| <= 5

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Answer:

The errors that may occur in the measurement of a physical quantity can be classified into six types: constant error, systematic error, random error, absolute error, relative error and percentage error.

Step-by-step explanation:

Hope this will be helpful for you.

The slope - intercept form of the equation -4 x+3 y=1 is y = 4/3x + 1/3.

The equation given is -

-4 x+3 y=1

As we know the slope - intercept form is -

y = mx + c

-4 x+3 y=1

Dividing the equation with 3

⇒ -4/3x + y = 1/3

Now, rearranging the equation

y = 4/3x + 1/3

where slope = 4/3

y - intercept = 1/3

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Answer:

$10

Step-by-step explanation:

Let's begin with adding all of the items Greg bought.

36.62 + 11.25 + 17.75 = 65.62

Let the money paid to the cashier be x.

Now, it's stated he paid 60 dollars to the cashier and that he also got $4.38 back from the cashier.

Then, it must be that x=65.62+4.38

x=70

The money he borrowed from friend = 70-60=10

Therefore, the money Greg borrowed from his friend to pay for all the items is $10.

Greg borrowed $1.24 from his friend.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilise this technique for math computations.

This approach allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

Given:

Greg bought a blanket for $36.62,

a flag for $11.25,

and a glove for $17.75.

Total expense of the objects he brought

= 36.62+ 11.25 + 17.75

= $65.62

He paid $60 then

=65.62 - 60 = $5.62 remaining

Also, he got $4.38 in change from the cashier

= 5.62 - 4.38

= $1.24.

Hence, Greg borrowed $1.24 from his friend.

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The probability that Danielle, Nora, and Li will dive first, second, and third, respectively is 1/1320.

Since we are provided that in the meet, the orders of the drivers are randomly selected so,  the total number of drivers is: 12

let A be the event in that  Danielle was the first to dive.

    B be the event that  Nora been the second to dive.

and C is the event that Li has been the third to dive into.

P(A), probability of Danielle to dive first = 1/12

P(B), probability of Nora to dive second = 1/11

and P(C), probability of Li to dive in third = 1/10

So, the total probability that Danielle, Nora, and Li will dive first, second, and third, respectively = P(A) x P(B) x P(C)

                                     = 1/12 x 1/11 x 1/10

                                     = 1/ 1320

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The given sequence is not geometric.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 1, 2, 3, 4, ....

Here, 2/1  ≠ 3/2 ≠ 4/3

Since, the none of the ratio of the consequent and the previous term is not equal, the sequence does not satisfy the required condition and hence, is not geometric.

Hence, The given sequence is not geometric.

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The statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

The formula for finding the confidence interval for population standard deviation as follows:

[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]

Where s is the standard deviation.

n is the sample size.

α is the significance level.

σ is the confidence interval for population standard deviation.

Calculating the confidence interval for population standard deviation:

We know significance level = 1 - confidence level

The statement is:

A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval.

As we know,

A 95% confidence interval is narrower than a 99% confidence interval.

Thus, the statement "A 95% confidence interval for the population mean will be wider than a corresponding 99% confidence interval." is true.

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According to the question, Namid bought [tex]20[/tex] raffle tickets. And the total number of raffles sold was [tex]500[/tex].

Now. to calculate the probability in which Namid will not win the raffle:

[tex]P(Win) = \frac{P(E)}{n(E)} = \frac{20}{500} = \frac{1}{25}[/tex]

[tex]P(No Win) = 1-P(Win) = 1 - \frac{1}{25} = \frac{24}{25} = 96%[/tex]

Therefore, the probability that Namid will not win the raffle is [tex]96[/tex] percentage.

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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The lessons from Clare B. Dunkie's The Hollow Kingdom, and the quote it matches are:

One lesson that we see is that people who care about someone, are able to make sacrifices to ensure the wellbeing of that person. We see it with the narrator saying that the person loved another so much that they sacrificed their world for that person.

Another less is that nature can often help us gain the courage we need to do something. This is shown with the subject looking to the moon and stars to back her up.

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Answer:

Answer: M=-9

Step-by-step explanation:

[tex]\frac{-4(m+3)}{-4} =\frac{24}{-4} M + 3 = -6 (Subtract -3 from 3 and -6) M = -9[/tex]

answer should be origin

The pattern of each number changes.. they are all factors of 4, the 4 turns into 8, than the 4 or 8 turns into 16.

7+4=11

11+8=19

19+16=35

[4×2=8, 8×2=16]

Answer:

1/2 + 3/4 + 5/8

4/8 + 6/8 + 5/8 = 15/8 or 1 7/8 cups

Step-by-step explanation:

probably right dunno

This is one batch right? if so shud be right

The slope for equation y = -5x + 4 in slope - intercept form is -5 and y - intercept is (x, 4 ).

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is.

The slope - intercept form is y = mx + c

5x + y = 4

Now, Rearrange the equation -

y = -5x + 4

m = -5 and y intercept = (x , 4)

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Answer:

6y ≤ 10

Step-by-step explanation:

6 times a number y= 6y

less than or equal to = ≤

10 = 10

so...

6y ≤ 10

Answer:

6y = 10

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

-9 × -4 = 36 (the two negatives cancel each other out)

36 - 6 = 30

The median is at 55. Therefore, the second quartile of the data set is: 55.

50% of any given data set lies below the second quartile. Thus, the second quartile can be described as the median of a data set.

In a box-and-whisker plot, the median is the mark at where the vertical line divides the box of the box-and-whisker plot.

In the box-and-whisker plot given, the median is at 55. Therefore, the second quartile of the data set is: 55.

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The equation of the line in slope-intercept form passing through point (-3 , 1) and perpendicular to y = -(2/5)x - 4 is y = (5/2)x + 17/2

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula

y = mx + b

where m is the slope of the line

b is the y- intercept

If the line is perpendicular to y = -(2/5)x - 4, then their slopes are negative reciprocal of one another.

y = -(2/5)x - 4 : m = -2/5

m = 5/2

Substitute the values of the slope and the point to solve for the y-intercept, b.

y = mx + b

1 = 5/2(-3) + b

b = 17/2

Write the equation of the line by plugging in the value of the slope and y-intercept.

y = mx + b

y = (5/2)x + 17/2

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The results of the expressions given are:

Part 1:

1)  -2

2) 12

3) 2

4) 11

5) -7

6) 7

7)  0

8)  0

9) - 6

10) - 10

Part 2:

1) 12

2) - 2

3)  2

4)  11

5) 5

6) 0

7) - 28

8) 0

9) - 17

10) -2

We solve the equations respecting the level of hierarchy:

Part 1:

1) -7+5= -2

2) 7+5 = 12

3) 7+ (-5) = 7 - 5 = 2

4) 2+9 = 11

5) 2+(-9) = 2 - 9 = -7

6) -2+9 = 7

7) 8+(-8) = 8 - 8 = 0

8) -5+5 = 0

9) -3+(-3) = - 3 - 3 = - 6

10) -5+(-5) = - 5 - 5 = - 10

Part 2:

1) 7- (-5) = 7 + 5 = 12

2) -7- (-5) = - 7 + 5 = - 2

3) 7- (+5) = 7 - 5 = 2

4) 2- (-9) = 2 + 9 = 11

5) -5- (-10) = - 5 + 10 = 5

6) 5-5 = 0

7) -8- (+20) = - 8 - 20 = - 28

8) -3- (-3) = - 3 + 3 = 0

9) -5- (+12) = - 5 - 12 = - 17

10) 8- (+10) = 8 - 10 = -2

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

Step-by-step explanation:

y = -3x + 7

since the slope of the line AB = (4 - 2) /( 3 - (-3)) = 1/3

slope of line perpendicular to AB will be -3

The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"

Given,

The statement "If p || q , then ∠2 and ∠8 are supplementary"

In the figure

p is parallel to q.

∠2 and ∠8 are lie on the opposite sides of the transversal and both are nonadjacent exterior angle

So, ∠2 and ∠8 are alternate exterior angles

If p || q , then ∠2 and ∠8 are congruent.

Hence, The statement "If p || q , then ∠2 and ∠8 are supplementary" is false because " If p || q , then ∠2 and ∠8 are congruent"

The complete question is :

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

If p || q , then ∠2 and ∠8 are supplementary .

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The prime factors of 80 are 2, 2, 2, 2, and 5, then its decomposition is:

80 = 2*2*2*2*5 = 2⁴*5

To do this, we start with our number, which in this case is 80, and we start dividing it by prime numbers.

The first prime number is 2, taking the quotient:

80/2 = 40

So 2 is a factor.

Now we try to divide again by 2:

40/2 = 20

Now we can divide by 2 again:

20/2 = 10

And again:

10/2 = 5

And 5 is another prime number, so now we only can divide by 5:

5/5 = 1

So, we divided by 2 four times and by 5 one time, then the decomposition in prime factors is:

80 = 2*2*2*2*5 = 2⁴*5

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Range - { 4 , 0 , -4 , -3 } is the domain and range of each relation.

What does the math term domain mean?

What is domain and range mathematics?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Domain - { 0, 4 , -3 , -4 }

Range - { 4 , 0 , -4 , -3 }

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