Lines AB and CD are parallel.

If the measure of N equals 67°, what is the measure of P?
A. 23°
B. 158°
C. 113°
D. 67°

Therefore, P(A|BC) = 4/7.

a. P(A|B)

We can use Bayes' theorem to calculate P(A|B):

P(A|B) = P(A ∩ B) / P(B)

We are given that P(A ∩ B) = 0.2 and P(B) = 0.3, so:

P(A|B) = 0.2 / 0.3 = 2/3

Therefore, P(A|B) = 2/3.

b. P(AC ∩ BC)

Using the complement rule, we can rewrite AC ∩ BC as (A ∪ B)C:

AC ∩ BC = (A ∪ B)C

Using De Morgan's laws, we can further rewrite this as:

AC ∩ BC = A'C ∩ B'C

Now, we can use the distributive property to write:

A'C ∩ B'C = (A ∪ B)'

Using the complement rule again, we have:

A'C ∩ B'C = 1 - P(A ∪ B)

We can use the inclusion-exclusion principle to calculate P(A ∪ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We are given that P(A) = 0.6, P(B) = 0.3, and P(A ∩ B) = 0.2, so:

P(A ∪ B) = 0.6 + 0.3 - 0.2 = 0.7

Therefore:

A'C ∩ B'C = 1 - 0.7 = 0.3

Hence, P(AC ∩ BC) = 0.3.

c. P(A ∩ BC)

Using the complement rule, we can write BC as 1 - B:

A ∩ BC = A ∩ (1 - B)

We can distribute the intersection over the complement:

A ∩ BC = A - (A ∩ B)

We are given that P(A) = 0.6 and P(A ∩ B) = 0.2, so:

A ∩ BC = 0.6 - 0.2 = 0.4

Therefore, P(A ∩ BC) = 0.4.

d. P(A|BC)

We can use Bayes' theorem again to calculate P(A|BC):

P(A|BC) = P(A ∩ BC) / P(BC)

Using the complement rule, we can write BC as 1 - B:

P(A|BC) = P(A ∩ (1 - B)) / P(1 - B)

We can distribute the intersection over the complement:

P(A|BC) = P(A) - P(A ∩ B) / P(1 - B)

We are given that P(A) = 0.6, P(A ∩ B) = 0.2, and P(B) = 0.3, so:

P(A|BC) = 0.6 - 0.2 / (1 - 0.3) = 0.4 / 0.7

Therefore, P(A|BC) = 4/7.

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The probability that 4 women have a mean weight below 108 lb is approximately 0.008.

The probability that 58 women have a mean weight below 108 lb is zero.

The probability is determined using the central limit theorem.

(b) If 4 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(4)

standard deviation = 14.5 lb.

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 14.5

z = -2.41

Using a standard normal distribution table or calculator, the probability of z being less than -2.41 is approximately 0.008.

(c) If 58 women are randomly selected, the sample mean weight (x) will also be normally distributed:

mean = 143 lb

standard deviation = 29/√(58)

standard deviation = 3.81 lb

We can use the z-score formula to find the probability that the sample mean weight is below 108 lb:

z = (108 - 143) / 3.81 ≈ -9.21

Using a standard normal distribution table or calculator, the probability of z being less than -9.21 is extremely small, practically zero.

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To find the measure of angle QZX, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle ZWQ:

Angle WZQ + Angle WZX = 180 degrees

92 degrees + 63 degrees = 155 degrees

Therefore, angle ZWQ has a measure of 155 degrees.

Now, we can find the measure of angle QZX:

Angle ZWQ + Angle QZX = 180 degrees

155 degrees + Angle QZX = 180 degrees

Subtracting 155 from both sides, we get:

Angle QZX = 25 degrees

Therefore, the measure of angle QZX is 25 degrees.

The data distribution is skewed to the right. This is because the bars are clustered towards the left side of the histogram and taper off towards the right side.

The histogram of distances students live from school provided in the question shows that the majority of students in Tuan's homeroom live within a short distance of the school, with only a few students living farther away. The distribution is skewed to the right because the bars are clustered towards the left side of the histogram and taper off towards the right side. This indicates that there are fewer students who live farther away from school. A skewed distribution means that the data is not evenly distributed and tends to cluster towards one end. In this case, the distribution is skewed to the right because there are fewer students living farther away from school.

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Complete question is in the image attached below

Answer:

B. skewed.

Step-by-step explanation:

and then the next part is

1

hope this helps :)

The newer energy star washing machines uses less water compare to older models is equals to 25%.

Newer Energy Star washing machines use approximately 25% less water than older models.

Energy Star-certified washing machines are designed to use less water.

And energy while still providing the same or better washing performance compared to traditional models.

According to Energy Star, certified models use about 25% less energy and 33% less water than non-certified models.

Therefore, the percent of less water used by newer energy star washing machine than older modals is equals to 25%.

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The numbers that would make the inequalities given true are 3 (first inequality) and 5 (second inequality).

To begin, an inequality is a mathematical expression that uses symbols such as < less than or > greater than. In the case presented, we need to find two numbers.

Based on this, some possible numbers are:

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After re-financeing his home loan, Garrets mortage payment is 30 percent less that it used to be the value of Garretts monthly payment now is 2191.

A hypothec loan, also known as a mortgage loan, is a type of loan that is commonly used by real estate purchasers to secure funds for the purchase of property, or by property owners seeking to obtain funds for any purpose, while simultaneously placing a lien on the property being mortgaged. In essence, a mortgage can be described as a situation where a borrower provides collateral in exchange for a loan.

we need to find how much is Garretts monthly payment now:

therefore first we need to find 30% of 3130 that is,

30 x 3130/100 = 939

now we need to subtract this value from the originally mortgage amount

therefore, 3130 - 939 = 2191

therefore, the value of Garretts monthly payment now is 2191.

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the percent increase from running 19 miles in the first week to 25 miles in the second week is 31.58%. This means that Mackenzie increased her mileage by 31.58% from the first week to the second week.

To calculate the percent increase from running 19 miles in the first week to 25 miles in the second week, we first need to find the difference between the two numbers.

The difference is calculated as follows:

25 - 19 = 6

So, the difference between the two weeks is 6 miles.

To find the percent increase, we need to divide the difference by the original value and then multiply by 100.

The formula for percent increase is:

(percent increase) = [(new value - old value) / old value] x 100%

Using this formula, we can find the percent increase in Mackenzie's training as follows:

(percent increase) = [(25 - 19) / 19] x 100%

(percent increase) = (6 / 19) x 100%

(percent increase) = 0.3158 x 100%

(percent increase) = 31.58%

So, the percent increase from running 19 miles in the first week to 25 miles in the second week is 31.58%. This means that Mackenzie increased her mileage by 31.58% from the first week to the second week.

It's important to note that a large percent increase in mileage can increase the risk of injury, so it's important to gradually increase mileage over time to prevent injury and ensure a successful training program.

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We can start by finding how much money Anastasia saves each week.

The difference between her starting balance and ending balance after 11 weeks is:

$665 - $225 = $440

So, over 11 weeks, Anastasia has saved a total of $440.

To find how much money she saves each week, we can divide the total savings by the number of weeks:

$440 ÷ 11 weeks = $40 per week

This means that Anastasia saves $40 each week.

To find out how much money she will have in her account after 24 weeks, we can multiply the amount she saves each week by the number of weeks:

$40 per week × 24 weeks = $960

Therefore, after 24 weeks, Anastasia will have $960 in her savings account.

Leslie's dad is 38.5 kg heavier than the combined weight of Leslie and her brother.

To solve the problem, we first need to find the total weight of the two children together, and then subtract that from the weight of Leslie's dad:

Total weight of the two children = Leslie's weight + her brother's weight

Total weight of the two children = 12.4 kg + 16.7 kg

Total weight of the two children = 29.1 kg

Weight difference between Leslie's dad and the two children = Leslie's dad's weight - Total weight of the two children

Weight difference between Leslie's dad and the two children = 67.6 kg - 29.1 kg

Weight difference between Leslie's dad and the two children = 38.5 kg

Therefore, Leslie's dad is 38.5 kg heavier than the two children combined.

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Answer:

domain (-4,8,9,1)

range. (4,-1,-9,2,8)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. -3 < x <= 4

x = -2, -1, 0, 1, 2, 3, 4.

b. -3 < x < 4

x = -2, -1, 0, 1, 2, 3.

Answer:

c

Step-by-step explanation:

8²+6²=c²

64+36=c²

100=c²

√100 = √c²

10=c

The segment GT1 is part of the radius of circle K, so it has a length of 10 units and segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that Triangle GHI is circumscribed about circle K with GH = 20 units, HI = 14 units, and IG= 12 units.

We have to find the  length of each segment whose endpoints are G and the points of tangency on GH and GI.​

Let's call the points of tangency on GH and GI T1 and T2 respectively.

The segment GT1 is part of the radius of circle K, so it has a length of 10 units.

The segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.

8²+6²=c²

64+36=c²

100=c²

√100 = √c²

10=c

Hence, the segment GT1 is part of the radius of circle K, so it has a length of 10 units and segment GT2 is also part of the radius of circle K, so it has a length of 10 units as well.

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The points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

The coordinate plane is a two-dimensional space formed by two perpendicular lines called the x-axis and y-axis. The point where the two axes intersect is called the origin. Each point in the plane is identified by a pair of numbers called its coordinates, where the first number represents its position along the x-axis and the second number represents its position along the y-axis. Coordinates are typically written as (x, y), with the x-coordinate listed first and the y-coordinate listed second. The coordinate plane is commonly used in mathematics to graph and analyze equations, functions, and geometric shapes.

Let x be the number of bags of popcorn and y be the number of bags of cotton candy. Then the cost constraint is:

3x + 7y ≤ 56

We also have the constraint that Chris needs at least 7 bags of popcorn:

x ≥ 7

To graph these constraints, we can rewrite them in slope-intercept form:

y ≤ (-3/7)x + 8

x ≥ 7

The first inequality has a slope of -3/7 and a y-intercept of 8, and the second inequality is a vertical line at x = 7.

To plot the points that are part of the solution set, we can simply plug them into the two inequalities and see if they are true. The points that satisfy both inequalities are part of the solution set.

(3, 7) satisfies both inequalities:

7 ≤ (-3/7)(3) + 8

3 ≥ 7

(2, 2) does not satisfy the first inequality:

2(7) > 3(2) + 7

(8, 1) satisfies both inequalities:

1 ≤ (-3/7)(8) + 8

8 ≥ 7

(10, 2) satisfies both inequalities:

2 ≤ (-3/7)(10) + 8

10 ≥ 7

(5, 5) does not satisfy the first inequality:

5(7) > 3(5) + 7

Therefore, the points that are part of the solution set are (3, 7), (8, 1), and (10, 2).

To graph these on the coordinate plane, we can plot the vertical line x=7 and the line y= (-3/7)x + 8, and then shade in the feasible region below the line and to the right of the vertical line.

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The measures of the angles are m∠1 = 74° and m∠2 = 74°.

Given,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

We need to find the measure of these angles.

The straight line angle is 180 degrees.

If the angle is split the sum must be equal to 180 degrees.

We have,

[tex]m\angle1 = 2x^\circ[/tex]

[tex]m\angle2 = (x + 69)^\circ[/tex]

The figure is at a straight-line angle.

So we have,

[tex]m\angle1 + m\angle2 = 180^\circ[/tex]

[tex]2x^\circ + (x + 69)^\circ = 180[/tex]

[tex]2x + x + 69 = 180[/tex]

[tex]3x + 69 = 180[/tex]

[tex]3x = 180 - 69[/tex]

[tex]3x = 111[/tex]

[tex]x = 111\div3[/tex]

[tex]x = 37[/tex]

Now,

[tex]- m\angle1[/tex]

[tex]= 2x[/tex]

[tex]=2 \times 37[/tex]

[tex]= 74[/tex]

[tex]- m\angle2[/tex]

[tex]= x + 37[/tex]

[tex]= 37 + 37[/tex]

[tex]= 74[/tex]

Thus the measures of the angles are m∠1 = 74° and m∠2 = 74°.

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Therefore , the solution of the given problem of angles comes out to be lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4.

Both the largest and the tiniest walls of a skew are determined by an intersection of the lines that connect that make up its ends. A junction could possibly bring two routes together. Another result of two objects interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their extremities to form a two-dimensional curve.

Here,

The abbreviated formula for f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x) is as follows:

f(x) = (4x³ - 3x² - 10x - 3)/(x³ - x² - 6x)

f(x) = [(4x³ - 12x) + (9x² - 3)] / (x(x² - x - 6))

f(x) = [4x(x² - 3) + 3(3x² - 1)] / [x(x - 3)(x + 2)]

f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]

Consequently, the abbreviated form is:

f(x) = [4x/(x-3)] + [3/(x+2)] - [3x/(x²-x-6)]

Direct substitution can be used to find the limit of the equation g(x) = (x2 - 4)/(x - 2) as x approaches 2, which results in the undetermined form 0/0. In order to take the derivative of the numerator and denominator with regard to x, we can apply L'Hopital's rule as follows:

g(x) = (x² - 4)/(x - 2)

g'(x) = [(2x) * (x - 2) - (x² - 4) * 1] / (x - 2)²

g'(2) = 4

As x gets closer to 2, the maximum of g(x) is as follows:

lim x→2 g(x) = lim x→2 [(x² - 4)/(x - 2)] = 4

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For each bag, BALLIO  would have needed 2.25 (or 2 1/4) yards of fabric.

"A way to find a multiple unit value from a single unit value as well as the reverse."

In every case, we first count the unit or amount value before figuring out the more or less amount value.

This method is referred to as a unified procedure for this reason.

By dividing the set value by the quantity of sets, one can find numerous set values.

By dividing several set values by the total number of sets, one can determine a set value.

According to our question-

9 bags you are making

must be the same

divide the nine bags by the four yards

2.25 yards per bag

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Answer:

Step-by-step explanation:

the sum of the internal angles in any triangle is 180°, we have a 60° angle and a right angle (90°). We remove the known angles (90° and 60°) from 180° and we have 30° which is the value of the unknown angle (L).

Angle L = 180 - 90 - 60 =

30°

Answer:yes

Step-by-step explanation: i took the test

Step-by-step explanation:

I will assume the candle burns 1 inch per hour  ( you left that out of your post)

Length of candle remaining = 9 - 1 x      where 'x' = hours

     amount of candle remaining =   0   =  9 - x

                                           x = 9 hrs  

If it is NOT one inch per hour ....put that number where '1' is and solve for x

Answer: 0.5 miles

Step-by-step explanation:

= 2 miles/4

= 0.5 miles

Answer:

1/10

Step-by-step explanation:

Just 6 and 16, so there are 2/20 numbers simplified is 1/10.

:)

Yes, the variable is statistically significant if the t-statistic is 2.54.

Follow these steps:

1. Identify the degrees of freedom (df) for your sample. The df is typically calculated as the sample size minus 1 (n-1).

2. Choose a significance level (α), commonly used values are 0.05 or 0.01.

3. Consult a t-distribution table using the chosen α and degrees of freedom to find the critical t-value.

4. Compare the t-statistic (2.54) to the critical t-value.

If the t-statistic (2.54) is greater than the critical t-value, the variable is statistically significant at the chosen significance level.

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The car that cost $[tex]$35750[/tex] in [tex]2014[/tex] will be valued $[tex]14,919.48[/tex] in [tex]2022[/tex] if the annual depreciation rate is [tex]10.5%[/tex]%

The depreciation rate is the percentage at which an object depreciates over its anticipated useful life.

It can also be described as the portion of an organization's long-term investment in an asset that the organization claims as a tax-deductible expenditure over the course of the asset's useful life.

Given.

Value for the [tex]1[/tex]st Year ([tex]2014-2015[/tex]) is $ [tex]$35,750[/tex] -$([tex]350,750*10.5[/tex]%) =

$[tex]31,981.25[/tex]

Value for [tex]2 years[/tex] [tex](2015-2016)[/tex] =$[tex]31,981.25-([/tex]$[tex]31,981.25*10.5[/tex]%) =

$[tex]28,604.41[/tex]

Value for [tex]8 years[/tex] ($[tex]16550.09[/tex] -$[tex]16550.09*10.5[/tex]%) = $[tex]14919.48[/tex]

Therefore the car that cost $[tex]$35750[/tex] in [tex]2014[/tex] will be valued $[tex]14,919.48[/tex] in [tex]2022[/tex] if the annual depreciation rate is [tex]10.5%[/tex]%

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Step-by-step explanation:

L X W X D = volume = 25 X 10 X 8 = 2000 cm^3

Answer:

2,000 cubic units are the volume of the fish tank

Step-by-step explanation:

The formula of volume is length x width x height

So to find the volume just multiply 25 x 10 x 8

To get the volume of the fish tank which is 2,000 cubic units

Answer: By using the slope

Step-by-step explanation:

Brianliest pls:)

The required answers are Part A: Domain: {n | n is a positive integer}, Part B: 12, Part C: 0.98 cm/day.

Part A:

To plot the growth function f(n), we need to consider a reasonable domain that includes all relevant values of n. Since we are dealing with the growth of a plant, the domain should only include positive integers, as it does not make sense to talk about fractional or negative days. Therefore, a reasonable domain to plot the growth function would be:

Domain: {n | n is a positive integer}

Part B:

The y-intercept of the graph of the function f(n) is the value of f(0), which can be found by substituting n = 0 into the equation:

[tex]$f(0) = 12(1.03)^0 = 12(1) = 12[/tex]

Therefore, the y-intercept of the graph represents the initial height of the plant, which is 12 cm.

Part C:

The average rate of change of the function f(n) from n = 3 to n = 10 can be found using the formula:

Average rate of change = (f(10) - f(3))/(10 - 3)

We can evaluate f(10) and f(3) using the given equation:

f(10) = 12(1.03)^10 ≈ 18.27

f(3) = 12(1.03)^3 ≈ 13.41

Substituting these values into the formula, we get:

[tex]$Average rate change=\frac{(f(10) - f(3))}{10-3} \approx0.98[/tex]

Therefore, the average rate of change of the function f(n) from n = 3 to n = 10 is approximately 0.98 cm/day. This represents the average daily growth rate of the plant during this period.

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