If m AB = 50° and mCD = 24°, what is the value of x? The figure is not drawn to scale.
x=26°
x= 62°
x=37°
x=74°

The value of d = 6 and the value of YZ = 42

Since XY=32, YZ=7d, and XZ=74

Based on this question, it should be noted that the addition of XY and YZ will equal to the value of XZ. Therefore,

XY + YZ = XZ

32 + 7d = 74

Collect like terms

7d = 74 - 32

7d = 42

Divide through by 7

7d/7 = 42/7

d = 6

Since d is 6, the value of YZ will be:

= 7d = 7 × 6 = 42

In conclusion, the value of d = 6 and the value of YZ = 42.

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Answer:

A

Step-by-step explanation:

36x = 535 - 31

36x = 504

36/36 x = 504/36

x = 14

\({ \green{ \boxed{ \red{ \sf{x = 14}}}}}\)

Step-by-step explanation:

\({ \purple{ \tt{36x + 31 = 535}}}\)

\({ \purple{ \tt36x = 535 - 31}}\)

\({ \purple{ \tt{36x = 504}}}\)

Divide both the sides by 36 then,

\({ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}\)

\({ \red{ \boxed{ \green{ \sf{x = 14}}}}}\)

The percentage of the household survey that owned televisions is 72%. And the sample is defined below.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Random sampling is the method of selecting the subset from the set to make a statical inference.

All states households 1565 households surveyed 1127 households that owned televisions. Then the percentage will be

\(\rm Percentage = \dfrac{1127}{1565}*100\\\\Percentage = 0.72*100\\\\Percentage = 72 \%\)

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Answer:

1565 households surveyed

Step-by-step explanation:

I did this on edge :)

Effective annual interest rates: 12.6825% for the first 14 years, 19.56182% thereafter.

Balance in present value: $444,117.28.

Balance in future value: $6,903,087.93.

   The effective annual interest rates for the given operations are 12.6825% for the first 14 years and 19.56182% thereafter. These rates take into account compounding on a monthly basis and reflect the actual annual return on the investments.

To calculate the effective annual interest rate for the first 14 years, we can use the formula: (1+monthly interest rate)12−1(1+monthly interest rate)12−1. Plugging in the monthly interest rate of 1%, we find that the effective annual interest rate is 12.6825%.

For the period after 14 years, the effective annual interest rate can be calculated using the same formula, but with the monthly interest rate of 1.5%. Substituting this value, we obtain an effective annual interest rate of 19.56182%.

   The balance in present value can be calculated as the sum of the present values of the contributions and withdrawals. The present value of a cash flow can be calculated using the formula: FV(1+r)n(1+r)nFV​, where FV is the future value, r is the interest rate, and n is the number of periods.

To calculate the balance in present value, we need to determine the present value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in present value is $444,117.28.

   The balance in future value can be calculated as the sum of the future values of the contributions and withdrawals. The future value of a cash flow can be calculated using the formula: PV×(1+r)nPV×(1+r)n, where PV is the present value, r is the interest rate, and n is the number of periods.

To calculate the balance in future value, we need to determine the future value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in future value is $6,903,087.93.

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Answer:

A

Step-by-step explanation:

area=πr²=π×2²=4π≈4×3.14≈12.56 km²

Answer:

12.56

Step-by-step explanation:

area of circle = pi r^ 2

pi= 22/7

r= 2km

22/7×2×2

22/7×4

22/28

12.56 is ans

Answer: its 41 dude

Answer:

1cm long, 18cm wide

2cm long, 9cm wide

3cm long, 6cm wide

6cm long, 3cm wide

9cm long, 2cm wide

18cm long, 1cm wide

Step-by-step explanation:

All examples given will equal to 18cm2

The largest side of the triangle is 52.

Checking pythagoraus theorem,

Thus, it is not a right angle triangle.

Thus, option (D) is correct.

A stem-and-leaf diagram separates each value of a data set into two parts: the stem and the leaf.

The stem is the first part of the number, typically the largest place value, and it is used to group similar values together. The leaves are the last part of the number, typically the smallest place value, and they provide the specific values within each group.

For example, consider a data set with the values 15, 19, 10, 11, 15. In a stem-and-leaf diagram, the stem for these values would be 1 and the leaves would be 5, 9, 0, 1, and 5, respectively.

The stem-and-leaf diagram would then look something like this:

This format allows for a quick visualization of the distribution of the data and can be useful for identifying patterns and relationships within the data set.

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the CDF is: F(y) = (area of triangle formed by AB and the point) / (area of triangle ABC)  = y / 2    for 0 ≤ y ≤ 2 and  the PDF is: f(y) = 1 / 2    for 0 ≤ y ≤ 2

To find the CDF and PDF of Y, the distance from a point chosen uniformly within the triangle to the line segment AB, we can proceed without relying on a diagram.

Let's consider the line segment AB first, which has a length of 2 units. The distance from the point within the triangle to AB can range from 0 to the length of AB.

1. CDF (Cumulative Distribution Function):

The CDF of Y, denoted as F(y), is the probability that Y is less than or equal to a given value y.

For 0 ≤ y ≤ 2:

Since the point can be anywhere within the triangle, the probability of Y being less than or equal to y is equal to the ratio of the area of the triangle formed by the line segment AB and the point within the triangle to the total area of the triangle ABC.

The area of triangle ABC is (1/2) * base * height = (1/2) * 2 * 2 = 2.

For 0 ≤ y ≤ 2, the area of the triangle formed by AB and the point within the triangle is (1/2) * y * 2 = y.

Therefore, the CDF is:

F(y) = (area of triangle formed by AB and the point) / (area of triangle ABC)

    = y / 2    for 0 ≤ y ≤ 2

2. PDF (Probability Density Function):

The PDF of Y, denoted as f(y), is the derivative of the CDF with respect to y.

For 0 ≤ y ≤ 2:

Since the CDF is a linear function within this range, the derivative is constant.

f(y) = d(F(y)) / dy

    = d(y / 2) / dy

    = 1 / 2    for 0 ≤ y ≤ 2

Therefore, the PDF is:

f(y) = 1 / 2    for 0 ≤ y ≤ 2

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Answer:

-0.8    -3/4    -2/3     -2/5

Step-by-step explanation:

Answer:

-3/4, -0.8, -2/3, -2/5

Step-by-step explanation:

The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

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Kate has encountered Simpson's Paradox because even though pepperoni pizza is the most popular flavor on weekdays.

Simpson's Paradox is the phenomenon that occurs when a trend appears to be in one direction when data is grouped in one way, but the trend is reversed when the data is grouped in another way.

In this case, Kate has encountered Simpson's Paradox because even though pepperoni pizza is the most popular flavor on weekdays, and again on the weekends when all the data is considered, the overall popularity of sausage pizza is greater.

Simpson's Paradox can be explained by the fact that the number of sausage pizza sales may be greater than the number of pepperoni pizza sales, even if the percentage of pepperoni pizza sales is higher.

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Kate has encountered the Simpson's Paradox. By definition, Simpson's Paradox is a phenomenon in which a trend appears in several different groups of data but disappears when these groups are combined. Option c is the right option

A relationship between two variables in a population might exist, vanish, or even change when the population is split up into subpopulations, a statistical phenomenon is known as Simpson's paradox.

Simpson's paradox is a statistical effect that arises when the marginal association between two categorical variables differs qualitatively from the partial association between the same two variables after adjusting for one or more other factors.

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The way that Robby responds to Keith confessing his fear of Chickens is;  by sharing that makes robby uneasy.

From the given text, we see that an aggressive chicken charged towards keith which made him scared that he ran to the gate.

Now, Robby noticed what happened and ran to keith but because he knew he was scared and wasn't easily going to open up his fears to him, he shared with him how he too can't swim in ponds as they make him nervous. He did that to show Keith that everyone has one fear or the other so that he does't feel bad.

Thus, we can say that the way that robby respond to keith confessing his fear of chickens is by sharing with him that also makes him uneasy.

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Answer:

2

Step-by-step explanation:

The principle of mathematical induction and strong induction, these two principles are powerful tools in proving mathematical statements, especially when it comes to proving results for an infinite number of cases.

The principle of mathematical induction and strong induction are equivalent, meaning that each can be shown to be valid from the other. To prove this, we first show that strong induction implies mathematical induction.

Assuming strong induction, we can prove mathematical induction by defining Q(n) as the statement that P(1), P(2), ..., P(n) are all true, and then using strong induction to prove that Q(n) is true for all integers n ≥ 1.

Next, we show that mathematical induction implies strong induction. Assuming mathematical induction, we can prove strong induction by defining Q(n) as the statement that P(1), P(2), ..., P(n) are all true, and then using mathematical induction to prove that Q(n) is true for all integers n ≥ 1.

Thus, we have shown that the principle of mathematical induction and strong induction are equivalent, and either one can be used to prove the other. These two principles are powerful tools in proving mathematical statements, especially when it comes to proving results for an infinite number of cases.

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Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

Answer:

14

Step-by-step explanation:

\(h(x) = 17 + \frac{x}{6} \\ \\ h( - 18) = 17 + \frac{ - 18}{6} \\ \\ h( - 18) = 17 - 3 \\ \\ h( - 18) = 14 \\ \\ \)

Answer:

from parallel concept

m1=m2

-7/5=-7/5

therefore,

line c and line d are parallel

Kaitlin rented 3 video games and 6 dvds.

2.60 x 3 = 7.50 (dollars and cents)

3.30 x 6 = 19.80 (dollars and cents)

add them together to get the total cost in the past month.

(to find the answer you know the price for a single video game/DVD so what you do is multiply those prices times how much they bought)

ex: $2.60 x 3 <-- the amount of games she bought.

i hope this helps you.

Answer:

Kaitlin spent $27.60 on video games and DVDs in the past month.

Step-by-step explanation:

We know the price of one video game, one DVD, and the amount that was rented in the past month.  

To find the total cost of the video games, multiply:

$2.60 x 3

= $7.80 spent on video games in the past month

To find the total cost of the DVDs, multiply:

$3.30 x 6

= $19.80 spent on DVDs in the past month

To find the total cost, add the total cost of video games and DVDs together:

$7.80 + $19.80 = $27.60

Conclusion: Kaitlin spent $27.60 in the past month on video games and DVDs.

Answer:

151,000

Step-by-step explanation:

1.14×105=119.7

151,000

The monthly payment if the interest rate was 11% will be $45.63.

The remaining amount is calculated as,

P = (1 - 0.20) x $925

P = 0.80 x $925

P = $740

The monthly payment is calculated as,

MP = [$740 + ($740 x 0.11)] / 18

MP = $821.4 / 18

MP = $45.63

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The monthly payment is $49.69.

We have,

The amount of the down payment is:

0.20 x $925 = $185

So the amount financed is:

$925 - $185 = $740

Using the formula for the monthly payment on a loan:

= (Pr(1+r)^n) / ((1+r)^n - 1)

where:

P = principal or amount financed = $740

r = monthly interest rate = 11%/12 = 0.0091667

n = total number of payments = 18

Plugging in the values, we get:

Monthly payment

= ($7400.0091667 x (1+0.0091667)^18) / ((1 + 0.0091667)^18 - 1)

= $49.69 (rounded to the nearest cent)

Therefore,

The monthly payment is $49.69.

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The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.

The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of

u1, u2 and u3.

The span of

{u1, u2, u3, u4}

will be a subset of the span of

{u1, u2, u3}.

This means that the span of

{u1, u2, u3, u4}

will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of

{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},

as there may be other vectors that are in the span of

{u1, u2, u3, u4}

but not in the span of {u1, u2, u3}. Hence, the statement is false.

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The complete question is

Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.

The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.

For the X-bar chart:

New process mean (after the shift) = 702.00

Standard deviation (constant) = 1.738

Sample size (n) = 6

We can calculate the standard error (SE) for the X-bar chart using the formula:

SE = Standard deviation / √(sample size)

SE = 1.738 / √(6) ≈ 0.709

Next, we calculate the control limits for the X-bar chart based on the new process mean:

New UCL = New process mean + 3 × SE

= 702.00 + 3 × 0.709

= 704.127

New LCL = New process mean - 3 × SE

= 702.00 - 3 × 0.709

= 699.873

Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.

To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:

z = (X - μ) / SE

where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.

For the UCL:

z = (New UCL - μ) / SE

= (704.127 - 702.00) / 0.709

= 2.999

For the LCL:

z = (New LCL - μ) / SE

= (699.873 - 702.00) / 0.709

= -2.999

We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.

Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:

Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)

Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

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Complete question =

Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:

X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80

R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052

natural tolerance limits for the process are ±5.214.

the estimated standard deviation is 1.738.

d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?

Answer:

64 cups

Step-by-step explanation:

1 gallon = 16 cups

Therefore, 4 gallons = 4 x 16 = 64 cups

Answer:

64

Step-by-step explanation:

hope this helps!!! :)

Answer:

x = 8

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{RT}{WU}\) = \(\frac{RS}{WV}\) ( substitute values )

\(\frac{6x+15}{28}\) = \(\frac{108}{48}\) ( cross- multiply )

48(6x + 15) = 28 × 108 = 3024 ( divide both sides by 48 )

6x + 15 = 63 ( subtract 15 from both sides )

6x = 48 ( divide both sides by 6 )

x = 8