Lots of points + brainlyist. Pls.

Based on the given inverse variation between x and y, y = 1 when x = 2.

x = k/y

Where,

k = constant of proportionality

When x = 1 and y = 2

x = k/y

1 = k/2

cross product

1 × 2 = k

2 = k

So,

x = 2/y

find y when x = 2.

x = 2/y

2 = 2/y

cross product

2y = 2

divide both sides by 2

y = 2/2

y = 1

Ultimately, the value of y when x = 2 is 1.

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The two given figures are neither similar nor congruent

Congruent figures are geometric figures that have the same shape and size. That is, if you can transform one figure into another figure by a sequence of translations , rotations , and/or reflections , then the two figures are congruent.

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Therefore, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, it is clear that both shapes are not congruent because the lengths are not congruent.

Similarly, the ratio of the two corresponding sides are not the same. Thus:

We can say neither of both are similar or congruent.

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The winning percentage for this team is  58.33 percent.

The formula for this percentage is:

P = 100%*(number of games won)/total number of games.

The total number of games is 120, and of these the team lost 50, then the number of games won is:

120 - 50 = 70

Now we can replace these two values in the formula given above, then we will find that the winning percentage is:

P = 100%*(70/120)

P = 58.33%

That is the percentage we wanted.

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We can say with 99% confidence that the true population mean commute time to work falls within the range of 29.95 to 37.25 minutes. The margin of error of 1.83 indicates that the sample mean of 33.6 minutes may differ from the true population mean by up to 1.83 minutes in either direction.

To construct a 99% confidence interval for the population mean commute time to work, we need to use the T distribution since the sample size is less than 30. From the given information, the sample mean commute time to work is 33.6 minutes and the standard deviation is 7.1 minutes.

The formula for the confidence interval is:

(sample mean) +/- (t-value)(standard error)

The t-value is found using a T distribution table with a degree of freedom of n-1 (29-1=28) and a confidence level of 99%. This gives us a t-value of 2.763.

The standard error is calculated as the standard deviation divided by the square root of the sample size. So,

standard error = 7.1/sqrt(29) = 1.32

Plugging in the values, we get:

33.6 +/- 2.763(1.32)

This simplifies to:

33.6 +/- 3.65

Therefore, the 99% confidence interval for the population mean commute time to work is (29.95, 37.25).

The margin of error of the mean is the difference between the upper and lower bounds of the confidence interval divided by 2. In this case, the margin of error is (37.25-29.95)/2 = 3.65/2 = 1.83.

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In 3rd part, option (c) is not a function. In the 4th part, option (b) is not a function. In the 5th part, option (d) is the parent function for the given y.

For 3rd part,

We have to identify that which relation is not a function. A relation is said to be a function if all the elements of one set have a unique image in another set. In our question, as we can see in option (c), element 1 is connected to 2 elements which are 1 and -1. Element 4 is also connected to two elements which are 2 and -1. Therefore, it is not a function. All the other options are functions as each element has a unique image.

For 4th part,

If we observe option (a), we will get one value of y on equating x to any value. In option (b), y = [tex]\pm\sqrt{36 - x^{2}}[/tex], if we equate x to something, we will get two values of y. In options (c) and (d) also, we will get a unique value of y. Therefore, option (b) is not a function as we do not get a unique image for y.

For 5th part,

y = [tex]3\sqrt{x - 2} + 7[/tex]

To identify the parent function, we strip away all the arithmetic values to leave behind one higher-order operation on just x. Therefore, we will first strip away 3 which is a multiple, and 7 which is being added. Then, we will strip away 2. Now, we are left with just one operation on x which is [tex]\sqrt{x}[/tex]. Therefore, option (d) is the parent function for the given function.

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You can expect approximately 46 seeds to sprout from a packet of 50 seeds.

Based on the given information, we know that the germination rate for the bush bean seeds is 92%, which means that 92 out of 100 seeds planted and tended according to the directions will sprout. We also know that the selection of seeds for packets is random and all seeds are independent of one another. Therefore, we can use the binomial probability formula to determine the expected number of seeds that will sprout:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:
n = 50 (number of seeds in the packet)
k = number of seeds that sprout
p = 0.92 (probability of a seed sprouting)
1-p = 0.08 (probability of a seed not sprouting)

Using this formula, we can calculate the expected value of X as follows:

E(X) = n * p
E(X) = 50 * 0.92
E(X) = 46

Therefore, we can expect around 46 seeds to sprout out of the 50 seeds in the packet. However, it's important to note that this is only an expected value and the actual number of seeds that sprout may vary.

To determine how many bush bean seeds you can expect to sprout from a packet of 50 seeds, you can use the germination rate provided and the assumption that all seeds are independent of one another.

Given:
- Germination rate = 92%
- Total seeds in the packet = 50

Since the seeds are independent, you can simply multiply the germination rate by the total number of seeds to calculate the expected number of seeds that will sprout.

Expected sprouts (X) = Germination rate × Total seeds
X = 0.92 × 50
X ≈ 46

So, you can expect approximately 46 seeds to sprout from a packet of 50 seeds.

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The resultant of the vector is 25 units.

The resultant of the vector is calculated as follows;

The given vector, v = 24i - 7j

The resultant of the vector is calculated by applying the following formula as shown below;

v = √ (vx² + vy² )

where;

The resultant of the vector is calculated as;

v = √ (24² + (-7)² )

v = 25 units

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I disаgree with thе stаtеmеnt becаuse thе surfасe аreа аnd volumе оf а cylindеr аre indеpеndеnt оf eаch othеr аnd cаn vаry indеpеndеntly.

An exаmple: twо сylinders cаn hаve thе sаme volumе but different heights or rаdii, which would rеsult in different surfасe аrеаs. Convеrsеly, twо сylinders cаn hаve thе sаme surfасe аreа but different heights or rаdii, which would rеsult in different volumеs.

To demonstrаte this, you cаn perfоrm аn exрeriment by tаking twо сylinders оf thе sаme volumе but different rаdii аnd heights. Fill eаch cylindеr with wаter to thе sаme lеvеl, аnd mаrk this lеvеl on thе insidе оf thе cylindеr. Then рour thе wаter from one cylindеr into thе othеr аnd mаrk thе nеw lеvеl.

Neхt, meаsure thе heights оf thе wаter lеvеls in both сylinders аnd cаlculаte thе surfасe аreа оf eаch cylindеr using thе formulа for thе surfасe аreа оf а cylindеr:

Surfаce аreа = 2πrh + 2πr^2

Уou will find thаt thе twо сylinders hаve different surfасe аrеаs, even though thеy hаve thе sаme volumе. This exрeriment demonstrаtes thаt thе stаtеmеnt "If thе volumе оf twо сylinders аre equаl, thеn thеir surfасe аrеаs must be equаl" is fаlse.

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The probability that a randomly selected junior biology major has taken either a statistics or a computer course is 0.68

To find the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both), we'll use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Where:
- P(A) is the probability of having taken a statistics course (52% or 0.52)
- P(B) is the probability of having taken a computer course (23% or 0.23)
- P(A and B) is the probability of having taken both courses (7% or 0.07)

Now, plug in the values:

P(A or B) = 0.52 + 0.23 - 0.07
P(A or B) = 0.68

So, the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both) is 0.68, or 68%.

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The total number of sweets after considering the ratio with both Raj and his friend is 180 sweets.

Total number of sweets = 180

The ratio in which sweets are split = 1:4

Calculating Raj's share -

1 part out of 1+4

= 1/5 of the total sweets

1/5 of 180

= (1/5) x 180

= 36

Similarly,

Calculating the friend's share -

4 parts out of 1+4

= 4/5 of the total sweets

4/5 of 180

= (4/5) x 180

= 144

Total sweets with both Raj and his friend:

Raj's share + Friend's share

= 36 + 144

= 180

Complete Question:

Raj has 180 sweets and splits them 1:4 with his friend. What is the total number of sweets with both?

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Answer: its 7 i took the quiz

The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

The Gompertz function is a solution of the differential equation:

dP/dt = c ln(K/P) P

where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.

To solve this differential equation, we can use separation of variables:

dP/P ln(K/P) = c dt

Integrating both sides, we get:

∫ dP/P ln(K/P) = ∫ c dt

Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:

-∫ du/u = -ln|u| = -ln|ln(K/P)|

The right-hand side is just:

c t + C

where C is an arbitrary constant of integration.

Putting these together, we get:

-ln|ln(K/P)| = ct + C

Taking the exponential of both sides, we get:

|ln(K/P)| = e^(-ct-C)

Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:

ln(K/P) = e^(-ct-C)

Solving for P, we get:

P = K e^(-e^(-ct-C))

This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

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The IQR(Inter Quartile Range) is the best measure of variability and equals 4.

The length of ribbons found at a seamstress are listed as the data set below.

5, 8, 10, 12, 12, 19

Here, Mean and median cannot be the best measure since it not even a measure of variability. They are the measures of central tendency.

The measures of variability are Range and IQR.

Range is the difference of the highest value and the lowest value. It will be affected by outliers.

So, range = 19 - 5 = 14

IQR is the difference of the third quartile and the first quartile.

Third quartile is the middle value of the second half which is 12 and the first quartile  = 8

IQR = 12 - 8 = 4

Hence the appropriate measure is IQR.

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By taking the quotient between the sizes, we can see that Company A's pepper grains are 3.0*10^2 times larger.

We know that Company A sells peppers that is ground to a thickness of 2.4x10^-2 inches. Company B makes a smaller sized pepper ground to a thickness of 8.0x10^-5 inches.

To compare the sizes, we need to take the quotient between the size for company A and the size for company B, we will get:

(2.4x10^-2 in)/(8.0x10^-5 in)

(2.4/8.0)*(10^-2/10^-5)

0.3*(10^(-2 + 5))

0.3*10^3

To use the proper scientific notation, there must be a digit in the left side of the decimal point, so we can write this as:

3.0*10^2

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Tatum earns more than Real.

We have,

Real works 36 hours a week and makes $612.

Tatum works 34 hours a week and makes $663

So, per hour earning of Real is

= 612 / 36

= $17

and, per hour earning of Tatum is

= 663 / 34

= $19.5

Thus, Tatum earns more than Real.

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Based on the random sample, there is not enough evidence to conclude that more than 65% of all adults in the US use television as one of their main sources of news.

To answer your question, we will perform a hypothesis test using the given information.
Step 1: State the hypotheses.
H0 (null hypothesis): p = 0.65 (65% of all adults in the US use television as one of their main sources for news)
Ha (alternative hypothesis): p > 0.65 (more than 65% of all adults in the US use television as one of their main sources for news)
Step 2: Determine the sample proportion (p-hat) and sample size (n).
p-hat = 0.66 (66% from the random sample of 1500 adults)
n = 1500
Step 3: Calculate the test statistic (z) using the formula:
z = (p-hat - p) / sqrt[(p * (1-p)) / n]
z = (0.66 - 0.65) / sqrt[(0.65 * (1-0.65)) / 1500]
z = 0.01 / 0.013 (given Sâ¢Eâ¢=â0.013)
z ≈ 0.77
Step 4: Find the p-value corresponding to the test statistic.
Using a z-table or calculator, we find the p-value for z = 0.77 is approximately 0.2206. Since this is a one-tailed test, we will use this p-value directly.
Step 5: Compare the p-value to the significance level (α) and make a decision.
Assuming a common significance level (α) of 0.05, our p-value (0.2206) is greater than α. Therefore, we fail to reject the null hypothesis (H0).

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The measure of angle D in is 19° which is option (A)

To measure D, recall that sum of the angles in a triangle is 180°. We have two angles in triangle BCD, so we can find the third angle as follows:

m∠BCD + m∠CBD + m∠DCB = 180°

46° + m∠CBD + 90° = 180° (since angle DCB is a right angle)

m∠CBD = 44°

Now, we can use the fact that the sum of the angles in triangle CDE is 180° to find the measure of angle D:

m∠CDE + m∠DCE + m∠ECD = 180°

m∠CDE + 71° + 90° = 180° (since angle ECD is a right angle)

m∠CDE = 19°

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Answer:

D. 37

Step-by-step explanation:

Step 1:

order the values from lowest to highest

15, 22, 37, 49, 72

Step 2:

the median is the value in the middle of the set of numbers, which in this case is 37

So the answer is D. 37

Using the inscribed angle theorem, the value of x is calculated as: x = 96 degrees.

We have to recall the inscribed angle theorem in order for us to create an equation that would enable us calculated the value of x in the circle that is given above. The theorem simply states the following:

Measure of intercepted arc = 2(measure of inscribed angle).

The intercepted arc = x

The inscribed angle = 48 degrees

Therefore, applying the theorem we have equation below:

x = 2(48)

x = 96°

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Answer:

Step-by-step explanation:

To calculate how much Gloria will pay over 30 years for her $70,000 mortgage at 7.5%, we need to use the formula for a standard mortgage payment, which is:

P = L[c(1 + c)^n]/[(1 + c)^n - 1]

Where:

P = the monthly payment

L = the loan amount

c = the monthly interest rate (annual interest rate divided by 12)

n = the total number of payments (30 years multiplied by 12 months per year)

First, we need to calculate the monthly interest rate:

c = 7.5% / 12 = 0.00625

Next, we need to calculate the total number of payments:

n = 30 years x 12 months per year = 360

Now we can plug in these values to the formula:

P = 70000[0.00625(1 + 0.00625)^360]/[(1 + 0.00625)^360 - 1]

P = $493.95

Therefore, Gloria will pay $493.95 per month for 30 years for her $70,000 mortgage at 7.5%. Over the course of the 30 years, she will pay a total of:

Total Payments = P x n = $493.95 x 360 = $177,822

So, Gloria will pay a total of $177,822 over 30 years for her $70,000 mortgage at 7.5%.

Answer:  A

Step-by-step explanation:

Draw a line going out in 3rd quadrant.

your opposite side from angle is5 using pythagorean

and it's positive because it's in the +5 y direction

so sin x = 5/13

According to the estimated model, holding all else constant, an additional year in age means the market value decreases by approximately $190 (0.019 x 1000).

The size of the house (X1) and the total number of rooms (X2) appear to be statistically significant (at the 0.05 level) in explaining the market value of residential property.

The proportion of the total variation in sales explained by the regression equation is 0.946.

The given F-value shows that the assessor can reject the null hypothesis that neither of the independent variables explains a significant (at the 0.05 level) proportion of the variation in income.

An approximate 95 percent prediction interval for the selling price of a 15-year-old house having 16.00 hundred sq. ft., 3 rooms, and an attached garage is (212.833, 244.525).

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The 99% confident interval that the true population mean for the pages per book in the library falls within the range of 313 to 355 pages.

To calculate a confidence interval at the 99% confidence level for the pages per book in a library, you will need the following parameters:

1. Sample mean (x): 334 pages (given)
2. Population standard deviation (σ): 33 pages (given)
3. Sample size (n): 16 books (given)
4. Z-score (z) corresponding to the 99% confidence level: 2.576 (from the provided z-values)

Now, let's calculate the confidence interval using these parameters:

Step 1: Calculate the standard error (SE) of the sample mean:
SE = σ / √n = 33 / √16 = 33 / 4 = 8.25

Step 2: Multiply the Z-score by the standard error:
Margin of error (ME) = z * SE = 2.576 * 8.25 ≈ 21.25

Step 3: Add and subtract the margin of error from the sample mean to find the confidence interval:
Lower endpoint: x - ME = 334 - 21.25 ≈ 312.75
Upper endpoint: x + ME = 334 + 21.25 ≈ 355.25

Step 4: Round the final confidence interval endpoints to the nearest whole number:
Lower endpoint: 313
Upper endpoint: 355

So, the 99% confidence interval for the pages per book in the library is approximately 313 to 355 pages.

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To answer your question, let's start with a quick review of the alternating series estimation theorem. So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1.

This theorem states that if we have an alternating series and the absolute value of the terms decrease in size as we move through the series, then the error of approximating the sum of the series with the nth partial sum is less than or equal to the absolute value of the (n+1)th term.
In other words, if we add up the first n terms of an alternating series and call that partial sum S_n, then the true sum S is somewhere between S_n and S_n+1, and the error in approximating S with S_n is at most |a_n+1|, where a_n+1 is the (n+1)th term in the series.
Now, to apply this to your question, we need to know a few more things. Specifically, we need to know what the alternating series in question looks like, and what the terms of the series are. We also need to know what it means for the series to be convergent.
So, let's say that the alternating series in question is of the form:
a_1 - a_2 + a_3 - a_4 + ...
According to the alternating series estimation theorem, we need to find the smallest value of n such that |a_n+1| < 0.00005. That is, we need to find the smallest value of n such that:
|(-1)^(n+2)b_n+1| < 0.00005
Since b_n decreases as n gets larger, we know that b_n+1 < b_n, so we can simplify this inequality to:
(-1)^(n+2)b_n+1 < 0.00005
Now, we could solve this inequality explicitly, but since we don't know what the b_n values are, it's easier to approximate the answer. Since we want the error to be less than 0.00005, we know that the (n+1)th term must be smaller than 0.00005. So, we can set up an inequality like this:
b_n+1 < 0.00005
we can use the largest value of b_n that we know of (let's call it B) to get an upper bound on n. That is:
B < b_n for all n
So, we can solve for n as follows:
b_n+1 < 0.00005
B < b_n for all n
B < b_n+1 for all n (since b_n decreases as n gets larger)
B < 0.00005
n+1 > log(B/0.00005)
n > log(B/0.00005) - 1
So, we need to find the smallest integer value of n that is greater than log(B/0.00005) - 1. This will give us the number of terms we need to add up in order to approximate the sum of the series to within an error of 0.00005.

To determine how many terms we need to add in a convergent alternating series to find the sum with an error less than 0.00005, we will use the Alternating Series Estimation Theorem. The theorem states that if we have a converging alternating series, the absolute error in the approximation by the sum of the first n terms is less than or equal to the absolute value of the (n+1)-th term.
Here's a step-by-step explanation:
1. Identify the series as an alternating series, which means it should have the form (-1)^n * a_n, where a_n is a sequence of positive numbers.
2. Make sure the series is convergent by checking that a_n is decreasing and approaches zero as n approaches infinity.
3. Apply the Alternating Series Estimation Theorem by setting the (n+1)-th term less than the desired error, which in this case is 0.00005: |(-1)^(n+1) * a_(n+1)| < 0.00005.
4. Solve for n in the inequality above to determine the minimum number of terms needed to achieve the desired error.
By following these steps, you will find the number of terms you need to add in the convergent alternating series to obtain a sum with an error less than 0.00005.

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The values of the trigonometry are as follows

8. cos x = 9/17

10. sin x = 0.8

12. cos x = 4/5

From trigonometry: cos² x + sin² x = 1

Let the angle be x

8.

cos² x + sin² x = 1

cos² x + (4√13)/17 = 1

cos² x = 1 - (4√13)/17

cos² x = 81 / 289

cos x = √(81 / 289)

cos x = 9/17

10.

sec x = 5/3 and sec x = 1 / cos x, therefore

cos x = 3/5

x = arc cos 3/5

x = 53.1301

sin x = 0.8

12.

sec x = 5/4 and sec x = 1 / cos x, therefore

cos x = 4/5

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The length of the major arc DFE is given as follows:

L = 5.11π

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius in this problem is of 4 ft, hence the length of the whole circumference is of:

C = 8π.

The entire circumference is of 360º, with a minor arc of 130º, hence the length of the major arc is given as follows:

360 - 130 = 230º.

Meaning that the length of the major arc is given as follows:

L = 230/360 x 8π

L = 5.11π

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The exact values of the trigonometric functions are listed below:

Case 9: sec θ = 5√2 / 7

Case 11: tan θ = 1 / 3

In this problem we must find the exact values of trigonometric functions, this can be done by means of definitions of trigonometric functions:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = 1 / tan θ

sec θ = 1 / cos θ

csc θ = 1 / sin θ

Where:

Case 9

cos θ = √2 / 10

√(x² + y²) = 10

√(2 + y²) = 10

2 + y² = 100

y² = 98

y = 7√2

sin θ = 7√2 / 10

sec θ = 10 / 7√2

sec θ = 10√2 / 14

sec θ = 5√2 / 7

Case 11

csc θ = √10

sin θ = 1 / csc θ

sin θ = 1 / √10

sin θ = √10 / 10

y = √10

√(x² + y²) = 10

√(x² + 10) = 10

x² + 10 = 100

x² = 90

x = 3√10

tan θ = √10 / 3√10

tan θ = 1 / 3

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1. There are 3 decision nodes in the tree.
2. The best course of action for the hospital is option B - seek approval first, and proceed with Plan B if approved, and Plan A if denied.
3. The answer is E) B & C only. The decision tree shows conditional probabilities, but TreePlan is not maximizing the EMV. The probability of approval for Plan B does not depend on when approval is sought.
4. The EMV for choosing Plan B from the start is -137.5.

1. Decision nodes are points in a decision tree where a decision must be made. To determine the number of decision nodes in the tree, count the number of places where a choice must be made between different options.

2. To determine the best course of action, you would analyze the decision tree by considering the expected monetary value (EMV) of each path. Choose the path with the highest EMV.

3. Examine your decision tree and determine which conclusions apply. Some things to consider are:
  A) Conditional probabilities: Are there probabilities given based on the outcomes of previous decisions?
  B) "Rolling back" the decision tree: Is the tree being analyzed by working backward from the final outcomes to determine the best course of action?
  C) Probability of approval: Does the chance of getting approval for Plan B change based on when approval is sought?

4. To find the EMV for choosing Plan B from the start, calculate the probability-weighted average of the possible monetary outcomes for that path. Multiply the probability of each outcome by its monetary value, then sum those products.

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We have 792 ways to pick five students for the student council from a group of twelve candidates.

We will use the combination formula, which is nCr = n! / r!(n - r)! is find  number of ways to pick five students.

In this case, we want to choose 5 students from 12 candidates:

12C5 = 12! / 5!(12 - 5)!

12C5 = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1)

12C5 = 95040 / 120

12C5 = 792

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The similarity ratio of given surface area of the cylinders is 7:9.

Given that, the surface area of small cylinder is 49 square centimeter and the surface area of large cylinder is 81 square centimeter.

When two figures are similar, the square of the ratio of their corresponding side lengths equals the ratio of their area.

Here, the ratio is

a²/b² = 49/81

(a/b)² = 49/81

a/b = √(49/81)

a/b = 7/9

a:b = 7:9

Therefore, the similarity ratio of given surface area of the cylinders is 7:9.

Learn more about the similar figure here:

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