suppose that you would like to construct a 95% confidence interval to estimate the proportion of all uconn students who graduate in 4 years. you would like to use a maximum error of 2.5%. a. how large a sample is needed if you know that in the past few years approximately 70% of all students have graduated in 4 years? note: always round up to the next integer value if your answer is not an integer. b. how large a sample is needed if you have no knowledge of what % of students typically graduate in 4 years? always round up to the next integer value if your answer is not an integer.

The equation for the linear equation perpendicular to y - 9 = - x is:

y = x +1

Two linear equations are perpendicular if the product betwen the slopes is -1.

Here we want a line perpendicular to:

y - 9 = -x

isolating y:

y = -x + 9

Then the slope is -1, thus, the slope of the perpendicular line a is:

a*-1 = -1

a = -1/-1

a = 1

Then our line is:

y = x + c

Now we want our line to pass through (2, 3), replacing these values we will get:

3 = 2 + c

3 - 2 = c

1 = c

The linear equation is:

y = x +1

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The jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.

According to the decibel scale, a sound that is 10 decibels higher is 10 times as loud. Therefore, a sound that is 20 decibels higher is 10 times 10, or 100 times as loud. This means that a 120-dB jet plane taking off is 100 times as loud as a sound that is 20 decibels lower, which is a 40-dB conversation.

To find out how many more times louder a 120-dB jet plane taking off is than a 40-dB conversation, we can divide the loudness of the jet plane by the loudness of the conversation

120 dB / 40 dB = 3

This means that a 120-dB jet plane taking off is 3 times as loud as a 40-dB conversation. However, we need to remember that the decibel scale is logarithmic, which means that each increase of 10 decibels represents a tenfold increase in loudness. Therefore, a 30-dB increase represents a thousandfold increase in loudness (10 to the power of 3).

Since the difference between 120 dB and 40 dB is 80 dB, which is 8 times 10 dB, the loudness of the jet plane taking off is 10 to the power of 8, or 100 million, times as loud as the conversation.

Therefore, the jet plane taking off is 100 million / 1 million = 100 times louder than the conversation.

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The surface area of each block can be found by adding up the areas of all six faces. The area of each face is simply the product of its length and width.

The block has two faces that are 8 cm long and 5 cm high, so each of these faces has an area of 8 cm x 5 cm = 40 cm^2.

The block also has two faces that are 4 cm wide and 5 cm high, so each of these faces has an area of 4 cm x 5 cm = 20 cm^2.

Finally, the block has two faces that are 8 cm long and 4 cm wide, so each of these faces has an area of 8 cm x 4 cm = 32 cm^2.

Adding up the areas of all six faces, we get:

Surface area = 2(40 cm^2) + 2(20 cm^2) + 2(32 cm^2)

Surface area = 80 cm^2 + 40 cm^2 + 64 cm^2

Surface area = 184 cm^2

Therefore, the surface area of each block is 184 square centimeters.

Answer:

Step-by-step explanation:

so add then dummy

Answer:

36

Step-by-step explanation:

If three candidates A, B and C in a school election got 153, 245, and 102 votes respectively, then the percentage of votes got by the winner is (B) 49%.

The percentage of votes obtained by the winning Candidate in the school election is the total votes obtained divided by the total votes.

The percentage is always obtained as the quotient of two values multiplied by 100.

The votes obtained by Candidate A = 153

The votes obtained by Candidate B = 245

The votes obtained by Candidate C = 102

The total number of votes = 500

The percentage of votes obtained by the winner, Candidate B = 49% (245 ÷ 500 × 100)

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The margin of error is approximately 0.014 grams, rounded to three decimal places.

To construct a 98% confidence interval for the mean of repeated measurements of the weight, we can use the following formula:

CI = x ± z × (σ/√n)

Where:
x = mean result = 10.230 grams
σ = standard deviation of scale readings = 0.020 gram
n = number of repeated measurements = 40
z = z-score for 98% confidence interval = 2.326

Plugging in the values, we get:

CI = 10.230 ± 2.326×(0.020/√40)
CI = 10.230 ± 0.014
CI = (10.216, 10.244)

Therefore, the 98% confidence interval for the mean of repeated measurements of the weight is (10.216, 10.244) grams.

The margin of error is the difference between the upper and lower bounds of the confidence interval divided by 2, so:

Margin of error = (10.244 - 10.216)/2
Margin of error = 0.014

Thus, the margin of error is 0.014 grams.

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The distance traveled by train would be 300 miles.

The relation between speed, distance, and time:

You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

A train travels for 3.75 hours at 80 miles per hour.

The distance traveled = speed * time

                                    = 3.75 * 80

                                    = 300 miles.

Hence, the distance traveled by train would be 300 miles.

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complete question;

A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where

d = distance, r = rate, and t = time, to find the distance the train traveled.

The distance traveled is

miles.

The solution is

The equation of the function that models the data is y = x² + 2x - 1

Given that

x    y

-2    -1

-1    -2

0    -1

1    2

2    7

A quadratic function is represented as

y = ax² + bx + c

Where c = y when x = 0

So, we have

y = ax² + bx - 1

Using the other points, we have

a + b - 1 = 2

4a + 2b - 1 = 7

So, we have

a + b = 3

4a + 2b = 8

When solved, we have

a = 1 and b = 2

So, the equation is

y = x² + 2x - 1

See attachment for the plot of the dataset

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15) The height of the hotel is given as follows: 250 foot.

16) A reasonable estimate would be for the height of the building to be taller than the height of the tower, as it casts a larger shadow.

The height of the hotel is obtained applying the proportions in the context of the problem.

The proportions are applied by a rule of three, between the height of the building and it's shadow, as follows:

x foot - 25 feet

120 foot - 12 feet

The height of the building is the height of the shadow multiplied by 10, hence the height is given as follows:

25 x 10 = 250 foot.

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question 11.

The correct statement should be option C: After 3 years, Bank A will pay Benjamin $23.13 more than Bank B.

question 12:

Jenny will earn $758.11 more interest will she earn if she invests $500 at 4.25% interest, compounded annually for 10 years, than if she invests $500 at 4.25% simple interest for 10 years.

Option A is correct.

Applying the  formula for simple interest, Jenny will earn $212.50 ($21.25 per year) in interest after 10 years, which means that she will have a total of $712.50.

When we also apply  the formula for compound interest, Jenny will earn $975.61 after 10 years which means that  after 10 years, she will have a total of $1475.61.

we then find the difference  the total amounts earned in compound interest and simple interest is $1475.61 - $712.50 = $763.11, which we can  rounds down to $758.11.

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If we compare price, length and number of plies in each "paper-towel-roll" from six different manufacturers, then "degree-of-freedom" is 5.

The "Degree-of-freedom" is defined as a statistical concept which is used in calculations to account for variability in the data.

In comparing price, length, and "number-of-plies" in each paper "towel-roll" from 6 different manufacturers, the "degree-of-freedom" will depend on the specific statistical test used.

The degree-of-freedom is = "total sample size" - 1,

The total sample-size is the number of different manufacturers, and we know that there are 6 different manufacturers,

So, Degree Of Freedom is = 6 - 1 = 5,

Therefore, the required "degree-of-freedom" is 5.

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The expected frequency of South campus and passed will be 36.5. Calculating the total number of students who took the aptitude exam is the first step in determining the expected frequency of South campus and passing.

Total number of students = 42 + 31 + 58 + 69 = 200

The marginal totals for South campus and passed need to be calculated as:

Marginal total for South campus is 42 + 58 = 100

Marginal total for passed is 42 + 31 = 73

Using the following formula, we can now know the anticipated frequency for the South campus and passed:

Expected frequency = (row total * column total) / grand total

Expected frequency for South campus and passed = (100 * 73) / 200 = 36.5

Therefore, the expected frequency of South campus and passed=36.5.

In the event that there is no appreciable difference between the two campuses' pass rates, this statistic represents the anticipated number of students who passed the aptitude exam at the South campus.

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Answer:

The answer is O6w³ cubic units.The volume of a rectangular prism is equal to the length of the base multiplied by the width of the base multiplied by the height. In this case, the length of the base is 2w, the width of the base is w, and the height is 3w. Therefore, the volume is:(2w)(w)(3w) = 6w³ cubic units

Step-by-step explanation:

The volume of the prism is 6 W³ cubic units.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

Volume is sometimes referred to as capacity.

We have,

The height of a right rectangular prism is three times the width of the base. The length of the base is twice the width.

So, L = 2 W and H = 3 W

Then,  volume of the right rectangular prism

= l w h

= 2W x W x 3W

= 6 W³ cubic units.

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The equation that represents the scatterplot is: y = -0.8x + 30

From the scatterplot, we see that when x = 25, y = 10

Option A: The equation is given as:

y = -0.8x + 30

At x = 25, we have:

y = -0.8(25) + 30

y = -20 + 30

y = 10

Option B: The equation is given as:

y = -1.5x + 50

At x = 25, we have:

y = -1.5(25) + 30

y = -37.5 + 30

y = -7.5

Option C: The equation is given as:

y = -2.8x + 73

At x = 25, we have:

y = -2.8(25) + 73

y = -70 + 73

y = 3

Option D: The equation is given as:

y = -3.5x + 82

At x = 25, we have:

y = -3.5(25) + 82

y = -87.5 + 82

y = -5.5

Thus, only option A is correct

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Susan would need 6(3/8) yards of fabric.

5/8 yards of fabric are left over after making the aprons.

Susan does not have enough fabric left to make another apron

We have,

Part A:

To make one apron, Susan needs 1 3/4 + 3/8 = 2 1/8 yards of fabric.

To make 3 aprons, Susan would need 3 × 2 1/8 = 6 3/8 yards of fabric.

Part B:

Susan needs 6 3/8 yards of fabric to make 3 aprons.

If she originally had 7 yards of fabric, then the amount of fabric left after making the aprons would be:

7 - 6 3/8 = 5/8 yards of fabric.

So, 5/8 yards of fabric are left over after making the aprons.

Part C:

Susan needs 2 1/8 yards of fabric to make one apron.

She has 5/8 yards of fabric left over after making 3 aprons.

Therefore, Susan does not have enough fabric left to make another apron because 5/8 yards is less than 2 1/8 yards required to make one apron.

Thus,

Susan would need 6(3/8) yards of fabric.

5/8 yards of fabric are left over after making the aprons.

Susan does not have enough fabric left to make another apron

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Answer:

Step-by-step explanation:

assuming there is no interest on the installment payment

6 years = 72 months

14,384.52 : 72 = 199.785 units

We want to find the probability of seeing more than 500 shooting stars in one night, when the average is 50 shooting stars per night.

Using the Poisson distribution, we can approximate the probability using a normal distribution with a mean of 50 and a standard deviation of √50. Standardizing for x=500, we get a result of about 30.14.

Using standard normal distribution tables, we know that the probability of a standard normal variable greater than 3 is less than 0.0013. The upper limit of the probability of seeing more than 500 shooting stars in one night is less than 0.0013.

If we assume that the average number of shooting stars seen per night is 50, then the parameter λ for the Poisson distribution is also 50. Therefore, the probability of seeing more than 500 shooting stars in one night is very low and can be considered negligible.

1. "Stars" - In this context, "stars" refer to the shooting stars you see at night.
2. "Average" - This is the mean value of a set of numbers, representing the typical or central value.
3. "Probability" - The measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1.

Now, let's consider the given information: you see an average of 50 shooting stars per night. To find an upper bound on the probability of seeing more than 500 shooting stars in one night, we can use the Poisson distribution as an approximation.

The Poisson distribution is used for counting the number of events (shooting stars) in a fixed interval (one night). The formula is:

P(X=k) = (e^(-λ) * λ^k) / k!

where:
- P(X=k) is the probability of observing k events (shooting stars)
- λ is the average number of events (50 shooting stars)
- k is the number of events we want to find the probability for (more than 500 shooting stars)
- e is the base of the natural logarithm (approximately 2.71828)
- ! denotes the factorial function

To find the upper bound on the probability of seeing more than 500 shooting stars, we can calculate the complementary probability, which is the probability of seeing 500 or fewer shooting stars, and then subtract it from 1:

To find the probability of seeing more than 500 shooting stars in one night, we can use the cumulative distribution function (CDF) of the Poisson distribution. The CDF gives the probability that the number of shooting stars seen in a night is less than or equal to a certain value. To find the probability that the number of shooting stars seen is greater than 500, we can subtract the probability that it is less than or equal to 500 from 1.

Using a calculator or statistical software, we can calculate that the probability of seeing 500 or fewer shooting stars in one night is approximately 2.2 x 10^-16. Subtracting this from 1, we get an upper bound on the probability of seeing more than 500 shooting stars in one night of approximately 1.

P(X>500) = 1 - P(X≤500)

Since it's highly unlikely to see more than 500 shooting stars when the average is only 50, the upper bound on the probability of seeing more than 500 shooting stars in one night would be close to 0. Note that computing the exact probability using the Poisson formula for such large numbers can be computationally challenging.

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Answer:

3% of 350 is 10.5. Because we're only calculating simple interest we multiply this by 5 to give $52.50 interest after 5 years. Therefore Frances will have earned $52.50.

Step-by-step explanation:

Not og answer credits to annikad

Well let’s start with what 3% of 350. It is 10.5 so at the end of 5 years the interest will be 52.50$. Your welcome btw!

Based on the sample data, it can be concluded that the statement "the average profit for Sunday's events is $20.25" is true.

The sample data only provides information on the average profit for Friday's and Sunday's activities. There is no information given regarding the average profit for each of the Carey's workouts. Therefore, it is impossible to determine whether or not the statement regarding the average profit for Carey's workouts is true or false.

Conclusion: In conclusion, based on the analysis of the sample data, the statement "the average profit for Sunday's events is $20.25" can be considered true. However, no information can be provided regarding the accuracy of the other statement regarding the average profit for Carey's workouts, as it is not included in the given data.

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The probability of picking 6 from the cards at first is  1/4 (or, 0.25) and  then picking a number less than 7 is 0.

You pick a card at random and without putting the first card back you pick a second card at random.

The given number of cards are picked from 6, 7, 8, 9

Total number of cards is = 4

The total number of  6 in the cards is 1.

Thus, the probability of picking a 6 is = 1/4 , at first pick.

Number of cards less than 7 is only 6 here in the given problem.

After picking a 6 at first, the probability of picking a card less than 7 is 0 since once a card drawn is not put back in the shuffle.

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There are 12 different choices of pens available with this brand, obtained by multiplying the number of colors (3) by the number of writing tips (4).

To calculate the number of different choices of pens with this brand, you can use the multiplication principle of counting, which states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

Using this principle, the number of different choices of pens can be calculated as

Number of colors x Number of writing tips = 3 x 4 = 12

Therefore, there are 12 different choices of pens available with this brand.

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The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:

2j - 10 = number of points scored by Avery

To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:

number of points scored by Avery = 2j - 10

Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.

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The next three terms of the sequence would be:

-20, - 27 , -34

The rule is to subtract 7 from the every term that is on the question in other to get the next term

Lets assume the rule =

T = a - 7

we have

15 - 7 = 8

8 - 7 = 1

1 - 7 = -6

- 6 - 7 = - 13

- 13 - 7 = - 20

-20 - 7 = -27

- 27 - 7 = - 34

- 34 - 7 = -41

-41 - 7 = -48

The next three terms of the sequence would be:

-20, - 27 , -34

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The computation time for the out-degree of every vertex, for an adjacency-list representation of a directed graph,is equals to O(|E|+|V|).

Adjacency-list is one of the most basic and frequently used node graph representation of a network. In this representation of a directed graph, the out-degree of a vertex is simply the number of adjacent vertices in the list

The time to calculate the out-degree is straight forward. The out-degree of a vertex is defined as the number of edges pointing outwards from that vertex. Consider the following adjacency list.

1 -> 2 -> 3

2 -> 5

3 -> 4

4 -> 2 -> 3

5 -> 1

To calculate the out-degree we loop in this adjacency list and count the number of vertices in each of the lists. For example, Vertex 4 in the above list has 2 nodes in the list. Therefore outdegree of node 4 is 2. Clearly time take by this algorithm is O(|E|+|V|).

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The probability that Martha will arrive first and Armando will arrive last is 1/120

For Martha to arrive first, there is only 1 possible order for her arrival, since she needs to be the first one. Similarly, for Armando to arrive last, there is only 1 possible order for his arrival, since he needs to be the last one.

Now that we have determined the number of ways that Martha can arrive first and Armando can arrive last, we can calculate the probability of this scenario occurring. To do this, we need to divide the number of ways that Martha can arrive first and Armando can arrive last by the total number of possible arrival orders.

This means that out of all possible arrival orders, there is only a 1/120 chance that Martha will arrive first and Armando will arrive last.

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The total cost of the fruits she bought​ is 3p + 5n + 4

Given that

We have

9 pears = 3 * 3 pears

So, we have

9 pears = 3 * p

9 pears = 3p

Also, we have

n + 2 apple = 2 * (n + 2)

n + 2 apple = 2n + 4

We simply add the total of each together

So, we have

Total = 3p + 2n + 4 + 1.50 * 2n

Total = 3p + 2n + 4 + 3n

Evaluate

Total = 3p + 5n + 4

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The value of the missing fraction for the given expression 1-  (3/7) - ___=  ( 5 /14 ) is equal to ( 3 /14).

Expression is equal to,

1-  (3/7) - ___=  ( 5 /14 ).

Let us consider 'y' represents the missing fraction .

Rewrite the expression as ,

⇒ 1 - ( 3 / 7) - y = ( 5 / 14 )

Simplify the expressions by taking the least common multiple.

⇒ ( 7 - 3 ) / 7 - y = ( 5 / 14 )

⇒ ( 4 / 7 ) - y = ( 5 / 14 )

Subtract ( 4 /7 ) from both the sides we get,

⇒ ( 4 / 7 ) - y  - ( 4 /7 ) = ( 5 / 14 ) - ( 4 /7)

⇒ -y = ( 5  - 8 ) / 14

⇒ y = 3 /14

Therefore, the value of the missing fraction is equal to ( 3/14) .

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The above question is incomplete, the complete question is:

Fill in the missing fraction 1-  (3/7) - ___=  ( 5 /14 ).

There are 130 shark cookies should they order this month.

We have to given that;

Last month, they sold 65 shark cookies and 85 clown fish cookies.

Hence, If they plan to order 170 clown fish cookies this month.

Then, Number of shark cookies should they order this month is, x

Hence, We get;

65 / 85 = x / 170

x = 130

Thus, There are 130 shark cookies should they order this month.

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A function that you can use to find the cost C of buying S songs is C = 0.90S.

In order to write a linear equation or function to describe this situation, we would assign variables to the cost of buying songs and the number of songs respectively, and then translate the word problem into a linear equation as follows:

Since this online music store sells songs for $0.90 each, a linear equation or function to describe this situation can be written as follows;

C = 0.90S

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