Roll a number cube 30 times. Record the results from each roll. In parts (a) and (b), find the sample proportion, the margin of error for a 95% confidence level, and the 95% confidence interval for the population proportion.


d. Compare your sample proportions to the theoretical proportions for parts (a) and (b). Would you expect the theoretical proportion to be within the confidence intervals you found? Explain.

The number of boxes containing both pens and pencils is 2.

What is set?

A set is defined as a well-defined collection of distinct objects. It is denoted by the capital letters of the English alphabet. Its value remains the same for every individual.

Calculation for the number of boxes containing both pens and pencils

Total number of boxes is given by the union of two sets A and B; i.e. A∪B= 20

Boxes having pencils is given by the set A = 13

Boxes having pens is given by the set B = 9

Boxes having neither pens nor pencils, A'∩B' = 3

Boxes containing both pens and pencils are given by the intersection of the sets, A∩B

A∩B = A + B - A∪B

= 13 + 9 - 20

= 2

Hence, the number of boxes containing both pens and pencils is 2.

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Answer:

B

Step-by-step explanation:

So, let's judge the items one by one, to see which one is true:

a)Triangle BFD is an acute scalene triangle. False, the triangle is isosceles.

b)Triangle BCF is a right isosceles triangle. False, it is right, but scalene.

c) Triangle DEF is an obtuse scalene triangle. True, Angle EDF is the obtuse one.

d) Triangle ABF is an obtuse isosceles triangle. False, it's not isosceles.

e) Triangle BFE is an acute equilateral triangle.​ False, it's not equilateral.

The decimal positional number system is the one that is most frequently used.

The consistent representation of numbers using digits and other symbols is known as a number system.

Some key features of number system are-

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The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

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Answer:

x : y = 9 : 13

Step-by-step explanation:

Given that

3x - y : x + 2y = 2 : 5

Express the ratio in fractional form, that is

\(\frac{3x-y}{x+2y}\) = \(\frac{2}{5}\) ( cross- multiply )

5(3x - y) = 2(x + 2y) ← distribute parenthesis on both sides )

15x - 5y = 2x + 4y ( subtract 2x from both sides )

13x - 5y = 4y ( add 5y to both sides )

13x = 9y ( divide both sides by 13 )

x = \(\frac{9}{13}\) y ( divide both sides by y )

\(\frac{x}{y}\) = \(\frac{9}{13}\) , that is

x : y = 9 : 13

Answer:

Any value greater than 19 hours.

Step-by-step explanation:

hope it helps

Answer:

(-1,0)

Step-by-step explanation:

Answer:

The 11 symmetries of a regular octagon. Lines of reflections are blue through vertices, purple through edges, and gyration orders are given in the center.

...

Symmetry of octagon.

r16

d8 g8 p8

d2 g2 p2

a1

Step-by-step explanation:

Hope it helps! Correct me if I am wrong :>

Im sure about my answer

Can you please mark me as brainlest?

Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

21 = 2.50 + 5x

21 - 2.50 = 5x

18.50 = 5x

x = 18.50 / 5

x = 3.7 bags of avocados

To get 3 bags of avocados or 9 avocados

= $5 × 3

= $15

Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

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Answer: 11/28

Step-by-step explanation:

Alright so this is just adding fractions:

First, find common denominator:

If it isn't the common denominator is not apparent, you can always find it by multiplying the two numbers together:

So... 4*7=28

Now that the we have the common denominator, we have to change the top value. Whatever we do to the denominator we must do to the numerator:

So in this instance, we multiplied 4 to 7 to get 28, so we must multiply 1 (the numerator) by 7 as well, giving us 7/28.

We must do this to the other fraction, we multiplied 7 by 4 to get 28 so we must do it to the numerator, giving 4/28.

Now just add the numerator only. Its a common mistake to add both the numerator and the denominator, when the denominator should just remain the same:

4+7=11

11/28 or in decimal form: 0.3928

Hello and regards 313samn

The solution to the sum of the fraction 1/4 + 1/7 is 11/28.

1/4 + 1/7

We write each numerator over the lowest common denominator.

We want to expand the fractions to have a common denominator and be able to add them.

(1 × 7)/(4 × 7) + 1/7

(1 × 7)/(4 × 7) + (1 × 4)/(7 × 4) = 7/28 + 4/28

We observe that both fractions have an equal denominator, in this case, we unite and add them.

(7 + 4)/28

11/28

The solution to the sum of the fraction 1/4 + 1/7 is 11/28.

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The probability that at least one of them has received immunizations is 97.5611%.

Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.

1 - P( no one was vaccinated).

1-71%=0.29

If you pick one person at random from the population, there is a \(29\)% chance they are not immunized. There is therefore no chance that any of the three people you choose will be an unvaccinated person \(0.29 X 0.29 X 0.29 = 0.024389.\) Your solution, calculated as a percentage by deducting from \(1\), is \(97.5611\)%.

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Answer:

Look at the explanation.

Step-by-step explanation:

Start y=-2x-3 at the Y -3 and X 0, then go up two and to the right one, like a staircase. For y=-x+3 start on Y 3 and X 0 and go down 1 x and 1 y like a downstair staircase with 1 unit down.

c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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The presence of conspecific nest parasitism in the population of birds being studied could potentially have an influence on the estimate of the heritability of beak shape.

Since some portion of the eggs in the survey may not be from the biological parents, there is a chance that the observed traits in offspring may not be fully representative of the traits that were passed down from their biological parents.

This could result in a weaker correlation between the measures of beak morphology in parents and offspring, and therefore a lower R2 value. As a result, the inferred heritability of the trait could be underestimated. It is important to keep in mind the potential impact of conspecific nest parasitism on the accuracy of the estimates when interpreting the results of the study.

With the presence of unrelated eggs in the nests, the correlation between parent and offspring beak morphology may be weakened, leading to a lower R² value in the scatterplot. This would cause you to underestimate the true heritability of beak shape, as unrelated individuals are more likely to exhibit random variation in beak traits. If you could accurately identify and exclude the parasitic eggs from your study, the resulting heritability estimate would likely be higher and more accurate.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

y=5x

please see the attached picture..

Hope it helps...

Good luck on your assignment.....

Y is proportional to x

☆ Remove the proportional sign

y = k x

if k = 5

y = 5x

Answer:

-2/2 wich is equal to -1

Step-by-step explanation:

Hi !

\(2x + 3 > 11\\\iff 2x > 8\\\iff x > \frac{8}{2}\\ \iff x > 4\)

Have a nice day ;)

Answer:

x > 4

Isolate the variable by dividing each side by the factors that don't contain the variable

Answer:

8 - w

Step-by-step explanation:

In my opinion, an expression for eight minus w would be 8 - w. Thanks.

Hope it helps.

We have the following equation to find the simple interes:

where P is the principal amount, r is the rate and n is the time period.

In this case, we have the following:

thus, the interest after 1 year is $240.

To find the future value, we can add the interest to the principal amount to get:

therefore, the future value is $6240

By Lagrange's Theorem, the order of any subgroup of a group must divide the order of the group. Therefore, any subgroup of order 5 in a group of order 20 must be a cyclic subgroup generated by an element of order 5.

There are four elements of order 5 in a group of order 20, and each generates a unique cyclic subgroup of order 5. Therefore, there are four subgroups of order 5 in a group of order 20.
There are 4 subgroups of order 5 in a group of order 20. This is because the number of subgroups of a given order can be found using the formula n(G)/n(H), where n(G) is the order of the group and n(H) is the order of the subgroup. In this case, n(G) = 20 and n(H) = 5, so the number of subgroups is 20/5 = 4.

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Answer:

\(3x - 9 = 2x + 21 \\ 3x - 2x - 9 = 2x - 2x + 21 \\ x - 9 = 21 \\ x - 9 + 9 = 21 + 9 \\ x = 30\)

m<DGI = 80°

\(3x - 9 = \\ 3(30) - 9 = \\ 90 - 9 = 81\)

The measure of angle ∠DGI can be obtained by finding the solution of the equation as 81°.

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

The ray GI bisects ∠DGH.

It implies that the new angles are equal in measurement.

⇒ m∠DGI = m∠IGH

⇒ 3x - 9 = 2x + 21

⇒ x = 30

Then, in order to calculate m∠DGI, plug x = 30 in  3x - 9 as,

3 × 30 - 9 = 81

Hence, the measure of angle ∠DGI is given as 81°.

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The percent increase in the cost of the airline ticket is 50%. If the airline charges an additional $50 baggage fee with the new ticket price, the percent increase with the additional baggage fee is 73.81%.

To calculate the percent increase, we first find the difference between the new cost and the original cost: $315 - $210 = $105. Then, we divide this difference by the original cost and multiply by 100 to get the percentage: ($105 / $210) * 100 = 50%. Therefore, the percent increase in the ticket price is 50%.

If the airline charges an additional $50 baggage fee with the new ticket price, the total increase in cost would be $105 + $50 = $155. We then divide this total increase by the original cost ($210) and multiply by 100 to get the percentage: ($155 / $210) * 100 = 73.81%. Therefore, the percent increase with the additional baggage fee is 73.81%.

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Answer:

3.19 (3sf)

Step-by-step explanation:

A = pi x r^{2}

32.1 = 3.142 x r^{2}

r = \(\sqrt{10,2164\)

Step 1

Total number of hats = 394

Cost per hat = $7.49

Step 2:

You will multiply to find the total cost of 394 hats.

Final answer

Total cost of 394 hats = $2951.06

Option C. 0.67. To estimate the value of √(2π/√5), we first need to simplify the expression as much as possible.

One approach is to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator:

√(2π/√5) * (√5/√5) = √(2π√5)/(√5√5) = √(10π)/√(5*5) = √(10π/25)

Now, we can simplify the expression further by canceling out the square root of 25:

√(10π/25) = √(2π/5)

Next, we can use a calculator to evaluate the expression. Simply input 2π/5 and then take the square root of the result. Doing this yields:

√(2π/5) ≈ 0.671

Therefore, the closest answer choice is C) 0.67.

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