Section III: Confidence Intervals
Using the acid rain measurements from assignment #2, answer the following questions.
Question 9: State the standard error of the mean and compute the 95% confidence interval around your
sample mean estimate (expressed as mean +/- standard error) (1 marks). Show your calculations.
Question 10: What does this confidence interval indicate about the acid rain in Winnipeg? (2 marks)
Question 11: Calculate the 90% and 99% confidence interval for the data (2 marks). Show your
calculations.
Question 12: What pattern emerges when you increase your confidence interval (from 90% to 95% to
99%)? Why does this pattern emerge? (3 marks)

The minimum value is 24

To find the minimum value of z=7x+3y, we must use the given constraints to determine the values of x and y.

First, solve 4x + 6y ≥ 24. Rearrange the equation to solve for x: x ≥ (24 - 6y) / 4.

Next, solve x + 6y ≥ 12. Rearrange the equation to solve for y: y ≥ (12 - x) / 6.

Using the two equations, determine the possible values of x and y:
If y = 0, then x = 6
If x = 0, then y = 2

Substitute the possible values of x and y into the equation z = 7x + 3y and find the minimum value:
z = 7(6) + 3(0) = 42
z = 7(0) + 3(2) = 24

Therefore, the minimum value of z is 24.

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Nathan will therefore have captured a total of 51 ladybirds over the previous 6 days after including the 8 that he collected today in his data set.

A set is a group of unique objects, known as elements, that are treated as a singular entity in mathematics. Anything, including letters, numerals, and even other sets, can be the objects. The components of sets are typically listed between curly braces and separated by commas. Sets are typically represented by capital letters. The set of even numbers, for instance, can be represented as 2, 4, 6, 8,..., where the dots signify that the pattern is infinite. Several operations, including union, intersection, and complement, can be used to modify sets. The set of all components that are members of either set A or set B or both is the union of the two sets A and B, denoted as A B.

given

Nathan's overall catch over the previous 6 days will rise if he includes the 8 ladybirds he caught today in his data set. The new data collection will be specifically:

8, 10, 6, 5, 14, 8

We merely add up all the figures in the data set to determine the new total number of ladybirds Nathan has captured:

8 + 10 + 6 + 5 + 14 + 8 = 51

Nathan will therefore have captured a total of 51 ladybirds over the previous 6 days after including the 8 that he collected today in his data set.

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The distribution of Sn + Tm is a binomial distribution with parameters (n+m, p).

This can be proved using the fact that the sum of independent binomial random variables follows a binomial distribution with the sum of the number of trials and the same probability of success.



Let X ~ Binomial(n, p) and Y ~ Binomial(m, p) be independent random variables representing the number of heads in the first n coin tosses and the last m coin tosses, respectively.

Then, the sum of X and Y, Z = X + Y, follows a binomial distribution with parameters (n+m, p).

The probability mass function of Z can be written as:

P(Z = k) = P(X + Y = k) = ∑ P(X = i) * P(Y = k-i) for i = 0 to k

Since X and Y are independent, we can write:

P(Z = k) = ∑ P(X = i) * P(Y = k-i) = ∑ (n choose i) * p^i * (1-p)^(n-i) * (m choose k-i) * p^(k-i) * (1-p)^(m-k+i)

Simplifying the above equation, we get:

P(Z = k) = (n+m choose k) * p^k * (1-p)^(n+m-k)

Therefore, Z ~ Binomial(n+m, p).

As a result, the distribution of Sn + Tm has the parameters (n+m, p) of a binomial distribution.

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Answer: yes

Step-by-step explanation:

yes because it is less than or equal to seeing that the dominoes reach the whole room

Answer:

A) 59°

Step-by-step explanation:

m<ADC is a right angle, therefore it is 90°

so that means you can now subtract the angle that you already know [31°] from it to get the angle that is left over, m<ADB

90°-31°= 59° (subtracting m<ADC [90°] from m<BDC [31°] leaves your remaining angle m<ADB [59°]

Answer:

x = 10.25

Step-by-step explanation:

congruent angles are equal , then

18x - 34 = 10x + 48 ( subtract 10x from both sides )

8x - 34 = 48 ( add 34 to both sides )

8x = 82 ( divide both sides by 8 )

x = 10.25

The area of the circle is 63.62 square meters

To work out the area of a circle, we need to use the formula A = πr^2, where A is the area of the circle, π is a mathematical constant approximately equal to 3.142, and r is the radius of the circle.

In this problem, we are given the diameter of the circle, which is the distance across the circle passing through its center. The radius is half of the diameter, so we can find it by dividing the diameter by 2.

In this case, the diameter is 9 meters, so the radius is 9/2 = 4.5 meters. We then substitute this value into the formula:

A = πr^2

A = 3.142 x (4.5)^2

A = 3.142 x 20.25

A = 63.6175

A ≈ 63.62 square meters

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The given question is incomplete, the complete question is:

Work out the area of the circle where diameter is 9 meter

Take π it to be 3.142 and give your answer to 2 decimal places.

According to the Census Bureau, of the people 21 to 64 years old, 12.3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. The words that look like different answers to one question are "not high school graduates," "graduated high school," "some college," "bachelor's degree," and "advanced degree."

These words all describe different levels of education and could be potential answers to a question about a person's education level. The paragraph describes the educational attainment of people between the ages of 21 and 64. The different percentages represent the proportion of individuals in each education category.

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The final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.

To multiply each term by the LCD, we need to first find the LCD of the given expression. The LCD of the expression is the product of the denominators, which is x(x-4)(x-3).

Now, we can multiply each term by the LCD to get rid of the denominators:

A[x(x-4)(x-3)]/(x) * x(x-4)(x-3) = A(x-4)(x-3)

B[x(x-4)(x-3)]/((x-4)) * x(x-4)(x-3) = B(x)(x-3)

C[x(x-4)(x-3)]/((x-3)) * x(x-4)(x-3) = C(x)(x-4)

Now, we can combine the terms to get the final expression:

A(x-4)(x-3) + B(x)(x-3) + C(x)(x-4) = (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC

So, the final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.

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The amount left over is  $120,499.85.

The present value of the amount invested in the municipal bond and the high yield savings account has to be determined.

Present value = FV ÷ (1 + r)^(nm)

Where:

r = interest rate

m = number of compounding

FV = future value

Present value of the future value in the high yield savings account:

r = 9/4 = 2.25%

m = 4

200,000 ÷ ( 1 + 0.0225)^(4 x 5)

200,000 ÷ (1.0225^20)

= 128,163.29

Present value of the future value of the municipal bond: r = 6.78 / 2 = 3.39%

m = 2

100,000 ÷ (1 + 0.0339)^(2 x 10)

100,000 ÷ (1.0339^20) = $51,336.86

Amount left over = $300,000 - $51,336.86 - 128,163.29 = $120,499.85

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If you put your hand on a hot stove and got burnt, it is a natural response to remove your hand from the stove to prevent further injury. However, if you choose to repeatedly put your hand back on the stove even after being burnt, you will continue to experience pain and potentially cause further damage to your skin and tissues.

Repeatedly exposing yourself to the source of the burn will not change the fact that it is hot and causing damage to your skin. In fact, each time you touch the hot surface, you are likely to make the burn worse, as the heat will continue to damage your skin and tissues.

Additionally, repeated exposure to the hot stove may lead to nerve damage, which can result in a loss of sensation in your hand, making it harder to recognize when you are in danger of burning yourself in the future.

It is important to listen to your body's natural responses to pain and remove yourself from harmful situations. In the case of a burn, it is best to seek immediate medical attention and follow proper first aid procedures to minimize damage and promote healing.

Answer:

28 are red

Step-by-step explanation:

(1/5) are blue.  The rest are red, which would be 4/5 of the total.  (1/5)+(4/5) = 1 or 100%

(1/5)*(35) = 7 are blue

(4/5)*(35 = 28 are red

--------------------

Total = 35 cars

Answer:

We know that cot A = adjacent side / opposite side = 21/20.

Let x be the length of the adjacent side and y be the length of the opposite side.

Using the Pythagorean theorem, we have:

x^2 + y^2 = (20k)^2, where k is some positive constant.

Since angle A is in Quadrant I, x is positive and y is positive. Thus, we can take the square root of both sides to get:

x + y = 20k.

Now, we can use the fact that cot A = adjacent side / opposite side = 21/20 to get:

x/y = 21/20.

Multiplying both sides by y, we get:

x = (21/20)y.

Substituting this into x + y = 20k, we get:

(21/20)y + y = 20k

Simplifying, we get:

(41/20)y = 20k

y = (20k)/(41/20) = (400k)/41

Now, we can use the Pythagorean theorem to find x:

x^2 + y^2 = (20k)^2

(21/20)y^2 + y^2 = (20k)^2

(441/400)y^2 = (20k)^2

y^2 = (400/441)(20k)^2

y = (20k/441)sqrt(441 x 20)

y = (20k/21)sqrt(20)

Therefore, angle A in simplest radical form using a rational denominator is given by:

tan A = y/x = [(20k/21)sqrt(20)] / [(21/20)y] = sqrt(20)/21

A = arctan(sqrt(20)/21)

The graph of the system of inequalities is a circle with center (0,0) and radius of 100 units for the regular version and 2000/21.95 units for the deluxe version.

Inequality in math is a mathematical statement that states two expressions are not equal. It can be written using symbols such as <, >, or ≠. Inequality statements are used to compare values or expressions and to describe ranges of values that satisfy certain conditions.

The salesperson must sell at least 100 units of either the regular or deluxe version and their total sales must be at least $2000 in order to receive the bonus.

The company offers a bonus to salespeople who can meet certain sales goals. This encourages salespeople to be more motivated to sell the product and to increase their overall sales. It also helps the company increase their profits by providing incentives for salespeople to increase their sales. By offering the bonus, the company is able to attract more salespeople who are willing to work hard and reach their sales goals in order to receive the bonus. This allows the company to increase their market share and their profits.

The bonus also helps to retain existing salespeople who might otherwise be tempted to leave the company. By offering the bonus, the company is able to reward loyal salespeople who have consistently performed well and have contributed to the company's success. This helps the company to maintain a stable and productive sales team, which is beneficial for the company's long-term success.

Overall, offering a bonus to salespeople who meet certain sales goals is a beneficial strategy for the company. It encourages salespeople to be more motivated and increase their sales, while also helping the company to attract and retain quality salespeople. This helps the company to grow and increase their profits in the long run.

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Answer is: AC= 9[tex]\sqrt{3}[/tex] Units, AB = 18 units.

Triangles have three interior angles that add up to 180 degrees, and they can be classified based on the lengths of their sides and the measures of their angles.

In ΔABC, angle C is right angle,

so the triangle is right angle triangle;

tan30° = BC/AC

[tex]\frac{1}{\sqrt{3} }[/tex] = 9/AC

AC= 9[tex]\sqrt{3}[/tex] Units

and

Sin 30° = BC/AB

1/2 = 9/AB

AB = 18 units

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I is convergent.

The Comparison Theorem is an important tool in the study of Probability and Statistics, as it allows us to determine the convergence or divergence of improper integrals without directly evaluating them. In this case, we are asked to determine the convergence or divergence of the improper integral I=∫ 2 [infinity] ​ e −x 2 dx using the Comparison Theorem.

1. To justify the inequality e −2x ≥e −x 2 for all x≥2, we can take the natural logarithm of both sides of the inequality to get -2x ≥ -x^2. Since x≥2, we can divide both sides of the inequality by -x to get 2 ≤ x, which is true for all x≥2. Therefore, the inequality e −2x ≥e −x 2 is true for all x≥2.

2. To evaluate ∫ 2 [infinity] ​ e −2x dx, we can use the substitution u=-2x, du=-2dx. This gives us ∫ 2 [infinity] ​ e −2x dx = ∫ -4 [-infinity] ​ (1/2)e^u du = (1/2)(-e^u)|-4 [-infinity] = (1/2)(-e^-4 + e^[infinity]) = (1/2)(-e^-4 + 0) = (1/2)e^-4.

3. To determine if I is convergent or divergent, we can use the Comparison Theorem. Since e −2x ≥e −x 2 for all x≥2, and ∫ 2 [infinity] ​ e −2x dx is convergent, then ∫ 2 [infinity] ​ e −x 2 dx is also convergent by the Comparison Theorem. Therefore, I is convergent.

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Jon's savings before he gave Rick the gift was $600.  An equation to represent this situation: 400 + (1/8)x = 475

To determine Jon's savings before he gave Rick the gift, we can use an equation. Let's represent Jon's savings with the variable x.

According to the problem, Jon gave Rick 1/8 of his savings, which is equal to (1/8)x. We also know that Rick originally had $400 and after receiving the gift, he had $475. So we can write an equation to represent this situation:
400 + (1/8)x = 475

Now, we can solve for x to find out Jon's savings before he gave Rick the gift. First, let's isolate the variable on one side of the equation:
(1/8)x = 475 - 400
(1/8)x = 75

Next, we can multiply both sides of the equation by 8 to get rid of the fraction:
x = 75 * 8
x = 600

So, Jon's savings before he gave Rick the gift was $600.

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The measure of angle KYC, considering the concept of vertical angles, is given as follows:

m < KYC = 69º.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

<KYC and 69º.

As they are opposite by the vertex at the crossing of the two diagonal segments for this problem.

Hence the measure of angle KYC is given as follows:

m < KYC = 69º.

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Exponent laws The abbreviated formula is -2x7y.

This leads to another exponent rule called the Power Rule for Exponents. A power of a power can be made simpler by multiplying the exponents while leaving the base fixed. In this instance, (23)5 equals 215. For any positive number x and integers a and b, (xa)b=xa b holds true.

Exponent laws comprise: Rule of the product of powers: Add the powers together when multiplying like bases. Take off the powers when separating like bases according to the quotient of powers rule. Rule of the power of powers: Add all the powers together when raising a power by another exponent.

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Complete question:

Find the Exponent law of the given formula [tex][(-2xyx^2)x^3]x^2[/tex] .

Answer:

The answer to your problem is, 1130

Step-by-step explanation:

Calculation of work:

discount=40% of 2500

=40/100 x 2500

=1000

discount price=1000

VAT = 13% of 1000

How to find /\:

Percetage graph:

=13/100*1000

=130

price=1000+130

=1130.

Thus, the answer to your problem is, 1130.

Cristiano is said to have racked up around 300 assists in his third year in power.

This estimate is based on the fact that Cristiano has been a prolific passer in his whole career and has frequently improved every season. Assuming he's maintained similar level of assists in his third season and Cristiano has improved season after season, his tally assists in his third year is likely higher than his average of 251 per season.

That's why it is safe to assume that Cristiano completed around 300 passes in his third year, a significant improvement over the previous 2 years. It increase in assists is likely due to Cristiano's increased confidence and comfort in the team, as well as learning more about the club and their plan. All of this together would allow Cristiano to make more passes and become a more efficient player overall.

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The distance between home plate and second base in a Major League Baseball field is approximately 127.28 feet.

The distance from home plate to second base in a major league baseball field is 127 feet and 3⅜ inches, or approximately 127.28 feet. This is because the distance between each base (from home to first, first to second, etc.) is 90 feet, and the diagonal of a square is found by using the Pythagorean theorem: a² + b² = c². In this case, a and b are both 90 feet, so the equation becomes 90² + 90² = c². Simplifying and solving for c gives us c = 127.28 feet. Therefore, the distance from home plate to second base is 127.28 feet.

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Answer:

-24x^8y^6+32x^2y^5

Step-by-step explanation:

Answer:

We can use the concept of proportion to estimate the total number of sweets in the jar.

Let's represent the total number of sweets in the jar by "x". We know that 90 of these are pear drops. So the proportion of pear drops in the jar is 90/x.

Leona takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. So the proportion of pear drops in the sample is 22/70.

We can assume that the proportion of pear drops in the sample is roughly equal to the proportion of pear drops in the jar. Therefore, we can set up a proportion and solve for "x":

90/x = 22/70

Cross-multiplying, we get:

22x = 90 * 70

Dividing both sides by 22, we get:

x = 90 * 70 / 22

Using a calculator, we get:

x ≈ 287

Therefore, an estimate for the total number of sweets in the jar is 287, rounded to the nearest integer.

Answer:

We can use the concept of proportion to estimate the total number of sweets in the jar.

Let's represent the total number of sweets in the jar by "x". We know that 90 of these are pear drops. So the proportion of pear drops in the jar is 90/x.

Leona takes a random sample of 70 sweets from the jar and finds that 22 of these are pear drops. So the proportion of pear drops in the sample is 22/70.

We can assume that the proportion of pear drops in the sample is roughly equal to the proportion of pear drops in the jar. Therefore, we can set up a proportion and solve for "x":

90/x = 22/70

Cross-multiplying, we get:

22x = 90 * 70

Dividing both sides by 22, we get:

x = 90 * 70 / 22

Using a calculator, we get:

x ≈ 287

Therefore, an estimate for the total number of sweets in the jar is 287, rounded to the nearest integer.

Step-by-step explanation:

The perimeter of the base is 32 cm.

The area of the base is 48 cm².

The total surface area of the triangular prism is 1184 cm².

The diagram above is a triangular prism. Therefore, let's find the perimeter of the base, area of the base and surface area of the triangular prism.

Hence,

perimeter of the base = 10 + 10 + 12

perimeter of the base = 20 + 12

perimeter of the base = 32 cm

Area of the base = 1 / 2 bh

where

Therefore,

Area of the base = 1 / 2 × 12 × 8

Area of the base = 48 cm²

Hence,

total surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

total surface area of the triangular prism = 12(8) + 34(10 + 10 + 12)

total surface area of the triangular prism = 96 + 34(32)

total surface area of the triangular prism =96 + 1088

total surface area of the triangular prism = 1184 cm²

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The option that best describes the value 1.5 in the linear equation; u = 0.75·t + 1.5 is option D

D. y-intercept and the initial amount of rain, in inches at midnight

A linear equation is an equation of the form; y = m·x + c, where, m is the slope, and c is the y-intercept of the graph of the equation.

The time at which the analysis of the rainstorm by the meteorologist starts = 10 p. m.

The linear model for the accumulation of rain is; u = 0.75·t + 1.5

The number of hours, t after midnight where; t > 0

The model for the accumulation of rain, indicates that the coefficient of t, which is 0.75 is the rate at which the rain accumulates in inches per hour, therefore, the rain accumulates at a rate of 0.75 inches per hour

The constant term in the linear equation, u = 0.75·t + 1.5, which is the constant, 1.5, is the y-intercept of the graph of the equation.

The y-intercept is the value of the equation, when the input value, the time, t = 0, which is the time at midnight

The 1.5 therefore, indicates that the y-intercept, and the level of the accumulated rain at midnight, when the time, t = 0, which is the initial amount of rain at midnight is 1.5 inches.

The correct option is therefore;

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