Prove that
△
ABC
is a right triangle. Select the correct answer from each drop-down menu.

According to a recent survey of 1,001 adult Canadians, 27 percent of respondents indicated that they do not want to be unionized.

The survey of 1,001 adult Canadians asked respondents about their preference regarding unionization. Out of the total respondents, 27 percent expressed that they do not want to be unionized. This percentage represents the proportion of individuals who indicated a lack of interest or desire to be part of a labor union.

It is important to note that without additional information about the survey methodology, sample representation, and any potential biases, the result should be interpreted within the context of the survey's limitations. The percentage obtained from the survey reflects the preferences of the respondents in the sample but may not necessarily represent the opinions of the entire population of adult Canadians.

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Answer:

5.2312 × \(10^{8}\)

\( = 9( - 6 + 8i) - 3i( - 6 + 8i) \\ = - 54 + 72i + 15i - 24 {i}^{2} \\ = - 54 + 87i - 24 {i}^{2} \)

ATTACHED IS THE SOLUTION

The left-endpoint sum (L) and right-endpoint sum (R) for the function f(x) = -x(x-1) on the interval [2, 5] can be calculated using n subintervals. The sum involves dividing the interval into smaller subintervals and evaluating the function at the left and right endpoints of each subinterval. The exact values of L and R will depend on the number of subintervals chosen.

To compute the left-endpoint sum (L), we divide the interval [2, 5] into n subintervals of equal width. Let's say each subinterval has a width of Δx. The left endpoints of the subintervals will be 2, 2 + Δx, 2 + 2Δx, and so on, up to 5 - Δx. We evaluate the function f(x) = -x(x-1) at these left endpoints and sum up the results. The value of L will depend on the number of subintervals chosen (n) and the width of each subinterval (Δx).

Similarly, to compute the right-endpoint sum (R), we use the right endpoints of the subintervals instead. The right endpoints will be 2 + Δx, 2 + 2Δx, 2 + 3Δx, and so on, up to 5. We evaluate the function at these right endpoints and sum up the results. Again, the value of R will depend on the number of subintervals (n) and the width of each subinterval (Δx).

To obtain more accurate approximations of the definite integral of f(x) over the interval [2, 5], we would need to increase the number of subintervals (n) and make the width of each subinterval (Δx) smaller. As n approaches infinity and Δx approaches zero, the left and right sums converge to the definite integral of f(x) over the interval.

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Answer:

The correct option is;

e. 2500

Step-by-step explanation:

The formula for sample size is given by the following formula;

\(n = \dfrac{z^2 \times \hat p(1 - \hat p)}{\epsilon ^2}\)

At 95%, z = 1.96

ε = Margin of error = 0.02 = 2%

Finding the sample size, n, given only the margin of error is by the following formula;

Margin of error = 100/√n

Therefore, we have;

2 = 100/√n

√n = 100/2 = 50

n = 50² = 2500

Therefore, the correct option is e. 2500.

Answer:

The correct option is;

e. 2500

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

Answer:A he is correct because the inner circle is a dilation of the outer circle

Step-by-step explanation: just did the test

The statement "He is correct because the inner circle is a dilation of the outer circle" is the best explanation.

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables.

The radius of the inner circle is 2 units, while the radius of the outer circle is 5 units.

Since dilations provide similar figures because multiplying by the scale factor yields proportionate sides while keeping the angle measure and form constant.

Troy is accurate if he claims the two circles are similar.

Hence, the statement (A) "He is correct because the inner circle is a dilation of the outer circle" is the best explanation.

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Answer:

Casey paid $2.75 for each gallon

Step-by-step explanation:

Ok, so do you want to know the amount of money per gallon?

Here is how you do it if you want to know:

20 ÷ 55

2.75

Casey paid $2.75 for each gallon.

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The correct option for the large bag contains marbles:

The given question:

marbles in the bag:

40 blue marbles

8 green marbles

16 yellow marbles

21 white marbles

One marble is selected by Tyra.

Then, the correct option are-

A: There is a two to one chance that the marble she chooses will be yellow rather than green.

16 yellow marbles = 2* 8 green marbles

B: Compared to all the other colors combined, the stone she chooses is more likely to be blue.

40 blue marbles have the highest number.

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The complete question is-

A large bag contains the following marbles: •

40 blue marbles

8 green marbles

16 yellow marbles

21 white marbles

Tyra selects a marble from the bag at random. Based on the information, which statement is true?

A The marble she selects is twice as likely to be yellow as it is to be green.

B.The marble she selects is more likely to be blue than all the other colors combined.

C. The marble she selects is equally likely to be yellow or white

D. The marble she selects is three times as likely to be white as it is to be green.​

Answer:

8

Step-by-step explanation:

2x = 16

2x/2 = 16/2

x = 8

Answer:

2 time 4 gives you 16

plz check

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

x=6 y=2

Step-by-step explanation:

Solve for the first variable in one of the equations and then plug into the other.

The total number of possible ways to create a license plate with 2 letters followed by 3 numbers if no repetition is 4,680,00.

To calculate the number of ways to create a license plate with 2 letters followed by 3 numbers, we need to consider two separate parts: the number of ways to choose the two letters, and the number of ways to choose the three numbers. Since no repetition is allowed, we have to take this into account in both parts.

For the first part, we have 26 choices for the first letter and 25 choices for the second letter, since we cannot choose the same letter twice.

For the second part, we have 10 choices for each of the three numbers. Again, we cannot choose the same number twice, so we have to decrease the number of choices by 1 for each subsequent number.

Thus, the total number of ways to create a license plate with 2 letters followed by 3 numbers is:

26 x 25 x 10 x 9 x 8 = 468,000

If no repetition of characters is allowed, then the number of possible ways to create a license plate with 2 letters followed by 3 numbers can be calculated as follows:

There are 26 choices for the first letter (A-Z).

There are 25 choices for the second letter (since no repetition is allowed).

There are 10 choices for the first number (0-9).

There are 9 choices for the second number (since no repetition is allowed).

There are 8 choices for the third number (since no repetition is allowed).

Therefore, the total number of possible ways to create a license plate with 2 letters followed by 3 numbers if no repetition is allowed is:

26 x 25 x 10 x 9 x 8 = 4,680,00

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Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

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Answer:

A

Step-by-step explanation:

The answer would be "The point where three medians of triangle intersect.

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Answer: A

Step-by-step explanation:

the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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1 dozen = 12 so 15/12 is 1.25

which means 1 fruit tart is $1.25

The number  300 can be written as 300/1 as a quotient of integers to show that it is rational.

A rational number is a number of the form p/q, where q not equal to 0 and p  and q must be co-primes.

To write a number in the form of quotient of integer, we write it as , where p/q.

Here,  300 can be written as  300/1 or 600/2 .

But we should also take care that p and q must be co-primes.

Co-primes are the pairs of numbers that have only one common factor which is 1.

So, 300 can be written as 300/1

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Answer:

A= 2w^2 + 11w +12

Step-by-step explanation:

(w + 4)(2w + 3) = l x b = A

2w^2 + 3w +8w +12 = A

A= 2w^2 + 11w +12

Answer:

105 degrees

Step-by-step explanation:

sum of angles in triangle is 180 degrees

11x-5+6x+5+x = 180

simplify this to get 18x=180

180/18 = 10 = x

plug in 10 for x

11(10) - 5

110-5

105

Answer:

Step-by-step explanation:

The quadratic equation in factored form:

We have:

Substitute them to get:

Converting this into standard form:

It (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

In statistics, a simple random sample (or SRS) is a subset of people (a sample) picked at random from a larger group of people (a population), all with the same probability.

It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people.  

An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that can be used in combination with other, more sophisticated sampling techniques.

So, in the given situation of Mr. Goodmain and with all the information given we can conclude that it cannot be concluded that there is a statistically significant difference in Mr. Goodman’s evaluations and the History Department’s.

Therefore, it (B) cannot be determined that there is a statistically significant difference between Mr. Goodman's ratings and those of the History Department in the context of Mr. Goodmain and with all the material provided.

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Complete question:

Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale – with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1’s, 15% 2’s, 34% 3’s, and 41% 4’s. Mr. Goodman sets a goal to outscore these numbers. At the end of the year, he takes a random sample of his evaluations and finds 11 1’s, 14 2’s, 47 3’s, and 53 4’s. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Departments?

Hypotheses:

H0: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

H1: There is (no difference /difference) in Mr. Goodman’s evaluations and the History Department’s.

Enter the test statistic - round to 4 decimal places.

Enter the p-value - round to 4 decimal places.

Can it be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s?

a. Yes

b. No

Answer:

1/3

Step-by-step explanation:

On left side its 6:2 so 6/2 is 3

the scale factor is 1/3 because figure is a reduction

hope it helps ;)

Answer:

1/3

Step-by-step explanation:

The side that's highest is 9 units, the the image its 3. 3/9= 1/3

The power series ∑n\(=2^ \infty^n(9x)^n[ln(7n)]^n\\\) converges for all real numbers x. To determine the radius and interval of convergence for the power series ∑n\(=2^{ \infty}^n(9x)^n[ln(7n)]^n\\\), we can use the ratio test.

The ratio test states that if we have a power series Σ \(a_nx^n,\) then the radius of convergence, R, is given by:

R = lim (n→∞) |a_n/a_(n+1)|

Let's apply the ratio test to the given power series:

\(a_n = (-1)^n(9x)^n[ln(7n)]^n\\a_{(n+1)} = (-1)^{(n+1)}(9x)^{n+1}[ln(7(n+1))]^{n+1}\)

Now, let's find the ratio:

\(|r| = |a_n/a_{n+1}| = |(-1)^n(9x)^n[ln(7n)]^n / (-1)^{n+1}(9x)^{n+1}[ln(7(n+1))]^{n+1}|\)

Simplifying, we get:

\(|r| = |(9x/(9x)) * [(ln(7n)/ln(7(n+1)))]^n|\\\\|r| = [(ln(7n)/ln(7(n+1)))]^n\)

Taking the limit as n approaches infinity:

\(\lim_{n \to \infty}[(ln(7n)/ln(7(n+1)))]^n = \lim_{n \to \infty}[ln(7n+1) / ln(7n)]^n\\\)

Since the limit evaluates to a value less than 1, the series converges for all x-values.

Therefore, the radius of convergence is infinite, and the interval of convergence is (-∞, +∞).

As a result, the power series ∑n\(=2^ \infty^n(9x)^n[ln(7n)]^n\\\) converges for all real numbers x.

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Answer:

a. 14 + x

b. There are several ways to write this, 6y, 6(y)

Step-by-step explanation:

Look for key words when you do these types of questions!

For addition, add, sum, greater than, etc.

For multiplication, product, times, etc.

For subtraction, difference, less than, minus, etc.

And for division, look for quotient, divide, etc.

Hope this helps : )

Answer:

5

Step-by-step explanation:

The length of AB is 37 units where AC is 12 units and CB is 35 units.

The Pythagorean theorem is a fundamental theorem in mathematics that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

The right angle is at C, then we can use the Pythagorean theorem to find the length of AB, where AB is the hypotenuse of the right triangle with sides AC and CB.

According to the Pythagorean theorem, the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.

So, we have:

AB² = AC² + CB²

Substituting the given values, we get:

AB² = 12² + 35²

Simplifying, we get:

AB² = 144 + 1225

AB² = 1369

When we square the two sides, we obtain:

AB = √(1369)

AB = 37

Therefore, the length of AB is 37 units.

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Answer:

B

Step-by-step explanation:

2x - 11 = k

     +11     +11

2x/2 = k + 11/2

x = k + 11/2