why does 16 to the power of 0 equal 1?

The expected value of y = cos(xÏ) is 0 and the expected value of y = sin(xÏ) is also 0, due to the symmetry of the random variable x.

The expected value (mean) of y = cos(x Ï) is 0.

The expected value (mean) of y = sin(x Ï) is also 0.

Since the random variable x is symmetric, the probability of both positive and negative values cancel out, resulting in an expected value of 0 for both cosine and sine functions.

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Applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

The inscribed quadrilateral conjecture states that the opposite angles in any inscribed quadrilateral in a circle measures up to 180 degrees.

Thus:

43° + m∠A = 180°

m∠A = 180 - 43

m∠A = 137°

Thus, applying the inscribed quadrilateral conjecture, the measure of m∠A = 137°.

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Answer:

  A.  XV

Step-by-step explanation:

The letters identifying the shortest side of ΔMNP are the last (P) and first (M) of the designator for that triangle. The corresponding side of ΔVWX will be identified by the last (X) and first (V) letters of that triangle's name. Hence the segment of interest is XV.

Jeffery's monthly loan payments for the loan will be $515.19.

To calculate the monthly loan payments for Jeffrey, we can use the formula for calculating the monthly payment of a loan. The formula is:

Monthly Payment = (Principal * Monthly Interest rate) / (1 - (1 + Monthly Interest rate) ^ (-n))

In this case, Jeffrey's principal is $30,000, the annual interest rate is 5.2%, and the loan term is 6 years. Since Jeffrey will graduate in 4 years, we need to adjust the loan term accordingly. The monthly interest rate can be calculated by dividing the annual interest rate by 12, and the number of monthly payments will be multiplied by 4.

Using these values in the formula, we can calculate the monthly loan payment for Jeffrey.

Monthly Payment = (30000 * 0.052/12) / (1 - (1 + 0.052/12) ^ (-24))

Monthly Payment = $515.19

Answer:

they have always the same

Step-by-step explanation:

Therefore, after plotting the points on the graph

What is the trigonometry?

Trigonometry states that the trigon means 'triangle', and the metry means 'metron' is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Here given angles are:-

[tex]y=sin(x)[/tex] and [tex]y=cos(x)[/tex]

Draw the graph

Hence, after plotting the points on the graph is:-

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The decimal 2.267 is equivalent to the simplified fraction 2267/1000.

To express the decimal 2.267 as a simplified fraction, we can consider the place values of each digit. The decimal portion .267 can be written as the fraction 267/1000 since there are three decimal places. Combining this with the whole number 2, we get:

2.267 = 2 + 267/1000.

To simplify this mixed number, we first find a common denominator, which is 1000. We convert the whole number 2 to an equivalent fraction with this denominator: 2 = 2000/1000. Now, we can add the fractions:

2 + 267/1000 = 2000/1000 + 267/1000 = 2267/1000.

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1, yielding the simplified fraction:

2267/1000.

In summary, 2.267 can be expressed as the simplified fraction 2267/1000.

The question probable may be:

Write the following 2.267 in simplified fraction.

If the measure of angle ACB = 30 and the measure of angle A = 80, the measure of angle B is 70 degrees.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

If the measure of angle ACB = 30 and the measure of angle A = 80, To find the measure of angle B

We know that the angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

∠ACB + ∠A + ∠B = 180

30 + 80 + ∠B = 180

∠B = 180 - 110

∠B = 70

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The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.

To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:

Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students

Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)

Applying the values from the given information:

Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9

Standard deviation of combined list

= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)

= 13.1

The diagonal of the rectangle can be calculated by using the Pythagorean Theorem , because the diagonal and the two sides , length and width, of the rectangle , makes a right triangle .

Now we have the measure of length and width and we have to find the measure of diagonal

So according to the Pythagorean theorem

[tex] d^2 = a^2 +b^2 [/tex]

where , d is the diagonal , a is the length and b is the width

lets plug the values

[tex] d^2 = 37^2 +60^2 [/tex]

[tex] d^2 = 1369+3600 [/tex]

[tex] d^2 = 4969 [/tex]

Taking square root on both sides

d=70.49 Inches

d=70.5 inches

hence the length of one of the braces is 70.5 inches

-4u +2v

= -4<-6, 1> +2<-5, 2>

= <(-4)(-6)+2(-5), (-4)(1) +2(2)>

= <14, 0>

The appropriate choice is ...

... B) <14, 0>

To find the result of -4u + 2v, calculate -4u and 2v separately, then add the results together to get <-34, 0>.

To find -4u + 2v, we first need to calculate -4u and 2v separately and then add them together.

Therefore, the answer is: -34, 0.

Answer:

[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.

Step-by-step explanation:

We are given four option and need to choose correct inequality for given graph.

In graph, we can see two line

Red line: It is horizontal solid line passing through (0,-1) and shaded region above the line.

Equation of line: y≥-1

Blue line: It is slant dotted line passing through origin and (-2,1)

Equation of line: [tex]y<-\frac{1}{2}x[/tex]

System of inequalities represented by the graph.

[tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex]

Thus, [tex]y\leq -1 \text{ and }y<-\frac{1}{2}x[/tex] are system of inequalities is represented by the graph.

We want to find the number of positive integers not exceeding 1000 that are either the square or the cube of an integer.

We will get that there are 38 of these.

First, the squares:

To get the number of square numbers not exceeding 1000, we need to find the largest integer that when squared is equal or smaller than 1000.

This is given by:

√1000 = 31.6

Then the largest square number smaller than 1000 is given by:

31^2 = 961

From this, we can conclude that there are 31 integers not exceeding 100 that are the square of an integer.

For the cubes we do the same thing:

∛1000 = 10

The largest cube number that meets the condition is:

10^3 = 1000

Then there are 10 cube numbers that meet the condition.

Now we need to find the common numbers in bot groups (this is, numbers that are a cube and a square of two integers and that are smaller than 1000).

The numbers that meet this condition are:

1)

1^2 = 1

1^3 = 1

64)

4^3 = 64

8^2 = 64

81)

9^3 = 279

27^2 = 729

These 3 numbers are in both groups, so we are counting them twice, thus we need to subtract 3 to the final result, in order to avoid counting the same number two times.

Then the total number of positive integers not exceeding 1000 that are either the square or the cube of an integer is:

31 + 10 - 3 = 38

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Using the mode concept, according to the stem-and-leaf plot, the missing value is of 71.

It is the value that appears the most times in the data-set. When it's unique, the mode is the value that appears the most often in a data set and it can be used as a measure of central tendency, like the median and mean.

Here, we have,

In this problem, following the key format of the stem-and-leaf plot, disconsidering the missing value, the values 71 and 64 each appear 3 times.

However, the mode is 71, meaning that is should appear more times than 64, which means that the missing value is of 71.

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complete question:

This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value of the unknown data item?

Using the hypergeometric distribution, it is found that there is a 0.0923 = 9.23% probability that 4 CPAs will be selected.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, there are 15 accountants, 9 are CPAs and 4 will be selected, hence N = 15, k = 9, n = 4.

The probability that 4 CPAs will be selected is P(X = 4), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,15,4,9) = \frac{C_{9,4}C_{6,0}}{C_{15,4}} = 0.0923[/tex]

0.0923 = 9.23% probability that 4 CPAs will be selected.

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To calculate the probability of selecting a pregnant subject from the 99 test subjects, the exact number of pregnant subjects in the group is needed. Without this data, the probability cannot be determined.

To ascertain the probability of randomly selecting a pregnant subject from a group of 99 test subjects, additional information is required regarding how many subjects are actually pregnant within the group. Without this information, we cannot compute an exact probability.

However, if we had data—let's say 15 out of the 99 subjects are pregnant—the probability would then be calculated using the formula for probability, which is the number of favorable outcomes divided by the total number of possible outcomes. In this scenario, the probability would then be 15/99.

Final answer:

Without specific information on the number of pregnant subjects among the 99 test subjects, it's impossible to compute the exact probability of randomly selecting a pregnant subject.

Explanation:

To answer the question about the probability of randomly selecting a pregnant subject from the 99 test subjects, we would need to know the number of pregnant subjects within the group. Without that information, we cannot calculate the exact probability. However, if we had that information, the probability (P) of selecting a pregnant subject would be calculated as P = (Number of Pregnant Subjects) / (Total Number of Subjects), which in this case is 99.

This is an example of a probability question that falls under the broader subject of mathematics, specifically within the topic of probability and statistics commonly covered at the high school level.