Given: ∠V ≅ ∠Y, bisects ∠VWY. Prove: ∆VWZ ≅ ∆YWZ Look at the figure. Which postulate or theorem proves the triangles are congruent? SSS Postulate AAS Theorem ASA Postulate SAS Postulate

Answer:

1/13

Step-by-step explanation:

Probability of Sarah drawing a letter in her name

= number of letters in her name: S, A, R and H / total number of letters

= 4/26

Probability of drawing an odd number

= odd numbers / total numbers

= 5/10

Combining the above, Probability of her drawing a letter in her name and an odd number = 4/26 * 5/10

= 1/13

Total Alphabetical cards Sarah has ⇢ 26

Total Letters Sarah's name has ⇢ 4

Probability of getting a card with one of the letter in her name ⇢ 4/26

Total numerical Cards Sarah has ⇢ 10

Total odd numbers in those cards⇢5

Probability of getting a card with an odd number⇢ 5/10

probability of her drawing a letter in her name and an odd number⇢ 4/26 x 5/10 = 1/13

Answer:

8

Step-by-step explanation:

AB=DC

BC=AD

BA=CD

CB=DA

The histogram with the narrow peak would be expected to contain more consistent numbers.

This is because the width of a histogram reflects the variability of the data that it represents. A histogram with a wide spread indicates that the data values are spread out and vary greatly, while a histogram with a narrow peak indicates that the data values are relatively consistent and cluster close together.

In a histogram with a widespread, the difference between the highest and lowest data values is large, indicating that the values are inconsistent and vary widely. On the other hand, in a histogram with a narrow peak, the difference between the highest and lowest data values is small, indicating that the values are more consistent and cluster closely together.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer: A

Step-by-step explanation:

Answer:

C. 4

Step-by-step explanation:

Because there is always a 50/50 chance of getting the similar result.

Hope this helps.

Answer:

8

Step-by-step explanation:

If other outcomes occurred it would not be valid.

Answer:

x = 8

Step-by-step explanation:

from the diagram

∠ CXD + ∠ DXE = ∠ CXE ( substitute values )

x² - 4 + 2x - 10 = 7x + 10

x² + 2x - 14 = 7x + 10 ( subtract 7x + 10 from both sides )

x² - 5x - 24 = 0 ← in standard form

(x - 8)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 5 = 0 ⇒ x = - 5

but x > 0 , then x = 8

Answer:

Option A

Step-by-step explanation:

The expression that completes the blank is A. 11  x  w * x 3 = 11  x 3  x  w.

The commutative property is a mathematical concept that states that the order in which we multiply the factors does not affect the product.

According to the commutative property, a mathematical principle, the product is unaffected by the order in which we multiply the integers.

According to the above, the example of a commutative property is:

11  x w x 3 = 11 x  3 x w

This expression is the one with the commutative property because it has the same factors on both sides of the equation in a different order and that does not affect the result.

Therefore, the correct answer is A.

This question is incomplete because you are missing the options, here are the options:

A. 11 x w x 3 = 11 x 3 x w

B. 11 x w x 3 = 11 x w x 3

C. (11 x w) x 3 = 11 x (w x 3)

D. 11 x (w x 3) = (11 x w) + (11 x 3)

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Answer:

neither arithmetic nor geometric

Step-by-step explanation

I got it wrong and assuming they don't have a common ratio/ constant difference  

Answer:

Step-by-step explanation:

True

True

True

False

False

True

Answer:

\(\frac{\sqrt{5} }{5}\)

Step-by-step explanation:

\(\frac{1}{\sqrt{5} }\)  multiply each side by \(\sqrt{5}\) which comes out to \(\frac{\sqrt{5} }{5}\)

Answer:

x^2

Step-by-step explanation:

ax^2 + bx + c is quadratic standard form

Answer:

2, 11, 38

Step-by-step explanation:

Multiply by 3 and then add 5 each time

1st term : 2

2nd term : 2*3 + 5 = 6 + 5 = 11

3rd term : 11*3 + 5 = 33 + 5 = 38

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.

Reason Behind a Biased Estimator

The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a  biased estimator.

Brief Description of Sample Mean Absolute Deviation

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.

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Answer:

x+4≤2x

Step-by-step explanation:

Answer:

Below:

Step-by-step explanation:

y = -0.5x + 2

m = -0.5

b = 2

In a flowchart proof, statements and conclusions are connected with arrows.

In terms of mathematics, a statement is simply any sentence in which it can be verifiably true or false. A statement cannot be a subjective opinion. It must be an objective fact and there must not be any ambiguity involved. A conclusion is also a statement that derives from the first statement made.

As an example, you can have the simple argument "if it rains, then it gets wet outside". So the box on the left would be "it rains" and the box on the right would be "it gets wet outside". An arrow connecting the two shows the logical flow of how the argument is set up.

See the diagram below.

Side note: the box on the left is also considered the antecedent because it comes before the conclusion.

Answer:

40 possible answers

Step-by-step explanation:

20 answers from the 10 true or false questions and 20 answers from the 5 multiple choice questions

Answer:

The number of laps Tonya swam last week were:

Step-by-step explanation:

To understand the ratio, you must know that 3:10 means that each time Tonya swam 3 laps, Randy swam 10 laps, by this reason, to identify the total number of laps you can divide the total difference given in the exercise (84 laps) into the difference indicated by the ratio (10 - 3 = 7 laps):

This number obtained is the number of times the ratio had to be met so that the difference in laps swam was 84. Now, you must multiply the obtained value (12) by the number of laps from Tonya given in the ratio (3):

As you can see, with the calculates, we obtained  36 laps in total. You could also do the iterations 12 times, subtracting the number of turns given by Tonya from the number of turns made by Randy and you would get the same result:

Answer:

75

Step-by-step explanation:

Answer:

Step-by-step explanation:

It can help to understand what the square of a binomial looks like when you are asked to solve a quadratic by completing the square.

  (x -a)² = x² -2ax +a²

In this form, the constant term a² is the square of half the x-coefficient. The x-coefficient and the constant in the binomial have the same sign.

Your quadratic is ...

  x² -12x +21 = 0

It can be easier to complete the square if the given constant term is subtracted from both sides:

  x² -12x = -21

Now, the square can be completed by adding the square of half the x-coefficient: (-12/2)² = (-6)² = 36.

  x² -12x +36 = -21 +36

  (x -6)² = 15 . . . . . . . . the form you want for your answer template

__

Taking the square root gives ...

  x -6 = ±√15

  x = 6 ± √15 ≈ {2.13, 9.87} . . . . solutions to the equation

_____

Additional comment

The form we use for solving by completing the square is only one step away from "vertex form." That is, knowing the vertex of the function graph, we can write the vertex form equation, and find a solution immediately using the complete the square procedure.

  vertex form equation: (x -6)² -15 = 0

  form used for "complete the square" solution: (x -6)² = 15

The n-point DFT of the signal x[n] = ax1[n] + bx2[n] is given by the linear combination of the individual DFTs: X[k] = a * X1[k] + b * X2[k], where X[k] is the n-point DFT of x[n], X1[k] is the n-point DFT of x1[n], X2[k] is the n-point DFT of x2[n], and a and b are constants.

The Discrete Fourier Transform (DFT) is a mathematical transformation that converts a discrete-time signal from the time domain to the frequency domain. When we have two signals x1[n] and x2[n] with their respective n-point DFTs X1[k] and X2[k], we can combine them in a linear manner to obtain the DFT of their sum or scaled versions.

In the case of x[n] = ax1[n] + bx2[n], where a and b are constants, we can apply the DFT to both sides of the equation. By linearity property of the DFT, the DFT of the left-hand side (x[n]) can be expressed as the sum of the DFTs of the individual terms on the right-hand side (ax1[n] and bx2[n]).

Thus, the n-point DFT of x[n], denoted as X[k], is given by the linear combination of the individual DFTs:

X[k] = a * X1[k] + b * X2[k],

This equation states that each frequency bin of the DFT of x[n] is obtained by multiplying the corresponding frequency bin of the DFTs of x1[n] and x2[n] by their respective constants (a and b), and then summing these contributions.

In summary, the DFT of a linear combination of signals can be computed by taking the corresponding linear combination of their individual DFTs.

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Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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Answer:2

Step-by-step explana2tion:

AS]