If the point A(1,2), B(k1,2)and C(6,7)are the vertice of triangle having B=90deg ,find value of k

Answer:

2.28 or 2.2

Step-by-step explanation:

46 angle and 18x+5 angle make a z formation and the interior is always the same

46 -5 =41

41/18 =2.2777

round it off and you get 2.2

you can always verify it by putting it in the place of x

Answer:

27

Step-by-step explanation:

divide 81 by 3 :p

Answer:

Step-by-step explanation:

81nBdivided by 3 is 28

The correct answer is option 2. Yes, the mean of the sample proportions is 0.6, which is the same as the population proportion.

To determine if the sample proportion is an unbiased estimator, we need to check if the mean of the sample proportions equals the population proportion. In this case, the population proportion of officers who are younger than 18 is given as 0.6. The sample proportions for all possible samples of size 2 are calculated and given in the table.
To calculate the mean of the sample proportions, we add up all the proportions in the table and divide by the total number of samples, which is 9.
Mean of sample proportions = (0 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 1 + 1 + 1) / 9 = 0.6
Since the mean of the sample proportions equals the population proportion, we can say that the sample proportion is an unbiased estimator.

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We have the following:

In this case, what we must do is calculate the weighted average, as follows:

The mean salary is $28112

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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Answer:

hi daisy can we be maths buddies helping each other with math

Answer:

152 inches

Step-by-step explanation:

P = 2 l + 2 w,

We know the length is 48 and width is 28

P = 2 *48 + 2 *28

P = 96+56

P =152

Given that,

→ Length is 48 inches.

→ Width is 28 inches.

We have to find,

The perimeter of the tabletop.

The formula we use,

→ P = 2(L) + 2(W)

Then find the perimeter of the tabletop,

→ 2(L) + 2(W)

→ (2 × 48) + (2 × 28)

→ 96 + 56

→ 152 inches

Thus, the perimeter is 152 inches.

Answer:

9000

Step-by-step explanation:

1km=1000m

9×1000=9000

6x + 4y = 50 for (3, y)

Let's plug 3 in for x

6(3) + 4y = 50

Simplify the left side.

18 + 4y = 50

Subtract 18 from both sides.

4y = 32

Divide both sides by 4

y = 8

C is the correct answer

Answer:

30/182 = 15/91.

Step-by-step explanation:

PROBABILITY: the likelihood of an event.

There are a total of 14 shirts in the basket.

Of the 14, 8 (8/14) of them are white, and 6 (6/14) of them are black.

The probability of picking a black shirt is 6 in 14, or 6/14.

The probability of picking a white shirt is 8 in 14, or 8/14.

WITHOUT REPLACING: This means that you take one without putting it back. (There will be one less).

6/14 × 5/13 = 30/182.

30/182 = 15/91.

The probability of randomly picking a black t-shirt from the basket, and then another one without putting the first one back is 15/ 91.

Probability refers to a possibility that deals with the occurrence of random events.

There are a total 14 shirts in the basket.

Out of the total of 14, 8 (8/14) of them are white, and 6 (6/14) of them are black.

The probability of picking a black shirt = 6/14.

The probability of picking a white shirt = 8/14.

The probability of randomly picking a black t-shirt from the basket, and then another one without putting the first one back

= 6/14 × 5/13

= 30/182.

= 15/91.

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Answer:

No, the teacher did not survey a representative sample of the students in the school. The sample of 30 students that he surveyed had a much higher percentage of students already enrolled in art classes (81%) compared to the overall percentage of students in the school who are studying art (11%). This indicates that the sample may have been biased and not representative of the entire student population. In order to obtain a representative sample, the teacher should have taken steps to ensure that the sample of students he surveyed was representative of the overall student population in terms of characteristics such as enrollment in art classes, age, gender, and other relevant factors.

The correct answer would be an option (D) Associative Property of Addition.

The associative property of addition is a rule which states that when adding three or more numbers, we can arrange them in any configuration, and the resultant sum is unaffected by how they are arranged.

(a + b) + c = a + (b + c)

Given Line 1 and Line 2 are shown below.

Line 1 as :

⇒ (3 + 9) + 5

Line 2 as :

⇒ 3 + (9 + 5)

According to Associative Property of Addition,

Line 1 as :

(3 + 9) +5 equals 12 + 5 which equals 17

Line 2 as :

3 + (9 + 5) equals 3 + 14 which equals 17

The correct answer would be an option (D) Associative Property of Addition.

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son 30 y si sumas con 20 son 96

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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The probability that none of the three adults get news from the newspaper is 0.378.

To understand why, let's break down the problem step by step.

Step 1: Calculate the total number of ways to choose 3 adults out of the 70 surveyed. This can be done using the combination formula:

C(n, r) = n! / (r!(n - r)!)

In this case, n = 70 (the total number of adults surveyed) and r = 3 (the number of adults being chosen).

C(70, 3) = 70! / (3!(70 - 3)!)

Step 2: Calculate the number of ways to choose 3 adults who don't get news from the newspaper. Since there are 12 adults who get news from the newspaper, we need to choose 3 adults from the remaining 70 - 12 = 58 adults who don't get news from the newspaper.

C(58, 3) = 58! / (3!(58 - 3)!)

Step 3: Calculate the probability by dividing the number of ways to choose 3 adults who don't get news from the newspaper by the total number of ways to choose 3 adults:

P = C(58, 3) / C(70, 3)

Step 4: Substitute the values and calculate the probability:

P = (58! / (3!(58 - 3)!)) / (70! / (3!(70 - 3)!))

P = (58! / (3!55!)) / (70! / (3!67!))

P = (58! * 67! * 3! * 3!) / (3! * 55! * 70!)

Many terms in the numerator and denominator will cancel out, leaving us with:

P = (58 * 57 * 56) / (70 * 69 * 68)

P = 0.378

So, the probability that none of the three adults get news from the newspaper is 0.378.

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Complete Question

A news organization surveyed 70 adults. Each said he or she gets news from only one source. Here is a summary of their sources of news. Source of news Number of adults 22 Radio 12 Newspaper 13 Television 23 Internet Three of the adults from the survey are selected at random, one at a time without replacement. What is the probability that none of the three adults get news from the newspaper? Do not round your intermediate computations. (Round your final answer to three decimal places)

Answer:

the probibiltiy that your roll 3 is 1/6  and 5 is 1/6 that is sepreate if its both together it is i belive 2/6

Step-by-step explanation:

Answer:

0.427

Step-by-step explanation:

Standard error for the sampling distribution refers to the standard deviation of the samples taken from a population. The standard error equals the standard deviation divided by the square root of the sample size

The probability of customers who drink tea (p) = 24% = 0.24, the sample size of customers (n) = 300.

Standard error = \(\frac{\sigma}{\sqrt{n} }\) where σ is the standard deviation.

\(\sigma=\sqrt{np(1-p)}\)

Standard error = \(\frac{\sigma}{\sqrt{n} }= \frac{\sqrt{np(1-p)} }{\sqrt{n} } =\sqrt{\frac{np(1-p)}{n} } =\sqrt{p(1-p)}=\sqrt{0.24(1-0.24)} =0.427\)

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

STEP 2: Simplify the given expression

Hence, the equivaent expression using same bases is:

Answer:

Step 2.

Step-by-step explanation:

Step 2. In step 1, they correctly wrote the factors of the polynomial as (x+6) and (x-2). But then in step 2, (x+6) suddenly became (x-6) and (x-2) became (x+2), which is incorrect.

The answers in step 3 should have been -6 and  2.

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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The margin of error for the confidence interval is approximately 0.014, indicating that the estimate of the proportion of dissatisfied customers could be off by approximately plus or minus 0.014. This means that we can be 95% confident that the true proportion of dissatisfied customers falls within the range of the estimated proportion ± 0.014.

(a) To find the sample size needed to achieve a margin of error of about 0.015 with a 95% confidence level, we can use the formula for sample size calculation for proportions:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = sample size

Z = critical value (corresponding to the desired confidence level)

p = estimated proportion of the population

E = margin of error

In this case, the estimated proportion of dissatisfied customers is 0.17, and the desired margin of error is 0.015. Since we want a 95% confidence level, the critical value can be obtained from a standard normal distribution table. The critical value for a 95% confidence level is approximately 1.96.

Plugging these values into the formula, we have:

n = (1.96^2 * 0.17 * (1-0.17)) / 0.015^2

n ≈ 1901.63

Therefore, the sample size needed is approximately 1902.

(b) If 25% of the sample say they are not satisfied, we can calculate the margin of error using the following formula:

MoE = Z * sqrt((p * (1-p)) / n)

Where:

MoE = margin of error

Z = critical value (corresponding to the desired confidence level)

p = proportion of the sample

n = sample size

Using the same critical value of 1.96 for a 95% confidence level and plugging in the values:

MoE = 1.96 * sqrt((0.25 * (1-0.25)) / 1902)

MoE ≈ 0.014

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A. Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

B. The recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

(a) If Manager B always truthfully reports the state of the economy (s = 0.7), Manager A would send a recommendation that minimizes their disutility Ua. In this case, Manager A wants the decision to be 0.4, so they would recommend a decision of 0.4 to the principal.

(b) In a Nash equilibrium, both managers strategically make their recommendations based on their own utility. Manager A wants to minimize their disutility Ua, which increases as the decision deviates from 0.4. Manager B wants to minimize their disutility UB, which increases as the decision deviates from 0.7.

To find the Nash equilibrium, we need to consider the recommendations made by both managers simultaneously. Let's denote the recommendations as rA (from Manager A) and rB (from Manager B). The principal's decision, d, would be the average of the recommendations, so d = (rA + rB) / 2.

Given that both managers strategically choose their recommendations, they will aim to minimize their disutility. In this case, Manager A would recommend a decision of 0.4 (as it minimizes Ua), and Manager B would recommend a decision of 0.7 (as it minimizes UB). Therefore, the recommendations in the Nash equilibrium would be rA = 0.4 and rB = 0.7.

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There are 846720 different values possible for the sum of xyx and yxy.

Let's denote the three digits of xyx as a, b, and c, such that xyx = 100a + 10b + c, and the three digits of yxy as d, e, and f, such that yxy = 100d + 10e + f. Note that x and y are distinct non-zero digits, so a, b, c, d, e, and f are all distinct non-zero digits.

The sum of xyx and yxy is (100a + 10b + c) + (100d + 10e + f), which simplifies to 100(a+d) + 20(b+e) + (c+f).

We want to find how many different values are possible for the sum. Since a, b, c, d, e, and f are all distinct non-zero digits, we can consider each of them separately.

For a given value of a, there are 9 choices for d (since d cannot be equal to a), and once we have chosen d, there are 8 choices for e (since e cannot be equal to either a or d). Similarly, there are 7 choices for f (since f cannot be equal to a, d, or e).

So, for a fixed value of a, the number of possible values of the sum is the number of possible values of (100(a+d) + 20(b+e) + (c+f)), which is simply the number of possible values of (20(b+e) + (c+f)), since 100(a+d) is fixed.

There are 8 choices for b (since b cannot be equal to a), and once we have chosen b, there are 7 choices for c (since c cannot be equal to either a or b). Similarly, there are 6 choices for e (since e cannot be equal to either a, d, or b), and 5 choices for f (since f cannot be equal to either a, d, e, or c).

Therefore, the total number of possible values of the sum is:

9 × 8 × 7 × 8 × 7 × 6 × 5 = 846720

Therefore, there are 846720 different values possible for the sum of xyx and yxy.

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Answer:

It is NOT a function because when putting a vertical line at a point of a graph it crosses 2 points.

Step-by-step explanation:

Answer:

The measure is the measure that it is you forgot the picture

Step-by-step explanation:

Answer:

A is the answer

Step-by-step explanation:

To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.

a. Probability that X > 85:

To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.

First, let's calculate the z-score:

z = (X - μ) / σ

z = (85 - 100) / 10

z = -15 / 10

z = -1.5

Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.

Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).

b. Probability that X < 80:

Similarly, we'll calculate the z-score for X = 80:

z = (X - μ) / σ

z = (80 - 100) / 10

z = -20 / 10

z = -2

Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.

Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).

c. Probability that X < 90 or X > 130:

To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.

For X < 90:

z = (90 - 100) / 10

z = -10 / 10

z = -1

Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.

For X > 130:

z = (130 - 100) / 10

z = 30 / 10

z = 3

Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.

Since these events are mutually exclusive, we can add their probabilities:

P(X < 90 or X > 130) = P(X < 90) + P(X > 130)

P(X < 90 or X > 130) = 0.1587 + 0.0013

P(X < 90 or X > 130) = 0.1600

Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?

To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.

For the left tail:

z = invNorm(0.005)

z ≈ -2.576

For the right tail:

z = invNorm(0.995)

z ≈ 2.576

Now we can find the corresponding X-values:

X1 = μ + z1 * σ

X1 = 100 + (-2.576) * 10

X1 = 100 - 25.76

X1 ≈ 74.24

X2 = μ + z2 * σ

X2 = 100 + 2.576 * 10

X2 = 100 + 25.76

X2 ≈ 125.76

Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).

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The height of the heater is 12.84 feet. The solution has been obtained by using Pythagoras theorem.

What is Pythagoras theorem?

Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.

We are given that a stainless-steel patio heater is shaped like a square pyramid.

The length of one side of the base is 2 feet and the slant height is 13 feet.

So, using Pythagoras theorem, we get

⇒(Height)² = (Slant height)²- (Base)²

⇒(Height)² = (13)²- (2)²

⇒(Height)² = 169 - 4

⇒(Height)² = 165

⇒Height = √165

⇒Height = 12.84

Hence, the height of the heater is 12.84 feet.

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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