Solve the triangle using the law of cosines

16^1/5 = 2^4/5 .. & .. 8^3/4 = 2^9/4

____________

2^4/5 × 2^x = 2^9/4

2^16/20 × 2^x = 2^45/20

2^[ ( 16/20 ) + x ] = 2^45/20

16/20 + x = 45/20

x = 45/20 - 16/20

x = 29/20

Answer:

f = 6

Step-by-step explanation:

Plug in what you know then solve:

f = d + 1

f = 5 + 1

f = 6

The evaluated integral is (7/4) (π - (3√3)/6) (rounded to an appropriate decimal approximation based on the given values of π and √3).

To evaluate the integral ∫∫(7/2 cos(x)) dV, where the region of integration is given by V: 1 ≤ c ≤ 2 and 0 ≤ x ≤ cos⁻¹(2c-1), we can reverse the order of integration.

Step 1: Write the integral with reversed order of integration:

∫∫(7/2 cos(x)) dc dx

Step 2: Determine the limits of integration for the reversed order. The variable c now varies from 1 to 2, and x varies from 0 to cos⁻¹(2c-1). Therefore, the integral becomes:

∫[1,2] ∫[0,cos⁻¹(2c-1)] (7/2 cos(x)) dx dc

Step 3: Integrate with respect to x first. The integral with respect to x is straightforward:

∫[1,2] [sin(x)] [0,cos⁻¹(2c-1)] (7/2) dc

Step 4: Evaluate the inner integral:

∫[1,2] [sin(cos⁻¹(2c-1))] (7/2) dc

Step 5: Simplify the inner integral using the trigonometric identity sin(cos⁻¹(u)) = √(1 - u²):

∫[1,2] [√(1 - (2c-1)²)] (7/2) dc

Step 6: Integrate with respect to c:

(7/2) ∫[1,2] [√(1 - (2c-1)²)] dc

Step 7: Evaluate the integral:

Using the trigonometric substitution u = sin(t), du = cos(t) dt, and the limits change to t: π/6 ≤ t ≤ π/2.

(7/4) ∫[π/6, π/2] [√(1 - sin²(t))] cos(t) dt

Step 8: Simplify the integrand:

(7/4) ∫[π/6, π/2] [cos²(t)] dt

Step 9: Apply the double-angle formula for cosine:

(7/4) ∫[π/6, π/2] [(1 + cos(2t))/2] dt

Step 10: Split the integral into two separate integrals:

(7/4) [∫[π/6, π/2] (1/2) dt + ∫[π/6, π/2] (cos(2t)/2) dt]

Step 11: Integrate each term separately:

(7/4) [(t/2) + (sin(2t)/4)] evaluated from π/6 to π/2

Step 12: Substitute the limits and simplify:

(7/4) [((π/2)/2 + (sin(2(π/2))/4) - ((π/6)/2) - (sin(2(π/6))/4)]

Step 13: Simplify further:

(7/4) [(π/4 + 0 - π/12 - (1/4)(√3/2))]

Step 14: Simplify and calculate the final value:

(7/4) [(π/4 - π/12 - (√3/8))]

= (7/4) [(3π - π - 3√3)/12]

= (7/4) [(2π - 3√3)/12]

= (7/4) (π - (3√3)/6)

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The population of interest in this case is (d) All of the answer options are correct. It includes all veterinarians, all veterinarians treating large animals, and all veterinarians in the United States treating large animals, including horses.

The population of interest in this study is defined as all veterinarians in the United States who treat large animals, including horses. This population includes all individuals who fit this criteria, regardless of their location or any other specific characteristics.

The researchers wanted to gather information about the prevalence of using nonsteroidal anti-inflammatory drugs (NSAIDs) for treating lameness in horses among veterinarians in the United States. To do this, they obtained a list of all veterinarians who treat large animals, including horses, and sent questionnaires to each of them.

The response rate refers to the percentage of veterinarians who completed and returned the questionnaires out of the total number of questionnaires sent. In this case, the response rate was 40%, meaning that 40% of the veterinarians who received the questionnaires responded to them.

By surveying a representative sample of veterinarians, the researchers can gather information and make inferences about the larger population of veterinarians in the United States who treat large animals, including horses. The data collected from the survey can provide insights into the widespread use of NSAIDs for treating lameness in horses and contribute to the overall understanding of veterinary practices in this context.

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In a survey project, an outcome variable refers to the variable that represents the main focus or result of interest in the study.

In a survey project, the outcome variable, otherwise known as the dependent variable, represents the main focus or result of interest.

It is the variable researchers seek to measure or predict based on the collected data. The purpose of an outcome variable is to provide insights into the specific aspect being studied, enabling researchers to understand relationships between independent variables and the outcome.

Analyzing the outcome variable allows for drawing conclusions, identifying patterns, and determining the impact of various factors. It serves as a crucial metric for evaluating success, making informed decisions, and drawing meaningful conclusions from the survey findings.

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The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.

Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx

where f(x) is the probability density function of X.

Similarly, E(X²) = ∫[0,∞] x²f(x) dx

We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx

Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)

E(X²) = 2/λ².

The exponential distribution is a continuous probability distribution that is widely used in probability theory and statistics. In probability theory, an exponential random variable is a continuous random variable that represents the waiting time between events in a Poisson process.

Suppose X is an exponential random variable. We have to show that E(X²) = 2/λ². We can show this by using the definition of expectation that is, E(X) = ∫[0,∞] xf(x) dx

where f(x) is the probability density function of X.

Similarly, E(X²) = ∫[0,∞] x²f(x) dx

We know that the probability density function of an exponential distribution with parameter λ is given by f(x) = λe^(-λx)So, E(X²) = ∫[0,∞] x²λe^(-λx) dx

Using integration by parts, we have ∫[0,∞] x²λe^(-λx) dx= [-x²e^(-λx)/λ] + [2xe^(-λx)/λ²] + [(-2/λ³)e^(-λx)]∞ 0= (2/λ²)Therefore, the main answer to this question is E(X²) = 2/λ².

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Answer:

x < -2 ?

Step-by-step explanation:

Answer: the answer is 56

Step-by-step explanation: since the f(x) is -7 it would be 9 times -7 then minus 7 and get the answer.

The standardized test statistic is 12.961

To test the claim that σ = 2.38.7 with n - 12, a = -0.05 and 52-32.4,

we need to calculate the standardized test statistic.

The appropriate response is 12.961.

So, the standardized test statistic is calculated as follows:

`x = (n - 1)s² / σ²`

Where `n` is the sample size, `s` is the sample standard deviation, and `σ` is the population standard deviation.

`n = 12, s = 52 - 32.4 = 19.6, and σ = 2.38.7`

Then, `x² = (12 - 1)(19.6)² / (2.38.7)² = 12.961`

Therefore, the appropriate response is 12.961`.

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Answer:

0.333333

Step-by-step explanation:

0.333 yards are in one foot

Answer:

i believe your answer is.

4,789,658,950

Step-by-step explanation:

A quadratic function with leading coefficient 1 and roots of p can be expressed as f(x) = (x - p)(x - p), which simplifies to f(x) = x^2 - 2px + p^2.

To construct a quadratic function with leading coefficient 1 and roots of p, we utilize the relationship between the roots and the factors of a quadratic equation. Since p is a root, the factors of the quadratic function would be (x - p) and (x - p). By multiplying these factors together, we obtain the quadratic function f(x) = (x - p)(x - p). Simplifying further, we can expand the expression:

f(x) = (x - p)(x - p) = x^2 - px - px + p^2 = x^2 - 2px + p^2

Hence, the quadratic function with leading coefficient 1 and roots of p is given by f(x) = x^2 - 2px + p^2. This form allows for easy identification of the coefficients and reveals that the constant term of the quadratic is p^2.

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Answer:

how many brain cells do you have compared to the average person?

Step-by-step explanation:

(a)  Explanation:  In order to prove that X and Y are dependent random variables, we need to show that: pX,Y(x,y)≠pX(x)pY(y) when (x,y) ∈ T which means the joint probability of X and Y is not equal to the product of the marginal probability of X and Y.

For (x,y) ∈ T, pX,Y(x,y) = P (X=1, Y=y) = 1+y

But pX(x) = P(X=1) = Σ pX,Y(1, y) = Σ (1+y)

where the summation is taken over all y for which (1, y) ∈ T. For (1,1) ∈ T,

we get pX,Y(1,1) = 2 and pX(1) = Σ pX,Y(1,y) = 2 + 3 = 5. So, pX,Y(1,1) ≠ pX(1)pY(1) which implies that X and Y are dependent random variables.

(b) E[XY] = Σ Σ xy pX,Y(x,y) where the summation is taken over all x and y for which pX,Y(x,y) > 0.

Substituting the values, we get, E[XY] = Σ Σ xy (1+y) where the summation is taken over all (x,y) ∈ T.

So, E[XY] = (1+1) (1+1) + (1+2) (1+2) + (1+3) (1+3) = 2*2 + 3*4 + 4*6 = 2 + 12 + 24 = 38.

(c) Covariance of X and Y can be determined as follows: Cov(X,Y) = E(XY) - E(X)E(Y)Now, E(X) = Σ x pX(x) and E(Y) = Σ y pY(y)

Substituting the values, we get E(X) = 5/9 and E(Y) = 20/9

Therefore, Cov(X, Y) = E(XY) - E(X)E(Y) = 38 - (5/9) (20/9) = 38 - 100/81 = 998/81.

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Answer:

5

Step-by-step explanation:

3x -12 = -36

-36 ÷ -3 = 12

-7 + 12 = 5

Answer:

The value of -7 + 3(-12) ÷ (-3) is 5

Step-by-step explanation:

First: -7 + -36 ÷ (-3)

Second: -7 + 12

Third: = 5

Therefore your value of this equation is 5.

your welcome.

The proportion of the low-income group who are social networking users is approximately 0.6928, and the proportion of the high-income group who are social networking users is approximately 0.6464.

a) To find the proportions, we divide the number of social networking users in each income group by the total number of respondents in that group. For the low-income group, the proportion is 300/433 ≈ 0.6928. For the high-income group, the proportion is 353/546 ≈ 0.6464.

b) The difference in proportions is obtained by subtracting the proportion of the high-income group from the proportion of the low-income group. The difference is approximately 0.6928 - 0.6464 = 0.0464.

c) The standard error of the difference can be calculated using the formula SE = √[(p1(1-p1)/n1) + (p2(1-p2)/n2)], where p1 and p2 are the proportions of social networking users in each group, and n1 and n2 are the sample sizes of each group. Plugging in the values, we get SE ≈ √[(0.6928(1-0.6928)/433) + (0.6464(1-0.6464)/546)] ≈ 0.0348.

d) To construct a confidence interval for the difference between the proportions, we can use the formula CI = (difference ± critical value × SE). For a 99% confidence level, the critical value can be found using a standard normal distribution table, which is approximately 2.576. Plugging in the values, we get the 99% confidence interval ≈ (0.0464 ± 2.576 × 0.0348) ≈ (0.0464 ± 0.0685).

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(i) The uniform and normal distribution for chromium is 2.4927 and 16.5762. (ii) The uniform and normal distribution for Barium is 0.0031 and 0.3323. (iii) The uniform and normal distribution for Fluoride is 0.0289 and 0.0167

For each substance, the standard deviation o is estimated by assuming uniform distribution and normal distribution. The uniform distribution standard deviation is computed using the formula as follows:

o = (b-a) / √12

where

a is the minimum value,

b is the maximum value.

The normal distribution standard deviation is calculated using the formula as follows:

o = (b - a) / 6.

Estimate the standard deviation o for each substance. Round your answers to 4 decimal places. Substance Chromium Barium Fluoride Uniform Distribution. The range of contaminant levels for chromium is from 0.45 to 8.61. The minimum value is 0.45 and the maximum value is 8.61.

(i) Chromium

Uniform distribution

o = (b-a) / √12

  = (8.61 - 0.45) / √12

  = 2.4927

  ≈ 2.4927 (rounded to 4 decimal places)

Normal Distribution

The maximum value for chromium is 100 and the minimum value is 0.45. Thus, the standard deviation o for chromium using normal distribution is:

o = (b-a) / 6

  = (100 - 0.45) / 6

  = 16.5762

  ≈ 16.5762 (rounded to 4 decimal places)

(ii) Barium

Uniform Distribution

The range of contaminant levels for barium is from 0.006 to 0.018. The minimum value is 0.006 and the maximum value is 0.018.

Thus, the standard deviation o for barium using uniform distribution is:

o = (b-a) / √12

  = (0.018 - 0.006) / √12

  = 0.0031

  ≈ 0.0031 (rounded to 4 decimal places)

Normal Distribution

The maximum value for barium is 2 and the minimum value is 0.006. Thus, the standard deviation o for barium using normal distribution is:

o = (b-a) / 6

  = (2 - 0.006) / 6

  = 0.3323

  ≈ 0.3323 (rounded to 4 decimal places)

(iii) Fluoride

Uniform Distribution  

The range of contaminant levels for fluoride is from 1.04 to 1.14. The minimum value is 1.04 and the maximum value is 1.14. Thus, the standard deviation o for fluoride using uniform distribution is:

o = (b-a) / √12

  = (1.14 - 1.04) / √12

  = 0.0289

  ≈ 0.0289 (rounded to 4 decimal places)

Normal Distribution

The maximum value for fluoride is 1.14 and the minimum value is 1.04. Thus, the standard deviation o for fluoride using normal distribution is:

o = (b-a) / 6

  = (1.14 - 1.04) / 6

  = 0.0167

  ≈ 0.0167 (rounded to 4 decimal places).

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Complete Question:

The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean.

For each substance, estimate the standard deviation σ by using one of the methods shown in Table 8.11 in section 8.8. (Round your answers to 4 decimal places.)

(i) The uniform and normal distribution is Chromium.  

(ii) The uniform and normal distribution is Barium.  

(iii) The uniform and normal distribution is Fluoride.

Answer:

E Z

10

Step-by-step explanation:

15 = 1.5t

so t = 15/1.5

      = 10

Answer: t = 10

1. Switch sides

- 1.5t = 15

2. Multiply both sides by 10

- 15t = 150

3. Divide both sides by 15

4. Simplify

t = 10

what inequality??????

There are 40,320 different ways the race with 8 runners can be completed.

To determine the number of different ways a race with 8 runners can be completed, we can use the concept of permutations.

In a race with no tie, the order in which the runners finish matters. We want to find the number of permutations of 8 runners.

The formula to calculate permutations is given by n!, where n represents the number of items being permuted.

In this case, there are 8 runners, so the number of different ways the race can be completed is:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

Each permutation represents a unique arrangement of the runners crossing the finish line. By considering the order of finish for each runner, we account for all possible outcomes in the race.

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Answer:

C. 672

Step-by-step explanation:

Answer:

C) 672

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

57%

Step-by-step explanation:

FORMULA:LESS/TOTAL × 100%

=52/92 × 100%

=56.52 %

ROUND OFF TO NEAREST WHOLE NUMBER

56.52%=57%

(because the 5 after the (.) is near 1)

Answer:

x = 19.5   or 19 1/2

Step-by-step explanation:

cos 41 = 14.7/x

x = 19.5

Answer:

? is there a option?

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

6x+7

6(5)+7

37

Answer:

Lololololo9lolo9lkiujyhgdfbhjkifewkjuhgsdvcgfh

Step-by-step explanation: