16 and 28 geometric mean

The value of each Trigonometric ratio in a right angle triangle given are;  sin X = 4/5 and cos C = 40/41

From the attached image, we can see the triangles to find the trigonometric ratios.

Now, the formula for sin and cos in a right angle triangle is;

sin = opposite/hypotenuse

cos = adjacent/hypotenuse.

Thus;

1) sin X = 32/40 = 4/5

2) cos C = 40/41

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a) The probability that the assembly takes less than 14 minutes is  0.9088.

b) The probability that the assembly takes less than 10 minutes is  0.0912.

c) The probability that the assembly takes more than 14 minutes is  0.0912.

d) The probability that the assembly takes more than 8 minutes is  0.9088.

e) The probability that the assembly takes between 10 and 15 minutes is  0.8176.

a) To find the probability that assembly takes less than 14 minutes, we need to calculate the z-score for 14 minutes using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

z = (14 - 12) / 1.5

z = 2 / 1.5

z = 1.33

Using the z-score of 1.33, we can find the corresponding probability from the standard normal distribution table.

P(Z < 1.33) = 0.9088.

b) For the probability of assembly taking less than 10 minutes, we calculate the z-score:

z = (10 - 12) / 1.5

z = -2 / 1.5

z = -1.33

Using the standard normal distribution table or a calculator, we find the probability P(Z < -1.33) is 0.0912.

c) To find the probability that assembly takes more than 14 minutes, we can find the complement of the probability found.

So, P(X > 14) = 1 - P(Z < 1.33).

= 1 - 0.9088

= 0.0912.

d) For the probability of assembly taking more than 8 minutes, we find the complement of the probability found.

So, P(X > 8) = 1 - P(Z < -1.33).

= 1 - 0.0912

= 0.9088.

e) Probability that assembly takes between 10 and 15 minutes:

To find P(10 < X < 15), we subtract the probability of X < 10 from the probability of X < 15:

P(10 < X < 15) = P(X < 15) - P(X < 10)

Using the z-scores obtained previously, let's assume P(Z < 1.33) = 0.9088 and P(Z < -1.33) = 0.0912.

P(10 < X < 15) = 0.9088 - 0.0912 = 0.8176.

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The time required to assemble an electronic component is normally distributed, with a mean of 12 minutes and a standard deviation of 1.5 minutes. Find the probability that a particular assembly takes:

a less than 14 minutes

b less than 10 minutes

c more than 14 minutes

d more than 8 minutes

e between 10 and 15 m

Answer:

132 ft

Step-by-step explanation:

The radius is 21 ft

We want to find the circumference

C = 2 * pi *r

Letting pi = 22/7

C = 2 * 22/7 * 21

C = 132 ft

Answer:

We want to find the circumference

The probability of the number of people who say auto racing is their favorite sport being more than 37 can be calculated using statistical methods.

This would require information on the total number of people surveyed, the number of people who said auto racing is their favorite sport, and other relevant data.

Depending on the specific scenario, the probability could be estimated or calculated exactly.

However, without this information, it is not possible to provide a specific answer to the question.

Therefore, it is important to have all relevant information and data before calculating probabilities or making any conclusions about the likelihood of an event occurring.

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As per the given correlation, the appropriate null and alternative hypothesis for calculating number of goggles is

H0 : No linear relation

H1 : there is a relation

What is meant by correlation?

In math, correlation is referred as a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

And it is a common tool for describing simple relationships without making a statement about cause and effect.

Based on the given question, a group of scientist randomly selected 20 piknits from the sea-floor and measured their respective weights in grams.

And we also know that, they wanted to know if the weight of the piknits can be used to predict the number of gogles.

Here from the given information, the null hypothesis : H0 : There is no linear relationship between the weight of piknits and the number of goggles

And the Alternative hypothesis : Ha: There is a linear relationship between the weight of piknits and the number of gogles

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Answer:

17. 86 miles

Step-by-step explanation:

Answer: 11 hours and 29 min

Step-by-step explanation:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

The curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 can be found by setting the two equations equal to each other:

x² + y² = y² + z² = 20

The intersection of the two cylinders is a circle.

To determine the radius of this circle, we use either of the two equations and solve for one variable in terms of the other two:

y² + z² = 20y²

= 20 - z²y

= ±sqrt(20 - z²)

If we substitute this expression for y into the equation x² + y² = 25, we can solve for x in terms of z:

x² + (20 - z²)

= 25x²

= 5 + z²x

= ±sqrt(5 + z²)

Thus, the curve of intersection can be expressed parametrically as follows:

r(t) = (x(t), y(t), z(t)) = (sqrt(5 + t²), sqrt(20 - t²), t)for -2sqrt(5) ≤ t ≤ 2sqrt(5)

At the point (3, 4, 2), t = 2.

To find the tangent vector to the curve at this point, we take the derivative of the position vector:

r'(t) = (x'(t), y'(t), z'(t)) = (t/sqrt(5 + t²), -t/sqrt(20 - t²), 1)

at t = 2:r'(2) = (2/sqrt(9), -2/sqrt(16), 1) = (2/3, -1/2, 1)

Finally, we obtain the vector equation of the tangent line by using the point-normal form of the equation of a line:

L(t) = r(2) + t r'(2)L(t)

     = (3, 4, 2) + t (2/3, -1/2, 1)L(t)

     = (2/3)t + 3, (-1/2)t + 4, t + 2

Therefore, a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2) is:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

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Answer:

x=4+ 2root14/4

by using quadratic formula

Answer:

Linear negative association

Step-by-step explanation:

All points are in a line, so it is linear.

As x increases, y decreases. That is a negative association.

Answer: Linear negative association

Answer:

5 days .......

Step-by-step explanation:

Stefan has 4½ cups of oat

He uses 3¼ to make granola

What he has left 4½-3¼ = 1¼

If he feeds ¼of a cup to parrots a day, then he has 5 days feed from 1¼

Calculation 1¼ ÷ ¼

Change to improper fraction

5/4 ÷ 1/4 = 5/4 x 4/1

Ans 20/4 = 5days

The number of cookies prepared in an hour is \(3\frac{27}{32}\) cookies.

Given that, 8 ⅕ cookies can make in 1 ¹/₃ of an hour.

Here, 8 ⅕ can be written as 41/8 and 1 ¹/₃ can be written as 4/3.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Now, unit rate = Number of cookies/Number of hours

= 41/8 ÷ 4/3

= 41/8 × 3/4

= 123/32

= \(3\frac{27}{32}\)

Therefore, the number of cookies prepared in an hour is \(3\frac{27}{32}\) cookies.

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In order to go from figure 1 to figure 2, there are a number of different transformations that can be selected.

First, notice that figure 2 is exactly three times as large as figure 1, therefore, there has been a dilation by a factor of three (3) that took place .

So Let's say that we do the dilation first.

Step 1: Dilation by a factor of "3" using the point (-1, -2) which is one of the vertices of the triangle, for reference. Then, the new triangle would have new coordinaes for the vertices at the points:

(-1, -2) (-1, 1) and (-6, -2)

I am making a drawing to show the change (give me a little time)

So, we see that the dilated triangle is represented by the green one in the image above.

Step 2: we are now going the "reflect the green triangle around the horizontal line y = 2 represented by the blue line . When we reflect the green triangle around that line, we obtain the orange triangle.

Step 3: we are going to do another reflection, this time a reflection around the vertical line x = 1 (noted in purple in the image above). After this, we obtain the triangle in figure 2.

So we

Answer:

You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$

Step-by-step explanation:

You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$

So you pay 4.95x + 3 for your drink and x sandwiches

The algebraic expression 4.95x + 3 can be described as the total cost of a product that has a fixed price of 3 dollars, and an additional price of 4.95 dollars per unit of the product. In this case, x represents the number of units purchased, and the expression represents the total cost of the purchase.

we are given the function f(x) = 1/(1+ x^4), and we need to compute three integrals involving this function. The first integral is over the interval [0, 2π/72], the second integral involves a complex exponential term, and the third integral involves a different complex exponential term.

(a) To compute the integral ∫[0, 2π/72] f(x) dx, we can use standard integration techniques. The function f(x) is rational, so we can decompose it into partial fractions and then integrate each term separately.

(b) To compute the integral ∫[-∞, ∞] -ikx f(k) e^(-tkr) dk, we have an integral over the real line with a complex exponential factor. We can use complex analysis techniques, such as contour integration, to evaluate this integral. The specific contour and residues will depend on the behavior of f(k) and the given exponential factor.

(c) To compute the integral ∫[-∞, ∞] f(k) e^(ikr) dk, we have a similar integral as in part (b), but with a different complex exponential factor. Again, we can use complex analysis techniques to evaluate this integral, taking into account the properties of f(k) and the exponential term.

The specific calculations and techniques used will depend on the properties of the function f(x) and the given integration limits. It is important to carefully evaluate the integrals using appropriate methods to ensure accurate results.

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To show that all three estimators are consistent, we need to demonstrate that they converge in probability to the true population parameter as the sample size increases.

For the three estimators:

$\hat{\theta}_1 = \bar{X}n = \frac{1}{n} \sum{i=1}^{n} X_i$

$\hat{\theta}2 = \frac{1}{n-1} \sum{i=1}^{n} X_i$

$\hat{\theta}_3 = X_n$

To show consistency, we need to show that for each estimator:

$\lim_{n\to\infty} P(|\hat{\theta}_i - \theta| < \epsilon) = 1$

where $\epsilon > 0$ is a small positive value, and $\theta$ is the true population parameter.

Let's consider each estimator separately:

$\hat{\theta}_1 = \bar{X}n = \frac{1}{n} \sum{i=1}^{n} X_i$

By the Law of Large Numbers, as the sample size $n$ increases, the sample mean $\bar{X}_n$ converges to the population mean $\mu$. Therefore, $\hat{\theta}_1 = \bar{X}_n$ is a consistent estimator.

$\hat{\theta}2 = \frac{1}{n-1} \sum{i=1}^{n} X_i$

Similar to estimator 1, as the sample size $n$ increases, the sample mean $\frac{1}{n-1} \sum_{i=1}^{n} X_i$ converges to the population mean $\mu$. Therefore, $\hat{\theta}_2$ is also a consistent estimator.

$\hat{\theta}_3 = X_n$

In this case, the estimator $\hat{\theta}_3$ takes the value of the last observation in the sample. As the sample size increases, the probability of the last observation being close to the population parameter $\theta$ also increases. Therefore, $\hat{\theta}_3$ is a consistent estimator.

(b) To determine which estimator has the smallest variance, we need to calculate the variances of the three estimators.

The variances of the estimators are given by:

$\text{Var}(\hat{\theta}_1) = \frac{\sigma^2}{n}$

$\text{Var}(\hat{\theta}_2) = \frac{\sigma^2}{n-1}$

$\text{Var}(\hat{\theta}_3) = \sigma^2$

Comparing the variances, we can see that $\text{Var}(\hat{\theta}_2)$ is smaller than $\text{Var}(\hat{\theta}_1)$, and both are smaller than $\text{Var}(\hat{\theta}_3)$.

Therefore, $\hat{\theta}_2$ has the smallest variance.

(c) The mean squared error (MSE) of an estimator combines both the bias and variance of the estimator. It is given by:

MSE = Bias^2 + Variance

To compare and discuss the MSE of the estimators, we need to consider both the bias and variance.

$\hat{\theta}_1 = \bar{X}_n$

The bias of $\hat{\theta}_1$ is zero, as the sample mean is an unbiased estimator. The variance decreases as the sample size increases. Therefore, the MSE decreases with increasing sample size.

$\hat{\theta}2 = \frac{1}{n-1} \sum{i=1}^{n} X_i$

The bias of $\hat{\theta}_2$ is also zero. The variance is smaller than that of $\hat{\theta}_1$, as it uses the term $(n-1)$ in the denominator. Therefore, the MSE of $\hat{\theta}_2$ is smaller than that of $\hat{\theta}_1$.

$\hat{\theta}_3 = X_n$

The bias of $\hat{\theta}_3$ is zero. However, the variance is the largest among the three estimators, as it is based on a single observation. Therefore, the MSE of $\hat{\theta}_3$ is larger than that of both $\hat{\theta}_1$ and $\hat{\theta}_2$.

In summary, $\hat{\theta}_2$ has the smallest variance and, therefore, the smallest MSE among the three estimators.

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Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

To solve this inequality, we need to find the values of x that make the expression on the left-hand side greater than or equal to zero.

First, we can look at the factors separately. The factor (x-4)^2 is always non-negative because it is a square. That means it is greater than or equal to zero for all values of x.

The factor (x+3) is positive when x is greater than -3 and negative when x is less than -3.

Now we can use the fact that the product of two non-negative numbers is non-negative. So, for the left-hand side of the inequality to be greater than or equal to zero, we need one of the following:

1. Both factors are non-negative, which means x is greater than or equal to 4 and x is greater than -3.
2. One factor is zero and the other is non-negative. The factor (x-4)^2 can only be zero when x=4, so we need to check if (x+3) is non-negative when x=4. It is not, so x=4 is not a solution.
3. Both factors are zero. This occurs when x=4 and x=-3, but x=-3 is not a solution because (x+3) is negative.

Therefore, the solution to the inequality is x is greater than or equal to 4.

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As per the U.S. population report, the black population is about 13.5% of the total U.S. population.

The black population in the United States refers to the total no people that identify themself as black or African American.

The exact percentage of the black population in the United States can vary based on the source and the methodology used to collect the data, but as of the population report from 2021, it was estimated to be about 13.5% of the total population.

This information can be used to understand the demographic composition of the United States and to help inform decisions about resource allocation, public policy, and other important issues that can affect different populations. it can be also noted that the demographics of a country can change over time, so it is crucial to regularly update this information to ensure that it remains accurate and relevant.

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Answer:

x=5, -3

Step-by-step explanation:

To find the roots, replace y with 0 and solve for x. Hope this helps!

Answer:

Step-by-step explanation:

To express the confidence interval 0.039 < p < 0.479 in the form p ± E, we need to find the midpoint of the interval and half of the width.

The midpoint of the interval is the average of the lower and upper bounds:

Midpoint = (0.039 + 0.479) / 2 = 0.259

The width of the interval is the difference between the upper and lower bounds:

Width = 0.479 - 0.039 = 0.44

Half of the width is obtained by dividing the width by 2:

Half Width = 0.44 / 2 = 0.22

Therefore, the confidence interval 0.039 < p < 0.479 can be expressed as:

p ± E = 0.259 ± 0.22

So, the correct option is:

D. 0.259 ± 0.22

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Answer:

a)   c)   d)    e)

Step-by-step explanation:

a) cross-products are equal; 24 = 24

c) cross-products are equal; 18 = 18

d) cross-products are equal; 30 = 30

e) cross-products are equal; 24 = 24

Answer:

A. 4/3 = 8/6 C. 3/2 = 9/6 D. 5/3 = 10/6 E. 4/2 = 12/6

Average is the best prediction. For the given case, if someone is wanting to  work for Fast Pax, then his salary is most likely to be around $39,500

Arithmetic mean is the best central measure available for representing the values of a data set.  It is also called average of the values of the considered data set.

It serves as one representation of the values of the data set. If for a data set, only its average is given, then we can't say much about the values of the data set, but we can  say that the data values are going to be around that average (average is closest number to its data set's values compared to any other number)

It serves as predicted value(in case no other information of the data is available) of that data set.

Average provides ill information in case of skewed data.

Thus, for the given case, as average annual salary for the Fast Pax is $39,800, so we can say that, the salaries of someone who wants to work for Fast Pax would be around $39,800 most probably.

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Answer:

The data is skewed, so the mean is not a good measure of the data.

A median of $20,000 is probably a better indicator of the salary you would earn.

75% of all employees make less than $25,000 annually.

Step-by-step explanation:

The diameter of one circle is 28 units

Find the diagram shown below:

Considering the semi-circle at the centre.

To get the value of "x"

x + 16  = 22

x = 22 - 16

x = 6

To get the value of "x"

16 +y  = 22

y = 22 - 16

y = 6

Diameter of one of the circle = x + 16 + y

Diameter of one of the circle = 6 + 16 + 6

Diameter of one of the circle = 28

Hence the diameter of one circle is 28 units

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The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Answer:

The answer is 3 2/5 hope this helps :)

Step-by-step explanation:

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

5,670

Explanation:

Given the expression

2(3⁴*5)7

= 2(81*5)*7

= 2(405)*7

= 2 * 405 * 7

= 14 * 405

= 5,670

hence the result of the expression is 5,670