Trigonometry review applications

I need help with 15-18

The cumulative probabilities for the given probability distribution were calculated, and the median of the discrete random variable was found to be 20.

To find the median, we need to find the smallest value of the random variable for which the cumulative probability equals or exceeds 0.5.

The cumulative probabilities are:

(≤0) = 0.02

(≤5) = 0.07

(≤10) = 0.15

(≤15) = 0.31

(≤20) = 0.58

(≤25) = 1

The cumulative probability is the sum of the probabilities of all events that have an outcome less than or equal to a given value. For example, the cumulative probability for the event of collecting 5 dollars or less is the sum of the probabilities for collecting 0 dollars and 5 dollars, which is 0.02 + 0.05 = 0.07. Similarly, the cumulative probability for the event of collecting 10 dollars or less is the sum of the probabilities for collecting 0 dollars, 5 dollars, and 10 dollars, which is 0.02 + 0.05 + 0.08 = 0.15. The same process is used to calculate the cumulative probabilities for all other values. The median is the smallest value of the random variable for which the cumulative probability is greater than or equal to 0.5.

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Answer:

[tex]\boxed{8-6i}[/tex]

Step-by-step explanation:

First, we developed the square binomial [tex](-3+\mathrm{i})^2[/tex].

[tex]\implies (-3+\mathrm{i})(-3+\mathrm{i})\\9-3\mathrm{i}-3\mathrm{i}+i^2\\9-6\mathrm{i}+\mathrm{i}^2[/tex]

Remember the next product:

[tex]i^2= \mathrm{i} \times \mathrm{i} = -1[/tex]

then:

[tex]9-6\mathrm{i}+ (-1)\\8-6i[/tex]

Hope it helps

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:

[tex]tan(x)=\frac{4}{3}[/tex]

Step-by-step explanation:

In the unit circle,

- [tex]cos(a)=\frac{x}{r}[/tex] where [tex]a[/tex] is the degree measure, [tex]x[/tex] is the x-coordinate of the triangle, and [tex]r[/tex] is the radius of the circle

- [tex]sin(a)=\frac{y}{r}[/tex] where [tex]a[/tex] is the degree measure, [tex]y[/tex] is the y-coordinate of the triangle, and [tex]r[/tex] is the radius of the circle

Thus, since tangent is equal to sine over cosine, we can simplify our knowledge to:  [tex]tan(a)=\frac{sin(a)}{cos(a)}=\frac{y}{x}[/tex]

In this problem, [tex]sin(x)=\frac{4}{5}[/tex]. We can conclude from our previous knowledge that [tex]y=4[/tex] and the radius is 5.

Similarly, [tex]cos(x)=\frac{3}{5}[/tex], which means [tex]x=3[/tex] and the radius is the same, at 5.

Since we know that [tex]x=3[/tex] and [tex]y=4[/tex], we can find the value of  [tex]tan(x)[/tex] by using the formula [tex]tan(x)=\frac{y}{x}[/tex] and plug in the numbers.

Therefore, [tex]tan(x)=\frac{4}{3}[/tex].

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The amount Angela earned this month is $2,618.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

Angela's earnings = percentage commission x worth of goods sold

[tex]11\% \times 23,800[/tex]

[tex]0.11 \times 23,800 = \bold{\$2618}[/tex]

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Answer:

P=2(l+w)=2·(9+10)=38ft

1. The equation for the line, which is tangent to the lemniscate at the point P is y = -√3x + (5/4 + √3/8). The equation for the line which is tangent to the lemniscate at Q is y = (-5/3)x + 11/3.

The pace at which a function is changing at a specific point is known as its derivative. It shows the angle at which the tangent line to the curve at that location slopes. A key idea in calculus, the derivative can be utilised to tackle a range of issues, such as curve analysis, rates of change, and optimisation.

The tangent line to the lemniscate at point P, is determined using the derivative of the function.

(x² + y²)² = 4(x² - y²)

Taking the derivative on both sides we have:

2(x² + y²)(2x + 2y(dy/dx)) = 8x - 8y(dy/dx)

dy/dx = (x² + y²)/(y - x)

Substituting  P= (√5/8, √3/8) for the x and y we have:

dy/dx = (√5/8)² + (√3/8)²) / (√3/8 - √5/8) = -√3

Thus, the slope of the tangent line at point P is -√3.

Using the point slope form:

y - y1 = m (x - x1)

Substituting the values we have:

y - (√3/8) = -√3(x - √5/8)

y = -√3x + (5/4 + √3/8)

Hence, equation for the line, which is tangent to the lemniscate at the point P is y = -√3x + (5/4 + √3/8).

Bonus question:

The equation of tangent for the lemniscate at point Q = (2,1) is:

dy/dx = (2² + 1²)/(1 - 2) = -5/3

Using the point slope form:

y - 1 = (-5/3)(x - 2)

y = (-5/3)x + 11/3

Hence, equation for the line which is tangent to the lemniscate at Q is y = (-5/3)x + 11/3.

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Answer: 16.5 gallons of water.

Step-by-step explanation:

If it was me. I would be setting up as a table to keep my work organized.

So first we find how much 1 minute is.

15g : 10m

15/10 : 10m/10

1.5g : 1m

Then I multiply how many minutes there are.

1.5g x 11 : 1m x 1

16.5g : 11m

And there we find the answer of 16.5 gallons.

Happy Solving

Answer:16.5

Step-by-step explanation:

Answer:

a) To find the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25, we need to integrate the given density function over the region where X1 ≤ 0.5 and X2 ≥ 0.25.

P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫∫(x1,x2) f(x1,x2) dxdy

where the limits of integration are:

0.25 ≤ x2 ≤ 1

0 ≤ x1 ≤ 0.5

Substituting the given density function:

P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 ∫0^0.5 (x1 + x2) dx1 dx2

Evaluating the inner integral:

P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(x1^2/2) + x1x2] |0 to 0.5 dx2

Simplifying the expression:

P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(0.125 + 0.25x2)] dx2

Evaluating the upper and lower limits:

P(X1 ≤ 0.5, X2 ≥ 0.25) = [0.125x2 + 0.125x2^2] |0.25 to 1

Substituting the limits:

P(X1 ≤ 0.5, X2 ≥ 0.25) = [(0.125 + 0.125) - (0.03125 + 0.015625)]

Solving for the final answer:

P(X1 ≤ 0.5, X2 ≥ 0.25) = 21/64

Therefore, the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25 is 21/64.

b) To find the probability that X1 + X2 is less than or equal to 1, we need to integrate the given density function over the region where X1 + X2 ≤ 1.

P(X1 + X2 ≤ 1) = ∫∫(x1,x2) f(x1,x2) dxdy

where the limits of integration are:

0 ≤ x1 ≤ 1

0 ≤ x2 ≤ 1-x1

Substituting the given density function:

P(X1 + X2 ≤ 1) = ∫0^1 ∫0^(1-x1) (x1 + x2) dx2 dx1

Evaluating the inner integral:

P(X1 + X2 ≤ 1) = ∫0^1 [(x1x2 + 0.5x2^2)] |0 to (1-x1) dx1

Simplifying the expression:

P(X1 + X2 ≤ 1) = ∫0^1 [(x1 - x1^2)/2 + (1-x1)^3/6] dx1

Evaluating the integral:

P(X1 + X2 ≤ 1) = [x1^2/4 - x1^3/6 - (1-x1)^4/24] |0 to 1

Substituting the limits:

P(X1 + X2 ≤ 1) = (1/4 - 1/6 - 1/24) - (0/4 - 0/6 - 1/24)

Solving for the final answer:

P(X1 + X2 ≤ 1) = 1/8

Therefore, the probability that X1 + X2 is less than or equal to 1 is 1/8.

Answer:

x > 2

Hope this helps!

Step-by-step explanation:

3x - 4 > 2

3x - 4 ( + 4 ) > 2 ( + 4 )

3x > 6

3x ( ÷ 3 ) > 6 ( ÷ 3 )

x > 2

Answer:

Let Haley be represented as x

Now Mateo has 8 more coins than haley

Mateo = 8 + x

total number of coins is Mateo coins and Haley coins.

x + 8 + x

2x + 8

The probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.

The sampling distribution of the sample mean follows a normal distribution with a mean of 120 and a standard deviation of 10/sqrt(90) = 1.0541 months (using the formula for the standard deviation of the sample mean).

To find the probability that the mean of a sample of 90 computers would be greater than 117.13 months, we can standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard deviation of sample mean) = (117.13 - 120) / 1.0541 = -2.6089

Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score greater than -2.6089 is approximately 0.9955.

Therefore, the probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.

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Answer:

yes.

Step-by-step explanation:

cause yes.

The values of function f(x) positive, and negatives are (-infinity, infinity )

A function is a procedure or link that connects every element of one non-empty set A to at least one element of another non-empty set B. The phrases "domain" and "co-domain" are used in mathematics to define a function f between two sets, A and B. The constraint F = (a,b)| is satisfied by all values of a and b.

In the case of the question,

f (x) = x²

f (x) will be positive for all x values. As a result of the function:

x² = x × x

That is, when any number or integer is multiplied by itself, the result is positive. (For example, - - = + and + + = +)

As a result, f (x) = x2 will be positive for (,).

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Answer:

O = { -4,-3,-2,-1,0,-1 }

The smallest that will qualify the window opening per the code is 0.71

What is rectangular?

A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Here, we have

Given: a basement bedroom must have a window with an opening area of at least 5.7 square feet per the international residential code. A rectangular basement window opening 0.75 meters wide.

First, we convert square feet into square meters.

5.7 square feet = 0.53 square meters

Now,

0.53 / 0.75 = 0.71

Hence, the smallest that will qualify the window opening per the code is 0.71

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Answer:

136 units

Step-by-step explanation:

All sides are equal in a rectangle:

Value of b : 16-8 = 8 units

h = 13-7 = 6 units.

So Area of triangle= bh/2 = 8*6/2 = 24 units

Area of rectangle = lb = 16*7 = 112 units

So Area of figure= 112+24 units = 136 units

The polynomial expression (−4b² + 8b) + (−4b³ + 5b² – 8b) when evaluated is −4b³ + b²

We can start by combining like terms.

The first set of parentheses has two terms: -4b² and 8b. The second set of parentheses also has three terms: -4b³, 5b², and -8b.

So we can first combine the like terms in the set of parentheses:

(−4b² + 8b) + (−4b³ + 5b² – 8b) = −4b³ + b²

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Check the picture below.

[tex]\cfrac{3^2}{4^2}=\cfrac{27}{A}\implies \cfrac{9}{16}=\cfrac{27}{A}\implies 9A=432\implies A=\cfrac{432}{9}\implies A=48[/tex]

Answer:

1025

Step-by-step explanation

The formula to find the sum of the first n terms of an arithmetic sequence is

Sn = n/2 * [2a1 + (n-1)d]

Where

a1 = the first term of the sequence

d = the common difference between consecutive terms

n = the number of terms we want to sum

Substituting the given values,  we get

a1 = 5

d = 3

n = 25

S25 = 25/2 * [2(5) + (25-1)3]

= 25/2 * [10 + 72]

= 25/2 * 82

= 25 * 41

= 1025

Our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.

A set of propositional formulae, sometimes referred to as a propositional theory, can be satisfiable in terms of propositional logic by having the quality of being true or untrue according to a certain interpretation or model. If there is at least one interpretation that makes all of a set of formulae true, the set is said to be satisfiable.

Using the proof by contradiction we have:

Assume that I U{—A} is satisfiable.

Then, by definition of satisfiability, every formula in the set I U{—A} is true in M.

Since I = A, every formula in I is also in A. Therefore, every formula in I is true in M, since A is true in M.

Consider the formula —A, which is in {—A}. Since M satisfies {—A}, —A is true in M.

But this contradicts the fact that A is true in M, since —A is the negation of A.

Therefore, our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.

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The correct statement that compares the distributions is:

D On average, nonsmokers weighed 13 lbs less than smokers.

What is the variability?

Variability refers to the amount of spread or dispersion in a set of data. It is a measure of how much the data values in a sample or population differ from each other.

One commonly used measure of variability is the standard deviation, which is the square root of the variance. The variance is the average of the squared differences from the mean.

Looking at the graph, we can see that the center of the distribution of smokers is around 178 lbs, while the center of the distribution of nonsmokers is around 165 lbs. This means that, on average, nonsmokers weigh less than smokers.

Option A is incorrect because the range is not a good measure of variability, and it does not necessarily mean that there is more variability in the weights of nonsmokers.

Option B is incorrect because the graph clearly shows that nonsmokers weigh less on average than smokers.

Option C is incorrect because we cannot make any conclusion about half of the smokers weighing more than all of the nonsmokers from the graph.

Option E is incorrect because the graph shows that the variability in the weights of smokers is greater than that of nonsmokers.

Hence, The correct statement that compares the distributions is:

D On average, nonsmokers weighed 13 lbs less than smokers.

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As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.

The area of mathematics known as probability is concerned with analysing the results of random events. It represents a probability or likelihood that a specific occurrence will occur. A number in 0 and 1 is used to represent probability, with 0 denoting an event's impossibility and 1 denoting its certainty. In order to produce predictions and guide decision-making, probability is employed in a variety of disciplines, such science, finance, economics, architecture, and statistics.

given

Given that there are 12 red marbles and a total of 24 marbles in the jar, the likelihood of choosing the first red marble is 12/24.

There are 11 red marbles and a total of 23 marbles in the jar after choosing the first red marble.

As a result, the likelihood of choosing a second red marble is 11/23.

We compound the probabilities to determine the likelihood of both outcomes occurring simultaneously (i.e., choosing two red marbles):

P(choosing 2 red marbles) = (12/24) x (11/23) = 0.2609, which is roughly 0.26.

As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.

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Answer:

3r^2+10r+3

Step-by-step explanation:

First, 6.7 % can be written in decimal form as 0.067  (6.7 / 100 = 0.067).

Let's use the variable x to represent the number of copies sold to date.

Then we can write and solve the following equation to represent 6.7% of the total sold to date:

0.067 • x = 33600

You can solve this equation by dividing both sides of the equation by 0.067:

0.067 • x  =  33600

0.067             0.067

x = 501493

To date, 500000 copies would have been sold rounded to the nearest whole.

Answer:

you just add a 0 at the end of the answer of what 32 divided by 4 is, so in this case 320 divided by 4 is 80

Step-by-step explanation:

32 divided by 4 is 8.

320 divided by 4 is 80.

To get from 32 to 320 all you need is a 0 at the end, so you can just add the 0 the end of the answer. This means you're going from an 8, to an 80.

OR

Another way you can look at it is 32 multiplied by 10 to get 320. So you need to mutiple your answer by 10 to get the right answer.

32*10=320

8*10=80

Hope this helps!

Answer:

The average temperature on the Equator is 137°F warmer than the average temperature at the South Pole.

76°c

Step-by-step explanation:

The perimeter is 27 feet and the area is 35 square feet

From the question, we have the following parameters that can be used in our computation:

The figure

The perimeter is the sum of tthe side lengths

So, we have

Perimeter = 7.5 + 6 + (6 - 2.5) + 4 + 2.5 + 3.5

Evaluate

Perimeter = 27

The area is calculated as

Area = 6 * 3.5 + 4 * (6 - 2.5)

Evaluate

Area = 35

Hence, teh area is 35 square feet

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