Using composition of functions, determine if the two functions are inverses of each other.

The probability that a newly arrived email which does mention "free gift card", is not spam is 0.0165.

Let S be the event that an email is spam, and let F be the event that an email mentions "free gift card". We want to find P(S' | F), the probability that the email is not spam given that it mentions "free gift card".

We can use Bayes' theorem to find P(S' | F):

P(S' | F) = P(F | S') P(S') / P(F)

We can calculate each of these probabilities as follows:

P(F | S') = the probability that a non-spam email mentions "free gift card". From the problem, we know that this probability is 0.005 (i.e., 99.5% of non-spam emails do not mention "free gift card").

P(S') = the probability that an email is not spam. From the problem, we know that this probability is 0.4 (i.e., 60% of emails are spam, so 40% are not spam).

P(F) = the probability that an email mentions "free gift card". This can be calculated using the law of total probability:

P(F) = P(F | S) P(S) + P(F | S') P(S')

= 0.20 × 0.60 + 0.005 × 0.40

= 0.121

In the first term, we use the given probability that 20% of spam emails mention "free gift card". In the second term, we use the probability that 0.5% of non-spam emails mention "free gift card".

Plugging these values into Bayes' theorem, we get:

P(S' | F) = 0.005 × 0.4 / 0.121 ≈ 0.0165

Therefore, the probability that a newly arrived email which does mention "free gift card" is not spam is approximately 0.0165 or 1.65%.

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Answer:

just get the cube root of 614

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Answer:

41-50

Step-by-step explanation:

Answer: 41-50

Step-by-step explanation:

It is the lowest one so it occurred less frequently.

Hope this helps :)

the 1st one goes to 2 and the 2nd one goes to 3 the 3rd one goes to 1 the and so on

Answer:

(a) 0.90

(b) 0.99

(c) 0.999

(d) Yes

Step-by-step explanation:

A particular detection system has a 0.90 probability of detecting a missile attack.

Let X = number of detection system that detects a missile attack.

The random variable X follows a Binomial distribution with probability of success as, p = 0.90.

(a)

Compute the probability that a single detection system will detect an attack as follows:

\(P(X=1)={1\choose 1}(0.90)^{1}(1-0.90)^{1-1}\\=1\times 0.90\times 1\\=0.90\)

(b)

Compute the probability that at least one of the two systems will detect the attack as follows:

\(P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1-{2\choose 0}(0.90)^{0}(1-0.90)^{2-0}\\=1-0.01\\=0.99\)

(c)

Compute the probability that at least one of the three systems will detect the attack as follows:

\(P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1-{3\choose 0}(0.90)^{0}(1-0.90)^{3-0}\\=1-0.001\\=0.999\)

(d)

On using only one system the probability that a single detection system will detect an attack is 0.90.

On using two systems the probability that at least one of the two systems detecting the attack is 0.99.

And on using three systems the probability that at least one of the three systems detecting the attack is 0.999.

So as the number of system is increasing the probability of detecting the attack is getting closer to 1.

Thus, it would be wise to recommend that multiple detection systems be used.

Answer:

Step-by-step explanation:

Complementary means angles that add up to 90°

Based on that you can write and equation by adding the 2 angles and making equal to 90

2x+6+1/2x=90          combine like terms on left

5/2x+6=90               subtract both sides by 6

5/2x=84                   multiply by the reciprocal of 5/2 => 2/5

x=168/5 or 33.6

Answer:

432 square feet

Step-by-step explanation:

The area of a trapezoid formula is: \(Area= \frac{a+b}{2} h\)

when plugging in the numbers for the letters;

a = 20

b = 28

h = 18

then solve, the correct answer is 432.

-----------------

Another way to solve is to brank down the shape;

what is 28 - 20? its

8 * 18 / 2 = 72

18 * 20 = 360

100 + 360 = 432

Answer:

The answer is 432 square ft

Step-by-step explanation:

So,

A = (20 + 28)/2 × 18 ft

A = 48/2 × 18 ft

A = 24 × 18 ft

A = 432 square ft

Thus, The area of trapezoid is 432 square ft

-TheUnknownScientist 72

Answer:

The perimeter can not be 26 inches

Step-by-step explanation:

Given

\(Side\ 1 =19\)

\(Side\ 2 =16\)

Required

Is a perimeter of 26 possible?

First, calculate the possible side 3

\(Side\ 3 = Perimeter - Side\ 1 - Side\ 2\)

\(Side\ 3 = 26 - 16 - 19\)

\(Side\ 3 = -9\)

The side length can not be negative.

So, the perimeter can not 26 inches

Answer:

Its 4

Step-by-step explanation:

\(2 + 2 = 4 \\ \)

Answer:

2+2=4 lol

And it says I need 20 characters so here are the 20 characters, bRaInLy

However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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Answer:

it a 26.64 units. hope it helps

The inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is 202.5 + 36.39x ≤ 480.

What is an inequality?

An inequality is a comparison between two or more mathematical expressions. It can be of the form ≤, ≥, < or >.

We are given per day charges as $36.39 and the charges per mile as $0.90.

Also, it is given that in total 225 miles have been driven.

So, the charges of 225 miles are:

⇒225 x 0.90

⇒$202.5

It is given that he can spend maximum $480.

So, for the maximum number of x days, we get the inequality as

202.5 + 36.39x ≤ 480

Hence, the inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480.

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Step-by-step explanation:

the answer is 72.70 cents

Answer: See explanation

Step-by-step explanation:

Markup is 39% of the cost.

Markup is what is added to the price to get the retail price.

39% × 72.72

0.39 × 72.72 = 28.3608

28.3608 ≈ 28. 36

Markup ≈ $28.36

Retail price is the price you get after you add the markup to the original price.

Retail price: Cost + Markup

Retail price: $72.72 + $28.36

Retail price = $101.08

The box plots provide visual representations of the distribution of salaries at two companies, Company A and Company B. To compare the ranges and medians of the data sets, we examine the characteristics of each box plot.

The range of a data set represents the difference between the maximum and minimum values. Looking at the box plots, we can determine that the range of Company A's salaries is larger than the range of Company B's salaries.

This can be inferred by observing the lengths of the whiskers, where the whiskers in Company A's box plot extend further in both the upper and lower directions compared to Company B's box plot.

The median of a data set represents the middle value when the data is arranged in ascending or descending order. Comparing the medians of the two box plots, we can determine that the median of Company A's salaries is higher than the median of Company B's salaries.

This is evident by comparing the positions of the medians within the boxes. In Company A's box plot, the median is closer to the upper quartile, indicating a higher median salary, while in Company B's box plot, the median is closer to the lower quartile, suggesting a lower median salary.

In summary, the range of salaries at Company A is larger than that of Company B, indicating a wider spread of salary values. Additionally, the median salary at Company A is higher than the median salary at Company B, suggesting a higher central tendency or midpoint in the distribution of salaries.

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Answer:

15. 52

16. 6

17. 59

18. 11

Step-by-step explanation:

Hey there!

\( \displaystyle{ \red{ \boxed{ \green{ \bold{m = - 1}}}}}\)

\( \\ \)

To find the slope of a line using two points \( \displaystyle{(x_1 , y_1)} \) and \( \displaystyle{(x_2 , y_2)} \) , we can use the slope formula.

This formula corresponds to the quotient of the change in y \( \: \) over \( \: \) the change in x :

\( \displaystyle{m = \frac{ \blue{y_2} - \orange{y_1}}{ \green{x_2} - \red{x_1} }}\)

\( \\ \)

\( \hookrightarrow \) We are given the points (-2 , 3) and (-5 , 6) where:

\( \\ \)

\(\displaystyle{ \hookrightarrow m = \frac{\blue{6} - \orange{3}}{\green{-5} - \red{(-2)}}} \\ \\ \displaystyle{\implies m=\frac{3}{-3}} \\ \\ \displaystyle{\purple{\implies} \boxed{\bold{m=-1}}}\)

Therefore, the slope of the line is -1.

\( \\ \)

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Answer:

Step-by-step explanation:

662

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

12 Squared Units

Step-by-step explanation:

Top length: 4 Units

Side length: 3 Units

The value of x in the equation is 16.

An equation is a mathematical expression that is made up of two expressions connected by an equal sign.

Therefore, let's solve the equation for variable x.

A variable is a number represented by letter in an equation.

Hence,

9 - (5x + 7) = - 2.8 - 4.7x

Therefore, let's open the bracket on the left side of the equation

9  - 5x - 7 = - 2.8 - 4.7x

2 - 5x =  - 2.8 - 4.7x

2 + 2.8x = -4.7x + 5x

4.8x = 0.3x

divide both sides of the equation by 0.3

x = 4.8 / 0.3

x = 16

Therefore,

x = 16

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Answer:

115.2 seconds

Step-by-step explanation:

5/4=0.8

So 1 meter every 0.8 seconds

114*0.8=115.2

The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.

The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.

The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:

= 5 - 1

= 4

The level of significance would be:

= 1 - 99. 0 %

= 0. 01

The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.

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Answer:

surface tension

Option A

A large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra. A biome is a large area characterized by its vegetation, soil, climate, and wildlife.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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Answer:

20.625 is the answer

Answer:

$13.52/4 = $3.38 per each towel.

4:13.52

1:n

To find n, divide 13.52 by 4; since, 4 divided by 4 gives us one.