Suppose g is a function from A to B and f is a function from B to C. a a) What's the domain of fog? What's the codomain of fog? b) Suppose both f and g are one-to-one. Prove that fog is also one-to-one. c) Suppose both f and g are onto. Prove that fog is also onto.

Part 1

Explanation:

The term "categorical" is the same as "nominal". Either refers to data labels or names, rather than numbers. The three categories are: Left, Right, No preference. We cannot apply math operations to names like this. It makes no sense to average Left vs Right vs No Preference.

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Part 2

Explanation:

Recall that the value of mu is calculated like so: \(\mu = \sum xp(x)\)

In other words, we multiply each x value with its corresponding p(x) probability. Then we add up those results to get mu. There's one glaring problem though: we aren't given numeric values for x. So there's no way to compute any of the x*p(x) values. Therefore, we don't have a mu value either. It doesn't make sense to determine what the center is when given labels. We would need x to take on values from the set {0,1,2,3,...} if we wanted to compute a mu value.

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Part 3

Explanation:

The value of sigma depends heavily on the value of mu.

One formula for sigma is \(\displaystyle \sigma = \sqrt{p(x_i)*\sum_{i=1}^{n}(x_i-\mu)^2\)

which is often abbreviated to \(\displaystyle \sigma = \sqrt{p(x)*\sum(x-\mu)^2\)

Because we can't find mu, we can't find sigma either.

Also, it makes no sense to determine how spread out categorical labels are. How can we determine the distance from "Left" to "Right"? The x values need to be numeric so we can calculate a numeric standard deviation from it.

Answer:

The answer is D

Step-by-step explanation:

Hope this helps! Please mark brainliest

Answer:

90 and 1000

Step-by-step explanation:

e 90 and 1000

a) The sample space for four flights selected at random, with arrival status "O" for on-time and "L" for late, is given as {OOOO, OOOL, OOLO, OOLL, OLOO,  OLOL, OLLO, OLLL, LOOO, LOOL, LLOO, LLOL, LLLO, LLLL}.

b) The probability that a randomly selected flight is from Airline A and on-time, denoted as P(A), is calculated by multiplying the probability of being on-time for Airline A (75/100) with the proportion of flights operated by Airline A out of the total (320/1000), resulting in P(A) = 24/100.

c) The probability that a randomly selected flight is either from Airline C or on-time, denoted as P(C), is obtained by dividing the sum of flights on-time (700) and flights operated by Airline C (240) by the total number of flights (1000), giving P(C) = 94/100.

d) The probability that a flight is from Airline B given that it is late, denoted as P(B | L), is computed by multiplying the proportion of late flights (300/1000) with the probability of being from Airline B (35/100), resulting in P(B | L) = 77/300.

e) The probability that a flight is late given that it is from Airline A, denoted as P(L | A), is calculated by multiplying the proportion of flights on-time for Airline A (25/100) with the proportion of flights operated by Airline A (320/1000), resulting in P(L and A) = 8/100. Therefore, P(L | A) = 1 - P(A | L) = 11/15.

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Answer:

1.

a settled way of thinking or feeling about something

Answer:

Altitude or height is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context.

Step-by-step explanation:

It is not wise to use the correlation coefficient r to summarize the association between this new pair of variables, without first examining the data and considering the context of the problem.

The correlation coefficient r measures the strength and direction of the linear relationship between two variables. However, it assumes that the relationship between the variables is linear, and that there are no outliers or influential points that could affect the results.

If the relationship between the variables is not linear or there are outliers, then the correlation coefficient r may not accurately summarize the association between the variables. In this case, it would be more appropriate to use other measures, such as nonparametric correlation coefficients or regression analysis.

Therefore, before using the correlation coefficient r, it is important to carefully examine the data and consider any potential issues that could affect the results. Only then can we determine whether the correlation coefficient r is an appropriate measure for summarizing the association between the variables.

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When the diameter is 12 cm, the rate at which it is decreasing is approximately 0.0398 cm/min.

The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere. Since the diameter is twice the radius, we have r = d/2, where d is the diameter. Thus, the surface area of the sphere in terms of the diameter is A = πd^2.

To find the rate at which the diameter is decreasing, we need to take the derivative of the surface area with respect to time and use the chain rule:

dA/dt = dA/dd * dd/dt

where dA/dt is the rate of change of the surface area, and dd/dt is the rate of change of the diameter.

Taking the derivative of the surface area gives us:

dA/dt = 2πd * dd/dt

Plugging in the given rate of change of the surface area (-3 cm^2/min) and the given diameter (12 cm), we get:

-3 = 2π(12) * dd/dt

Solving for dd/dt, we get:

dd/dt = -3 / (24π) = -0.0398 cm/min (rounded to 4 decimal places)

This means that for every minute that passes, the diameter of the snowball is decreasing by about 0.0398 cm.

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13/1 × 5/8 - 3/1 × 2/3

= 13×5 / 1×8 - 3×2 / 1×3

= 65/8 - 6/3

= 195/24 - 48/24

=147/24

=49/8

Answer:

1. f(n+1) = f(n) + 0.09

2. The correct answer is 403 = x. The student’s error is that she did not cancel out properly the constant by the inverse add ended to find the answer of the variable.

3. B

4. D 34 + 6(25.3)

Answer:

-80

Step-by-step explanation:

you pass the 25 to the right side adding and the the 1/5 multiplying by -5 to the right side

Answer:

Check below

Step-by-step explanation:

a. Salaries in a company employing 100 factory workers and 2 highly paid executives: The mean (average) salary would probably be higher than the median salary because the 2 highly paid executives would greatly increase the overall average salary, but would not greatly affect the median salary, which is the middle value when the data is arranged in order.

b. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly: The median age at death would probably be higher than the mean age at death because the mean age at death would be affected by infant deaths and other early deaths, while the median age at death would be the middle value of the data set when arranged in order.

c. Prices of all new cars sold in 1 month in a large city: The mean and median prices would probably be about equal because the data set is likely to be normally distributed, which means that the mean and median values would be similar.

d. Heights of all 7-year-old children in a large city: The mean and median heights would probably be about equal because the data set is likely to be normally distributed.

e. Shoe sizes of adult women: The mean and median shoe sizes would probably be about equal because the data set is likely to be normally distributed.

The distribution would tend to skew to the left (meaning a lot more people die in the older ages than in the younger ages), hence the median would be higher than the mean.

a. Salaries in a company employing 100 factory workers and 2 highly paid executives: The mean (average) salary would probably be higher than the median salary because the 2 highly paid executives would greatly increase the overall average salary, but would not greatly affect the median salary, which is the middle value when the data is arranged in order.

b. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly: The median age at death would probably be higher than the mean age at death because the mean age at death would be affected by infant deaths and other early deaths, while the median age at death would be the middle value of the data set when arranged in order.

c. Prices of all new cars sold in 1 month in a large city: The mean and median prices would probably be about equal because the data set is likely to be normally distributed, which means that the mean and median values would be similar.

d. Heights of all 7-year-old children in a large city: The mean and median heights would probably be about equal because the data set is likely to be normally distributed.

e. Shoe sizes of adult women: The mean and median shoe sizes would probably be about equal because the data set is likely to be normally distributed.

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There are 35 boys in the movie theater to see Wonder Woman

There are 150 people in a movie theater to see Wonder Woman

7/30 of this number of people are boys

The number of boys that came to see the movie can be calculated by multiplying 7/30 by 150. It can be expressed as follows;

7/30 × 150

= 1050/30

= 35

Hence there are 35 boys in the movie theater to see Wonder Woman movie

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a. The percentage of men meeting the height requirement for U.S. Air Force pilots can be calculated by finding the proportion of men with heights between 64 in. and 77 in. b. The new height requirements, excluding the top 2.5% and bottom 2.5% of heights, will be the range that encompasses the remaining 95% of men's heights.

a. To find the percentage of men meeting the height requirement, we need to calculate the proportion of men whose heights fall between 64 in. and 77 in. We can do this by subtracting the percentage of men shorter than 64 in. from the percentage of men shorter than 77 in. This can be obtained from a standard normal distribution table or by using statistical software.

b. If the height requirements are changed to exclude the tallest 2.5% and shortest 2.5% of men, the new requirements will encompass the remaining 95% of men. This means that the new height requirements will be defined by the range of heights that capture the middle 95% of the male population. To determine these new requirements, we need to find the corresponding heights on the distribution curve, which can be obtained from a standard normal distribution table or statistical software. The new range will exclude the top 2.5% and bottom 2.5% of heights, while including the remaining 95% of heights

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Answer:

\(3x\cdot \:2-5x-2=0\)

\(6x-5x-2=0\)

\(6x-5x=x\)

\(x-2=0\)

\(x-2+2=0+2\)

\(x=2\)

\(-----------\)

Hope it helps..

Have a great day!!

Answer:

2, -1/3

Step-by-step explanation:

3x^2 - 5x - 2 = 0

Find the factors of 3*-2 that are the same as the addends for -5:

3*-2 = -6

Factors of -6: -6*1

Addends: -6 + 1

3x^2 - 6x + x - 2 = 0

(3x^2 - 6x) + (x - 2) = 0

(factor in each parantheses)

3x(x - 2) + 1(x - 2) = 0

(3x + 1)(x - 2) = 0

(set each of the terms to 0 and solve)

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Hope it helps (●'◡'●)

In point-slope form, the equation for line that passes through (-3 , -8) and slope -5 is :

y + 5x = -23.

Given a line with the coordinates (-3, -8) and a slope of m = -5.

For the line, we must find an equation in point slope form.

(y - y1 ) = m(x - x1) is the point slope form of a line.

According to the question,

(m) slope = - 5

And the line goes through (x1 , y1) = ( -3 , -8 )

Therefore( y - y1 ) = m ( x - x1)

y + 8 = -5 ( x + 3 )

y + 8 = -5x - 15

y + 5x = - 23

Therefore the equation for line in point-slope form is y + 5x = -23.

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Step-by-step explanation:

To find the product, we'll be using the FOIL method.

F - Front.

O - Outer.

I - Inner.

L - Last.

When applying the FOIL method:

\(a(a) + - 3(a) + 5(a) - 3(5)\)

Multiplying:

\( {a}^{2} - 3a + 5a - 15\)

Combine Like-Terms:

\( {a}^{2} + 2a - 15\)

a^2 + 2a - 15 is your product.

Answer:

2.62$

Step-by-step explanation:

Answer:

If she buys the pens she can use 2.62 dollars on a notebook

Step-by-step explanation:

10.75-3.96=6.43

1.39x3=4.17

6.43-4.17

2.62

Approximately a rate of 14.4% would be required to turn $500 into $2,000 in 10 years

To arrive at this estimate, we can use the rule of 72, which states that to determine the number of years required to double your investment at a certain rate of return, you can divide 72 by that rate. In this case, we want to quadruple our investment, so we need to divide 72 by 4, which equals 18.

Next, we can divide the number of years by the amount of interest earned to arrive at an estimated rate. In this case, we can divide 10 years by 18, which equals approximately 0.56. To convert this to a percentage, we multiply by 100, which gives us an estimate of 56%.

However, we need to subtract the rate of inflation, which is typically around 2-3%, to arrive at a more realistic estimate. This gives us a final estimate of approximately 14.4%.

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The null hypothesis is rejected, and the alternative hypothesis is accepted. Thus, it can be concluded that there is sufficient evidence at the 0.01 level to support the testing firm's claim that the manufacturer's claim is incorrect. Yes, there is sufficient evidence at the 0.01 level to support the testing firm's claim

Given, a manufacturer gives its van a 38.8 miles per gallon (MPG) rating. An independent testing firm was contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 260 vans, they found a mean MPG of 39.0 and the population standard deviation is known to be 2.1.As the sample size (n) is greater than 30 and the population standard deviation is known, a Z-test will be appropriate to check the hypothesis at 0.01 level of significance.Hypothesis: H0:

μ = 38.8 (The claim of the automobile manufacturer)H1:

μ ≠ 38.8 (The claim of the testing firm)The level of significance is 0.01.Z-score calculation,

Z = (X - μ) / (σ / √n)Where X is the sample mean = 39.0μ is the population mean = 38.8σ is the population standard deviation = 2.1n is the sample size = 260Substituting the values, Z = (39.0 - 38.8) / (2.1 / √260) = 3.20.

Here, the level of significance (α) is 0.01 for a two-tailed test, and the Z-score is 3.20. The critical value of Z at α/2 = 0.005 is ± 2.58, obtained from the standard normal distribution table. Since the calculated Z-score is greater than the critical value, it falls in the rejection region of the null hypothesis.

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Answer:

2.55 is the answer!

Step-by-step explanation:

Depth = 1200 metres --> x = 1200 --> T = 4500 / 1200 = 3.75°C

Depth = 3750 metres --> x = 3750 --> T = 4500 / 3750 = 1.2 °C

The difference of the temperatures is 3.75°C - 1.2°C = 2.55°C

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The percentage of Japanese-Americans under 35 in Santa Clara County, CA is approximately 11.3%.

Santa Clara County, CA is home to approximately 27,873 Japanese-Americans. To determine what percentage of this population is under age 35, it is necessary to first calculate the total number of Japanese-Americans under 35. To do this, we can subtract the estimated number of Japanese-Americans over age 35 from the total population of Japanese-Americans. We can then divide this number by the total population of Japanese-Americans to find the percentage of Japanese-Americans under age 35. In Santa Clara County, CA, the estimated number of Japanese-Americans over age 35 is 24,672, and the total population of Japanese-Americans is 27,873. Subtracting 24,672 from 27,873 yields 3,201 Japanese-Americans under age 35. We can then divide 3,201 by 27,873 to get a percentage of 11.3%. Therefore, approximately 11.3% of the Japanese-American population in Santa Clara County, CA is under age 35.

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Answer:

The volume of the triangular prism is 677.6 cubic meters.

Step-by-step explanation:

The formula for the volume of a triangular prism is:

\(\sf\qquad\dashrightarrow Volume \: (V) = \dfrac{1}{2} \times b\times h \times l \)

where:

Substituting the given values, we have:

\(\sf:\implies Volume \: (V) = \dfrac{1}{2} \times 11 \times 11 \times 11.2\)

\(\sf:\implies \boxed{\bold{\:\:Volume \: (V) = 677.6\: meters^3\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the volume of the triangular prism is 677.6 cubic meters.

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

\(72 = 2^3 * 3^2\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\48 = 2^4 * 3\\\\\)

The GCD of the crayons is \(2^3 * 3\), which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = \(2^3 * 3 * 5\)

The GCD of the drawing paper is also \(2^3 * 3\), which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The function with an amplitude of 3 and a phase shift of π/2 is h(x) = 3 cos (2x - π/2) + 3.

The amplitude of a function is the distance between the maximum and minimum values of the function, divided by 2. The phase shift of a function is the horizontal shift of the function from the standard position,

(y = cos(x) or y = sin(x)).
To find the function with an amplitude of 3 and a phase shift of π/2, we need to look for a function that has a coefficient of 3 on the cosine term and a horizontal shift of π/2.
Looking at the given options, we can eliminate option a) because it has a coefficient of -3 on the cosine term, which means that its amplitude is 3 but it is inverted.

Option b) has a coefficient of 3 on the cosine term but it has a phase shift of -π/2, which means it is shifted to the left instead of to the right. Option d) has a phase shift of π/2, but it has a coefficient of -2 on the cosine term, which means its amplitude is 2 and not 3.
A*cos(B( x - C)) + D

Where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

f(x) = -3 cos(2x - π) + 4

Amplitude: |-3| = 3

Phase shift: π (not π/2) b) g(x) = 3cos(2x + π) -1

Amplitude: |3| = 3

Phase shift: -π (not π/2) c) h(x) = 3 cos (2x - π/2) + 3

Amplitude: |3| = 3

Phase shift: π/2 d) j(x) = -2cos(2x + π/2) + 3200

Amplitude: |-2| = 2 (not 3)

Phase shift: -π/2
Therefore, the only option left is c) h(x) = 3 cos (2x - π/2) + 3. This function has a coefficient of 3 on the cosine term and a horizontal shift of π/2, which means it has an amplitude of 3 and a phase shift of π/2.
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Answer:

See explanation

Step-by-step explanation:

The question is incomplete as the invested amount and the interest rate are not given. However, I will give a general method of solving it.

Assume that:

\(r = 5\%\) --- interest rate

\(PV =9000\) --- Present value or invested amount

To calculate time (in years), we make use of the following formula of future value

\(FV = PV(1 + r)^n\)

Where

\(FV = 11800\)

So:

\(11800 = 9000( 1 + 5\%)^n\)

Divide both sides by 9000

\(1.31 = ( 1 + 5\%)^n\)

Take logarithm of both sides

\(Log(1.31) = Log(1 + 5\%)^n\)

Apply law of logarithm

\(Log(1.31) = nLog(1 + 5\%)\)

Make n the subject

\(n = \frac{Log(1.31)}{Log(1 + 5\%)}\)

Express 5% as decimal

\(n = \frac{Log(1.31)}{Log(1 + 0.05)}\)

\(n = \frac{Log(1.31)}{Log(1.05)}\)

\(n = \frac{0.1173}{0.0212}\)

\(n \approx 6\)

The time to reach the future value is approximately 6 years.

Use the above explanation to answer your question

The statements that are true about the given algorithms are: I. Algorithm 1 does not work on lists where the smallest value is at the start of the list or the largest value is at the end of the list.  II. Algorithm 2 does not work on lists that contain all negative numbers or all numbers over 1000.

Algorithm 1's reliance on initializing minVal to the first value and maxVal to the last value can lead to incorrect results if the smallest or largest value is not properly updated during the iteration. Similarly, Algorithm 2's fixed initial values for minVal and maxVal can result in incorrect differences when dealing with lists containing all negative numbers or all numbers over 1000.

It is important to consider these limitations and potential failure cases when choosing and implementing an algorithm for calculating the difference between the smallest and largest values in a list.

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The solution to the linear function M(x) = 180 is of x = -5.

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

In this problem, the function is defined as follows:

M(x) = 120 - 12x.

M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.

The domain of the situation is given as follows:

x ≥ 0. {discrete}

As the number of tickets cannot assume negative neither decimal values.

The equation is:

M(x) = 180.

The solution is calculated as:

120 - 12x = 180

12x = -60

x = -60/12

x = -5.

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In summary, mutually exclusive events are events that cannot occur at the same time.

In probability and statistics, mutually exclusive events are events that cannot occur at the same time. They are also known as disjoint events.

For example, consider the events "rolling a 1 on a fair die" and "rolling an even number on a fair die". These events are mutually exclusive because they cannot occur at the same time. If a die is rolled, it can either be a 1 or an even number, but it cannot be both at the same time.

On the other hand, consider the events "rolling an even number on a fair die" and "rolling a number less than 5 on a fair die". These events are not mutually exclusive because they can occur at the same time. A die can roll an even number and a number less than 5 at the same time, for example 2.

Another way to determine if two events are mutually exclusive is to check if the intersection of the two events is empty. If the intersection of the two events is empty, then the events are mutually exclusive.

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