Determine the probability density function for the following cumulative distribution function. F(x)= ⎩
⎨
⎧
​
0
0.2x
0.04x+0.64
1
​
x<0
0≤x<4
4≤x<9
9≤x
​
Find the value of the probability density function at x=6.

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, the change in the mean is calculated as follows:

Change in mean = Mean of second data set - Mean of first data set

Since none of the values in the second data set have changed, the mean of the second data set is the same as the mean of the first data set. Therefore, the change in the mean is:

Change in mean = Mean of second data set - Mean of first data set

= Mean of first data set - Mean of first data set

= 0

Thus, the change in the means between Kelly's original survey and her second survey is zero.

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Answer:

D

Step-by-step explanation:

-3x + 4y = 16

y = 3/4x +4 A is a no

B are perpendicular so No

8x -2y = 20

y = 4x -10 C perpendicular to No

-3x +4y = 18

y= 3/4x + 18/4 yes slopes are the same so parallel

Answer:

distance = 6.0 m

Step-by-step explanation:

1. Take note of the given.

Force = 50 N Work Done = 300 J m = ?

2. Write the formula.

J = Nm

3. Substitute.

300 J = (50N)(m)

4. Divide both sides by 50 N to isolate m.

300 J / 50 N = m

6 = m

Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The person who is an american author, anthropologist, and filmmaker who portrayed racial struggles in the early 1900 american south and published research on hoodoo is Zora Neale Hurston.

She is known for portraying racial struggles in the early 1900s American South and published research on hoodoo. Her most popular novel, "Their Eyes Were Watching God," was published in 1937. She also wrote over 50 short stories, plays, and essays.

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The function y = √(x + 7) + 5 represents a horizontal shift of 7 units to the left and a vertical shift of 5 units upwards compared to the parent function y = √x.

The parent function y = √x represents the square root function, where the graph starts at the origin (0, 0) and increases as x increases. The transformation y = √(x + 7) + 5 introduces a horizontal shift of 7 units to the left. This means that every point on the graph of the transformed function is shifted 7 units to the left compared to the parent function. For example, the point (1, 1) on the parent function would now be located at (-6, 1) on the transformed graph.

Additionally, the transformation includes a vertical shift of 5 units upwards. This means that every point on the graph of the transformed function is shifted 5 units upwards compared to the parent function. For instance, the point (1, 1) on the parent function would now be located at (1, 6) on the transformed graph.

Overall, the transformation y = √(x + 7) + 5 shifts the entire graph of the parent function y = √x by 7 units to the left and 5 units upwards. These shifts alter the position of the points on the graph, resulting in a different shape and position of the transformed graph compared to the parent function.

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It took Paul a total of 12 hours and 40 minutes to complete all three parts of the Ironman triathlon.

Paul’s time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for biking was 5 hours longer than her swimming time, so her biking time was (1 hour + 5 hours) = 6 hours 25 minutes. She ran for 4 hours 50 minutes. The total time it took her to complete all three parts of the race is (1 hour 25 minutes) + (6 hours 25 minutes) + (4 hours 50 minutes) = 12 hours 40 minutes.

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The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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Answer:

2/4 and 3/4

Step-by-step explanation:

To make both fractions have the same denominator, multiply 1/2 by 2. 1/2 times 2 equals 2/4

ok

Cost = 67.99 + 0.41*mi + 114.20

Total number of miles = 620

Cost = 67.99 + 0.41(620) + 114.20

Cost = 67.99 + 254.2 + 114.20

Cost = $436.4

Cost/mi = 436.4/620

Result

Cost/mi = $0.73

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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Answer:

11.67

Step-by-step explanation:

Data given in the question

∠ADC = 42°

∠BAC = 68°

Let us assume that AC be Y

Now

In ΔACD

tan 42° = AC ÷ CD = Y ÷ x ...............................(i)

In ΔACB  

tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)

Now take the value of Y from the equation (ii)

Y = 26 ÷ Tan 68° ...................... (iii)

Now place the value of Y in equation (i)

So,

Tan 42° = 26 ÷ tan 68° × X

X = 26 ÷  tan 68° × Tan 42° ......................(iv)

Now placing the values of tan 42° and tan 68° in equation (iv)

So,

X = 26 ÷ 0.900 × 2.475

= 11.67

The tan 42° = 0.900

And, the tan 68° = 2.475

Answer:

10

Step-by-step explanation:

refer attachment for detailed answer

Step-by-step explanation:

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Step-by-step explanation:

\( = \frac{1}{5} + \frac{1}{10} \\ \)

Now make the denominator same...

\( = \frac{1}{5} \times \frac{2}{2} + \frac{1}{10} \\ \)

\( = \frac{2}{10} + \frac{1}{10} \\ \)

\( = \frac{3}{10} \\ \)

:)

..

Answer: To find the value of (f - g)(2), we need to first evaluate f(2) and g(2), and then subtract g(2) from f(2).

Starting with f(x), we substitute x = 2:

f(2) = 3(2^2) + 1 = 3(4) + 1 = 12 + 1 = 13

Next, we evaluate g(x) at x = 2:

g(2) = 1 - 2 = -1

Now we can calculate (f - g)(2) by subtracting g(2) from f(2):

(f - g)(2) = f(2) - g(2) = 13 - (-1) = 14

Therefore, the value of (f - g)(2) is 14.

Step-by-step explanation:

a. If you travel 56 miles, your cost would be $54. (b) If your cost was $59.75, you were charged for traveling 239 miles.

For a maximum budget of $100, you can travel up to 240 miles.

a. To calculate the cost of traveling 56 miles, we substitute x with 56 in the equation y = 40 + 0.25x. Multiplying 0.25 by 56 gives us an additional cost of $14. Adding this to the base cost of $40, the total cost would be $54.

b. To determine the number of miles traveled for a cost of $59.75, we rearrange the equation y = 40 + 0.25x to x = (y - 40) / 0.25. Substituting y with $59.75, we have x = (59.75 - 40) / 0.25 = 19.75 / 0.25 = 79 miles.

For a maximum budget of $100, we use the same equation x = (y - 40) / 0.25 and substitute y with $100. Solving for x, we get x = (100 - 40) / 0.25 = 60 / 0.25 = 240 miles. Therefore, you can travel a maximum of 240 miles within the $100 budget.

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A) The probability is approximately 0.257. B) The expected number of customers is 5, and the standard deviation is approximately 1.71.

A) The number of customers who qualify for the membership follows a binomial distribution with parameters n = 20 and p = 0.1. The probability of having between 2 and 5 (inclusive) customers who qualify for the membership can be calculated by summing the probabilities of having exactly 2, 3, 4, or 5 customers who qualify for the membership.

Using the binomial probability formula or a binomial probability table, we find that this probability is approximately 0.257.

B) The expected number of customers who qualify for the membership in a randomly selected sample of 50 customers can be calculated using the formula E(X) = np, where X is the number of customers who qualify for the membership.

Thus, E(X) = 50 × 0.1 = 5. The variance of X is given by Var(X) = np(1-p), so the standard deviation is given by the square root of the variance, which is approximately 1.71.

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Answer:

slope is -1/2 and y- intercept is 1/3

Step-by-step explanation:

use y=mx+b

m=slope

b= y-intercept

rearrange your equation

y=1/3-1/2x

y=-1/2x+1/3

Answer:

please mark me brainliest and follow me my friend.

Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.

If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).

Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.

c^2 = a^2 + b^2

where c is the total displacement from the starting point to the end point

a is the distance he walks up north

b is the distance he walks to the west

c^2 = 100^2 + 100^2

c^2 = 10,000 + 10,000

c^2 = 20,000

c = 141.42 meters

Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.

100 meters + 100 meters - 141.42 meters = 53.58 meters

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Answer:

Y-int (0,-6)

x-int (-8,0)

Step-by-step explanation:

Answer:

Give more clear question pls

Step-by-step explanation:

its line a

Step-by-step explanation:

Answer:

170 kg. of parsnips are left

Step-by-step explanation:

Given:

850 kg. of parsnips

30 % to the local market

50 % to a local supermarket

Solution:

First, add the two percentages.

30 + 50 = 80%

That means 80 % of parsnips mass go to the markets.

Now let's find the mass of delivered parsnips.

Change 80% to decimal form.

80% = 0.8

Now multiply it by 850 kg.

850 x 0.8 = 680

The delivered parsnips mass is 680 kg.

Now to find the mass of parsnips left, subtract 680 to 850

850 - 680 = 170 kg.

170kg. of parsnips are left.

Answer:

mean=81.81

median=85

Step-by-step explanation:

MEAN.

\( \frac{65 + 70 + 70 + 80 + 80 + 85 + 85 + 85 + 90 + 90 + 100}{11} \)

\( = 81.81\)

MEDIAN

Since it's already arranged in ascending order, the middle number is taken as the median

which is 85.

i hope this helps

Answer:

See below ↓↓

Step-by-step explanation:

Mean

Median

Answer:

47

Step-by-step explanation:

Answer:

P1. |x+12|<22
P2. -22<x+12<22
P3. -34<x<10
Hope this assists anybody that comes across this

After a three-day visit to a hacienda, the student finds themselves approximately 14.2 km away from the barn, in a direction of 43 degrees south of east.

Let's break down the three days of travel. On the first day, the student walks 5 km southeast from the barn. This creates a right-angled triangle with one leg of length 5 km. On the second day, they walk 12 km in a 30-degree north-east direction. This adds another leg to the triangle, forming a parallelogram. Using trigonometry, we can determine that the second leg has a length of approximately 10.4 km. On the third day, the student walks 12 km west, which completes the triangle.

To find the total distance and direction from the barn, we can combine the lengths and directions of the three sides. By adding the horizontal components and vertical components separately, we get approximately 12 km east and 12 km south. Applying Pythagoras' theorem, the total distance from the barn is approximately 16.97 km. To find the direction, we use inverse trigonometry, which yields approximately 43 degrees south of east.  

To return to the starting point, the student needs to retrace their steps. Since the third day's walk was in the opposite direction, they need to travel a distance of approximately 12 km west. Combining this with the 10.4 km north-east component from the second day, we get a total distance of approximately 20.4 km. To find the direction, we again use inverse trigonometry, which gives us approximately 57 degrees north of west.

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The set of all points equidistant from the endpoints of a segment is called the perpendicular bisector of the segment.  All the points on the perpendicular bisector are equidistant from the endpoints of the original segment.

1. Points: These are the locations in space that have a specific position.
2. Equidistant: This term means that the points are at the same distance from certain other points.
3. Endpoints: These are the points at the ends of a segment.
4. Segment: This is a part of a line that has a fixed length and is defined by two endpoints.

So, the perpendicular bisector is a line or segment that passes through the midpoint of the given segment and is perpendicular to it. The midpoint is the point that is equidistant from both endpoints.

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When the second number is 89, the corresponding first number is 84.

Based on the given pattern, it appears that each second number is obtained by adding 5 to the corresponding first number.

To find the second number when the first number is 50:

First number: 50

Second number: 50 + 5 = 55

To find the second number when the first number is 200:

First number: 200

Second number: 200 + 5 = 205

To find the first number when the second number is 89:

First number: (89 - 5) = 84

Second number: 89

Therefore, when the second number is 89, the corresponding first number is 84.

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