The following questions are about exponential and Gamma distributions. Question 6 1 pts Given the parameter, B = 1, and X is an exponential distribution, find P(X>0.5). Question 7 1 pts If we set a = 1 in the Gamma's distribution, which distribution we will get? Exponential None of these. Normal Uniform Question 8 1 pts X is a Gamma random variable with mean 3, and variance 5. Find a. Question 9 1 pts Use the same condition is question 8, find 8. Question 10 1 pts For a standard normal variable, Z, using Z table to find P(X>0.23).
Answers
Since the total area under the standard normal distribution curve is 1, we can find P(Z > 0.23) by subtracting the area to the left of 0.23 from 1:
Question 6:
Given B = 1, the parameter of the exponential distribution, the probability of X being greater than 0.5 can be calculated as follows:
P(X > 0.5) = e^(-B*0.5) = e^(-0.5) = 0.6065
Therefore, the probability of X being greater than 0.5 is 0.6065.
Question 7:
If we set a = 1 in the Gamma's distribution, we will get an exponential distribution. Therefore, the answer is Exponential.
Question 8:
Given that the mean of the Gamma random variable X is 3 and the variance is 5, we can write the following equations:
Mean of X = a*B = 3
Variance of X = a*B^2 = 5
Substituting B = 1/a in the second equation, we get:
a*(1/a)^2 = 5
a = 5
Therefore, a = 5.
Question 9:
Using the same conditions as in Question 8, we can find the value of B as follows:
B = Mean of X / a = 3/5 = 0.6
Therefore, B = 0.6.
Question 10:
To find P(Z > 0.23), we can use a standard normal distribution table.
Looking up the value of 0.23 in the table, we find that the area to the left of 0.23 is 0.5902.
Since the total area under the standard normal distribution curve is 1, we can find P(Z > 0.23) by subtracting the area to the left of 0.23 from 1:
P(Z > 0.23) = 1 - 0.5902 = 0.4098
Therefore, the probability of a standard normal variable being greater than 0.23 is 0.4098.
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Related Questions
HELP PLS I CAnt DO THIS
Answers
Using the two given solutions and the general absolute value function we will get:
|x + 9| = 27
Which absolute value function has that solution set?The two solutions are:
x = 0 and x = -18.
Remember that the absolute value equation is something like:
|x - a| = b
If we want to have these solutions, then:
|0 - a| = b
|-18 -a| = b
From the first one, we have:
|-a| = b
Replacing that on the second equation we get:
|-18 -a| = |-a|
Notice that if we take a = -9, then we have:
|-18 + 9| = |+9|
|-9| = |+9|
This is true, so a = -9.
Then we find the value of b:
|18 + 9| = b = 27
Then the absolute value equation is:
|x + 9| = 27
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The graph shows the distribution of the length (in
seconds) of videos on a popular video-streaming site.
The distribution is approximately Normal, with a mean
of 264 seconds and a standard deviation of 75
seconds.
Streaming Videos
What percentage of videos on the streaming site are
between 114 and 489 seconds?
50%
68%
97.35%
99.7%
Answers
Using the normal distribution, we have that 97.35% of videos on the streaming site are between 114 and 489 seconds.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given as follows:
\(\mu = 264, \sigma = 75\)
The proportion of videos that are between 114 and 489 seconds is the p-value of Z when X = 489 subtracted by the p-value of Z when X = 114, hence:
X = 489:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (489 - 264)/75
Z = 3
Z = 3 has a p-value of 0.9987.
X = 114:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (114 - 264)/75
Z = -2
Z = -2 has a p-value of 0.0228.
0.9987 - 0.0228 = 0.976.
The closest percentage is 97.35%, hence 97.35% of videos on the streaming site are between 114 and 489 seconds.
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Your baseball team is selling bags of popcorn to raise money for a trip. For each bag of popcorn you sell, $3 goes towards your trip. You hope to earn at least $150 for the trip. Write and solve an inequality that represents the numbers x of bags of popcorn you must sell to reach your goal.
Answers
Answer:
x > 50
Step-by-step explanation:
Let
x = number of bags of popcorns to sell
Price of each bag of popcorn = $3
You hope to earn at least $150 for the trip.
At least in inequality = >
The inequality is
Price × quantity of popcorns to sell > 150
3x > 150
Divide both sides by 3
x > 150 / 3
x > 50
in a plane, four circles with radii 1,3,5, and 7 are tangent to line l at the same point a, but they may be on either side of l. region s consists of all the points that lie inside exactly one of the four circles. what is the maximum possible area of region s?
Answers
Answer: Let us call the centers of the four circles C1, C3, C5, and C7, respectively, where the subscript refers to the radius of the circle. Without loss of generality, we can assume that the tangent point A lies to the right of all the centers, as shown in the diagram below:
C7
o-----------o
C5 / \ C3
/ \
o-----------------o
C1
|
|
| l
|
A
Let us first find the coordinates of the centers C1, C3, C5, and C7. Since all the circles are tangent to line l at point A, the centers must lie on the perpendicular bisector of the line segment joining A to the centers. Let us denote the distance from A to the center Cn by dn. Then, the coordinates of Cn are given by (an, dn), where an is the x-coordinate of point A.
Using the Pythagorean theorem, we can write the following equations relating the distances dn:
d1 = sqrt((d3 - 2)^2 - 1)
d3 = sqrt((d5 - 4)^2 - 9)
d5 = sqrt((d7 - 6)^2 - 25)
We can solve these equations to obtain:
d1 = sqrt(16 - (d7 - 6)^2)
d3 = sqrt(4 - (d7 - 6)^2)
d5 = sqrt(1 - (d7 - 6)^2)
Now, let us consider the region S that lies inside exactly one of the four circles. This region is bounded by the circle of radius 1 centered at C1, the circle of radius 3 centered at C3, the circle of radius 5 centered at C5, and the circle of radius 7 centered at C7. Since the circles are all tangent to line l at point A, the boundary of region S must pass through point A.
The maximum possible area of region S occurs when the boundary passes through the centers of the two largest circles, C5 and C7. To see why, imagine sliding the circle of radius 1 along line l until it is tangent to the circle of radius 3 at point B. This increases the area of region S, since it adds more points to the interior of the circle of radius 1 without removing any points from the interior of the other circles. Similarly, sliding the circle of radius 5 along line l until it is tangent to the circle of radius 7 at point C also increases the area of region S. Therefore, the boundary of region S must pass through points B and C.
Using the coordinates we obtained earlier, we can find the x-coordinates of points B and C as follows:
x_B = a - 2 - sqrt(9 - (d7 - 6)^2)
x_C = a + 6 + sqrt(9 - (d7 - 6)^2)
To maximize the area of region S, we want to maximize the distance BC. Using the distance formula, we have:
BC^2 = (x_C - x_B)^2 + (d5 - d3)^2
Substituting the expressions we derived earlier for d3 and d5, we get:
BC^2 = 32 - 2(d7 - 6)sqrt(9 - (d7 - 6)^2)
To maximize BC^2, we need to maximize the expression inside the square root. Let y = d7 - 6. Then, we want to maximize:
f(y) = 9y^2 - y^4
Taking the derivative of f(y) with respect to y and setting it equal to zero, we get:
f'(y) = 18y - 4y^3 = 0
This equation has three solutions: y = 0, y = sqrt(6)/2, and y = -sqrt(6)/2. The only solution that gives a maximum value of BC^2 is y = sqrt(6)/2, which corresponds to d7 = 6 + sqrt(6)/2.
Substituting this value of d7 into our expressions for d1, d3, and d5, we obtain:
d1 = sqrt(16 - (sqrt(6)/2)^2) = sqrt(55/2)
d3 = sqrt(4 - (sqrt(6)/2)^2) = sqrt(19/2)
d5 = sqrt(1 - (sqrt(6)/2)^2) = sqrt(5/2)
Using these values, we can compute the coordinates of points B and C as follows:
x_B = a - 2 - sqrt(9 - (sqrt(6)/2)^2) = a - 2 - sqrt(55)/2
x_C = a + 6 + sqrt(9 - (sqrt(6)/2)^2) = a + 6 + sqrt(55)/2
The distance between points B and C is then:
BC = |x_C - x_B| = 8 + sqrt(55)
Finally, the area of region S is given by:
Area(S) = Area(circle of radius 5 centered at C5) - Area(circle of radius 7 centered at C7)
= pi(5^2) - pi(7^2)
= 25pi - 49pi
= -24pi
Since the area of region S cannot be negative, the maximum possible area is zero. This means that there is no point that lies inside exactly one of the four circles. In other words, any point that lies inside one of the circles must also lie inside at least one of the other circles.
Step-by-step explanation:
PLS HELP ANSWER QUICK PLEASE SHOW WORK
Answers
Answer: NIKES
Step-by-step explanation:
BEFAUSE 5/2 IS THE WHG0LE D[IWJAEOIDHNC;SHCOWIADHJA[OISHWNIOD
Answer: the answer is nike
Step-by-step explanation: Because the shipping fee on callaway is more than the order.
Find an LU factorization of the matrix A (with L unit lower triangular). A=
⎣
⎡
4
−8
10
−8
8
−4
3
5
−7
7
6
−7
0
3
−3
⎦
⎤
Answers
The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].
Let's go step by step to find the LU factorization of matrix A.
Matrix A:
A =
[4, -8, 10]
[-8, 8, -7]
[6, -7, 3]
Step 1:
Initialize the L matrix as an identity matrix of the same size as A.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 2:
Perform Gaussian elimination to obtain U.
- Multiply the first row of A by (1/4) and replace the first row of A with the result.
A =
[1, -2, 2.5]
[-8, 8, -7]
[6, -7, 3]
- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[6, -7, 3]
- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Step 3:
Update the L matrix based on the operations performed during Gaussian elimination.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 4:
The resulting matrix A is the upper triangular matrix U.
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Therefore, the LU factorization of matrix A is:
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
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(x+4) ² remove bracket and simplify
Answers
Answer:
To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.
So,
(x + 4)² = x² + 2(x)(4) + 4²
= x² + 8x + 16
Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.
Step-by-step explanation:
Answer:
x²n+ 8x + 16
Step-by-step explanation:
(x + 4)²
= (x + 4)(x + 4)
each term in the second factor is multiplied by each term in the first factor, that is
x(x + 4) + 4(x + 4) ← distribute parenthesis
= x² + 4x + 4x + 16 ← collect like terms
= x² + 8x + 16
Substitute 7 for x and evaluate the expression below. (x-3) - 2 O A. 12 OB. 2 O C. 6 D. 8
Answers
Answer: B
Step-by-step explanation:
First you have to do what’s in parentheses so you do 7-3, which is 4. Then you do 4 - 2 = 2. Hope this helped!
"If x = y, then x + 4 = y + 4" represents the
property of equality.
OA) substitution
B) subtraction
C) addition
D) transitive
Answers
Answer:
C
Step-by-step explanation:
Look in your old textbooks
x + 4 = y + 4
—only $4.95!" Thus, each daily lunch special consists of a salad, a soup, a sandwich, and a drink. How many different daily lunch specials are possible?
Answers
Answer:
120 different possible lunch specials
Step-by-step explanation:
To calculate the overall number of possible lunch specials that can be made we would need to multiply together all of the options from each one of the items found in the lunch special. These values are provided in the question so we can simply multiply them all together to calculate the total possible lunch specials that can be made...
Salads=3Soups=2Sandwiches=5Drinks=43 * 2 * 5 * 4 = 120 possibilities
Finally, we can see that there are a total of 120 different possible lunch specials that can be made with the availble options.
the teacher has a small class with only 7 students. the teacher grades their homework and reports scores of: 10, 7, 8, 12, 9, 11, and 13. what is the median?
Answers
Answer:
10
Step-by-step explanation:
To find the median in a set of data, organize the data from least to greatest.
Here, our data is the homework scores, those being:
10, 7, 8, 12, 9, 11, 13
Let's organize them in ascending order, like so:
7, 8, 9, 10, 11, 12, 13
The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.
We can find that the number in the middle is 10.
Thus, the median of the scores is 10.
how do you calculate the area of each tringle:
hight 3cm
base 9cm
base 8cm
hight 5cm
base 3.5cm
hight 9.8cm
Answers
Answer:
The formula for area of a triangle is 1/2bh or one half base times height.
Step-by-step explanation:
First, multiply both numbers.
Then divide the product by 2. (This is the same as multiplying by 1/2)
And there you go, just make sure to label cm².
A composite figure is shown.
Which of the following represents the total area of the figure
A. 10.663 in2
B. 24.413 in2
C. 28.448 in2
D. 34.355 in2
Answers
Answer:
B- 24.413
Step-by-step explanation:
3.3*3.15=10.395
10.395/2=5.1975
To find the right side of the bottom triangle- 6.3-3.15=3.15
3.15*3=9.45
9.45/2=4.725
4.6*3.15=14.49
Adding all the areas
14.49+4.725+5.1975=24.4125
24.4125 rounded is 24.413
For what value of k are the graphs of 12y = 9x + 8 and 4y = k(x + 4) parallel?
perpendicular? I HAVE THE ANSWER, just need step to step explanation on how to solve it (pls be clear, answers in pic)
Answers
Answer:
parallel: k = 3perpendicular: k = -16/3Step-by-step explanation:
You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.
ParallelThe slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...
y = k/4x +1y = 3/4x +2/3For parallel lines, we want to choose the value of k so that the slopes are equal:
k/4 = 3/4
k = 3 . . . . . . . . multiply by 4
PerpendicularThe slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...
(k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1
k = -16/3 . . . . . . . . . multiply by 16/3
__
Additional comment
The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.
for a two-tailed hypothesis test with a sample size of 37 and a 0.10 level of significance, what are the critical values of the test statistic t?
Answers
For a two-tailed hypothesis test with a sample size of 37 and a 0.10 level of significance, the critical values of the test statistic t are approximately ±1.691. These values determine whether we reject or fail to reject the null hypothesis based on the calculated t-value.
To find the critical values of the test statistic t for a two-tailed hypothesis test, we need to use the t-distribution table or statistical software. The critical values of t depend on the level of significance and the degrees of freedom (df), which are calculated as n-1, where n is the sample size.
For a two-tailed test with a level of significance of 0.10 and 37 degrees of freedom, we need to find the t-value that cuts off 0.05 of the area in each tail of the t-distribution. Using a t-distribution table or software, we find that the critical values of t are approximately ±1.691.
This means that if the calculated t-value falls outside the range of ±1.691, we reject the null hypothesis at the 0.10 level of significance, and conclude that there is significant evidence to support the alternative hypothesis. If the calculated t-value falls within the range of ±1.691, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.
It is important to note that the critical values of t depend on the sample size and the level of significance. As the sample size increases, the degrees of freedom increase and the t-distribution approaches the normal distribution. Also, as the level of significance decreases, the critical values of t become more extreme, making it harder to reject the null hypothesis.
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Solve for X
7x – 7= 2x – 1
Give your answer as an improper fraction in its simplest form.
Answers
Answer:
7x+2x=7-1
9x=6
9÷6= 9/6
Step-by-step explanation:
Move numbers with (x) on one side turning it into (-)
x = 6/5
Step-by-step explanation:
Rearrange unknown terms to the left side of the equation:
7x − 2x = −1 + 7
Combine like terms:
5x = −1 + 7
Calculate the sum or difference:
5x = 6
Divide both sides of the equation by the coefficient of variable:
x = 6 ÷ 5
Calculate the product or quotient:
x = 1.2
Express the number in fractions:
x= 6/5
Answer:
x = 6/5
Evaluate 4(3 - 1)^2..
Answers
Answer:
16
Step-by-step explanation:
4(3 - 1)^2
~Simplify using PEMDAS
4(2)^2
4(4)
16
Best of Luck!
A new car is purchased for 24800 dollars. The value of the car depreciates at 7.25% per year. To the nearest tenth of a year, how long will it be until the value of the car is 9000 dollars?
Answers
Answer:
pretty sure the answer is 13.5 years. sorry if wrong
Step-by-step explanation:
what’s the answer ??
Answers
Answer:
Left box: 1/2n
Right box = 2n - 22
Step-by-step explanation:
Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.
Thus, you want to put 1/2n in box on the left.
Twice the number and 22 less than this is given by: y: 2n - 22 less than this means we subtract. Thus, we have 2n - 22 as the numerator on the right hand side of the equation.
Thus, you want to put 2n - 22 in the box on the right.
What is the lateral surface area?
5 mm
5 mm
5 mm
Answers
Almost sooo close guys just 5 more left sorry if it’s taking long
Answers
Answer:
As a decimal its 6.34, If you round up then its 6.35
As a fraction its 400/63
As a mixed number its 6 22/63
If anybody can help me pls do
the average of 5 numbers is 64. When a sixth number is added, the average becomes 66. What is the sixth number?
Answers
Step-by-step explanation:
5x64=32066=(320+x} 666x6={320+x)396=320+x=396-320
anyone know an easy way to do statistics without being complicated
Answers
Answer: Use distributive practice rather than massed practice. ...
Study in triads or quads of students at least once every week. ...
Don't try to memorize formulas (A good instructor will never ask you to do this). ...
Work as many and varied problems and exercises as you possibly can. ...
Look for reoccurring themes in statistics.
If a = (x-3) and b = (x+3), show that 2ab = 2x square - 18
Answers
Step-by-step explanation:
ab = (x - 3)(x + 3)
multiply
ab = x² + 3x - 3x - 9
Simplify
ab = x² - 9
---------------------------
2ab = 2(x² - 9)
Distribute
2ab = 2x² - 18
Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG indicate that the first two children born are boys and the third child is a girl, let GBG indicate that the first and third children born are girls and the second is a boy, and so forth.
a. List the eight elements in the sample space whose outcomes are all possible genders of the three children.
b. Write each of the events in the next column as a set and find its probability.
(i) The event that exactly one child is a girl.
(ii) The event that at least two children are girls.
(iii) The event that no child is a girl.
Answers
In a family with three children, assuming each child is equally likely to be a boy or a girl, we can analyze the sample space and calculate the probabilities of different events. The sample space consists of eight possible outcomes indicating the genders of the three children. The events of interest include exactly one child being a girl, at least two children being girls, and no child being a girl.
(a) The eight elements in the sample space, representing all possible genders of the three children, are as follows:
1. BBB (Three boys)
2. BBG (Two boys and one girl)
3. BGB (One boy and two girls)
4. BGG (One boy and two girls)
5. GBB (One girl and two boys)
6. GBG (One girl and two boys)
7. GGB (Two girls and one boy)
8. GGG (Three girls)
(b) Now let's calculate the probabilities of the given events:
(i) The event of exactly one child being a girl can be represented as {BGG, GBG, GGB}. The probability is 3/8 since there are three favorable outcomes out of the eight possibilities in the sample space.
(ii) The event of at least two children being girls can be represented as {BGG, GBB, GBG, GGB, GGG}. The probability is 5/8 since there are five favorable outcomes out of the eight possibilities.
(iii) The event of no child being a girl can be represented as {BBB}. The probability is 1/8 since there is only one favorable outcome out of the eight possibilities.
By analyzing the sample space and defining the events of interest as sets, we can determine the probabilities associated with each event based on the principles of probability theory.
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The graph of the function f ( x ) is shown
Answers
The true statements for the given function f(x) are:
The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .
How to calculate the values of the function?The function g(x) = f( x - 3 )
g (1) = f (1 -3 )
= f (-2 )
= 3
g (-1) = f (-1 -3)
= f (-4)
= - 1
Substituting , x = 0 to find the y intercept of g(x)
g ( 0 ) = f ( 0 - 3)
=f (-3)
=1
The y intercept of g(x) is at the point (0, 1)
Thus, options 1 and 4 are the true statements for the given function.
What are functions?Function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable.In science, engineering, and the majority of the mathematical disciplines, functions are often utilized.Functions are reportedly the central objects of inquiry in the majority of mathematical disciplines. Although some authors establish a distinction between maps and functions, functions are also referred to as maps or mappings.To learn more about functions, refer:
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Some one please help
Answers
Answer: d
|4x + 1| ≤ 5
⇒ - 5 ≤ 4x + 1 ≤ 5
⇔ -6 ≤ 4x ≤ 4
⇔ -1.5 ≤ x ≤ 1
⇒ x ∈ [-1.5; 1]
Step-by-step explanation:
Instructions: Find the lengths of the other two sides of the isosceles triangle
Answers
Answer:
x=5
h = 5 sqrt 2
Step-by-step explanation:
isosceles right triangles are always 45-45-90, ratio of those triangles are always x:x:x*sqrt 2
Then use pythagorean theorem to solve for the hypotenuse.
a^2 + b^2 = c^2
5^2 + 5^2 = c^2
25 + 25 = c^2
50 = c^2
√50 = c
7.07 = c
T/F the square root of a number will always have two outcomes one is positive and the other is negative.
Answers
we have only one outcome that is neither positive nor negative, then the statement is false.
What is square root?
A value known as the square root of a number is one that, when multiplied by itself, yields the original number. An alternative to square rooting a number is to use it. Therefore, the concepts of squares and square roots are connected. The original number is equal to the square root of any integer, which is equivalent to a number.
Let's assume that m is an integer that is positive, such that (m.m) = (m2) = m.
This seems to be true because:
-2*-2 = 2*2 = 4
So √4 = 2 and -2
But particularly the square root of zero is:
√0 = 0
So here we have only one outcome that is neither positive nor negative, then the statement is false.
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What are the closest 2 integers to 300
Answers
Answer:
17 and 18
Step-by-step explanation:
I'm pretty sure the two integers are 17 and 18
(let me know if I'm wrong)