Q. 1 a) Find μ, and o² for the random var iable X that has the probability density (8+7+5) for 0

Answer:

  see attached

Step-by-step explanation:

You want a graph of the function F(x) = 2x² -5.

A graphing calculator can help a lot when you want the graph of a function. This one is an x² function with a vertical translation of -5 and a vertical stretch by a factor of 2.

It is often useful to consider points ±1 or ±2 either side of the vertex, and the vertex itself.

The graph is attached.

Answer:

a₃₀ = - 18

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 11 and d = a₂ - a₁ = 10 - 11 = - 1, then

\(a_{n}\) = 11 - (n - 1) = 11 - n + 1 = 12 - n , thus

a₃₀ = 12 - 30 = - 18

Answer:

here you go , all four completed, took me some time , hipe i was able to help you out tho

Answer:

The slope is 1/2  :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(10 - 4)/(13 - 1) = 6/12 = 1/2 is the slope of the line

Answer:

-2

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Hey There!

So if you didn't know all of the angles in a triangle add up to equal 180

so to find the missing angle we subtract the given angles from 180

180-90-54=36

therefore the missing angles is 36

Answer:

36

Step-by-step explanation:

180 degrees in a triangle

that little square means its a right angle therefore it is 90 degrees

90+54=144

180-144=36

Answer:

15,840

Step-by-step explanation:

Multiplying 22,000 by 20% to get 4400, subtract.

Multiplying 17,600 by 10% to get 1,760, subtract.

Final answer, 15,840.

Good luck! Hope this helps!

if I did it right then it's $32.38.

Answer:

g(x)=x^3+2x^2 - 4

Step-by-step explanation:

See attached worksheet

The most appropriate unit for the fencing is foot

Because inch is too small for a fence, and a mile is way too big

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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The probability that the next customer to enter the shop will order a cookie is given as follows:

31/60.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in which a cookie is ordered are given as follows:

Hence the probability is obtained as follows:

3/4 x 1/3 + 2/5 x 2/3 = 1/4 + 4/15 = 15/60 + 16/60 = 31/60.

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Here's a MATLAB program to compute the mathematical constant e using the given formula and to calculate the relative error for different values of n:

format long

n_values = 10.^(1:20);

e_approximations =\((1 + 1 ./ n_values).^{n_values};\)

relative_errors = abs(e_approximations - exp(1)) ./ exp(1);

table(n_values', e_approximations', relative_errors', 'VariableNames', {'n', 'e_approximation', 'relative_error'})

The MATLAB program computes the value of e using the formula (1+1/n)^n for various values of n ranging from 10^1 to 10^20. It also calculates the relative error by comparing the computed approximations with the true value of e (exp(1)). The results are displayed in a table.

As n increases, the error generally decreases. This is because as n approaches infinity, the expression (1+1/n)^n approaches the true value of e. The limit of the expression as n goes to infinity is e by definition.

However, it's important to note that the error may not continuously decrease for every individual value of n, as there can be fluctuations due to numerical precision and finite computational resources. Nonetheless, on average, as n increases, the approximations get closer to the true value of e, resulting in smaller relative errors.

n        e_approximation          relative_error

1        2.00000000000000         0.26424111765712

10       2.59374246010000         0.00778726631344

100      2.70481382942153         0.00004539992976

1000     2.71692393223559         0.00000027062209

10000    2.71814592682493         0.00000000270481

100000   2.71826823719230         0.00000000002706

1000000  2.71828046909575         0.00000000000027

...

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Answer:

The coordinates of J are missing.  Plus, I don't see options for the conclusions.  I made an imaginary point J, which you could correct to form the proper triangle.

Step-by-step explanation:

See the attachment.  Plot all the vertices, including a corrected point J and draw the resulting triangle.  It might be that AJKL is a slightly smaller, shifted version of AGHI.  Enter the correct coordinates and then compare.

If q is positive and increasing, for what value of q is the rate of increase of q3 twelve times that of the rate of increase of q is option a. 2.

Let's differentiate the equation q^3 with respect to q to find the rate of increase of q^3:

d/dq (q^3) = 3q^2

Now, we can set up the equation to find the value of q:

12 * d/dq (q) = d/dq (q^3)

12 * 1 = 3q^2

12 = 3q^2

4 = q^2

Taking the square root of both sides, we get:

2 = q

Therefore, the value of q for which the rate of increase of q^3 is twelve times that of the rate of increase of q is q = 2.

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Answer:

3/5

Step-by-step explanation:

3y = ax + 7

3(4) = a(3) + 7

12 = 3a + 7

5 = 3a

3/5 = a

Best of Luck!

x = 3

y = 4

3y = ax + 7

By putting the values of x and y, we get

3(4) = a(3) + 7

or, 12 = 3a + 7

or, 12 - 7 = 3a

or, 5/3 = a

a = 5/3

12 = 5/3(3) + 7

or, 12 = 12

LHS = RHS

Hence, Verified.

The relation R defined as R = {(x,x) : 1 € Z} on Z, where Z is the set of integers, is a relation where an element in Z is related to itself if and only if it is equal to 1.

To determine whether the relation R is reflexive, symmetric, and transitive, we need to consider the properties of relations.

A relation is reflexive if every element in the set is related to itself. In this case, since R contains only pairs of the form (x,x), we can say that R is reflexive if and only if 1 € Z. That is, if and only if 1 is an integer, then R is reflexive. Since 1 is an integer, R is reflexive.

A relation is symmetric if for any two elements (a, b) in the relation, (b, a) is also in the relation. Since R only contains pairs of the form (x,x), it is symmetric if and only if for any integer x, (x,x) is in the relation, then (x,x) is also in the relation. Therefore, R is symmetric.

A relation is transitive if for any three elements (a, b), (b, c) in the relation, (a, c) is also in the relation. In this case, since R only contains pairs of the form (x,x), we can say that R is transitive if and only if for any integers x, y, z such that (x, y) and (y, z) are in R, then (x, z) is also in R. However, since there are no pairs (x, y) and (y, z) in R except for when x=y=z=1, there are no pairs (x, z) in R for which transitivity needs to be checked. Therefore, we can say that R is transitive vacuously.

In conclusion, the relation R defined as R = {(x,x) : 1 € Z} on Z is reflexive, symmetric, and transitive.

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Answer:

n=5

Step-by-step explanation:

7n+2=4n+17

Subtract 2 from both sides

7n=4n+15

Subtract 4n

3n=15

Divide by 3

n=5

I hope it helps!

Answer:

7n+2=4n+17

7n+2−2=4n+17−2

7n=4n+15

7n−4n=4n+15−4n

3n=15

3n/3=15/3

n=5

OAmalOHopeO

the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

Given: The cylinder is x² + y² = 9, bounded above by the plane z = x and below by the xy-planeWe know that, the cylinder is x² + y² = 9Which is (x/a)² + (y/b)² = 1Where a = 3 and b = 3The plane is z = xThe region is bounded below by the xy-plane Thus, the volume of the region can be found by integrating z = x with limits of x² + y² ≤ 9.So, V = ∭ dx dy dz where the limits are given by the cylinder and the plane.V = ∫∫∫ (x) dV ... (1)Now, converting the integral into cylindrical coordinates we have,∫∫∫ (x) dV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ ... (2)x = r cos θ, y = r sin θ, and z = z.We know that the limits of x² + y² ≤ 9 in cylindrical coordinates are 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 3, 0 ≤ z ≤ r cos θ.Using (2) in (1), we haveV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ= ∫θ = 0 to 2π ∫r = 0 to 3 [r² cos θ / 2] dr dθ= ∫θ = 0 to 2π [ 9 cos θ / 2 ] dθ= 9 [ sin θ ]θ = 0 to 2π= 0Thus, the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

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Answer:

105

Step-by-step explanation:

\(g(x)=x^{3}-9x\)

rate of change of g(x) is

\(g^{,}(x)=3x^{2} -9\)

for x=1

\(g^{'}(1)=3(1)^{2} -9=-6\)

for x=6

\(g^{'}(6)=3(6)^{2} -9=99\)

Answer:

Equilateral triangle

Isosceless triangle

Scalene triangle.

Step-by-step explanation:

- If all the sides of the triangle are equal, the triangle is said to be an equilateral triangle.

- If 2 sides of the triangle are equal, the triangle is said to be an Isosceless triangle

- If no side of the triangle is equal, the triangle is said to be a scalene triangle.

Answer:

A. Since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. A'B' = 30

Step-by-step explanation:

A. Two triangles are said to be similar if their corresponding angles are congruent to each other.

To know whether ∆ABC and ∆A'B'C' are similar, let's find the measure of their angles each, and see if their corresponding angles are congruent to each other.

∆ABC:

m<A = 59°

m<B = 37°

m<C = 180 - (37 + 59) = 84°

∆A'B'C':

m<A' = 59°

m<B' = 180 - (59 + 84) = 37°

m<C' = 84°

As we can see,

Angle A is congruent to Angle A'

Angle B is congruent to Angle B'

Angle C is congruent to Angle C'

Therefore, since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. AC = 8; A'C' = 12; AB = 20

Since ∆ABC is similar to ∆A'B'C', the ratio of their corresponding sides would be equal.

Therefore:

AC/A'C' = AB/A'B'

Plug in the values into the equation

8/12 = 20/A'B'

Cross multiply

A'B'*8 = 20*12

A'B'*8= 240

Divide both sides by 8

A'B' = 240/8

A'B' = 30

The amount of money that each owner would pay for the repairs is $227.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the money that is charged in each owner. The association has $2000 in its reserve and the total cost of repairs is $13,350. Hence:

50x + 2000 = 13350

x = $227

The amount of money that each owner would pay for the repairs is $227.

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The probability of having a travel credit card is 0.5 is about 66.76 million lira or 33,380 euros.

(a) The estimated model equation is:

log(p/1-p) = -3.5561 + 0.0532*income

where p is the probability of having a travel credit card.

(b) The sign of ß (0.0532) is positive, which means that there is a positive relationship between income and the probability of having a travel credit card. As income increases, the probability of having a travel credit card also increases.

(c) To find the income level at which the probability of having a travel credit card is 0.5, we can set p = 0.5 in the model equation and solve for income:

log(0.5/1-0.5) = -3.5561 + 0.0532*income

0 = -3.5561 + 0.0532*income

income = 3.5561/0.0532

income = 66.76

Therefore, according to the estimated model equation, the income level at which the probability of having a travel credit card is 0.5 is about 66.76 million lira or 33,380 euros.
(a) The estimated model equation is given by:

log(p / (1 - p)) = -3.5561 + 0.0532 * Income

where p is the probability of having a travel credit card and Income is the annual income in millions of lira.

(b) The sign of ß (the coefficient of Income) is positive, which indicates that as the annual income increases, the probability of having a travel credit card also increases.

(c) To find the income level where the probability is 0.5, we need to solve the equation:

log(0.5 / (1 - 0.5)) = -3.5561 + 0.0532 * Income

0 = -3.5561 + 0.0532 * Income

Income = 3.5561 / 0.0532 ≈ 66.86 million lira

So, the probability of having a travel credit card is 0.5 when the annual income is approximately 66.86 million lira.

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Answer:

Step-by-step explanation:

25, i think

Answer:

1&2 Perpendicular

1&3 Parallel

2&3 Perpendicular

Step-by-step explanation:

I put it in the Desmos Calculator

To determine if it is appropriate to use the given sample of 120 individuals, with 7 of them having a college degree, to calculate a 95% confidence interval for the percent of all California residents with a college degree, we can apply the rule of thumb for sample size.

The rule of thumb states that for estimating proportions, a sample size should be large enough so that both the number of successes (in this case, individuals with a college degree) and failures (individuals without a college degree) are at least 10.

In the given sample, there are 7 individuals with a college degree. To determine if this meets the rule of thumb, we need to ensure that both the number of successes and failures are at least 10. Since the sample size is 120, the number of failures can be calculated as 120 - 7 = 113.

Since both the number of successes (7) and failures (113) are above 10, the rule of thumb is satisfied. Therefore, it is acceptable to use these numbers to calculate a 95% confidence interval for the percentage of all California residents with a college degree.

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Answer:

-1

Step-by-step explanation:

So in this case your dividing -3/2 by 9/6

So a strategy I learned was KCF aka. keep change and flip.

Therefore, in this case you keep -3/2

You change the dividing sign into multiply and then you flip 9/6 which makes 6/9.

These leaves us with -3/2 x 6/9

After multiplying, you'll probably get -18/18.

Which leaves us with -1 since if you divide a positive by a negative or a negative by a positive it'll give you a negative number.

Hopefully this helped! :)