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15. If the continuous random variable X has a uniform distribution on an interval (-2,3), then find: a) The MGF of X. (0.5) b) P(X < 1). (0.5)

Answer:

2.05m

Step-by-step explanation:

Answer:

7 years

Step-by-step explanation:

First, create expressions to represent the problem:

\(a(x) = 10(12) + 7x \\ b(x) = 3(12) + 19x\)

Simplify:

\(a(x) = 120 + 7x \\ b(x) = 36 + 19x\)

Now make the expressions equal to each other and solve:

\(120 + 7x = 36 + 19x \\ 84 = 12x \\ x = 7\)

The answer is 7 years

Answer:

See below for proof using trigonometric identities.

Step-by-step explanation:

\(\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\tan \theta=\dfrac{\sin \theta}{\cos \theta}$\\\\\\$\cot \theta=\dfrac{\cos \theta}{\sin \theta}$\\\\\\$\csc \theta=\dfrac{1}{\sin \theta}$\\\\\\$\sin^2 \theta+\cos^2 \theta=1$\\\end{minipage}}\)

To prove the given equation, use trigonometric identities to rewrite the left side of the equation.

\(\begin{aligned} \dfrac{\cot x}{\csc x}-\dfrac{\csc x}{\cot x}&=\dfrac{\dfrac{\cos x}{\sin x}}{\dfrac{1}{\sin x}}-\dfrac{\dfrac{1}{\sin x}}{\dfrac{\cos x}{\sin x}}\\\\&=\dfrac{\cos x}{1}-\dfrac{1}{\cos x}\\\\&=\dfrac{\cos x}{1} \cdot \dfrac{\cos x}{\cos x}-\dfrac{1}{\cos x}\\\\&=\dfrac{\cos^2 x-1}{\cos x}\\\\&=\dfrac{\cos^2 x-(\sin^2 x + \cos^2 x)}{\cos x}\\\\&=\dfrac{-\sin^2 x}{\cos x}\\\\&=-\dfrac{\sin x }{\cos x} \cdot \dfrac{\sin x}{1}\\\\&=-\tan x \sin x\end{aligned}\)

Hence proving that:

\(\dfrac{\cot x}{\csc x}-\dfrac{\csc x}{\cot x}=-\tan x \sin x\)

Answer:

333

Step-by-step explanation:

Answer:

Jack is 16

48 divided by 3= 16

Eric is 48

50-2=48

Answer:

A. 0.2, 0.25, 0.2

B. the scores are a quarter of the whole

Answer:

so the three numbers can be turned into fractions.

1/5, 1/4, and 4/20.

fractions can be turned into decimals by dividing the denominator into the numerator.

now we have 0.2 , 0.25 , and 0.2

greatest to least, the numbers are 0.25 , 0.2 , and 0.2

(both 0.2s are equal, so order of those doesn't matter)

Step-by-step explanation:

⅕ of shots

Dwayne 25%

4 out 20

Write each score as decimal

Compare the three score.

Answer:

19

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

dsff

A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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Answer:

B: (2, -1)

Step-by-step explanation:

Answer

<CFE

Step-by-step explanation:

alternate means across Interior between the lines

Answer:

31, 32, 29, 31

u < 28

Step-by-step explanation:

To find if a value works for an inequality, one has to substitute in the value and simplify. If the resulting equation is true, then the value is a part of the solution set of the inequality.

When simplifying an inequality, one must follow all the same rules as simplifying an equation. The only difference is that when one multiplies or divides by a negative number one must flip the inequality sign for the inequality to remain true. In this case, this rule won't come into play.

\(\frac{u}{4}<7\)

*4   *4

u < 28

Answer:

The 5 for $10 because its 2 dollars for a bag while the first is 3 dollars for a bag

Step-by-step explanation:

Answer:

I'm guessing the five for $10. If you were to by 5 for $3 it would be more than the five for $10. If there are 5 bags for $10 I'm assuming each bag is $2 which is lower than $3.

Step-by-step explanation:

∠1≅∠3 line 2 and 3 have the same reason.

∠1 and ∠3 are vertical angles, so they are formed by intersecting lines. Therefore ang1 and ∠2 are a linear pair, and ∠2 and ∠3 are a linear pair. By the Linear Pair Theorem, ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. So by the Congruent Supplements Theorem, ∠1 ≅ ∠3.

Statements  - Reason

1. ∠1 and ∠3 are vertical angles  -  Given.

2. a and b are intersecting lines  -  definition of vertical angles

ang1 and ∠2 are a linear pair

3. ∠2 and ∠3 are a linear pair  -  definition of a line

4. ∠ 1 and 2 are supplementary ang2 and ang3 are supplementary - definition of linear pair.

5. ∠1 ≅ ∠3  -  ≅ Supplements theorem

Hence the answer is ∠1≅∠3 line 2 and 3 have the same reason.

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This loan has an interest 4. 5% compounded quarterly, account balance after 10 years:

The initial loan amount is $20,000, and it has an interest rate of 4.5% compounded quarterly. You would like to know the account balance after 10 years.

To calculate the account balance, we will use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the loan
P = the initial loan amount ($20,000)

r = the annual interest rate (0.045)
n = the number of times the interest is compounded per year (4, since it is compounded quarterly)

t = the number of years (10)

Plugging in the values:

A = 20000(1 + 0.045/4)^(4*10)

A = 20000(1.01125)^40

A ≈ 30,708.94

The account balance after 10 years will be approximately $30,708.94.

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Answer:

136

Step-by-step explanation:

10x5=50

10-6=4

4x8x.5=16

10x7=70

50+16+70=136

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The Value of A=2x³ - 7x + 1 and B =-8x² + 9x - 2 then value of the expression 2(A- B) is equal to 4x³ +16x² -32x +6.

As given in the question,

Value of A=2x³ -7x+1

Value of  B =-8x² + 9x - 2

Value of the expression is given by

2(A - B)

=2{(2x³ - 7x + 1) - (-8x² + 9x - 2)}

Open the parenthesis we get

 2(2x³ - 7x + 1 +8x² - 9x + 2)

=2(2x³ + 8x² - 16x +3)

=4x³ +16x² -32x +6

Therefore, the value of A= 2x³ - 7x + 1 and B=-8x² + 9x -2 then the value of the expression 2(A - B) is equal to 4x³ + 16x² -32x + 6.

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Answer: G=62, I = 62, H =54

Step-by-step explanation:

3x+26=4x+14

x=12

G=36+26 = 62

180-62-62=54

============================================

Use law of cosines to find angle A

a^2 = b^2 + c^2 - 2*b*c*cos(A)

9^2 = 6^2 + 14^2 - 2*6*14*cos(A)

81 = 36 + 196 - 168*cos(A)

81 = 232 - 168*cos(A)

81 - 232  = -168*cos(A)

-151  = -168*cos(A)

-168*cos(A) = -151

cos(A) = (-151)/(-168)

cos(A) = 0.8988095

A = arccos(0.8988095)

A = 25.9979801

A = 26 degrees approximately

The angle m∠A will be 27. so option C is correct.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

Use law of cosines to find angle A

a^2 = b^2 + c^2 - 2*b*c*cos(A)

9^2 = 6^2 + 14^2 - 2*6*14*cos(A)

81 = 36 + 196 - 168*cos(A)

81 = 232 - 168*cos(A)

81 - 232  = -168*cos(A)

-151  = -168*cos(A)

-168*cos(A) = -151

cos(A) = (-151)/(-168)

cos(A) = 0.8988095

A = 25.9979801

A = 26 degrees approximately

Therefore, the angle m∠A will be 27. so option C is correct.

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Answer:

$1596

$1597.28

$1598.33

bank A

Step-by-step explanation:

The formula for calculating compound interest:

FV = P (1 + r/m)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

m = number of compounding

Bank A = $1500(1.064) = $1596

Bank B = $1500( 1 + 0.063/12)^12 = 1597.28

Bank C = $1500( 1 + 0.0635/365)^365 = $1598.33

Bank A pays the least amount of interest

It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.

The Discrete uniform distribution is a symmetric probability distribution used in probability theory and statistics. It contains a finite number of values that are equally likely to be observed; each value has an equal chance of 1/n. "A known, finite number of outcomes equally likely to occur" is another approach to describe the discrete uniform distribution.

The perfect example of Discrete uniform distribution is throwing a die. Tossing a fair dice is an easy illustration of the discrete uniform distribution. The possible results are 1, 2, 3, 4, 5, and 6, and the likelihood of a certain result is 1/6 each time the die is thrown. Because not all sums have an equal chance, the distribution that results when two dice are thrown and their values are summed is no longer uniform.  

From the above observation, we can say that the sum of the number of dots that show up when we roll three dice simultaneously will follow a discrete uniform distribution.

It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.

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The coordinates of point R as an integer or decimal to the nearest 0. 5 is (-1, 4.5)

The coordinates indicate the position of a point in the 2D coordinate plane relative to the origin The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis. The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis.

First the The coordinates of R

coordinates of the x-axis position of R from the x-axis is -1

The coordinate of the y-axis position from the y-axis is 4.5

Coordinates of the point R can be written as (x, y)

x = -1 , y = -4.5

Coordinates of point R = ( -1, 4.5 )

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The question is incomplete the complete question is :

What are the coordinates of point R?

Write your answer as an integer or decimal to the nearest 0. 5

Answer:

The answer is "\(\frac{26}{7}\)"

Step-by-step explanation:

The whole question can be found in the file attached.

\(\to x + \frac{5}{7} = \frac{31}{7}\\\\\)

Subtracting the \(\frac{5}{7}\) from both sides of the equations:

\(\to x +\frac{5}{7} - \frac{5}{7} = \frac{31}{7} - \frac{5}{7} \\\\\)

                    \(= \frac{31-5}{7} \\\\= \frac{26}{7} \\\\\)

Answer:

16:81

Step-by-step explanation:

explanation: Scale factor for the sides of these triangles. k=49. Therefore the ratio of the area will be k2=Area Triangle area.

Answer:

Use calculator it's easy ....

Answer :

3765.8

Answer:

\((2.2 \times 1019) + (1.5 \times 1016) \\ = 2241.8 + 1524 \\ = 3765.8\)

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).

What is function ?

A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.

Have given ,

Two functions , f(x) and g(x)

The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .

So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).

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a. Probability distribution function: X = {7, 4, -3} with respective probabilities {1/6, 1/6, 4/6}, b. Expected value (mean): -0.17, c. Your friend would gain, on average, $0.17 in one round of the game, d. If you play 20 rounds, you can expect to lose, on average, approximately $3.40.

Explanation:

a. Probability Distribution Function:

Let X be the amount of money gained in one round of the game.

P(X = 7) = Probability of rolling a 1 = 1/6

P(X = 4) = Probability of rolling a 6 = 1/6

P(X = -3) = Probability of rolling any other number = 4/6

b. Expected Value (Mean):

The expected value is calculated by multiplying each possible outcome by its corresponding probability and summing them up.

Expected Value (E(X)) = (7 * 1/6) + (4 * 1/6) + (-3 * 4/6) = (7/6) + (4/6) - (12/6) = -1/6 ≈ -0.17

Therefore, the expected value (mean) for X, the amount of money gained in one round of this game, on average, is approximately -$0.17.

c. Amount of Money Your Friend Would Gain:

The amount of money your friend would gain in one round of the game is the negative of the expected value. Since the expected value is approximately -$0.17, your friend would gain, on average, $0.17.

d. Amount of Money Expected to Win (or Lose) in 20 Rounds:

To find the amount of money you can expect to win or lose in 20 rounds of the game, multiply the expected value by the number of rounds.

Amount of Money = Expected Value * Number of Rounds

Amount of Money = (-$0.17) * 20 = -$3.40

Therefore, if you play 20 rounds of this game with your friend, you can expect to lose, on average, approximately $3.40.

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