Suppose X1,X2,X3 are random variables, each with expected value mand variance v, and cov(Xi,Xj) = c, i not equal j. Calculate the covariance and correlation coefficient of U,V , where U = 2−X1−2X2, and V = 3+3X2−X3.

Option c 15.8% is the required rate of return for Warp-O common stock.

Given,

The market price of share = $45

Beta = 1.4

The rate of return on Treasury bonds = 6%

Market rate of return = 13%

We have to find the required rate of return on Warp-O common stock;

Here,

Rate of return = The rate of return on Treasury bonds + beta × (market rate of return -The rate of return on Treasury bonds  )

= 6% + 1.4 × (13% - 6%)

= 6% + 1.4 ×7%

= 6% + 9.8%

= 15.8%

That is,

The required rate of return on Warp-O common stock is option c 15.8%

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Answer:

The base equals 4 units².

Step-by-step explanation:

Formula:

A = hbB/2

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Answer:

base = 4 units

Step-by-step explanation:

[tex]A=bh/2\\bh=2A[/tex]

[tex]b=2A/h[/tex]

Replace values:

[tex]b=2(24)/12=48/12[/tex]

[tex]b=4[/tex]

Hope this helps

Yes, I agree with all equilateral triangles are similar to isosceles triangles because Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.

When three straight lines come together, a triangle is created. Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides. Each polygon has a unique name depending on how many sides it has. For instance, the polygon with three sides is known as a triangle since the word "tri" denotes the number three. Additionally, the name of the polygon suggests that it contains three angles. "Poly" is a prefix that means many.

Given,

All equilateral triangles are similar to isosceles triangles,

Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.

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The Submarine is 7.74 Km away from its base .

In the question ,

it is given that ,

the distance travelled by Submarine from base in East direction = 4.2 Km let the distance from base to east direction be denoted by AB ,that means AB = 4.2 Km

the distance travelled by Submarine from East to North direction = 6.5 Km let the distance from east to north direction be denoted by BC . that means BC = 6.5 Km

the given situation form a right triangle ,

So , the distance from submarine to its base is the hypotenuse of the right triangle , that is AC .

So By Pythagoras Theorem ,

AC² = AB² + BC²

Substituting the values , we get

AC² = 4.2² + 6.5²

AC² = 17.64 + 42.25

AC² = 59.89

AC = √59.89

AC = 7.7388

AC = 7.74

Therefore , The Submarine is 7.74 Km away from its base .

The given question is incomplete , the complete question is

A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?

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Probability is simply how likely something is to happen, so the probability of landing heads up on the next flip is 1/2.

The probability is obtained by dividing the total number of outcomes by the entire number of potential ways an event may occur. Odds are a separate concept from probability. The probability of an event happening is divided by the probability that it won't, and the result is the odds.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value among 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

P(H)= Probability of getting  head while flipping a coin is 1/2

and,

P(T)= Probability of getting  tail while flipping a coin is 1/2

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Answer:

40min per day

Step-by-step explanation:

Answer: 40 minutes

Step-by-step explanation: All you have to do is subtract 55 and 15, which equals 40 minutes.

hope this helps!

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The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15

When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.

The price of the individual shares are also divided into the same ratio as the shares.

This means that the price per share for BBQ Corp. post - split is:

= Price per share before split / 3

= 72. 45 / 3

= $24. 15

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Using the equation of the model:

a. About 150.4 thousand students studied in abroad in 2011.

b. About 467.5 thousand students would be studying in abroad in 2018.

An example of an equation of a model that can be used to make predictions or determine the value of one variable, is the equation that models the number of college students who studied abroad each year. This is given as y = 123.1(1.069)^x, here, we have:

Using the equation, y = 123.1(1.069)^x, we would solve the following:

a. 2001 after 1998 would be x = 3 years. Therefore, substitute x = 3 into the equation y = 123.1(1.069)^x to find the number of students that are studying abroad in 2001:

y = 123.1(1.069)^3 = 150.4

This implies that about 150.4 thousand students studied in abroad in 2001.

b. 2018 after 1998 would be x = 20 years. Therefore, substitute x = 20 into the equation y = 123.1(1.069)^x to find the number of students that would be studying abroad in 2018:

y = 123.1(1.069)^20 = 467.5

This implies that about 467.5 thousand students studied in abroad in 2018.

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The null and alternative hypothesis test using μ as mean hours of sleep for LMC students is [tex]H_0[/tex] : μ = 6.9 and ([tex]H_a[/tex] : μ ≠ 6.9).

Given:

Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.

here

μ = 6.9

σ = 1.45

Null hypothesis:

[tex]H_0[/tex] : μ = 6.9

Alternative hypothesis:

([tex]H_a[/tex] : μ ≠ 6.9)

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Full question:

Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.

what are the null and alternative hypothesis?(use  μ = mean hours of sleep for LMC students).

The expectation of the required  random variable is Ex(r) for the given number of days when a relaxed student delays for laundry is Ex(r) = 5.

As given in the question,

6-sided fair die was rolled by relaxed student

Rolls of fair die represents  1  it mean laundry is done ( no delay in laundry)

Count the number of days when laundry gets  done = 1 / (1 /6)

                                                                                       = 6

Number of days when laundry gets delays = 6 - 1

                                                    = 5

Probability of laundry delay = 5/6

Expectation of the required number of random variables

Ex(r) = [tex]\sum\limits^\infty_0 {P_{r} } \,[/tex]

       = [tex]\frac{5}{6} + (\frac{5}{6}) (\frac{5}{6}) +....[/tex]

       = (5/6)( 1+ ( 5/6) + (5/6)(5/6) + (5/6)(5/6)(5/6) +...)

       =  [tex]( 5/ 6)[ \frac{1}{1- (\frac{5}{6} )}][/tex]

       = 5

Therefore, the number of days when relaxed student delays for laundry is equal to Ex(r) = 5.

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The statements which are true is 4∈W, 7.5∈W and W= ∅

What does the term "universal set" mean?

A set that contains elements from all related sets, without any repetition of elements, is known as a universal set (typically denoted by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

What are the 8 different kinds of sets?

Empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.

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By using the concept of bell shaped curve of normal distribution, it can be concluded that

The histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is given by

f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}[/tex]

Where z = [tex]\frac{x - \mu}{\sigma}}[/tex] where [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.

Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in  all the case.

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The expressions are written as

(a) The expression from east side of ski trail to reach skier's current position is θ = π/2 + 3.1 × t

(b) The expression for skier's distance to east of  ski trail is 1.9 × cos(π/2 + 3.1 × t)  km .

(c) The expression for skier's distance to north of ski trail  is 1.9 × sin(π/2 + 3.1 × t)  km  .

In the question ,

it is given that ,

the radius of the circular ski trail is = 1.9 km

The Skier starts from the Northern most point

the radians that is sweeped in per hour is = 3.1 radians per hour

that means the angular speed is = 3.1 radians per hour ,

Part(a)

From the above data the expression in terms for t that represents number of radians swept out from each side of ski trail to reach skier's current position is written as ,

θ = π/2 + 3.1 × t

Part(b)

From the above data , expression in terms of t to represent skier's distance to the east of ski trail is written as ,

we know that , x = rcosθ

Substituting the value of θ from part(a) ,

we get ,

= 1.9 × cos(π/2 + 3.1 × t)  km

Part(c)

From the above data , expression in terms of t to represent skier's distance to the north of ski trail is written as ,

we know that , y = rsinθ

Substituting the value of θ from part(a) ,

= 1.9 × sin(π/2 + 3.1 × t)  km

Therefore , The expressions are (a) for radians is θ = π/2 + 3.1 × t

(b) the distance to the east is 1.9 × cos(π/2 + 3.1 × t)  km  ,

(c) the distance to the north is 1.9 × sin(π/2 + 3.1 × t)  km  .

The given question is incomplete , the complete question is

A skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing.

(a) write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position.

(b) write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km).

(c) write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).

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After applying Baye's Rule , the value of P(A/B) is 1 , the correct option is (d) .

In the question ,

it is given that ,

probability of A is P(A) = 1/2 ,

P(B) is = 1/3 , and

P(A/~B) = 1/4

we know that Baye's Rule for any two events A and B is ,

P(A/B) = (P(B/A) × P(A))/ P(B)

Substituting the values of P(A) and P(B) from above in the Baye's Rule ,

we get ,

P(A/B) = 3/2 × P(B/A)

given that P(A/~B) = 1/4 ,

and we know that , P(B/A) = 1 – P(~B/A)      ....equation(1)

by Baye's rule ,

P(~B/A) = (P(A/~B) × P(~B)) / (P(A))

= (1/4 * 2/3 )/(1/2)

= 1/3

Substituting it in equation(1) , we get

P(B/A) = 1 - 1/3

= 2/3

Substituting the value of P(B/A) in P(A/B) = 3/2 × P(B/A) ,

we get ,

P(A/B) = 3/2 × 2/3

P(A/B) = 1

Therefore , the value of P(A/B) is 1 .

The given question is incomplete , the complete question is

Given two Boolean random variables, A and B, where P(A) = 1/2 , P(B) = 1/3, and P(A/~B) = 1/4 , Apply Baye's Rule and calculate the value of  P(A/B) ?

A. 1/6

B. 1/4

C. 3/4

D. 1

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I don't know so like ya I don't know

Answer:

0.6293

Step-by-step explanation:

The [tex]z[/tex] score for $24000 is [tex]\frac{24000-25000}{3000} \approx 0.333[/tex].

[tex]P(z<0.333)=0.6293[/tex]

In 120 ways 5 numbers can be arranged through permutations.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation." The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Given,

In following ways 5 numbers can be arranged through permutations,

5!

5 × 4 × 3 × 2×1

120

In 120 ways 5 numbers can be arranged through permutations.

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Using the test statistic z, the value of z is 1.20.

In the given question,

Given:

Sample Size(n) = 12

Population Mean([tex]\mu[/tex]) = 25

Standard Deviation(S) = 4.6

Statistic of intereset(x) = 26.6

The test statistic z is

[tex]z=\frac{x-\mu}{\frac{s}{\sqrt{{n}}}}[/tex]

Putting the value

[tex]z=\frac{26.2-25}{4.6/\sqrt{12}}[/tex]

z = 1.6/(4.6/3.46)

z = 1.6/1.329

z = 1.20

Hence, the value of z is 1.20.

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The probability that Chuck will shop for k hours be,

C(n , k).p^k.q^(n - k)

Given, Chuck will go shopping for probability books for K hours.

K is a random variable and is equally likely to be 1, 2, 3, or 4.

The number of books N that he buys is random and depends on how long he shops.

The probability that chuck will shop for k hours be,

P(X = k) = C(n , k).p^k.q^(n - k)

So, we can find the probability that chuck will shop for k hours by,

C(n , k).p^k.q^(n - k)

Hence, the probability that Chuck will shop for k hours be,

C(n , k).p^k.q^(n - k)

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The transtors produced by one machine have a lifetime which is Exponentially Distributed. let X be the lifetime of a transistor.

a) P(X≥200 hours) = 0.29

b) E(x) = 166.7

c) Var(x) = 12222.22

We have given the exponential distribution of lifetime of transtors produced by one machine

So, X∼Exp(x)

a) The probability density function is

f(x)=m × e⁻ᵐˣ

The number e = 2.71828182846e

we have , mean , u = 100 for first machine

and it follows that

P(X≥200) = e⁻²·⁴¹² + e⁻¹·⁸¹² = 2e⁻²≈0.29.

(b) By the tower property of conditional expectation, E(X) = E[E(X|Y)] = XyE(X|Y=y)

pY(y)=E(X|Y= 1)P(Y= 1) +E(X|Y= 2)P(Y= 2).

Again using the conditional distributions of X|Y, we have E(X|Y= 1) = 100, E(XY= 2) = 200.

Hence,E(X) = 100·412+ 200·812=5003≈166.7.

(c) The general formula for a random variable depending on a parameter is:

Var(X) = E(Var(X|Y)) + Var(E(X|Y))

In this case, Y is a random variable which is "100" with a probability of 1/3 and "200" with a probability of 2/3, and X is an exponential distribution with mean Y.

Var(X|Y) = Y² so E(Var(X|Y)) = (1/3)100² + (2/3) 200² = 90000/9

E(X|Y) = Y, so Var(E(X|Y)) = Var(Y) = E(Y²) - E(Y)² = 30000 - (500/3)² = (30000 * 9 - 250000)/9

= 20000/9

Var(X) = 110000/9 = 12222.22

Hence, a) the P(X≥200) = 0.29

b) E(x) = 166.7

c) var(x) = 12222.22

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The answer of two iterations of newton's method to approximate a zero of the function using the given initial guess is 1.5262!

Iteration refers to doing a procedure repeatedly. Starting with an initial value, enter it into the iteration formula to get a new value. Next, use the new value for the next substitution, and so on, to solve an equation using iteration.

By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1,

and by using the previous guess, xn, like so-

xn+1 = xn - f(xn)/f'(xn)

and herethe case is f(x) = cos(x), and so f'(x) = -sin(x).

Also, furthermore, cos(x)/(-sin(x)) = -cot(x).

here, we have to simplify the formula to get a better guess for a zero to:

xn+1 = xn + cot(xn)

x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...

And x3 = 2.06170... + cot(2.06170...) = 1.52615...

Ans =  1.5262!

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Option (d) is correct. Criteria for assigning fixed costs to sectors include relative utility, sustainability, and fairness.

Fixed cost and allocation:

Fixed costs are costs that are essentially constant and do not change with fluctuations in the output of the relevant sector. Fixed costs are borne by the company and exist independently of business activities. Rent, insurance, and depreciation are examples of fixed costs. Cost attributes help identify, total, and assign costs to cost objects.

Fixed cost allocation involves identifying the beneficiaries of outputs and allocating costs to beneficiaries in proportion to the benefits received. Fixed costs can also be allocated in relation to the payer's ability to bear the allocated costs. Fairness is a criterion met where cost allocation is the basis for determining a satisfactory price (such as government contracts).

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[tex]x=number\hspace{5em}x^2=\textit{squared number} \\\\\\ \stackrel{\textit{difference of }x^2\textit{ and 18}}{x^2~~ - ~~18}~~ = ~~\stackrel{\textit{three times }x}{3x} \\\\\\ x^2-3x-18=0\implies (x-6)(x+3)=0\implies x= \begin{cases} 6\\\\ -3 ~~ \checkmark \end{cases}[/tex]

The line containing the slope -1/5 and coordinates (1,-4) can be graphed by moving one unit negative of y and running 5 towards of x axis

Slope is defined as the rate of change of y to rate of change of x

How to graph the slope of a line?

To graph an equation in point slope form,  

The first step is to extract the known point and slope from the equation.

The equation of the line is given by:   y−yₐ=m(x−xₐ)

From the parameter; M=[tex]\frac{Y-Y_{1} }{X-X_{1} }[/tex]

The given parameters are

[tex]-\frac{1}{5} =\frac{y+4}{x-1}[/tex]

Solving the equation,

x+1=-y+20

x+y=20-1

x+y=19

The slope -1/5 is used  to find which way the line extends.

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The dollar duration of the given bond is $3.71

Dollar duration:

Dollar duration means a linear approximation of how a bond's value will change in response to changes in interest rates.

Given,

Here we have to assume that a bond sells at $92.10 and its modified duration is 4.03.

And we need to compute dollar duration. answer with two decimal digits accuracy and the correct sign.

As per the formula of dollar duration, the values of

bond price = $92.10

duration = 4.03

interest rate = 0.01

So, the dollar duration is calculated as follows,

=> dollar duration = 0.01 x 92.10 x 4.03

=> dollar duration = 3.71

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Answer:

its A

Step-by-step explanation:

-x²+x+(4x²-x-1)

-x²+x+4x²-x-1

-x²+4x²-1

3x²-1

:: means average mean in mathematics.

A number system is defined as a system of writing to express numbers.

We need to find what is :: in maths

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas.

: : is a mathematical notation, it is called as double colon and it is used to find the average mean.

a:b: : c:d

In the above expression it acts as an equivalent ration between a:b and c:d

Hence, :: means average mean in mathematics.

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The equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

What is a parabola?

A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

The given equation is x² + y² = 25 ; (4, 3)

Now when we put x = 4 and y = 3

then LHS = RHS.

Now find the slope:

      2x + yy' = 0

       ⇒ y' = -x/y

Now at (4, 3) slope would be y' = -4/3.

The equation of the tangent would be

      y - y1 = m(x - x1)

      y - 3 = (-4/3)(x-4)

     3y - 9 = -4x + 16

     4x + 3y = 25

     y = -4x/3 - 25/3

Now equation of the normal is:

  y - y1 = (-1/m)(x - x1)

  y - 3 = 3/4(x - 4)

  y = 3x/4

Hence, the equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.

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Answer:

shaded area

unlikely

Step-by-step explanation:

She should guess a shaded portion of a rectangle that has a height of 10 and a length of 8 to maximize her chances of winning. The unlikely word describes the likelihood of the ball stop.

First, we need to find the areas of all the regions.

The area of the shaded rectangle = Length x Breadth = 10 x 8 = 80 square units

Area of unshaded rectangle = Length x Breadth = 5 x 2 = 10 square units

Area of unshaded triangle = 1/2 x base x height = 1/2 x 4 x 8 = 32/2 = 16 square units

Area of unshaded square = Side^2 = 4^2 = 16 square units

The area difference between the shaded and unshaded areas = The area of the shaded rectangle - (Area of unshaded rectangle + Area of unshaded triangle + Area of the unshaded square)

The area difference between the shaded and unshaded areas = 80 - (10 + 16 + 16)

The area difference between the shaded and unshaded areas = 80 - 42 = 38

As we see that the area of the shaded region is 38 more than the unshaded region so to maximize her chances of winning she should guess the shaded region or area.

Probability percentage of the shaded rectangle = 80/122 x 100 = 65.57%

Probability percentage of an unshaded rectangle = 10/122 x 100 = 8.20%

Probability percentage of an unshaded triangle = 16/122 x 100 = 13.11%

Probability percentage of an unshaded square = 16/122 x 100 = 13.11%

The unlikely word describes the likelihood of the ball stopping in a square or rectangular-shaped area because one is shaded and unshaded and the other is only unshaded. So, both are having different probabilities because of shape, area, and portion.

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