Suppose that X is a random variable with mean 2 and variance 3. (a) Compute Var(2X + 1). (b) Compute E[(3X - 4) ^ 2]

The cosine of angle S is 4/5.

In mathematics, cosine is a trigonometric function that relates the angles of a right-angled triangle to the ratio of the length of its adjacent side to its hypotenuse.

More formally, cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse of a right-angled triangle containing that angle.

The cosine of an angle theta, denoted as cos(theta), is given by the formula:

cos(theta) = adjacent side / hypotenuse

The cosine function has a range of values between -1 and 1, and is periodic with a period of 2π radians or 360 degrees.

The ratio of the neighboring side to the hypotenuse is known as the cosine of an acute angle in a right triangle.

In triangle RST, the hypotenuse is RS = 10 and the adjacent side to angle S is ST = 8.

Therefore, the cosine of angle S is:

cos(S) = adjacent/hypotenuse = ST/RS = 8/10

To simplify this fraction to lowest terms, we can divide both the numerator and denominator by their greatest common factor, which is 2.

8/10 = (8/2)/(10/2) = 4/5

So, the cosine of angle S is 4/5.

To know more about angle  visit:

https://brainly.com/question/15277238

#SPJ1

The amount of money that each student has to pay will be $9.61.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' be the amount that each student pay. Then the equation is given as,

34x = 326.74

Solve the equation for 'x', then we have

34x = 326.74

x = 326.74 / 34

x = $9.61

The amount of money that each student has to pay will be $9.61.

More about the solution of the equation link is given below.

https://brainly.com/question/29797035

#SPJ9

The system of transformation used to map ∆RST onto ∆UVW using algebraic notation is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).

Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Just the object's location changes during translation; its size stays the same.

Every point in a form, such as a triangle, rectangle, square, line, circle, and so on, will move by five units in the same direction if one point in the shape moves five units forward. If one point of a triangle travels four units to the left, all three points of the triangle should also move four units to the left.

From the figure we see that the coordinates of the points are:

R = (2, 3)

T = (-1, 0)

U = (1, -2.5)

W = (-0.5, -4)

The first transformation is that the ∆RST is translated down by 4 units.

(x, y) → (x, y - 4)

The second transformation is dilation, since the ∆UVW is smaller in size than the original image.

The distance between RT is:

d = √(-1 -2)² + (0 - 3)²

d = √9 + 9 = √18

The distance between UW is:

d = √(-0.5 - 1)² + (4 + 2.5)²

d = √2.25 + 42.25 = √44.5

The scale factor is:

SF = length of the original figure/ length of new image

SF = √18 / √44.5 = 6.6

Hence, the system of transformation used to map ∆RST onto ∆UVW is (x, y) → (x, y - 4) that is translated down by 4 units and dilation using the scale factor 6.6(x, y).

Learn more about dilation here:

https://brainly.com/question/13176891

#SPJ1

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function [tex]y=20(1.04)^{t}[/tex] represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

[tex]y=20(1.04)^{t}[/tex]

t = 10

[tex]y=20(1.04)^{10}[/tex]

[tex]y=20(1.48024428492)[/tex]

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

learn more on function here: https://brainly.com/question/12431044

#SPJ1

The pilot should turn approximately 50.7° to fly directly to the airport.

The problem can be solved using trigonometry.

Let x be the angle the pilot should turn in order to fly directly to the airport.

Then, we have:

tan(x) = 107 / 172

x = arc tan^-1(107 / 172)

x = 50.7 degrees

Learn more about angles:

https://brainly.com/question/25770607

at:#SPJ1

The expression is 16w².

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

(4w)²

This can be expressed as,

= 4² x w²

[ 4 x 4 = 16 ]

= 16 x w²

= 16w²

Thus,

The expression is 16w².

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Sam spent 1 hour and 55 minutes at school.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Sam went to school at 8:15.

He was in homeroom for 20 minutes, math for 35 minutes, and reading for 35 minutes and then had a 15-minute break.

The total time is,

= 20 + 35 + 35 + 25

= 115 minutes.

= 1 hour and 55 minutes.

Therefore, Sam spends 1 hour and 55 minutes at school.

To learn more about the addition;

brainly.com/question/29464370

#SPJ1

[tex] \bf \: {x}^{2} - 2x - 24 = 0[/tex]

[tex] \bf \: {x}^{2} - 6x + 4x- 24 = 0[/tex]

[tex] \bf \: {x}^{}( x- 6) + 4(x- 6) = 0[/tex]

[tex] \bf \: {}^{}( x + 4)(x- 6) = 0[/tex]

[tex]x = - 4 \: \: or \: \: 6[/tex]

The length of the two legs is 25√2 cm

From the question, we have the following parameters that can be used in our computation:

A right, isosceles triangle has hypotenuse length 50cm

Represen the length of each leg with x

Using the above definition as a guide, we have the following:

x = Hypotenuse/√2

So, we have

x = 50/√2

This gives

x = 25√2

HEnce, the legs are 25√2 cm each

Read more about isosceles right triangle at

https://brainly.com/question/23499443

#SPJ1

The solution is:

Bigger volume the cylinder wich radius is (L/2) and h = WHow much according to the relation L/W Let´s call L and W the dimensions of the piece of paper

Let´s assume that

 L > WThe Volume (V) of a cylinder is:V(c) = π×r²×h   where r is the radius of the circular base, and h is the height of the cylinderFor the first cylinder (V₁)  (the one which h = w then r = (L/2)V₁ = π×(L/2)²×w

For the second cylinder (V₂) ( the one with h = L and r = (W/2)V₂ = π×(W/2)²×LThe relation

 V₂/V₁  is:V₂/V₁  =  π×(W/2)²×L/π×(L/2)²×wV₂/V₁  = W/LBut   L > W    then       V₂/V₁ < 1     or V₂ < V₁The volume of the first cylinder is bigger than the second one:

n:

Hope this helped :]

The relationship exhibiting conversion factor correctly is the option c. 1 ft /12 in, where ft is foot and in is inches.

As per the mentioned information, the relationship will be expressed as -

12 inches = 1 foot

So, now we will use unitary method to find 1 inches, which will be the conversion factor.

Now, the formula for conversion factor (that is one unit of inches) will be = number of unit in foot/number of unit in inches

Conversion factor = 1/12

Based on this, the correct option indicating conversion factor is c. 1 ft /12 in.

Learn more about unit conversion -

https://brainly.com/question/13016491

#SPJ4

The minimum payment for this month would be:

minimum payment = 3% of $3,400 = 0.03 x $3,400 = $102

The interest charged on the remaining balance after the minimum payment is made can be calculated as:

interest = APR/12 x remaining balance

where APR is the annual percentage rate and the division by 12 is to convert it to a monthly rate.

So for this month, the interest charged would be:

interest = 0.27/12 x $3,298 = $74.32

where $3,298 is the remaining balance after the minimum payment is made.

Therefore, the balance next month would be:

balance = previous balance - payment + interest

balance = $3,400 - $102 + $74.32 = $3,372.32

So the balance next month should be $3,372.32 if you only make the minimum payment and do not use the card again.

The amount of hockey sticks sell for in 2019 will be $22.26.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A certain sporting goods store sold a hockey stick for $20.00 in 2017. The store increased the price by 5% in 2018 and by another 6% in 2019.

Then the amount of hockey sticks sell for in 2019 will be given as,

⇒ $20 x (1 + 0.05) x (1 + 0.06)

⇒ $20 x 1.05 x 1.06

⇒ $22.26

The amount of hockey sticks sell for in 2019 will be $22.26.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ9

The class width, class midpoint of the first class, and class boundaries of the first class of the given frequency distribution is 3, 51, and 49.5-52.5, respectively.

A frequency distribution is a table that shows how often different values or ranges of values occur in a set of data. In other words, it displays the frequency or count of each distinct value or range of values in a dataset.

To find the class width, we need to subtract the lower limit of the first class from the lower limit of the second class (since all the classes have the same width):

Class Width = Lower limit of second class - Lower limit of first class

= 53 - 50

= 3

Therefore, the class width is 3.

To find the class midpoint of the first class, we need to find the average of the lower limit and upper limit of the first class:

Class Midpoint = (Lower limit + Upper limit) / 2

= (50 + 52) / 2

= 51

Therefore, the class midpoint of the first class is 51.

To find the class boundaries of the first class, we first need to subtract the upper class limit for the first class from the lower class limit for the second class and divide it by two.

(Lower class limit of the second class - Upper class limit of the first class)/2

= (53 - 52)/2

= 0.5

Then, subtract the result to the lower limit of the first class and add to the upper class of the first class:

Class Boundaries = (Lower limit - 0.5) to (Upper limit + 0.5)

= (50 - 0.5) to (52 + 0.5)

= 49.5 to 52.5

Therefore, the class boundaries of the first class are 49.5-52.5.

Based on these calculations, the class width is 3, the class midpoint of the first class is 51, and the class boundaries of the first class is 49.5-52.5.

The problem seems incomplete, it must have been...

"Use the given frequency distribution to find the

(a) class width.

(b) class midpoint of the first class.

(c) class boundaries of the first class.

Height (in inches)

Class | Frequency, f

50-52     5

53-55     8

56-58     12

59-61     13

62-64     11

Learn more about frequency distribution here: https://brainly.com/question/1094036

#SPJ4

So, Lan's total monthly insurance expense is $221.67.

A time period is a duration of time characterized by specific events, trends, or conditions. Time periods can be defined by various factors such as historical, cultural, or scientific significance. Examples of time periods include the Renaissance, the Industrial Revolution, the Bronze Age, and the Jurassic period in Earth's geological history. Time periods can vary in length from a few years to millions of years, depending on the context in which they are being discussed.

Given by the question: -

First, let's prorate the semiannual premium for automobile insurance.

Since semiannual means twice a year, we need to divide $450 by 2 to get the premium for a single 6-month period:

$450 ÷ 2 = $225

To find the monthly premium, we need to divide this by 6 (since there are 6 months in a 6-month period):

$225 ÷ 6 = $37.50

So, the monthly premium for automobile insurance is $37.50.

Next, we don't need to prorate the monthly premium for health insurance since it is already a monthly expense. Therefore, the monthly premium for health insurance is simply $155.

Finally, to prorate the annual premium for life insurance, we need to divide it by 12 to get the premium for a single month:

$350 ÷ 12 = $29.17

So, the monthly premium for life insurance is $29.17.

Therefore, the total monthly expense for these three types of insurance is: $37.50 + $155 + $29.17 = $221.67

To learn more about factor:

https://brainly.com/question/14209188

#SPJ1

Answer:

t = 47

Step-by-step explanation:

47 - 38 = 9

Answer:

The insect population increased at a rate of 20% each month.

Step-by-step explanation:

i looked it up on gogle and it popped up on brainly asked by someone else and already answered

a) The probability that the chosen letter is R is 1/10.

b) The probability mass function of X is P(X = 3) = 1/5, P(X = 4) = 2/5, P(X = 5) = 2/5

c) If k = 3 , then P(X = 3 | X = 3) = 1. Otherwise, P(X = k | X = 3) = 0

d)  The conditional probability P(the chosen letter is R | X > 3) is 1/11.

e) Given that the chosen letter is R, the probability that the word was BROWN is 1/2.

a) The probability that the chosen letter is R is equal to the number of R's divided by the total number of letters in the sentence. There are two R's in the sentence "SOME DOGS ARE BROWN", so the probability of choosing an R is 2/20 = 1/10.

b) To find the probability mass function of X, we need to find the probability of choosing a word of a certain length. There are five words in the sentence, one of length 3, two of length 4, and two of length 5.

The probability of choosing a word of length 3 is 1/5, the probability of choosing a word of length 4 is 2/5, and the probability of choosing a word of length 5 is 2/5. So, the probability mass function of X is:

P(X = 3) = 1/5

P(X = 4) = 2/5

P(X = 5) = 2/5

c) To find the conditional probability P(X = k | X = 3), we need to find the probability of choosing a word of length k given that we know the word has length 3. If X = 3, then the word must be "DOG". So, the only possibility is P(X = 3 | X = 3) = 1.

For all other values of k, P(X = k | X = 3) = 0 because the word must have length 3 given that X = 3.

d) To find the conditional probability P(the chosen letter is R | X > 3), we need to find the probability of choosing an R given that we know the length of the word is greater than 3. The number of R's in words with length greater than 3 is 1, and the number of letters in these words is 11, so the probability is 1/11.

e) Given that the chosen letter is R, the probability that the word was BROWN is equal to the number of R's in the word BROWN (1) divided by the number of R's in the sentence (2). So, the probability is 1/2.

To learn more about probability click on,

https://brainly.com/question/16976825

#SPJ4

The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

Learn more about Boolean expressions here:

https://brainly.com/question/30378141

#SPJ4

Answer: I believe it is the first bubble but it could also be the third one im sorry that is kinda confusing.

Answer:

  a.  3800

Step-by-step explanation:

You want the product (0.82 +0.042)(4.4×10³) expressed to an appropriate number of significant figures.

The number of significant figures in a product is the least of the numbers of significant figures in the contributors. Here, 4.4×10³ has 2 significant figures, so the result needs to be rounded to 2 significant figures.

  (0.82 +0.042)(4.4×10³) ≈ 3800

__

Additional comment

This is the only answer choice with 2 significant figures, so it can be chosen on that basis alone.

The rounded answer is that approximately 68% of scores were between 473 and 559.

To calculate this, we can use the formula for a normal distribution: P(μ−σ < X < μ+σ) = 68%, where μ is the mean and σ is the standard deviation.

For our problem, our mean is 516 and our standard deviation is 43. Therefore, our equation becomes P(473 < X < 559) = 68%. This means that 68% of scores were between 473 and 559, which is our answer.

For more questions like National average visit the link below:

https://brainly.com/question/17631851

#SPJ4

The given statement for b is a positive real number and m and n are positive integers, is true.

An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 2, -8...

Given that, b is a real number and m and n are positive integers.

According to the above information, the calculation is as follows:

[tex]b^\frac{m}{n} = \sqrt[n]{b^m} = (\sqrt[n]{b} )^m[/tex]

Hence, the statement is true.

Learn more about integers, click;

https://brainly.com/question/1768255

#SPJ9

Yes, the given equation  y + 2x = 9  is consistent.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The equation y + 2x = 9 is a linear equation in two variables, x and y.

Now let us solve for y

y=-2x+9

We plot this equation graphically.

This equation represents a line with slope -2 and y-intercept 9.

So the graph of this equation is a straight line that passes through the point (0, 9) and has a slope of -2.

To determine if the equation y + 2x = 9 is consistent or inconsistent, we need to know if there exists at least one pair of values (x, y) that satisfy the equation.

We can see from the graph that there are infinitely many points on the line y + 2x = 9.

Hence, the given equation  y + 2x = 9  is consistent.

To learn more on slope intercept form click:

https://brainly.com/question/9682526

#SPJ9

The probability of winning third prize in the lottery game is 0.0011 or about 0.11%.

In the given lottery game, the player picks 6 numbers from 1 to 48.

Learn more about probability:

https://brainly.com/question/30034780

#SPJ4

am going through this and will send me an update tomorrow when you can get back in touch if we have time I would love for a bf of you and I was wondering what I could see for my bad credit cards at least once said that they have no interest and they are not going on the right back side and it doesn't look at the world with me anymore but it will take a little more longer then it might have gone out of there so much more to do it all the

Step-by-step explanation:

Firstly thaj, that's not her. that's not a real picture

Secondly, it's C. The answer is C because all the purple is below the line, making it negative so < since it's all bottom, we use y.

all bottom = y

all top = y

all left = x

all right = x

The degree of the polynomial is 5 and the maximum number of real zeroes in the polynomial is 5.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics.

f(x) = 6x⁵ - 3x⁴ + 5x² + 4

According to the fundamental theorem of algebra, the polynomial with n number of degrees will have n number of zeroes and no more, so the zeroes will be the same here 5.

Therefore, The polynomial has a degree of 5, and it can have a maximum of five real zeroes.

To learn more about polynomials, visit here:

https://brainly.com/question/11536910

#SPJ1

We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal). We can use a formula to find the monthly interest where:

P = (r(PV)) / (1 - (1 + r)^(-n))

Where:

P = monthly payment

r = monthly interest rate

PV = present value of the loan (the amount borrowed)

n = total number of months

r (monthly interest)= (1 / n) * ((P / PV) + ((1 / (1 + r)^n) - 1))

we can start by guessing an interest rate of 0.01 (or 1%). putting it into a formula:

r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.01)^60) - 1))

r = 0.004968

monthly payment is

P can be (0.004968 * 10000) / (1 - (1 + 0.004968)^(-60))

P = $323.52

By using this value we can find the value of the month. Plugging it back into the formula, we get:

r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.004968)^60) - 1))

r = 0.004974

This new interest rate gives us a monthly payment of:

P can be (0.004974 * 10000) / (1 - (1 + 0.004974)^(-60))

P = $323.53

We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal).

To know more about monthly interest

brainly.com/question/17306633

The correct question is

Table 33 gives spending data for the football programs at the 10 universities that spent the most money on football in 2012 Click here for the Excel Data File Calculate the population range variance and standard deviation of the ten total football spending figures Do the same for the ten spending per scholarship player figures. (Round your range and variance answers to 2 decimal places and standard deviation answer to 4 decimal places.) Total Spending (Smil) Spending per Scholarship Player (5) Range Variance Std Deviation 7 College Football A B C D 1 Footballs bending Data for 2012's Top Ten College Football Spenders 2 3 Rank School Total Spending (Smil) Spending per Scholarship Player (3) 4 1 The Ohio State University 34.36 5 400,000 2 University of Alabama 37.77 360,000 6 3 Auburn University 33.33 303,000 7 4 University of Wisconsin 24.23 285,000 8 5 University of Arkansas 24.33 9 6 Oklahoma State University 283,000 26.24 10 279,000 7 Virginia Tech 24.72 11 275,000 8 University of Arizona 24.12 12 9 274,000 University of Florida 23.25 13 273,000 University of Michigan 23.64 14 272,000 15 10

#SPJ4