Recall the definition of covariance for two random variables, X and W: Cov(X,W) =
E(X − E(X))(W − E(W)).

Prove or disprove

Cov(aX + b, cW) = ac Cov(X,W)

where a, b, and c are constants. Start with applying the covariance definition to Cov(aX +
b, cW), proceed by applying appropriate properties of expectation operator, and see if your
simplified expression is the same as ac Cov(X,W).

The solutions exist at x=-8 and x=3, so the graph will have points at (-8,0) and (3,0).

To learn more about Quadratic Formula refer to:

https://brainly.com/question/1214333

#SPJ1

Answer:

Step-by-step explanation:

To solve the equation x/75 = 25, you can multiply both sides by 75 to isolate x:

x/75 * 75 = 25 * 75

x = 1875

Progression is an experiment in a series of successive events.

What is a successive term?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Successive Events: Independent and Dependent. In order to find the probability of several events occurring in succession, multiply the probabilities of the individual events. Successive events can be Independent or Dependent. Independent events are not affected by each other.

Progression is a series of successive events.

Hence, Progression is an experiment in a series of successive events.

To learn more about the successive event visit,

https://brainly.com/question/29555551

#SPJ1

[tex](1.7\times 10^{4})(8.5\times 10^{-2})\implies (1.7\times 8.5)(10^4\times 10^{-2}) \implies (1.7\times 8.5)(10^{4-2}) \\\\\\ (1.7\times 8.5)(10^2)\implies (14.45)(10^2)\implies 14.45\times 100\implies 1445[/tex]

Answer:

[tex]r=14\mathring{}[/tex]

Step-by-step explanation:

[tex](5r-5)\mathring{}+(8r+3)\mathring{}=180\mathring{}\\5r-5+8r+3=180\mathring{}\\13r-2=180\mathring{}\\13r=180\mathring{}+2\\13r=182\mathring{}\\r=\frac{182}{13} \\\\r=14\mathring{}[/tex]

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's "Distributive Property"

Multiplication's identity property.

The Japanese technique of multiplication is only a graphic representation of the four stages. Two integers are multiplied by each of the four smaller products represented by each cluster of intersections.

6666652222 - 12

6666652210 * 2 / 78 = 175438216.05

6666652210 * 6 / 78 = 512819400.76

6666652210 * 8 /78 = 701752864.21

6666652210 * 9 / 78 = 789471972.23

To learn more about Multiplication's refer to:

https://brainly.com/question/10873737

#SPJ1

The function's value is f(x). The line's slope is m.When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.

The function's value is f(x). The line's slope is m.

When x is equal to 0, the function's value is equal to b, which is also the coordinate at where the line in the coordinate plane crosses the y-axis.

The x-value coordinate's is given by x.

Graph Rules for Derivatives

The graph of f'(x) will be below the x-axis if f(x) has a negative slope.

The graph of f'(x) will be above the x-axis if f(x) has a positive slope.

The x-intercepts of f' will be all relative extrema of f(x) (x).

Given that ;

f(x)= x³

f(x)-4 = x³- 4

See attached graph using the graph tool

To learn more about graph refer

https://brainly.com/question/13070228

#SPJ1

the amount that results from the given investment $500 invested at 12% compounded quarterly after a period of 3 years is:  $711.66. This can be solved using the concept of compound interest.

When calculating compound interest, the starting principle amount is multiplied by one together with the yearly interest rate raised to the number of compound periods minus one. The resultant value is then reduced by the whole initial loan amount. When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. Compound interest accelerates the growth of your money since it calculates interest on both your original principle and the interest that has accrued over time. The initial investments and the revenue generated by those investments increase simultaneously as a result of compounding, which can have a snowball effect.

Principal amount (P) = $500

interest rate (r) = 12%

time (t) = 3 years

period (n) = 3

Final amount = A

As we know, A = P ( 1 + r/n) ^{nt}

or, A = 500 (1 + 0.12 / 3)^{3*3}

or, A = $711.66

To know more about compound interest refer to:

https://brainly.com/question/28020457

#SPJ1

If we randomly choose a point on which Federer served and get distracted before seeing his first serve but look up in time to see Federer win the point , then the probability that he missed his first serve given he won the point is (a) 0.3000

To calculate the probability that Federer missed his first serve given that he won the point, we Let , event A is = Federer missed his first serve and

event B is = Federer won the point.

So, probability of Federer missing his first serve = (100-63)% = 37% = 0.37,

probability of Federer winning point given he missed his first serve= 57%.

⇒the probability he first serve and misses point = (0.37)(0.57) = 0.2109  .

The probability of Federer winning the point, regardless of whether he made his first serve or not, can be calculated as

⇒ (0.63)(0.78) + (0.37)(0.57) = 0.7023  .

So , the probability of Federer missing his first serve given that he won the point is 0.2109/0.7023 = 0.300    .

The given question is incomplete , the complete question is

Tennis great Roger Federer made 63% of his first serves in a recent season. When Federer made his first serve, he won 78% of the points. When Federer missed his first serve and had to serve again, he won only 57% of the points. Suppose you randomly choose a point on which Federer served. You get distracted before seeing his first serve but look up in time to see Federer win the point.

What is the probability that he missed his first serve given he won the point?

(a) 0.3000

(b) 0.37

(c) 0.63

Learn more about Probability here

https://brainly.com/question/28987950

#SPJ4

506 is 27 times the value of 18.74 because the sum of the two numbers is 506.

We divide both sides by 27 to get x on its own, and then we can solve for x. The math is illustrated below:

27 • x = 506

27x = 506

27x/27 = 506/27

x = 18.74

Every day, we deal with decimals while calculating length, weight, and other variables. When whole numbers are insufficient to offer the level of precision needed, decimal numbers are utilized. For instance, we don't always find that our weight is equal to a whole number on the scale when we calculate it on the weighing machine.

Simply said, round down the preceding digit if the last digit is less than 5. The previous digit should be rounded up if the number is five or higher.

To learn more about value refer to:

brainly.com/question/1827193

#SPJ1

Complete Question is :How do I show work for 27x is 506 and Find the value of x?

Mean of the sampling distribution of sample means is 5.9 years.

A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.

Population mean, μ = 5.9 years

Population standard deviation, σ = 0.8 years

If the sample size is at least 30, we can use the normal approximation of sampling distribution of sample means.

Here, sample size for the sampling distribution, n = 68 > 30.

For a sample which is drawn from a normally distributed population, mean of the sampling distribution of sample means is equal to the population mean and standard deviation = σ / √n.

Mean of the sampling distribution of sample means = μ = 5.9 years.

Hence mean is same as the population mean.

Learn more about Normal Distribution here :

https://brainly.com/question/29509087

#SPJ1

Answer:

The range is the difference between the largest and smallest values in a set of data. In this case, the heights of the 11 plants are listed as:

14, 15, 15, 16, 16, 16, 17, 17, 18, 19, 20

The smallest height is 14 inches and the largest height is 20 inches, so the range is 20 - 14 = 6 inches.

If another plant with a height of 17 inches is added to the data, the smallest and largest values do not change, so the range would still be 6 inches.

Answer:

Answer to the question posted: The range would stay the same value of 6 inches.

Answer to the question in the comments: The mean would decrease in value to about 16.8 inches.

Step-by-step explanation:

Answer to the question posted:

First, to figure out if the range increases, decreases, or stays the same, we need to find the range. The range is siply the difference between the largest ans smallest number. In this problem, the smallest plant height is 14 while the largest plant height is 20. Since the difference between the smallest and largest plant is 20-14, or 6, inches, the range is 6 inches.

Now, let's figure out what would happen if we added a plant with a height of 17 inches. Well, since our smallest plant height and largest plant height would not be changed, the range would stay the same value of 6 inches.

Answer to the question in the comments:

The first step is to find the mean of the plant heights. To find mean, you need to add up all the plant heights and divide it by the number of plants. Since 13+14+15+15+16+16+16+17+17+18+19+20+22+23=241 and there are 14 plants, we can divide 241 by 14 to find the original mean of the plant heights. When we solve 241/14, we get 17.2142857143.

Now, let's figure out what would happen to the mean if we added a plant with a height of 11 inches. Again, we would need to total up all the plant heights, and it should be 11 inches larger than last time, as we are adding 11 inches to the total plant height. Since our original total height was 241, or new total height, adding in the 11 inch plant, would be 252 inches. Now that we have our total plant height including the 11 inch plant, we need to figure out how many total plants we have. If we started with 14 plants and add another plant into the data set, then the total number of plants, including the 11 inch plant, must be 15. Now that we know the new total plant height and new amount of plants, we can find the new mean, The new mean is 252/15, or 16.8.

So, if our mean went from 17.2142857143 to 16.8 when we added the 11 inch plant, the mean would decrease in value to about 16.8 inches.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

The matrix of the system is [tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

The complete question is added as an attachment

From the question, we have the following system of equations that can be used in our computation:

11x + 3y = 20

x - 2y = 5

Remove the variables

So, we have the following representation

x    y

11   3   20

1     -2   5

Next, we input the numbers in a matrix

This gives

[tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

Read more about matrix at

https://brainly.com/question/2456804

#SPJ1

Answer:

x = 7/3

Step-by-step explanation:

Given equation,

→ 4x - 5 = -2x + 9

Now the value of x will be,

→ 4x - 5 = -2x + 9

→ 4x + 2x = 9 + 5

→ 6x = 14

→ x = 14/6

→ [ x = 7/3 ]

Hence, value of x is 7/3.

Answer:

50 days

Step-by-step explanation:

Grace=3x+200

Joseph=6x+50

3x+200=6x+50

3x=150

x=50

As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

It is possible either multiply, distribute, add, or negate in mathematics. The trying to follow is how a expression is put together: Number, expression, and scientific operator The ingredients of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) It is possible to combine expressions and phrases. An expressions, often known as an arithmetic operation, is any mathematical statement that contains variables, numerals, and a numerical operation between them. That instance, the word m there in given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

To address this issue, we just need to determine the total or difference that yields 2x2 + 2x + 2

Option A: ( x2 + 4x -2) + (x2 - 2x - 4) = 2x2 + 2x - 6

Option B: ( x2 + 4x - 2 ) + ( x2 + 2x + 4 ) = 2x2 + 6x + 2

Option C: ( x2 + 4x - 2) - ( -x2 + 2x - 4)= x2 + 4x - 2 + x2 - 2x + 4

= 2x2 + 2x + 2

As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The complete question is:-

Select the correct answer.

Which sum or difference is modeled by the algebra tiles?

A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2

B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2

C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2

D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2

The chance that the third number is bigger than twice the first number is equal to the number of combinations where the first number is between 1 and 5 (inclusive) and the third number is between 2 * first number + 1 and 10 (inclusive).

Here's the calculation:

Therefore, the answer is:

= 21/1000

= 21/10^3

= 0.021

which is closest to choice B, so the answer is B.

For more questions like Tickets numbered visit the link below:

https://brainly.com/question/14282795

#SPJ4

the daily balance equals the previous day's balance plus new purchases minus the payments and credits

New purchases included indicates that at the conclusion of each day, the firm adds any new purchases to the balance. In other words, the daily balance is equal to the previous day’s amount plus any new purchases less any payments or credits. Credit card issuers will also impose a late fee if payment is not received by the due date.

The daily balance approach calculates your finance fee based on your actual amount on each day of your billing cycle rather than an average of your balance throughout the course of the billing cycle. Finance costs are computed by adding each day’s amount and multiplying it by the daily rate, which is 1/365th of your APR.

To learn more about daily balance to refer;

https://brainly.com/question/29142021

#SPJ1

The J (Jenny) has $15 , C (Charlie) has $20 and A(Aldo) has $30 in their wallets with total sum of $65.

Since Jenny, Charlie and Aldo have a total of $65 in their wallets. This could be represented as

J + C + A = 65      (equation 1)

Jenny has $5 less than Charlie

J = C - 5         (equation 2)

Aldo has 2 times what Jenny has

A = 2 * J   (equation 3)

Now we can solve the above equations by substitution.

Rearranging Equation 2 as

C = J + 5

Now substituting the values of A and C in equation 1 from 2 and 3. So equation 1 would become

J + (J+5) + (2*J) = 65

Solving the above equation

J + J + 5 + 2J = 65

4J = 65-5

4J = 60

J = 60/4

J = 15

Now if we insert the value of J in equation 2 and 3 we will get C and A.

C = J + 5

C = 15 + 5

C= 20

And

A = 2*J

A= 2*15

A = 30

The J (Jenny) has $15 , C (Charlie) has $20 and A(Aldo) has $30 in their wallets with total sum of $65.

The complete question is,

Jenny, Charlie, and Aldo have a total of $65 in their wallets. Jenny has $5 less than Charlie. Aldo has 2 times what Jenny has. How much do they each have in their wallets?

To learn more about mathematical equation refer to:

https://brainly.com/question/22688504

#SPJ1

Answer:

9a - 18

Step-by-step explanation:

3a + 6a - 27 +9

→ gather like terms

(3a + 6a) + (-27 +9)

→ collect coefficients of like terms

(3 + 6) × a + (-27 +9)

→ calculate the sum/difference

9a + (-27 +9)

→ calculate the sum/difference (again)

9a - 18

Answer: 9a - 18

hope this helps!

On solving the provided question we can say that The coordinates are = ( 9 , - 6 ); the slope intercept will be y + 6 = 9xm - m

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

The coordinates are = ( 9 , - 6 )

the slope intercept will be y + 6 = 9xm - m

To know more about slope intercept visit:

https://brainly.com/question/19824331

#SPJ1

Answer:

D

Step-by-step explanation:

You just multiplied it times 4 ....it is four times taller

The polynomial we obtain by subtraction is -2a³-10a²+5a+4.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

We have to find the  difference by subtracting the polynomial 4a³+6a²-11a-3 from the polynomial 2a³-4a²-6a+1

2a³-4a²-6a+1-(4a³+6a²-11a-3)

Multiply minus with the parenthesis terms

2a³-4a²-6a+1-4a³-6a²+11a+3

Add the like terms

-2a³-10a²+5a+4

Hence, the polynomial we obtain by subtraction is -2a³-10a²+5a+4.

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ1

Answer:

x + 9

Step-by-step explanation:

Sum is addition

Answer:

12

Step-by-step explanation:

[tex] ( {5}^{2} - {3}^{2} ) - (5 - 3) {}^{2} [/tex]

is 12

The value of m + n is 53.

Let's consider the first roll "a". The second, third, and fourth rolls will be represented as "b", "c", and "d".

The first roll of a can be any integer from 1 to 6.

For the second roll of b, there are 5 possible integers that are greater than or equal to the first roll "a".

For the third roll of c, there are 4 possible integers that are greater than or equal to the subsequent roll "b".

For the fourth roll of d, there are 3 possible integers that are greater than or equal to the third roll "c".

Thus, the total number of possible outcomes that meet the rules is 6 * 5 * 4 * 3 = 360.

The total number of possible outcomes for rolling a fair die multiple times is 6 * 6 * 6 * 6 = 1296.

This is how the probability of every one of the last three rolls being in some measure as extensive as the roll going before it is 360/1296, which can be improved to 5/18.

In this way, m + n = 5 + 18 = 23.

To learn more about probability:

https://brainly.com/question/13604758

#SPJ4

Answer:

Mean

Step-by-step explanation:

You need to find the average amount of time that tents stay inflated. You could argue Mode but then you'd only get 24 when it could be 27

Length of the curve is 1

Arc length or length of a curve is the distance travelled by a point it follows the graph of a function along a some particular interval.

Given,

[tex]y=\int\limits^0_x {\sqrt{cost2t} } \, dt[/tex]

Let find the derivative of the function,

[tex]\frac{dy}{dt} =\frac{d}{dt} (\int\limits^0_x {\sqrt{cost2t} } \, dt)[/tex]

[tex]\frac{dy}{dt} = \sqrt{cos2t}[/tex]

Now using arc length formula,

[tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{1+(\sqrt{cos2t})^{2} } } \, dt[/tex]

[tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{1+cos2t} } \, dt[/tex]

Using trigonometric identities, [tex]cos^{2} t+sin^{2} =1[/tex] and[tex]cos2t = cos^{2}t-sin^{2} t[/tex][tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{cos^{2} t+sin^{2} + cos^{2}t-sin^{2} t } } \, dt[/tex][tex]L= \int\limits^0_\frac{\pi }{4} {\sqrt{2cos^{2} t} } \, dt[/tex]

[tex]L= \sqrt{2} \int\limits^0_\frac{\pi }{4} cos t} } \, dt = \sqrt{2} sint[/tex]

Apply limits we get,  L=1.

Hence, length of the curve , L=1.

Learn more about arc length here:

https://brainly.com/question/29141691

#SPJ1

If Miss Shaw has some counters. If she gives her pupil 3 counters each, she will have 12 counters left.

a) The number of pupils that are there is 24.

b) The number of counters she have is 84.

a) Let's p represent the number of pupils

3p + 12 = number of counters

4p = number of counters + 24

We can substitute the first equation into the second:

4p = (3p + 12) + 24

4p = 3p + 36

p = 24 pupils

Counters:

3p + 12

= 3 * 24 + 12

= 84 counters

Therefore the number of pupils that are there is 24 and the number of counters she have is 84.

Learn more about number of pupils here:https://brainly.com/question/30061152

#SPJ1