Sin (x) = -radical 3/2

The probability density function is of E(Y1) and E(Y2) is 1/6 and variance is 1/18.

To find the expected value E(Y1+Y2), we can use the linearity of expectation and the fact that the expected value of a constant is that constant:

E(Y1+Y2) = E(Y1) + E(Y2)

To find E(Y1) and E(Y2), we need to integrate y1 and y2 respectively over their joint probability density function:

E(Y1) = ∫∫ y1 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y1) 2y1 dy2 dy1

= ∫0^1 2y1(1-y1)/2 dy1

= ∫0^1 y1-y1^2 dy1

= [y1^2/2 - y1^3/3] from 0 to 1

= 1/6

Similarly,

E(Y2) = ∫∫ y2 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y2) 2y2 dy1 dy2

= ∫0^1 2y2(1-y2)/2 dy2

= ∫0^1 y2-y2^2 dy2

= [y2^2/2 - y2^3/3] from 0 to 1

= 1/6

Therefore, E(Y1+Y2) = E(Y1) + E(Y2) = 1/6 + 1/6 = 1/3.

To find the variance V(Y1+Y2), we can use the formula:

V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2

To find E((Y1+Y2)^2), we need to integrate (y1+y2)^2 over their joint probability density function:

E((Y1+Y2)^2) = ∫∫ (y1+y2)^2 f(y1,y2) dy1 dy2

= ∫0^1 ∫0^(1-y1) (y1+y2)^2 2 dy2 dy1

= ∫0^1 [(2/3)y1^3 + y1^2 + (1/3)y1] dy1

= 5/18

Therefore, V(Y1+Y2) = E((Y1+Y2)^2) - [E(Y1+Y2)]^2 = 5/18 - (1/3)^2 = 5/18 - 1/9 = 1/18

The variance is 1/18.

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Answer:

Positive

Step-by-step explanation:

The graph goes up (puff puff positive)

Answer:

<1 = <5 is True

<2 = <4 is True

<2 = <7 is False

<3 and <6 are not a linear pair

<4 and <5 are not supplementary angles

m<5 is 75°

m<11 is 75°

m<16 is 65°

Answer:

y = -2x+7

Step-by-step explanation:

2x+y=7

Subtract 2x from each side

2x+y -2x=-2x+7

y = -2x+7

2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

\( \frac{1}{4} \)

Step-by-step explanation:

25/100

divide both sides with 25

\( \frac{25 \div 25 }{100 \div 25} \)

simplify

= 1/4

Answer:

1/4

Step-by-step explanation:

Find HCD (Highest Common Factor) for both numerator and denominator.

The HCF for 25 and 100 is 25

Now divide the numerator and denominator by 25  

(25/25) / (100/25)

1/4

And Viola, you got your simplified form!

Answer:

90, 45

Step-by-step explanation:

0.3x = 27

x = 90

50% of 90 = 45

By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The expression expressed as a difference is (a - 2) - (-7).

We have,

We can express a + 5 as a difference by subtracting a suitable term from it.

One way to do this is to subtract 2 and add 2, like this:

a + 5 = a + 5 - 2 + 2   (adding and subtracting 2)

     = (a - 2) + 7     (rearranging)

Now,

We can express a + 5 as the difference between a - 2 and -7, like this:

a + 5 = (a - 2) - (-7)

Thus,

The expression expressed as a difference is (a - 2) - (-7).

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The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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Answer: 1 1/2

Step-by-step explanation:

According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer:

Savings accounts typically pay interest.

Step-by-step explanation:

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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Answer:

YES

Step-by-step explanation:

To determine a function on a graph use the vertical line test!

put a vertical line through the graph at ANY POINT and if it only passes through one point then it is a function.

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

Sum :-    -76   Product :-    768

Step-by-step explanation:

Answer:

\(36\)

Step-by-step explanation:

\( {x}^{2} \)

\( = {6}^{2} \)

\(= (6 \times 6)\)

\(= 36\)

Answer:

x/2=3

Step-by-step explanation:

x=6

x/2=?

6/2=3

Therefore,x=3.

Answer:

Step-by-step explanation:

The sampling distribution of the sample mean for samples of size n is approximately normal with mean μ and standard deviation σ/sqrt(n), where μ is the mean of the population, σ is the standard deviation of the population, and sqrt(n) is the square root of the sample size.

In this case, the population mean is μ = 112 and the population standard deviation is σ = 22. We are interested in the sampling distribution of the sample mean for samples of size n = 16.

The mean of the sampling distribution of the sample mean is the same as the population mean, which is μ = 112.

The standard deviation of the sampling distribution of the sample mean is σ/sqrt(n) = 22/sqrt(16) = 5.5.

Therefore, the sampling distribution of the sample mean for samples of size 16 is approximately normal with mean 112 and standard deviation 5.5.

Answer:

11.6 lbs

Step-by-step explanation:

Answer:

The answer to your question is Dependent Variable.

In a linear regression model, the variable that is being predicted or explained is known as Dependent Variable . It is denoted by y and is often referred to as the response variable

Step-by-step explanation:

I don't really know how to explain sorry.

Brainliest pls! :)

Answer:Dependent Variable

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

When you add a negative number, you're basically subtracting it.

7 - 3 = 4

Hope this helps! Good luck :)

Answer:

75.99

Step-by-step explanation:

Answer:

\(( - 1 \div x^{2} ) + sec ^{2} \)

The probability that a bottle will be filled with less than 330ml of cola is 0.1587

The probability that a bottle will be filled with more than 340ml of cola is 0.1587

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

We will assume that the distribution of the volume of cola filled by the machine is normal.

Now,

We can use the mean and standard deviation.

X = the volume of cola filled by the machine.

X ~ N (335, 5)

Where N denotes a normal distribution.

This means,

The mean volume of cola filled by the machine is 335ml.

The standard deviation is 5ml.

Now,

Using this normal distribution.

We can find the probability of certain outcomes.

For example:

The probability that a bottle will be filled with less than 330ml of cola.

P(X < 330)

= P(Z < (330 - 335) / 5)

= P(Z < -1)

= 0.1587

Where Z is a standard normal random variable.

Similarly,

The probability that a bottle will be filled with more than 340ml of cola.

P(X > 340)

= P(Z > (340 - 335) / 5)

= P(Z > 1)

= 0.1587

Thus,

The probability that a bottle will be filled with less than 330ml of cola is 0.1587

The probability that a bottle will be filled with more than 340ml of cola is 0.1587

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The complete question.

The machine is used to fill cola in bottles for sale. The mean volume of cola is 335ml with a standard deviation of 5ml.

The distribution of the volume of cola filled by the machine is normal.

Find the probability that a bottle will be filled with less than 330ml of cola and the probability that a bottle will be filled with more than 340ml of cola.

Answer:

First notice that θ is in quadrant I, where the sine and tangent will also be positive.

Then draw the angle in quadrant I. Drop a perpendicular to the x axis.

Since cosθ= 7/25, label the horizontal leg 7, and the hypotenuse 25; the vertical leg will be 24 by Pythagorean theorem.

Then sinθ=vertical/hypotenuse=  24/25 and tanθ= vertical/horizontal=  24/7

Step-by-step explanation: I hope this helps!

Answer:

First notice that θ is in quadrant I, where the sine and tangent will also be positive.

Then draw the angle in quadrant I. Drop a perpendicular to the x axis.

Since cosθ= 7/25, label the horizontal leg 7, and the hypotenuse 25; the vertical leg will be 24 by Pythagorean theorem.

Then sinθ=vertical/hypotenuse=  24/25 and tanθ= vertical/horizontal=  24/7

Step-by-step explanation: