If the variance of the sum is Var(X + Y)= 6 and Var(X) = Var(Y) = 4, then what is the correlation between X and Y? Corr = ___ (Type an integer or a decimal.)

Answer:

x = 26

Step-by-step explanation:

1. Information

One can partition this figure into three different parts, two congruent triangles, and one rectangle. To find the value of x, one has to find the base of the two triangles, and then the base of the rectangle. Since opposite sides are congruent, the base of the rectangles is 10. To find the base of the triangle, one has to use the Pythagorean theorem.

2. Base of the rectangle

Again, opposite sides are congruent, hence the base of the rectangle is equivalent to the top part. Hence the base is 10.

3. Base of the triangle

Use the Pythagorean theorem;

\(a^{2}+b^{2} = c^{2}\\a-leg\\b-leg\\c-hypotenuse\)

Substitute in the given value and solve

\(a^{2}+15^{2} = 17^{2}\\a^{2} + 225 = 289\\a^{2} = 64\\a = 8\)

4. Finding x

There are two congruent trinagles, hence one has to add the base of the triangle twice. The equation will be

x = base_of_triangle + base_of_rectagle + base_of_triangle

x = 8 + 10 + 8

x = 26

Answer:

120 degrees

Step-by-step explanation:

First, you need to find the measurement of the angle that is supplementary to D.

To do that you do 180-130=50, we know this is true because the two angles make a straight line.

Then you can find angle 2 because we have two of the angles in the triangle. All triangles have measurements of 180, we can use this information by doing

180-(50+70)=60, so angle 2 equals 60, then to find angle 1 you do

180-60=120, because they make a straight line.

angle 1=120

f(x) = 5x - 6 and f⁻¹(x) = (x + 6)/5 are verified as inverse functions using composition of functions.

What is an inverse function and how can they be checked by composition of functions?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. In general, we can combine f and g to see if they are inverse functions. The functions are inverses if the answer is x. If not, they are not.

Given, the original function is y = f(x) = 5x - 6
Let the inverse function of y be represented by g(x).
Also, y⁻¹ = g(x) = (x + 6)/5
Now, f(g(x)) = ([5(x + 6)]/5) - 6 = x + 6 - 6 = x
Again, g(f(x)) = ((5x - 6) + 6)/5 = 5x/5 = x
Therefore, f(x) and g(x) are inverses because f(g(x)) = g(f(x)) = x.
Thus, f(x) = 5x - 6 and f⁻¹(x) = (x + 6)/5 are verified as inverse functions using composition of functions.

To learn more about this, tap on the link below:
https://brainly.com/question/20759055

#SPJ13

9514 1404 393

Answer:

  -13 < x ≤ 4

Step-by-step explanation:

The round bracket means the lower limit is not included in the interval. The square bracket means the upper limit is included.

  -13 < x ≤ 4

The mandible is moving and the cusp "moving" with the arrow is in the either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

Given that;

The mandible is moving and the cusp "moving" with the arrow is in the ?

Now, We know that;

The side of the mandible that moves sideways is referred to as either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

Thus, The mandible is moving and the cusp "moving" with the arrow is in the either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ4

The solution of the quadratic equation is \(x = \dfrac{5\pm\sqrt5}{2}\).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the quadratic equation is x²-5x+5=0. The equation can be solved as below:-

x²-5x+5=0

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

\(x = \dfrac{-b \pm\sqrt{(b^2-4ac}}{2a}\)

\(x=\dfrac{5\pm\sqrt{25 - 4\times1\times5}}{2}\)

\(x = \dfrac{5\pm\sqrt5}{2}\)

The value of x for the quadratic equation will be \(x = \dfrac{5\pm\sqrt5}{2}\).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

Answer:

C: x=9

Step-by-step explanation:

DE is half of AC.

2x6=12

3x-15=12

3x=27

x=9

Answer:

3.1

Step-by-step explanation:

Answer:

3.1

Step-by-step explanation:

Answer:H=18

Step-by-step explanation:

If you subtract 54 from 36 that get's you 18

Answer:

J

A=7.07cm^2

Step-by-step explanation:

A= (pi)(r^2)

diameter=3

radius= 1/2 of the diameter = 1.5

pi = approximately 3.14

A= (3.14) (1.5)^2

A= 7.065 ----> rounds to 7.07

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

Explanation:

Preimage = A = (10, 15)

Image = A' = (4, 6)

Divide the x coordinates of the image over preimage

4/10 = 0.4 is the scale factor

Or you could do the same for the y coordinates

6/15 = 0.4

The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.

To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.

First, we need to standardize the distribution using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 1,950 hours:

z = (1,950 - 1,975) / 25 = -1

For x = 2,050 hours:

z = (2,050 - 1,975) / 25 = 3

Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:

0.9987 - 0.1587 = 0.84

for such more question on  probability

https://brainly.com/question/13604758

#SPJ11

The maximum area of the garden is obtained when the length (L) and width (W) are both 25 meters. The corresponding dimensions for the maximum area are a square-shaped garden with sides measuring 25 meters.

To find the maximum area of the garden, we need to determine the dimensions of the rectangle that would maximize the area while using a total of 100 meters of fencing.

Let's assume the length of the rectangle is L and the width is W.

Given that the garden is surrounded by 100 meters of fencing, the perimeter of the rectangle would be:

2L + 2W = 100

Simplifying the equation, we get:

L + W = 50

To find the maximum area, we can express the area (A) in terms of a single variable. Since we know the relationship between L and W from the perimeter equation, we can rewrite the area equation:

A = L * W

Substituting the value of L from the perimeter equation, we get:

A = (50 - W) * W

Expanding the equation, we have:

A = 50W - W^2

To find the maximum area, we can take the derivative of A with respect to W and set it equal to 0:

dA/dW = 50 - 2W = 0

Solving the equation, we find:

2W = 50

W = 25

Substituting the value of W back into the perimeter equation, we find:

L + 25 = 50

L = 25

Know more about area here:

https://brainly.com/question/30307509

#SPJ11

First determine how much dirt is "cut"

V = l*w*h

V = 35 ft * 67 ft * 4 ft

V =9380 ft^3

Now determine how much dirt is used

V = l* w * h

V = 27 ft* 24ft * 6ft

V =3888 ft ^3

Subtract to determine how much is left

9380 - 3888

5492 ft^3

But the question asks for yd^3

5492 ft^3 * 1yd/ 3 ft * 1 yd / 3ft * 1 yd / 3 ft

5492 / 27 yd ^3

203.407407 yd^3

203.4 yd^3

I think the anwser for this is 60 in miles

Answer:

23

Step-by-step explanation:

The area of the base of the prism is 110 square meters

The formula that is used for calculating the volume of a pentagonal prism is expressed as;

V = Ah

Such that the parameters of the formula are enumerated as;

From the information given, we have that;

Volume of the prism = 880 cubic meters

Height of the prism = 8 inches

Now, substitute the values, we have;

880 = 8(A)

expand the bracket

880 = 8A

Divide both sides by the coefficient, we have;

A = 110 square meters

Learn more about volume at: https://brainly.com/question/1972490

#SPJ1

Answer: D i think

Step-by-step explanation:

The equivalent expression of the expression − 7x + 6 (x − 8/2) − 2 (x + 3) + 10 will be − (3x + 20). Then the correct option is C.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ − 7x + 6 (x − 8/2) − 2 (x + 3) + 10

Simplify the expression, then we have

⇒ − 7x + 6 (x − 8/2) − 2 (x + 3) + 10

⇒ − 7x + 6x − 24 − 2x − 6 + 10

⇒ − 3x − 20

⇒ − (3x + 20)

The equivalent expression of the expression − 7x + 6 (x − 8/2) − 2 (x + 3) + 10 will be − (3x + 20). Then the correct option is C.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ5

56 different arrangements are possible for the evening

Selections and combinations are synonyms. Combinations represent the choice of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. Out of a set of n objects, we count the number of unique r-selections or combinations. It is given by the formula ⁿCr. Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.

Required numbers = 5

Numbers available = 8

The number of arrangements possible:

⁸C₅ = 56

Learn more about permutations and combinations:

https://brainly.com/question/13387529

#SPJ4

Answer: 6.5 or 2/13

Step-by-step explanation: add all the numbers together first

2+8+5= 15

then add 1 purple and 1 blue together over 13 (because it says without replacement) so 2/13 then divide = 6.5

I'm pretty sure let me know if i got it wrong

Answer:

slope =  4

Step-by-step explanation:

recall that for a linear equation in the form:

y = mx + b,

m = slope of line and b is the y-intercept.

In our case, we are given

y = 4x

If we compare this with the general equation above,

we can see that m = 6 and b = 0

hence slope = m = 4

Answer:

Step-by-step explanation:

We can use combinations

20 choose 4:

20!/(16!*4!)

= (20*19*18*17)/4!

= 4845

(a) The slope of an indifference curve at an arbitrary consumption bundle (x0, y0) is given by the negative ratio of the marginal utilities of x and y, i.e., -MUx/MUy.

(b) Taking the derivative of the expression in part (a) gives the second-order derivative of the indifference curve. If the utility function u is quasiconcave on R+2, this second-order derivative will be positive, demonstrating the law of diminishing marginal rate of substitution.

In economics, an indifference curve represents the combinations of two goods (x and y) that provide the same level of utility or satisfaction to an individual.

The slope of an indifference curve measures the rate at which the individual is willing to substitute one good for another while remaining indifferent.

To derive an expression for the slope of an indifference curve at a given consumption bundle (x0, y0), we consider the marginal utilities of x (MUx) and y (MUy).

The slope is determined by the negative ratio of MUx to MUy, which indicates the relative change in x compared to y that maintains the same level of utility.

Taking the derivative of this expression provides the second-order derivative of the indifference curve. If the utility function u is quasiconcave on R+2, which means that indifference curves are convex, the second-order derivative will be positive.

This confirms the law of diminishing marginal rate of substitution, stating that as an individual consumes more of one good, they are willing to give up less of the other good to maintain the same level of satisfaction.

Learn more about utility theory

brainly.com/question/32602236

#SPJ11

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A linear function is a straight line when graphed so is not B.

For confirmation of A note how for each increase of 3 in x we get the same increase of 5 in y.

Answer:

16°

Step-by-step explanation:

Reference angle = \( \theta \)

Side Opposite to reference angle = 14

Adjacent side = 48

Hypotenuse = 50

Let's apply arcsin:

Thus:

\( \theta = sin^{-1}(\frac{Opp}{Hyp}) \) (recall: SOHCAHTOA)

Plug in the values

\( \theta = sin^{-1}(\frac{14}{50}) \)

\( \theta \) = 16.2602047° = 16°

9514 1404 393

Answer:

  A = (y2 -y1)(x3 -x1)/2

Step-by-step explanation:

It is convenient to use the vertical line as the base. Its length will be the difference of y-coordinates: (y2 -y1)

Then the altitude is the perpendicular distance from that line to (x3, y3). That distance will be the difference of the x-coordinates: (x3 -x1).

The area is given by the usual formula for the area of a triangle:

  A = 1/2bh

  A = 1/2(y2 -y1)(x3 -x1)

Answer:

the

Step-by-step explanation:

sale would be $20 for every item, duh

Hello!

x = 1 score

the mean:

16x/16 = 8

x = 8

so the sum of the 16 scores = 8 × 16 = 128

verify:

128/16 = 8

If a set of 16 scores has a mean of 8, the sum of the scores is 128.

Given: Total number of scores =  16

Mean of scores = 8

The formula for calculating the mean of a given data is given as,

x = ∑x / n ...........(i)

where x⇒ mean of scores,

∑x ⇒ sum of the scores

n⇒ total number of scores,

∴ Putting the relevant values in equation (i), we get,

8 = ∑x /16

⇒ ∑x  = 8 x 16 ;

∴ ∑x = 128

So, if a set of 16 scores has a mean of 8, the sum of the scores is 128.

Learn more about mean average on:

https://brainly.com/question/22056321