Find the variances of V and W,σV2​ and σW2​ This question and some of the following questions are linked to each other. Any mistake will propagate throughout. Check your answers before you move on. Show as many literal derivations for partial credits. Two random variables X and Y have means E[X]=1 and E[Y]=1, variances σx2=4 and σγ2=9, and a correlation coefficient rhoXY=0.5. New random variables are defined by V=−X+2YW=X+Y Find the means of V and W,E[V] and E[W]

The all values have been obtained.

As per data function is:

f(x, y, z) = xe + 4z cos'(Inx)

To find: Directions in which f(x, y, z) increases and decreases most rapidly at P(1, In2, 1/2) and Rates of change in these directions.

Let's first calculate the gradient vector,

∇f(x, y, z) = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k,

∂f/∂x = eˣ + 4z cos'(lnx) * 1/x

∂f/∂y = 0

∂f/∂z = 4cos'(lnx)

Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of vector,

v = ai + bj + ck is given by

D_vf(P) = ∇f(P).v

Now we need to find a unit vector in the direction of increasing f(x, y, z) and another unit vector in the direction of decreasing f(x, y, z) most rapidly.

Let's find the unit vector in the direction of increasing f(x, y, z) by taking

v = ∇f/|∇f| and the unit vector in the direction of decreasing f(x, y, z) most rapidly by taking

v = -∇f/|∇f|.

For increasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + 4²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v1

     = (1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v1 = (1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

   = (1/sqrt(45))(e + 4k)

For decreasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + (-4)²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v2

     = (-1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v2 = (-1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

    = (-1/sqrt(45))(e + 4k)

Now, we need to find the rates of change in the directions v1 and v2. Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v1 is,

D_v1f(P) = ∇f(P).v1

             = (1/sqrt(45))(e + 4k).(e + 4k)

            = (1/sqrt(45))(e² + 16)

            = (1/sqrt(45))(e² + 16)

For the direction of v2,Rates of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v2 is,

D_v2f(P) = ∇f(P).v2

              = (-1/sqrt(45))(e + 4k).(e + 4k)

              = (-1/sqrt(45))(e² + 16)

              = -(1/sqrt(45))(e² + 16)

Therefore, Direction of increasing is (1/sqrt(45))(e + 4k), direction of decreasing is (-1/sqrt(45))(e + 4k), rates of change in the direction of increasing is (1/sqrt(45))(e² + 16) and rates of change in the direction of decreasing is -(1/sqrt(45))(e² + 16).

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Answer:

(3, 15) and (4, 12)

Step-by-step explanation:

x2 - 7x+12 = 0 factors to (x - 4)(x - 3) = 0, and so x:  {3, 4}.

Since y= -3x + 24, y = 15 when x = 3 and y = 12 when x = 4.  The solutions are thus (3, 15) and (4, 12).  This is the third answer choice.

Answer:

see the explanation

Step-by-step explanation:

Y = –x2 + 4x + 12

y = –3x + 24

so

–x2 + 4x + 12 =  –3x + 24

x^2 -7x + 12 = 0

(x - 4)(x - 3) = 0

x - 4 =0; x =4

x - 3 = 0; x= 3

y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)

y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)

answer

(3, 15) and (4, 12)

(give this a heart cause why not)

Answer:

I'm sorry, I can help you with only this one :( ∠F = 44°

Step-by-step explanation:

∠F = 180° - (46° + 90°) = 44°

The greatest possible integer value of x for which \(\sqrt{x - 5}\) is an imaginary number is 4

The root expression is given as:

\(\sqrt{x - 5}\)

For the above number to be a complex number, the greatest value of the radicand must be -1.

So, we have:

x - 5 = -1

Add 5 to both sides

x = 4

Hence, the greatest possible integer value of x for which \(\sqrt{x - 5}\) is an imaginary number is 4

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Answer:

its B got it right on edge 2022

The sum of the matrices A and C from the list of options is the matrix B

Given the following matrices

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

To find the sum of matrices A and C, we add the corresponding elements in each matrix:

So, we have: A + C

| 0 - 2  6 + 5  2 + 3 |

| 1 - 1    5 - 7  -2 + 3|

Evaluate the sum

| -2  11  5 |

| 0   -2  1 |

This represents option B

Therefore, the sum of matrices A and C is (B)

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Complete question

What is the sum of A+C?

Matrix A

| 0  6  2 |

| 1  5  -2 |

Matrix C

| -2  5  3 |

| -1  -7  3|

The sentence can be turned to the equation;

15.00r+20.00(r−3)=500.00

We have to read the sentence carefully and identify the quantities or variables involved.

We are told that a  barber offers two options at his barbershop; a $15 regular haircut and a $20 deluxe haircut.

Then  On a certain day the barber gave r regular haircuts and 3 fewer deluxe haircuts than regular haircuts. He earned $500 total from the two types of haircuts.

It then follows that the correct equation is 15.00r+20.00(r−3)=500.00

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Missing parts;

A barber offers two options at his barbershop: a $15.00 regular haircut and a $20.00 deluxe haircut. On a certain day, the barber gave r regular haircuts and 3 fewer deluxe haircuts than regular haircuts. He earned $500.00 total from the two types of haircuts. Which of the following equations best models this situation?

Answer Choices:

A. 15.00r+20.00(r−3)=500.00

B. 15.00r+20.00(r+3)=500.00

C. 15.00(r−3)+20.00r=500.00

D. 15.00(r+3)+20.00r=500.00

Answer:

i think the answer is -33

Step-by-step explanation:

Answer:

1. 30/14

2. -26.775

3. 0.1668

4. -44/7 which can be simplified into -6 and -2/7

5. $10.96

Answer:

number · 0.50 = 50% of a number

number · 0.10 = 10% of a number

number · 0.75 = 75% of a number

Step-by-step explanation:

50% = 0.50

10% = 0.10

75% = 0.75

Answer:

11.75 please give brainliest

Step-by-step explanation:

Answer: a

Step-by-step explanation:

The lineab bisects bi equally

Answer:

i need to see the graph

Step-by-step explanation:

Answer:

if Z = 6 then your answer is going to be -109

Step-by-step explanation:

Answer:

(3√8x3)25451+2√22√2−3

Step-by-step explanation:

Answer:

7 busses

Step-by-step explanation:

The word description "3 to the power of a + 4" should be written as 3^{a + 4}.

In Mathematics, an exponent is sometimes referred to as power and it can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

By applying the property of exponents based on the law of indices for powers, we have the following:

Expression = 3^{a + 4}.

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Complete Question:

What is 3 to the power of a+4?

Analysis of variance (ANOVA) is a statistical method of comparing the means of several populations.

ANOVA is used when there are three or more groups or populations that need to be compared. It determines whether there are any statistically significant differences among the means of these groups. The method analyzes the variation within each group as well as the variation between the groups to assess whether the differences observed are due to random chance or if there are true differences in the population means.

The primary goal of ANOVA is to test the null hypothesis that the population means are equal across all groups. If the null hypothesis is rejected, it indicates that at least one group significantly differs from the others.

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Answer: the mean temperature is  6? ._.

Step-by-step explanation:

The unit rate for chapters per hour is calculated as 16/21

In order to find the unit rate for the number of chapters Gregory reads in an hour, we must firstly divide the total amount of chapters read by the amount of hours devoted to the activity:

= 2/3 chapters ÷ 7/8 hours

= 2/3 chapters × 8/7 hours

= 16/21 chapters per hour

Consequently, the unit rate for chapters per hour is calculated as 16/21, which already exists in its most simplified form.

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Answer:

y = -2x² + 8x + 10

Step-by-step explanation:

let's adjust the coordinates of vertex to a whole number: (2 , 17.75) to (2 , 18)

Quadratic equation: y = ax² + bx  c    or    y = a(x-h)² + K  (h,k) is the vertex

y = a (x-2)² + 18

a = (y-18) / (x-2)² = (16-18) / (1-2)² = -2    : calculate use point (1 , 16)

y = -2 (x-2)² + 18

y = -2x² +8x + 10

Answer:

uhm 22 - 2 = 20?

Step-by-step explanation:

Im confused what you're trying to say.

Identifying majors with specific language and mathematics requirements using the degree search selection filters help you solve Structured business problem.

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Work Shown:

45.40 - 40 = 5.40

She made $5.40 in profit. Divide this over the original price to find the percentage profit

(5.40)/(40) = 0.135 = 13.5%

The total amount of that Harry will need for the project is nineteen and one third feet and Hence the option B is correct.

Addition of Fraction

Wood 1:

Length of each = 2 3/4 feet

Number of pieces = 4

Total = Length of each × Number of pieces

= 2 3/4 × 4

= 11/4 × 4

= 11 meters

Wood 2:

Length of each = 1 2/3 feet

Number of pieces = 5

Total = Length of each × Number of pieces

= 5/3 ×5

= 25/3 meters

Total amount of wood needed for the project = 11meters + 25/3 meters

= 11 +25/3

= (33+25)/3

= 58/3

=19 1/3 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and one third feet

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False. Line charts are best suited for representing data that follows a sequential order, such as time series data. Nonsequential data is better represented by other types of charts, like scatter plots or bar graphs.

Line charts are graphical representations of data points connected by lines. They are commonly used to display trends over time or sequential data. For example, they are often used to show the change in stock prices over a period of time or the temperature variations throughout the day. This sequential order is the key feature of line charts.

However, for data that does not follow a sequential order, line charts may not be the best choice. Nonsequential data, such as categorical or unrelated data points, are better represented by other types of charts. Scatter plots, for instance, are useful for showing the relationship between two variables that are not necessarily ordered. Bar graphs can also be used to compare nonsequential data points in different categories.

In summary, line charts are not best suited for representing data that follows a nonsequential order. They are most effective when used to display data that has a clear sequential relationship, allowing for easy interpretation of trends and patterns.

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Answer:

There are 25 yellow flowers.

Step-by-step explanation:

The ratio is yellow/all and 5/9.

We know that all the flowers in total equal 45, which is a multiple of 9.

So 45 divided by 9 = 5.

So all I had to do was multiply 5/9 times 5/5.

So then we get the ratio of 45 total flowers with 25 yellow flowers.

Hope this helps!

Answer:

Step-by-step explanation:

c2-7x+12=0

= -132

To guarantee having at least 3 animals of the same type, you would need to adopt a total of 5 animals.

In the worst-case scenario, you would first adopt 2 cats and 2 dogs. By adopting a 5th animal, you would then have at least 3 animals of the same type, either 3 cats and 2 dogs, or 3 dogs and 2 cats. This is due to the Pigeonhole Principle, which states that if you have n categories and n+1 items, at least one category will contain more than one item.

In order to guarantee having at least 3 cats, you would need to adopt a total of 13 animals. This is because, in the worst-case scenario, you could first adopt all 10 dogs, followed by 3 cats. After adopting 13 animals, you would be certain to have at least 3 cats, as you would have exhausted the entire population of dogs in the shelter.

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Answer:

$247.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{sin 82}{28} =\frac{sin A}{8} \\sin A=\frac{8}{28} \times sin 82\\A=sin^{-1} (\frac{2}{7} \times sin~82) \approx 16.4 ^\circ\)