(03.01)

Factor completely x2 − 4x − 12. (1 point)

We have shown that \(cov(x_1, x_1) = v(x_1) = \sigma^2_1(x 1 ,x 1 ).\)

To show that \(cov(x_1, x_1) = v(x_1) = \sigma^2_1(x 1 ,x 1 )\), we need to first understand what each of these terms means:

\(cov(x_1, x_1)\) represents the covariance between the random variable x_1 and itself. In other words, it is the measure of how two instances of x_1 vary together.

v(x_1) represents the variance of x_1. This is a measure of how much x_1 varies on its own, regardless of any other random variable.

\(\sigma^2_1(x 1 ,x 1 )\)represents the second moment of x_1. This is the expected value of the squared deviation of x_1 from its mean.

Now, let's show that \(cov(x_1, x_1) = v(x_1) = \sigma^2_1(x 1 ,x 1 ):\)

We know that the covariance between any random variable and itself is simply the variance of that random variable. Mathematically, we can write:

\(cov(x_1, x_1) = E[(x_1 - E[x_1])^2] - E[x_1 - E[x_1]]^2\\ = E[(x_1 - E[x_1])^2]\\ = v(x_1)\)

Therefore, \(cov(x_1, x_1) = v(x_1).\)

Similarly, we know that the variance of a random variable can be expressed as the second moment of that random variable minus the square of its mean. Mathematically, we can write:

\(v(x_1) = E[(x_1 - E[x_1])^2]\\ = E[x_1^2 - 2\times x_1\times E[x_1] + E[x_1]^2]\\ = E[x_1^2] - 2\times E[x_1]\times E[x_1] + E[x_1]^2\\ = E[x_1^2] - E[x_1]^2\\ = \sigma^2_1(x 1 ,x 1 )\)

Therefore, \(v(x_1) = \sigma^2_1(x 1 ,x 1 ).\)

Thus, we have shown that \(cov(x_1, x_1) = v(x_1) = \sigma^2_1(x 1 ,x 1 ).\)

for such more question on  covariance

https://brainly.com/question/25573309

#SPJ11

Answer:

-2 5/12

Step-by-step explanation:

Took the test

Given the exponential growth of scientific knowledge, medicine is far less (C) vulnerable to unsubstantiated fads than it used to be; its record of folly, however, remains an undeniable embarrassment.

To find the correct option:

Therefore, given the exponential growth of scientific knowledge, medicine is far less (C) vulnerable to unsubstantiated fads than it used to be; its record of folly, however, remains an undeniable embarrassment.

Know more about scientific knowledge here:

https://brainly.com/question/1729104

#SPJ4

Answer/Step-by-step explanation:

The formula for the surface area of a rectangular prism is SA = 2B + Ph

We can create a base from two of the measurements and the height for another. I will make 5 and 5 base lengths (a square base) while 11 is the height.

SA = 2(5*5) + (5+5+5+5)(11)

2(25) + (20)(11)

270 cm²

Tyson:

SA = (5+5+5+5)(11)

(20)(11)

220 cm²

This shows that Tyson did not include the bases in the surface area, which is also known as the lateral area.

Bella:

SA = 2(5*5) + (5+5+5+5)(11) + 5

2(25) + (20)(11) + 5

275 cm²

The only way I can think Bella made a mistake is because she added 5 on accident. Otherwise, how would 270 become 275 without any major changes to the equation?

Answer: The number of points added for r right answers is 12r. The number of points taken away for w wrong answers is 4w, so Olga's total points will be

... 12r -4w

To win, she needs this number to be more than 400. Your inequality is ...

... 12r -4w > 400

Answer:12r -4w > 400

Step-by-step explanation:

Answer:

120.22

Step-by-step explanation:

hope this helps

The percentile score of 71 on test score is 27 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

\(R_{100} =\frac{100(N < )+\frac{1}{2} }{N}\)

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60th percentile.

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

To learn more on Statistics click:

brainly.com/question/29342780

#SPJ1

Answer:

A=122

Step-by-step explanation:

The sum of degree of angles in a triangle=180

Angle a =180-43-15=122

Answer:

15 boxes

Step-by-step explanation:

364/24= 15

Answer:

$2.80

Step-by-step explanation:

14.00 for 5 mangos and 8 oranges

14/5=2.8 for each mango

2.8+1.50=4.30

Answer:

Point Form:

( 0 , 3 )

Equation Form:

x = 0 , y = 3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

b. BC

Step-by-step explanation:

The first thing is to calculate the dimensions of each matrix, that is, the number of rows x number of columns:

dimensions of A: 2x2

B dimensions: 2x3

C dimensions: 3x3

D dimensions: 1x3

 We have that a matrix multiplication is defined, the internal numbers of its dimensions must be the same: we analyze each option:

BA: (2x3) * (2x2): the internal numbers do not match (a 3 for B and a 2 for A), so the multiplication of the matrix is not defined

BC: (2x3) * (3x3): the internal numbers are both 3, so the matrix multiplication is defined

CB: (3x3 ) * (2x3): the internal numbers do not match (a 3 for C and a 2 for B), so the multiplication of the matrix is not defined

CD: (3x3) * (1x3): the internal numbers do not match (a 3 for C and a 1 for D) so the multiplication of the matrix is not defined

Therefore the answer is b. BC

The value of x which is hypotenuse is 4 units .

Using pythagoras theorem ,

( a ^ 2 ) + ( b ^ 2 ) = ( h ^ 2 )

where a is the base , b is a side and h is the hypotenuse of a right- angled triangle .

First triangle's hypotenuse = \(\sqrt{2}\)

Second triangle's hypotenuse = \(\sqrt{3}\)

Third triangle's hypotenuse = 2

Therefore ,

Last triangle's hypotenuse = \(\sqrt{15}\)

Hence ,

( \(\sqrt{15}\) ^ 2 ) + [ ( 1 ) ^ 2 ] = x ^ 2

15 + 1 = x ^ 2

16 = x ^ 2

x = 4

Therefore , the value of x which is hypotenuse is 4 units .

To learn more on pythagoras theorem follow link :

https://brainly.com/question/21332040

#SPJ9

The problem involves finding the optimal amounts of different variations of a product to maximize total revenue while considering ingredient availability and production requirements. A linear programming model can be formulated with decision variables for the amounts of each variation and constraints on ingredient availability, and the objective is to maximize the total revenue. Julia can be used to implement and solve the model using an optimization solver like JuMP.

Based on the problem statement, we can formulate the following linear programming model:

Sets:

I: Set of ingredients

V: Set of variations

Parameters:

Decision Variables:

Objective:

Maximize the total revenue: max sum(r[j] * x[j] for j in V)

Constraints:

Ingredient availability constraint:

For each ingredient i in I, the sum of the amount used in each variation j should not exceed the available amount:

sum(a[i,j] * x[j] for j in V) <= b[i] for i in I

Non-negativity constraint:

The amount of each variation produced should be non-negative:

x[j] >= 0 for j in V

Once the model is formulated, you can use an optimization solver in Julia, such as JuMP, to solve it and find the optimal values for x[j] that maximize the total revenue.

To know more about revenue refer to-

https://brainly.com/question/29567732

#SPJ11

Complete question

"Problem Statement: Walt and Jesse are sitting on an assortment of ingredients (I) for making Blue Sky. They have bᵢ units of ingredient i∈I. While they are able to achieve a 99.1% chemically pure product, they have found that by tweaking the process, they can achieve different variations (V) of Blue Sky which trade off purity for lower resource consumption. One pound of variation j∈V takes aᵢⱼ units of ingredient i∈I to make and sells for rⱼ dollars. Find how much of each variation they should cook in order to maximize their total revenue.

Table 1: Data for the problem. (Not necessary for writing the model, but may be helpful to see.)

Model: Write a general model. To recap, the following are the sets and parameters:

Ingredients (I)

Variations (V)

bᵢ units of ingredient i∈I available

Amount (units/lb) aᵢⱼ of ingredient i∈I that variation j∈V requires

Revenue ($/lb) rⱼ for variation j∈V

Julia: Download the starter code disc3_exercise.ipynb from Canvas. Implement the model in Julia. Remember, you can always begin with an existing model and modify it accordingly."

The task is to create a mathematical model and implement it in Julia to determine the optimal amounts of each variation that Walt and Jesse should cook in order to maximize their total revenue, given the available ingredients, ingredient requirements, and revenue per pound for each variation.

Answer:

261 cm²

Step-by-step explanation:

To find the surface area of a square pyramid, you must first recognize all of the shapes.

There are four triangles and one square.

The triangles have a base of 9 and a height of 10.

\(9*10=90\)

Multiply the product by 1/2.

\(90*1/2 = 45\)

There are four triangles.

\(45*4=180\)

The area of all three triangles is 180 centimeters; the area of a single triangle is 45 centimeters.

There square has sides of 9 centimeters.

\(9*9=81\)

The area of the square is 81 centimeters.

Lastly, we add the areas of the shapes.

\(45+45+45+45+81 = 261.\)

Therefore, the surface area of this square prism is 261 cm².

You can use this layout to find the surface area of a square pyramid.

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

144 cubic inches

Step-by-step explanation:

V=lwh

6x4=24

24x6=144

1) Flipping the equation 32 = 2 + 3(n-1)

3(n-1)+2=32 Subtract 2 from both sides

3(n-1)+2 -2=32-2

3(n-1) =30 Divide by 3 on both sides

n-1=10

n-1+1=10+1 Add 1 on both sides

n=11

2) Then term "n" = 11.

The three statements that are true about this situation using function notation are;

The statements which can be deduced from the graph as given in the question are as listed above in which case, the distance from post in feet is a function of the time in seconds.

The function given is an elongated curve and can be represented by notation as, f(t) whose value is plotted on the vertical axis against t, whose value is plotted on the horizontal axis.

Where; t = time and f(t) = distance from post in feet

Hence, by considering the graph;

Read more on functions;

https://brainly.com/question/10439235

Answer:

Step-by-step explanation:

f(0)=1.5ft

f(60)=4ft

f(80)<3ft

Answer:

y = -1/3x + 19/3

Step-by-step explanation:

let the equation of the line be y = mx + b

since it is perpendicular to y = 3x - 1, these two lines's gradient when producted gives -1.

hence, 3 x m = -1

m = -1/3

sub m = -1/3 and (7, 4):

4 = -1/3(7) + b

b = 19/3

therefore, equation of the line is y = -1/3x + 19/3

Topic: coordinate geometry

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

The ratio of unshaded squares to shaded squares is 15:10. This means that for every 15 unshaded squares, there are 10 shaded squares. This can also be simplified to 3:2, which means that for every 3 unshaded squares, there are 2 shaded squares.

It is important to keep in mind that the ratio is not equal to the fraction, it's just a way to express the relationship between the two.

Answer:

15:10

Step-by-step explanation:

15:10 which means that for every 15 unshaded squares there are 10 shaded squares which can also be simplified to 3:2 which means pretty much the same thing, for every 3 unshaded squares there will be 2 shaded ones. A ratio is not a fraction, so i advise not treating it like one.

Answer:

21 and 35

Step-by-step explanation:

Prime factorization of 21 is 3*7

Prime factorization of 35 is 5*7

Answer:

21 and 35

Step-by-step explanation:

Notice that

We say that a vertical stretch occurs when a base graph is multiplied by a certain factor greater than 1.

As 1.1>1, f_2(x) is a vertical stretch of f_1(x)

Thus, the answer is The graphs have different vertical stretches, option A.

If the sum of two consecutive multiples of a given number is 120 then the given number is 20.

Let x be the number we are looking for, then the consecutive multiples of x can be expressed as x and 2x. We are given that the sum of these consecutive multiples is 120, which can be expressed mathematically as:

x + 2x = 120

Simplifying this equation, we get:

3x = 120

Dividing both sides of the equation by 3, we get:

x = 40

Therefore, the number we are looking for is 40. However, we are asked for the consecutive multiples of x, which are x and 2x.

Substituting x = 40 into these expressions, we get:

Consecutive multiples of 40: 40 and 80

However, we are not done yet. The problem asks for two consecutive multiples of the number x that add up to 120. The multiples we found above do not satisfy this condition, as their sum is 120 but they are not consecutive.

Therefore, we need to find the consecutive multiples of 20 that add up to 120. These can be expressed as 20 and 40, which are consecutive multiples of the number 20. We can check that their sum is indeed 120:

20 + 40 = 60

Therefore, the correct answer is that the number we are looking for is 20.

To learn more about consecutive multiples, click here: brainly.com/question/63850

#SPJ11

Answer:

314 \(cm^{2}\)

Step-by-step explanation:

A = \(\pi\)\(r^{2}\)

A = 3.14\((10)^{2}\)

A = 314 \(cm^{2}\)

Answer:

314.1592654 cm

Step-by-step explanation:

20 cm = circumference

circumference/2 = radius

radius = 10

π\(r^{2}\) = area

π\(10^{2}\) = 314.1592654 cm

The given integral ∫(4x^2 + 4x + 2) dx can be evaluated to obtain an expression in the form P arctan(ax + b) + c, where P, a, b, and c are constants. The common divisor of P and q is 1, and the value of P is 9.

In the given expression, the integral of 4x^2 is (4/3)x^3, the integral of 4x is 2x^2, and the integral of 2 is 2x. Summing up these integrals, we get (4/3)x^3 + 2x^2 + 2x + C, where C is the constant of integration.

To express this in the form P arctan(ax + b) + c, we need to manipulate the expression further. We can rewrite (4/3)x^3 + 2x^2 + 2x as (4/3)x^3 + (6/3)x^2 + (6/3)x, which simplifies to (4/3)x^3 + (6/3)(x^2 + x).

Comparing this with the form arctan(ax + b), we can see that a = √(6/3) and b = 1. Therefore, the expression becomes 9 arctans (√(6/3)x + 1) + C, where C is the constant of integration.

Learn more about common divisor here: brainly.com/question/13257989
#SPJ11

Answer:

5%

1 of the 20 crayons is red, so...

1/20 = 5% or 0.05

Answer: 5%

Step-by-step explanation:

You want to use the summarize() and mean() functions to find the mean rating for your data. add the code chunk that lets you find the mean value for the variable rating. 1 reset. the mean rating is 3.185933

To determine the mean value for the variable Rating, you must add the code snippet summarize(mean(Rating)). Trimmed flavors df%>% summarize(mean(Rating)) is the right code. In this section of code:

You can display summary statistics using the summarize() method. To generate specific statistics, you can combine the summarize() method with others like mean(), sd(), and max().

In this instance, you compute the mean value for the variable Rating using the mean() function.

Learn more about mean rating at:

https://brainly.com/question/28213340

#SPJ1

Distance = 50 meters

Slowest means, longest time =58 seconds

Speed is equal to distance divided by time:

Speed = 50/58

=25/29 m/s

=0.86m/s which is the answer.

Linda kept track of her times in the 50-meter freestyle at her team's swim meets. Swim times (sec.) H 40 44 48 52 56 60 What was Linda's slowest time in the 50-meter freestyle? 60 seconds 52 seconds 56 seconds 58 seconds

To know more about solutions,click below

https://brainly.com/question/3951473