This is crazy confusing help.

Answer:

3/10

Step-by-step explanation:

2/5 + 1/5 = 3/5, which gets changed to 6/10, amd 6/10 - 3/10 = 3/10

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer:

13

Explanation:

The explicit formula of a sequence is given below:

When n=3

The 3rd term of the sequence is 13.

12x^3+12x^2-8x-8

This is because you use the distributive property and you put g(x) first because you go from the inside out.

\(-2x+6=12\\2x=-6\\x=-3\)

Answer: No, it fails the vertical line test.

Step-by-step explanation:

The required value of the given integral \(\int\limits_C xydx+x^2y^3dy\) and vertices (0, 0), (1, 0), and (1, 4) by both direct and Green's theorem method is 20.  

The integral of a function over a line or curve is known as a line integral. First, we have to determine the limit of the integral using the given vertices.

\(\mathrm{C_1:(0,0)\;to\;(1,0): r_1(t)=ti\;\;\ 0 \geq t\geq1}\\\mathrm{C_2: (1,0)\;to\;(1,4): r_2 (t) = i+4tj\;\;\ 0 \geq t\geq1}\\\mathrm{C_3: (1,4)\;to\;(0,0):r_3 (t) = (1-t)i+(4-4t)j\;\;\; 0\geq t\geq1}\)

Then, the required direct line integral is,

\(\begin{aligned}\int\limits_C xydx+x^2y^3dy&=\int\limits^1_0 (t)(0)(1)+t^2(0)^3(0)dt\\&+\int\limits^1_0(1)(4t)(0)+1^2(4t)^3(4)dt\\&+\int\limits^1_0 (1-t)(4-4t)(-1) +(1-t)^2 (4 - 4 t )^3 (-4) dt \\&=\int\limits^1_0 256t^3dt+\int\limits^1_0 -4(1-t)^2-256(1-t)^5dt\\&=64-\frac{4}{3}-\frac{128}{3}\\&=20\end{aligned}\)

b) A simple link between the macroscopic circulation around curve C and the total amount of the microscopic circulation that is inside C is known as Green's theorem. A line integral can occasionally be converted into a double integral using Green's theorem, and the reverse is also sometimes true. By Green's theorem, \(\oint Mdx+Ndy= \iint_R \frac{\partial N}{\partial x}-\frac{\partial M}{\partial y} dA\)

Then, the required line integral using Green's theorem,

\(\begin{aligned}\oint xydx+x^2y^3dy&=\int\limits^1_0 \int\limits^{4x}_0(2xy^3-x) dydx\\&=\int\limits^1_0 \left[\frac{xy^4}{2}-xy \right]^{4x}_0dx\\&=\int\limits^1_0 (128x^5-4x^2)dx\\&=\left[\frac{64x^6}{3}-\frac{4x^3}{3}\right]^1_0\\&=20\end{aligned}\)

The required answer obtained by both direct and Green's theorem method is 20.

The complete question -

Evaluate the line integral by the two following methods.

\(\int\limits_C xydx+x^2y^3dy\) C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4).

(a) directly

(b) using Green's Theorem

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If his employer pays 60% of the cost. The annual premium amount for Jonathan's group health insurance is $2,550.

Annual premium can simply be defined as the premium a person is expected to pay per year or annually.

First step is to find the cost

Cost = $85/ (1-.60)

Cost = $85/.40

Cost = $212.5

Now let find the annual premium amount

Annual premium amount = Cost × 12 months

Annual premium amount = $212.5 × 12 months

Annual premium amount = $2,550

Therefore the annual premium amount  is the amount of $2,550.

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The inequality expression that represents the number line is |x + 1| > 6

The number line represents the given parameter

From the number line, we have the following endpoints

Endpoint 1 = -7

Endpoint 2 = 5

Take the average of the endpoints

This is calculated using

Average = 1/2 * (Endpoint 1 + Endpoint 2)

So, we have

Average = 1/2 * (-7 + 5)

Evaluate

Average = -1

Calculate half the difference of the endpoints

This is calculated using

Half difference = 1/2 * (Endpoint 2 - Endpoint 1)

So, we have

Half difference = 1/2 * (5 + 7)

Evaluate

Half difference = 6

The inequality expression is then represented as

|x - Average| > Half difference

This gives

|x + 1| > 6

Hence, the inequality expression is |x + 1| > 6

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The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Answer:

Could you show me the expression?

Step-by-step explanation:

ANSWER:

2nd option: Strong and negative correlation

STEP-BY-STEP EXPLANATION:

The degree of association is measured by a correlation coefficient, denoted by r. The correlation coefficient is measured on a scale ranging from +1 to 0 to -1.

The closer the value is to 1 or -1, the stronger the correlation becomes.

Which means that if it is equal to -0.9, it is a strong correlation.

Therefore, the correct answer is the 2nd option: Strong and negative correlation

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Answer:

wait what grade is this question??

Step-by-step explanation:

The area of the cross-section would be the area of a square with side length of 3 inches, which is 3 x 3 = 9 square inches.

A cube is a three-dimensional geometric shape that has six square faces of equal size and angles, 12 edges of equal length, and eight vertices of equal distance from the center of the cube. A cube is a special case of a rectangular parallelepiped in which all the edges are equal in length.

To divide a cuboid into two cubes, we need to make sure that the dimensions of the cuboid are multiples of the side length of the cubes.

Since the side length of each cube is 3 inches, we can divide the height of the cuboid (which is 8 inches) into two parts, each measuring 4 inches. The base of each cube would then be a square with side length of 3 inches, which means the area of each cube's base is 3 x 3 = 9 square inches.

To find the area of the cross-section, we need to determine which face of each cube will be exposed after dividing the cuboid. Since the cuboid was divided into two cubes, we can assume that the cross-section will be a square with side length of 3 inches (the same as the side length of each cube).

Therefore, the area of the cross-section would be the area of a square with side length of 3 inches, which is 3 x 3 = 9 square inches.

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The Correl function is the easiest way to for calculating correlation between two variables.

What is correlation ?

correlation can be defined as the measure of relation between two variables.

In case you want to measure of degree the power of a dating between two variables, you can accomplish that through using a complicated or on line calculator. you could additionally placed your mathematical abilities to apply and calculate it through hand. while calculating a correlation coefficient via hand.

To find correlation using data points are as follows  :

Determine your data sets.

Calculate the standardized value for your x variables.

Calculate the standardized value for your y variables.

Multiply and find the sum.

Divide the sum and determine the correlation coefficient.

Hence, The Correl function is the easiest way to for calculating correlation between two variables.

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Answer:

ab=a×b

cb=c×b

ad=a×d

cd=c×d

Answer:

well the factor: Add and subtract the second term to the expression and factor by grouping.     (a+c)(b+d)

Step-by-step explanation:

Hope this is helpful! God Bless you !

The value gotten when 5/8 is divided by 3/4 is 5/6.

A fraction is a non-integer that is made up of numerator and a denominator. An example is 5/8. Division is the process of grouping a number into equal parts using another number.

5/8 ÷ 3/4

5/8 × 4/3 = 5/6

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Answer:

11

Step-by-step explanation:

when y = 4

x = 3(4) -1

x= 12-1 = 11

Answer:

3/4 and 1/6 are already reduced the farthest they can go.

Answer:

I hope you can help

Answer:

it droped 40 degres

Step-by-step explanation:

Answer:

The temperature dropped 4 degrees per 1000 feet.

Step-by-step explanation:

90 - 50)/(10,000:1,000) = 40/10 = 4 degrees per 1000 ft

Answer:

Answer 1008

Step-by-step explanation:

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

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Answer:

31.25

Step-by-step explanation:

Firstly, we need to identify the pattern.

Pattern: every next number is obtained by dividing the previous number by 2.

1st number = 1000

2nd number = 1000/2 = 500

3rd number =  500/2 = 250

4th number = 250/2 = 125

5th number = 125/2 = 62.5

6th number = 62.5/ 2 = 31.25.

_______________________________________________

It can be also solved using concept of geometric progression

In GP

any nth number is given by = \(ar^(n-1)\)

where a is first number

r is the common ratio for the gp

r common ratio is calculated by = nth/(n-1)th

here r = 500/1000 = 1/2

a = 1000

next term which we need to find is 6th terms

Thus, 6th terms = \(1000*(1/2)^(6-1)\)

 \(=1000/2^5\)

=1000/32 = 31.25