Finding the Distance Between Two Vectors In Exercises 19–22, find the distance between u and v. 19. u = (1, -1), v = (-1,1) 20. u = (1, 1, 2), v = (-1,3,0) llu-vll 21. u = (1, 2, 0), v = (-1,4, 1) (22) u = (0, 1, - 1, 2), v = (1, 1, 2, 2) Finding Dot Products

The correct value of the simplified expression is 2A + 26B.

To simplify the expression, let's break it down step by step:

Expression: 2[9(A−B) + 7(2B−A)] − 2[3(2B+A)−2(A+3B)−5(A+B)]

Step 1: Distribute the coefficients inside the brackets:

2[9A - 9B + 14B - 7A] - 2[6B + 3A - 2A - 6B - 5A - 5B]

Step 2: Simplify the terms inside the brackets:

2[2A + 5B] - 2[A - 8B]

Step 3: Distribute the coefficients outside the brackets:

4A + 10B - 2A + 16B

Step 4: Combine like terms:

2A + 26B

So, the simplified expression is 2A + 26B.

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Dunno what the RACE method is, never heard of it before but.

3x is positive, has a variable.

-3 is negative, has no variable.

-3x^2 is negative, has a variable, and an exponent.

-5x is negaitive, has a variable.

Answer:

The process capability index for this system is 0.9103

Step-by-step explanation:

Upper specification = 1.649 inches

Lowe Specification = 1.507 inches

Mean = 1.57 inches

Standard Deviation = 0.026 inches

Process Capability Index = PCI

PCI = (Upper specification - lower specification)/6(standard deviation)

So, we get,

PCI = (1.649 - 1.507)/((6)(0.026))

PCI = 0.142/0.156

PCI = 0.9102564

To four decimal places, we get,

PCI = 0.9103

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer: 84

Step-by-step explanation: 110% of 40 is 44

                                                                         40+44=84

y = -2x + 1

y = -2x -3

none cuz they're both -2x

Answer: no solution

Step-by-step explanation:

2x+y=1

convert to y=mx+b

y=-2x+1

2x+y=-3

convert to y=mx+b

y=-2x-3

they are parallel

To find out the intervals for which the given function is positive, we need to analyze the sign of the function in different intervals.

Here is the solution: Let f(x) be the given function.

Then,\(f(x) = (x + 4)(x − 6)(x − 8)\)

We can see that the function f(x) changes its sign when x = −4, 6, and 8.

So, these are the critical points that divide the real line into different intervals.

We can check the sign of f(x) in each interval using the following table:x-∞-4-40668f(x)+-+-+-+

\(:x-∞-4-40668f(x)+-+-+-+\)

Therefore, the intervals for which the function is positive are (−4, 0) and (6, 8).

Hence, the correct options are (−4, 0) and (6, 8).

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For a 90 Degree rotation the original x value becomes the new y value and the new x value is the opposite of the original y value.

The answer would be (-6,-7)

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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The diameter of a human hair is 7 times greater than the diameter of a spider's silk.

To determine how much greater the diameter of a human hair is than the diameter of a spider's silk, we can calculate the difference between the two diameters. The diameter of a human hair is given as 10^(-5) meters, and the diameter of a spider's silk is given as 3*10^(-6) meters.

To find the difference, we subtract the diameter of the spider's silk from the diameter of the human hair:

Difference = (10^(-5)) - (3*10^(-6))

= (10^(-5)) - (10^(-6))

= (10^(-5)) - (1/10^6)

= (10^(-5)) - (10^6/10^6)

= (10^(-5)) - (10^6 * 10^(-6))

= (10^(-5)) - (10^(6-6))

= (10^(-5)) - (10^(0))

= (10^(-5)) - 1

= 10^(-5) - 1

= 0.99999

Therefore, the diameter of a human hair is approximately 7 times greater than the diameter of a spider's silk.

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Alyssa and Caleb ate 5/6 of the nachos together.

To calculate the fraction of nachos that Alyssa and Caleb ate together, add the fractions representing the portions that they each ate. However, because the fractions have different denominators, we must first find a common denominator.

2 and 3 share a common denominator of 6. With a denominator of 6, we can rewrite 1/2 and 1/3 as follows:

1/2 = 3/6

1/3 = 2/6

We can now add these fractions:

3/6 + 2/6 = 5/6

As a result, Alyssa and Caleb shared 5/6 of the nachos.

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If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

What are the Permutation and Combination?

Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.

If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =

                        \(=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270\)

Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.

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The values οf the basic trigοnοmetric functiοns fοr an angle in standard pοsitiοn passing thrοugh (6,8) are:

\(\sin \theta &= 0.8\\\) \(\cos \theta &= 0.6\), etc.

Trigοnοmetry is a branch οf mathematics that deals with the study οf triangles and the relatiοnships between their sides and angles.

We can begin by finding the length οf the hypοtenuse οf the right triangle fοrmed by the given pοint and the οrigin. This will give us the value οf the trigοnοmetric functiοns sine, cοsine, and tangent.

The hypotenuse can be found using the Pythagorean theorem:

\(c^2 &= a^2 + b^2\)

\(&= 6^2 + 8^2\)

\(&= 36 + 64\)

\(&= 100\)

\(c &= \sqrt{100}\)

\(c &= 10\)

Therefore, the point (6,8) is 10 units away from the origin.

The sine of the angle can be found by dividing the opposite side (8) by the hypotenuse (10):

\(\sin \theta &= \frac{8}{10}\)

\(&= 0.8\)

The cosine of the angle can be found by dividing the adjacent side (6) by the hypotenuse (10):

\(\cos \theta &= \frac{6}{10}\)

\(&= 0.6\)

The tangent of the angle can be found by dividing the opposite side (8) by the adjacent side (6):

\(\tan \theta &= \frac{8}{6}\)

\(&= \frac{4}{3}\)

Therefore, the values of the basic trigonometric functions for an angle in standard position passing through (6,8) are:

\(\sin \theta &= 0.8\)

\(\cos \theta &= 0.6\)

\(\tan \theta &= \frac{4}{3}\)

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The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.

Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.

The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.

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Answer: −18x-1

Step-by-step explanation: Hope this helps

The location of the y value of R' after using the translation rule is -10

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (-17, -3)

Rewrite as

R = (-17, -3)

When the translation rule is applied, we have:

R' = (-17 + 4, -3 - 7)

Evaluate

R' = (-13, -10)

Remove the x coordinate

R'y = -10

Hence, the location of the y value of R' after using the translation rule is -10

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The volume of the pot is = 731.2 cubic inches.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Since the forms of various three-dimensional objects vary, so do their volumes.

According to our answer-

volume of a pot is = πr²h + 2πr³

22/7 * 698/3

731.2 cubic inches

Hence, The volume of the pot is = 731.2 cubic inches.

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Sampling techniques are particularly important in quantitative research studies. In these studies, researchers aim to collect data from a subset of individuals or entities (the sample) to make inferences about a larger population.

Sampling techniques help researchers select participants from the population in an unbiased and systematic manner. By using appropriate sampling methods such as random sampling, stratified sampling, or cluster sampling, researchers can minimize sampling errors and increase the likelihood that the sample represents the characteristics of the population accurately.

By employing sound sampling techniques, researchers can enhance the external validity of their findings, allowing them to make meaningful and reliable generalizations about the larger population.

This is particularly crucial in fields such as public health, social sciences, market research, and opinion polling, where the goal is to draw valid conclusions about the broader target audience based on a representative sample.

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I believe the answer is D: 6×9÷3.

The question is a word problem, and they are asking you to put it into a numerical problem, meaning with numbers. 6 times 9 divided by 3 put into a numerical equation is 6×9÷3.

If this is incorrect, please, don't refrain to tell me. Thank you.

Option D is the correct response, and it is false to say that it is always necessary to use the Pythagorean Theorem when finding the distance between two points on a coordinate plane.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The correct response is D) false; If the two points create a horizontal or vertical line segment, the Pythagorean Theorem is not needed.

When finding the distance between two points on a coordinate plane, the Pythagorean Theorem is used to calculate the distance only when the two points do not create a horizontal or vertical line segment.

If the two points create a horizontal line segment, then the distance between the two points is simply the difference between their x-coordinates. If the two points create a vertical line segment, then the distance between the two points is simply the difference between their y-coordinates. In both cases, the Pythagorean Theorem is not needed.

Therefore, option D is the correct response, and it is false to say that it is always necessary to use the Pythagorean Theorem when finding the distance between two points on a coordinate plane.

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Answer:

300 seconds

Step-by-step explanation:

The first dog run at v₁ = 15 m/sec     the second one run at  v₂ = 12 m/sec

we know that  d = v*t  then  t  =  d/v

Then the first dog will take  300/ 12  =  25 seconds to make a turn

The second will take   300 / 15   =   20 seconds to make a turn

Then the first dog in 12 turns 12*25 will be at the start point, and so will the second one at the turn 15.

To check  first dog    12 *  25 = 300

And the second dog 15 * 20 = 300

That means that time required for the two dogs to be at the start point together is

300 seconds, in that time the first dog finished the 12 turns, and the second had ended the 15.

Another procedure to solve this problem is as follows:

between  12  m/sec and  15 m/sec   the minimum common multiple  is 300 ( 300 is the smaller number that accept 12 and 15 as factors         12*15 = 300) Then when time arrives at 300 seconds the two dogs will be again in the starting point

Answer:

it would be 4

Step-by-step explanation:

The irrational numbers from greatest to lowest is ∛88 , √19 , and 28 / 9.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers.

The Irrational numbers can be arrange from greatest to the lowest as follows:

The irrational numbers can be express in decimal form to know the greatest.

∛88 = 4.44796018114

∛88 = 4.448

28 / 9 = 3.11111111111

28 / 9 = 3.111

√19 = 4.35889894354

√19 = 4.359

Therefore, the irrational numbers from greatest to lowest is ∛88 , √19 , and 28 / 9.

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The following can be answered by the concept of integration.

a. A(n) = 1/(2n-1) × (x/(x²+4))⁽ⁿ⁻¹⁾ × (x²/2n-3 + 2(n-1)/(2n-3))     B(n) = (n-1)/(2n-1)

b. 4/17 + (1/85) × [(1/(x²+4))⁴ × (x²/6 + 8/5) + 4/5]

c. The given expression, we get: a = 1, b = 7, c = 3, d = 64.

In this question, we are asked to find expressions A(n) and B(n) such that I(n+1) = A(n)I(n) + B(n), where I(n) is the given integral with n as a positive integer. We are also asked to use this result to evaluate another integral and to use Simpson's rule on four subintervals to find a rational approximation of a given integral.

Let's start with part (a). Using integration by parts, we can write:

I(n) = ∫(1/(x²+4))⁽ⁿ⁻¹⁾ dx

= (1/2) ∫(1/(x²+4))⁽ⁿ⁻²⁾ d(x²+4)

= (1/2) [(1/(x²+4))⁽ⁿ⁻²⁾ × (x²+4)/2 - ∫(x²/2)/(x²+4)ⁿ dx]

= (1/2n-1) [(x/(x²+4))⁽ⁿ⁻¹⁾ × (x²/2n-3 + 2(n-1)/(2n-3)) + (n-1)/(2n-1) × I(n-1)]

where we have used the formula for integration by parts and made a substitution u = x²+4 in the second step.

Using this result, we can then find A(n) and B(n) as follows:

A(n) = 1/(2n-1) × (x/(x²+4))⁽ⁿ⁻¹⁾ × (x²/2n-3 + 2(n-1)/(2n-3))

B(n) = (n-1)/(2n-1)

Moving on to part (b), we can use the result from part (a) to evaluate the given integral:

∫(-2 to 0) (x²+4)⁵/(4(x²+4)⁴) dx = I(6)

= A(5)I(5) + B(5)

= (1/17) × [(x/(x²+4))⁴ × (x²/6 + 8/5) + 4/5] × I(5) + 4/17

= 4/17 + (1/85) × [(1/(x²+4))⁴ × (x²/6 + 8/5) + 4/5]

Finally, for part (c), using Simpson's rule on four subintervals, we have:

T_4 = (1/3) [f(0) + 4f(1.333) + 2f(2.667) + 4f(4) + f(8)]

where f(x) = 1/(x²+4).

Substituting the values and simplifying, we get:

T_4 = 119/64

Using this result, we can write the given integral as:

∫(0 to 8) 1/(x²+4) dx ≈ T_4

= 119/64

Solving for a, b, c, and d in the given expression, we get:

a = 1, b = 7, c = 3, d = 64.

Therefore, we have found expressions A(n) and B(n) for the given integral I(n), evaluated another integral using the result from part (a), and found a rational approximation.

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Answer:

I would say the answer is 5.03m^2

Step-by-step explanation:

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Answer:

a

Step-by-step explanation:

The P-value in each of the given situations for testing the null hypothesis H₀: p = 0.6 using a z-test can be determined as follows:

A. Hₐ: p > 0.6, z = 1.47: The P-value is the probability of observing a z-score greater than 1.47, which can be found by calculating the area under the standard normal curve to the right of 1.47.

B. Hₐ: p < 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70, which can be found by calculating the area under the standard normal curve to the left of -2.70.

C. Hₐ: p ≠ 0.6, z = -2.70: The P-value is the probability of observing a z-score less than -2.70 or greater than 2.70, which can be found by calculating the sum of the areas under the standard normal curve to the left of -2.70 and to the right of 2.70.

D. Hₐ: p < 0.6, z = 0.25: The P-value is the probability of observing a z-score less than 0.25, which can be found by calculating the area under the standard normal curve to the left of 0.25.

To determine the P-value, we need to calculate the corresponding areas under the standard normal curve based on the given z-scores. The P-value represents the probability of observing a z-score as extreme or more extreme than the given value, assuming the null hypothesis is true.

By using standard normal distribution tables or statistical software, we can find the probabilities associated with the given z-scores. These probabilities represent the P-values for each scenario, providing a measure of evidence against the null hypothesis.


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Addition and subtraction:- The value of x and y is -13 and 16 respectively.

Division:- The value of x is - 8.

Multiplication:- The value of m is - 7

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

Addition & Subtraction

Consider the equations,

3 + x = - 10

y - 12 = 4

For the equation 3 + x = - 10,

Subtracting 3 from each side of the equation.

x + 3 - 3 = - 10 - 3

x = - 13

For equation y - 12 = 4,

Adding 12 on both sides.

y - 12 + 12 = 4 + 12

y = 16

Division

Consider the equation,

\(\frac{x}{4}=-2\)

Multiplying each side of the equation by 4

\(\frac{x}{4} \times 4 = - 2 \times 4\\ x = -8\)

Multiplication

Consider the equation,

- 5m = 35

Dividing each side of the equation by - 5.

\(\frac{-5m}{-5} =\frac{35}{-5}\)

\(m=-7\)

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Answer: The point estimate for this population proportion is 0.2

Step-by-step explanation:

The point estimate for this population proportion is also referred to as the sample proportion. This is also known as the probability of success, p. The formula for determining p is expressed as

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 200

x = 40

p = 40/200 = 0.2

Answer:

We know that in the box there are:

4 twix

3 kit-kat

Then the total number of candy in the box is:

4 +3 = 7

a)

Here we want to find the probability that we draw two twix.

All the candy has the same probability of being drawn from the box.

So, the probability of getting a twix in the first drawn, is equal to the quotient between the number of twix and the total number of candy in the box, this is:

p = 4/7

Now for the second draw, we do the same, but because we have already drawn one twix before, now the number of twix in the box is 3, and the total number of candy in the box is 6.

this time the probability is:

q = 3/6 = 1/2

The joint probability is the product of the individual probabilities, so here we have

P = p*q = (4/7)*(1/2) =  2/7

b) same reasoning than in the previous case:

For the first bar, the probability is:

p = 3/7

for the second bar, the probability is:

q = 2/6 = 1/3

The joint probability is:

P = p*q = (3/7)*(1/3) = 1/7

c) Suppose that first we draw a twix.

The probability we already know that is:

p = 4/7

Now we want another type, so we need to draw a kit-kat, the probability will be equal to the quotient between the remaining kit-kat bars (3) and the total number of candy in the box (6)

q = 3/6

The joint probability is:

P = p*q = (4/7)*(3/6) = 2/7

But, we also have the case where we first draw a kit-kat and after a twix, so we have a permutation of two, then the probability in this case is:

Probability = 2*P = 2*2/7 = 4/7

we can use a number line

the distance between two numbers on number line is calculated subtracting the greater number from the other

then to calculate each distance from 0

-7 to 0

0 to 7

it's the same distance