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The orthonormal set derived from the original set is {(-1/√10, 3/√10), (3/√2, 1/√2)}.

(a) We must prove that the dot product of the set of vectors (-1, 3), and (15, 5) in R² is zero in order to show that they are orthogonal.

Ac + bd is the formula for the dot product of the two vectors (a, b) and (c, d). Let's determine the dot product of the vectors provided:

(-1, 3) · (15, 5) = (-1)(15) + (3)(5) = -15 + 15 = 0.

The set (-1, 3), (15, 5) is orthogonal because the dot product of the two vectors is zero.

(b) We divide each vector by its magnitude (length) to create unit vectors in order to normalize the set and create an orthonormal set.

(A² + B²) provides the magnitude (length) of a vector (a, b). Let's determine the magnitudes of the vectors provided:

||(-1, 3)|| = √((-1)² + 3²) = √(1 + 9) = √10,

||(15, 5)|| = √(15² + 5²) = √(225 + 25) = √250 = 5√2.

By dividing each vector by its magnitude, we may normalize the vectors:

=((-1, 3) / √10, (15, 5) / (5√2))

= (-1/√10, 3/√10), (15/(5√2), 5/(5√2))

= (-1/√10, 3/√10), (3/√2, 1/√2).

The orthonormal set that results from the original set is therefore (-1/10, 3/10), (3/2, 1/2).

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Answer:

1st take PQ - 6 cm

then take an arc of PR of 6cm , and form QR of 6cm ...

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.

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Answer:

The coordinate plane

Step-by-step explanation:

Graph the line \(y=-x+10\) with a dotted boundary and shade the region above the line.

If they both had the same amount of sales and the same compensation for a particular week, compensation will be $545.

Pay is a money or non-cash installment made in return for administrations delivered. Pay can incorporate base compensation, rewards, commissions, merit pay, and tip pay. It can likewise incorporate subordinate or conceded installments, for example, investment opportunities, excursion pay, annuity benefits, free stopping, and clinical protection. Pay alludes to the compensation given to a representative in return for their administrations. The degree of pay offered is reliant upon various elements, including pay rates paid by comparable organizations for comparative jobs, the worker's range of abilities and efficiency and the organization's current and projected monetary strength.

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Answer:

Step-by-step explanation:

The term that suggests that the threat of loss has a greater impact on a decision than the possibility of an equivalent gain is prospect theory.

Prospect theory is a theory that describes how individuals make decisions under uncertainty. The theory suggests that people think about gains and losses differently and that the value they assign to a particular change in their situation depends on their current situation. The theory is based on the observation that people often violate the principle of expected utility. They make decisions that do not maximize their expected utility. The theory suggests that people evaluate outcomes based on changes from a reference point, rather than in absolute terms. This means that people are more sensitive to changes in their situation than to the situation itself.

For example, a loss of $100 is more painful than the pleasure of gaining $100, and the pleasure of gaining $100 is less than the pain of losing $100.

In summary, Prospect theory suggests that the threat of a loss has a greater impact on a decision than the possibility of an equivalent gain.

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Answer: 4800 containers

Step-by-step explanation:

We can see that along the length, the ship can carry (1200 / 30) = 40 containers and along the width, it can carry (300/10) = 30 containers.

Since the containers can be stacked four high, the number of containers that the ship can carry at a time would be:

= 40 × 30 × 4.

= 4800 containers

Answer:

Step-by-step explanation:

Distribute –4 to get –8x + 4 > 5 – 3x.

We can actually deduce here that the correct first step in solving the inequality –4(2x – 1) > 5 – 3x is: A. Distribute –4 to get –8x + 4 > 5 – 3x.

An inequality refers to the relationship that exist between two expressions that shows that they are not equal to each other. The signs used in an inequality are:

We see here that the first step is to use -4 to multiply the digits in the bracket. If that happens, we will have: –8x + 4 > 5 – 3x.

Then solving the inequality:

-8x + 3x > 5 - 4

-5x > 1

x < -1/5

Thus, we see that option B: Distribute –4 to get –8x + 4 > 5 – 3x. is the correct answer.

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Answer:

Step-by-step explanation:

Given points are P(-1,4) and Q(-4,-2)

we know that slope m between two points (x1,y1) and (x2,y2) is m=y2-y1/x2-x1

so,slope m between points P and Q is m=-2-4/-4-(-1)

m=-6/-3

m=2

Now,we know that equation of line

with slope m having points (x1,y1) and (x2,y2) is y-y1=m(x-x1)

so equation of line between P and Q is y-4=2(x+1)

y-4=2x+ 2

y=2x+6

Answer:

-29

Step-by-step explanation:

-5•5=-25

-25-4=-29

Answer:

the sum is 900

Step-by-step explanation:

use formula (n-2)x180

substitue 7 for n

then subtract 2

you get 5

5 times 180 equals 900

Answer:

900°

Step-by-step explanation:

The sum of interior angles can be solved by using the expression (n -2) * 180 , in which "n" denotes the number of sides. In this case, you are given a 7-sided polygon. Plug in 7 for n in the given expression:

\((n - 2) * 180\\(7 - 2) * 180\\(5) * 180\\900\)

900° will be the sum of your interior angles.

~

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The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.

To prove that the statement is true for all natural numbers, n, we can use mathematical induction.

The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.

Base Case (n = 1):

First, let's prove the statement for the base case, n = 1.

For n = 1:

d(1) + (1 + 1) = d(1) + 2

Now, consider a single square with 1 dot.

In this case, d(1) = 1.

So, we have:

1 + 2 = 3

Now, let's consider a pattern of 2 squares (n = 2).

The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.

So, the statement is true for n = 1.

Inductive Hypothesis (Assume true for n = k):

Now, assume that the statement is true for some arbitrary natural number k.

That is, assume that: d(k) + (k + 1) = d(k + 1)

Inductive Step (Prove true for n = k + 1):

To prove that the statement is true for n = k + 1.

d(k + 1) + (k + 2) = d(k + 2)

Now, consider a pattern of (k + 1) squares.

By the inductive hypothesis, assume that the statement is true for k squares:

d(k) + (k + 1) = d(k + 1)

Now, let's add one more square to the pattern.

This square will have (k + 2) dots.

So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:

d(k + 1) + (k + 2)

And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).

Therefore:

d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)

Now, simplify:

d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)

So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.

Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.

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Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Answer:

a) -900 L/min

b) 63000 L

c)  -900t +63000

 d) 7200 L

Step-by-step explanation:

a) You are given two points on the curve of volume vs. time:

(t, V) = (20, 45000) and (70, 0)

The rate of change of volume

= ΔV/Δt = (0 -45000)/(70 -20) = -45000/50 = -900 liters per minute

b) In the first 20 minutes, the change in volume was

(20 min)(-900 L/min) = -18000 L

So, the initial volume was

initial volume - 18000 = 45000

initial volume = 63,000 liters

c) Since we have the slope and the intercept, we can write the equation in slope-intercept form as

 V= -900t +63000.

d) now putting the number in the equation and do the arithmetic.

When t=62, the amount remaining is

= -900(62) +63000 = -55800 +63000 = 7200

Thus, 7200 L remain after 62 minutes.

The formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

Total tires needed by each car = 4 + 1

= 5

Total number of tires, t needed for c cars.

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5 × c

t = 5c

For instance,

if 5 cars are produced per day

Number of tires needed, t = Total tires needed by each car × Number of cars produced per day

t = 5c

= 5 × 5

t = 25 tires

Therefore, the formula which shows how to calculate the number of tires, t, needed if they produce c cars per day is t = 5c. option D

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Answer:

square root of 27 = 5.19615242271  square root of 75 = 25403784  square roots simplified =  75: 8.660        27: I don't know sorry

Step-by-step explanation:

i don't know

how to s explain but those are the answer s

Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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The first six terms of the sequence defined by an = (5n -1 )/3n+1 Q1 = a1= 1, a2=1.286 , a3=1.4, a4=1.462 , a5=1.5 ,a6=1.526 . Therefore, the sequence has a limit of 5/3.

To find the first six terms of the sequence defined by an = (5n -1 )/3n+1, we need to substitute the values of n=1, 2, 3, 4, 5, and 6 into the expression given.

Then we will have the values of the first six terms of the sequence:

a1 = (5(1) - 1)/(3(1) + 1) = 4/4 = 1

a2 = (5(2) - 1)/(3(2) + 1) = 9/7 ≈ 1.286

a3 = (5(3) - 1)/(3(3) + 1) = 14/10 = 1.4

a4 = (5(4) - 1)/(3(4) + 1) = 19/13 ≈ 1.462

a5 = (5(5) - 1)/(3(5) + 1) = 24/16 = 1.5

a6 = (5(6) - 1)/(3(6) + 1) = 29/19 ≈ 1.526

To find whether the sequence appears to have a limit or not, we can observe the values of the sequence. As we can see, the values of the sequence are increasing, but they do not seem to be increasing without bound.

Therefore, the sequence appears to have a limit. Using the limit formula, we can find the limit of the sequence as follows: lim n→∞ (5n - 1)/(3n + 1) = lim n→∞ [(5/n) - (1/n)] / [(3/n) + (1/n)] = lim n→∞ [5 - 1/n] / [3 + 1/n] = 5/3

So, the sequence has a limit of 5/3.

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Answer:

23/26 1 3/26

Step-by-step explanation:

you make to where all the denmanters are the same and add

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

The cost of 1 drink is $1.20.

How to solve word problems?

Let cost of 1 hamburger be x

cost of 1 drink be y

The equations will be

x + 2y = 6  →  (i)

2x + 2y = 9.60  → (ii)

To solve the equations multiple the equation (i) by 2

2x + 4y = 12

2x + 2y = 9.60

Subtracting the equation (i) and (ii)

2y= 2.4

y = 2.4/1.2

y = 1.2

Hence, the cost of drink is $1.2.

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To practice adding mixed numbers with like denominators, you can use worksheets that include problems with varying variables.

Adding mixed numbers with like denominators. Since you mentioned worksheets, I'll explain the process step-by-step, and you can apply these steps to any worksheet problems you have.

Step 1: Identify the mixed numbers and their like denominators.
In a given problem, you'll be given mixed numbers (a whole number and a fraction combined) with like denominators (same number in the denominator).

Example: 2 1/4 + 3 3/4 (Both fractions have the denominator 4)

Step 2: Add the whole numbers.
Add the whole numbers of the mixed numbers together.

Example: 2 + 3 = 5

Step 3: Add the fractions with like denominators.
Add the numerators (top numbers) of the fractions and keep the denominators the same.

Example: 1/4 + 3/4 = (1+3)/4 = 4/4

Step 4: Simplify the fraction, if needed.
If the fraction is improper (numerator is equal to or greater than the denominator), simplify it to a mixed number.

Example: 4/4 = 1

Step 5: Combine the whole numbers and simplified fractions.
Add the whole numbers from Step 2 and the simplified fraction from Step 4.

Example: 5 (whole number) + 1 (simplified fraction) = 6

Final Answer: 2 1/4 + 3 3/4 = 6

Now, you can apply these steps to any problem in your adding mixed numbers with like denominators worksheets. Good luck!

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Answer:

\(8y = 20x\)

Step-by-step explanation:

Given

\(y=\dfrac{5}{2}x\)

Required

Determine equivalent expressions

A. 5y = 2x

\(y=\dfrac{5}{2}x\)

Multiply through by 5

\(5 * y=\dfrac{5}{2}x * 5\)

\(5y=\dfrac{25}{2}x\)

This is not equivalent

B.  8y = 20x

\(y=\dfrac{5}{2}x\)

Multiply both sides by 8

\(8 *y=\dfrac{5}{2}x * 8\)

\(8y=\dfrac{5 * 8}{2}x\)

\(8y=\dfrac{40}{2}x\)

\(8y = 20x\)

The other options are not clear.

However, another possible relationship is when

\(y=\dfrac{5}{2}x\)is cross multiplied

This gives:

\(2y = 5x\)

Answer:

d=          y =x

Step-by-step explanation

i clicked on all the awnser and got it write

The vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)

Point with position vector 2i^−j^+4k^Direction i^+2j^−k^Cartesian form: In Cartesian form, the equation of the line is given by

\({(x-x_0)/a = (y-y_0)/b= (z-z_0)/c}\)

Here, we will use the point-slope form of the equation of the line to get the Cartesian form.

Since the vector equation is in the form r = a + λb. Therefore, we need to find two points that lie on the line. Let's consider two points A (2,-1,4) and B (3,1,3) lying on the line then the direction vector is given by i^+2j^−k^,Therefore, the vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)→r= (2+λ)i−j+(4−λ)k.

Now the Cartesian equation of the line passing through the point with position vector 2i^−j^+4k^ and in the direction of i^+2j^−k^ is

\({(x-2)/(1)=(y+1)/(2)=(z-4)/(-1)}.\)

Vector form: A vector equation of a line in space is given by the position vector of any point on the line plus a scalar multiple of a direction vector of the line. If r is the position vector of any point on the line and an is the direction vector of the line, then the vector equation of the line can be written as r = a + λb. Here, the position vector is given as 2i^−j^+4k^ and the direction vector is given as i^+2j^−k^

Therefore, the vector equation of the line passing through the point 2i^−j^+4k^ and in the direction of i^+2j^−k^ is given by r= 2i^−j^+4k^ + λ(i^+2j^−k^)

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Answer:

see below

Step-by-step explanation:

The equation of a circle can be written as

( x-h) ^2 + (y-k) ^2 = r^2

( x-3)^2 + (y+4) ^2 = 36

Rewriting this equation

( x - 3)^2 + ( y - -4)^2 = 6^2

The center is at (3,-4) and the radius is at 6

Susan did not use the formula correctly.

It is x-h and y-k so she needed to rewrite to get the equation in the proper form

Also the radius is r^2 not r/2

Answer:

28.27

Step-by-step explanation:

π x 6^2 x 90/360 = 28.27