what does it mean for a graph to be a vertical stretch of the parent fuction?

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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PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

There are 14 dogs and 46 chickens in the farmyard.

The supposition that there are d dogs and c chickens.

Each chicken has two legs, but each dog has four.

Consequently, the total number of legs may be written as follows:

4d + 2c

Since we are aware that there are 148 legs in total, we can construct the following equation:

4d + 2c = 148

We may create another equation since we know that there are a total of 60 heads (dogs and chickens):

d + c = 60

Now that we have two equations with two variables, we may answer them both at the same time.

2d + 2c = 120 is the result of multiplying the second equation by two.

When we deduct this from the first equation, we obtain 2d = 28.

So, d = 14.

Reintroducing this into the second equation, we get:

14 + c = 60

So, c = 46.

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Division by 0 is a mathematical concept that cannot be expressed in any natural notation because it's not defined.

If the numerator of a fraction is something different from zero, and the denominator is zero, the quotient is undefined.

But if both numbers are zero, then the division is undetermined. These two terms are very different and it's important to tell from them in, for example, calculus.

Answer: B. The quotient is undefined

Answer:

-3÷2

Step-by-step explanation:

if you have solving for x

1st step: will be to set up the function =0

so 2x+3=0

then 2x=-3

so x= -3/2

Answer:

C. Simulation

Step-by-step explanation:

The answer is Simulation the modeling events using random numbers is known as a simulation option (C) Simulation is correct.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

It is given that:

Modeling events using random numbers is known:

As we know, a simulation recreates random occurrences by specifying event outcomes with relative frequencies that match the real-world relative frequencies we're aiming to simulate using random numbers.

It's called a simulation when you use random numbers to model an event.

Modeling events using random numbers is known as a simulation.

Thus, the answer is Simulation the modeling events using random numbers is known as a simulation option (C) Simulation is correct.

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Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

Answer:

100 drops of water weigh about 9 grams. So how many tons do 100 million drops of water weigh?

Step-by-step explanation:

please mark my answer in brainlist plz

Using the Venn diagram, each set and the number of elements in each set are:

a. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b. A = {1, 3, 4, 5, 6, 8}

c. B = {4, 5, 6, 7, 9, 11}

d. C = {6, 8, 9, 12}

e. A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f. A ∩ B = {4, 5, 6}

A Venn diagram is a pictorial representation used to visualize the relationships between different sets of objects or concepts.

a.) U is the universal set. This implies it contains all the elements in the set. Thus:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b.) A is all element (number) is set A (circle A). Thus:

A = {1, 3, 4, 5, 6, 8}

c.) B is all element is set B (circle B). Thus:

B = {4, 5, 6, 7, 9, 11}

d.) C is all element is set C (circle C). Thus:

C = {6, 8, 9, 12}

e.) A ∪ B is all element is sets A and B (circles A and B). Thus:

A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f.) A ∩ B is all element is sets A and B (circles A and B) have in common. Thus:

A ∩ B = {4, 5, 6}

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The probability that you receive at most 9 calls is 0.2.

Probability in mathematics is the possibility of an event in time. In simple words how many times does that incident is happening in any given time interval?

Given:

Every day you receive a certain number of calls from your friend but not more than 10.

If the probability that on a given day you receive exactly 10 calls is 0.8,

then the probability that you receive at most 9 calls is,

P(X ≤ 9) =  1 - P(X ≥ 10)

P(X ≤ 9) = 1 - P(X = 10)

P(X ≤ 9) = 1 - 0.8

P(X ≤ 9) = 0.2

Therefore, P(X ≤ 9) = 0.2.

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the measure of total interior angles of any quadrilateral is 360°.

so, k+ 160°+ 90° + 90° = 360°

k + 340°= 360°

therefore, k = 20°

Answer:

a) x^3 b) y^5

Step-by-step explanation:

you can combine the x's and y's to make a exponent equal to the number of x's or y's.

how many solutions does the following equation have \( 8u+3(1/3u-6)=9u+2u+12\)

Without even working out anything we can easily tell the answer is \(1\) because the degree of the equation is one.

If you haven't learned this yet let me know and I will post the manual work.

:)

Answer:

  1 solution

Step-by-step explanation:

When put in general form, the coefficient of u is non-zero, so there is 1 solution.

  0 = 9u +2u +12 -(8u +3(1/3u -6))

  0 = 11u +12 -8u -3(1/3u -6)

  0 = 3u +12 -u +18

  0 = 2u +30 . . . general form equation

  0 = u +15

  -15 = u . . . . . one solution

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~0 - 2~~)^2 + (~~9 - 1~~)^2} \implies d=\sqrt{( -2 )^2 + ( 8 )^2} \\\\\\ d=\sqrt{ 4 + 64 } \implies d=\sqrt{ 68 }\implies d\approx 8.246\)

Answer:

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Suppose a sample of 333 tankers is drawn. Of these ships, 257 did not have spills.

333 - 257 = 76 have spills.

This means that \(n = 333, \pi = \frac{76}{333} = 0.228\)

80% confidence level

So \(\alpha = 0.2\), z is the value of Z that has a pvalue of \(1 - \frac{0.2}{2} = 0.9\), so \(Z = 1.28\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 - 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.199\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 + 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.257\)

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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As a result, the provided point (6, 8) is said to be in the second quadrant.

What is Quadrant?

Each of the four divisions of the coordinate plane is referred to as a quadrant. Additionally, when we refer to the sections, we mean the sections as they are divided by the coordinate axes. The x-axis is located here, and the y-axis is located on this up-down axis. As you can see, it creates four portions on a coordinate plane.

A point is expressed mathematically as:

           A(x, y )

The cartesian plane is divided into four quadrants by the junction of the coordinate axes (x and y-axis).

Both the x and y coordinates in the first quadrant are positive.

                                    (x, y)

In the second quadrant, y  is positive whereas x is negative.

                                 (-x, y)

If x  and  y are equally negative, the point will be in the third quadrant.

                                      (-x, -y)

If both x and y are positive, the point will be in the fourth quadrant.

                                             (x, -y)

Given point;

   A(-6, 8)

In the indicated point, the y-coordinate (8) is positive and the  x-coordinate (-6) is negative.

Recall that the point is in the second quadrant if the  x-coordinate is negative and the  y-coordinate is positive.

Thus, we can say that the given point (−6,8) lie in the second quadrant.

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The total home work problems she have is 10 (option D)

A ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.

for example if the ratio of boys to girls in a school is 10:8, to get the number of boys in the school,it will be 10/8×no of students in the school.

Similarly the ratio of problems finished to unfinished problems is 4:1. the number of finished problems is 8.

Represent the total number of problems by y, then ⅘×y= 8

multiply both sides by 5

4y= 40

divide both sides 4

y = 40/4= 10

therefore the total number of problems is 10

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Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Answer:

x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631.

Step-by-step explanation:yes

Answer:

The answer is 4. 16y^6/x^2

The interval of convergence of the Maclaurin series of (A)-1 is x≈P(x)=x

The concept of Maclaurin series states that the function is just the part of Taylor series of the function if in the Taylor series the center is taken as c = 0 then the Taylor series is called Maclaurin series.

Here we need to find the the interval of convergence of the Maclaurin series.

Let us consider  x up to n=3. and the function is x.

Then the Maclaurin series is given by

Find the 1st derivative: f(1)(x)=(f(0)(x))′=(x)′=1

valuate the 1st derivative at the given point: (f(0))′=1

Find the 2nd derivative: f(2)(x)=(f(1)(x))′=(1)′=0

Evaluate the 2nd derivative at the given point: (f(0))′′=0

Find the 3rd derivative: f(3)(x)=(f(2)(x))′=(0)′=0 (steps can be seen here).

Evaluate the 3rd derivative at the given point: (f(0))′′′=0

Now, use the calculated values to get a polynomial:

f(x)≈0/0! x⁰ + 1/1! x¹ + 0/2! x² + 0/3! x³

Finally, after simplifying we get the final answer:

=> f(x)≈P(x)=x

Therefore the Taylor (Maclaurin) series of x up to n=3 is x≈P(x)=x

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Answer:

0.04411764705

Step-by-step explanation:

Answer:

0.04411764705 is the correct answer ┌(・。・)┘♪

hi!

first, you have to graph the piecewise function. a piecewise function is basically where there are multiple different lines, but they all have different sections on the graph that they are applicable.

on the graph, graph the first equation, in the piecewise function, which is y= -3x + 2.

then, you have to erase all parts except the segment between x=-1 and x=1. at the endpoints, place a filled in dot to mark the point.

do the same with y = x - 2, however, this time, the restraints are at x=1 and x=3. you'll see that the endpoint at x=1 coincides with the previous equation! for the endpoint on the side of x=3, you should place another filled in dot to mark that it includes x=3.

i've attatched a screenshot below (scroll down a bit!) of what the graph should look like, in case that was confusing :)

next, you can fill in the table by finding what the function outputs for the given x. for the first one, x = -3. first, look at the function. is x between -1 and 1, or between 1 and 3? neither. that means that it is no solution for that point.

continue down the table. it is the same with x=-2.

next, x = -1. this is in the interval of -1<=x<=1, so you should look at the first equation in the piecewise function, which is 2-3x. if we plug in -1 for x, we get 2 - 3(-1) = 2+3 = 5. this means that the point is (-1, 5). you should make sure that this is a point that you plotted on the graph, and if not, the graph is wrong :(

continue down the table and keep doing that!

next question is if there is a min or max. there is! as you can see, the piecewise function only goes from x=-1 through x=3, and all other values give a no solution output. so, the minimum is -1 and the maximum is 3.

next: turning point or vertex. this would be at the point when x = 1, since that would be where the graph changes direction. the vertex is at (1, -1).

the zeroes of the function is where the graph crosses the x-axis. this means that y=0. we can see that this happens when x=2/3 and when x=2.

i hope this was helpful! :)

The completed contingency table that summarizes the classification of students by weight and gender is attached below.

a. For a randomly selected student, describe the following in words

W1 is an event in which a randomly selected student is obese.

P(W1) is the probability that a randomly selected student is obese.

b. The following probabilities: (Round the answers to 4 decimal places)

i. P(W2) = (42 + 55) / 173 = 0.574

ii. P(G1) = (76 + 76) / 173 = 0.500

iii. P(W1 and G2) = (76) / 173 = 0.440

iv. P(W3 or G2) = (30 + 22 + 76 + 76) / 173 = 0.884

v. P(W3 | G2) = (22) / (22 + 76) = 0.214

c. For the following:

i. W3 and G1 are not mutually exclusive. This is because there are students who are both obese and male. For example, the value in the cell (W1, G1) is 76.

ii. W3 and G1 are not independent. This is because the probability of being obese is different for male students than it is for female students. For example, the probability of being obese is 0.440 for male students, but it is only 0.130 for female students.

iii. W3 and W2 are not mutually exclusive. This is because there are students who are both underweight and normal. For example, the value in the cell (W2, W3) is 30.

iv. W3 and W2 are not independent. This is because the probability of being underweight is different for normal students than it is for obese students. For example, the probability of being underweight is 0.300 for normal students, but it is only 0.154 for obese students.

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Answer:

20

Step-by-step explanation:

20

Answer:

240 meters all you are doing is finding 40 percent off 400

Step-by-step explanation:

The center of the hanger represents an equal sign, since both sides of the hanger are equal.

Given different coloured triangles and shapes, we can assign a variable to each of them.

Let one green triangle be equal to \(a\).

Let one blue square be equal to \(b\)

Let one red circle be equal to \(c\).

Let one yellow pentagon be equal to \(d\).

On the left side of the hanger/equation, there are 3 green triangles. This means that one of our terms in our equation will be \(3a\).

Under the triangles on the left side is 1 blue square. This means that the next term could be \(1b\), or just \(b\).

Next is 2 red circles ⇒ \(2c\)

And finally are 3 yellow pentagons ⇒ \(3d\)

To sum up the left side as an expression, we can write all the terms we have just written as a sum:

\(3a+b+2c+3d\)

Now, after doing the same procedure for the right side of the hanger, we get:

\(2a+3b+c+2d\)

For now, we only have two expressions representing the two sides of the hanger:

Left: \(3a+b+2c+3d\)

Right: \(2a+3b+c+2d\)

To turn these into an equation, we must have an equal sign.

Remember that both sides of the hanger are equal. Knowing this, we can state the following:

Left side = Right side

\(3a+b+2c+3d = 2a+3b+c+2d\)

\(3a+b+2c+3d = 2a+3b+c+2d\)

Answer:

11/3

Step-by-step explanation:

-4(r-2/3)+4<-8

-4r+8/3+4<-8

8/3+4<-8+4r

8/3+4+8<4r

44/3<4r

44/12=r

11/3=r

Answer:

i don't know sorry b a b y g i r l

Step-by-step explanation:

Answer:

0.5 (any number between 0 and 1)

Step-by-step explanation:

34 * 0.5 = 17

34 > 17 > 0