This table shows how many t-shirts of each color Marcus has in his closet. If he chooses a t-shirt without looking, what is the probability that it will be white?

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

First, identify the three vectors in component form (remember to have the direction angle for each vector account for the quadrants they are in!):

\(u=\langle90\cos220^\circ,90\sin220^\circ\rangle\\v=\langle 60\cos110^\circ,60\sin110^\circ\rangle\\w=\langle 40\cos30^\circ,40\sin30^\circ\rangle\)

Secondly, we add them:

\(u+v+w=\langle90\cos220^\circ+60\cos110^\circ+40\cos30^\circ,90\sin220^\circ+60\sin110^\circ+40\sin30^\circ\rangle\approx\langle-54.824,18.531\rangle\)

Thirdly, find the magnitude of the new vector:

\(||u+v+w||=\sqrt{(-54.824)^2+(18.531)^2}\\||u+v+w||\approx57.871\)

And finally, find the direction of the new vector:

\(\theta=tan^{-1}(\frac{18.531}{-54.824})\\\theta\approx-18.675^\circ\approx-19^\circ\)

Because our new vector is in Quadrant II, our found direction angle is a reference angle, telling us that the actual direction of our vector is 19° clockwise from the negative x-axis, which would be 180°-19°=161°

Thus, B is the best answer

Problem 2

To find the component form of a vector, we simply subtract the initial point from the terminal point. In this case, our initial point is at (7,-1) and our terminal point is at (1,6). We subtract the horizontal and vertical components separately:

\(\langle1-7,6-(-1)\rangle=\langle-6,7\rangle\)

Thus, A is the correct answer

Problem 3

Again, subtract the initial point from the terminal point to find the vector, and then apply scalar multiplication:

\(-\frac{1}{2}v=-\frac{1}{2} \langle-8-8,10-4\rangle=-\frac{1}{2}\langle-16,6\rangle=\langle8,-3\rangle\)

Thus, C is the correct answer

Problem 4 (top one in 4th image)

Remember that scalar multiplication only affects the magnitude of the vector and not the direction. Thus, \(-3u=-3\bigr[20\langle\cos30^\circ,\sin30^\circ\rangle\bigr]=-60\langle\cos30^\circ,\sin30^\circ\rangle\), which means our magnitude is -60 and our direction remains 30°.

Thus, B is the correct answer

Problem 5 (fake #6, bottom one in 4th image)

Basically, whatever is in front of the i represents the horizontal component, and whatever is in front of the j represents the vertical component, so:

\(u=-3i+8j=\langle-3,8\rangle\)

Thus, B is the correct answer

Problem 6 (real one, 5th image)

Recall:

Knowing these facts, let us compute the dot product:

\(u\cdot v=(-4*28)+(7*-49)=(-112)+(-343)=-455\)

Since the dot product of the two vectors is not 0, then the vectors are not orthogonal, so we can eliminate choices A and B

To check if the vectors are parallel, find the angle between them:

\(\displaystyle\theta=cos^{-1}\biggr(\frac{u\cdot v}{||u||\:||v||}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{(-4)^2+(7)^2}\sqrt{(28)^2+(-49)^2}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{16+49}\sqrt{784+2401}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{65}\sqrt{3185}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{\sqrt{207025}}\biggr)\\\\\theta=cos^{-1}\biggr(\frac{-455}{455}\biggr)\\\\\theta=cos^{-1}(-1)\\\\\theta=180^\circ\)

So, since the angle between the two vectors is 180°, this implies that cosθ=-1, and the two vectors must be parallel.

Thus, D is the correct answer

If the perimeter of the  rectangle is 56m with length 18m the breadth is 10m

You should know that the breath of the rectangle is the two shorter sides of the rectangle.

The perimeter of the rectangle is the distance round the rectangle

In every rectangle, there are 2 Lengths and 2 breadths

This implies that the perimeter is

P= L+B+L+B

P=2L+2B

This implies that

56=2(18)+2B

⇒56=36+2B

56-36=2B

20=2B

Making B the subject of the relation we have

B=20/2

B=10m

Therefore the breadth of the rectangle is 10m

Learn more about the perimeter of a rectangle on https://brainly.com/question/29595517

#SPJ1

Answer:

Yes

Step-by-step explanation:

1/4 = 4/16 because 1/4 of 16 is 4

Also,

1/4 is just a simplified version of 4/16

The answer to whether 1/4 and 4/16 are equivalent fractions is that; Yes, they are equivalent fractions

We have two fractions which are; 1/4 and 4/16

Now, the first fraction is already in simplified form and can't be simplified further. However, the second fraction can be further simplified.

For the second fraction which is 4/16, the numerator and denominators have a common term which is 4. Thus, we can factor it out to get;

(4/4) * (1/4)

4/4 =1 and so we see that 4/16 can be reduced to the first fraction and so they are the same.

Read more about Fractions at; https://brainly.com/question/11562149

#SPJ2

9514 1404 393

Answer:

  y = -1/2x +11/2

Step-by-step explanation:

The slope of the line is ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -2)/(9 -7) = -1/2

The y-intercept is ...

  b = y -mx

  b = 2 -(-1/2)(7) = 11/2

Then the slope-intercept equation is ...

  y = -1/2x +11/2

_____

Alternative solution

A general form equation for the line can be ...

  (y1 -y2)(x -x1) -(x1 -x2)(y -y1) = 0

  (2 -1)(x -7) -(7 -9)(y -2) = 0

  x-7 +2y -4 = 0

  x +2y -11 = 0 . . . . . general form equation

  x +2y = 11 . . . . . . . standard form equation

Note that we want the x-coefficient to be positive, so we chose the order of the points to make that be the case.

Answer:11

Step-by-step explanation:

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

for such more question on radioactive isotope

https://brainly.com/question/20596678

#SPJ8

Combining like terms you have 500x - 200x = 300x

Answer: 300x

Answer:

300x = 300000

Step-by-step explanation:

500x - 200x = 300x

300x + 300,000 = 600,000

600000 - 300000 = 300000

300x = 300000

Answer:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25

The value of the expression is -4

The cube root of a number can be defined as the factor multiplied by three times by itself  to get that number.

Cube root is represented using the formula, '∛'

From the information given,

c³ = -64

Take the cube root of both sides

∛c³ = ∛ - 64

c = - 4

Thus, the value of the expression is -4

Learn more about cube root here:

https://brainly.com/question/28256285

#SPJ1

Answer:

y = -248

Step-by-step explanation:

Hi there!

Set up a proportion:

\(\displaystyle\frac{124}{12} =\frac{y}{-24}\)

Cross-multiply:

\(12y=(-24)(124)\\12y=-2976\\y=-248\)

I hope this helps!

The solutions for all three questions regarding two-way frequency tables are given below.

A two-way frequency table is a method used to visually represent two sets of categorical data. Unlike one-way frequency tables which have only one categorical variable, these have two. The important parts of a two-way frequency table are the topmost rows that have the name of the category. The leftmost column also has the categories listed. The middle columns and rows contain the data (frequency).

The number in the bottom right-hand corner of a two-way frequency is used to denote the total number of data points that are there in the data set given. This is also equal to the sum of the total rows/columns.

Learn more about frequency tables on

https://brainly.com/question/28931302?referrer=searchResults

#SPJ4

Answer:

The number of ways to distribute 30 batteries among the six different types is 33,649.

Step-by-step explanation:

It is provided that a camera shop stocks six different types of batteries, one of which is type A7b.

Also, the camera shop has only twelve A7b batteries but at least 30 of each of the other types.

Combinations would be used to determine the number of ways to distribute 30 batteries among the six different types. Here repetition is allowed.

\(C(n+r-1, r)={n+r-1\choose r}=\frac{(n+r-1)!}{r!(n-1)!}\)

The number of A7b batteries is 12.

Then the number of ways to distribute 30 batteries among the six different types is:

\(C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}\)

The number of ways is:

\(C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}\)

                                          \(=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}\\\\=\frac{(6+(30-12)-1)!}{(30-12)!\times (6-1)!}\\\\=\frac{23!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19\times 18!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19}{ 5!}\\\\=33649\)

Thus, the number of ways to distribute 30 batteries among the six different types is 33,649.

Answer: 1

Step-by-step explanation:

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

We know that a café charges $0.10 per minute to use the internet.

That means that the total charges will increase $0.1 per minute.

So, now we can make a table that models the situation

Number of minutes Total charges

1 $0.10

2 $0.20

3 $0.30

4 $0.40

Another way to make the table is modeling a function.

In this case the function is

Where y is the total charges and x is the number of minutes.

We can verify each value of the table with the function and we will see that it is correct.

Finally, the answer is the first option.

The perimeter of the triangle OQR is 68 cm

From the question, we have the following parameters that can be used in our computation:

Circles with the centers O, Q and R

When these centers are connected, the connection forms a triangle

The triangle OQR

Also from the question, we have the following values of radii

Radii = 8 cm, 11 cm and 15 cm

The perimeter of the triangle OQR is calculated as

Perimeter = Twice the sum of the radii

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 *(8 + 11 + 15)

Evaluate the sum

Perimeter = 2 * 34

Evaluate the products

Perimeter = 68

Hence, the perimeter is 68 cm

Read more about perimeter at

https://brainly.com/question/18019422

#SPJ1

Answer: A.

Step-by-step explanation: we just need to distribute and see that the only plausible answer is a because when distributed it equals 3x=6

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

For more such questions on hypotheses , Visit:

https://brainly.com/question/25263462

#SPJ11

Answer:4.6

Step-by-step explanation:2.3-(-2.3) is the same thing as 2.3+2.3 which is 4.6

Answer:

4.6

Step-by-step explanation:

Answer:

17.5

Step-by-step explanation:

Answer:

17.5

Step-by-step explanation:

The graph of the equation is shown below

From the question, we are to graph the given equation

The given equation is

-3 = 5x - y

To graph the equation,

First we will determine the x-intercept and y-intercept

x-intercept

Put y = 0 in the equation

-3 = 5x - 0

-3 = 5x

x = -3/5

y-intercept

Put x = 0 in the equation

-3 = 5(0) - y

-3 = 0 - y

-3 = -y

y = 3

Using the x-intercepts and y-intercepts, we can plot the graph of the equation.

The graph of the equation is shown below

Learn more on Graphs of linear equations here: https://brainly.com/question/4074386

#SPJ1

Answer:

900

Step-by-step explanation:

Answer:

\( x = {\sin^{ - 1} 2} \: \: or \: \: x = \frac{7\pi}{6}, \: \: \frac{5\pi}{3} \)

Step-by-step explanation:

\(2 { \cos}^{2} x + 3 \sin x = 0 \\ 2 {(1 - \sin}^{2} x) + 3 \sin x = 0 \\ 2 - 2 \sin^{2} x+ 3 \sin x = 0 \\ 2 \sin^{2} x - 3 \sin x - 2 = 0 \\ 2 \sin^{2} x - 4\sin x + \sin x- 2 = 0 \\ 2\sin x(\sin x - 2) + 1(\sin x - 2) = 0 \\ (\sin x - 2)(2\sin x + 1) = 0 \\ (\sin x - 2) = 0 \: or \: (2\sin x + 1) = 0 \\ \sin x = 2 \: or \: 2\sin x = - 1 \\ x = {\sin^{ - 1} 2} \: \: or \: \: \sin x = - \frac{1}{2} \\ x = {\sin^{ - 1} 2} \: \: or \: \: x = \frac{7\pi}{6}, \: \: \frac{5\pi}{3} \)

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

For more questions on cross-product property:

https://brainly.com/question/14542172

#SPJ8

Answer:y=-1/6*x-1/18

Step-by-step explanation:answer = y=-1/6*x-1/18

18y=1-3x

y=1/18-3/18x

y=-1/6*x-1/18

Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.

Answer:

A) 10

Step-by-step explanation:

3(8)(5) / 6(2) = 120/12 which equals 10

Answer: A = 10

Step-by-step explanation:

substitute the value of the variable into the equation and simplify

Hope this helps !

Answer:

see below

Step-by-step explanation:

Line 2 (the line that is darker in your pic) is wrong because the sign for 8 goes from "+" to "-". It should be +4x-8 in order for it to be correct