EASY QUESTION

Focus on question 9

Topic: Volume

For u = (-6,8) and v = (7,1), the vector u can be written as the sum of two orthogonal vectors (-4.76, -0.68) and (-1.24, 8.68) where one is the projection of u onto v.

First, we need to find the vector projection of u onto v. The formula to find the vector projection of u onto v is given by: projv(u) = [(u.v)/(v.v)] * v. Here '.' represents dot product of vectors.

So, substitute the given vectors u = (-6,8) and v = (7,1) into the formula.

This is one of the vectors. The other vector, orthogonal to v, is given by u minus the projection: u - projv(u) = (-6,8) - (-4.76, -0.68) = (-1.24, 8.68).

So, the vector u can be written as the sum of two orthogonal vectors (-4.76, -0.68) and (-1.24, 8.68).

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Answer:

1) 4/20

2) 11/20

3) 4/11

Step-by-step explanation:

Answer:

A, D, A  or 4/20, 11/20,  4/11

Step-by-step explanation:

i just did it on edge and it was correct

Answer:

5 right triangle

6 not a right triangle

Step-by-step explanation:

We can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

5^2 + 12^2 = 13^2

25+144 = 169

160 = 169

This is true so this is a right triangle

15^2 +16^2 = 18^2

225 +256 = 324

481 does not equal 324

This is not a right triangle

Answer:

5. Yes

6. No

Step-by-step explanation:

5. 13² = 12² + 5²

169 = 144 + 25

169 = 169

Satisfies pythagoras theorem, so it is a right angle triangle

6. 18² = 16² + 15²

324 = 256 + 225

324 = 481 (false)

Doesn't satisfy the pythagoras theorem, so it is not a right angle triangle

The correct length of AC is 18

Step-by-step explanation:

Midpoint=(X1+X2/2,y1+y2/2

[(0+10)/2,(7-10)/2]

(5,-3/2)

Answer:

Mass on mars is 150 grams.

Step-by-step explanation:

We have, mass of a book is 150 grams on the surface of Earth. The amount of matter contained in it is called its mass.

Mass of an object remains constant always. Its value is same in every location.

If the mass of a book on the surface of Earth is 150 grams, then its mass on Mars is also 150 grams. This is because, mass of an object is independent of its location.

Answer:

72

Step-by-step explanation:

Divide x2 x 2 by 1 1 . Divide 72 72 by 2 2 . Take the square root of both sides of the equation to eliminate the exponent on the left side. The complete solution is the result of both the positive and negative portions of the solution.

Answer:

6 days

210 pages

Step-by-step explanation:

As stipulated by the question, let the number of days Amir has been reading be x and the number of pages he had read to be y.

Now since he reads 35 pages per day.

Then mathematically;

y = 35x

For Jesse, He started reading a day before, this means that the number of days he had read would be x + 1. Since he reads 30 per day, the total number of pages he would have read is 30(x+1)

To find the number of days which is x, we have to assume that at a point in time, the number of books they would have read would be the same meaning that

Also; y = 30(x + 1)

Equating the two situations

35x = 30(x + 1)

35x = 30x + 30

35x -30x = 30

5x = 30

x = 30/5

x = 6 days

This means that it will take Amir 6 days to catch Jese.

The number of books they would have read by then is y = 35x = 30(x + 1)

= 35 * 6 or 30(6+1)

= 210

The total number of pages that he read will be 210 pages.

Based on the equation given, the equation to represent Amir's information will be:

y = 35 × x

y = 35x

Jesse's equation will be:

y = 30(x + 1)

Then, we'll equate both equations together. This will be:

35x = 30(x + 1)

35x = 30x + 30

35x - 30x = 30

5x = 30

x = 30/5

x = 6

Therefore, the number of pages read will be:

y = 35x

y = 35 × 6

y = 210 pages.

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Answer:

7%

Step-by-step explanation:

To work this out you would simply multiply 0.07 by 100, which gives you 7. This is because percentages are out of 100.

Answer: 7%

Step-by-step explanation:

Answer: the answer is B

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

We have been given an image of a trapezoid. We are asked to find the area of the given trapezoid.

We will use area of trapezoid formula to solve our given problem.

[tex]A=\frac{1}{2}(a+b)\times h[/tex], where,

A = Area of trapezoid,

a and b = Parallel sides or bases of trapezoid.

h = Height of trapezoid.

We can see that one base is 45 feet. The other base would be 45 plus 15 feet that is [tex]45+15=60[/tex].

Now we will use Pythagoras theorem to find the height of the trapezoid as:

[tex]h^2=17^2-15^2[/tex]

[tex]h^2=289-225[/tex]

[tex]h^2=64[/tex]

[tex]\sqrt{h^2}=\sqrt{64}[/tex]

[tex]h=8[/tex]

[tex]A=\frac{1}{2}(45+60)\times 8[/tex]

[tex]A=(105)\times 4[/tex]

[tex]A=420[/tex]

Therefore, the area of the given trapezoid is 420 square feet.

Answer:

3.64

Step-by-step explanation:

Based on the calculations, the radius of Circletown is equal to 3.64 kilometer.

Given the following data:

First of all, we would determine the area of Circletown by dividing the total population by its population density as follows:

Area = 20,000/480

Area = 41.67 square kilometer.

Mathematically, the area of a circle is calculated by using this formula:

Area = πr²

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

41.67 = 3.142 × r²

r² = 41.67/3.142

r = √13.26

r = 3.64 kilometer.

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Calculate the mean of the data set, find the absolute deviation of each data point, and then average those deviations. For this data set, the mean absolute deviation is 4.33.

To start off with, the mean absolute deviation is a measure of the dispersion or spread that represents the average difference between the values of the data set and the mean (average).

First, add up all the numbers of the data set. So, 8 + 6 + 6 + 18 + 17 + 11 = 66. Then divide this sum by the number of values (6) to calculate the mean (average). So, 66 ÷ 6 = 11.

Next, find the absolute deviation of each number in the set by subtracting the mean from each number and taking absolute value: |8-11|, |6-11|, |6-11|, |18-11|, |17-11|, |11-11|. This gives us: 3, 5, 5, 7, 6, 0.

Add these absolute deviations: 3 + 5 + 5 + 7 + 6 + 0 = 26. Then divide it by the count of the numbers in the data set (6). So, 26 ÷ 6 = 4.33, which is your mean absolute deviation to two decimal places.

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Final answer:

To find the mean absolute deviation for the data set 8, 6, 6, 18, 17, 11, you first calculate the mean of these numbers, then find the absolute deviations from this mean, and finally calculate the mean of those absolute deviations, which is approximately 4.33.

Explanation:

The student is asking how to find the mean absolute deviation (MAD) for a data set. The data set provided is 8, 6, 6, 18, 17, 11. To calculate the MAD, we first need to find the mean of the data set, then calculate the absolute deviation of each data value from the mean, and finally find the average of those absolute deviations.

Calculate the mean of the data set: (8 + 6 + 6 + 18 + 17 + 11) / 6 = 66 / 6 = 11.

Find the absolute deviation of each data value from the mean: |8 - 11| = 3, |6 - 11| = 5, |6 - 11| = 5, |18 - 11| = 7, |17 - 11| = 6, |11 - 11| = 0.

Calculate the mean of these absolute deviations: (3 + 5 + 5 + 7 + 6 + 0) / 6 = 26 / 6 = 4.33.

Hence, the mean absolute deviation for this data set is approximately 4.33.

Answer:

0.027 to the nearest thousandth.

Step-by-step explanation:

There are 14 marbles in the bag, so:

Prob( a blue on the first draw) = 5/14.

Prob( a blue on the 2nd draw) = 4/13.

Prob( a blue on the 3rd draw) = 3/12 = 1/4.

So the required probability is 5/14 * 4/13 * 1/4

= 20/ 728

= 0.02747.

To calculate the probability of drawing three blue marbles without replacement, multiply the probabilities of drawing a blue marble in each draw. The final probability to the nearest thousandth is approximately 0.043.

To find the probability that all three marbles drawn will be blue, we use the formula for calculating the probability of successive independent events (drawing without replacement). We calculate the probability of drawing a blue marble each time and then multiply these probabilities together.

Calculating this, we get approximately 0.043 when rounded to the nearest thousandth. So, the probability that all three marbles drawn will be blue is 0.043.

Answer: 14

Step-by-step explanation: To get the hypotenus of a triangle all you have to do is:

7 x 7 = 14

1 x 1 = 1

14 x 1 = 14

14 x 14 = 196

square root of 196 is 14

Equation form:

a² + b² = c²

7² + 1² = 14²

Sqrt(196) = 14

Answer:

416

Step-by-step explanation:

first find the area of the one triangle

12 times 8/2=96/2=48

and there are two triangles, so 48 times 2=96

and then find the area of one of the rectangle

10 times 12=120

and two are 10 times 10

10 times 10=100

100 times 2=200

200+120=320

320+96= 416

Answer: [tex]\frac{4}{35}[/tex]

Step-by-step explanation: The probability of Captain Ishaan hitting the pirate's ship is:

P(A) = [tex]\frac{4}{5}[/tex]

The probability of the pirate hitting Captain's ship is:

P(B) = [tex]\frac{1}{7}[/tex]

So, the probability of both hitting each other is a probability of A and B occuring, which means:

P(A) . P(B) = [tex]\frac{4}{5} . \frac{1}{7}[/tex]

P(A) . P(B) = [tex]\frac{4}{35}[/tex]

The probability of both the pirate and the Captain hit each other's ship is

[tex]\frac{4}{35}[/tex] or 11.43%

Answer:

5.1 is rational because it can be expressed in the form of a fraction.  In proper form the fraction is 5 1/10 and in improper form it is 51/10.

Step-by-step explanation:

Answer:

44 pi centimeters cubed

Step-by-step explanation:

Since, base radius and height of cone are equal to to that of cylinder. Hence,

[tex]Volume \: of \: cone \\ = \frac{1}{3} \times Volume \: of \: cylinder \\ = \frac{1}{3} \times132\pi \\ = 44\pi \: {cm}^{3} [/tex]

Answer:44 pi centimeters cubed

Step-by-step explanation:

Final answer:

After calculating distances between each pair of points and evaluating the properties of the resulting figure, it has been determined that the most precise name for the figure is a kite. This is due to the specific lengths of its sides and diagonals and their relationship to one another, which fits the definition of a kite.

Explanation:

To determine the most precise name for the figure formed by points A(-1,-4), B(-1,-1), C(4,1), and D(2,-2), we need to calculate the distances between each pair of points (sides of the figure) and evaluate their slopes where applicable.

AB = √(((-1)-(-1))^2 + ((-1)-(-4))^2) = 3

BC = √((4-(-1))^2 + (1-(-1))^2) = √(25 + 4) = √29

CD = √((4-2)^2 + (1-(-2))^2) = √(4 + 9) = √13

DA = √((2-(-1))^2 + ((-2)-(-4))^2) = √(9 + 4) = √13

AC (diagonal) = √((4-(-1))^2 + (1-(-4))^2) = √(25 + 25) = √50

BD (diagonal) = √((2-(-1))^2 + ((-2)-(-1))^2) = √(9 + 1) = √10

With sides AB and CD equal and AD and BC equal, and none of the sides being equal to each other, and considering two unequal diagonals, we can conclude that this figure is a kite, given that a kite has two pairs of adjacent sides that are equal but not all sides are equal and the diagonals are of different lengths.

Answer:

xfgfjfgxjfgj

Step-by-step explanation:gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

Answer: 31/50

Step-by-step explanation: 0.62= 62/100. After we must find the Greatest Common Factor which is two.

62/2=31  100/2=50

Answer:

31/50

Step-by-step explanation:

Answer: 8

Step-by-step explanation: 7.874007874011811 rounded is 8

Answer:

Step-by-step explanation:

If you don't want to use a calculator, then you must know your square roots

The first step is to think, "what is the closest number to 62, that when squared rooted, it would be a whole number?"

The closest numbers would be 49 (square root is 7)and 64 (square root is 8). But 64 is wayyy closer so by knowing the square root, you can work your way down to solve.

So you know that the square will inevitably be a decimal, and that the whole number will have to be 7 ( it can't be 8 because then it'll be higher than 64) and the decimal would have to be really high, like in between 5 and 9 bc 62 and 64 are really close.

Now this is just an estimate is it doesn't have to be exact. but I'm guessing the root would be around 7.8ish (rounded to nearest tenth)

but you can have a different answer, maybe closer :)

** if anything didn't make sense pls tell me !

Answer:

a. 1.5 kg of tuna, 1 kg of onion, 0.75 kg of red pepper and 2.4 kg of tomatoes

b. 16 empanadas

Step-by-step explanation:

Since each of these ingredients is needed and the recipe is for a single empanada, each ingredient in the recipe must be multiplied by 6 since they are 6 empanadas, like this:

1/4 kg tuna * 6 = 6/4 = 3/2 kg tuna

1/6 kg of onion * 6 = 6/6 = 1 kg of onion

1/8 kg of red pepper * 6 = 6/8 = 3/4 kg of red pepper

2/5 kg of tomatoes * 6 = 12/5 kg of tomatoes

Therefore 1.5 kg of tuna, 1 kg of onion, 0.75 kg of red pepper and 2.4 kg of tomatoes need it.

Now, with 2 kg of red pepper, what we should do is divide this quantity by the quantity for a recipe, like this:

2 / (1/8) = 16

that is to say that with 2 kg of red pepper, a total of 16 empanadas would be made

Answer:

1.)4/9

2.)4

3.)9

4.)1/2

5.)-2/9

6.)-1

7.)1

8.)7/4

Step-by-step explanation:

Answer:

we choose C

Step-by-step explanation:

We need to understand an infinite number of solutions happens when all numbers are solutions. This situation means that there is no one solution.

So let analyse 3 options:

A.

Substitute (2) in (1) we have:

2x – 6(x - 9)  = 18

<=> -4x + 54 = 18

<=> x = 9

=> y = 0

There is only 1 solution => A is wrong

B.

Substitute (1) in (2) we have:

(9+ 3y) + 3y = 9

<=> 3y = 0

<=> y = 0

=> x = 9

There is only 1 solution => B is wrong

C.

2x – 6y = 18  (1)

x – 3y = 9 <=> x = 9+ 3y (2)

Substitute (2) in (1) we have:  

2(9+3y) - 6y = 18

<=> 18 + 6y - 6y = 18

<=> 18=18

Yes, this system of equations has an infinite number of solutions

So we choose C

Final answer:

The system of equations with an infinite number of solutions is when one equation is a multiple of the other, which results in the same line and infinite solutions.

Explanation:

The system of equations that has an infinite number of solutions is:

A. 2x – 6y = 18
x – y = 9

To determine this, we notice that the second equation x - y = 9 is a multiple of the first equation 2x - 6y = 18. Since one equation is a multiple of the other, these equations represent the same line, leading to an infinite number of solutions.

Answer:

A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.

A cross-section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.

A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

Step-by-step explanation:

the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.

Answer:

Step-by-step explanation:

3 x 4 = 12

this is the answer

This response provides a general approach to solving mathematical problems due to lack of specific details in the student's question. The steps involve identifying the problem, understanding the problem, setting a plan, implementing the plan, and verifying the correctness of the solution.

Due to the limited information provided in the question, I'll assume this is a general Mathematics question. Brainly is a platform where students can ask questions about their schoolwork and tutors will assist by providing accurate responses based on their knowledge. Since a video was mentioned but not provided, I am unable to address specific content from it. However, in Mathematics, it's crucial to understand that solutions typically involve identifying the problem, understanding the problem, making a plan, carrying out the plan, and finally, checking your work to ensure correctness. This process is universally applicable, be it Arithmetic, Algebra, Geometry, or any other branch of Mathematics.

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Answer:

Step-by-step explanation: since average speed = total distance/time

a)average speed of the journey from my home town to A = 10 miles/20 minutes = 0.5

b)journey from my home town to B = 20 miles/30 minutes = 0.7

c)10 miles + 20 miles = 30 miles

which takes 50 minutes

so: 30 miles/50 minutes = 0.6