in a class of 48,30. are boys. what are the probability that a girl is picked randomly to represent the class in debate​

To find the value of angle h in the given decagon, we can use the fact that the sum of all the interior angles of a decagon is equal to (n - 2) * 180 degrees, where n is the number of sides of the polygon.

In this case, a decagon has 10 sides, so the sum of its interior angles is (10 - 2) * 180 = 8 * 180 = 1440 degrees.

To find angle h, we subtract the sum of the known angles from the total sum of the interior angles:

h = 1440 - (150 + 140 + 150 + 160 + 165 + 170 + 115 + 130 + 140)

h = 1440 - 1370

h = 70

Therefore, the value of angle h in the given decagon is 70 degrees.

P(Y=0) = p*((1-q)n).

EXPLANATION:

We can calculate this by using the law of total probability. Since X has a geometric distribution, the probability of Y given X = n is binomial with parameters n and q. Therefore, P(Y = 0) can be calculated as the sum of the probability of Y = 0 given X = n multiplied by the probability of X = n.

P(Y = 0) = p*((1-q)n).

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An organism that occupies multiple trophic levels in the given food web is the omnivore.

In the given food web, an example of an organism occupying multiple trophic levels is an omnivore. Omnivores are organisms that have a diet consisting of both plants and animals. They can consume producers (plants) as well as other consumers (animals).

By feeding at multiple trophic levels, omnivores play a significant role in energy transfer and nutrient cycling within an ecosystem.

Omnivores have the flexibility to obtain energy and nutrients from different sources, allowing them to occupy multiple trophic levels. They have the ability to adapt their feeding behavior based on the availability of resources. This adaptability contributes to their ecological success and their role in maintaining the balance of the ecosystem.

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Answer:

3. w=P/2-L

Step-by-step explanation:

Given formula:

Solving for w:

Correct answer choice is:

The Probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.

To find the probability that the defective bulb was produced by machine B, we can use Bayes' theorem.

Let event A be the defective bulb being chosen, and event B be the bulb being produced by machine B. We want to find P(B|A), the probability that the bulb was produced by machine B given that it is defective.

From the information given, we know that machine A produces 300 bulbs per day, of which 1% (3 bulbs) are defective, while machine B produces 720 bulbs per day, of which 1.5% (10.8 bulbs) are defective.

Thus, the total number of defective bulbs produced per day is 3 + 10.8 = 13.8.

The probability of choosing a defective bulb is equal to the total number of defective bulbs divided by the total number of bulbs produced per day:

P(A) = 13.8 / (300 + 720) = 0.016

The probability of machine B producing a bulb is equal to the number of bulbs produced by machine B divided by the total number of bulbs produced per day:

P(B) = 720 / (300 + 720) = 0.706

The probability of a bulb being defective given that it was produced by machine B is equal to the number of defective bulbs produced by machine B divided by the total number of bulbs produced by machine B:

P(A|B) = 10.8 / 720 = 0.015

Now, we can use Bayes' theorem to find P(B|A):

P(B|A) = P(A|B) * P(B) / P(A)

Substituting in the values we have calculated, we get:

P(B|A) = 0.015 * 0.706 / 0.016

Simplifying the equation, we get:

P(B|A) = 0.664

Therefore, the probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.

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The probability of obtaining exactly seven heads can be calculated using the binomial probability formula: P(X=7) = (10 choose 7) * (0.7)^7 * (0.3)^3 = 0.2668, where (10 choose 7) represents the number of ways to choose 7 heads out of 10 tosses.

The probability of obtaining exactly ten heads is also calculated using the binomial probability formula: P(X=10) = (10 choose 10) * (0.7)^10 * (0.3)^0 = 0.0282, where (10 choose 10) represents the number of ways to choose all 10 heads out of 10 tosses.

The probability of obtaining no heads can be calculated by using the complement rule: P(no heads) = 1 - P(at least one head). Since there are only two outcomes (heads or tails) for each toss, the probability of obtaining no heads is simply (0.3)^10 = 0.000005904.

=The probability of obtaining at least one head can also be calculated using the complement rule: P(at least one head) = 1 - P(no heads) = 1 - (0.3)^10 = 0.999994096.\

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Answer:

10. 3 musicians

11. a) 10 feet

   b) can't read all of it

Step-by-step explanation:

Answer:

#10 should be 3

Step-by-step explanation:

The distance between two points a and b on the real line is given by the absolute difference between the two points, which is calculated as the positive difference between the values of a and b regardless of their order.

The distance function, denoted as d(a, b), is a metric that satisfies the properties of non-negativity, symmetry, and the triangle inequality. It is used to quantify the distance between two points in one-dimensional space, and is an important concept in geometry, analysis, and other fields of mathematics. The distance formula can be extended to higher dimensions and is used in various applications such as optimization, clustering, and machine learning.

The distance between two points a and b on the real line is given by the absolute difference between the two points: d(a, b) = |a - b|

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The number of ways to draw four marbles from the bag is 330.

The number of ways to draw four marbles if two must be red and two must be white from the bag is 150.

The number of ways to draw four marbles if all must be the same color from the bag is 20.

To find the number of ways the concept of combination is used. The formula for finding combination is as follows,
\(^nC_r=\frac{n!}{r!(n-r)!}\)

Where C is for combination, n is number of terms out of which r is selected terms, and ! is a sign of factorial.

Now, finding the number of ways to draw four marbles from the bag,

Total number of marbles = 5 + 6 = 11

Here, n = 11 and r = 4, so putting the values in the formula,

\(^{11}C_4=\frac{11!}{4!(11-4)!}\\\\=\frac{11\times10\times9\times8\times7!}{4\times3\times2\times1\times7!} \\\\=330\)

Similarly, now finding the number of ways to draw four marbles if two must be red and two must be white from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_2\times^{6}C_2=\frac{5!}{2!(5-2)!}\times\frac{6!}{2!(6-2)!}\\\\=\frac{5\times4\times3!}{2\times1\times3!}\times \frac{6\times5\times\times4!}{2\times1\times4!}\\\\=150\)

Similarly, now finding the number of ways to draw four marbles if all must be the same color from the bag,

Here, n = 5 for red and r = 2 and n = 6 and r = 2, so putting the values in the formula,

\(^{5}C_4+^{6}C_4=\frac{5!}{4!(5-4)!}+\frac{6!}{4!(6-4)!}\\\\=\frac{5\times4!}{4!\times1!}+\frac{6\times5\times\times4!}{4!\times2\times1}\\\\=5+15\\\\=20\)

Therefore, The number of ways to draw four marbles from the bag is 330 and the number of ways to draw four marbles if two must be red and two must be white from the bag is 150 and the number of ways to draw four marbles if all must be the same color from the bag is 20.

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Answer:

Rs 19.20

Step-by-step explanation:

Buying price = Rs 20

Profit = 20% = 0.20 × 20 = Rs 4

Selling price = buying price + profit = Rs 20 + Rs 4 = Rs 24

He wants to make a 25% profit.

Let's say he should buy the pen at Rs 'a' in order to make that amount of profit.

∴ a + \(\frac{25}{100} a\) = 24

1.25a = 24

a = \(\frac{24}{1.25} = 19.20\)

So he should buy the pen at Rs 19.20

The given function is

f(x) = - 2|x+5| + 2

The x intercept is the value of x when f(x) = 0

Substituting f(x) = 0 into the function, we have

0 = - 2|x+5| + 2

Subtract 2 from both sides

0 - 2 = - 2|x+5| + 2 - 2

- 2 = - 2|x+5|

Divide both sides by - 2. It becomes

- 2/- 2 = - 2|x+5|/- 2

1 = |x+5|

x + 5 = 1 or x + 5 = - 1

x = 1 - 5 or x = - 1 - 5

x = - 4 or x = - 6

x intercepts are x = - 6, x = - 4

Writing the x intercepts as points, they are

(- 6, 0) and (- 4, 0)

The y intercept is the value of f(x) when x = 0

substituting x = 0 into the function, we have

f(0) = - 2|0+5| + 2

f(0) = - 2|5| + 2 = - 2(5) + 2 = - 10 + 2

f(0) = - 8

y intercept = (0, - 8)

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The mean of a standard normal probability distribution is 0.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The probability density function of a standard normal distribution is given by:

f(x) = (1/√(2π)) * e^(-x^2/2)

where x is a random variable that follows a standard normal distribution. The mean of a probability distribution is the expected value of the random variable, which is given by the integral of the product of the random variable and the probability density function over its entire range.

For a standard normal distribution, this integral is equal to:

E(x) = ∫(-∞ to ∞) x * f(x) dx = ∫(-∞ to ∞) x * (1/√(2π)) * e^(-x^2/2) dx

This integral evaluates to 0, which means that the mean of a standard normal distribution is 0.

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Answer:

It would take either 13 hours, or there is not enough informatino to solve this problem.

Answer:

It would take them 13 hours to work together on the job.

Step-by-step explanation:

Just add 5 hours + 8 hours.

The experimental probability of selecting a red marble is 12/20, which simplifies to 3/5 or 0.6 as a decimal.

The theoretical probability of selecting a red marble can be calculated by dividing the number of red marbles by the total number of marbles:

P(red) = number of red marbles / total number of marbles

In this case, there are 27 red marbles out of 70 total marbles:

P(red) = 27/70

Therefore, the theoretical probability of selecting a red marble is 27/70, which cannot be simplified further as a fraction. As a decimal, it is approximately 0.386.

Answer:

it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.

Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.

Step-by-step explanation:

a is wrong because it only describes positive correlation, not negative correlation.

c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.

d and f are wrong because they assume causation from correlation, which is a logical fallacy.

e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.

If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.

If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.

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The probability that a hand of five cards contains exactly two aces and no other pairs is approximately 0.00000423 and P(A∪B') is equal to 0.76.

To determine the probability of a hand of five cards containing exactly two aces and no other pairs, we need to calculate the probability of selecting two aces from the four available aces and three non-aces from the remaining 48 cards, divided by the total number of possible five-card hands.

The probability of selecting two aces is (4 choose 2) / (52 choose 5), which represents choosing 2 aces from 4 aces. The probability of selecting three non-aces is (48 choose 3) / (52 choose 5), which represents choosing 3 non-aces from the remaining 48 cards.

Since these events are independent, we can multiply the probabilities together to get the overall probability:

P = [(4 choose 2) / (52 choose 5)] * [(48 choose 3) / (52 choose 5)]

Simplifying the expressions, we have:

P = (6/2598960) * (17296/2598960)

P ≈ 0.00000423

Therefore, the probability that a hand of five cards contains exactly two aces and no other pairs is approximately 0.00000423.

P(A∪B') represents the probability of either event A or the complement of event B occurring. Since B' is the complement of B, P(B') = 1 - P(B) = 1 - 0.3 = 0.7.

P(A∪B') = P(A) + P(B') - P(A∩B') (by the inclusion-exclusion principle)

Given that A and B are independent events, P(A∩B) = P(A) * P(B), so P(A∩B') = P(A) * P(B').

Substituting the given probabilities, we have:

P(A∪B') = 0.2 + 0.7 - (0.2 * 0.7)

P(A∪B') = 0.2 + 0.7 - 0.14

P(A∪B') = 0.76

Therefore, P(A∪B') is equal to 0.76.

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PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.

\( = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} \)

THE ANSWER IS OPTION C.

Ms. Sanders bought 6 packages of cheese sticks and 3 packages of waffles.

Let c = cheese sticks and w = waffles.

We have

c + w = 9

4c + 7w = 45

Solving using substitution,

w = 9 - c

4c + 7(9 - c) = 45

4c + 63 - 7c = 45

-3c = -18

c = 6

6 + w = 9

w = 3

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Hi! I'd be happy to help answer your question.
a) The sun will rise tomorrow. This is a scientifically predictable event. The rotation of the Earth causes the sun to appear to rise in the morning.

b) It will rain tomorrow. The weather is influenced by various factors such as air pressure, temperature, and humidity. Weather forecasts are made based on these factors, but they are not always 100% accurate.

c) You will see a dog with only three legs when you leave the room. Since I am an AI, I cannot see the physical world. However, if there is a dog with only three legs in the room.

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Out of the given statements, "the sun will rise tomorrow" can be considered as the only statement that can be confidently concluded as true. The rising of the sun is a natural occurrence that happens every day. It is supported by scientific knowledge and observations made over centuries. The rotation of the Earth causes the sun to appear to rise and set. The option (a) is correct.

On the other hand, statements b, c, d, and e cannot be conclusively determined as true or false without further information or evidence. These statements involve future events or specific occurrences that cannot be predicted with certainty.

Statement b, "it will rain tomorrow," depends on weather conditions that are subject to change. While meteorologists can provide forecasts, they are not always accurate, as weather patterns can be unpredictable.

Statement c, "you will see a dog with only three legs when you leave the room," depends on factors such as the presence of a dog in the vicinity and the likelihood of encountering a dog with a specific disability. It is highly unlikely to be true for the majority of people.

Statement d, "a fair die will come up with a score of 6 four times in a row," depends on the probability of rolling a specific number on a fair die. The probability of rolling a 6 four times in a row is very low, but not impossible.

Statement e, "there will be a plane crash somewhere in the world within the next five minutes," depends on numerous factors related to air travel and global incidents. While plane crashes do occur, predicting them within a specific timeframe is not possible.

Thus, the option (a) is correct.

Therefore, out of the given statements, only the first statement, "the sun will rise tomorrow," can be considered as a correct answer. The remaining statements require further evidence or are dependent on unpredictable factors.

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Answer:

1.7 × 10^2.

Step-by-step explanation:

Hope this helped, Have a Wonderful Day!!

$4065.66  is the investment worth at the end of 5 years.

What is compound interest?

The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.

Here, we have

Given: Kenji invests $3,500 at an interest rate of 3%, compounded monthly.

A = P(1+r/n)ⁿˣ

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per time period

x = number of time periods elapsed

P = $3,500

r = 3% = 3/100 = 0.03

n = 12 (As there are 12 months in a year)

x = 5 years

A = 3500(1+0.03/12)⁶⁰

3,500 x (1.161616)

$4065.658 = $4065.66

Hence, $4065.66  is the investment worth at the end of 5 years.

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Answer:

I think its -1

Step-by-step explanation:

Gary, Mary, and Rory have 96 candies altogether.

Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".

After Gary gives Mary half of all his candies, he would have x/2 candies.

Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.

And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.

Now, we know that Gary would have 12 more candies than he had originally, which means:

x/2 + x/8 = x/2 + x/4 - 12

We can combine like terms and simplify the equation:

x/2 + x/8 = x/4 + x/4 - 12

x/8 = 12

x = 8 * 12

x = 96

Thus, Gary, Mary, and Rory have 96 candies altogether.

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A monomial is an algebraic expression that consists of a single term. A monomial can contain constants and/or variables, which are multiplied together.

The expression 3x²y is a monomial. It contains the constant 3, the variable x squared, and the variable y. The variables can be raised to an exponent, as in this example; however, the exponent must be a whole number.A monomial can also contain coefficients, which are the numbers that are multiplied with a variable. In the example above, the coefficient is 3. If there is no coefficient stated, then the coefficient is assumed to be 1. Therefore, the expression x²y is also a monomial, with the coefficient being 1.Additionally, a monomial can contain a product of numbers and variables, such as the expression 2xyz. This is also considered a single term, since all of the numbers and variables are multiplied together.

Monomials can be used to calculate polynomials, which are algebraic expressions consisting of multiple terms. By adding, subtracting, and multiplying monomials together, you can create a polynomial. For example, the expression (3x²y) + (2xyz) is a polynomial, since it consists of two terms. The first term is the monomial 3x²y, and the second term is the monomial 2xyz.

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Set the expressions equal to each other because the angles are congruent.

2x+25 = 3x-10

35 = x

Now plug the x (35) into either of the expressions.

2(35)+25 = 75+25 = 100°

X= 100°

Y = 80°

**Y is 80° because A straight line measures 180° and if one part measures 100°, then the other part has to measure 80° for the angle measure 180° total.

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Answer: a) y=0.50x+15  

b) The graph of this equation form on a coordinate plane is a line.

c) Slope  =0.50 and y-intercept = 15

Step-by-step explanation:

Let x = Number of miles driven by car

Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

a) Total cost = 0.50x+15

If y =total cost of renting the car, then y=0.50x+15   (i)

b) Above equation is similar to y= mx+c  (ii) [m = slope , xc=y-intercept] which a linear equation .

So the graph of this equation form on a coordinate plane is a line.

c) Comparing (i) and (ii)

m=0.50 , c=15

Slope  =0.50 and y-intercept = 15

Answer:

12

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

3x^2+6x+8=6

3x^2+6x+8-6=0

3x^2+6x+2=0

here  a=3 ,b=6,c=2

Discriment=b^2-4ac

  =(6)^2-4(3)(2)

=36-24

=12

a) 214 in base-five is 1324.

b) 62 in base-five is 222.

c) 8 in base-five is 13.

d) 95 in base-five is 340.

a) To determine the base five representation of 214, we need to   find the largest power of five that  is less than or equal to  214.

In this case, 125 (5³) is the largest power of five   that is less than 214.

Now, we divide 214 by 125 -  

214 ÷ 125 = 1 remainder 89

Next, we divide the remainder, 89, by the next lower power of five, which is 25 (5²) -  

89 ÷ 25 = 3 remainder 14

Finally, we divide the remaining 14 by the lowest power of five, which is 5 itself -  

14 ÷ 5 = 2 remainder 4

Therefore, the base-five representation of 214 is 1324 in base-five.

b) Following the same steps as above -  

62 ÷ 25 = 2 remainder 12

12 ÷ 5 = 2 remainder 2

Hence,  the base-five representation of 62 is 222 in base-five.

c) 8 ÷ 5 = 1 remainder 3

this menas that  the base-five representation of 8 is 13 in base-five.

d) Following the same steps as above -  

95 ÷ 125 = 0 remainder 95

95 ÷ 25 = 3 remainder 20

20 ÷ 5 = 4 remainder 0

Hence, the base-five representation of 95 is 340 in base-five.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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