The law of cosines is a^2+b^2-2abcos(C). Find the value of 2abcos(C).
A. 37
B. -40
C. 40
D. 20

To solve this problem, we must assume that the man undergoes constant acceleration as he goes down the river (therefore no other forces must act on him except gravity). Therefore we can use the formula below to calculate for the duration of his fall:

y = y0 + v0 t + 0.5 a t^2

where y is the distance and y0 = 0 since we set the reference point at the bridge, v0 is the initial velocity and is also equal to v0 = 0 since the man started from rest, therefore the equation becomes:

y = 0 + 0 t + 0.5 a t^2

y = 0.5 a t^2

Rewriting in terms of t:

t^2 = 2 y / a

t = sqrt (2y / a)

a is acceleration due to gravity = 9.8 m/s^2

t = sqrt [2 * 23 / 9.8]

t = 2.17 s

Therefore the jump last only about 2.17 seconds.

The coordinates of the vertices of the triangle are A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the coordinates of the triangle are

A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )

And , length of AB is given by the distance formula .

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

AB = √ ( 16 + 0 ) = 4 units

BC = √ ( 16 + 9 ) = 5 units

Hence , the lengths of AB and BC are 4 and 5 units respectively

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When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable, a t-test is appropriate.

To add, The analysis of two populations means through the use of statistical examination is called a t-test. Small sample sizes commonly use a t-test with two samples.  What statisticians call as test statistics are identified as t-values. A systematized value that is calculated from sample data during a hypothesis test is called a test statistic. The procedure that calculates the test statistic compares your data to what is expected under the null hypothesis.

You already have an experience with the basic principles behind a t-test if you’ve tried to communicated with a distracted teenager.

The solution is, the growth factor b is, 1.02

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Using the formula:

P = P0(1+r)^t

where

P0 is the initial population

r is the rate in decimal

b = 1+r is the growth factor

t is the time in years.

As per the statement:

the bear population increases at a rate of 2% each year there are 1573 bears this year,

⇒P0 = 1573,

r = 2% = 0.02

then;

solving using the formula,

we get,

⇒ b = 1.02

Therefore, the growth factor b is, 1.02.

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The correct answer to this would be:

“No, because the sample is not representative of the whole population.”

Since the sample values are the 10 highest annual salaries of TV personalities, they give almost no information about the salaries of TV personalities as a whole or in general. 

The standard deviation of a sample can indicate the variation in salaries of TV personalities, but may not always be accurate if the sample isn't representative or if outliers exist. The median salary is often a better measure for skewed distributions, and multiple statistics should be reported to fully describe economic data.

When considering the variation of salaries of TV personalities, the standard deviation of a sample is a crucial statistic that helps understand the dispersion around the mean salary. However, if the sample is not representative of the entire population or if there are outliers, such as extremely high salaries among TV personalities, it may not be a good estimate of the variation in general. The median salary might provide a more accurate descriptor of the central tendency, especially in a skewed distribution.

It is possible for the standard deviation to be greater than the average in cases where there is a significant spread of values, including outliers. For example, if a few TV personalities earn vastly more than others, it will increase the standard deviation. Additionally, the likelihood of the average salary of a larger group falling within a certain range is determined by the mean and standard deviation. If the distribution is normal, salaries will tend to cluster around the mean, which is why certain salary ranges are expected to be more common.

In a scenario where two companies wish to compare the average salaries of their employees, statistical tests that consider both the mean and standard deviation can help determine if there is a significant difference between the two. Similarly, when evaluating how long employees stay with a company, a study with the average time and associated standard deviation for each company would provide insight into retention rates.

When reporting salaries or any economic data, it is often wise to report multiple measures of central tendency and dispersion, such as the mean, median, and standard deviation, to provide a comprehensive view. This approach takes into account the full range of values, including any potential outliers or skewness in the distribution.

The digit 2 in the number 258,364 stands for two hundred thousand, occupying the hundred thousands place in the place value system.

The value of the 2 in the number 258,364 represents two hundred thousand. In place value terms, this means the 2 is in the hundred thousands place. To understand this concept clearer, consider the alignment of digits in each place value when written in a column:

2 is in the hundred thousands place (200,000)

5 is in the ten thousands place (50,000)

8 is in the thousands place (8,000)

3 is in the hundreds place (300)

6 is in the tens place (60)

4 is in the ones place (4)

Therefore, the digit 2 represents 200,000.

Answer:

In the number 258,364, the 2 is in the hundred thousand's place. So, its place value is 2 * 100,000 = 200,000.

Explanation:

In the number 258,364, each digit's place value is determined by its position relative to the decimal point. The 2 is in the hundred thousand's place, representing 200,000. In whole numbers, the place values increase from right to left, with each place being 10 times the value of the place to its right. So, the hundred thousand's place has a value of 100,000. Thus, the digit 2 in this position contributes 200,000 to the total value of the number 258,364, indicating that there are 200,000 hundred thousands in it.

Question:

What is the place value of the 2 in 258,364?

If I spent $186. Then my weekly income will be $930.

The quantity of anything is stated as though it were a fraction of a hundred.

I spent 20% of my weekly income on food.

If I spent $186.

Then my weekly income will be

Let x my weekly income.

0.2x = $186

     x = $930

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The correct option is A )[tex]\frac{8}{\pi }[/tex]

To find the rate of change of a function from x = 0 to x = \\frac{\\pi}{2}, we need to apply the concept of the average rate of change.

This is essentially the change in the function's value divided by the change in x. Assume the function we are analyzing is y = f(x).

Step-by-Step Solution:

Average Rate of Change =[tex]\frac{f(\frac{\pi}{2}) - f(0)}{\frac{\pi}{2} - 0}[/tex]

When x = 0, f( x ) = - 4,

When x = π / 2, f( x ) = 0

Average Rate of Change =[tex]\frac{0- (-4)}{\frac{\pi}{2} - 0}[/tex]

Average Rate of Change =[tex]\frac{8}{\pi }[/tex]

The correct option is A )[tex]\frac{8}{\pi }[/tex]

To answer this problem, we use the binomial distribution formula for probability:

P (x) = [n! / (n-x)! x!] p^x q^(n-x)

Where,

n = the total number of test questions = 10

x = the total number of test questions to pass =   >6

p = probability of success = 0.5

q = probability of failure = 0.5

Given the formula, let us calculate for the probabilities that the student will get at least 6 correct questions by guessing.

P (6) = [10! / (4)! 6!] (0.5)^6 0.5^(4) = 0.205078

P (7) = [10! / (3)! 7!] (0.5)^7 0.5^(3) = 0.117188

P (8) = [10! / (2)! 8!] (0.5)^8 0.5^(2) = 0.043945

P (9) = [10! / (1)! 9!] (0.5)^9 0.5^(1) = 0.009766

P (10) = [10! / (0)! 10!] (0.5)^10 0.5^(0) = 0.000977

Total Probability = 0.376953 = 0.38 = 38%

There is a 38% chance the student will pass.

Answer:

[tex]cos(theta)=\frac{5}{13}[/tex]

Ratio is 5:13

Step-by-step explanation:

We are given with right angle triangle with side lengths

cos theta ratio is adjacent side divide by hypotenuse

In the triangle , adjacent side for theta is 5  and hypotenuse is 13

[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(theta)=\frac{5}{13}[/tex]

Answer:

A

Step-by-step explanation:

edge 2020 Dec 14

marathon = 26.2

hill is at least 10

26.2-10=16.2

X=  miles left

X<=16.2

The sum of the first 30 odd numbers is equal to the square of 30. To find the sum, we can use a formula for the sum of an arithmetic series. Plugging in the values, we get a sum of 900.

Conjecture: The sum of the first 30 odd numbers is equal to the square of the 30. To prove this conjecture, we can use a formula for the sum of an arithmetic series which is given by: S = n/2(2a + (n-1) d), where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference. In this case, the first term a is 1, the common difference d is 2 (since we are adding odd numbers), and the number of terms n is 30. Plugging in the values, we have: S = 30/2(2(1) + (30-1)2) = 15(2 + 58) = 900. Thus, the sum of the first 30 odd numbers is 900, which is equal to the square of 30.

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To solve this problem, we should first identify the number of units that point Z was translated. The number of units of movement of point Z should be similar to the number of units of movement of points A and P.

Let us say that the movement is Δx and Δy for horizontal and vertical translations respectively.

From Z to Z’:

Δx = 1 – (-1) = 2

Δy = 1 - 5 =  - 4

Therefore the translation is in the form of (x + 2 , y – 4). Points A and P then becomes:

A’ = (1 + 2 , 3 – 4)

A’ = (3, -1)

P’ = (-2 + 2, 4 – 4)

P’ = (0, 0)

Answers:

A’ = (3, -1)

P’ = (0, 0)

Answer:

Step-by-step explanation:

lets be honest whos reading this when theres an expert answer

The mathematics problem set with cookies deals with basic addition: if you have 1 cookie and you take another from a friend, you have a sum of 2 cookies.

The subject here is basic arithmetic, a branch of mathematics.

If you start with 1 cookie (your own), and then you take || 'steal' || another cookie from your friend, you are basically adding that 1 cookie to the 1 cookie you already have. So, 1 cookie (yours) + 1 cookie (your friend's) = 2 cookies. Hence, you would have 2 cookies.

Remember, in real life, it's not nice to steal. This is just a math problem to help you understand the concept of addition.

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B is (-3,2) E is (4,-2)

4-(-3) = 4+3 =47

-2 -2 = -4

7^2 = 49

-4^2 = 16

Sqrt( 49+16)

Sqrt(65) = 8.062

 Round off to 8

the midpoint formula