What is the correlation coefficient for the data shown in the table?

What is the area of a triangle with vertices (1,0) (5,0) (3,4)

Aleksandr-060686 [28]

Answer:

The area of the triangle is of 8 units of area.

Step-by-step explanation:

Answer:

The area of the triangle is of 21 units of area.

Step-by-step explanation:

The area of a triangle with three vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by the determinant of the following matrix:

$A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|$

In this question:

Vertices (1,0) (5,0) (3,4). So

$A = \pm 0.5 \left|\begin{array}{ccc}1&0&1\\5&0&1\\3&4&1\end{array}\right|$

$A = \pm 0.5(1*0*1+0*1*3+1*5*4-1*0*3-0*5*1-1*1*4)$

$A = \pm 0.5*(20-4)$

$A = \pm 0.5*16 = 8$

The area of the triangle is of 8 units of area.

3 0

3 years ago

Find the mean 35 40 12 16 25 10

ruslelena [56]

Answer: Mean = 23

Step-by-step explanation:

Given information:

35, 40, 12, 16, 25, 10

Given formula:

$Mean~=~\frac{Sum~of~terms}{Number~of~terms}$

Substitute values into the formula

$Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}$

Combine like terms

$Mean~=~\frac{75~+~28~+~35}{6}$

$Mean~=~\frac{103~+~35}{6}$

$Mean~=~\frac{138}{6}$

Simplify the fraction

$\Large\boxed{Mean=23}$

Hope this helps!! :)

Please let me know if you have any questions

4 0

2 years ago

Find the missing value. Show your work. Round to the nearest hundredth. SOMEONE PLEASE HELP ME W THIS ! ILL VOTE BRAINIEST ANSWE

Olenka [21]

Since the side which measures 10 is a vertical projection of the hipotenuse x on a 20 degree angle:

10 = x*sin(20°)

x = 29.238044

Since we have to round to the nearest hundreth:

x = 29.24 m

8 0

3 years ago

Read 2 more answers

The prior probabilities for events A1 and A2 are P(A1) = 0.35 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(

forsale [732]

Answer:

Step-by-step explanation:

Hello!

Given the probabilities:

P(A₁)= 0.35

P(A₂)= 0.50

P(A₁∩A₂)= 0

P(BIA₁)= 0.20

P(BIA₂)= 0.05

a)

Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)

Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.

b)

Considering that $P(BIA)= \frac{P(AnB)}{P(A)}$ you can clear the intersection from the formula $P(AnB)= P(B/A)*P(A)$ and apply it for the given events:

$P(A_1nB)= P(B/A_1) * P(A_1)= 0.20*0.35= 0.07$

$P(A_2nB)= P(B/A_2)*P(A_2)= 0.05*0.50= 0.025$

c)

The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:

P(B)= (A₁∩B) + P(A₂∩B)= 0.07 + 0.025= 0.095

d)

The Bayes' theorem states that:

$P(Ai/B)= \frac{P(B/Ai)*P(A)}{P(B)}$

Then:

$P(A_1/B)= \frac{P(B/A_1)*P(A_1)}{P(B)}= \frac{0.20*0.35}{0.095}= 0.737 = 0.74$

$P(A_2/B)= \frac{P(B/A_2)*P(A_2)}{P(B)} = \frac{0.05*0.50}{0.095} = 0.26$

I hope it helps!

5 0

3 years ago

In a group of 60 numbers, average of

Arada [10]

Answer:

c. 18

Step-by-step explanation:

First, you would find the total sum of the 60 numbers. The average is always the sum of the numbers divided by the number of numbers.

35*18=630

15*10=150

Now we do not know how many numbers the last group has. However, we can find it out doing 60-35-15 to see how many numbers are left. There would be 10 numbers left

10*30=300

630+150+300=1080

1080/60=18

Hence, the answer is C(18)

4 0

3 years ago