Which of the angles below are vertical angles?

8k = 0 jsdfsiuefhwejbnmdshurefjnsfse

Elanso [62]

Answer:

k=0

Step-by-step explanation:

$8k = 0 \\ k = \frac{0}{8} \\ k = 0$

8 0

3 years ago

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Solve the system of equation

nikdorinn [45]

Answer:

So the Point of intersection is (-4,-2)

Which is option A

Step-by-step explanation:

The given system of equations is

-0.1x - 0.8y = 2 ...................(i)

0.6x - 0.5y = -1.4 ...................(ii)

Let us take equation (i) and use method of substitution for solving it

the equation (i) is

-0.1 x - 0.8y = 2

Adding 0.8y on both sides

-0.1 x + 0.8 y - 0.8 y = 2 + 0.8 y

-0.1 x = 2 + 0.8 y

Dividing both sides -0.1

$\frac{-0.1 x}{-0.1}=\frac{0.8 y}{-0.1}+\frac{2}{-0.1}$

x = -8 y - 20 ..........................(iii)

Now we will use this value and put it into equation (ii) to find the value of y

Equation (ii) is

0.6 x - 0.5 y = -1.4

Put value of x

0.6(-8 y - 20) - 0.5 y =-1.4

It becomes

-4.8 y - 12 - 0.5 y = -1.4

adding 12 on both sides

-4.8 y - 0.5 y - 12 + 12 = -1.4 + 12

it becomes by solving

-5.3 y = 10.6

Dividing both sides by -5.3

$\frac{-5.3*y}{-5.3}=\frac{10.6}{-5.3}$

So

y = -2

Now we have the value of y putting it in equation (iii)

Equation (iii) is

x = -8 y - 20

Putting value of y

x = -8*(-2) - 20

x = 16-20

x=-4

So the Point of intersection is (-4,-2)

7 0

3 years ago

The probability of an economic decline in the year 2020 is 0.23. There is a probability of 0.64 that we will elect a republican

olasank [31]

Answer:

1) D and R are NOT independent events

2) The probability of electing a Republican president and an economic decline in 2020 is 0.224

3) If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739

4) the probability of economic decline or a Republican president elected in 2020 or both is 0.646

Step-by-step explanation:

Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president

Given that;

P(D) = 0.23

P(R) = 0.64

Conditional P(D | R) = 0.35

1) Are R and D independent events?

we know that two events A & B are independent events if; P(B | A) = P(B)

here, P(D | R) = 0.35 and P(D) = 0.23

so; P(D | R) ≠ P(D)

Therefore D and R are NOT independent events

2) The probability of electing a Republican president and an economic decline in 2020;

we know that;

P(D | R) = P(D ∩ R) / P(R)

we substitute

0.35 = P(D ∩ R) / 0.64

P(D ∩ R) = 0.35 × 0.64

P(D ∩ R) = 0.224

Therefore, The probability of electing a Republican president and an economic decline in 2020 is 0.224

3) If we experience an economic decline in 2016, what is the probability that a Republican president will have been elected in 2020?

P(R | D) = P(D ∩ R) / P(D)

we substitute

P(R | D) = 0.224 / 0.23

P(R | D) = 0.9739

Therefore, If we experience an economic decline in 2016, the probability that a Republican president will have been elected in 2020 is 0.9739

4) the probability of economic decline or a Republican president elected in 2020 or both

P(D ∪ R) = P(D) + P(R) - P(D ∩ R)

we subtitute

P(D ∪ R) = 0.23 + 0.64 - 0.224

P(D ∪ R) = 0.646

Therefore, the probability of economic decline or a Republican president elected in 2020 or both is 0.646

6 0

3 years ago

Rolff recently completed a book of 20 deduction puzzles. the scatterplot below shows the time it took rolff to solve a puzzle ve

vlada-n [284]

I have the scatterplot in front of me, and what the question is asking is what is the probability of the dot chosen being in any of the three categories. They only leave out three dots, so the probability is 17/20 or 85%.

6 0

3 years ago

What number is 15% of 60?

BabaBlast [244]

Answer:

9

Step-by-step explanation:

15% of 60 is 9.

4 0

3 years ago

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