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Genrish500 [490]
3 years ago
10

Write the slope-intecept form of the equation of the line using the following:

Mathematics
1 answer:
Dominik [7]3 years ago
8 0
Y = -3/4x + 5.....the slope here is -3/4...but for a perpendicular line, we need the negative reciprocal slope. All that means is " flip " the slope and change the sign. So the slope we need is 4/3 (see how I flipped the slope and changed the sign)

now we use y = mx + b
slope(m) = 4/3
(3,-1)...x = 3 and y = -1
now we sub and solve for b, the y int
-1 = 4/3(3) + b
-1 = 4 + b
-1 - 4 = b
-5 = b

so ur perpendicular line is : y = 4/3x - 5
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Answer:

a) P(X∩Y) = 0.2

b) P_1 = 0.16

c) P = 0.47

Step-by-step explanation:

Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.

So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67

Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:

P(X∩Y) = P(X) + P(Y) - P(X∪Y)

P(X∩Y) = 0.36 + 0.51 - 0.67

P(X∩Y) = 0.2

On the other hand, the probability P_1 that he must stop at the first signal but not at the second one can be calculated as:

P_1 = P(X) - P(X∩Y)

P_1 = 0.36 - 0.2 = 0.16

At the same way, the probability P_2 that he must stop at the second signal but not at the first one can be calculated as:

P_2 = P(Y) - P(X∩Y)

P_2 = 0.51 - 0.2 = 0.31

So, the probability that he must stop at exactly one signal is:

P = P_1+P_2\\P=0.16+0.31\\P=0.47

7 0
3 years ago
When a number is increased by 2.8%, the result is 56. What is the original number to
Sever21 [200]

Answer:

The original number was 54.5.

Step-by-step explanation:

If a number is increased by 2.8%, then it is 102.8% of it's original number.

In mathematics, "of" in virtually all cases means "multiplied by".

Therefore, we do the opposite:

1. Convert to a decimal.

102.8% = 1.028

2. Divide by the decimal.

56 \div 1.028 = 54.47

3. Round it to the nearest tenth.

54.47 rounds to 54.5.

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3 years ago
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The  first one shows 25%

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In the second case its divide into 3 boxes so.. 100/3% and when we solve we get 33.3333333.......and this is not what we want

THEREFORE, THE CORRECT ANSWER IS 1ST MODAL

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