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IrinaK [193]
3 years ago
14

Find the equation of the line through (0,4) perpendicular to the line y = 3x

Mathematics
1 answer:
Rufina [12.5K]3 years ago
3 0

Answer:

y =  -  \frac{1}{3} x + 4

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

The product of the gradients of perpendicular lines is -1.

Gradient of given line= 3.

(Gradient of line)(3)= -1

3m= -1

m= -  \frac{1}{3}

subst. m= -  \frac{1}{3} into the equation:

y =  -  \frac{1}{3} x + c

To find the value of c, substitute a coordinate.

When x=0, y=4,

4 =  -  \frac{1}{ 3} (0) + c \\ 4 = c \\ c = 4

Thus the equation of the line is y =  -\frac{1}{3} x + 4.

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Suppose that 40 percent of the drivers stopped at State Police checkpoints in Storrs on Spring Weekend show evidence of driving
lesantik [10]

Answer:

a) 0.778

b) 0.9222

c) 0.6826

d) 0.3174

e) 2 drivers

Step-by-step explanation:

Given:

Sample size, n = 5

P = 40% = 0.4

a) Probability that none of the drivers shows evidence of intoxication.

P(x=0) = ^nC_x P^x (1-P)^n^-^x

P(x=0) = ^5C_0  (0.4)^0 (1-0.4)^5^-^0

P(x=0) = ^5C_0 (0.4)^0 (0.60)^5

P(x=0) = 0.778

b) Probability that at least one of the drivers shows evidence of intoxication would be:

P(X ≥ 1) = 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - ^5C_0 (0.4)^0 * (0.6)^5

= 1 - 0.0778

= 0.9222

c) The probability that at most two of the drivers show evidence of intoxication.

P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)

^5C_0  (0.4)^0  (0.6)^5 + ^5C_1  (0.4)^1  (0.6)^4 + ^5C_2  (0.4)^2  (0.6)^3

= 0.6826

d) Probability that more than two of the drivers show evidence of intoxication.

P(x>2) = 1 - P(X ≤ 2)

= 1 - [^5C_0  (0.4)^0  (0.6)^5 + ^5C_1  (0.4)^1  (0.6)^4 + ^5C_2 * (0.4)^2  (0.6)^3]

= 1 - 0.6826

= 0.3174

e) Expected number of intoxicated drivers.

To find this, use:

Sample size multiplied by sample proportion

n * p

= 5 * 0.40

= 2

Expected number of intoxicated drivers would be 2

7 0
3 years ago
What is greater than one in 5 1/2
Ira Lisetskai [31]
I think 6 1/2,but I could be wrong so take that with a grain of salt
5 0
3 years ago
Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of ? Why or why not?
Nady [450]

Answer:

No, because AB is 2/5 the length MN but CD is 1/3 the length QP.  

Step-by-step explanation:

Comparing the corresponding sides, the length of AB is 4.  The length of MN is 10.  This makes their ratio 4/10 = 2/5.

The length of CD is 2.  The length of QP is 6.  this makes their ratio 2/6 = 1/3.

The ratios of the sides are not the same, so the figure is not proportional and is therefore not a dilation.

8 0
3 years ago
Read 2 more answers
20 points and brainliest!
Cerrena [4.2K]

Answer:

yes

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
I NEED HELP!! I GO TO BED IN 10 MINUTES AND THIS ASSIGNMENT LOCKS TONIGHT!!!
77julia77 [94]

Answer:

y − 1 = -2 (x − 3)

Step-by-step explanation:

Point slope form is:

y − y₁ = m (x − x₁)

where m is the slope and (x₁, y₁) is a point on the line.

Given that m = -2 and (x₁, y₁) = (3, 1):

y − 1 = -2 (x − 3)

3 0
3 years ago
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