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Rashid [163]
3 years ago
5

The probability that a traffic light will be green is 40%. If you pass through 3 lights on your way to the store, what is the pr

obability that all three will be red?
Mathematics
1 answer:
larisa [96]3 years ago
7 0

Answer:

0.216

Step-by-step explanation:

If the probability of green, P(green) is 40%, the probability of red, P(red) is 60%.

The probability of a light being red is not affected by the colour of the previous light, so at each of the 3 lights, the probability of red is always 60%.

To find the probability that all three lights will be red, multiply the three probabilities together. (Convert them to decimals first).

0.6 x 0.6 x 0.6 = 0.216

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an equilateral triangle and a regular pentagon have the same perimeter. Each side of the pentagon is 3 inches shorter than each
klemol [59]
The answer is 4.5 for the side length of the pentagon and 7.5 is the side length for the triangle because 7.5*3(3 sides) = 22.5 and 4.5*5(5 sides)= 22.5. The perimeter is 22.5
6 0
3 years ago
Write an equation in point-slope form for the line through the given point with the given slope.
zlopas [31]

Answer:

y+1 = -1(x+10)

Step-by-step explanation:

The point slope equation of a line is

y-y1 = m(x-x1) where m is the slope  and (x1, y1) is a point on the line

y - -1 = -1 (x --10)

y+1 = -1(x+10)

8 0
3 years ago
Read 2 more answers
Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6
Alla [95]

Given:

The expression is:

2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

m+n=-6

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

P(x)=2x^3+mx^2+nx+c

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

P(2)=P(-1)              ...(i)

Substituting x=-1 in the given polynomial.

P(-1)=2(-1)^3+m(-1)^2+n(-1)+c

P(-1)=-2+m-n+c

Substituting x=2 in the given polynomial.

P(2)=2(2)^3+m(2)^2+n(2)+c

P(2)=2(8)+m(4)+2n+c

P(2)=16+4m+2n+c

Now, substitute the values of P(2) and P(-1) in (i), we get

16+4m+2n+c=-2+m-n+c

16+4m+2n+c+2-m+n-c=0

18+3m+3n=0

3m+3n=-18

Divide both sides by 3.

\dfrac{3m+3n}{3}=\dfrac{-18}{3}

m+n=-6

Hence proved.

7 0
3 years ago
In a normal distribution, 95% of the data fall within how many standard deviations of the mean? O A. Three standard deviations B
Galina-37 [17]

Answer:

Two standard deviations

Step-by-step explanation:

The Z score is obtained using the mean and standard deviation, according to the empirical. Rule, which gives percentage of values that lie within an interval estimate in a normal distribution ;

one standard deviation lie within 68% of the mean

Two standard deviations lie within 95%

Three standard deviations lie within 99.7%

Hence, for the question given, 95% fall within 2 standard deviations of the mean

4 0
3 years ago
A cylinder has a base diameter of 16 inches and a height of 18inches. What is the volume in cubic inches, of the nearest tenths
Stolb23 [73]

Answer:

3619.11 cubic inches

Step-by-step explanation:

volume of a cylinder is V=\pi r^2h

diameter is 16 in, so radius (r) is 8 in

plug in values: V=\pi 8^2(18) = 3619.11 cubic inches

8 0
3 years ago
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