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ElenaW [278]
2 years ago
8

The ratio of boys and teacher in a school is 2:3 the ratio of teachers to the girls is 4:5.Find the ratio of all the three in a

school.
Mathematics
1 answer:
Scorpion4ik [409]2 years ago
7 0

Answer:

Step-by-step explanation:

2:3 boy:teacher 8:12

4:5 teacher:girl 12:15

8:12:15 boy:teacher:girl

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if tom spins the spinner 80 times work out an estimate for the number of times the spinner will land on 3 please help me
NNADVOKAT [17]

Answer:

The estimated number of times the spinner will land on 3 is 20.

Step-by-step explanation:

The complete question is:

A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.

Solution:

Assume that the four-sided spinner is unbiased.

That is all the four outcomes are equally likely to be selected.

The probability that the spinner lands on any of the four numbers is:

P(1) = P (2) = P (3) = P (4) = 0.25

It is provided that Tom spins the spinner <em>n</em> = 80 times.

The spinner can land on any of the four numbers independently.

The random variable <em>X</em>, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters <em>n</em> = 80 and <em>p</em> = 0.25.

The expected value of <em>X</em> is:

E(X)=np

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Thus, the estimated number of times the spinner will land on 3 is 20.

7 0
2 years ago
Find the line through (3, 1, −2) that intersects and is perpendicular to the line x = −1 + t, y = −2 + t, z = −1 + t. (HINT: If
mel-nik [20]

Answer:

( xo , yo , zo ) = ( 1 , 0 , 1 )

Step-by-step explanation:

Given:-

- A line passing through point (3, 1, −2) intersects and is perpendicular to line with coordinates:

                  x = −1 + t, y = −2 + t, z = −1 + t   .... t = arbitrary parameter.

Find:-

The coordinates for point of intersection.

Solution:-

- The line that passes through point (3, 1, −2) = ( a, b , c ) and an a arbitrary point on the given line have the following direction vector d2 :

                 d2 = ( x2 , y2 , z2 )

                 x2 = a - ( x ) = 3 - ( -1 + t ) = 4 - t

                 y2 = b - ( y ) = 1 - ( -2 + t ) = 3 - t

                 z2 = c - ( z )  = -2 - ( -1 + t ) = -1 - t

                d2 = (  4 - t , 3 - t , -1 - t )

- The direction vector d1 of the given line is:

                 d1 = ( x1 , y1 , z1 )

                 x1 = 1

                 y1 = 1

                 z1 = 1

                 d1 = ( 1 , 1 , 1 )

- The dot product of two orthogonal vectors is always equal to zero:

                 d1.d2 = 0

                 (  4 - t , 3 - t , -1 - t ) . ( 1 , 1 , 1 ) = 0

- Solve for parameter (t):

                 (4 - t) + (3 - t) + (-1 - t) = 0

                  6 -3t = 0

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- The coordinates of the point of intersections can be evaluated by substituting the value of "t" into the given equation of line:

                 xo ( t = 2) = - 1 + 2 = 1

                 yo ( t = 2) = - 2 + 2 = 0

                 zo ( t = 2) = - 1 + 2 = 1

- The coordinates are:

                 ( xo , yo , zo ) = ( 1 , 0 , 1 )

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Total people in the cafeteria = 7 + 48 + 45 = 100

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The probability would be the number of boys over the total number of people:

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