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Radda [10]
3 years ago
13

A 0.2-kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. A 0.4-kilogram green

ball is thrown horizontally from the same height at a speed of 8 meters per second. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is (A) four times as great (C) the same (B) twice as great (D) one-half as great
Mathematics
1 answer:
Stolb23 [73]3 years ago
7 0

Answer:

option (C) the same

Step-by-step explanation:

In the given question , it is mentioned that the ball of mass 0.2 kilograms is thrown with the velocity of 4 m/s in the horizontal direction

and, the 0.4 kilogram green ball is thrown in the horizontal direction with the velocity of 8 m/s

Here in both the cases no component of velocity in the vertical direction is provided.

Hence, it will be a case of free fall in the vertical direction.

Now,

from Newton's equation of motion, we have

s=ut+\frac{1}{2}at^2

here,  

s is the distance

a is the acceleration

t is the time

in the above equation, mass has no role and the value of acceleration i.e acceleration due to gravity and distance of fall in the vertical direction is same.

Hence, the time taken for both the balls will be same.

Hence,

The correct answer is option (C) the same

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At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper
Korvikt [17]

Answer:

90.67% probability that John finds less than 7 golden sheets of paper

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.

This means that p = 0.3

14 of these containers of paper.

This means that n = 14

What is the probability that John finds less than 7 golden sheets of paper?

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{14,0}.(0.3)^{0}.(0.7)^{14} = 0.0068

P(X = 1) = C_{14,1}.(0.3)^{1}.(0.7)^{13} = 0.0407

P(X = 2) = C_{14,2}.(0.3)^{2}.(0.7)^{12} = 0.1134

P(X = 3) = C_{14,3}.(0.3)^{3}.(0.7)^{11} = 0.1943

P(X = 4) = C_{14,4}.(0.3)^{4}.(0.7)^{10} = 0.2290

P(X = 5) = C_{14,5}.(0.3)^{5}.(0.7)^{9} = 0.1963

P(X = 6) = C_{14,6}.(0.3)^{6}.(0.7)^{8} = 0.1262

P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0068 + 0.0407 + 0.1134 + 0.1943 + 0.2290 + 0.1963 + 0.1262 = 0.9067

90.67% probability that John finds less than 7 golden sheets of paper

7 0
2 years ago
jester has a piece of wood measuring 1 and 2/3 m.he needs to cut in pieces measuring 3/4 m long.how many pieces of wood did jest
sveticcg [70]

Answer:

2 pieces

Step-by-step explanation:

Given

Length = 1\frac{2}{3}m

Pieces = \frac{3}{4}m

Required

Calculate the number of pieces

To do this, we have to divide the length of the wood by the length of each piece.

Represent this with x

x= \frac{Length}{Pieces}

x= 1\frac{2}{3}/\frac{3}{4}

Convert mixed numbers to improper fraction

x= \frac{5}{3}/\frac{3}{4}

Change division to multiplication

x= \frac{5}{3}*\frac{4}{3}

x= \frac{20}{9}

x = 2.22

<em></em>x = 2<em> </em>

6 0
2 years ago
A) Write down 375 as the product of prime factors.
ddd [48]

Answer:

a) 3x5³

b) 75

Step-by-step explanation:

a) find the Prime factors of 375 by dividing your number by prime numbers (you answers must be whole) use a factor tree to help you

a) do the same to 150

one you have you answers in this case we have

375- 3x5x5x5

150 - 2x3x5x5

you collect all the like terms, this will be 3x5x5 then you just simply multiply it And it gives you 75

6 0
3 years ago
A line contains the points (3, 8) and (6, 5). Write the equation of the line in slope-intercept form. Use no spaces in your equa
Artyom0805 [142]
5-8
------ =-3/3=1
6-3
y=1x+b
4 0
2 years ago
Read 2 more answers
Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its b
Natalija [7]

Answer:

Slope of the base segment line is zero, hence base segment is horizontal

Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical

Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base

Step-by-step explanation:

Here we prove the required relation as follows;

Let the isosceles be ABC

The coordinates of the points are

C = (0, 0) (Vertex)

A =  (-a, b)

C = (a, b)

P = (0, b) (Midpoint of base)

Therefore, the gradient or slope of the base AC is presented as follows;

Slope, m \, of \. base, \, AC= \frac{dy}{dx}  = \frac{b - b}{a - (-a)}  = \frac{0}{2\cdot a} = 0

Hence, segment AC is vertical

Slope, m \, of \, segment \ CP \,  joining \, vertex, \, to \, midpoint, P, on  \,AC = \frac{0 - b}{0 - 0}  = \frac{-b}{0} = Undifined.

Hence, segment CP is vertical

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.

6 0
3 years ago
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