This figure has two intersecting lines and a ray. What is the value of x?

den301095 [7]

4 0

2 years ago

The 6 members of the homecoming decorating committee want to make 525 paper flowers for the homecoming dance. Each flower takes

stiv31 [10]

<h3>Answer:</h3>

6 hours 36 minutes, or 6 hours 31 1/2 minutes

<h3>Step-by-step explanation:</h3>

Dividing the task among the 6 committee members means each member will be making 525/6 = 87.5, that is, either 87 or 88 flowers. (We doubt that two people working together on the same flower will finish it in half the time.)

Each of the three committee members making 88 flowers will take ...

... 88 × 4 1/2 minutes = 396 minutes = 6 hours 36 minutes

Each member making 87 flowers will be finished 4 1/2 minutes sooner, after 6 hours 31 1/2 minutes.

_____

<em>Comment on the problem</em>

This problem seemingly invites you to divide the labor evenly among committe members. Doing that would give you an answer of 6 hours 33 3/4 minutes. You need to ask yourself whether that is practical for this situation.

4 0

2 years ago

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

Stolb23 [73]

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

7 0

2 years ago

Which transformation maps hexagon 1 into 3?

umka2103 [35]

Let's look at the possibilities:

1. Reflection along the y-axis and rotation of 180 degrees by the origin 0. (Gives us 4 and then 2 in the end)

2. Reflection along the y-axis and reflection along the x-axis. (Gives us 4 and then 3 in the end)

3. Reflection along the x-axis and rotation 90 degrees by the origin 0. (Gives us 4 and then 1 in the end)

4. Rotation of 270 degrees by the origin 0. (Gives us 2 in the end)

Option 2 is the answer.

Best of luck!

5 0

2 years ago

Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set

SOVA2 [1]

Answer:

The correct option is (A).

Step-by-step explanation:

Let <em>X</em> = number of orange milk chocolate M&M’s.

The proportion of orange milk chocolate M&M’s is, <em>p</em> = 0.20.

The number of candies in a small bag of milk chocolate M&M’s is, <em>n</em> = 55.

The event of an milk chocolate M&M being orange is independent of the other candies.

The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 55 and <em>p</em> = 0.20.

The expected value of a Binomial random variable is:

$E(X)=np$

Compute the expected number of orange milk chocolate M&M’s in a bag of 55 candies as follows:

$E(X)=np$

$=55\times 0.20\\=11$

It is provided that in a randomly selected bag of milk chocolate M&M's there were 14 orange ones, i.e. the proportion of orange milk chocolate M&M's in a random bag was 25.5%.

This proportion is not surprising.

This is because the average number of orange milk chocolate M&M’s in a bag of 55 candies is expected to be 11. So, if a bag has 14 orange milk chocolate M&M’s it is not unusual at all.

All unusual events have a very low probability, i.e. less than 0.05.

Compute the probability of P (X ≥ 14) as follows:

$P(X\geq 14)=\sum\limits^{55}_{x=14}{{55\choose x}0.20^{x}(1-0.20)^{55-x}}$

$=0.1968$

The probability of having 14 or more orange candies in a bag of milk chocolate M&M’s is 0.1968.

This probability is quite larger than 0.05.

Thus, the correct option is (A).

4 0

2 years ago