Choose the graph of y = 2cosx

The average density of the material in intergalactic space is approximately 2.5 × 10–27 kg/m3. what is the volume of a lead samp

Lesechka [4]

Answer:

e. $1.8\times 10^{-6}m^3$

Step-by-step explanation:

It is given that,

The density of intergalactic space material is $2.5 \times 10^{-27}$ kg per cubic meter.

And the volume of intergalactic space material is $8.0\times 10^{24} m^3$

So the mass of that much intergalactic space material is,

$m= \rho\times v$ , where 'm' is the mass, and 'v' is the volume.

Putting the values we get,

$m=2.5 \times 10^{-27}\times 8.0 \times 10^{24}$

$m=20\times 10^{(-27+24)}=20\times 10^{-3} kg$

It is also given that the mass of lead is the same as the mass of the intergalactic space material. Therefore, the mass of lead is $20 \times 10^{-3}=2 \times 10^{-2}kg$

So the volume of lead is,

$v=\frac{m}{\rho} =\frac{2 \times 10^{-2}}{11300} = 0.00000177 m^3$

$v=1.77 \times 10^{-6}=1.8\times 10^{-6}m^3$

So the volume of lead is $v=1.8\times 10^{-6}m^3$ .

3 0

3 years ago

In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$

3 0

3 years ago

A quality-control manager randomly selects 80 bottles of oil that were filled on january 14 to assess the calibration of the fi

Simora [160]

Is this all the information provided or are you missing something?

6 0

3 years ago

Rectangle is 5 feet wide and 11 feet long. What is the perimeter

Ahat [919]

Answer:

Just add all side

5+11+5+11=32 feet

4 0

3 years ago

Read 2 more answers

|-4| - 8 + 10 = ???<br> answer for points

Elis [28]

Answer:

6

Step-by-step explanation:

As you might know, the two lines surrounding the -4 represent the absolute value, which is basically the distance from 0, and the distance is always positive. To clear any confusion, the absolute value of positive number will not be it's opposite because remember, distance is always positive, so absolute value is always positive (because it is basically the distance from zero).

To help, here is an example (that is not related to the problem!):

|-6| = 6

|6| = 6

<em>Now, back to the problem...</em>

Since you now know that the absolute value is always positive, |-4| would equal 4. So now you have:

4 - 8 + 10 = ???

From here, you can just solve and the answer is 6, so:

4 - 8 + 10 = 6

You final answer is 6.

Hope this helped somehow :D

4 0

3 years ago

Read 2 more answers