What is f and g answers

alex41 [277]

X is equal to -12
7-(-12)=19

5 0

4 years ago

A playground merry-go-round of radius R = 1.80 m has a moment of inertia I = 255 kg · m2 and is rotating at 9.0 rev/min about a

Degger [83]

Answer:

7 rpm = 0.73 rad/s

Step-by-step explanation:

R = Radius of merry-go-round = 1.8 m

$I_M$ = Moment of inertia of merry-go-round = 255 kg m²

$I_C$ = Moment of inertia of child

ω = 9 rev/min

m = Mass of child = 24 kg

From the conservation of angular momentum

$I\omega=I'\omega '\\\Rightarrow I\omega=(I_M+I_C)\omega'\\\Rightarrow \omega'= \frac{I\omega}{(I_M+I_C)}\\\Rightarrow \omega'=\frac{I\omega}{(I_M+mR^2)}\\\Rightarrow \omega'=\frac{255\times 9}{(255+24\times 1.8^2)}\\\Rightarrow \omega'=6.9\ rev/min$

∴ New angular speed of the merry-go-round is 7 rpm = $7\times \frac{2\pi}{60}=\mathbf{0.73\ rad/s}$

3 0

4 years ago

What is the area of figure shown below!??

Novosadov [1.4K]

Answer:26

Step-by-step explanation:

Add them all up

8 0

3 years ago

The population of a colony of mosquitoes obeys the law of uninhibited growth. if there are 1000 mosquitoes initially and there a

inna [77]

6554 Assuming that the growth the function will be of the form f(n) = P*R^n where P = Initial population R = Growth rate per period n = number of periods In this problem, the only period or interval I see are days. So we'll use n to represent the number of days since the start. The initial population is 1000, and the ratio would be 1600/1000 = 1.6. So the formula becomes f(n) = 1000*1.6^n So let's evaluate that function using n=4. f(n) = 1000*1.6^n f(4) = 1000*1.6^4 f(4) = 1000*6.5536 f(4) = 6553.6 Since we can't have a fractional mosquito, round to the nearest integer, giving 6554.

7 0

3 years ago

"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the

STALIN [3.7K]

Answer:

$\\ P(z>-2) = 0.97725$ or P(x>49) is about 97.725% (or being less precise 97.5% using the empirical rule).

Step-by-step explanation:

We solve this question using the following information:

We are dealing here with normally distributed data, that is "the frequency distribution of the life length data is known to be mound-shaped".
The normal distribution is defined by two parameters: the population mean ( $\\ \mu$ ) and the population standard deviation ( $\\ \sigma$ ). In this case, we have that $\\ \mu = 55$ months, and $\\ \sigma = 3$ months.
To find the probabilities, we have to use the standard normal distribution, which has $\\ \mu = 0$ and $\\ \sigma = 1$ . The probabilities for this distribution are collected in the standard normal table, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
For most cases, we need to use the cumulative standard normal table, and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: $\\ z = \frac{x - \mu}{\sigma}$ [1]. A z-score tells us the distance from the mean that a raw score is from it in standard deviations units. If this value is negative, the raw score is below the mean. Conversely, a positive value indicates that it is above the mean.
The cumulative standard normal table is made for positive values of z. Since the normal distribution is symmetrical around the mean, we can find the negative values of z using this formula: $\\ P(z$ [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

First Step: Use formula [1] to find the z-score of the raw score x = 49 months.

$\\ z = \frac{49 - 55}{3}$

$\\ z = \frac{-6}{3}$

$\\ z = -2$

This means that the raw score is represented by a z-score of $\\ z = -2$ , which tells us that it is two standard deviations below the population mean.

Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.

For a z = 2, the probability is 0.97725.

Then

$\\ P(z$

$\\ P(z2)$

But we are not asked for P(z<-2) but for P(z>-2) = P(x>49). This probability is the complement of the previous result, that is

$\\ P(z>-2) = 1 - P(z$

$\\ P(z>-2) = 1 - 0.02275$

$\\ P(z>-2) = 0.97725$

That is, the "percentage of the manufacturer's grade A batteries will last more than 49 months" is

$\\ P(z>-2) = 0.97725$ or about 97.725%

A graph below shows this result.

Notice that if we had used the 68-95-99.7 rule (also known as the empirical rule), that is, in a normal distribution, the interval between one standard deviation below and above the mean contains, approximately, 68% of the observations; the interval between two standard deviations below and above the mean contains, approximately, 95% of the observations; and the interval between three standard deviations below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last less than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the symmetry of the normal distribution, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0

4 years ago