Give the area of a rectangle that has a length of 8 and a width of 9.

A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other w

hoa [83]

Answer:

64,717.36 Joule is the total amount of work needed to pump the gasoline out of the tank.

Step-by-step explanation:

Volume of cylinder = V

Radius of cylinder = r = 0.5 m

Height of the cylinder = 5 m

Volume of cylinder = $\pi r^2h$

$V=3.14\times (0.5 m)^2\times 5 =3.925 m^3$

Mass of gasoline = m

Density of gasoline = d = $673 kg/m^3$

$m=d\times V=673 kg/m^3\times 3.925 m^3=2,641.525 kg$

Work done to pump the gasoline out of the tank W

Acceleration due to gravity = g $.8 m/s^2$

The center of gravity of fuel in fully filled tank will be centre so, the value of h = 2 m + 0.5 m = 2.5 m

$W =m\times g\times h$

$W=2,641.525 kg\times 9.8 m/s^2\times 2.5 m=64,717.36 J$

64,717.36 Joule is the total amount of work needed to pump the gasoline out of the tank.

6 0

3 years ago

5.0x 10^10 in scientific notation

AysviL [449]

5.0x10^10
is it a scientific notation\

5 0

3 years ago

Write an equation for the parabolla

pentagon [3]

well, is noteworthy that an x-intercept is when y = 0 or namely is a solution or root of the quadratic, so we know then that the x-intercepts or solutions are at (-1,0) and (3,0), that simply means that

$\bf (\stackrel{x}{-1},\stackrel{y}{0})\qquad (\stackrel{x}{3},\stackrel{y}{0})\qquad \begin{cases} x = -1\\ x+1=0\\ \cline{1-1} x=3\\ x-3=0 \end{cases}~\hfill \implies ~\hfill \stackrel{\textit{equation of the parabola}}{y = a(x+1)(x-3)} \\\\\\ \textit{we also know that } \begin{cases} x = 1\\ y = -8 \end{cases}\implies \underline{-8}=a(\underline{1}+1)(\underline{1}-3)$

$\bf -8=a(2)(-2)\implies -8=-4a\implies \cfrac{-8}{-4}=a\implies \boxed{2=a} \\\\[-0.35em] ~\dotfill\\\\ y=2(x+1)(x-3)\implies y=2(\stackrel{\mathbb{FOIL}}{x^2-2x-3})\implies y=2x^2-4x-6$

4 0

3 years ago

At least 96.00% of the data in any data set lie within how many standard deviations of the mean? Explain how you arrived at yo

zheka24 [161]

The answer assumes that the question is about the normal distribution.

Answer:

96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the standard normal distribution that permits obtaining any probability from any normally distributed data, doing the following transformation:

$\\ z = \frac{x-\mu}{\sigma}$

That is, in this case, we subtract a given value x from the population mean and then divide the result by the population standard deviation. This is a z-score, and this value is associated with the probability for a standard normal distribution, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the standard normal distribution, there is associated a ubiquitous standard normal table for possible values of z and the corresponding probability. Then, knowing that the data are normally distributed and having both distribution parameters, namely, the population mean and population standard deviation, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that the z-score value tells us how many standard deviations from the mean are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a cumulative standard normal table from the mean.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a cumulative standard normal table from the mean. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

5 0

3 years ago

Write and solve a real-world word problem in which there are 3 tables for every 8 chairs.

alekssr [168]

That means there are 24 chairs. What you would do is multiply 8 by 3 which gives you 24.

4 0

3 years ago