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sergiy2304 [10]
3 years ago
10

Russel throws a soda from the balcony of his house to his friend Jones in the pool. If the soda is released 20 feet from the gro

und, and is thrown with a downward velocity of 2 ft/s, how long till the soda hits the pool, ignoring air resitance? Use the formula , where h is the height of the soda in feet and t is the time in seconds since Russel threw it. Round your answer to the nearest tenth.
A. 0.5 seconds B. 0.8 seconds C. 1.1 second D. 1.6 seconds
Mathematics
2 answers:
stepladder [879]3 years ago
3 0
Using the formula S = ut +1/2at²
S=h= 20ft, u = 2ft/s, and a = 10m/s²
Thus; 20 =2t + 20t²
Therefore; 20t²+2t-20=0
Solving the equation quadratically for the value of t,
we get; t = 1.057 or t=-1.182
But t can not be negative,
 Therefore, t= 1.1 seconds (to the nearest tenth)


ki77a [65]3 years ago
3 0

Answer:

C. 1.1 seconds

Step-by-step explanation:

The formula to use is :

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

Where: h is the height of 20 ft, u is the velocity of 2ft/s and a is the gravitational acceleration of 9.8m/s². The acceleration should be converted to ft/sec² to simplify calculations. The value is then 32.15ft/sec².

Substituting these values into the equation:

20=2t+0.5*32.15t^{2} \\20=2t+16.075t^{2} \\0=16.075t^{2}+2t-20

Using the quadratic formula, t can be solved.

a = 16.075, b = 2, c = -20:

t=\frac{-b+-\sqrt{b^{2}-4ac} }{2a} \\t=\frac{-2+-\sqrt{2^{2}-4(16.075)(-20)} }{2(16.075)}\\t=\frac{-2+-35.92}{32.15}\\t=1.055 \\OR\\t=-1.179

The answer cannot be negative, therefore the answer is t = 1.055 ≈ 1.1seconds

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3 years ago
Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or
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Answer:

a) \bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)

b) Since the sample size is large enough n>30 and the original distribution for the random variable X  doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) P(\bar X \leq 77)=P(Z

d) See figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

E(X) = 75

sd(X) = 7

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean \bar X is also normal and is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X  doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}

And we want to find this probability:

P(\bar X \leq 77)=P(Z

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

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ohn is interested in purchasing a multi-office building containing five offices. The current owner provides the following probab
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Answer:

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=$28,875

4 0
3 years ago
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