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Delvig [45]
3 years ago
6

When the tortoise raced the hare, the former maintained a constant pace of one mile per hour throughout the race; while the latt

er, being overconfident, wasted much time and averaged only 3/4 miles per hour for the first half of the course. How fast must the hare run over the second half of the course in order to win?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
6 0
<span>The tortoise is runing one mile per hour the entire race. The hare is runing 3/4 only the first half. If we multiply by 2 totis =2 miles and hare =1.50 the hare need to run 1/2 or .50 faster to beat the tortis.</span>
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A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to
nordsb [41]

Answer:

The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.

CV smokers: 0.387

CV non-smokers: 0.234

Step-by-step explanation:

We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).

Then, first we calculate the mean and standard deviation for the smokers data:

Mean: 43.7

Standard deviation: 286.5

M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\

The mean and standard deviation for the non-smokers is:

Mean: 30.3

Standard deviation: 50.9

M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\

Now, we can calculate the coefficient of variation:

CV smokers:

CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387

CV non-smokers:

CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234

3 0
4 years ago
For a moving object, the force acting on the object varles directly with the object's acceleration. When a force of 25 N acts on
Radda [10]

\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}

According to the Question,

\large{\sf{ f \propto \: a}}

<h3>From the Question,</h3>

  • Initial Acceleration,a = 5 m/s²

  • Force at a = 5 m/s²,f = 25 N

  • Final Acceleration,A = 9 m/s²

<h3>To find</h3>

Force exerted on the object at a = 9 m/s²

We Know that,

\huge{\boxed{ \boxed{ \sf{f = ma}}}}

Firstly,we need to find the mass of the object

Thus,

\sf{m =  \frac{f}{a} } \\  \\  \implies \:  \sf{m =  \frac{25}{5} } \\  \\  \huge{ \implies \:  \sf{m = 5 \: kg}}

Now,

\sf{F = mA} \\  \\  \implies \:  \sf{F = (5)(9)} \\  \\  \huge{ \implies \:  \sf{F = 45 \: N}}

7 0
3 years ago
* The American Diabetes Association estimates that 8.3% of people in the
Leto [7]

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = <u><em>event that the diagnostic test is accurate</em></u>

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

<u>Now, the probability that the diagnosis is correct is given by; </u>

    Probability = P(D) \times P(A/D) + P(D') \times P(A/D')

                      = (0.083 \times 0.98) + (0.917 \times0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

8 0
3 years ago
What is the value of​ n?<br> 7.8x10^6=(3x10^4) (2.6x10^n<br> The value of n is...
Vsevolod [243]

Answer:

n = log(\frac{100}{x^2})

Step-by-step explanation:

Take the logarithm of both sides of the equation to remove the variable from the exponent.

7 0
3 years ago
How will increasing the level of confidence without changing the sample size affect the width of a confidence interval for a pop
atroni [7]

Answer:

The width of the confidence interval is going to be wider

Step-by-step explanation:

When we Increase the level of confidence without changing the sample size the width of the confidence interval is going to be affected in the following way;

The margin of error (M.E) is going to be larger or be increased. This increase is due to the fact that the critical value is going to increase. Then the increased margin of error would cause the width of the confidence interval to become wider.

This answers your question.

3 0
3 years ago
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