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Nat2105 [25]
2 years ago
8

In a mid-size company in Philadelphia, the distribution of the number of phone calls answered each day by each of the 12 recepti

onists is bell-shaped and has a mean of 57 and a standard deviation of 7. Using the empirical (68-95-99.7) rule, what is the approximate percentage of daily phone calls numbering between 50 and 64
Mathematics
1 answer:
alexandr1967 [171]2 years ago
8 0

Answer:

Approximately 68% of daily phone calls will be in this interval.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 57

Standard deviation = 7

What is the approximate percentage of daily phone calls numbering between 50 and 64

50 = 57 - 7

So 50 is one standard deviation below the mean

64 = 57 + 7

So 64 is one standard deviation above the mean

By the Empirical Rule, approximately 68% of daily phone calls will be in this interval.

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5d-2/3c if d =4 and c =3 evaluate fast fast
Mademuasel [1]

Answer:

2

Step-by-step explanation:

Plug 4 in for d and 3 in for c

5d-2/3c

5(4)-2/3(3)

Multiply in the numerator and the denominator

20-2/9

Subtract in the numerator

18/9

2

Hope this helps! :)

4 0
3 years ago
An isosceles triangle has (5 points) A, at least two congruent sides B. two sides that are perpendicular C. three sides with the
aev [14]

Answer:

A. at least two congruent sides

Step-by-step explanation:

Since, we know that,

'An isosceles triangle is a triangle having two sides of equal length or at least two sides of equal length (special case is equilateral triangle)'.

Thus, from the options, we see that,

Options B, C and D are not correct.

<em>Since, congruent sides means that the lengths of the sides are equal.</em>

Thus, we get that,

'An isosceles triangle has at least two congruent sides'.

Hence, option A is correct.

4 0
3 years ago
Read 2 more answers
Evaluate a +6 for a = 10.<br> NEXT QUESTION<br> ©<br> ASK FOR HELP
eduard

Answer:

16

Step-by-step explanation:

10+6=16

5 0
3 years ago
Xyz^(2) if x=2 y=7 and z=-4
Afina-wow [57]

Answer:

-224

Step-by-step explanation:

xyz^2

(2)(7)(-4)^2

14 x -16

-224

8 0
2 years ago
Consider the differential equation:
Wewaii [24]

(a) Take the Laplace transform of both sides:

2y''(t)+ty'(t)-2y(t)=14

\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s

where the transform of ty'(t) comes from

L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)

This yields the linear ODE,

-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s

Divides both sides by -s:

Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}

Find the integrating factor:

\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C

Multiply both sides of the ODE by e^{3\ln|s|-s^2}=s^3e^{-s^2}:

s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}

The left side condenses into the derivative of a product:

\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}

Integrate both sides and solve for Y(s):

s^3e^{-s^2}Y(s)=7e^{-s^2}+C

Y(s)=\dfrac{7+Ce^{s^2}}{s^3}

(b) Taking the inverse transform of both sides gives

y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that \frac{7t^2}2 is one solution to the original ODE.

y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7

Substitute these into the ODE to see everything checks out:

2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14

5 0
3 years ago
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