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lapo4ka [179]
2 years ago
6

Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that th

e average salary of a group of 16 randomly selected ph.d. students is more than $13,000.

Mathematics
1 answer:
Ainat [17]2 years ago
7 0
It is about 41.4% according to my TI-83/84 calculator.

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A manufacturer finds that the revenue generated by selling of cortan commodity is given by function R(x)=80x-0.2x^ 2 , where he
Nina [5.8K]

The maximum units is 200 and , Total revenue is $8,000

<u>Step-by-step explanation:</u>

Here we have , A manufacturer finds that the revenue generated by selling of cortan commodity is given by function R(x)=80x-0.2x^ 2 , where he maximum reveremany should be manufactured to obtain this maximum units .Let's find out:

We have following function as R(x)=80x-0.2x^ 2 . Let's differentiate this and equate it to zero to find value of x for which the function is maximum!

⇒ R(x)=80x-0.2x^ 2

⇒ \frac{d(R(x))}{dx}=\frac{d(80x-0.2x^ 2)}{dx}

⇒ \frac{d(R(x))}{dx}=\frac{d(80x)}{dx}-\frac{d(0.2x^ 2)}{dx}}

⇒ 0=80-2x(0.2)

⇒ \frac{80}{0.4}=x

⇒ x=200

Now , Value of function at x=200 is :

⇒ R(200)=80(200)-0.2(200)^ 2

⇒ R(200)=16000-8000

⇒ R(200)=8000

Therefore , The maximum units is 200 and , Total revenue is $8,000

7 0
2 years ago
A volunteer has 12 pounds of birdseed to put in the bird feeders in all of the city parks. There are 13/4 cups of birdseed in a
kozerog [31]

Answer:

\large \boxed{28}

Step-by-step explanation:

1. Calculate the number of cups

\text{Cups} = \text{12 lb}\times\dfrac{1\frac{3}{4} \text{ cups}}{\text{1 lb}} =12\times\dfrac{\text{7 cups}}{4} = 3\times7\text{ cups}= \text{21 cups}

2. Calculate the number of bird feeders

\text{ Feeders}= \text{21 cups} \times \dfrac{\text{1 feeder}}{\frac{3}{4}\text{ cup}}=\text{21 cups} \times \dfrac{\text{4 feeders}}{\text{3 cups}} = 7 \times \text{ 4 feeders}\\\\= \textbf{28 feeders}\\\text{The volunteer can fill $\large \boxed{\textbf{28 feeders}}$}

5 0
3 years ago
{(-3,9), (-2, 4), (0, 0), (1, 1)}<br> Find the inverse
Elena-2011 [213]

Answer:

Step-by-step explanation:

to find the inverse, just switch x and y

so if u have these points : (-3,9) , (-2,4), (0,0), (1,1)

the inverse would be : (9,-3) , (4,-2), (0,0), (1,1)

5 0
2 years ago
How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these simila
jeyben [28]

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

\frac{a}{b} =c

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If a = x^{2} and b = x, then:

c = \frac{x^{2}}{x}

c = x

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If a = 3\cdot x^{3} and b = x, then:

c = \frac{3\cdot x^{3}}{x}

c = 3\cdot x^{2}

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If a = 10^{2x} and b = 3\cdot 10^x, then:

c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}

c = \frac{1}{3}\cdot 10^{2\cdot x -x}

c = \frac{1}{3}\cdot 10^x

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If a = 5\cdot e^{x} and b = -3\cdot e^{x}, then:

Example

c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}

c = -\frac{5}{3}

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

5\cdot a^2\cdot x -9

7 0
3 years ago
Find a value for a that makes each statement true.
Tamiku [17]

Answer:

Dude there is no picture ‍♂️ repost

Step-by-step explanation:

8 0
2 years ago
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