1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
3 years ago
8

We conduct a simulation to mimic randomly sampling from a population with of college graduates. In the population 62% had studen

t loans. Each sample has 50 graduates in it. What will be the mean of the distribution of sample proportions
Mathematics
1 answer:
fiasKO [112]3 years ago
6 0
1.24 % college graduate
You might be interested in
henry has 68 miles to destination after 45 minutes and 51.5 miles to destination after 71 minutes of driving. How many miles to
Airida [17]
Let d represent the distance of the destination from the starting point.

After 45 min, Henry has already driven d-68 miles.  After 71 min., he has already driven d-51.5 miles.

So we have 2 points on a straight line:

(45,d-68) and (71,d-51.5).  Let's find the slope of the line thru these 2 points:

                                 d-51.5 - (d-68)         16.5 miles
slope of line = m = ----------------------- = ------------------
                                     71 - 45                   26 min

Thus, the slope, m, is   m = 0.635 miles/min

The distance to his destination would be d - (0.635 miles/min)(79 min), or 

d - 50.135 miles.  We don't know how far his destination is from his starting point, so represent that by "d."

After 45 minutes:  Henry has d - 68 miles to go;

After 71 minutes, he has        d - 51.5 miles to go; and

After 79 minutes, he has         d -  x miles to go.  We need to find x.

Actually, much of this is unnecessary.  Assuming that Henry's speed is 0.635 miles/ min, and knowing that there are 8 minutes between 71 and 79 minutes, we can figure that the distance traveled during those 8 minutes is

(0.635 miles/min)(8 min) = 5.08 miles.  Subtracting thix from 51.5 miles, we conclude that after 79 minutes, Henry has (51.5-5.08), or 46.42, miles left before he reaches his destination.




7 0
3 years ago
What if i=radical -1, what is the value of i^3
aleksklad [387]

\bf i^3\implies \sqrt{-1}\cdot \sqrt{-1}\cdot \sqrt{-1}\implies (\sqrt{-1})^2\sqrt{-1}\implies \sqrt{(-1)^2}\cdot \sqrt{-1} \\\\\\ -1\cdot i\implies \boxed{-i}

6 0
3 years ago
The student council wants to rent a chocolate fountain for an overnight dance-a-thon. Their budget allows them to spend a maximu
vekshin1
$125 is a "must budget" so it will be the constant in the inequality

The fountain is $30 per hour. If they spend x hours, then their budget for fountain will be
fountain = 30x

The inequality
Their budget is maximum $250, that means they are able to spend less than or equal to $250
constant + fountain ≤ 250
125 + 30x ≤ 250
<em>This is the inequality expression</em>
6 0
3 years ago
Read 2 more answers
Find the integral using substitution or a formula.
Nadusha1986 [10]
\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx

Derivative of the denominator:
\rm (x^2+2x+5)'=2x+2

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx

and then split the fraction,

\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx

Based on our previous test, we know that a simple substitution will work for the first integral: \rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx

So the first integral changes,

\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx

integrating to a log,

\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2

So we have this going on,

\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx

Bringing all that stuff together as a single square,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx

Making the substitution: \rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx

giving us,

\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du

simplying a lil bit,

\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du

and hopefully from this point you recognize your arctangent integral,

\rm ln|x^2+2x+5|+\frac52arctan(u)

undo your substitution as a final step,
and include a constant of integration,

\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c

Hope that helps!
Lemme know if any steps were too confusing.

8 0
3 years ago
The function f(x)=x^2-12x+5written in vertex form is f(x)=(x-6)^2-31what are the coordinates of the vertex
schepotkina [342]
The vertex to this question is (6, -31)
5 0
3 years ago
Other questions:
  • Help me plzzzzzzzzzz help me
    7·1 answer
  • A dog kennel uses 95 lbs of dog food per day. How many pounds are used in a year?
    5·2 answers
  • Your friends weekly profit is more than $40 and at the most $130. Write your friends weekly profit as an inequality
    9·1 answer
  • HELP!!! What is the missing term , x, in the pattern?
    7·1 answer
  • What is the domain of the function represented in the graph?
    9·1 answer
  • Ecuación de la hipérbola con centro en (0;0), focos en abrir paréntesis 0 coma espacio menos raíz cuadrada de 28 cerrar paréntes
    15·1 answer
  • Colin buys a car for £27900 he
    10·1 answer
  • The normal to the curve y = x^3 - 5x2 +3x +1, at the points a(4, - 3) and b(1, 0) meet at point c. a) Find the coordinates of C.
    10·2 answers
  • Watch it and tell me what u think
    10·2 answers
  • If you replace the outlier of 113°F with 100°F, what happens to the range? Why do you think this occurs?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!