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3 years ago

How much would $100 invested at 8% interest compounded continuously be worth after 15 years?

1 answer:

4 0

The correct formula to use for continuous compounding is:
$A=Pe^{rt}$
where the exponential number e is the base of natural logarithms.
$A=100\times e^{(0.08\times15)=332.01$
So the amount after 15 years is $332.01

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A USA Today/CNN/Gallup survey of 369 working parents found 200 who said they spend too little time with their children because o

KengaRu [80]

Answer: a. 0.542

b. 0.051

c. $(0.491,\ 0.593)$

Step-by-step explanation:

Let p be the population proportion of parents spend too little time with their children because of work commitments

As per given , we have

n= 369

$\hat{p}=\dfrac{200}{369}=0.542005420054\approx0.542$

Since the sample proportion is the best estimate for the population proportion.

So , the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments = 0.542

z-value for 95% confidence interval : $z_{\alpha/2}=1.96$

Margin of error : $E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$E=(1.96)\sqrt{\dfrac{0.542(1-0.542)}{369}}\\\\=0.0508364564574\approx0.051$

The margin of error = 0.051

Confidence interval : $\hat{p}\pm E$

$0.542\pm0.051\\\\=(0.542-0.051,\ 0.542+0.051)\\\\=(0.491,\ 0.593)$

95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments : $(0.491,\ 0.593)$

6 0

4 years ago

1. You have a bag of marbles. There are green, yellow and red marbles in it. Each marble has a number 1 or 2 on it. G = event of

umka2103 [35]

Answer:

P means probability. R means event of picking a red marble. 2 means event of picking a marble with 2 on it.

Step-by-step explanation:

4 0

3 years ago

Students planted 6 equal size gardens on Earth Day. They divided each garden into 3 equal sections and planted herbs in 2 of the

professor190 [17]

12/18 of the gardens are herbs. First,you multiply 6×3 and get 18 sections in all the gardens. Then you multiply 2×6 and get 12 sections are herbs. So,12 out of 18 are herbs ( 12/18 ). Hope I helped :P

6 0

4 years ago

Pouvez vous maider pour la questuon deux merci

Vanyuwa [196]

quelle est ta question?

6 0

3 years ago

A curve passes through the point ( 0 , 7 ) (0,7) and has the property that the slope of the curve at every point P P is twice th

STatiana [176]

Answer:

The equation for the curve is:

$f(x) = 7*e^{2*x}$

Step-by-step explanation:

We know that for a curve defined as:

y = f(x)

The slope of the curve at the point x is:

y = f'(x)

where f'(x) = df(x)/dx

Here we know that we have a function that passes through the point (0, 7)

We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))

Then we have two equations:

f(0) = 7

f'(x) = 2*f(x)

From the shape of the equation, we can assume than this is an exponential equation like:

$f(x) = A*e^{k*x}$

Replacing that in the second equation, we get:

$k*A*e^{k*x} = 2*A*e^{k*x}$

From that equation, we can conclude that k = 2

Then:

$f(x) = A*e^{2*x}$

Now we can use the first equation:

f(0) = 7

With this, we can find the value of A.

$f(0) = 7 = A*e^{2*0}\\7 = A*e^0 = A*1\\7 = A$

Then we can conclude that the equation for the curve is:

$f(x) = 7*e^{2*x}$

6 0

3 years ago