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Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)

alexdok [17]

Answer:

Step-by-step explanation:

Using the compound interest formula to calculate the amount compounded after 10years.

$A = P(1+r)^{nt}$

P = principal = $2000

r = rate (in %) = 5.6%

t = time (in years) = 10years

n = 1year = time used in compounding

$A = 2000(1+0.056)^{10} \\A = 2000(1.056)^{10}\\A = 2000*1.7244046\\A = 3448.81 (to\ 2dp)$

Amount compounded after 10 years is $3448.81

4 0

3 years ago

1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several ti

uysha [10]

Answer:

1) $0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

b) $ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

Step-by-step explanation:

Information given

0.082601, 0.082621, 0.082589, 0.082617, 0.082598

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=0.0826052$ represent the sample mean

$\mu$ population mean

s=0.000013424 represent the sample standard deviation

n=5 represent the sample size

Part 1

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom, given by:

$df=n-1=5-1=4$

The Confidence level is 0.95 or 95%, and the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ , the critical value would be using the t distribution with 4 degrees of freedom: $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

Part 2

The original margin of error is given by:

$ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

3 0

2 years ago

Find the point on the line 2x+4y−3=0 which is closest to the point (2,0)

Finger [1]

L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.

Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)

Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10

=> the point on L1 closest to (2,0) is (19/10, -1/5)

7 0

2 years ago

Which equation describes a line that passes through (-6, 8) and is parallel to the line described by y = 2x − 4?

AleksandrR [38]

Answer:

hey, there!

Step-by-step explanation:

The given is a point (-6,8) through which a line passes. And is perpendicular to the line y = 2x-4

The equation for point (-6,8) is,

(y-8)= m1(x+6)...........(i)

and given equation is y = 2x-4............(ii)

Now, from equation (ii).

slope (m2)= 2 { as equation (ii) is in the form of y= mx+c where m is a slope}.

Now, For perpendicular,

m1×m2= -1

m1×2= -1

Therefore, m1 = -1/2.

Putting, the value of m1 in equation (i).

(y-8) = -1/2×(x+6)

2(y-8)= -1(x+6)

2y - 16 = -x -6

x+2y-10 = 0......... is the required equation.

Hope it helps...

6 0

2 years ago

determine the length of a rectrangular prism having a volume of 2,830.5 cubic meters, width of 18.t meters, and height of 9 mete

Nat2105 [25]

The length may be 17m

7 0

2 years ago