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3 years ago

7

You have a balance of $4,500 on your credit card. The interest rate is 12% (1% per month). The late payment fee is $40. You miss

a payment. Solve for your fees plus interest for the month.
a) $40
b) $45
c) $65
d) $85

1 answer:

Montano1993 [528]3 years ago

3 0

I started by figuring out how much interest you get in a month by multiplying 4500 by .01. This gave me $45 as in interest. Then I added the payment fee, $40. 40+45 is 85, so the answer should be d). However, I'm not 100% positive. Somebody verify please? :)

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Let Y1, Y2, . . . , Yn be independent, uniformly distributed random variables over the interval [0, θ]. Let Y(n) = max{Y1, Y2, .

Anettt [7]

Answer:

a) $F(y) = 0, y$

$F(y) = \frac{y}{\theta} , 0 \leq y \leq \theta$

$F(y)= 1, y>1$

b) $f_{Y_{(n)}} = \frac{d}{dy} (\frac{y}{\theta})^n = n \frac{y^{n-1}}{\theta^n}, 0 \leq y \leq \theta$

$f_{Y_{(n)}} =0$ for other case

c) $E(Y_{(n)}) = \frac{n}{\theta^n} \frac{\theta^{n+1}}{n+1}= \theta [\frac{n}{n+1}]$

$Var(Y_{(n)}) =\theta^2 [\frac{n}{(n+1)(n+2)}]$

Step-by-step explanation:

We have a sample of $Y_1, Y_2,...,Y_n$ iid uniform on the interval $[0,\theta]$ and we want to find the cumulative distribution function.

Part a

For this case we can define the CDF for $Y_i$ , $i =1,2.,,,n$ like this:

$F(y) = 0, y$

$F(y) = \frac{y}{\theta} , 0 \leq y \leq \theta$

$F(y)= 1, y>1$

Part b

For this case we know that:

$F_{Y_{(n)}} (y) = P(Y_{(n)} \leq y) = P(Y_1 \leq y,....,Y_n \leq y)$

And since are independent we have:

$F_{Y_{(n)}} (y) = P(Y_1 \leq y) * ....P(Y_n \leq y) = (\frac{y}{\theta})^n$

And then we can find the density function calculating the derivate from the last expression and we got:

$f_{Y_{(n)}} = \frac{d}{dy} (\frac{y}{\theta})^n = n \frac{y^{n-1}}{\theta^n}, 0 \leq y \leq \theta$

$f_{Y_{(n)}} =0$ for other case

Part c

For this case we can find the mean with the following integral:

$E(Y_{(n)}) = \frac{n}{\theta^n} \int_{0}^{\theta} y y^{n-1} dy$

$E(Y_{(n)}) = \frac{n}{\theta^n} \int_{0}^{\theta} y^n dy$

$E(Y_{(n)}) = \frac{n}{\theta^n} \frac{y^{n+1}}{n+1} \Big|_0^{\theta}$

And after evaluate we got:

$E(Y_{(n)}) = \frac{n}{\theta^n} \frac{\theta^{n+1}}{n+1}= \theta [\frac{n}{n+1}]$

For the variance first we need to find the second moment like this:

$E(Y^2_{(n)}) = \frac{n}{\theta^n} \int_{0}^{\theta} y^2 y^{n-1} dy$

$E(Y^2_{(n)}) = \frac{n}{\theta^n} \int_{0}^{\theta} y^{n+1} dy$

$E(Y^2_{(n)}) = \frac{n}{\theta^n} \frac{y^{n+2}}{n+2} \Big|_0^{\theta}$

And after evaluate we got:

$E(Y^2_{(n)}) = \frac{n}{\theta^n} \frac{\theta^{n+2}}{n+2}= \theta^2 [\frac{n}{n+2}]$

And the variance is given by:

$Var(Y_{(n)}) = E(Y^2_{(n)}) - [E(Y_{(n)})]^2$

And if we replace we got:

$Var(Y_{(n)}) =\theta^2 [\frac{n}{n+2}] -\theta^2 [\frac{n}{n+1}]^2$

$Var(Y_{(n)}) =\theta^2 [\frac{n}{n+2} -(\frac{n}{n+1})^2]$

And after do some algebra we got:

$Var(Y_{(n)}) =\theta^2 [\frac{n}{(n+1)(n+2)}]$

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3 years ago

Hello, I need help on this question. I dont understand it and have been getting the answer incorrect. I am embarrassed to ask my

dmitriy555 [2]

Answer:

1). 16 π cm^2

2). 112 π cm^3

3). 351.68 cm^3

***If the explanation doesn’t make sense, let me know, and I’ll try to explain in a different way.

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3 years ago

Given the slope of 3 and the y-intercept 6, write the<br> equation in slope-intercept form.

Maslowich

9514 1404 393

Answer:

y = 3x +6

Step-by-step explanation:

Put the numbers in the formula in their corresponding places.

y = mx + b . . . . slope-intercept form with slope m, intercept b

y = 3x +6 . . . . . slope-intercept form with slope 3, intercept 6

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3 years ago

Louis wants to carpet the rectangular floor of his basement. The basement has an area of 675 square feet. The width of the basem

artcher [175]

I am reading this correctly, the width = 1/3 of the length?

If this is the case, and we know that the area is 675, the equation is as follows.

Width x Length = 675 ft2

X = length

1/3 X x X = 675 ft2

To solve for X we have to multiply both sides by 3.

X square 2 = 2601 square feet.

Take the square of each side.

X = 225 sqare feet.

I hope this helps, let me know if you have any questions.

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3 years ago

I will give thanks and five stars to the person that helps me.

weqwewe [10]

Answer:

$1. \: \: x > - 16 \\ 2. \: \: x > - 16 \\ 3. \: \: x >16$

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3 years ago

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