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3 years ago

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Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the

DVD. Write an expression that can be used to determine the final cost of the DVD.
1 y − 0.15y
2 0.05(0.85y)
3 y − 0.85y + 0.05y
4 1.05(0.85y)

1 answer:

inna [77]3 years ago

5 0

The answer is 4. 1.05(0.85y)

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Radioactive isotopes are commonly used to estimate artifact ages. Let X be the time in years for a Carbon-14 atom to decay to Ni

Alexeev081 [22]

Answer:

a) 1 / years

b) P ( 5000 < X < 6000) = 0.06222

c) 8267 years

d) T_1/2 = 5730.25 years

Step-by-step explanation:

Given:

- The decay constant λ = 1 / 8267

- X is an exponential random Variable

Find:

a. What are the units of What are the units of λ?

b. What is the probability the decay time is between 5000 and 6000 years?

c. Compute SD(X).

d. Compute the median decay time. The result is called the half-life of Carbon-14?

Solution:

- The decay constant λ means the rate at which the C-14 atoms decays into N-14 atom. The rate is expressed in units of 1 / year.

- The random variable X follows an exponential distribution which has a probability mass function and cumulative density functions as follows:

P ( X = t ) = λ*e^(-λ*t)

P ( X = t ) = e^(-t/8267) / 8267

P ( X < t ) = 1 - e^(-λ*t) = 1 - e^(-t/8267)

- The probability of the decay time between years 5000 and 6000 years is:

P ( 5000 < X < 6000) = 1 - e^(-6000/8267) - 1 + e^(-5000/8267)

P ( 5000 < X < 6000) = 0.06222

- The standard deviation of the exponential distribution is given by:

SD(X) = 1 / λ = 8267 years

- The median decay time for an exponential distribution is given by:

T_1/2 = Ln(2) / λ = Ln(2)*8267

T_1/2 = 5730.25 years

3 0

4 years ago

Read 2 more answers

Order these rational numbers from least to greatest: -1 8/9, -1.68, , -1.98, -0.9

mestny [16]

Answer:

Least to Greatest

-1.98, -0.9, -1 $\frac{8}{9}$ , -1.68

Step-by-step explanation:

In the case of negative numbers the "larger" the number is, the least it is. For the fraction I just tossed 8/9 into my calculator to get the decimal version that way I could put it in order accuratly.

4 0

4 years ago

The diagram was constructed with straightedge and compass tools. Point A is the center of one circle, and point C is the center

Murrr4er [49]

Answer:

CE = AD/2

Step-by-step explanation:

C is the center of small circle

Point E is on same circle, therefore CE = radius of small circle

AD passes through the center of small circle and both points are on same circle, therefore AD is diameter of small circle

<u>Since diameter is double of radius:</u>

AD = d, CE= r

d = 2r

AD = 2*CE or CE = AD/2

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3 years ago

An ecological group suspects lobsters are consuming dangerous levels of mercury in a region of the world. Dangerous levels of me

Crank

Part A: 5 out 25 lobsters have dangerous levels of mercury

Part B: the 95% confidence interval is given by (4.45, 5.65)

since everything is given all I had to do is find the critical value which can be found from the resource packet = 2.064

Using the formula we find 5.05+-2.064*1.45/5 = ( 4.45,5.65)

For this case, we have 95% of confidence that the true mean for the average number of lobsters with dangerous levels of mercury is between 4.45,5.65

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3 years ago

Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨2,−3,4⟩, b=⟨−4,5,−1⟩, and c=⟨−2,−1,5⟩.

NikAS [45]

Answer:

derivative of the vector function given = ( -16-22t, 14-36t, -2-16t )

Step-by-step explanation:

given data:

vector function : r(t) = ta*(b+tc)

a = ( 2,-3.4) . b = (-4,5,-1). c = ( -2,-1,5)

to find the derivative of the vector function we will differentiate with respect to x attached below is the detailed solution

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3 years ago