Teresa is making iced tea. She has a container that has a volume of 3.95 gallons to store the iced tea.

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the o

Korvikt [17]

Answer:

a) $k = 0.000124$

b) According to these data, the Shroud of Turin has around 760 years.

Step-by-step explanation:

The amount of carbon-14 is modeled by the following equation:

$C(t) = C_{0}e^{-kt}$

In which $C_{0}$ is the initial amount and k is the rate of decrease.

(a) Find the value of the constant k in the differential equation.

Half-life of 5595 years.

So $C(5595) = 0.5C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.5C_{0} = C_{0}e^{-5595k}$

$e^{-5595k} = 0.5$

Applying ln to both sides

$-5595k = -0.69$

$k = 0.000124$

b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material. How old is the Shroud of Turin, according to these data?

This is t when $C(t) = 0.91C_{0}$

$C(t) = C_{0}e^{-kt}$

$0.91C_{0} = C_{0}e^{-0.000124t}$

$e^{-0.000124t} = 0.91$

Applying ln to both sides

$-0.000124t = -0.094$

$t = 760.57$

According to these data, the Shroud of Turin has around 760 years.

8 0

4 years ago

Write an expression that evaluates to true if x is non-negative and y is negative?

joja [24]

Answer:

x >= 0 & y<0

x >= 0 means that x is non-negative

y<0 means that y is negative

6 0

2 years ago

Calculate gcd(77, 30) by using the Euclidean algorithm. Find also integers u and v such that 49u + 30v = 1. Furthermore, find su

VladimirAG [237]

Answer:

1. gcd(77,30)=1

$77=2*30+17\\30=1*17+13\\17=1*13+4\\13=3*4+1\\4=4*1+0$

Since 1 is the last non zero remainder appearing in these equations then, 1 is the gcd of 77 and 30.

2. u=-11, v=18

Using the Euclidean Algorithm we have that

$49=1*30+19\\30=1*19+11\\19=1*11+8\\11=1*8+3\\8=2*3+2\\3=1*2+1\\2=1*2+0$

Now, we express the remainder as linear combinations of 49 and 30.

$1&=3-2\\ &=3-(8-2*3)=3-8+2*3\\&=(11-8)-8+2(11-8)=3*11-4*8\\&=3*11-4(19-11)=7*11-4*19\\&=7(30-19)-4*19=7*30-11*19\\&=7*30-11(49-30)=\\&=18*30-11*49$

Then $1=(-11)49+18*30$

3. x=18

If $30x\equiv 1\text{mod 77}$ then

$30x=k*77+1$ for some $k\in \mathbb{Z}$ .

Then, if k=7,

$30x=7*77+1=540\\x=\frac{540}{30}=18$

6 0

3 years ago

A website manager has noticed that during the evening hours, about 3.23.2 people per minute check out from their shopping cart

aleksandrvk [35]

Answer:

1. c. Poisson

2. 0.9592 = 95.92% probability that in any one minute at least one purchase is made.

3. 0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.

Step-by-step explanation:

We have only the mean, which means that the Poisson distribution is used to solve this question, and thus the answer to question 1 is given by option c.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$