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2 years ago

I will mark you as brainiest AND if u answer it correctly, you will get 50 points.

Mathematics

1 answer:

Gekata [30.6K]2 years ago

4 0

Answer:

17/6

Step-by-step explanation:

You have to multiply the whole number (2) by the denominator (6) then add the numerator (5) which equals 17.

Next you put 17 over the original denominator (6) to get the improper fraction 17/6

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What is the lcm of 84, 56

Veronika [31]

<span>The Least Common Multiple (LCM) is: 2 x 2 x 2 x 3 x 7 = 168</span>

3 0

3 years ago

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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

3 years ago

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Shobos mother present age is six times shobos present age. Shobos age five from now will be one third of his mother's present ag

r-ruslan [8.4K]

Answer:

Step-by-step explanation:

From the problem statement, we can setup the following equations:

$M = 6S$

$S + 5 = \frac{1}{3}M$

where $S$ is the current age of Shobos and $M$ is the current age of his mother.

Substituting the first equation into the second will allow us to solve for $S$ :

$S + 5 = \frac{1}{3}M$

$S + 5 = \frac{1}{3}(6S)$

$S + 5 = 2S$

$S = 5$

Substituting this value into the first equation gives us the age of the mother:

$M = 6S$

$M = 6(5)$

$M = 30$

5 0

3 years ago

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The diagram shows a straight line ABCD.

Nady [450]

Answer:

B (0, 285 ) , C (380, 0 )

Step-by-step explanation:

the first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = A(- 260, 480 ) and (x₂, y₂ ) = D (620, - 180 )

m = $\frac{-180-480}{620-(-260)}$ = $\frac{-660}{620+260}$ = $\frac{-660}{880}$ = - $\frac{66}{88}$ = - 0.75 , then

y = - 0.75x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equatio

using (620, - 180 ) , then

- 180 = - 465 + c ⇒ c = - 180 + 465 = 285

So y- intercept is B (0, 285 )

y = - 0.75x + 285 ← equation of line

to find the x- intercept , let y = 0 in the equation and solve for x

0 = - 0.75 + 285 ( subtract 285 from both sides )

- 285 = - 0.75x ( divide both sides by - 0.75 )

380 = x

x- intercept is C (380, 0 )

4 0

1 year ago

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The temperature in Greenland is -8.3°C. The temperature in Jamaica is 30°C. What is the difference between the temperatures in t

Fantom [35]

Answer:

The difference between the temperatures in the two countries is 38.3°C.

Step-by-step explanation:

Given:

Temperature in Greenland = - 8.3°C

Temperature in Jamaica = 30°C

To find :

The difference between the temperature in the two countries = ?

$\textrm{difference between the temperature in the two countries} =\textrm{temperature in Jamaica} - \textrm{temperature in Greenland}\\= 30 - (-8.3)\\= 30 +8.3\\= 38.3\°C$

Therefore,the difference between the temperatures in the two countries is 38.3°C

6 0

3 years ago