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umka21 [38]
3 years ago
10

A package states that there are 60 calories in 12 crackers and 75 calories in 15 crackers. Since the relationship is proportiona

l, how many calories are there in 180 crackers? x y 12 60 15 75
Mathematics
1 answer:
masha68 [24]3 years ago
7 0

Answer:

  900

Step-by-step explanation:

We can write the proportion as ...

  calories/crackers = 60/12 = y/180

Multiplying by 180, we have ...

  180(5) = y = 900

There are 900 calories in 180 crackers.

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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
Read 2 more answers
Use the midpoint formula to find the midpoint between the following 2 points<br> R(6,-6) and G (4,2)
Likurg_2 [28]

Answer:

(5,-2)

Step-by-step explanation:

6+4=10

10/2=5

-6+2=-4

-4/2=-2

3 0
3 years ago
Vivi is a drummer for a band. She burns 756 calories while drumming for 3 hours. She burns the same
german

The question you asked uses the concept of division, something that a bit tricky at first but gets easier as you master it!

So first let’s write and equation for your problem:

Let x = the amount of calories she burns each hour.

So we already know that Vivi was drumming for 3 hours, that she burned 756 calories, and that she burned the same amount of calories each hour.

Since she burned 756 calories in total, we know that the equation will have to equal 756:

= 756

We also know that the answer will be 3(hours) times x(the amount of calories), so now we just plug it into the equation:

3x = 756

To find what ‘x’ equals we have to divide both side by 3:

3x/3 = 756/3

Now all we have to do is simplify and you have your answer!

x = 252

And there you have it, Vivi burned 25 calories per hour!

Hope this helps! :)

6 0
3 years ago
There are five marbles in a bag two are yello and three are green. You draw a marble, replace it, and then draw another. What is
Sphinxa [80]

Answer: 2/5

Step-by-step explanation:

Since there are 5 marbles and 3 aren't yellow, you have a 2/5 chance to choose the other two yellow marbles

Hope this helps:)

5 0
2 years ago
People produce 5,650,00 card each year Ben wrote that they make 6,550,000 cars. What mistake did he make and how can u fix it? :
Masja [62]
How much more does it need to, get to 6,550,000?


7 0
3 years ago
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