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arsen [322]
3 years ago
5

A bag contains ten marbles of equal size and weight. One marble is blue, one marble is white, three are yellow, and five marbles

are red. A marble is taken from the bag two times. Each time a marble is taken out, it is not replaced. What is the probability of picking a blue marble and picking a white marble? A) 1/100 B) 1/5 C) 1/90 D) 2/15
Mathematics
1 answer:
Andrej [43]3 years ago
4 0
Itz B because 10-2=8
It would be like this 2/10 (btw it's not division...is a fraction) simplified to 1/5
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A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha
8_murik_8 [283]
To model this situation, we are going to use the decay formula: A=Pe^{rt}
where 
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P is the initial population 
e is the Euler's constant
r is the decay rate 
t is the time in years

A. We know for our problem that the initial population is 1,250, so P=1250; we also know that after a year the population is 1000, so A=1000 and t=1. Lets replace those values in our formula to find r:
A=Pe^{rt}
1000=1250e^{r}
e^{r}= \frac{1000}{1250}
e^{r}= \frac{4}{5}
ln(e^{r})=ln( \frac{4}{5} )
r=ln( \frac{4}{5} )
r=-02231

Now that we have r, we can write a function to model this scenario:
A(t)=1250e^{-0.2231t}.

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C. 
- The function is decreasing
- The function doe snot have a x-intercept 
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0: 
A(0)=1250e^{(-0.2231)(0)
A_{0}=1250e^{0}
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- Over the interval [0,10], the function will have a minimum at t=10:
A(10)=1250e^{(-0.2231)(10)
A_{10}=134.28

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: m= \frac{A(0)-A(10)}{10-0}
where 
m is the rate of change 
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A(0) is the function evaluated at 0
We know from previous calculations that A(10)=134.28 and A(0)=1250, so lets replace those values in our formula to find m:
m= \frac{134.28-1250}{10-0}
m= \frac{-1115.72}{10}
m=-111.572
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0
2 years ago
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