Answer: a. AB = 15cm long.
b. AB = 11.1cm long.
Step-by-step explanation: Image of AB after a dilation of scale factor 5 is 5 × 3cm = 15cm long.
Image of AB after a dilation of scale factor 3.7 is 3cm × 3.7 = 11.1cm long.
Answer:

Step-by-step explanation:
Without loss of generality, let there be 5 star shaped cookies. Following the proportions given, there will be 6 circular cookies. We can set up the following proportion to find out how many triangular cookies there would be:
.
Therefore, for every 5 star shaped cookies there will be 20 triangular cookies.
Simplifying this ratio we have
.
Answer:
x < -11
Step-by-step explanation:
Let x be the number
- 2x - 2 < -24
- Add 2 to each side, so it now looks like this: 2x < -22
- Divide each side by 2 to cancel out the 2 next to x. It should now look like this: x < -11
I hope this helps!
Raymond has consumed 84 calories
Answer:

And we can calculate this with the complement rule like this:

And using the cdf we got:
![P(X>2) = 1- [1- e^{-\lambda x}] = e^{-\lambda x} = e^{-\frac{1}{2.725} *2}= 0.480](https://tex.z-dn.net/?f=%20P%28X%3E2%29%20%3D%201-%20%5B1-%20e%5E%7B-%5Clambda%20x%7D%5D%20%3D%20e%5E%7B-%5Clambda%20x%7D%20%3D%20e%5E%7B-%5Cfrac%7B1%7D%7B2.725%7D%20%2A2%7D%3D%200.480)
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable of interest:

Solution to the problem
We want to calculate this probability:

And we can calculate this with the complement rule like this:

And using the cdf we got:
![P(X>2) = 1- [1- e^{-\lambda x}] = e^{-\lambda x} = e^{-\frac{1}{2.725} *2}= 0.480](https://tex.z-dn.net/?f=%20P%28X%3E2%29%20%3D%201-%20%5B1-%20e%5E%7B-%5Clambda%20x%7D%5D%20%3D%20e%5E%7B-%5Clambda%20x%7D%20%3D%20e%5E%7B-%5Cfrac%7B1%7D%7B2.725%7D%20%2A2%7D%3D%200.480)