Answer:
a) The probability that this whole shipment will be accepted is 30%.
b) Many of the shipments with this rate of defective aspirin tablets will be rejected.
Step-by-step explanation:
We have a shipment of 3000 aspirin tablets, with a 5% rate of defects.
We select a sample of size 48 and test for defectives.
If more than one aspirin is defective, the batch is rejected.
The amount of defective aspirin tablets X can be modeled as a binomial distribution random variable, with p=0.55 and n=48
We have to calculate the probabilities that X is equal or less than 1: P(X≤1).
Answer:
<em>y=-6</em>
Step-by-step explanation:
<em>Geometric Sequences</em>
Any given sequence is said to be geometric if each term 
can be obtained as the previous term 
by a constant value called the common ratio.
or equivalently
Looking closely at the sequence 2, y, 18,-54, 162 we can try to find out if it's a geometric sequence or not. We compute the possible common ratios
and we see they both result -3. If we use r=-3 and try to find the second term (y), then
y=2*(-3)=-6
Now we compute the third term: (-6)(-3)=18
Since we got the third term as given in the original sequence.
So y=-6
Tan x=opposite/adjacent
cot x=adjacent/opposite
so you need to inverse the fraction
tan x=.78 as a fraction is 78/100
-> inversed= 100/78=1.28=cot x
so it is the second option
Answer:
Step-by-step explanation:
So, the function, P(t), represents the number of cells after t hours.
This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.
C)
So, we are given that the quadratic curve of the trend is the function:
To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:
![\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5BP%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2-9.28t%2B16.43%5D)
Expand:
![P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]](https://tex.z-dn.net/?f=P%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B-9.28t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B16.43%5D)
Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:
![P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]](https://tex.z-dn.net/?f=P%27%28t%29%3D6.10%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D-9.28%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5D)
Differentiate. Use the power rule:
Simplify:
So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:
Multiply:
Subtract:
This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.
And we're done!
Answer:
C
Step-by-step explanation:
3/4 of 1000 is 750 and 1/5 of 750 is 150 so your answer is C
