To find the average rate of change, use the following formula:
a and b represent the values of the interval:
Simplify the original equation by combining like terms:
Plug the interval values into the f(x) equation:
Plug in these values into the average rate of change formula:
The average rate of change over this interval is
-11.
Answer:
n < -6
Step-by-step explanation:
-4n>24
Divide each side by -4, remembering to flip the inequality
-4n/-4 < 24/-4
n < -6
Answer:
The mean change of the stock price of those 5 days is $1.34.
Step-by-step explanation:
First let's list the differences then find the mean.
1.20, 2.30, 1.00, 1.80, 0.40
Now we add up all of the numbers and divide by how many numbers there are.
Mean = 1.34
The mean change of the stock price of those 5 days is $1.34.
Answer:
1992.50 mL; 825 mL
Step-by-step explanation:
Given that :
Capacity of bottles in the attachment = 2L
Amount of soft drink in bottle 1 = 7.50mL
Amount of soft drink in bottle 2 = 1175mL
Converting liter milliliter
1Litre = 1000 milliliters
Therefore 2Litres = 2000 milliliters
Capacity each of bottle = 2000 milliliters
Volume of drink required to completely fill bottle 1:
2000mL - 7.50mL = 1992.50 mL
Volume of drink required to completely fill bottle 2:
2000mL - 1175mL = 825 mL
<span>(a) This is a binomial
experiment since there are only two possible results for each data point: a flight is either on time (p = 80% = 0.8) or late (q = 1 - p = 1 - 0.8 = 0.2).
(b) Using the formula:</span><span>
P(r out of n) = (nCr)(p^r)(q^(n-r)), where n = 10 flights, r = the number of flights that arrive on time:
P(7/10) = (10C7)(0.8)^7 (0.2)^(10 - 7) = 0.2013
Therefore, there is a 0.2013 chance that exactly 7 of 10 flights will arrive on time.
(c) Fewer
than 7 flights are on time means that we must add up the probabilities for P(0/10) up to P(6/10).
Following the same formula (this can be done using a summation on a calculator, or using Excel, to make things faster):
P(0/10) + P(1/10) + ... + P(6/10) = 0.1209
This means that there is a 0.1209 chance that less than 7 flights will be on time.
(d) The probability that at least 7 flights are on time is the exact opposite of part (c), where less than 7 flights are on time. So instead of calculating each formula from scratch, we can simply subtract the answer in part (c) from 1.
1 - 0.1209 = 0.8791.
So there is a 0.8791 chance that at least 7 flights arrive on time.
(e) For this, we must add up P(5/10) + P(6/10) + P(7/10), which gives us
0.0264 + 0.0881 + 0.2013 = 0.3158, so the probability that between 5 to 7 flights arrive on time is 0.3158.
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