Answer: 
Step-by-step explanation:
Given
The inequality is 
adding both side 7
Multiply both sides by 
the shaded region in the figure indicates the solution set.
Answer:
10/21
Step-by-step explanation:
After the first balloon is gone, there is only 21 balloons left with 10 being yellow. Therefore, the is a 10/21 probability that it is yellow.
Answer:
It would take 19 hours and 36 minutes until there are 1040 bacteria present.
Step-by-step explanation:
Given that in a lab experiment, 610 bacteria are placed in a petri dish, and the conditions are such that the number of bacteria is able to double every 23 hours, to determine how long would it be, to the nearest tenth of an hour, until there are 1040 bacteria present, the following calculation must be performed:
610X = 1040
X = 1040/610
X = 1.7049
2 = 23
1.7049 = X
1.7049 x 23/2 = X
39.2131 / 2 = X
19.6 = X
100 = 60
60 = X
60 x 60/100 = X
36 = X
Therefore, it would take 19 hours and 36 minutes until there are 1040 bacteria present.
Answer:
Step-by-step explanation:
So we have the integral:
First, let's use substitution to get rid of the x/2. I'm going to use the variable y. So, let y be x/2. Thus:
Therefore, the integral is:
Now, as you had done, let's expand the tangent term. However, let's do it to the fourth. Thus:
Now, we can use a variation of the trigonometric identity:
So:
Substitute this into the integral. Note that tan^4(x) is the same as (tan^2(x))^2. Thus:
Now, we can use substitution. We will use it for sec(x). Recall what the derivative of secant is. Thus:
Substitute:
Expand the binomial:
Spilt the integral:
Factor out the constant multiple:
Reverse Power Rule:
Simplify:
Distribute the 2:
Substitute back secant for u:
And substitute back 1/2x for y. Therefore:
And, finally, C:
And we're done!
1) Julius and Olivia collect coins. {Qualitative statement}
2) Julius (J) has 338 coins in his collection. {Quantitative statement}
J = 338
3) The number of coins Olivia (V) has is 57 less than double the number of coins Julius has. {Quantitative statement}
V = 2*J - 57
V = 2*338 - 57
V = 619
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Olivia has 619 coins.
