I have a feeling I've seen this question before
anyway
A=number of hours that plan A is
B=number of hours that plan B is
so
on wednesday, 7hr
5A and 6B so
5A+6B=7
on thursday, 3 hours
3 of A and 2 of B
3A+2B=3
so we gots
5A+6B=7
3A+2B=3
elimination
eliminate B's
multiply 2nd equation by -3 and add to 1st equation
5A+6B=7
<u>-9A-6B=-9 +</u>
-4A+0B=-2
-4A=-2
divide both sides by -4
A=1/2
A=0.5
sub back
3A+2B=3
3(0.5)+2B=3
1.5+2B=3
minus 1.5 both sides
2B=1.5
divide by 2 both sides
B=0.75
plan A lasts 1/2 hour or 0.5 hour or 30 mins
plan B lasts 3/4 hour or 0.75 hour or 45 mins
Answer:
The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is (-∞,2] ∪ [8,∞)
Step-by-step explanation:
When solving absolute value inequalities, there are two cases to consider.
Case 1: The expression within the absolute value symbols is positive.
Case 2: The expression within the absolute value symbols is negative.
The solution is the intersection of the solutions of these two cases.
In other words, for any real numbers a and b,
- if |a|> b then a>b or a<-b
- if |a|< b then a<b or a>-b
So, being |3x-9|≤15
Solving: 3x-9 ≤ 15
3x ≤15 + 9
3x ≤24
x ≤24÷3
x≤8
or 3x-9 ≥ -15
3x ≥-15 +9
3x ≥-6
x ≥ (-6)÷3
x ≥ -2
The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]
So, being |2x-3|≥5
Solving: 2x-3 ≥ 5
2x ≥ 5 + 3
2x ≥8
x ≥8÷2
x≥8
or 2x-3 ≤ -5
2x ≤-5 +3
2x ≤-2
x ≤ (-2)÷2
x ≤ -2
Expressing the solution as an interval: (-∞,2] ∪ [8,∞)
Answer:
15.9% of babies are born with birth weight under 6.3 pounds.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 6.8 pounds
Standard Deviation, σ = 0.5
We are given that the distribution of birth weights is a bell shaped distribution that is a normal distribution.
Formula:
P(birth weight under 6.3 pounds)
P(x < 6.3)
Calculation the value from standard normal z table, we have,
15.9% of babies are born with birth weight under 6.3 pounds.
We start at 62 Fahrenheit. And every hour we drop two degrees. We want to know how long it took for the temperature to drop to 40 Fahrenheit.
If one hour passed, then the temperature dropped two degrees.
If two hours passed, then the temperature dropped 4 degrees.
See the pattern? We can define this as 2h. Where h represents time in hours.
We subtract 2h from 62.
We can write this as a function. F(h) = 62 - 2h.
Where F is the temperature in Fahrenheit. And h is the hour(s).
Now that we have the formula, let's plug in the value 40 Fahrenheit to see how long it took for the temperature to drop to 40 degrees.
40 = 62 - 2h
Subtract 62 from each side
-22 = -2h
Divide both sides by 2
h = 11
So, it took 11 hours for the temperature to drop to 40 Fahrenheit.
Answer:
The % increase is 7.179 but see the remark I made below. What I have given and what it could be is a rounding error. Less than 2 dollars error is not much when you are calculating something for someone just to show them how to do it.
Step-by-step explanation:
242,555 * x/100 = 259,970 Multiply by 100
242,555 * x = 259970 * 100
242,555 * x = 25997000 Divide by 242555
x = 24997000/242444
x = 107.179
That's the total increase.
What you want is 7.179%
If you take 7.179% of 242,555 and add it onto 242555 you should get 259,970
7.1797/100 * 242555 = 17413.02
17413.02 + 242555 = 259968.02
Why isn't it exact. I'm out just about 2 whole dollars. The reason is that the % isn't exact. It's only out to 3 decimal places which apparently is not enough. You can go over my numbers if you want more exactness us use something that is rounded to 7.180 if you like.
