Answer:
Cycling Speed is 15km/hr
Step-by-step explanation:
Let the cycling speed of Peter be xkm/hr
His walking speed is (x-10km/hr)
Distance cycling is 2/3 x 30 = 20km
Distance walking 1/3 x 30 = 10km
Time taken in cycling = distance/ speed
Time = 20/x
This gives 20/x km/hr
Time walking is 10 / (x-10)
= 10/x-10) hrs
Total time = (20/x + 10/x+10)
Therefore 10/x+10/x-10 = 10/3
60(x-10)+30(x)=10x(x-10)
10x² - 190x+600=0
x²-19+60=0
x=<u>19±√361-240</u>
2
x=15 0r x =4
His cycling speed is 4
Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
Answer:30 and 7
Step-by-step explanation:
Answer: The probability in (b) has higher probability than the probability in (a).
Explanation:
Since we're computing for the probability of the sample mean, we consider the z-score and the standard deviation of the sampling distribution. Recall that the standard deviation of the sampling distribution approximately the quotient of the population standard deviation and the square root of the sample size.
So, if the sample size higher, the standard deviation of the sampling distribution is lower. Since the sample size in (b) is higher, the standard deviation of the sampling distribution in (b) is lower.
Moreover, since the mean of the sampling distribution is the same as the population mean, the lower the standard deviation, the wider the range of z-scores. Because the standard deviation in (b) is lower, it has a wider range of z-scores.
Note that in a normal distribution, if the probability has wider range of z-scores, it has a higher probability. Therefore, the probability in (b) has higher probability than the probability in (a) because it has wider range of z-scores than the probability in (a).
Answer:
m>11
Step-by-step explanation:
2(m+3)<-5+3m
2(m+3)>3m-5
2m+6>3m-5
6<3m-5-2m
6<m-5
6+5<m
11<m
m>11
