Answer:
Step-by-steplanation:
Add: 1
2
+ 2
5
= 1 · 5
2 · 5
+ 2 · 2
5 · 2
= 5
10
+ 4
10
= 5 + 4
10
= 9
10
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(2, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the next intermediate step the fraction result cannot be further simplified by cancelling.
In words - one half plus two fifths = nine tenths.
Conversion a mixed number 6 2
7
to a improper fraction: 6 2/7 = 6 2
7
= 6 · 7 + 2
7
= 42 + 2
7
= 44
7
To find new numerator:
a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7
7
= 42
7
b) Add the answer from previous step 42 to the numerator 2. New numerator is 42 + 2 = 44
c) Write previous answer (new numerator 44) over the denominator 7.
Six and two sevenths is forty-four sevenths
Add: the result of step No. 1 + 44
7
= 9
10
+ 44
7
= 9 · 7
10 · 7
+ 44 · 10
7 · 10
= 63
70
+ 440
70
= 63 + 440
70
= 503
70
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(10, 7) = 70. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 7 = 70. In the next intermediate step the fraction result cannot be further simplified by cancelling.
In words - nine tenths plus forty-four sevenths = five hundred three seventieths.
1/9 + 1/2 = 1/x
Let x = length of time it will take both hoses to work together
Multiply both sides by 18x.
2x + 9x = 18
10x = 18
x = 18/10
x = 9/5
x = 1.8 hours
In other words, if both hoses work together, the pool can be filled in 1 hour and 48 minutes.
To evaluate the probability that a randomly selected day will be between 28 and 34 minutes we proceed as follows:
P(28<x<34)
First we evaluate the z-score for the above values:
z=(x-σ)/μ
μ=26.7
σ=5.1
when:
x=28
z=(28-26.7)/5.1
z=0.26
P(z<0.26)=0.6026
when x=34
z=(34-26.7)/5.1
z=1.43
P(z<1.43)=0.9236
hence:
P(28<x<34)=0.9236-0.6026=0.321~32.1%
Measuring tool or observer of force being applied to the ball
