jackie brought 3/4 gallon of ice tea to a party
bill brought 7/8 of a gallon of ice tea to party.
To find total gallons of ice tea they have, we add the fractions
To add two fractions , we make the denominators same
Now add the numerators
So, They have gallons of ice tea.
Step-by-step explanation:
Ariana and Mackenzie exercised for 20 minutes more than Brinley and Seth.
x = Seth exercise minutes
Ariana minutes = 3x
Brinley minutes = 3x - 17
Mackenzie minutes = 1/2 × (3x - 17)
so, in total we have
3x + ½(3x - 17) = x + (3x - 17) + 20
statement 1 is true.
6x + (3x - 17) = 2x + 2(3x - 17) + 40
6x + 3x - 17 = 2x + 6x - 34 + 40
9x - 17 = 8x + 6
x = 23
statement 2 is false.
Brinley and Seth exercised together for
x + 3x - 17 = 23 + 3×23 - 17 = 4×23 - 17 = 75 minutes
statement 3 is false.
Mackenzie exercised for
½(3x - 17) = ½(3×23 - 17) = ½(69 - 17) = ½×52 = 26 minutes
statement 4 is true.
Answer:
£3.25
Step-by-step explanation:
You would add £1.25 and £00.50 which is £1.75 then you would do £5.00-£1.75 which is £3.25
Given:
(i) The measurements of the data in increasing order are 4,5,6,8,10 and X
(ii) Total number of observations (n) = 6 which is even
(iii) Median = (6 / 7)× Arithmetic Mean
Concept: If there are even number of observations then the median can be calculated as
Median = [(n /2)the term + {(n/2)+1} term] / 2
Here, n = 6,
Median = [(6 /2)the term + {(6/2)+1} term] / 2 = [ 3rd term + 4th term] /2
Median = [ 6 + 8] /2 = 7
Arithmetic Mean (AM) = Sum of the observation / Number of observations
or, = [ 4 + 5 + 6 + 8 + 10 + X] / 6
or, = [33 + X] / 6
According to the problem,
Median = (6 / 7)× AM
or, 7 = ( 6 / 7 ) × ( 33 + X) /6
or, 49 = 33 + X
or, X = 16
Hence, the value of X will 16
Notice that
(1 - <em>x</em>)⁵ (1 + 1/<em>x</em>)⁵ = ((1 - <em>x</em>) (1 + 1/<em>x</em>))⁵ = (1 - <em>x</em> + 1/<em>x</em> - 1)⁵ = (1/<em>x</em> - <em>x</em>)⁵
Recall the binomial theorem:
Let <em>a</em> = 1/<em>x</em>, <em>b</em> = -<em>x</em>, and <em>n</em> = 5. Then
We get an <em>x</em> ³ term for
2<em>k</em> - 5 = 3 ==> 2<em>k</em> = 8 ==> <em>k</em> = 4
so that the coefficient would be