I set it up as a ratio with hours on the top and the fraction of the job on the bottom. It looks like this: 5/(2/3) / x/1, because 1 is the whole job if 2/3 is only a fraction of it. Cross multiplying gives you 2/3x = 5. Solving for x gives you that it will take 7.5 hours to complete a whole job if it takes 5 hours to complete 2/3 of it.
Answer:
1
= -----------
6(x + 7)
Step-by-step explanation:
3x - 21 x^2 - 49
----------- ÷ -------------
18x - 18 x - 1
3x - 21 x - 1
----------- × -------------
18x - 18 x^2 - 49
Factor the top left:
3x - 21 = 3(x - 7)
Factor the bottom left:
18x - 18 = 18(x - 1)
Factor the new bottom right:
x^2 - 49 = (x + 7)(x - 7)
Multiply and simplify the faction:
3(x - 7) x - 1
----------- × -----------------
18(x - 1) (x + 7)(x - 7)
1
= -------------
6(x + 7)
To more easily graph this, convert it to slope-intercept form (y = mx + b, where m is the slope and b is the y-intercept):
x - y = 1
-y = -x + 1
y = x - 1
The slope is 1 and the y-intercept is -1. To graph this, plot the point (0, -1) and count 1 unit down and 1 unit to the right. Do this once more, connect the points, and you have your line.
Hope this helps.
Answer:
a. 81.5%
Step-by-step explanation:
The z-score for 400 is ...
Z = (X -μ)/σ = (400 -500)/100 = -1
The z-score for 700 is ...
Z = (700 -500)/100 = 2
The empirical rule tells you that 68% of the distribution is within ±1σ of the mean, and 95% is within ±2σ of the mean. Half of that first number is in the range Z = -1 to 0, and half that second number is in the range Z = 0 to +2. So, the probability you want is ...
(1/2)(68%) + (1/2)(95%) = 81.5% . . . . matches choice A
Answer:
2
Step-by-step explanation:
Slope (m) is equal to the change in the y-coordinate divided by the change in the x-coordinate.
The change in y= 6
The change in x= 3
6/3 =2
