Answer:
Which is the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively? 204.
Step-by-step explanation:
Have a great summer.
Answer:
32,768.
Step-by-step explanation:
There are 12 lots of 5 minutes in 1 hour.
The equation is 8*(2^12)
= 8 * 4096
= 32,768.
Answer:
Step-by-step explanation:
First let us consider how we calculate the mean test mark in the first place, we add up the individual test marks of the entire class to give the total test mark then we divide by the number of students. This means we need two pieces of information to calculate the boys' mean mark, the total boys' mark and the number of boys. We already know the number of boys but how do we work out the total boys' test mark? If we can work out the total class mark and total girls' mark we can find the total boys' mark by subtracting the total girls' mark from the total class mark. To do this we can work backwards to find the total mark for the whole class by taking the mean mark and multiplying it by the number of students, this gives us Total Class Mark = Mean Class Mark x Number of Students = 60 x 30 = 1800. We can do the same for the girls' mark giving us Total Girls' Mark = Mean Girls' Mark x Number of Girls = 54 x 20 = 1080. This then gives us the total boys mark as Total Boys' Mark = Total Class Mark - Total Girls' Mark = 1800 - 1080 = 720. Now we have everything we need to work out the boys' mean mark and we get Boys' Mean Mark = Total Boys' Mark/Number of Boys = 720/10 = 72.
Answer:
17. y=1/2x+5
18. y=-2x+15
19. y=2x-7
Step-by-step explanation:
Number 17.
(4,7); parallel to y=1/2x-1
You know that lines that are parallel to each other have the same slope, so the slope is 1/2x.
1. Use the point-slope formula to solve for the slope-intercept equation.
y-y1=m(x-x1)
m= 1/2
x= 4
y= 7
y-7= 1/2(x-4)
y-7= 1/2x-2
y=1/2x+5
Number 18.
(4,7); perpendicular to y=1/2x-1
You know that lines that are perpendicular to each other have the opposite reciprocal slope, so the slope is -2.
1. Use the point-slope formula to solve for the slope-intercept equation.
y-y1=m(x-x1)
m= -2
x= 4
y= 7
y-7=-2(x-4)
y-7=-2x+8
y=-2x+15
Number 19.
f(3)=-1
f(4)=1
To write a linear equation, first find the slope with the slope formula.
x1= 3
y1= -1
x2= 4
y2=1
(y2-y1)/(x2-x1)
(1-(-1))/(4-3)
2/1
m=2
Use the point-slope formula and solve for the slope-intercept equation.
y-y1=m(x-x1)
y-1=2(x-4)
y-1=2x-8
y=2x-7
5. x = 9
6. x = 8
Just solve by simplifying both sides of the equation and then isolating the variable.
