584 is the total number of students in the school.
5/8 are in seventh grade and 3/8 are in eighth grade.
4/5 of the seventh graders participated in the track meet, so there were (4/5 · 5/8) · 584 students in the seventh grade participating in the track meet.
7/8 of the eighth graders participated, so there were (7/8 · 3/8) · 584 students in the eighth grade participating in the track meet.
So, all together, there were
(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 students from the school in the track meet.
Let's simplify as you asked:
(4/5 · 5/8) · 584 + (7/8 · 3/8) · 584 = [(4/5 · 5/8) + (7/8 · 3/8)] · 584 (distributive property - factoring)
= [20/40 + 21/64] · 584 (multiply fractions)
= (1/2 + 21/64) 584 (reduce the first fraction to lowest terms)
= (32/64 + 21/64) 584 (getting a common denominator)
= (53/64) 584 (combine/add the two fractions)
= 483.625 (multiply together)
All together, there were: 483.625 students in the meet.
Answer:
B. The functions f(x) and g(x) are reflections over the y-axis.
Step-by-step explanation:
From the information given the table appears as;
x f(x)=2^x g(x)=0.5^x
2 4 0.25
1 2 0.5
0 1 1
-1 0.5 2
-2 0.25 4
Plotting the two graphs to view the trends;
In the graph of f(x)=2^x against x you notice a curve with increasing positive slope.
In the graph of g(x)=0.5^x against x you notice a curve with a negative slope that is increasing.
In combining both graphs you notice that f(x) and g(x) are reflections over the y-axis.
Correct answer is ;The functions f(x) and g(x) are reflections over the y-axis.
First you'd substitute x= y-3 in the first equation.
10(y-3) -10y= 1
10y - 30 -10y= 1
The y's cancel each other out, so you're left with -30= 1. That means there's no solution :)
<span>7^2•3^2+(1+2)^0•3-4^2•1
= 49</span>•9 + 1•3 - 16<span>•1
= 441 + 3 - 16
= 428</span>
Answer: 11.775
If you plug in the radius (0.5 because the radius is half of the diameter) and the height to the formula for volume of a cylinder you will get pi•0.5 squared•15 which when solved is 11.775.
