This is what is in the middle of the second paragraph. That statement is correct.
I don't know that it is any simpler or not, but what they have done in the answer is rationalize the denominator. That means that the denominator is no longer under the square root sign.
To get that result, you multiply numerator and denominator by √F
When you do that, your get
This results in the middle answer.
4 people paint 8 walls in 60 minutes
1 person paints 8 walls in 240 minutes
1 person paints 1 wall in 30 minutes
5 people paint 1 wall in 6 minutes
5 people paint 4 walls in <em>24 minutes</em>
Answer:
1/5
Step-by-step explanation:
The Constraint is ; those who rode the bus, hence it is conditional because we aren't focused on students, only students who rode the bus.
Now we want the frequency of those who were late Given that they rode the bus : for these we have 3 students
Total number of students who rode the bus , total possible outcome = 15
Hence, the conditional frequency = (number who rode bus and were late / otal number who rode the bus)
Hence, we have ; 3 / 15 = 1 / 5
Answer: The area of the rectangle is: " 77 m² " .
__________________________________________________________
Note: The formula for the area, "A" of a rectangle:
→ A = L * w ;
in which:
A = "area (of rectangle)" ; [in units of "m² " ; that is: "square meters" ] ;
L = length = "(4 + w)" {in units of "meters (m)" } ;
w = width {in units of "meters (m)" } ;
_______________________________________________________
So; " A = L * w " ;
Substitute the known expression for the "length, L" ; & rewrite the formula for the given area of OUR area for the rectangle in OUR GIVEN PROBLEM:
→ A = (4 + w) * w '' ;
______________________________________________________
Note the formula for the perimeter, "P" ;
→ P = 2L + 2w ;
↔ 2L + 2w = P
→ 2L + 2w = 36 m ;
_____________________________________________________
We want to find the "area" , "A" :
_____________________________________________________
Using the formula for the "perimeter, "P" (of the rectangle) ; & given that the perimeter is: "36" (meters) ;
→ 2L + 2w = 36 ;
→ Let us plug in the values for "Length (L)" & "width (w)" ;
→ 2(w + 4) + 2w = 36 ;
So; (2*w) + (2*4) + 2w = 36 ; Solve for "w" ;
→ 2w + 8 + 2w = 36 ;
→ Combine the "like terms" :
+ 2w + 2w = 4w ;
→ And rewrite:
4w + 8 = 36 ;
Now, subtract "8" from EACH SIDE of the equation:
4w + 8 − 8 = 36 <span>− 8 ;
</span>
to get:
4w = 28 ;
Now, divide EACH SIDE of the equation by "4" ;
to isolate "w" on EACH SIDE of the equation ; & to solve for "w" ;
4w / 4 = 28 / 4 ;
→ w = 7 ; → The "width" of the rectangle is: " 7 m " .
Now, we can find the "length" of the rectangle:
The length, "L" , of the rectangle = 4 + w = 4 + 7 = 11 .
→ L = 11 . → The "length" of the rectangle is: " 11 m " .
___________________________________________________
Now, we can find the area, "A", of the rectangle.
A = L * w = 11 m * 7 m = " 77 m² " .
→ The area of the rectangle is: " 77 m² <span>" .
</span>__________________________________________________
To check our answer:
__________________________________________________
→ " P = 2L + 2w " ;
Given that "P = 36 m" ;
Plug in "36 m" (for "P") ; into the equation ;
and plug in our calculated values for
"length, L" (which is "11 m") ; & "width, w" (which is "7 m") ;
to see if the equation holds true ; that is, to see if both sides of the equation are equal ;
_______________________________________________________
→ 36 m = ? 2L + 2w ?? ;
→ 36 m = ? 2(11 m) + 2(7 m) ?? ;
→ 36 m = ? 22 m + 14 m ?? ;
→ 36 m = ? 36 m ? Yes!
__________________________________________________
