The answer is this :) hope I helped
Step-by-step explanation:
The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms. Example: 3 + 7 + 11 + 15 + ··· + 99 has a1 = 3 and d = 4.
Answer:
The width of the frame is 0.0746 meters
Step-by-step explanation:
We are told that after the frame has been attached to the solar collector, the area that is left exposed is
. As we see in the figure, the dimensions of this area are
and 
where
is the width of the frame.
The product of these dimensions must equal the exposed area:

Now since
and
we have:

we expand this and solve for x using the quadratic formula:


we get two solutions:


We take the second solution i.e
, because first one gives a width larger than the dimensions of the solar collector which cannot be possible.
Thus the width of the frame is 0.0746 meters.
Answer:
The Perimeter of the Figure to the nearest tenth is 18.7 units
Step-by-step explanation:
Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them. Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them. Perimeter on Figure 1:The Perimeter of a Triangle is given by the Sum of the three sides as:
AT=a+b+c
Perimeter on Sketched Figure:The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together. Now since the figure is on a graph paper, we can read of the size of some sides, thus the left side of the triangle is units and the base of the triangle is also units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°). Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle. So here we can say that: where is the hypotenuse and our unknown side. So plugging in values and solving for we have: units.
Perimeter on Figure 2:
The Perimeter of the Rectangle is given by:
Ar=2(w+l)
Answer:
5/12
Step-by-step explanation:
Assuming the each number is equally likely
1,2,3,4,5,6,7,8,9,10,11,12
There are 12 numbers on the spinner
Number less than or equal to 5: 1,2,3,4,5
There are 5 choices
P ( # < = 5) = Number less than or equal to 5/ total
=5/12