Hello!
To solve this, first write two equations. We are given two facts about the situation, so we can write the equations accordingly.
Say the length of the rectangle is l, and the width is w.
<u>The length of a rectangle is 9 inches more than twice its width:</u> 2w + 9 = l, as you're adding 9 to two times the width.
<u>The perimeter of the rectangle is 48 inches:</u> The equation for perimeter is 2l + 2w, so we can just use that in this case to make the equation - 2l + 2w = 48
Now, set up the system of equations.
Now, we can already use substitution to solve. We get from one of the equations that l = 2w + 9, so we can substitute 2w + 9 for l in the other equation, and then solve for w.
2l + 2w = 48
2 (2w + 9) + 2w = 48
4w + 18 + 2w = 48
6w = 30
w = 5
We know one of our variables now. Now, all that's left to do is substitute 5 for w in one of the original equations to solve for l.
2w + 9 = l
2 (5) + 9 = l
10 + 9 = l
19 = l
Therefore, we now have our dimensions. The length of the rectangle is 19 inches, and the width is 5.
Hope this helps!
Answer:
The median score of class A is 73
The interquartile range of class B is 8
The difference of the medians of class A and class B is 9
the interquartile range of either data set should be 8 because that is what b was.
Step-by-step explanation:
The interquartile range is the difference between the upper quartile and the lower quartile. In example 1, the IQR = Q3 – Q1 = 87 - 52 = 35. The IQR is a very useful measurement. It is useful because it is less influenced by extreme values as it limits the range to the middle 50% of the values.
Answer:
a) 72.25sec
b) 6.25secs
c) after 10.5secs and 2 secs
Step-by-step explanation:
Given the height reached by the rocket expressed as;
s(t)= -4t^2 + 50t - 84
At maximum height, the velocity of the rocket is zero i.e ds/dt = 0
ds/dt = -8t + 50
0 = -8t + 50
8t = 50
t = 50/8
t = 6.25secs
Hence it will reach the maximum height after 6.25secs
To get the maximum height, you will substitute t - 6.25s into the given expression
s(t)= -4t^2 + 50t - 84
s(6.25) = -4(6.25)^2 + 50(6.25) - 84
s(6.25) = -156.25 + 312.5 - 84
s(6.25) = 72.25feet
Hence the maximum height reached by the rocket is 72.25feet
The rocket will reach the ground when s(t) = 0
Substitute into the expression
s(t)= -4t^2 + 50t - 84
0 = -4t^2 + 50t - 84
4t^2 - 50t + 84 = 0
2t^2 - 25t + 42 = 0
2t^2 - 4t - 21t + 42 = 0
2t(t-2)-21(t-2) = 0
(2t - 21) (t - 2) = 0
2t - 21 = 0 and t - 2 = 0
2t = 21 and t = 2
t = 10.5 and 2
Hence the time the rocket will reach the ground are after 10.5secs and 2 secs
Answer:
I think a or C
Step-by-step explanation:
1/2 × 1/2
1/4 or 25%
probability of tails both times
