3 5/8 x 2 1/2 x 4 = 36 1/4
Answer:
25
Step-by-step explanation:
It takes 1/5 of a gallon of water to fill up a package of water balloon
There are 5 gallons of water in total
Therefore the number of packs of balloons that can be filled can be calculated as follows
= 5 ÷ 1/5
= 5 × 5/1
= 25
Hence 25 packs of the balloon can be filled
79, 79, 91, 91, 91, 91, 98, 98, 118, 130, what is the mean median and mode?
Rus_ich [418]
To get the mean you add the numbers and divide by how many numbers there are and then you would get: 784 divided by 10 which would be 78.4 for the mean
Answer:
121 degrees
Step-by-step explanation:
The "arc length" formula is s = rФ, where Ф represents the central angle in radians (not degrees).
Here r = 18 ft and s = 38 ft, and so:
38 ft
s = rФ becomes Ф = ------------ = 2.111 radians
18 ft
which, in degrees, is:
2.111 rad 180 deg
------------- * --------------- = 121 degrees, to the nearest degree
1 3.142
<h3>
Answer: x = 1/2</h3>
=========================================================
Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
---------------------
Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
