Step 1
find the volume of sand
volume of sand=8*20*3------------>Volume of sand=480 in³
Volume of sand in the new terrarium=10*24*h
where
h------------> is the <span>deep in the new terrarium
</span>remember that
the volume of sand is the same
so
10*24*h=480----------> h=480/(10*24)-----------> h=2 in
the answer is 2 in
Answer:
A. 4x-10
Step-by-step explanation:
We see that this is a rectangle. To find the perimeter, we do L+W+L+W. So in this case, we can do (x+2)+(x-7)+(x+2)+(x-7). We can also simplify this to 2(x+2)+2(x-7)
Combine like terms now.
Simplify this to:
2x+4+2x-14
Simplify further:
4x-10
Answer:
Step-by-step explanation:
1) Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
2) Solution to the problem
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
For what proportion of groups will at most two of the households have cable tv?
So we want to find this probability:
Answer:
These two triangles are <em>similar triangles. </em>This means that their side lengths are proportional to each other.
Thus, making line segment EC equal to "x", and BC equal to "y" we can write:
8/y = 28/(10+y)
The next step is to get rid of the fractions, which can be done by cross multiplying.
So we have:
8(10+y) = 28(y)
After distribution and some simplification, you should get the value of y.
80+8y = 28y
80 = 20y
80/20 = 20y/20
4 = y
y = 4
Knowing that y = BC, and y = 4, it is clear that BC = 4.
Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)
In our case, a and b are 8 and 4 (the order doesn't really matter here).
So we have: 8^2 + 4^2 = c^2
64 + 16 = c^2
80 = c^2
c = sqrt 80
c = 4 sqrt 5
And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.
Hope this helps!
Answer:
yes it is the 10th term in the series
Step-by-step explanation:
The nth term of a geometric sequence is
= a₁ 
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = 
= 
= 2 , then
= 7 
Equate to 3584 and solve for n
7 = 3584 ( divide both sides by 7 )
= 512 , that is
= 
Since the bases on both sides are equal, both 2 , then equate the exponents
n - 1 = 9 ( add 1 to both sides )
n = 10
3584 is the 10th term in the series
