Answer:
Step-by-step explanation:
This is permutation, since order matters. The formula for us is
₁₈P₅ = 
which simplifies to
₁₈P₅ = 
The factorial of 13 cancels out on the top and bottom leaving you with
₁₈P₅ = 18 × 17 × 16 × 15 × 14
which comes to 1,028,160 ways
Another way to look at it is: the first 5 people of 18 finish and the others you don't care about. Once the first place person is first, there are only 4 of the 18 left to finish in second place. Then there are only 3 left to finish in third place, etc. So if we use that reasoning, we don't even need to use the formula, we can just say
18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.
Answer:
13 over 3
Step-by-step explanation:
Hi Jakeyriabryant! I hope you’re fine!
I hope I have understood the problem well.
If so, what the exercise raises is the following equality:
(x-1) / 5 = 2/3
From this equation you must clear the "x".
First, we pass the 5 that is dividing on the side of the x, to the other side and passes multiplying
(X – 1) / 5 = 2/3
(X – 1) = (2/3)*5
X – 1 = 10/3
Then we pass the one that is subtracting from the side of the x, to the other side and passes adding
X = 10/3 + 1
Remember that to add or subtract fractions they must have the same denominator or a common denominator (in this case we can write 1 as fraction 3/3). Then,
X = 10/3 + 3/3
X = 13/3
I hope I've been helpful!
Regards!
Answer:
The height of rectangle is 5 inches
Step-by-step explanation:
<u><em>The correct question is</em></u>
A rectangle is drawn so the width is 7 inches longer than the height. If the rectangle’s diagonal measurement is 13 inches, Find the height
Let
x -----> the width of the rectangle in inches
y ----> the height of the rectangle in inches
d ---> diagonal measurement of the rectangle in inches
we know that
Applying the Pythagorean Theorem
we have
so
----> equation A
---> equation B
substitute equation B in equation A
solve for y
solve the quadratic equation by graphing
using a graphing tool
The solution is y=5
see the attached figure
therefore
The height of rectangle is 5 inches
Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
8x8x8 or 8 with the power of 3
