The equivalent algebraic monomial expression of the expression given as (-8a^5b)(3ab^4) is -24a^6b^5
<h3>How to determine an equivalent algebraic monomial expression?</h3>
The expression is given as:
(-8a^5b)(3ab^4)
Multiply -8 and 3
So, we have:
(-8a^5b)(3ab^4) = (-24a^5b)(ab^4)
Multiply a^5 and a (a^5 * a = a^6)
So, we have:
(-8a^5b)(3ab^4) = (-24a^6b)(b^4)
Multiply b and b^4
So, we have:
(-8a^5b)(3ab^4) = -24a^6b^5
Hence, the equivalent algebraic monomial expression of the expression given as (-8a^5b)(3ab^4) is -24a^6b^5
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Answer:
502.4ft^3
Step-by-step explanation:
Given data
Height= 10ft
radius= 4 ft
Hence the volume for the cylinder can be gotten as
v= πr^2h
v= 3.14*4^2*10
v=3.14*16*10
v=502.4ft^3
Therefore the volume of the cylinder is 502.4ft^3
Answer:
18.
Step-by-step explanation:
If there were 90 runners, and in the first half 2/5 of them dropped out, here's how we get those who continued the race in the second half.
1. Firstly we need to calculate how many of them dropped out:
2/5 of 90 = 90 ÷ 5 × 2
2/5 of 90 = 18 × 2
2/5 of 90 = 36
2. Now we have to take away the number of dropped-out runners <u>from</u><u> </u><u>the total number of runners from the beginning of the race</u>:
90 - 36 = 54
Now we are left with 54 runners, 2/3 of which dropped out before the finish line.
1. In order to get the number of runners that finished the race, we first need to see how many of them gave up in the second half:
2/3 of 54 = 54 ÷ 3 × 2
2/3 of 54 = 18 × 2
2/3 of 54 = 36
2. Now we just take away the number of runners that dropped out in the second half <u>from the number on the beginning of the half</u>:
54 - 36 = 18
<em>18 runners finished the race.</em>
The percent of runners between these two times is 47.72.
We find the z-scores associated with each end of this interval using the formula
z=(X-μ)/σ
For the lower end,
z=(4.11-4.41)/0.15 = -0.3/0.15 = -2
Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this score is 0.0228.
For the upper end:
z=(4.41-4.41)/0.15 = 0/0.15 = 0
Using a z-table we see that the area to the left of, less than, this score is 0.5000.
We want the area between these times, so we subtract:
0.5000-0.0228 = 0.4772
This corresponds with 47.72%.
