Last Tuesday was silly hat day at Toby's school. 74 students wore a silly hat and 666 students did not. What percentage of the s
1 answer:
Answer:
10%
Step-by-step explanation:
The total population of students will be equal to the sum of both those who wore the silly hat and those who didn't hence
Total students= 74+666=740
Number of students who wore silly hat is given as 74 hence when expressed as a percentage of the total students' population we get that
percentage of the students wore a silly hat=
Therefore, 10% of students wore a silly hat last Tuesday
You might be interested in
Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.
Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,
<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)
These so-called first differences are
<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18
<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26
<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34
<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42
Now consider this sequence of differences,
18, 26, 34, 42, …
and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:
26 - 18 = 8
34 - 26 = 8
42 - 34 = 8
and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule
<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10
for <em>n</em> ≥ 1.
So we have
<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10
or, replacing <em>n</em> + 1 with <em>n</em>,
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2
We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:
<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2
<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2
<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2
<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2
and so on. The pattern should be clear; we end up with
<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2
The middle group is the sum,
so that
<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)
<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3
Answer:
The new amount paid to mechanics per after by new owner is $ 19 Answer
Step-by-step explanation:
Given as :
The amount paid to mechanics initially = $ 20 per hour
Now, The new owner paid less at the rate = 5%
Let the amount paid to the mechanics after 5 % less = x per hour
So, According to question
The new amount paid to mechanics per hour = initial amount paid per hour × ( 1 - )
or, The new amount paid to mechanics per hour = $ 20 × ( 1 - )
I.e The new amount paid to mechanics per hour = $ 20 × 0.95
∴ The new amount paid to mechanics per hour = $ 19
Hence The new amount paid to mechanics per after by new owner is $ 19 Answer