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iragen [17]
3 years ago
6

Liam is paid $25/hr at full rate, and $18/hr at a reduced rate. The hours of work are paid at a ratio of 3:1, full rate : reduce

d rate. For example, if he worked 4 hours, he would be paid 3 hours at full rate and 1 hour at reduced rate. Calculate his pay for 6 hours of work.
Mathematics
1 answer:
Lyrx [107]3 years ago
8 0

Answer:

4h30min full rate and 1h30 min reduced rate

So, for 6h of work Liam is owed $ 9×25/2+3×18/2=225/2+32=144.5

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.
Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have S_1=3\times2^{1-1}+2(-1)^1=3-2=1, which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}

and

S_k=3\times2^{k-1}+2(-1)^k

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}

From the given recurrence, we know

S_{k+1}=S_k+2S_{k-1}

so that

S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)

S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}

S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)

S_{k+1}=3\times2^k-2(-1)^k

S_{k+1}=3\times2^k+2(-1)(-1)^k

\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}

which is what we needed. QED

6 0
3 years ago
Does a kilogram have more or less mass than a gram?
maks197457 [2]
More, a kilogram is 1000x the mass of a gram
6 0
3 years ago
Write the prime factorization of each number in exponential notation
n200080 [17]

18225|5\\.\ 3645|5\\.\ \ 729|3\\.\ \ 243|3\\.\ \ \ 81|3\\.\ \ \ 27|3\\.\ \ \ \ 9|3\\.\ \ \ \ 3|3\\.\ \ \ \ 1|\\\\18,225=5\cdot5\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3=5^2\cdot3^6

8 0
3 years ago
About 7% of the population has a particular genetic mutation. 400 people are randomly selected. Find the standard deviation for
Deffense [45]

Answer:

5.10 people

Step-by-step explanation:

Calculation to Find the standard deviation for the number of people with the genetic mutation

Using this formula

Standard deviation = √ ( n * p * q)

Where,

n = 400

p = .07

q = 100%-7% = 93% or .93

Let plug in the formula

Standard deviation =√400*07*.93

Standard deviation =√26.04

Standard deviation = 5.10 people

Therefore the standard deviation for the number of people with the genetic mutation is 5.10 people.

5 0
3 years ago
What is the rule for 0.7, 1.7, 2.7, 3.7
larisa86 [58]
Add 1

0.7+1=1.7

1.7+1= 2.7

etc., etc.
5 0
4 years ago
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