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2 years ago

6. Matthew is planning to build a right triangular

Mathematics

1 answer:

saul85 [17]2 years ago

8 0

The answer to this question will be B

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Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the in

Sonja [21]

Answer with step-by-step explanation:

We are given that the recurrence relation

$f_n=5f_{n-4}+3f_{n-5}$

for n=5,6,7,..

Initial condition

$f_0=0,f_1=1,f_2=1,f_3=2,f_4=3$

We have to show that Fibonacci numbers satisfies the recurrence relation.

The recurrence relation of Fibonacci numbers

$f_n=f_{n-1}+f_{n-2}$ , $f_0=0,f_1=1$

Apply this

$f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}$

$f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}$

$f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}$

Substitute n=2

$f_2=f_1+f_0=1+0=1$

$f_3=f_2+f_1=1+1=2$

$f_4=f_3+f_2=2+1=3$

Hence, the Fibonacci numbers satisfied the given recurrence relation .

Now, we have to show that $f_{5n}$ is divisible by 5 for n=1,2,3,..

Now replace n by 5n

$f_{5n}=5f_{5n-4}+3f_{5n-5}$

Apply induction

Substitute n=1

$f_5=5f_1+3f_0=5+0=5$

It is true for n=1

Suppose it is true for n=k

$f_{5k}=5f_{5k-4}+3f_{5k-5}$ is divisible 5

Let $f_{5k}=5q$

Now, we shall prove that for n=k+1 is true

$f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)$

$f_{5k+5}=5(f_{5k+1}+3q)$

It is multiple of 5 .Therefore, it is divisible by 5.

It is true for n=k+1

Hence, the $f_{5n}$ is divisible by 5 for n=1,2,3,..

8 0

2 years ago

Michelle receives 32K per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retireme

ryzh [129]

Answer:

The annual salary of Michelle including benefits = $48, 440

Step-by-step explanation:

<em>Since, you have not specified the table to show the value of each benefit.</em>

<em>So, I am assuming this table as the reference table to show the value of each benefit.</em>

<h3 /><h3><u>Benefits Value Table:</u></h3>

<h2> Benefit Value</h2>

Health Insurance $7,550

Paid Holidays $660

Retirement Contributions $4,500

Paid Vacation $1,230

Uniform Supplied $2,500

Here are the benefits details from the table:

Michelle receiving per year without benefits = $32000

Health Insurance as benefit = $7,550

Paid Holidays as benefit = $660

Retirement Contributions as benefit = $4,500

Paid Vacation as benefit = $1,230

Uniform Supplied as benefit = $2,500

So, the amount she gets from benefits = $7,550 + $660 + $4,500 + $1,230 + $2,500 = $16,440

So, the annual salary, including benefits could be calculated as:

Michelle receiving per year without benefits = $32000

The amount Michelle gets from benefits = $16,440

Michelle have annual salary including benefits = $32000 + $16,440

= $48, 440

Hence, the annual salary of Michelle including benefits = $48, 440

Keywords: calculation, salary, benefits, saving

Learn more about salary calculation from brainly.com/question/5715627

#learnwithBrainly

8 0

1 year ago

A prticular type of tennis racket comes in a midsize versionand an oversize version. sixty percent of all customers at acertain

svetlana [45]

Answer:

a) P(x≥6)=0.633

b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).

c) P(x≤7)=0.8328

Step-by-step explanation:

a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).

The number of trials is n=10, as they select 10 randomly customers.

We have to calculate the probability that at least 6 out of 10 prefer the oversize version.

This can be calculated using the binomial expression:

$P(x\geq6)=\sum_{k=6}^{10}P(k)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\geq6)=0.2508+0.215+0.1209+0.0403+0.006=0.633$

b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:

$\sigma=\sqrt{np(1-p)}=\sqrt{10*0.6*0.4}=\sqrt{2.4}=1.55$

The mean of this distribution is:

$\mu=np=10*0.6=6$

As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.

$LL=\mu-\sigma=6-1.55=4.45\approx4\\\\UL=\mu+\sigma=6+1.55=7.55\approx8$

The probability of having between 4 and 8 customers choosing the oversize version is:

$P(4\leq x\leq 8)=\sum_{k=4}^8P(k)=P(4)+P(5)+P(6)+P(7)+P(8)\\\\\\P(x=4) = \binom{10}{4} p^{4}q^{6}=210*0.1296*0.0041=0.1115\\\\P(x=5) = \binom{10}{5} p^{5}q^{5}=252*0.0778*0.0102=0.2007\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\\\P(4\leq x\leq 8)=0.1115+0.2007+0.2508+0.215+0.1209=0.8989$

c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.

Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.

$P(x\leq7)=1-\sum_{k=8}^{10}P(k)=1-(P(8)+P(9)+P(10))\\\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\leq 7)=1-(0.1209+0.0403+0.006)=1-0.1672=0.8328$

7 0

2 years ago

PLEASE HELP NEED TO PASS!!!!!!!!The graph shows the relationship between the number of ounces of cereal in a box and the price o

Sergio039 [100]

For this case, the first thing we must do is observe the relationship between the variables:

Independent variable: Weight of the box (ounces)

Dependent variable: Price of the box ($)

Observing the behavior between both variables, we see that there is no specific relationship between the increase or decrease in the weight of the box and the increase or decrease in the price.

Therefore, there is no correlation between the variables.

Answer:

the correlation between the weight and price of a box of cereal is:

none

4 0

2 years ago

Read 2 more answers

Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?

Tema [17]

Your x values are 1.24 and -0.404.
First you need to make the equation equal 0, and you can do this simply by subtracting 5x, so you get
6x² - 3 - 5x = 0
The quadratic formula is (-b +- √b² - 4ac)/2a, where a is the x², b is the x, and c is the value. This means we can just substitute it in.
You find the value of the part inside the square root, which is -5² - 4 × 6 × -3 = 97. Now we can use this to substitute in to (5 +- √97)/12. We can do it with the plus sign, and get 1.24, and then with the subtract sign and get -0.404.

I hope this helps!

4 0

1 year ago