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andrey2020 [161]

2 years ago

14

Chris spent half of his money on a pair of headphones. Then he spends half of his remaining money of recordable CDs. Finally, he

spent his remaining $12.75 on a book. How much money did Chris have to begin with?

2 answers:

otez555 [7]2 years ago

4 0

I think the answer would be $50.50

kompoz [17]2 years ago

4 0

Assume that Chris began with m dollars in his pocket.

Half of that, or m/2, went to purchase a pair of headphones.

Half of that, or (1/2)(m/2), or m/4, went to purchasing CDs. By now Chris has spent (1/2 + 1/4) of his money: (3/4)m. He had (1/4)m left, and that (m/4) = $12.75.

Solve this for m:
$12.75
m = ------------ = $5 (answer).
(1/4)

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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

Circle 1 has center (−4, −7) and a radius of 12 cm. Circle 2 has center (3, 4) and a radius of 15 cm.

CaHeK987 [17]

<h3>Answer with explanation:</h3>

It is given that:

Circle 1 has center (−4, −7) and a radius of 12 cm.

Circle 2 has center (3, 4) and a radius of 15 cm.

Two circles are said to be similar if by some translation and dilation it could be placed over the other to form the same circle.

The circles are similar because the transformation rule ( x,y ) → (x+7,y+11) can be applied to Circle 1 and then dilate it using a scale factor of 5/4

( Since, as the center of circle 1 is (-4,-7)

so,

(-4+7,-7+11) → (3,4)

( Since, the radius of circle 1 is 12 and that of circle 2 is 15 cm.

so, let the scale factor be k .

that means :

$12\times k=15\\\\k=\dfrac{15}{12}\\\\k=\dfrac{5}{4}$ )

7 0

1 year ago

Read 2 more answers

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nikdorinn [45]

Answer:

It is in the tenths place

Step-by-step explanation:

In the number 9.365, 3 is in the tenths place.

8 0

1 year ago

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Ms. Velez will use both x gray bricks and y red bricks to build a wall around her garden. Gray bricks cost $0.45 each and red br

Alekssandra [29.7K]

It is given in the question that

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Maximum she can spend is $200. That is

$0.45x + 0.58y \leq 200
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And

$x\geq 0 , y \geq 0$

And that's the required inequalities .

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2 years ago

Stevic's earnings. Sunday newspaper: Start at $ 36 and add $ 4 . Saturday newspaper: Start at $ 12 and add $ 2.50 . Part B Stevi

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Your Answer is 14.50.b is 27

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