Need the answer asap

The Fibonacci sequence is defined by $F_1 = F_2 = 1$ and $F_{n + 2} = F_{n + 1} + F_n$. Find the remainder when $F_{1999}$ is di

zavuch27 [327]

Answer:

The remainder is 1

Step-by-step explanation:

Given the Fibonacci sequence

F_1 = F_2 = 1, and

F_(n + 2) = F_(n + 1) + F_n

We want to find the remainder when F_(1999) is divided by 5.

Let us write the first 20 numbers of the sequence in (mod 5). They are

F_1 = 1,

F_2 = 1,

F_3 = 2,

F_4 = 3,

F_5 = 5 = 0 (mod 5),

F_6 = 3,

F_7 = 3,

F_8 = 1

F_(9) = 4

F_(10) = 0

F_(11) = 4

F_(12) = 4

F_(13) = 3

F_(14) = 2

F_(15) = 0

F_(16) = 2

F_(17) = 2

F_(18) = 4

F_(19) = 1

F_(20) = 0

We have: 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0

Now, 1999 = 19(mod 20)

The 19th number in the sequence is 1.

So, the remainder is 1.

6 0

2 years ago

At a garden shop, a customer buys 5 geraniums and 4 lilies for $48. Another customer pays $58 for 4 geraniums and 6 lilies. Writ

masha68 [24]

Answer:

A lily costs $7 and a geranium $4.

Step-by-step explanation:

From the question, we can write two equations. let the number of lilies be l and the number of geraniums be g, then:

5 g + 4 l = 48

4 g + 6 l = 58

Multiply the first equation by 4 and the second by 5, the number of lilies in the other gives:

20 g + 16 l = 192

20 g + 30 l = 290

Subtract the first equation from the second gives:

14 l = 98 which dividing by 14 gives l = 7

Substituting the value l = 7 in the first equation gives:

5 g + 28 = 48

Subtract 20 from both sides gives:

5 g = 20 divide by 5 gives g = 4

So, a lily costs $7 and a geranium costs $4.

7 0

2 years ago

Which statements are true about the expression

bazaltina [42]

Answer:

Wheres the question?

6 0

3 years ago

please answer fast!!! drag each figure to show if it is similar to the figure shown or why it is not similar

igomit [66]

Answer:

The similar figures are shown in the attached drawing created with Microsoft Visio;

The similar figures are the rectangles in figures 2, and 5

Step-by-step explanation:

The given figure is a rectangle with dimensions of 3 yd. by 9 yd., therefore the length = 3 × The width of the rectangle

1) The 9 yd. by 18 yd. figure is a rectangle with the length = 2 × The width of the rectangle, therefore, the figure is not similar to the given rectangle

2) The 3 yd. by 1 yd. figure is a rectangle with the width = 3 × The length of the rectangle, therefore, the figure is similar to the given rectangle

3) The figure is a trapezium, while the given figure is a rectangle, therefore, they are not similar

4) The 6 yd. by 3 yd. figure is a rectangle with the width = 2 × The length of the rectangle, therefore, the figure is not similar to the given rectangle

5) The 6 yd. by 18 yd. figure is a rectangle with the length = 3 × The width of the rectangle, therefore, the figure is similar to the given rectangle

6) The 2 yd. by 8 yd. figure is a rectangle with the length = 4 × The width of the rectangle, therefore, the figure is not similar to the given rectangle

3 0

2 years ago

4. A typical smartphone battery (yes that includes iphones) degrades at approximately 1%

Zielflug [23.3K]

Answer:

a. $f(t) = (0.99)^{t} 100%\\$

b. The x - intercept represents the time at which the battery life drops to 0 %.

c. The y - intercept represents the initial battery life.

Step-by-step explanation:

a. Construct an equation using f(t) and t that represents the relationship between

"f(t)" the battery capacity of a typical smartphone after "t" months and "L" the

number of months the smartphone has been in normal use.

Let the initial battery life be I.

After one month, it decreases by 1%. So, our new value, I' = initial value - decrease = I - 1%I = 99%I.

After two months, it decreases by 1% to our new value I". So, our new value, I" = initial value - decrease = I' - 1%I' = 99%I' = 99%(99%)I = (99%)²I

After three months, it decreases by 1% to our new value I'". So, our new value, I"' = initial value - decrease = I" - 1%I" = 99%I" = 99%(99%)²I = (99%)³I

We see a pattern here.

After t months, f(t)

$f(t) = (0.99)^{t} 100%\\$

b. What does the horizontal intercept represent in context? (The x-intercept)

The x - intercept represents the time at which the battery life drops to 0 %.

c. What does the vertical intercept represent in context? (The y-intercept)

The y - intercept represents the initial battery life.

5 0

3 years ago