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3 years ago

A sequence is defined recursively using the formula f(n + 1) = -0.5f(n). If the first term of the sequence is 120, what is f(5)?

Mathematics

2 answers:

Dmitriy789 [7]3 years ago

5 0

Answer:

Third choice

Step-by-step explanation:

i just did it on edgen and got it right

PolarNik [594]3 years ago

3 0

Answer: 7.5

Step-by-step explanation:

The given formula tells us that the next term f(n+1) of the sequence is -0.5 times the previous term f(n)

First term of the sequence is f(1) = 120

Second term of the sequence is f(2) = f(1+1) = -0.5 f(1) = -0.5 (120) = -60

Third term of the sequence is f(3) = f(2+1) = -0.5 f(2) = -0.5 (-60) = 30

Fourth term of the sequence is f(4) = f(3+1) = -0.5 f(3) = -0.5 (30) = -15

Fifth term of the sequence is f(5) = f(4+1) = -0.5 f(4) = -0.5 (-15) = <em>7.5</em>

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Choose the correct fraction and decimal equivalent for 78%.

vazorg [7]

Answer: 0.78 and 39/50

<h3>Explanation:</h3>

What we know:

We need to find 78% as a fraction and decimal

How to solve:

The decimal is easy enough, and then the fraction can be found from there. D will represent decimal, p will represent percentage, and F will represent fraction.

<h3>Process:</h3>

Decimal

Set up equation D = p / 100

Substitute D = 78% / 100

Simplify D = 0.78%

Remove % sign D = 0.78

Fraction

Set up equation F = p / 100

Substitute F = 78% / 100

Remove % sign F = 78 / 100

Simplify if needed F = /2 /2

F = 39 / 50

Solution: 0.78 and 39/50

Check:

Multiply the decimal by 100 to check the decimal

0.78 x 100 = 78; 78%

Divide the fraction to check the fraction

39/50 = 0.78; see above

8 0

2 years ago

Read 2 more answers

A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to

melisa1 [442]

Answer:

Mean = 1.42

Variance = 0.58

Step-by-step explanation:

Given: X denote the number of luxury cars sold in a given day, and Y denote the number of extended warranties sold.

Also, joint probability function of X and Y are given.

To find:

mean and variance of X

Solution:

From the given joint probability function of X and Y,

$P(X=0)=\frac{1}{6}\\P(X=1)=\frac{1}{12}+\frac{1}{6}=\frac{1+2}{12}=\frac{3}{12}\\P(X=2)=\frac{1}{12}+\frac{1}{3}+\frac{1}{6}=\frac{1+4+2}{12}=\frac{7}{12}$

Mean of X:

$E(X)=\sum XP(X)\\=0\left ( \frac{1}{6} \right )+1\left ( \frac{3}{12} \right )+2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{14}{12}\\=\frac{17}{12}=1.42$

Variance of X:

$E(X^2)=\sum X^2P(X)\\=0^2\left ( \frac{1}{6} \right )+1^2\left ( \frac{3}{12} \right )+2^2\left ( \frac{7}{12} \right )\\=0+\frac{3}{12}+\frac{28}{12}\\=\frac{31}{12}$

$var(X)=E\left [ X^2 \right ]-\left ( E\left [ X \right ] \right )^2\\=\frac{31}{12}-\left ( \frac{17}{12} \right )^2\\=\frac{31}{12}-\frac{289}{144}\\=\frac{372-289}{144}\\=\frac{83}{144}\\=0.58$

5 0

4 years ago

The area of a polygon is the number of square units contained in its interior true or false

Vsevolod [243]

<span>False. Perimeter is a linear measure. Square units are for area.</span>

5 0

3 years ago

Let f and g be the functions defined by f(x) = 10^ (x+2 / 3) and g(x) = log (x3 / 100) for all positive real numbers,

Vaselesa [24]

Answer:

F(x) and g(x) are not inverse functions.

Step-by-step explanation:

In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.

As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.

$[tex]y=10^{(x+\frac{2}{3}) }\\\\log y=log 10^{(x+\frac{2}{3}) }\\log y = (x+\frac{2}{3}) . log10\\\frac{log Y}{log10} = (x+\frac{2}{3})\\\frac{log Y}{1} = (x+\frac{2}{3})\\log Y-\frac{2}{3}=x$ [/tex]