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2 years ago

The sum of the series 5(1/2)^i is x/1024 Then x =

Mathematics

2 answers:

Tatiana [17]2 years ago

8 0

I just got this question. I think the answer is 5.

Oksanka [162]2 years ago

7 0

Answer:

The value x is 10240.

Step-by-step explanation:

The sum of the series 5(1/2)^i is x/1024.

The sum of an infinite series $a_n=ar^n$ is

$Sum=\frac{a}{1-r}$

The given series is

$a_i=5(\frac{1}{2})^i$

Here, $a=5,r=\frac{1}{2}$ .

The sum of given series is

$Sum=\frac{5}{1-\frac{1}{2}}$

$\frac{x}{1024}=\frac{5}{\frac{1}{2}}$

$\frac{x}{1024}=10$

$x=10240$

Therefore value x is 10240.

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jose is choosing a 3-letter password from the letters a,b,c,d. the password cannot have the same letter repeated in it. how many

kvasek [131]

Alright, so we are dealing with permutations. Permutations are the number of combinations in a specific order possible for the set.

There's 4 letters, each one can be paired with 3 other letters, but those letters could be in different orders. To figure out how many variations of each combination there are (aka the number of permutations) use this formula:

$_{n}P_{r}= \frac{n!}{(n-r)!}$

$r=$ number of elements in the subset

$n=$ number of elements in the set

$P=$ permutations of the set

There are only 3 elements in the subset because there is 1 that will not be repeated in each set, and there are 4 elements in the set.

Here's the math:

$_{n}P_{r}= \frac{n!}{(n-r)!}$

$_{4}P_{3}= \frac{4!}{(4-3)!}$

$_{4}P_{3}= \frac{4!}{(1)!}$

$_{4}P_{3}= \frac{4(3)(2)(1)}{1}$

$_{4}P_{3}=24$

There are 24 permutations. I can prove this by showing you the model:

ABCD, ABDC, ACBD, ACDB, ADBC, ADCB are the 6 arrangements possible of the set starting with the letter A. Because there are 4 letters, the total amount of permutations without repeated letters is 4 (letters) times 6 (possible arrangements), which equals 24.

Hope this helps!

Answer: 24 passwords are possible

5 0

2 years ago

Imogen sees a design for a garden in a magazine. She changes the scale because she wants a smaller garden. The figure below show

faust18 [17]

Answer:

Length A of the magazine garden is 28 feet is true.

Length B of the Magazine garden is 17.5 feet is true.

Length C of the Magazine garden is 35 feet is true.

Step-by-step explanation:

Please refer the attached figure.

Given:-

Magazine Scale is 1 inch = 3.5 feet.

Imogen's scale is 2 inches = 6 feet,

Therefore Imogen's scale is 1 inch = 3 feet.

In Triangle ABC,

side a = 8 inches, side b= 5 inches, side c= 10 inches.

To find:- The correct 3 options(actual size of sides of triangle ABC).

Solution:-

In triangle ABC,

Let,

AB=side a =8 inches

BC=side b =5 inches

AC=side c= 10 inches

Now, as per the given scale's of Magazine and Imogen's we can find the actual sizes.

Length A as per Magazine scale (1 inch = 3.5 feet) is,

$\therefore Length\ A=8\times 3.5$ -------------(as per scale)

$\therefore Length A=28\ feet$

and Length A as per Imogen's scale(1 inch =3 feet) is,

AB = side a

$\therefore Length\ A=8\times 3$ -------------(as per scale)

$\therefore Length A=24\ feet$

Therefore Length A of the magazine garden is 28 feet is true.

Now, Length B as per Magazine scale (1 inch = 3.5 feet) is,

BC = side b

$\therefore Length\ B=5\times 3.5$

$\therefore Length B=17.5\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

BC = side b

$\therefore Length\ B=5\times 3$

$\therefore Length B=15\ feet$

Therefore Length B of the Magazine garden is 17.5 feet is true.

Now, Length C as per Magazine scale (1 inch = 3.5 feet) is,

AC = side c

$\therefore Length\ C=10\times 3.5$

$\therefore Length C=35\ feet$

Length B as per Imogen's scale (1 inch = 3 feet) is,

AC = side c

$\therefore Length\ C=10\times 3$

$\therefore Length B=30\ feet$

Therefore Length C of the Magazine garden is 35 feet is true.

8 0

2 years ago

Read 2 more answers

jeffrey purchased a card for $180 that gives him 20 visits to a new gym and includes a one-time fee for unlimited use of the sau

yawa3891 [41]

There is many ways to do this but i did it this way.

180-123.75= 56.25

56.25/5=11.25

=11.25

7 0

2 years ago

Read 2 more answers

Yuki's guppies have begun to have babies. She started with 5 guppies. One week later, Yuki counted twice as many guppies in the

s2008m [1.1K]

Week 1 = 5 guppies.
week 2 = 5x 2 = 10 guppies
week 3 = 10 x 2 = 20 guppies
week 4= 20 x 2 = 40 guppies
week 5 = 40 x 2 = 80 guppies
week 6= 80 x 2 = 160 guppies
Yuki had 160 guppies in 6 weeks.

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2 years ago

Which is the graph of arctan(x)?

Delvig [45]

Answer:

First graph (see below)

Step-by-step explanation:

The graph of the arctan(x) is the first graph attached, see below. This is because if you were to plug in the equation in any TI calculator, you would get this graph.

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2 years ago