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3 years ago

What is the value of the fourth term in a geometric sequence for which a1=15 and r=1/3

Mathematics

2 answers:

zlopas [31]3 years ago

4 0

Answer: The required fourth term in the given geometric sequence is $\dfrac{5}{9}.$

Step-by-step explanation: We are given to find the fourth term of a geometric sequence with the following first term and common ratio :

$a=15,~~r=\dfrac{1}{3}.$

We know that

the nth term of a geometric sequence with first term a and common ratio r is given by

$a_n=ar^{n-1}.$

Therefore, the forth term of the given geometric sequence is

$a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.$

Thus, the required fourth term in the given geometric sequence is $\dfrac{5}{9}.$

OlgaM077 [116]3 years ago

3 0

Nth term = a1r^(n-1)

4th term = 15* (1/3)^3 = 15/27 = 5/9

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Determine the value of y is x is -10: y=x-91+2

cestrela7 [59]

Answer:

$y = x - 91 + 2 \\ x = - 10 \\ y = - 10 - 91 + 2 \\ y = - 101 + 2 \\ x = - 99$

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2 years ago

How do I simplify this? Include steps. <img src="https://tex.z-dn.net/?f=%20%28%5Cfrac%7B5i%5E3t%5E4%7D%7B7%7D%29-2%20%20%20

navik [9.2K]

Simplify the following:
(5 i^3 t^4)/7 - 2
i^3 = i^2×i = (-1) i = -i:
(5×-i t^4)/7 - 2
Put each term in (5 (-i) t^4)/7 - 2 over the common denominator 7:
(5 (-i) t^4)/7 - 2 = (-5 i t^4)/7 - 14/7:
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2 years ago

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

As we see, the situation is exactly the same, but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

2 years ago

Which expression is equivalent to 2(-3x+5)? A.-6x+5 B.-6x+10 C.6x-10 D.6x-5

pochemuha

B if you’re doing distributive property

5 0

2 years ago

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Given that f(x) = x2 + 3x + 6 and g(x) = the quantity of x plus two, over three, solve for f(g(x)) when x = 1

MaRussiya [10]

Easy
f(g(1))
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f(g(1))=
f(1)=(1)^2+3(1)+6
f(1)=1+3+6
f(1)=10
f(g(1))=10

3 0

2 years ago

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