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3 years ago

Solve 9x-14-2x=5(2x-6)

1 answer:

8 0

$9x-14-2x=5(2x-6)\qquad\text{use distributive property}\\\\(9x-2x)-14=(5)(2x)+(5)(-6)\\\\7x-14=10x-30\qquad\text{add 14 to both sides}\\\\7x=10x-16\qquad\text{subtract 10x from both sides}\\\\-3x=-16\qquad\text{divide both sides by (-3)}\\\\\boxed{x=\dfrac{16}{3}}$

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Woo-Jin and Kiran were asked to find an explicit formula for the sequence 64\,,\,16\,,\,4\,,\,1,...64,16,4,1,...64, comma, 16, c

olya-2409 [2.1K]

Answer:

$f(n)=64(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The given sequence is

64, 16, 4, 1

$r_1=\dfrac{a_2}{a_1}=\dfrac{16}{64}=\dfrac{1}{4}$

$r_2=\dfrac{a_3}{a_2}=\dfrac{4}{16}=\dfrac{1}{4}$

$r_3=\dfrac{a_4}{a_3}=\dfrac{1}{4}$

It is a geometric series because it has a common ratio $r_1=r_2=r_3=\dfrac{1}{4}$ .

First term is 64.

The explicit formula of a geometric series is

$f(n)=ar^{n-1}$

where, a is first term and r is common ratio.

Substitute a=64 and r=1/4 in the above function.

$f(n)=64(\frac{1}{4})^{n-1}$

Therefore, the required explicit formula is $f(n)=64(\frac{1}{4})^{n-1}$ .

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3 years ago

Read 2 more answers

Simplify: x36y64‾‾‾‾‾‾√

AleksandrR [38]

Answer:

Step-by-step explanation:

x18y32 x18y x6y4 x6y32

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2 years ago

There are 92 students in a chemistry class. The instructor must choose two students at random. Students in a Chemistry Class Aca

Sergio039 [100]

Answer:

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability that a sophomore non-Chemistry major

Out of 92 students, 9 are non-chemistry major sophomores. So

$P(A) = \frac{9}{92}$

Then a junior non-Chemistry major are chosen at random.

Now, there are 91 students(1 has been chosen), of which 10 are non-chemistry major juniors. So

$P(B) = \frac{10}{91}$

What is the probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random

$P = P(A)*P(B) = \frac{9}{92}*\frac{10}{91} = \frac{9*10}{92*91} = 0.0108$

0.0108 = 1.08% probability that a sophomore non-Chemistry major and then a junior non-Chemistry major are chosen at random.

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3 years ago

Three coins are flipped.

Darina [25.2K]

Step-by-step explanation:

when 3 coins are flipped the following outcomes are possible

h = heads, t = tails

h h h

h h t

h t h

h t t

t h h

t h t

t t h

t t t

yes, there have to be 8 options, because we have 3 positions with 2 possible outcomes. that means

2×2×2 = 2³ = 8 possibilities.

at least 2 tails means 2 or 3 t in the list item :

h t t

t h t

t t h

t t t

so, 4 out of the 8 possible outcomes. the probability is then therefore

4/8 = 1/2 = 0.5

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2 years ago

The 6 elephants at the zoo have a combined weight of 11,894 pounds. About how much does each elephant weigh?

Sidana [21]

Answer: 14,000 i think

Step-by-step explanation:

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2 years ago

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