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3 years ago

Study the geometric sequence {-4, -84, -1764, -37044, ...}.

Mathematics

1 answer:

Nonamiya [84]3 years ago

3 0

Answer:

$\bold{a_n=(-4)21^{n-1}}$

Step-by-step explanation:

$a_1=-4\,,\ a_2=-84\,,\ a_3=-1764\,,\ a_4=-37044\quad\implies\ \ r=21$

{-84:(-4)=21 and -1764:(-84)=21 and -37044:(-1764)=21}

geometric sequence formula: $a_n=a_1r^{n-1}$

$a_1=-4\quad and \ \ r=21$

$a_n=(-4)21^{n-1}$

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18 2/5 - n = -10 1/3

Wewaii [24]

Answer:

The answer is $n=28\frac{11}{15}$ .

Step-by-step explanation:

Given:

18 2/5 - n = -10 1/3.

Now, to solve the equation:

$18\frac{2}{5} - n = -10 \frac{1}{3}$

Converting the mixed fractions to improper:

⇒ $\frac{92}{5} -n=-\frac{31}{3}$

Moving the numbers on one side and variable to the other:

⇒ $\frac{92}{5} +\frac{31}{3}=n$

Now, solving the factions:

⇒ $\frac{92\times 3+31\times 5}{15}=n$

⇒ $\frac{276+155}{15}=n$

⇒ $\frac{431}{15}=n$

⇒ $28\frac{11}{15}=n$

Therefore, the answer is $n=28\frac{11}{15}$ .

3 0

3 years ago

. The volume of a box is 405 cubic units. The length is x units, the width 4 units greater than the length, and the height is 9

lukranit [14]

Answer:

length = 5

width = 9

Step-by-step explanation:

V = lwh

let 'x' = length

let '4+x' = width

9 = height

405 = 9x(4+x)

405 = 36x + 9x²

this is a quadratic equation: 9x² + 36x - 405 = 0

factor out a 9 to get:

9(x² + 4x - 45) = 0

9(x-5)(x+9) = 0

one root is 5 and the other is -9

since distance cannot be negative we use 5 as the length and 9 is the width

3 0

2 years ago

The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 7 small, 8 medium, and 4 large

umka21 [38]

Answer:

P(at least 1 large) = 0.648

P(at least 1 large) = 64.8%

Step-by-step explanation:

We have 7 small shirts, 8 medium shirts and 4 large shirts

Total number of shirts = 7 + 8 + 4 = 19 shirts

The probability that at least one of the first four shirts he checks is a large is given by

P(at least 1 large) = 1 - P(no large)

So first we need to find the probability that the none of the first four shirts he checks are large.

For the first check, there are 15 small and medium shirts and total 19 shirts so,

15/19

For the second check, there are 14 small and medium shirts and total 18 shirts left so,

14/18

For the third check, there are 13 small and medium shirts and total 17 shirts left so,

13/17

For the forth check, there are 12 small and medium shirts and total 16 shirts left so,

12/16

the probability of not finding the large shirt is,

P(no large) = 15/19*14/18*13/17*12/16

P(no large) = 0.352

Therefore, the probability of finding at least one large shirt is,

P(at least 1 large) = 1 - P(no large)

P(at least 1 large) = 1 - 0.352

P(at least 1 large) = 0.648

P(at least 1 large) = 64.8%

4 0

2 years ago

You and three friends go out to dinner. The cost of the dinner was $112.80. You leave an 18% tip. How much is your tip?

34kurt

Answer:

Bill

112.80

Tip %

15%

Number of people

Tip

per person

$4.23

Total

per person

$32.43

Step-by-step explanation:

4 0

2 years ago

All positive numbers not including 0

Leno4ka [110]

1,2,3,... they are also known as the Natural Numbers

4 0

3 years ago