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3 years ago

What is the explicit formula that represents the geometric sequence -2, 8, -32, 128

Mathematics

1 answer:

lubasha [3.4K]3 years ago

3 0

$a_n=a_1r^{n-1}\\\\a_1=-2;\ a_2=8;\ a_3=-32;\ a_4=128\\\\r=a_2:a_1\to r=8:(-2)=-4\\\\\boxed{a_n=-2\cdot(-4)^{n-1}}$

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I theater sells tickets for a concert. Tickets for lower-level seats sell for $35 each and tickets for upper-level seats sell fo

lora16 [44]

Let X= the number of tickets sold at $35 each

Let 350 -X = the number of tickets sold at $25 each

The number of tickets sold for each type will be computed as follows:

X(35)+(350-X)25=10250

35X+8750-25X=10250

10X=10250-8750

X=1500/10

X=150 the number of tickets sold at $35 each

350-150 the number of tickets sold at $25 each

To recheck:

150(35)+200(25)

5250+5000

10250

7 0

3 years ago

Michael uses a uniform probability model for an experiment using a deck of 45 cards. There are 15 blue card, 15 red cards, and 1

vampirchik [111]

Answer:

P = 2/3

Step-by-step explanation:

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15 red

15 green

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15 + 15 = 30

Since the total is 45, this is how many 30 will be out of.

30 out of 45 = 30/45

Simplify 30/45 by dividing each side by 15

30 ÷ 15 = 2

45 ÷ 15 = 3

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6 0

2 years ago

Write 0.09 as a simplified fraction

Illusion [34]

9/100, let me know if this helps.

4 0

3 years ago

A research study investigated differences between male and female students. Based on the study results, we can assume the popula

garri49 [273]

Using the normal distribution and the central limit theorem, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of $\mu = 3.5$ .

The standard deviation is of $\sigma = 0.5$ .

Sample of 100, hence $n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05$

The interval that contains 95.44% of the sample means for male students is between Z = -2 and Z = 2, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$