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3 years ago

Using sigma notation write the geographic series: 6+12+24+48+96

Mathematics

1 answer:

Alika [10]3 years ago

4 0

Answer:

$\sum_{n=1}^{5} 6(2^{n-1})$

Step-by-step explanation:

6 + 12 + 24 + 48 + 96 =

= 6 + 6 * 2 + 6 * 4 + 6 * 8 + 6 * 16

= 6 + 6 * 2^2 + 6 * 2^2 + 6 * 2^3 + 6 * 2 * 4

= 6 * 2^(n - 1)

$\sum_{n=1}^{5} 6(2^{n-1})$

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Step-by-step explanation:

reciprocal of 1/3 = 3/1

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3 years ago

Read 2 more answers

A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salari

guajiro [1.7K]

Answer:

The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

$F_{critical} = 1.8608$

$F = 2.9085$

The decision rule is

Reject the null hypothesis

There is sufficient evidence to support the researchers claim

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 30$

The sample variance for elementary school is $s^2_1 = 8324$

The second sample size is $n_2 = 30$

The sample variance for the secondary school is $s^2_2 = 2862$

The significance level is $\alpha = 0.05$

The null hypothesis is $H_o : \sigma^2_1 = \sigma^2 _2$

The alternative hypothesis is $H_a : \sigma_1 ^2 > \sigma^2_2$

Generally from the F statistics table the critical value of $\alpha = 0.05$ at first and second degree of freedom $df_1 = n_1 - 1 = 30 - 1 = 29$ and $df_2 = n_2 - 1 = 30 - 1 = 29$ is

$F_{critical} = 1.8608$

Generally the test statistics is mathematically represented as

$F = \frac{s_1^2 }{s_2^2}$

=> $F = \frac{8324 }{2862}$

=> $F = 2.9085$

Generally from the value obtained we see that $F > F_{critical }$ Hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to support the researchers claim

4 0

3 years ago