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enyata [817]
3 years ago
13

I’m stuck on this please someone help

Mathematics
1 answer:
kakasveta [241]3 years ago
6 0

Answer:   \bold{a_{n+1}=\dfrac{1}{2}a_n}

<u>Step-by-step explanation:</u>

Term-to-term rule is also called the recursive rule.

The recursive rule for a geometric sequence is: a_{n+1}=a_n\cdot r  where

  • a_n\ \text{is the previous term}
  • r is the common ratio

The common ratio (r) is the second term divided by the first term <em>(which is the same ratio for each term divided by its previous term) </em>

In the given sequence {64, 32, 16, 8, 4}, r=\dfrac{32}{64}\quad \rightarrow \quad r=\dfrac{1}{2}

So, the recursive rule is: {a_{n+1}=a_n\cdot \dfrac{1}{2}

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5) In a certain supermarket, a sample of 60 customers who used a self-service checkout lane averaged 5.2 minutes of checkout tim
Ne4ueva [31]

Answer:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

S_p=2.940

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

df=60+72-2=130

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

Step-by-step explanation:

Data given

Our notation on this case :

n_1 =60 represent the sample size for people who used a self service

n_2 =72 represent the sample size for people who used a cashier

\bar X_1 =5.2 represent the sample mean for people who used a self service

\bar X_2 =6.1 represent the sample mean people who used a cashier

s_1=3.1 represent the sample standard deviation for people who used a self service

s_2=2.8 represent the sample standard deviation for people who used a cashier

Assumptions

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

And t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

System of hypothesis

Null hypothesis: \mu_1 \geq \mu_2

Alternative hypothesis: \mu_1 < \mu_2

This system is equivalent to:

Null hypothesis: \mu_1 - \mu_2 \geq 0

Alternative hypothesis: \mu_1 -\mu_2 < 0

We can find the pooled variance:

\S^2_p =\frac{(60-1)(3.1)^2 +(72 -1)(2.8)^2}{60 +72 -2}=8.643

And the deviation would be just the square root of the variance:

S_p=2.940

The statistic is given by:

t=\frac{(5.2 -6.1)-(0)}{2.940\sqrt{\frac{1}{60}+\frac{1}{72}}}=-1.751

The degrees of freedom are given by:

df=60+72-2=130

And now we can calculate the p value with:

p_v =P(t_{130}

Assuming a significance level of \alpha=0.05 we have that the p value is lower than this significance level so then we can conclude that the mean for checkout time is significantly less for people who use the self-service lane

5 0
3 years ago
What id the greatest common factor shared by 24 and 54
Marysya12 [62]

Answer:

6.

Step-by-step explanation:

3 0
3 years ago
What is 0.29 of 200 rounded to the nearest hundred
jekas [21]

Answer:

100

Step-by-step explanation:

<u>Step 1:  Make an expression</u>

<u />200 * 0.29 = x

58 = x

<u>Step 2:  Round</u>

<u />58

100

Answer:  100

3 0
3 years ago
The radius of a circle is 16 cm. Find its area in terms of \piπ
Kitty [74]

Answer256pi

Step-by-step explanation:

Area=pi*r^2

=pi*16^2

256pi

3 0
3 years ago
Find the area of this figure.
kakasveta [241]

Answer:

pretty sure it's 360 :)

Step-by-step explanation:

...

5 0
3 years ago
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