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tatyana61 [14]
3 years ago
12

A video game sets the points needed to reach the next level based on the function g(x) = 7(3)^(x − 1), where x is the current le

vel. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 4x. How many points will a player need on the hardest setting of level 4?
Answer choices:
16
189
3024
12096
Mathematics
1 answer:
AleksandrR [38]3 years ago
7 0
Good morning.


In level 4, the experience needed is:

\mathsf{g(4) = 7\cdot3^{4-1}}\\ \\ \mathsf{g(4) = 7\cdot3^3 = 7\cdot27}\\ \\ \mathsf{g(4) = 189}


In the hardest settings, the multiplier is:

\mathsf{h(4) = 4\cdot 4}\\ \\ \mathsf{h(4) = 16}


So, the adjusted experience points are: multiplier . base experience

\mathsf{E(x) = h(x)g(x)}\\ \\ \mathsf{E(4) = h(4)g(4) = 16\cdot 189}\\ \\ \boxed{\mathsf{E(4) = 3024 \ points}}
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Answer:

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The degrees of freedom are given by:

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The p value for this case is given by:

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And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}

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s=3.239 represent the sample standard deviation

n=10 sample size  

\alpha=0.05 represent the significance level

t would represent the statistic  

p_v represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:  

Null hypothesis:\mu \leq 55  

Alternative hypothesis:\mu > 55  

Replacing the info given we got:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

And replacing the info given we got:

t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296    

The degrees of freedom are given by:

df=n-1=10-1=9  

The p value for this case is given by:

p_v =P(t_{(9)}>4.296)=0.001  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

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