Using the principle of mathematical induction, show that 41^n-14^n is a multiple of 27

Ex 14 dau coroana va rog

Lelechka [254]

Answer:

dont know the answer

Step-by-step explanation:

8 0

3 years ago

The percent, X , of shrinkage o n drying for a certain type of plastic clay has an average shrinkage percentage :, where paramet

never [62]

Answer:

a) $t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

b) $p_v =P(t_{(44)}>2.744)=0.0044$

Step-by-step explanation:

Information given

$\bar X=18.4$ represent the sample mean

$s=2.2$ represent the sample standard deviation

$n=45$ sample size

$\mu_o =17.5$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 17.5$

Alternative hypothesis: $\mu > 17.5$

The statistic is given by:

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

And replacing we got:

$t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744$

The degrees of freedom are given by:

$df=n-1=45-1=44$

The critical value for this case is $t_{\alpha}=1.68$ since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

Part b

The p value would be given by:

$p_v =P(t_{(44)}>2.744)=0.0044$

5 0

4 years ago

Steve ordered plastic cases for storing his baseball cards. Each case has a length of 12 centimeters, a width of 6.5 centimeters

Minchanka [31]

For this case you should see the box as a rectangular prism.
The volume of a rectangular prism is given by:
V = (L) * (W) * (H)
Where,
L: length
W: width
H: height.
Substituting the values we have:
V = (12) * (6.5) * (1.25)
V = 97.5 cm ^ 3
Answer:
the volume, in cubic centimeters, of one baseball card case is:
V = 97.5 cm ^ 3

3 0

4 years ago

Help please quickly if possible

rusak2 [61]

Answer:

i dont get the question

Step-by-step explanation:

3 0

4 years ago

X-9=o what is it guys

creativ13 [48]

Add 9 to both sides

x-9=0

x-9+9 = 0+9

x = 9

3 0

3 years ago

Using the principle of mathematical induction, show that 41^n-14^n is a multiple of 27​

Using the principle of mathematical induction, show that 41^n-14^n is a multiple of 27