What is the value of k in the product of powers below? welp

Mathematics

2 answers:

8090 [49]3 years ago

7 0

I guess : k = -1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

defon3 years ago

6 0

Answer: The required value of k is -1.

Step-by-step explanation: We are given to find the value of k in the product of the following powers :

$10^{-3}.10.10^k=10^{-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following properties of exponents to solve the given equation.

$(i)~a^b.a^c=a^{b+c},\\\\(ii)~a^x=a^y~~~~\Rightarrow x=y.$

From equation (i) we have

$10^{-3}.10.10^k=10^{-3}\\\\\Rightarrow 10^{-3+1+k}=10^{-3}\\\\\Rightarrow 10^{-2+k}=10^{-3}\\\\\Rightarrow -2+k=-3\\\\\Rightarrow k=-3+2\\\\\Rightarrow k=-1$

Therefore, the required value of k is -1.

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In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the popu

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Answer:

$19.6-2.42\frac{5.8}{\sqrt{42}}=17.43$

$19.6+2.42\frac{5.8}{\sqrt{42}}=21.77$

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

$\bar X= 19.6$ represent the sample mean

$\mu$ population mean

$\sigma= 5.8$ represent the population deviation

n=42 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.98 or 98%, the significance would be $\alpha=0.02$ and $\alpha/2 =0.1$ , and the critical value would be $t_{\alpha/2}=2.42$