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125 = 5^3 = 25 * 5
The simplification you are trying to do involves finding the prime factorization of a number. Since 125 is not divisible by 2, move on to 3. 125 is also not divisible by 3, so move on to 5. Then 125/5 = 25, and 25/5 = 5, so 125 = 5^3. The prime factorization of 125 is 5^3.
We are 114.28 m from the base of the plateau .
<u>Step-by-step explanation:</u>
Here we have , suppose that you are headed toward a plateau 80 meters high. if the angle of elevation to the top of the plateau is 35 degree, WE need to find that how far are you from the base of the plateau . If we see in question , it's clearly a question from application of trigonometry :
We have ,
( between base & hypotenuse )
It's a right angled triangle , So
⇒
⇒
⇒
⇒
⇒
Therefore, We are 114.28 m from the base of the plateau .
Answer:
1 a
1b
1c
2a
2b
2c
Step-by-step explanation:
Considering question a
The alternative hypothesis is H1:μ>μ0
The test statistics is z =1.88
Generally from the z-table the probability of z =1.88 for a right tailed test is
Considering question b
The alternative hypothesis is H1:μ<μ0
The test statistics is z=−2.75
Generally from the z-table the probability of z=−2.75 for a left tailed test is
Considering question c
The alternative hypothesis is H1:μ≠μ0
The test statistics is z=2.88
Generally from the z-table the probability of z=2.88 for a right tailed test is
Generally the p-value for the two-tailed test is
=>
Considering question 2a
The alternative hypothesis is H1:μ>μ0
The sample size is n=16
The test statistic is t = 3.733
Generally the degree of freedom is mathematically represented as
=>
=>
Generally from the t distribution table the probability of t = 3.733 at a degree of freedom of for a right tailed test is
Considering question 2b
The alternative hypothesis is H1:μ<μ0
The degree of freedom is df=23
The test statistic is ,t= −2.500
Generally from the t distribution table the probability of t= −2.500 at a degree of freedom of df=23 for a left tailed test is
Considering question 2c
The alternative hypothesis is H1:μ≠μ0
The sample size is n= 7
The test statistic is ,t= −2.2500
Generally the degree of freedom is mathematically represented as
=>
=>
Generally from the t distribution table the probability of t= −2.2500 at a degree of freedom of for a left tailed test is
Generally the p-value for t= −2.2500 for a two tailed test is