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Alinara [238K]
3 years ago
7

Which of the following is a solution of x2 − 10x = –36? negative 5 minus i square root of 10 5 plus i square root of 61 negative

5 minus i square root of 11 5 plus i square root of 11
Mathematics
1 answer:
Serga [27]3 years ago
5 0
X^2 - 10x + 36 = 0;
We use the quadratic formula: x = ( - b + or - i\sqrt{ -b^{2}+4ac })/ (2a);
We have a = 1; b = -10; c = 36;
Then, x = ( 10 + or -i\sqrt{44})/2 = 5 + or - \sqrt{11})/2 ;
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2 years ago
A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average len
Gnom [1K]

Answer:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

E. -0.723

df=n-1=93-1=92  

p_v =2*P(t_{(92)}  

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

Step-by-step explanation:

Information provided

\bar X=5.97 represent the sample mean for the length

s=0.4 represent the sample standard deviation

n=93 sample size  

\mu_o =6 represent the value that we want to test

\alpha=0.05 represent the significance level

t would represent the statistic  

p_v represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:  

Null hypothesis:\mu = 6  

Alternative hypothesis:\mu \neq 6  

since we don't know the population deviation the statistic is:

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

Replacing in formula (1) we got:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

E. -0.723

P value

The degrees of freedom are given by:

df=n-1=93-1=92  

Since is a two tailed test the p value would be:  

p_v =2*P(t_{(92)}  

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

5 0
3 years ago
Verify the identity. cotangent x equals StartFraction 1 plus cosine 2 x Over sine 2 x EndFractioncot x= 1+cos2x sin2x Use the ap
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Answer with Step-by-step explanation:

We are given that

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Using the formula

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\frac{Cosx}{Sinx}

Cot x

By using the formula

Cotx=\frac{Cosx}{Sinx}

LHS=RHS

Hence, verified

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