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Fofino [41]
3 years ago
15

Choose the solution(s) of the following system of equations: x² + y² = 6 x² - y=6

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
8 0

Answer:

see attachment

Step-by-step explanation:

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A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has b
baherus [9]

Answer:

Null hypothesis:\mu \leq 6  

Alternative hypothesis:\mu > 6  

t=\frac{6.5-6}{\frac{1.5}{\sqrt{36}}}=2    

df=n-1=36-1=35

t_{crit}=1.690 with the excel code:"=T.INV(0.95,35)"

t_{crit}=1.306 with the excel code:"=T.INV(0.90,35)"

p_v =P(t_{(35)}>2)=0.0267  

If we compare the p value and the significance level given \alpha=0.05,0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the true mean it's significantly higher than 6 at 5% and 10% of significance.  

Step-by-step explanation:

Data given and notation  

\bar X=6.5 represent the mean time for the sample  

s=1.5 represent the sample standard deviation for the sample  

n=36 sample size  

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

\alpha=0.05,0.1 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 6 days, the system of hypothesis would be:  

Null hypothesis:\mu \leq 6  

Alternative hypothesis:\mu > 6  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{6.5-6}{\frac{1.5}{\sqrt{36}}}=2    

Critical value and P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=36-1=35

In order to calculate the critical value we need to find a quantile on the t distribution with 35 degrees of freedom that accumulates \alpha on the right. Using the significance level of 0.05 we got:

t_{crit}=1.690 with the excel code:"=T.INV(0.95,35)"

And using the significance of 0.1 we got

t_{crit}=1.306 with the excel code:"=T.INV(0.90,35)"

Since is a one side right tailed test the p value would be:  

p_v =P(t_{(35)}>2)=0.0267  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05,0.1 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the true mean it's significantly higher than 6 at 5% and 10% of significance.  

6 0
3 years ago
Plzzzz help this is really important!!
borishaifa [10]

Answer:

i cant see the question it wont load sorry

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using functio
ruslelena [56]

Answer:

f(x)=-3x+4

Step-by-step explanation:

just took the test

4 0
3 years ago
A liquid substance was left at the scene of the crime. Krisann uses a beaker that measures to the nearest tenth of a liter and f
AVprozaik [17]
4.85 <= x < 4.95 .  does not intersect x > 5.No it does not need to be sent to the lab. B.
<span>yes, since the beaker meaures to the nearest tenth of a liter , the range of the actual value is plus or minus 0.1 liters , which means there could be up to 5 liters of the substance </span>
8 0
3 years ago
Suppose that 7 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at ra
katen-ka-za [31]

Answer:

(a) 350

(b) 175

(c) 21

(d) 196

Step-by-step explanation:

Number of females = 7

Number of males = 5

Total ways of selecting r items from n items is

^nC_r=\dfrac{n!}{r!(n-r)!}

(a)

Total ways of selecting 3 females and 2 males.

\text{Total ways}=^7C_3\times ^5C_2

\text{Total ways}=\dfrac{7!}{3!(7-3)!}\times \dfrac{5!}{2!(5-2)!}

\text{Total ways}=35\times 10

\text{Total ways}=350

(b)

Total ways of selecting 4 females and 1 male.

\text{Total ways}=^7C_4\times ^5C_1

\text{Total ways}=32\times 5

\text{Total ways}=175

(c)

Total ways of selecting 5 females.

\text{Total ways}=^7C_5\times ^5C_0

\text{Total ways}=21\times 1

\text{Total ways}=21

(d)

Total ways of selecting at least 4 females.

Total ways = 4 females + 5 females

\text{Total ways}=175+21

\text{Total ways}=196

6 0
3 years ago
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