What is the conjugate of 1 + √5

Use the quadratic formula to find both solutions to the quadratic equation given below x^2+6x=27

docker41 [41]

Answer:

x=3 or x=−9

Step-by-step explanation:

Step 1: Subtract 27 from both sides.

x2+6x−27=27−27

x2+6x−27=0

Step 2: Factor left side of equation.

(x−3)(x+9)=0

Step 3: Set factors equal to 0.

x−3=0 or x+9=0

x=3 or x=−9

Answer:

x=3 or x=−9

7 0

3 years ago

Read 2 more answers

Suppose the standard deviation of a normal population is known to be 3, and H0 asserts that the mean is equal to 12. A random sa

blagie [28]

Answer:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

$p_v =P(z>1.9)=0.0287$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=12.95$ represent the sample mean

$\sigma=3$ represent the population standard deviation for the sample

$n=36$ sample size

$\mu_o =12$ represent the value that we want to test

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

z 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 equal to 12, the system of hypothesis would be:

Null hypothesis: $\mu \leq 12$

Alternative hypothesis: $\mu > 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

P-value

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

$p_v =P(z>1.9)=0.0287$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

4 0

3 years ago

Read 2 more answers

28 miles ran in 5<br> hours

sergejj [24]

Answer: 5.6 miles per hour

Step-by-step explanation:

4 0

3 years ago

What is a possible solution for x+6≥10

ira [324]

Answer:

4,5,6

Step-by-step explanation:

*The sign of ≥ means that it must be greater or equal to 10 in this case

1). 3 isn't a possible solution due to 9 being less than 10

3+6_10

9_10

9<10

2). 4 is a possible solution due to the sum of 4 and 6 being equal to 10

4+6_10

10_10

10=10

3). 5 is a possible solution due to the sum of 5 and 6 being larger than 10

5+6_10

11_10

11>10

4).6 is a possible solution due to the sum of 6 and 6 being larger than 10

6+6_10

12_10

12>10

Hope this helped! (:

6 0

3 years ago

Which is the solution to (8.5 x 103)(2 x 105) expressed in scientific notation?

kenny6666 [7]

We have been given an expression $(8.5\times 10^3)(2\times 10^5)$ . We are asked to find the solution to our given expression expressed as scientific notation.