The equation sec^2x-1=tan^2 x is an identity. True or false?

Add. Write fractions in simplest form.<br> 4-12 EVENS

Virty [35]

4. 1/3 6.-0.9 or -9/10 8. 2 1/3 10. -3.45 12.4.54 or 4 27/50

7 0

3 years ago

A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$

The standard error is given by the following formula:

$SE=\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$

And replacing we have:

$SE=\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=1.118$

Confidence interval

Now we have everything in order to replace into formula (1):

$5-1.88\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=2.898$

$5+1.8\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=7.102$

So on this case the 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

7 0

3 years ago

Simplify 2y^2 + 2y + 2y + 2x^2.

klio [65]

Answer:

2x^2+2y^2+4y would be your answer

Step-by-step explanation:

7 0

3 years ago

Carbon-14 tests are often performed to determine the age of an organism that died a long time ago. Carbon-14 has a half-life of

Crank

Answer:

2006 years old.

Step-by-step explanation:

If it had 50% of its carbon-14 it would be 5730 years old.

Since it has 65% left it is younger than 5730 years.

So it is (1 - 0.65) * 5730

= 2005.5 years old.

7 0

2 years ago

How do you factorise 14x -21xy

alexandr402 [8]

<span>Simplifying 14x + -21xy

Factor out the Greatest Common Factor (GCF), '7x'. 7x(2 + -3y)

Final result:
7x(2 + -3y)

that is the answer on how to do it</span>

4 0

3 years ago

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