Solve by completing the square:

Cooper was out at a restaurant for dinner when the bill came. His dinner came to $18. After adding in a tip, before tax, he paid

ozzi

Answer: Copper paid 13%

Step-by-step explanation:

4 0

3 years ago

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Who was the best president in history

vova2212 [387]

Answer:

Abraham Lincoln

Step-by-step explanation:

Abraham Lincoln was the 16th president of the United States and is regarded as one of America's greatest heroes due to his role as savior of the Union and emancipator of enslaved people. Lincoln's distinctively humane personality and incredible impact on the nation have endowed him with an enduring legacy. With his ability to command a room, give a powerful speech and negotiate, he is regarded as one of the best presidents in American history. As a leader, Lincoln was determined to hold together a nation that was falling apart at the seams. Abraham Lincoln was voted the best US president in a survey where nearly 100 historians and biographers rated past commanders in chief on 10 leadership qualities

3 0

2 years ago

A sample of 41 observations is selected from one population with a population standard deviation of 3.4. The sample mean is 100.

Marizza181 [45]

Answer:

a) If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

b) (-1.9886, 1.9886)

c) $t=\frac{(100 -98.4)-(0)}{\sqrt{\frac{3.4^2}{41}}+\frac{5.6^2}{45}}=1.617$

d) $p_v =2*P(t_{84}>1.617) =0.1096$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 is NOT significantly different than the mean for the group 2.

e) $p_v =2*P(t_{84}>1.617) =0.1096$

We can use the following excel code to calculate it: "=2*(1-T.DIST(1.617;84;TRUE))"

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =41$ represent the sample size for group 1

$n_2 =45$ represent the sample size for group 2

$\bar X_1 =100$ represent the sample mean for the group 1

$\bar X_2 =98.4$ represent the sample mean for the group 2

$s_1=3.4$ represent the sample standard deviation for group 1

$s_2=5.6$ represent the sample standard deviation for group 2

Part a

If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

Part b

On this case since the significance level is 0.05 and we are conducting a bilateral test we have two critical values, and we need on each tail of the distribution $\alpha/2 = 0.025$ of the area.

The distribution on this cas since we don't know the population deviation for both samples is the t distribution with $df=n_1+n_2 -2= 41+45-2=84$ degrees of freedom.

We can use the following excel codes in order to find the critical values:

"=T.INV(0.025,84)", "=T.INV(1-0.025,84)"

And we got: (-1.9886, 1.9886)

Part c

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(100 -98.4)-(0)}{\sqrt{\frac{3.4^2}{41}}+\frac{5.6^2}{45}}=1.617$

The degrees of freedom are given by:

$df=41+45-2=84$

Part d

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{84}>1.617) =0.1096$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 is NOT significantly different than the mean for the group 2.

Part e

$p_v =2*P(t_{84}>1.617) =0.1096$

We can use the following excel code to calculate it: "=2*(1-T.DIST(1.617;84;TRUE))"

8 0

3 years ago

-26 1/3 10 yards to get a first down

goblinko [34]

Answer:

What is the question?

Step-by-step explanation:

I don't understand this question.

5 0

3 years ago

When 1.5 and a number, "n", are multiplied together, the result is 13.65. a.) Translate this into an equation. b.) Find the valu

alexandr402 [8]

The answer is 2. a)1.5n = 13.65 b) n = 9.1

5 0

3 years ago

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