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3 years ago

2.

Mathematics

2 answers:

sp2606 [1]3 years ago

8 0

Here’s the answer w steps :)

Dafna1 [17]3 years ago

3 0

Slope (y2-y1)/(x2-x1)
(0-4)/(-5-5) = -4/-10 = 2/5
Y = 2/5x + b
Plug in any point
4 = 2/5(5) + b
4 = 2 + b, b= 2
Final equation: y = 2/5x + 2

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Find the number that must be added to each expression to form a perfect square trinomial. Then write the trinomial as a binomial

maksim [4K]

<h2>Hello!</h2>

The answers are:

a) $\frac{49}{4}$

b) $(x+\frac{7}{2})^{2}$

First, we need to know that for this case:

$a=1\\2ab=7$

So,

$b=\frac{7}{2}$

$b^{2} =(\frac{7}{2})^{2}=\frac{49}{4}$

We must add $\frac{49}{4}$ to the expression in order to form a perfect square trinomial,

$x^{2} +7x+\frac{49}{4}$

Writing the trinomial as a binomial square:

$(x+\frac{7}{2})^{2}=x^{2}+2*\frac{7}{2}*x+(\frac{7}{2})^{2}=x^{2} +7x+\frac{49}{4}$

Have a nice day!

8 0

3 years ago

Read 2 more answers

A journalist reported that the average amount of time that a French person spends eating lunch at a restaurant is 22 minutes. Pe

maw [93]

Answer:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Step-by-step explanation:

Data given

American: 21,17,17,20,25,16,20,16 (Sample 1)

French: 24,18,20,28,18,29,17 (Sample 2)

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

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 :

$n_1 =8$ represent the sample size for group 1

$n_2 =7$ represent the sample size for group 2

$\bar X_1 =19$ represent the sample mean for the group 1

$\bar X_2 =22$ represent the sample mean for the group 2

$s_1=3.117$ represent the sample standard deviation for group 1

$s_2=5.0$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$S^2_p =\frac{(8-1)(3.117)^2 +(7 -1)(5.0)^2}{8 +7 -2}=16.770$

And the deviation would be just the square root of the variance:

$S_p=4.095$

And now we can calculate the statistic:

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Now we can calculate the degrees of freedom given by:

$df=8+7-2=13$

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

$p_v =2*P(t_{13}$

So with the p value obtained and using the significance level assumed $\alpha=0.1$ 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 10% of significance we don't have significant differences between the two means.