Some one help me on this one

Mathematics

1 answer:

aleksandrvk [35]3 years ago

5 0

The answer is III only, or D.

We can start to solve this by knowing what the HL theorem means. The HL theorem, like its name implies, shows says that if a hypotenuse and leg of a triangle are congruent to the hypotenuse and leg of a different triangle, then the triangles are congruent. The only triangle that we see a hypotenuse congruent in is in figure III. In figure II, those congruent sides are both legs while in figure I we just see 2 congruent angles. Now in figure III, we can also see that two legs are congruent because of the reflexive property. That means that the answer is III, or D.

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A tuter promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tuto

creativ13 [48]

Answer:

t48 = 1.7500

Step-by-step explanation:

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation

x=test value before , y = test value after

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 50$

Alternative hypothesis: $\mu_y -\mu_x >50$

We have the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=53$

And the sample standard deviation for the differences, is:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =12$

Now we can calculate the statistic given by :

$t=\frac{\bar d -\Delta}{\frac{s_d}{\sqrt{n}}}=\frac{53 -50}{\frac{12}{\sqrt{49}}}=1.75$

Since we don't have the population standard deviaition we need to use the t distribution and we can calculate the degrees of freedom given by:

$df=n-1=49-1=48$

Now we can calculate the p value, since we have a right tailed test the p value is given by:

$p_v =P(t_{(48)}>1.75) =0.0432$

If we use a significance level of 5% we have that $p_v$ , and on this case we reject the null hypothesis . And we don't have enough evidence to conclude that the difference of means it's higher than 50 points.