Write the coordinates of the vertices after a reflection over the x-axis. 1072

Mathematics

1 answer:

Liula [17]8 months ago

6 0

The reflection about x-axis results in same x coodinate with oppositive of y coordinate. It can be expressed as,

$(x,y)\rightarrow(x,-y)$

Determine the coordinates of the vertices after reflection over the x-axis.

$Q(6,-8)\rightarrow Q^{\prime}(6,8)$ $R(7,-8)\rightarrow R^{\prime}(7,8)$ $S(7,-5)\rightarrow Q^{\prime}(7,5)$ $T(6,-5)\rightarrow T^{\prime}(6,5)$

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$t=\frac{(14-20)-0}{\sqrt{\frac{5^2}{31}+\frac{6^2}{31}}}}=-4.28$

Now we can calculate the p value with the following probability:

$p_v =2*P(t_{60}$

The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.

Step-by-step explanation:

Information given

$\bar X_{1}=14$ represent the mean for sample 1 (younger)

$\bar X_{2}=20$ represent the mean for sample 2 (older)

$s_{1}=5$ represent the sample standard deviation for 1

$s_{f}=6$ represent the sample standard deviation for 2

$n_{1}=31$ sample size for the group 2

$n_{2}=31$ sample size for the group 2

t would represent the statistic

System of hypothesis

We want to test if that people under the age of forty have vocabularies that are different than those of people over sixty years of age, the system of hypothesis are:

Null hypothesis: $\mu_{1}-\mu_{2}=0$