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3 years ago

Given triangle STU equal to KLM complete each of the following statements TU= KM= LK=

Mathematics

2 answers:

SVEN [57.7K]3 years ago

6 0

Answer:

TU = LM

KM = SU

LK = TS

Step-by-step explanation:

It is given that ΔSTU ≅ ΔKLM

Since, the corresponding parts of congruence triangle are equal,

The corresponding sides TU of ΔSTU and LM of ΔKLM are equal.

The corresponding sides KM of ΔKLM and SU of ΔSTU are equal.

The corresponding sides LK of ΔKLM and TS of ΔSTU are equal.

Hence,

TU = LM

KM = SU and

LK = TS

wlad13 [49]3 years ago

3 0

Answer:

Notice that $\triangle STU \cong \triangle KLM$ , by given,

From this congruence, we deduct several congruences between corresponding elements.

$TU \cong LM$

$KM \cong SU$

$LK \cong TS$

$\angle M \cong U$

$\angle T \cong \angle L\\\angle UST \cong \angle MKL$

$\triangle UST \cong \triangle MKL$

$\triangle TUS \cong \triangle LMK$

Notice that elements correspond each other according to the given congruence between triangles.

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Answer:

a)Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

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Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

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When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

$\sum Y_i =17375 , \sum X_i = 7665.5$

Part a

The slope is given by this formula:

$\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}$

If we replace we got:

$\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

We can find the intercept with the following formula

$\hat \beta_o = \bar y -\hat \beta_1 \bar x$

We can find the average for x and y like this:

$\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955$

And replacing we got:

$\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

Part b

In order to calculate the correlation coefficient we can use this formula:

$r=\frac{\sum (x-\bar x)(y-\bar y) }{\sqrt{[\sum (x-\bar x)^2][\sum(y-\bar y)^2]}}$

For our case we have this:

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$

So we can find the correlation coefficient replacing like this:

$r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

And the determination coeffecient is $r^2 = 0.657^2 =0.432$

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Answer:

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Step-by-step explanation:

This can be determined as follows

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Since Ivy decides that she wants to spend at least twice as much on bagged lunches as at restaurants, we have

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Since Ivy wants to keep her weekly budget to less than $50, using the x and y, we have:

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We can now solve for x as follows:

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Substituting the x < 17 into equation (1) noting that Ivy wants to keep her weekly budget to less than $50, we have:

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