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3 years ago

MN and KL are parallel. If JM = 6, MK = 12, and LN = 18, what is NJ?

Mathematics

2 answers:

Galina-37 [17]3 years ago

5 0

6/12=X/18
Using the ratio of 18:12, you multiply 18/12 with 6, which equals 9.

Answer: NJ=9

marusya05 [52]3 years ago

5 0

Answer:

$NJ=9$

Step-by-step explanation:

We have been given that MN and KL are parallel. If JM = 6, MK = 12, and LN = 18. We are asked to find the measure of NJ.

Since line MN is parallel to KL, so triangle JMN is similar to JKL.

We know that corresponding sides of similar triangle are proportional. We will use proportion to solve for NJ as:

$\frac{NJ}{LN}=\frac{JM}{MK}$

$\frac{NJ}{18}=\frac{6}{12}$

Multiplying both sides by 18, we will get:

$\frac{NJ}{18}*18=\frac{6}{12}*18$

$NJ=\frac{1}{2}*18$

$NJ=9$

Therefore, measure of NJ is 9 units.

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2 years ago

At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

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Answer:

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

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

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

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

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.

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

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 $r^2 = 0.657^2 =0.432$

6 0

3 years ago

Jim drives his children to their sports activities outside of school. When he drives his son to baseball practice, it is a 6-km

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Answer:

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Step-by-step explanation:

we know that

The number of kilometers that Jim drives a week is equal to the number of baseball practice multiplied by its round trip plus the number basketball practice multiplied by its round trip

Remember that

$1\ km=1,000\ m$