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ruslelena [56]
3 years ago
9

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
6 0

Answer:

-5, 5

Step-by-step explanation:

The line in this problem can be  written in the form

y=mx+q (1)

where:

m=\frac{2}{3} is the slope

q is the y-intercept

We know that the line passes through the point (-2,5), so substituting these values into eq.(1), we find the value of the y-intercept:

q=y-mx=5-(\frac{2}{3})(-2)=5+\frac{4}{3}=\frac{19}{3}

So the equation of the line is

y=\frac{2}{3}x+\frac{19}{3} (2)

Now we know that point A has coordinates

A(x,3)

So by substituting into eq.(2), we find the missing x-coordinate:

3=\frac{2}{3}x+\frac{19}{3}\\9=2x+19\\x=\frac{9-19}{2}=-5

Similarly, point B has coordinates

B(-2,y)

so substituting into eq(2), we find the missing y-coordinate:

y=\frac{2}{3}(-2)+\frac{19}{3}=5

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Answer:

Probability of having student's score between 505 and 515 is 0.36

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Step-by-step explanation:

As we know from normal distribution: z(x) = (x - Mu)/SD

where x = targeted value; Mu = Mean of Normal Distribution; SD = Standard Deviation of Normal Distribution

Therefore using given data: Mu (Mean) = 510, SD = 10.4 we have z(x) by using z(x) = (x - Mu)/SD as under:

In our case, we have x = 505 & 515

Approach 1 using Standard Normal Distribution Table:

z for x=505: z(505) = (505-510)/10.4 gives us z(505) = -0.48

z for x=515: z(515) = (515-510)/10.4 gives us z(515) = 0.48

Afterwards using Normal Distribution Tables and rounding the values to two decimals we find the probabilities as under:

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Similarly we have:

P(515) using z(515) = 0.68

Now we may find the probability of student's score between 505 and 515 using:

P(505 < x < 515) = P(515)-P(505) = 0.68 - 0.32 = 0.36

PS: The standard normal distribution table is being attached for reference.

Approach 2 using Excel or Google Sheets:

P(x) = norm.dist(x,Mean,SD,Commutative)

P(505) = norm.dist(505,510,10.4,1)

P(515) = norm.dist(515,510,10.4,1)

Probability of student's score between 505 and 515= P(515) - P(505) = 0.36

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