Can anyone help me out? Find a and b

Mathematics

1 answer:

Natali5045456 [20]3 years ago

8 0

If you look at your graph you see that there is a hole at x = 3. This results from a removeable discontinuity. That means that when we factor the numerator to (x-3)(x-1), that (x-3) cancels out between the numerator and denominator and a hole is what results from that cancelation. The other factor for the denominator is found where the vertical asymptote of the function is, which is found at x = -4. That means that the 2 factors for the denomonator are (x-3) and (x+4). When you FOIL those out, you get $x^2+x-12$ . That means that a = 1 and b = -12

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The test scores of 32 students are listed below. Construct a boxplot for the data set and include the values of the 5-number sum

zhenek [66]

Answer:

Boxplot is constructed using quartiles and 5 No. summary means including minimum value of data, 1st quartile, 2nd quartile, 3rd quartile and maximum value of data.

As data already in increasing order, we find quartiles using the following formula,

$value\:of\:K_{th}\:Quartile\:,\, Q_k=\:value\:of\:(\frac{k\times{(n+1)}}{4})\,\:th\,observation$

where n = No. of Observations.

∴, 1st Quartile,

$Q_1 = \frac{1\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=8.25\,th\:observation\\\: \:\:= 8th\,+0.25(9th-8th)\\\:\:\:= 55 + 0.25(57-55)\\\:\:\:= 55.5$

2nd Quartile,

$Q_2 = \frac{2\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=16.5\,th\:observation\\\: \:\:= 16th\,+0.5(17th-16th)\\\:\:\:= 69 + 0.5(70-69)\\\:\:\:= 69.5$

3rd Quartile,

$Q_3 = \frac{3\times{(32+1)}}{4}\, th\:\:observation\\\\ \:\:\:=24.75\,th\:observation\\\: \:\:= 24th\,+0.75(25th-24th)\\\:\:\:= 79 + 0.75(81-79)\\\:\:\:= 80.5$