2(2x − 5 − 4) = 160 − 17

Mathematics

2 answers:

aksik [14]3 years ago

8 0

4x-9=143

+9 +9

4x=152

x=38

wariber [46]3 years ago

3 0

4x - 9 = 143

4x = 152

x = 38

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Four friends split equally a lunch bill of $36.69 plus 20% tip how much did each person pay

nikdorinn [45]

20% of 36.69 is 7.338

36.69 + 7.338 = 44.02800 divided by 4 = $11.007 (rounded)

Each friend paid $11.01

7 0

3 years ago

The table shows the average annual cost of tuition at 4-year institutions from 2003 to 2010.

nata0808 [166]

Answer: 1) The best estimate for the average cost of tuition at a 4-year institution starting in 2020 =$ 31524.31

2) The slope of regression line b=937.97 represents the rate of change of average annual cost of tuition at 4-year institutions (y) from 2003 to 2010(x). Here,average annual cost of tuition at 4-year institutions is dependent on school years .

Step-by-step explanation:

1) For the given situation we need to find linear regression equation Y=a+bX for the given situation.

Let x be the number of years starting with 2003 to 2010.

i.e. n=8

and y be the average annual cost of tuition at 4-year institutions from 2003 to 2010.

With reference to table we get

$\sum x=36\\\sum y=150894\\\sum x^2=204\\\sum xy=718418$

By using above values find a and b for Y=a+bX, where b is the slope of regression line.

$a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}=\frac{150894(204)-(36)718418}{8(204)-(36)^2}=\frac{30782376-25863048}{1632-1296}=\frac{4919328}{336}\\\\=14640.85$

and

$b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}=\frac{8(718418)-(36)150894}{8(204)-(36)^2}=\frac{5747344-5432184}{1632-1296}=\frac{315160}{336}\\\\=937.97$

∴ To find average cost of tuition at a 4-year institution starting in 2020.(as n becomes 18 for year 2020 if starts from 2003 ⇒X=18)

So, Y= 14640.85 + 937.97×18 = 31524.31

∴The best estimate for the average cost of tuition at a 4-year institution starting in 2020 = $31524.31

4 0

4 years ago

What is the value of z in the equation 2(4z − 6 − 6) = 170 − 46? 12.5 15.5 16.5 18.5

vivado [14]

2(4z - 6 - 6) = 170 - 46

2(4z - 12) = 124 |use distributive property: a(b - c) = ab - ac

8z - 24 = 124 |add 24 to both sides

8z = 148 |divide both sides by 8

z = 18.5

4 0

3 years ago

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yKpoI14uk [10]

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