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3 years ago

Write the equation of a line in slope intercept form that passes through the points (0, 7) and (5, 3)

Mathematics

2 answers:

malfutka [58]3 years ago

5 0

first you find the slope by making using the quation for slope

(7-3)/(0-5) and you find your slope is 4/-5. Then you can plug this into point slope form using on of the coordinates so:

y-y1=m(x-x1) --> y-3=-4/5(x-5)

then you distribute the -1 so -----> y-3=-4/5x+4 and then move the 3 over

so the answer is y= -4/5x+7

IrinaVladis [17]3 years ago

3 0

To solve this problem, we must remember that the formula for slope, represented by the variable m, is m = y2-y1/x2-x1, and slope-intercept form is y=mx + b, where the variable m again represents the slope and the variable b represents the y-intercept. First, we will solve for the slope by plugging in the values we are given in our ordered pairs into the formula and simplifying using subtracting and then division:

m = y2-y1/x2-x1 = (7-3)/(0-5) = 4/-5 = -4/5

The y-intercept is found where the x value is equal to 0, which is given to us in the point (0,7). This means that b = 7 because the variable b represents the y-intercept.

Now, we can substitute in these values into slope-intercept form to create our equation.

y = mx + b

y = -4/5x + 7

Therefore, your answer is y = -4/5x + 7.

Hope this helps!

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A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special c

fredd [130]

Answer:

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Step-by-step explanation:

Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as

H0 :p 0.5 against Ha: p ≠ 0.5

The significance level is approximately 0.05

The test statistic to be used is number of heads x.

Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution

Heads (x) Probability (X=x) Cumulative Decumulative

0 1/16384 (1) 0.000061 0.000061

1 1/16384 (14) 0.00085 0.000911

2 1/16384 (91) 0.00555 0.006461

3 1/16384(364) 0.02222

4 1/16384(1001) 0.0611

5 1/16384(2002) 0.122188

6 1/16384(3003) 0.1833

7 1/16384(3432) 0.2095

8 1/16384(3003) 0.1833

9 1/16384(2002) 0.122188

10 1/16384(1001) 0.0611

11 1/16384(364) 0.02222

12 1/16384(91) 0.00555 0.006461

13 1/16384(14) 0.00085 0.000911

14 1/16384(1) 0.000061 0.000061

We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).

We observe that P (X≤2) = 0.006461 > 0.025

and

P ( X≥12 ) = 0.006461 > 0.025

Therefore true significance level is

∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122

Hence critical region is (X≤0) and ( X≥14)

Computation x= 12

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

3 0

3 years ago

Is this triangle equilateral? yes

Doss [256]

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6 0

3 years ago

Read 2 more answers

What is an inverse statement

shusha [124]

Answer:

1 | noun | a message that is stated or declared; a communication (oral or written) setting forth particulars or facts etc

2 | noun | a fact or assertion offered as evidence that something is true

3 | noun | (music) the presentation of a musical theme

4 | noun | a nonverbal message

5 | noun | the act of affirming or asserting or stating something

6 | noun | (computer science) a line of code written as part of a computer program

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(7 meanings)

4 0

4 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

If K is the midpoint of JL, JK=9x-1 and KL=2x+27, find JL.

ratelena [41]

Answer:

The answer is B. 70

Step-by-step explanation:

First, since K is the midpoint of line segment JL, JK must equal KL.

So, set 9x-1 = 2x+27 and solve.

7x=28 so x=4

Then, since they are asking for JL, using x=4, add together JK and KL.

So, 9x-1+2x+27 = 11x+26 = 11(4) + 26 = 44+26 = 70

3 0

3 years ago