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3 years ago

Write in equation of the line in the graph

Mathematics

2 answers:

salantis [7]3 years ago

6 0

To write the equation of a line, we use the equation: y = mx +b.

m is the slope of the line, which can be calculated using the equation:
m = (y2 - y1)/(x2 - x1)
We can choose any two points on the line to put into this equation. The red dots are at (0,0) and (-6,-2), so we will use those, but you would get the same answer by using any other pair of coordinates on the blue line.
m = (-2 - 0)/(-6 - 0) = 2/6 = 1/3

b is the y-intercept of the line. The y-intercept is the y-coordinate when the line crosses the y-axis. It crosses the y-axis at (0,0), so the y-intercept is 0.

Now, we plug our values back into the full equation to get the equation of the line.
y = mx + b
y = (1/3)x + 0

So the final answer is y = (1/3)x or y = x/3, depending on how you want to write it.

iogann1982 [59]3 years ago

5 0

Y=3x because it passes through the origin (has b (or y-intercept) 0), and slope of 3

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The value of <img src="https://tex.z-dn.net/?f=%5Csin%20%5E%7B-1%7D%5Cleft%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright%29-%5Csi

Mademuasel [1]

Answer:

$\displaystyle \frac{\pi}{6}$

Explanation:

According to the unit circle, $\displaystyle \frac{\pi}{3}$ and $\displaystyle \frac{\pi}{6}$ are the radian measures you are looking for because all y-coordinates are associated with the sine function, so when evaluating, you will arrive at this:

$\displaystyle \boxed{\frac{\pi}{3}} = \frac{\pi}{3} - \frac{\pi}{6}$

I am joyous to assist you at any time.

6 0

2 years ago

At the museum, the O'Rourke family bought 3 adult tickets and 2 children tickets for $23.50. The Patel family bought 2 adult tic

Tresset [83]

6.25 for each kids ticket and 11.75 for each adult ticket

4 0

3 years ago

Express as a trinomial. (3x+3)(2x−4)

Artyom0805 [142]

Use the FOIL method: First, Outside, Inside, Last

3x(2x) = 6x²

3x(-4) = -12x

3(2x) = 6x

3(-4) = -12

6x² -12x + 6x-12

Combine like terms

-12x + 6x = -6x

6x² - 6x - 12 is your answer

hope this helps

5 0

4 years ago

A college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of

Alla [95]

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of hours of TV watched per week = $\frac{\sum X}{n}$ = 9.65

s = sample standard deviation = $\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }$ = 4.61

n = sample of people = 20

$\mu$ = true average number of hours of TV watched per week

Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the true average, $\mu$ is ;

P(-1.33 < $t_1_9$ < 1.33) = 0.80 {As the critical value of t at 19 degrees of

freedom are -1.33 & 1.33 with P = 10%}

P(-1.33 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.33) = 0.80

P( $-1.33 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.33 \times {\frac{s}{\sqrt{n} } }$ ) = 0.80

P( $\bar X-1.33 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.33 \times {\frac{s}{\sqrt{n} } }$ ) = 0.80

80% confidence interval for $\mu$ = [ $\bar X-1.33 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.33 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }$ , $9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }$ ]

= [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

7 0

3 years ago

Which expressions are equivalent to 2(b+3c)?

Rina8888 [55]

Answer:

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step-by-step explanation:

we have

$2(b+3c)$

Distribute the number 2

$2(b+3c)=2b+2(3c)=2b+6c$

Verify each case

case A) 3(b+2c)

distribute the number 3

$3(b+2c)=3b+3(2c)=3b+6c$

$3b+6c \neq 2b+6c$

therefore

Choice A is not equivalent to the given expression

case B) (b+3c)+(b+3c)

Combine like terms

$b+3c)+(b+3c)=(b+b)=(3c+3c)=2b+6c$

$2b+6c= 2b+6c$

therefore

Choice B is equivalent to the given expression

case C) 2(b)+2(3c)

Multiply both terns by 2

$2(b)+2(3c)=2b+6c$

$2b+6c= 2b+6c$

therefore

Choice C is equivalent to the given expression

6 0

3 years ago

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