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Ierofanga [76]
3 years ago
6

2. Which of the following systems of inequalities represents the graph?

Mathematics
2 answers:
Rom4ik [11]3 years ago
8 0

Answer:

Option: D is the correct answer.

D)  –2x + y ≥ 4

         x + y < 2

Step-by-step explanation:

We are asked to find the linear inequality that represents the following graph.

Clearly from the graph we could observe that one line is dotted and the other is solid line.

i.e. one inequality is strict while the other is a inequality with equality sign.

<u>Dashed line:</u>

It passes through (0,2) and  (2,0).

Hence, the equation of line is:

y-2=\dfrac{0-2}{2-0}\times (x-0)\\\\\y-2=\dfrac{-2}{2}\times x\\\\y-2=-x\\\\x+y=2

As the shaded region is towards the origin.

Hence, the inequality will be:

x+y<2.

<u>Solid line:</u>

The line passes through (-2,0) and (0,4).

hence equation of line is:

y-0=\dfrac{4-0}{0-(-2)}\times (x+2)\\\\

i.e

y=\dfrac{4}{2}\times (x+2)\\\\y=2\times (x+2)\\\\y=2x+4\\\\-2x+y=4

Now, as the shaded region is away from the origin hence the inequality which will be used is:

-2x+y\geq 4

Hence, option: D is the correct answer.

D.   –2x + y ≥ 4

       x + y < 2

Irina18 [472]3 years ago
5 0

Answer:

D.–2x + y ≥ 4

x + y < 2

<3

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13x+15=11x-25 \\ \\ 13x-11x=-25-15 \\\\ 2x=-40 \\\\ \boxed{x=-\frac{40}{2}=-20}

You pass the free terms wich don't contain 'x' in the othe part of the equal with changed signe ans the same for the terms wich contain x.
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3 years ago
Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining wh
Molodets [167]

Answer:

(A) The mean for the differences is 2.0.

(B) The test statistic is 1.617.

(C) At 90% confidence the null hypothesis should not be rejected.

Step-by-step explanation:

We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.

The following data (in miles per gallon) show the results of the test;

Driver         Manufacturer A               Manufacturer B

   1                      32                                       28

  2                      27                                       22

  3                      26                                       27

  4                      26                                       24

  5                      25                                       24

  6                      29                                       25

  7                       31                                       28

  8                      25                                       27

Let \mu_1 = mean MPG for the fuel efficiency of Manufacturer A brand

\mu_2 = mean MPG for the fuel efficiency of Manufacturer B brand

SO, Null Hypothesis, H_0 : \mu_1-\mu_2=0  or  \mu_1= \mu_2    {means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}

Alternate Hypothesis, H_A : \mu_1-\mu_2\neq 0  or  \mu_1\neq  \mu_2   {means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}

The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;

                      T.S.  = \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t__n__1+_n__2-2

where, \bar X_1 = sample mean MPG for manufacturer A = \frac{\sum X_A}{n_A} = 27.625

\bar X_2 = sample mean MPG for manufacturer B =\frac{\sum X_B}{n_B} = 25.625

s_1 = sample standard deviation for manufacturer A = \sqrt{\frac{\sum (X_A-\bar X_A)^{2} }{n_A-1} } = 2.72

s_2 = sample standard deviation manufacturer B = \sqrt{\frac{\sum (X_B-\bar X_B)^{2} }{n_B-1} } = 2.20

n_1 = sample of cars selected from manufacturer A = 8

n_2 = sample of cars selected from manufacturer B = 8

Also, s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2}  }{n_1+n_2-2} }   =  \sqrt{\frac{(8-1)\times 2.72^{2}+(8-1)\times 2.20^{2}  }{8+8-2} }  = 2.474

(A) The mean for the differences is = 27.625 - 25.625 = 2

(B) <u><em>The test statistics</em></u>  =  \frac{(27.625-25.625)-(0)}{2.474 \times \sqrt{\frac{1}{8}+\frac{1}{8}  } }  ~  t_1_4

                                     =  1.617

(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.

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Answer:

-1/4

Step-by-step explanation:

Hello!

The rate of change is also known as the slope.

Standard equation of a line: y = mx + b

  • y: output
  • m:  slope
  • x: input
  • b: y-intercept

So, if we match the standard form to the given function:

  • y = mx + b
  • y = -1/4x + 1

-1/4 is m, or the rate of change.

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DanielleElmas [232]
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