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2 years ago

Graph the linear equation: 2x-y=4

Mathematics

1 answer:

juin [17]2 years ago

8 0

Answer:

$Slope=2$

$x-intercept=\frac{4}{2} =2$

$y-intercept=\frac{4}{-1} =-4.00000$

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2*x-y-(4)=0

Step 1:

Equation of a Straight Line

Solve 2x-y-4 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-y-4 = 0 and calculate its properties

Graph of a Straight Line :

( see attatchment)

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/-1 so this line "cuts" the y axis at y=-4.00000

y-intercept = 4/-1 = -4.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000

x-intercept = 4/2 = 2

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -4.000 and for x=2.000, the value of y is 0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.000 - (-4.000) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 2

Geometric figure: Straight Line

1. Slope = 2

2. x-intercept = 4/2 = 2

3. y-intercept = 4/-1 = -4.00000

- clarification for graph - green means rise red means run , bottom black is x intercept which is 2.000 under rise is y-intercept and under the y axis is 0.000 and -4.000.

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Answer:

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3 years ago

A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

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(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

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So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

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Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

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Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

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So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

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$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

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