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3 years ago

Which of the following equations is equivalent to

Mathematics

1 answer:

andrew-mc [135]3 years ago

5 0

Answer:

B. y=3x+12

Step-by-step explanation:

Hi there!

We want to find out which equation is equivalent to -6x+2y=24

The equation is currently written in standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b CANNOT equal zero

We can change the equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept, as all of the answer options are in slope-intercept form.

To do that, we'll need to isolate y by itself on one side

So let's add 6x to both sides to remove it from the left side

-6x+2y=24

+6x +6x

__________________

2y=6x+24

Now divide both sides by 2 to get the value of y by itself (1y)

y=3x+12

The answer is B. y=3x+12

Hope this helps!

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Answer:

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3 years ago

A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Kar

ch4aika [34]

Answer:

We conclude that the mean waiting time is less than 10 minutes.

Step-by-step explanation:

We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.

Let $\mu$ = mean waiting time for bus number 14.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 minutes {means that the mean waiting time is less than 10 minutes}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

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

where, $\bar X$ = sample mean waiting time = 7.8 minutes

s = sample standard deviation = 2.5 minutes

n = sample of different occasions = 18

So, test statistics = $\frac{7.8-10}{\frac{2.5}{\sqrt{18} } }$ ~ $t_1_7$

= -3.734

The value of t test statistics is -3.734.

Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.

Since our test statistic is less than the critical value of t as -3.734 < -2.567, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean waiting time is less than 10 minutes.

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