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3 years ago

What should be the first step in adding these equation to eliminate y 12x - 2y = -1 + 4x + 6y =-4

Mathematics

1 answer:

barxatty [35]3 years ago

6 0

Answer:

See below

Step-by-step explanation:

<u>Assumed you need to solve the system:</u>

12x - 2y = - 1
4x + 6y = - 4

In order to solve this by elimination, triple the first equation and add the second one.

<u>It will make the coefficients of y same with opposite signs:</u>

-6y and 6y

When added together these cancel, leaving x as the only variable.

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A company is approached by a new warehouse management systems vendor to adopt a new system. The vendor claims that the warehouse

Ludmilka [50]

Answer:

The null hypothesis is $H_o : \mu = 180$

The alternative hypothesis is $H_a : \mu < 180$

The decision rule is fail to reject the null hypothesis

The conclusion

There no sufficient evidence to support the vendor claim that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 3 \ minutes = 180 \ seconds$

The sample size is n = 25

The excel sheet is show on the first uploaded image

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu = 180$

The alternative hypothesis is $H_a : \mu < 180$

Generally the sample mean is mathematically represented as

$\= x = \frac{156 + 136 + \cdots + 181}{25}$

=> $\= x = 173.2$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x )^2 }{n} }$

=> $\sigma = \sqrt{\frac{ (156 - 173.2 )^2 + (136 - 173.2 )^2 + \cdots + (181- 173.2 )^2 }{25} }$

=> $\sigma = 24.261$

Generally the test statistics is mathematically represented as

$t = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }$

=> $t = \frac{173.2 - 180 }{\frac{24.261}{\sqrt{25} } }$

=> $z = -1.40$

Generally p-value is mathematically represented as

$p-value = P(Z < z)$

=> $p-value = P(Z < -1.40)$

From the z-table

$P(Z < -1.40) = 0.080757$

=> $p-value = 0.080757$

From the obtained value we that $p-value > \alpha$

The decision rule is fail to reject the null hypothesis

The conclusion

5 0

2 years ago

Niko uses 12 marshmallows and 8 graham crackers to make 4 s'mores.

Lerok [7]

Answer:

6 crackers, 9 marshmallows

Step-by-step explanation:

You have to divide to find how many graham crackers and marshmallows are needed to make 1 s'more:

8 / 4 = 2, so 2 crackers per s'more. Then,

12 / 4 = 3, so 3 marshmallows per s'more. Now that we know this, all we have to do is multiply each number by 3 to make 3 s'mores.

2 * 3 = 6, so 6 crackers, and

3 * 3 = 9, so 9 marshmallows.

3 0

3 years ago

Read 2 more answers

Start with the point A (3, 1). Translate the point 1 unit to the left and 4 units down. What are the new coordinates of the poin

Over [174]

This is the transformations: See the picture, here we find the coordinate:

A' = (2,-3) and A''=(0.5,-2). There is many ways to get back to A from A'', i have showed one way (the red lines). This is done by going 5 units right and then 6 units up.

see image at https://imgur.com/a/fWQl8

3 0

2 years ago

Estimate 62.853+33.51 by first rounding each number to the nearest whole number

Karolina [17]

63+34=97 thats the answer

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2 years ago

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Find the equation of a parabola with a focus at (0,-1) and a directrix at y = 4.

Anastasy [175]

Answer:

y = -1/10x^2 +2.5

Step-by-step explanation:

The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:

-1 -4 = -5

So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).

The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...

y = (1/(4p))(x -h) +k

y = -1/10x^2 +2.5

_____

You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.

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3 years ago