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padilas [110]
3 years ago
14

A rectangles length is three more than twice the width. The perimeter of the rectangle is 72 units. Write a let statement that c

an be used to find the length and width of the rectangle. Write an equation that can be used to find the length and width of the rectangle. Solve the equation. What is the length of the rectangle? What is the width of the rectangle?
Mathematics
1 answer:
photoshop1234 [79]3 years ago
3 0

Answer:

The length is 25 units and the width is 11 units

Step-by-step explanation:

Let the length of the rectangle be l.

Let the width of the rectangle be w.

We are given that the length of the rectangle is three times more than twice its width. This means that:

l = 3 + 2w

The perimeter of a triangle is given as:

P = 2(l + w)

This implies that:

P = 2[(3 + 2w) + w]

P = 2(3 + 3w)

We can use this to find the width of the rectangle and then the length.

The perimeter of the rectangle is 72 units.

Therefore:

72 = 2(3 + 3w)

72 = 6 + 6w

=> 6w = 72 - 6 = 66

w = 66 / 6 = 11 units

The length, l, is therefore:

l = 3 + 2(11) = 3 + 22 = 25 units

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Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because th
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We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

<u><em>Let </em></u>\mu<u><em> = mean contents of cola bottles.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq  300 ml   {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, H_A : \mu < 300 ml   {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;

                       T.S.  = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean contents of cola bottle = \frac{\sum X}{n} = 299.03 ml

            \sigma = population standard deviation = 3 ml

            n = sample of bottles = 6

So, <em><u>test statistics</u></em>  =  \frac{299.03-300}{\frac{3}{\sqrt{6} } }     

                               =  -0.792

<em>Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

8 0
3 years ago
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