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Alex73 [517]
3 years ago
15

Suppose you and a partner want to make a recipe for 25 friends. Adjust the amount of each ingredient below to 25 servings.

Mathematics
2 answers:
Rufina [12.5K]3 years ago
6 0
The recipe is 4 times bigger than you need it to be. 100/25=4 Now just divide all ingredients by 4.

1.)100/4=25
2.)72/4=18
3.)14/4=3.5
4.)6/4=1.5
5.)24/4=6
6.)80/4=20
7.)50/4=12.5
mel-nik [20]3 years ago
5 0
Well, we are starting with 100 servings, and we're trying to find the amount of ingredients necessary to create 25 servings. To do this, we must first simply divide 25 by 100 to see what the ratio would be, and when we do this, we can see that

25 / 100 = \frac{25}{100} = \frac{1}{4}

Now, all we have to do is multiply all of the ingredients by the ratio to find out how much we would use for only a quarter of the amount that the original recipe calls for.

In order to multiply by a whole number by a fraction, you just need to make sure that the numerator is lined up with the whole number, and then put a 1 below the whole number to turn it into a fraction. Then, you can divide the numerators and denominators together, respectively.

1.) 100 * \frac{1}{4} = \frac{100}{1} *  \frac{1}{4} = \frac{100 * 1}{1 * 4} = \frac{100}{4} = 25

2.) 72 * \frac{1}{4} =  \frac{72}{1} *  \frac{1}{4} =\frac{72 * 1}{1*4} = \frac{72}{4} = 18

3.) 14 * \frac{1}{4} = \frac{14}{1} * \frac{1}{4} = \frac{14 *1}{1*4} = \frac{14}{4} = 3 \frac{1}{2}

4.) 6 * \frac{1}{4} = \frac{6}{1} * \frac{1}{4} = \frac{6*1}{1*4} = \frac{6}{4} = <span>1 \frac{1}{2} </span>

5.) 24 * \frac{1}{4} = \frac{24}{1} * \frac{1}{4} = \frac{24*1}{1*4} = \frac{24}{4} = 6

6.) 80 * \frac{1}{4} = <span>\frac{80}{1} * \frac{1}{4} = \frac{80*1}{1*4} = \frac{80}{4} = <span>20</span>

</span>7.) 50 * \frac{1}{4} = \frac{50}{1} * \frac{1}{4} = \frac{50*1}{1*4} = \frac{50}{4} = 12 \frac{1}{2}

And there you have the recipe ingredients necessary for 25 servings.
Hope that helped! =)
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In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%
lions [1.4K]

Answer:

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59  

And rounded up we have that n=350  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p represent the real population proportion of interest

\aht p represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:  

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96  

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}} (a)  

And on this case we have that ME =\pm 0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2} (b)

And replacing into equation (b) the values from part a we got:  

n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59  

And rounded up we have that n=350  

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OLEGan [10]
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