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2 years ago

To make his famous chocolate cake, a baker uses chocolate that is 75% cocoa.

Mathematics

1 answer:

Masja [62]2 years ago

8 0

The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

<h3>Equation </h3>

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the amount of 90% chocolate. Using equation:

100 * 70% + x * 90% = (x + 100) * 75%

100 * 0.7 + 0.9 * x = (x + 100) * 0.75

70 + 0.9x = 0.75x + 75

x = 100/3

The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

Find out more on Equation at: brainly.com/question/22688504

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Read 2 more answers

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people.

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Answer:

$8.2-2.58\frac{2.2}{\sqrt{18}}=6.86$

$8.2+2.58\frac{2.2}{\sqrt{18}}=9.54$

So on this case the 90% confidence interval would be given by (6.86;9.54) And the error is given by:

$ME= 2.58\frac{2.2}{\sqrt{18}} =1.338$

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".

$\bar X=8.2$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=2.2$ represent the population standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$