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Ne4ueva [31]
3 years ago
8

Please help on this question !

Mathematics
1 answer:
netineya [11]3 years ago
5 0
To do this problem hand, you have to start by changing the mixed number into an improper fraction. A handy trick for that is to:
1) Multiply the denominator of the fraction part, 4, by the whole number, 4. So 4*4=16.

2) Add the number in the numerator to the value from step one. So 16+3=19.

3) Put the value from step two over the denominator to get your improper fraction! 19/4

Now you need to multiply to get a common denominator in both values in order to subtract. You have 19/4 - 1/3. This is when you could use a calculator if allowed haha, or multiply 19/4 by 3/3 and 1/3 by 4/4 to get 57/12 - 4/12. Subtract to get 53/12.

Now just do simple division and put the remainer over 12 and simplify the fraction if needed! 53/12 = 4R5. So 4 5/12 is the answer :)
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No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).

Step-by-step explanation:

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8 = b - 1 + 8b

group like terms

8 + 1 = b + 8b

9 = 9b cus b standing alone me 1b

divide both side by 9

<u>9</u><u> </u> = <u>9</u><u>b</u>

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A grower believes that one in five of his citrus trees are infected with the citrus red mite. How large a sample should be taken
mihalych1998 [28]

Answer:

n=6147

Step-by-step explanation:

1) Notation and definitions

X=1 number of citrus trees that are infected with the citrus red mite.

n=5 random sample taken

\hat p=\frac{1}{5}=0.2 estimated proportion of citrus trees that are infected with the citrus red mite.

p true population proportion of citrus trees that are infected with the citrus red mite.

Me=0.01 represent the margin of error desired

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".  

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 values 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 values would be given by:

t_{\alpha/2}=-1.96, t_{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 0.01 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{0.2(1-0.2)}{(\frac{0.01}{1.96})^2}=6146.56  

And rounded up we have that n=6147

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3 years ago
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