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3 years ago

-2/3a+5/6a-1/6 simplify

Mathematics

2 answers:

ratelena [41]3 years ago

8 0

Answer:

$\frac{1}{6} a-\frac{1}{6}$

Step-by-step explanation:

$-\frac{2}{3} a+\frac{5}{6}a-\frac{1}{6}$

$=-\frac{4}{6} a+\frac{5}{6}a -\frac{1}{6}$

$= \frac{1}{6} a-\frac{1}{6}$

Anarel [89]3 years ago

3 0

Answer:

$\frac{( - 2)}{3} a + \frac{5}{6}a - \frac{1}{6} \\ = \frac{(- 4a) + 5a - 1}{6} = \frac{(a - 1)}{6}$

hope this helps.

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What is the range of the following data set?

sashaice [31]

Answer: The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

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3 years ago

Ally is making a fruit punch using 48 ounces of grape juice and some seltzer water. She wants to make 10 equal servings that are

yaroslaw [1]

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3 years ago

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A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

Helen [10]

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =16$ represent the sample variance

s=4 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

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 mean or variance 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.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.01,19)" "=CHISQ.INV(0.99,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=36.191$

$\chi^2_{1- \alpha/2}=7.633$

And replacing into the formula for the interval we got:

$\frac{(19)(16)}{36.191} \leq \sigma^2 \leq \frac{(19)(16)}{7.633}$

$8.400 \leq \sigma^2 \leq 39.827$

So the 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

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3 years ago

Maya runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?

andreev551 [17]

Answer:

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Step-by-step explanation:

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3 years ago

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wolverine [178]

We know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
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Circle 1 is centered at (4,3) and has a radius of 5 centimeters
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Move the center of the circle 1 onto the center of the circle 2
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(x,y)--------> (x+2,y-5)
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step 2
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