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3 years ago

The following frequency table summarizes a set of data.

Mathematics

1 answer:

strojnjashka [21]3 years ago

6 0

Answer:

Part A

The population standard deviation is suitable for this dataset as it isnt given whether its a sample or a population distribution and it sure doesn't seem like the findings from such a dataset is to be generalized for some population distribution.

Part B

This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.

Step-by-step explanation:

The spread of a dataset is usually the measure of dispersion, a measure of the way the distribution spreads out from a particular mean value.

The problem of which type of standard deviation one should calculate usually arises a lot in Statistics. As the name sounds, population standard deviation usually uses all of the distribution to compute while the sample standard deviation uses the data from the sample distribution

The best advice on when to use the population stamdard deviation formula is that

(1) we have the entire population or

(2) we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize the statistical findings to the population.

The sample standard deviation formula is used when one has a sample of a larger population, one is not only interested in this sample and one wishes to generalize the findings to the population.

The population standard deviation is given as

σ = √[Σ(x - xbar)²/N]

Sample standard deviation

σ = √{[Σ(x - xbar)²]/N-1)}

The only difference is the N and (N-1).

So, for the questions presented,

Part A.

Here, it is evident that the findings for this dataset in the question is just for this dataset, hence,the population standard deviation is suitable for this dataset.

Part B

Hope this Helps!!!

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devlian [24]

Answer:-

The two inverses are,

$y = \sqrt {\frac{x+4}{9}}$

and, $y = - \sqrt {\frac{x+4}{9}}$

Step-by-step calculation:-

$y = 9 \times x^{2} - 4$

⇒ $x^{2} = \frac{y+4}{9}$

⇒ $x = \mp \sqrt {\frac{y+4}{9}}$

So, the two inverses are,

$y = \sqrt {\frac{x+4}{9}}$

and, $y = - \sqrt {\frac{x+4}{9}}$

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3 years ago

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Express the fractions 1/2,3/16,and 7/8 with and LCD

Alexeev081 [22]

LCD is the least common multiple of the denominators of the fraction. The use of finding the LCD of a fraction is to simplify the adding, subtracting, dividing and multiplying the fractions. For ½, 2 is the least common denominator. For 3/16, 16 is the least common denominator. For 7/8, 8 is the least common denominator. Each of these fractions cannot be reduced to a simpler form because these are their simpler forms. If it can be reduced, the LCD would vary.

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4 years ago

LenKa [72]

Answer:

D. terms.

Step-by-step explanation:

Terms they are examples of terms.

Answer:

2a, 3b and -4c are examples of terms.

Step-by-step explanation:

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To find : 2a, 3b and -4c are examples of ?

Solution :

We have given the expression

A term is made up of a constant multiplied by a variable.

In the given expression,

Variables are a, b and c.

Constant are 2,3 and -4.

So, 2a, 3b and -4c will make a term.

Therefore, 2a, 3b and -4c are examples of terms.

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3 years ago

A researcher recorded the number of e-mails received in a month and the number of online purchases made during that month for 50

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Step-by-step explanation:

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3 years ago

Need help with trig problem in pic

Sidana [21]

Answer:

a) $cos(\alpha)=-\frac{3}{5}\\$

b) $\sin(\beta)= \frac{\sqrt{3} }{2}$

c) $\frac{4+3\sqrt{3} }{10}\\$

d) $\alpha\approx 53.1^o$

Step-by-step explanation:

a) The problem tells us that angle $\alpha$ is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

$tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}$

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

$cos(\alpha)=-\frac{3}{5}$

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

$cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}$

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find $sin(\alpha -\beta)$ by using the identity:

$sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\$

Notice that we need to find $sin(\alpha)$ , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

$sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}$

Then:

$sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}$

Since $sin(\alpha)=\frac{4}{5}$

then $\alpha=arcsin(\frac{4}{5} )\approx 53.1^o$

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3 years ago