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Fiesta28 [93]
2 years ago
11

A health fitness research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend eac

h week exercising at the center. They want to estimate the mean within a margin of error of 0.4 hours with a 95% level of confidence. Previous data suggest that the population standard deviation (sigma) is 2.6 hours. What is the smallest sample size that meets these criteria
Mathematics
1 answer:
Arlecino [84]2 years ago
6 0

Answer:

the smallest sample size is 163

Step-by-step explanation:

The computation of the smallest sample size that meets these criteria is shown below:

n = (Z a/2 ×  Standard deviation  ÷ Margin of error ) ^2

Zα/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )

Standard Deviation ( S.D) = 2.6

Margin of error i.e. ME =0.4

n = ( 1.96 × 2.6 ÷ 0.4) ^2

= 163

Hence, the smallest sample size is 163

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Tju [1.3M]
<h3>Answer:  8</h3>

=====================================

Work Shown:

y = 192\left(4^{x-3}\right)\\\\196,608 = 192\left(4^{x-3}\right)\\\\\frac{196,608}{192} = 4^{x-3}\\\\1024 = 4^{x-3}\\\\4^{x-3} = 1024\\\\\log\left(4^{x-3}\right)=\log\left(1024\right)\\\\(x-3)*\log\left(4\right)=\log\left(1024\right)\\\\x-3=\frac{\log\left(1024\right)}{\log\left(4\right)}\\\\x-3=5\\\\x=5+3\\\\x=8\\\\

It will take 8 hours for the population to reach 196,608 bacteria.

3 0
2 years ago
75=-5(3+6m) I need this​
alisha [4.7K]
Are you finding m? If so here is the answer:

75 = -5(3 + 6m)

Distribute:
75 = -15 - 30m

Add 15 to both sides:
75 = -15 - 30m
+15 +15
90 = -30m

Divide by -30 on both sides:
90/-30 = (-30m)/-30

You should get: m = -3
7 0
3 years ago
Andrew claims the initial value and y - intercept are the same thing on a graph. Is he correct?
Agata [3.3K]

Answer:

We conclude that the initial value and y-intercept are the same thing on a graph.

Please check the attached graph of the equation y = 2x+1.

Step-by-step explanation:

We know that the initial value on a graph is basically the out-put value y of the point where the line meets or crosses the y-axis.

In other words, the initial value is the y-value or output of the point at x = 0

For example,

Let the equation

y = 2x+1

substitute x = 0

y = 2(0)+1

y = 0+1

y = 1

Thus, the initial value of the equation y = 2x+1 is: y = 1

Please check the attached graph of the equation y = 2x+1.

It is clear from the graph that at x = 0, the value of y = 1.

Thus, at y = 1, the line meets the y-axis.

Hence, the initial value of the line is: y = 1

Similarly, we know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

For example,

Let the equation

y = 2x+1

substitute x = 0

y = 2(0)+1

y = 0+1

y = 1

Thus, the y-intercept of y = 2x+1 is y = 1.

Please check the attached graph of the equation y = 2x+1.

It is clear from the graph that at x = 0, the value of y = 1.

Therefore, the y-intercept of y = 2x+1 is y = 1.

Conclusion:

Therefore, we conclude that the initial value and y-intercept are the same thing on a graph.

Please check the attached graph of the equation y = 2x+1.

6 0
3 years ago
Jenny picked 25 roses. she gave away 10 roses. What percent of the roses did Jenny give away?
diamong [38]
Divide 10 by 25, which would get you 4. Move the decimal over two to the left, because you wanted a percentage.

Jenny gave away 40% of the roses.
3 0
3 years ago
Helppppppppppppp plzzzzzzzzzzzzzzzzzzzzzz
zhuklara [117]

Answer:

These parallel lines cross 1 line. Because they are parallel they will form the same angles on that line. Therefore, x+50 = 3x-100 since those angles are corresponding angles made by a pair of parallels.

To find x we need to find what value of x gives the same answer for 3x-100 and x+50 since those 2 angles are equal.

x+50 = 3x-100 - now all we need to do is solve for x:

x+50 = 3x-100

50=2x-100

150=2x

75=x

x=75

Step-by-step explanation:

6 0
3 years ago
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