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ozzi
2 years ago
10

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The es

timate must be within 0.75 milligrams of the population mean. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.10 milligrams
Mathematics
1 answer:
Mrrafil [7]2 years ago
5 0

Answer:

The minimum sample size required to construct a 95% confidence interval for the population mean is 65.

Step-by-step explanation:

We are given the following in the question:

Population standard deviation,

\sigma = 3.10\text{ milligrams}

We need to construct a 95% confidence interval such that the estimate is within 0.75 milligrams of the population mean.

Thus, the margin of error must me 0.75

Formula for margin of error:

z_{critical}\times \dfrac{\sigma}{\sqrt{n}}

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

Putting values, we get,

0.75 = 1.86\times \dfrac{3.10}{\sqrt{n}}\\\\\sqrt{n} = \dfrac{1.96\times 3.10}{0.75}\\\\\sqrt{n} = 8.101\\\Rightarrow n = 65.63\approx 65

Thus, the minimum sample size required to construct a 95% confidence interval for the population mean is 65.

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f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex
DerKrebs [107]

Answer:

see below

Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

Set equal to zero to find the x intercepts

0  = −16x^2 + 24x + 16

Factor out -8

0 = -8(2x^2 -3x-2)

Factor

0 = -8(2x +1) (x-2)

Using the zero product property

2x+1 =0    x-2 =0

x = -1/2      x=2

The x intercepts are -1/2   ,2

Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum

The x value of the maximum is 1/2 way between the zeros

(-1/2+2) /2 = 1.5/2 =.75

To find the y value substitute into the function

f(.75) = -8(2x +1) (x-2)

        =-8(2*.75+1) (.75-2)

        = -8(2.5)(-1.25)

         =25

The vertex is at (.75, 25)

We have the zeros, and  the vertex.  We know the graph is symmetrical about the vertex

3 0
2 years ago
Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the pro
kondaur [170]
\bf (x)(x+2)=255\implies x^2+2x=255\implies x^2+2x-255=y
\\\\
\textit{setting y=0}\implies x^2+2x-255=0
\\\\
\textit{now, factoring that}
\\\\
(x+17)(x-15)=0\implies 
\begin{cases}
x=-17\\
x=15
\end{cases}

notice the picture of the graph added here
low and behold, x = -17, y is 0, and x= 15, y is 0
the graph is touching the x-axis, an x-intercept
or so-called, a "solution"

3 0
2 years ago
Read 2 more answers
There are 12 inches in 1 foot and 5,280 feet in 1 mile. Is Elena ran 2-1/2 miles how many inches is that ?
puteri [66]

Answer:

158400 inches is 2 1/2 miles

Step-by-step explanation:

2.5* 5280 because 2.5 miles is 13200 feet.

13200*12 because 13200 feet is 158400 inches.

The answer would be 158400 inches.

Please mark as brainliest! Hope this helps! If you need anymore help just ask! :D

4 0
2 years ago
Read 2 more answers
An epidemiologic survey of roller-skating injuries in Metroville, a city with a population of 100,000 (during the midpoint of th
Ahat [919]

Answer: c. \dfrac{90}{1800}\times100\%

Step-by-step explanation:

As per given , we have

Total number of residents injured from roller-skating =1,800

Total number of deaths from roller-skating = 90

Formula for Mortality rate : Mortaility\ rate= \dfrac{Deaths\ due \ to\ injury}{Tota\ injuries}

Then, the proportional mortality ratio (%) due to roller-skating was

=\dfrac{90}{1800}\times100\%

= 5%

Hence, the correct answer is c.\dfrac{90}{1800}\times100\%

8 0
2 years ago
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believ
olga_2 [115]

Answer:

Value of v that minimizes E is v = 3u/2

Step-by-step explanation:

We are given that;

E(v) = av³L/(v-u)

Now, using the quotient rule, we have;

dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²

Expanding and equating to zero, we have;

[3av³L - 3av²uL - av³L]/(v - u)² = 0

This gives;

(2av³L - 3av²uL)/(v-u)² = 0

Multiply both sides by (v-u)² to give;

(2av³L - 3av²uL) = 0

Thus, 2av³L = 3av²uL

Like terms cancel to give;

2v = 3u

Thus, v = 3u/2

5 0
2 years ago
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