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denis23 [38]
2 years ago
15

A market research company wishes to know how many energy drinks teenagers drink each week. They want to construct a 80% confiden

ce interval with an error of no more than 0.08. A consultant has informed them that a previous study found the mean to be 7.3 energy drinks per week and found the standard deviation to be 0.7. What is the minimum sample size required to create the specified confidence interval
Mathematics
1 answer:
mash [69]2 years ago
7 0

Answer: 126 samples

Step-by-step explanation:

Given that :

Standard deviation (σ) = 0.7

Mean (m) = 7.3

Error (E) = 0.08

α = 80%

The sample size n can be obtained using the relation :

n = [(Zcrit * standard deviation) / Error]^2

The Zcritical at 80% = 1.282

Hence,

n = ((1.282 * 0.7) / 0.08)^2

n = (0.8974 / 0.08)^2

n = 11.2175^2

n = 125.83230625

n = 126

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Lina20 [59]

Option D: Two irrational solutions

Explanation:

The equation is 17+3 x^{2}=6 x

Subtracting 6x from both sides, we have,

3x^{2} -6x+17=0

Solving the equation using quadratic formula,

x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}

Simplifying the expression, we get,

\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}

Taking out the common terms and simplifying, we have,

\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}

Dividing by 3, we get,

x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}

Hence, the equation has two irrational solutions.

8 0
2 years ago
The value of y is directly proportional to the value of x. If y = 180 when x = 50, the value of y when x = 25?​
Triss [41]

Answer: y = 90

Step-by-step explanation:

Since x and y are proportional, when x =25 (which is 50 divided by 2), y would be 90 since 90 is 180 divided by 2.

8 0
3 years ago
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What is the approximate volume of the cone?
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Whats the difference between linear equations and quadratic equation
SIZIF [17.4K]

Answer:

Step-by-step explanation:

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3 years ago
The circumference of a circle is 23π m. What is the area, in square meters? Express your answer in terms of \piπ
LenaWriter [7]

Answer:

Area of the circle =   \frac{529}{4}  π  m²    or      132.25 π  m²

Step-by-step explanation:

To find the area, we will follow the steps below.

First write down the formular for the circumference of a circle, then use the formula to find the radius of the circle after which you can now find the area of the circle.

That is;

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From the question given, circumference C = 23π

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Divide both-side of the equation by 2π

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Formula for calculating the area of a circle is given by;

A = πr²

where A= area of the circle   and   r is the radius of the circle

A = π ( \frac{23}{2} )²

A = \frac{529}{4}  π  m²    or      132.25 π  m²

Area of the circle =   \frac{529}{4}  π  m²    or      132.25 π  m²

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