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Angelina_Jolie [31]
3 years ago
5

The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average ag

e in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years
Mathematics
1 answer:
Lelu [443]3 years ago
8 0

Answer:

a.1.90 years

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

In this question:

n = 25, \sigma = 3.8

So

M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90

So the correct answer is:

a.1.90 years

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A right rectangular prism has edges of 2 1/4 in, 1 1/2 in and 1 1/2 in. How many cubes with lengths of 1/4 in would be needed to
Zielflug [23.3K]

The volume of a rectangular prism is (length) x (width) x (height).

The volume of the big one is  (2.25) x (1.5) x (1.5) = <em>5.0625 cubic inches</em>.

The volume of the little one is  (0.25)x(0.25)x(0.25)= 0.015625 cubic inch

The number of little ones needed to fill the big one is

             (Volume of the big one)  divided by (volume of the little one) .

       5.0625 / 0.015625  =  <em>324 tiny cubies</em>

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

Doing it with fractions instead of decimals:

The volume of a rectangular prism is (length) x (width) x (height).
Dimensions of the big one are:

   2-1/4  =  9/4
   1-1/2  =  3/2
   1-1/2  =  3/2

   Volume = (9/4) x (3/2) x (3/2) =
 
                 (9 x 3 x 3) / (4 x 2 x 2)  =

                           81 / 16  cubic inches.

          As a mixed number:    81/16  =  <em>5-1/16 cubic inches</em>

Volume of the tiny cubie = (1/4) x (1/4) x (1/4) =  1/64 cubic inch.   

The number of little ones needed to fill the big one is

             (Volume of the big one)  divided by (volume of the little one) .

                 (81/16) divided by (1/64)  = 

                     (81/16) times (64/1)  = 

                             5,184/16  =  <em>324 tiny cubies</em>.


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Figure A best represents it because if you add 576 and 49 you get 625, which shows the theorem of a^2+b^2=c^2.

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Answer:

Multiply by 3 on both sides of the equation.

2.78 × 3 = 8.34, so t = 8.34.

Substitute 8.34 for t to check the solution.

Step-by-step explanation:

To solve the equation  = 2.78

we will use the steps below to solve this equation;

First, multiply by 3 on both-side of the equation. That is;

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On the left hand side of the equation 3 will cancel-out 3, leaving us with just t while 3 will be multiply by 2.77 on the right-hand side of the equation to give 8.34

t = 8.34

we can further substitute 8.34 for t to check the correctness of the solution

that is;

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