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Naddika [18.5K]
3 years ago
10

A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression

Mathematics
1 answer:
Darya [45]3 years ago
7 0

Answer:

$27.2

Step-by-step explanation:

A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression (0.85).32 represents the final price of the cake in dollars.

This is explained in the calculation below

= A cake that costs $32 is on sale for 15% off

The amount off the cake is calculated as

= 15% of $32

= 15/100 × 32

= $4.8

The amount he is paying for the cake =>$32 - $4.8

= $27.2

The above expression is obtained as

(0.85).32

= (100% - 15%) × 32

=( 1 - 0.15) × 32

= 0.85 × 32

= $27.2

The final price of the cake = $27.2

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There were 800 math instructors at a mathematics convention. Forty instructors were randomly selected and given an IQ test. The
Leya [2.2K]

Answer:

95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].

Step-by-step explanation:

We are given that there were 800 math instructors at a mathematics convention.

Forty instructors were randomly selected and given an IQ test. The scores produced a mean of 130 with a standard deviation of 10.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                           P.Q. = \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean score = 130

             s = sample standard deviation = 10

             n = sample of instructors = 40

             \mu = population mean of 800 instructors

<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.</em>

So, 95% confidence interval for the population mean, \mu is ;

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                                         freedom are -2.0225 & 2.0225 with P = 2.5%}  

P(-2.0225 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.0225) = 0.95

P( -2.0225 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.0225 \times {\frac{s}{\sqrt{n} } } ) = 0.95

P( \bar X-2.0225 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.0225 \times {\frac{s}{\sqrt{n} } } ) = 0.95

<u><em /></u>

<u><em>95% confidence interval for</em></u> \mu = [ \bar X-2.0225 \times {\frac{s}{\sqrt{n} } } , \bar X+2.0225 \times {\frac{s}{\sqrt{n} } } ]

                   = [ 130-2.0225 \times {\frac{10}{\sqrt{40} } } , 130+2.0225 \times {\frac{10}{\sqrt{40} } } ]

                   = [126.80 , 133.20]

Therefore, 95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].

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