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valina [46]
3 years ago
7

What is 10^4 in standard notation

Mathematics
2 answers:
NARA [144]3 years ago
7 0

Answer:

10,000

Step-by-step explanation:

Standard notation is just the normal way of writing things. 10 x 10 x 10 x 10 = 10,000.

frutty [35]3 years ago
6 0
ANSWER : 10,000

BECAUSE: 10 x 10 x 10 x 10 = 10,000
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CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed
tatyana61 [14]

Answer:

(a) Null Hypothesis, H_0 : \mu = 8 minutes    

    Alternate Hypothesis, H_A : \mu \neq 8 minutes

(b) The P-value of the test statistics is 0.0436.

(c) We conclude that the actual mean waiting time equals the standard at 0.05 significance level.

(d) 95% confidence interval for the population mean is [7.93 minutes , 9.07 minutes].

Step-by-step explanation:

We are given that the length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes.

A sample of 120 shoppers showed a sample mean waiting time of 8.5 minutes. Assume a population standard deviation of 3.2 minutes.

<u><em>Let </em></u>\mu<u><em> = actual mean waiting time.</em></u>

(a) So, Null Hypothesis, H_0 : \mu = 8 minutes     {means that the actual mean waiting time does not differs from the standard}

Alternate Hypothesis, H_A : \mu \neq 8 minutes     {means that the actual mean waiting time differs from the standard}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                        T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean waiting time = 8.5 minutes

            \sigma = population standard deviation = 3.2 minutes

            n = sample of shoppers = 120

So, <u><em>test statistics</em></u>  =  \frac{8.5-8}{\frac{3.2}{\sqrt{120} } }  

                               =  1.71

The value of t test statistics is 1.71.

(b) Now, the P-value of the test statistics is given by;

                    P-value = P(Z > 1.71) = 1 - P(Z \leq 1.71)

                                  = 1 - 0.9564 = 0.0436

(c) Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the actual mean waiting time equals the standard.

(d) Now, the pivotal quantity for 95% confidence interval for the population mean is given by;

                        P.Q. = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean waiting time = 8.5 minutes

            \sigma = population standard deviation = 3.2 minutes

            n = sample of shoppers = 120

            \mu = population mean

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

<u>So, 95% confidence interval for the population proportion, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times{\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times{\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times{\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times{\frac{\sigma}{\sqrt{n} } } ]

  = [ 8.5-1.96 \times{\frac{3.2}{\sqrt{120} } } , 8.5+1.96 \times{\frac{3.2}{\sqrt{120} } } ]

  = [7.93 minutes , 9.07 minutes]

Therefore, 95% confidence interval for the population mean is [7.93 minutes , 9.07 minutes].

Yes, it support our above conclusion.

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3 years ago
Find the missing side length using pythagorean theorem. simplify radicals if necessary* PLEASE HELP!!
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Answer:

15

Step-by-step explanation:

a^2 + b^2 = c^2

9=a

12-b

Plug in the numbers

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Write 8 7/50 as a decimal number
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Answer: 8.14

Step-by-step explanation:

8 0
2 years ago
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QUESTION 4
patriot [66]

Answer:

<u>The probability of drawing four red cards in a row (with replacement)is 0.1975</u>

Step-by-step explanation:

Assuming we have a standard card deck, we'll have this color distribution:

  • Spades : Black
  • Clubs : Black
  • Diamonds : Red
  • Hearts : Red

In consequence, if we remove all of the clubs from the deck, we will have 26 red cards out of 39 cards left.

Now, let's recall that the formula of probability is:

Probability = Number of favorable outcomes/Total number of possible outcomes

Replacing with the values we know:

  • Probability of drawing a 1st red card = 26/39 = 2/3
  • We return the 1st card to the deck, reshuffle and draw a new card:
  • Probability of drawing a 2nd red card = 2/3
  • We return the 2nd card to the deck, reshuffle and draw a new card:
  • Probability of drawing a 3rd red card = 2/3
  • We return the 3rd card to the deck, reshuffle and draw a new card:
  • Probability of drawing a 4th red card = 2/3

Therefore,

Probability of drawing four red cards in a row (with replacement):

2/3 * 2/3 * 2/3 * 2/3 = 16/81

<u>16/81 = 0.1975</u>

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3 years ago
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