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Alinara [238K]
2 years ago
14

Distribute and Simplify: (p + 3)5

Mathematics
1 answer:
Tanzania [10]2 years ago
4 0

Answer:

5p+5

Explanation:

5(p+3)

(5*p)+(5*3)

5p+5

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3 years ago
You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval (i.e
victus00 [196]

You intend to estimate a population mean μ from the following sample. 26.2 27.7 8.6 3.8 11.6 You believe the population is normally distributed. Find the 80% confidence interval.  Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.

Answer:

The  Confidence interval = (8.98 , 22.18)

Step-by-step explanation:

From the given information:

mean = \dfrac{ 26.2+ 27.7+ 8.6+ 3.8 +11.6 }{5}

mean = 15.58

the standard deviation \sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2 }{n}}

the standard deviation = \sqrt{\dfrac{(26.2  - 15.58)^2 +(27.7 - 15.58)^2 +(8.6  - 15.58)^2 + (3.8  - 15.58)^2  + (11.6  - 15.58)^2  }{5 }  }

standard deviation = 9.62297

Degrees of freedom df = n-1

Degrees of freedom df = 5 - 1

Degrees of freedom df = 4

For df  at 4 and 80% confidence level, the critical value t from t table  = 1.533

The Margin of Error M.O.E = t \times \dfrac{\sigma}{\sqrt{n}}

The Margin of Error M.O.E = 1.533 \times \dfrac{9.62297}{\sqrt{5}}

The Margin of Error M.O.E = 1.533 \times 4.3035

The Margin of Error M.O.E = 6.60

The  Confidence interval = ( \mu  \pm M.O.E )

The  Confidence interval = ( \mu  +  M.O.E , \mu - M.O.E )

The  Confidence interval = ( 15.58 - 6.60 , 15.58 + 6.60)

The  Confidence interval = (8.98 , 22.18)

7 0
3 years ago
Cos4theta+cos2theta/ cos4theta-cos2theta= _____
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\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}

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8 0
3 years ago
In 1911, the temperature in Rapid City,
Sliva [168]

The 3.1 °F/min rate of change of the temperature and 15 minutes change duration gives the change in temperature as 46.5 °F

<h3>How can the change in temperature be found from the rate of change?</h3>

The rate at which the temperature changed = 3.1 °F/min

The duration of the change in temperature = 15 minutes

The relationship between the change in temperature, the rate of change in temperature and the time can be presented as follows;

3.1  ^{\circ} F/min =  \frac{ \delta T }{\delta t}  =  \frac{ \Delta T }{ \Delta t}

Where;

∆T = The required change in temperature

∆t = The duration of the change = 15 minutes

Which gives;

∆T = 3.1°F/min × 15 minutes = 46.5 °F

  • The change in temperature, ∆T = 46.5 °F

Learn more about the rate of change of a variable here:

brainly.com/question/10208814

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1 year ago
I have tried multiple times to do this many different ways and I have not gotten the correct answer. #9
hodyreva [135]

It's 1.18^{10}  which gives 5.23 times increase in 10 years, so 523% of oryginal price

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3 years ago
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