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3 years ago

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The population, P, of a small island was 6380, correct to the nearest 10. Complete the statement about the limits of P. ……………………

…………. ≤ P < ……………………………

1 answer:

Lady bird [3.3K]3 years ago

8 0

Answer:

6375 ≤ P < 6385

Step-by-step explanation:

When rounding to the nearest 10, the unit value is either rounded to 1 and added to the tens value (if value is greater than or equal to 5) or rounded to 0 (if less Than 5)

Hence, the lower limit of a number p which gives 6380 when rounded to the nearest ten would be 6375 ;

The upper limit of the number p in other to give 6380 when rounded to the nearest 10 will be 6384 (< 6385)

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Construct a 95% confidence interval for the population mean, mu. Assume the population has a normal distribution. A random sam

aniked [119]

Given Information:

Number of lithium batteries = n = 16

Mean life of lithium batteries = μ = 645 hours

Standard deviation of lithium batteries = σ = 31 hours

Confidence level = 95%

Required Information:

Confidence Interval = ?

Answer:

$CI = 628.5 \: to \: 661.5 \: hours$

Step-by-step explanation:

The confidence interval is given by

$CI = \mu \pm t_{\alpha/2} (\frac{\sigma}{\sqrt{n}})$

Where μ is the mean life of lithium batteries, σ is the standard deviation, n is number of lithium batteries selected, and t is the critical value from the t-table with significance level of

tα/2 = (1 - 0.95) = 0.05/2 = 0.025

and the degree of freedom is

DoF = n - 1 = 16 - 1 = 15

The critical value (tα/2) at 15 DoF is equal to 2.131 (from the t-table)

$CI = 645 \pm 2.131(\frac{31}{\sqrt{16}})$

$CI = 645 \pm 2.131(7.75})$

$CI = 645 \pm 16.515$

$CI = 645 - 16.515 \: and \: 645 + 16.515$

$CI = 628.5 \: to \: 661.5 \: hours$

Therefore, the 95% confidence interval is 628.5 to 661.5 hours

What does it mean?

It means that we are 95% confident that the mean life of 16 lithium batteries is within the interval of (628.5 to 661.5 hours)

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3 years ago

The yearly expenses for the Glenn family are represented in the circle graph. The Glenn’s have just purchased a new car. A new c

tiny-mole [99]

Answer:

Car: 18.4% Other: 4.9%

Step-by-step explanation:

Glenn family yearly total expenses are

$\$8,600+\$4,800+\$5,400+\$2,400+\$7,000+\$1,800=\$30,000$

Other expenses are $7,000.

The payments for the new car are: $375.00 per month and the insurance for the new car $85.00 per month, in total, $460 per month. Yearly expenses for car are

$\$460\cdot 12=\$5,520$

Now, the expenses for the following two categories are

Car - $5,520

Other - $7,000 - $5,520 = $1,480

Percentage:

Car:

$\dfrac{5,520}{30,000}\cdot 100\%=18.4\%$

Other

$\dfrac{1,480}{30,000}\cdot 100\%\approx 4.93\%$

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3 years ago

Help!! !,<br>is it right or not

Dahasolnce [82]

Answer:

No

Step-by-step explanation:

The answer is to find the sum of each number, because factors are pulling out from total numbers, but when multiplying you don't need to pull out anything so it would be number

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2 years ago

Suzanne bought a sweater at the sale price of $25. The original cost of the sweater was $40. What percent represents that discou

Blizzard [7]

15/40 x 100 = 37.5
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3 years ago

Find the third side in simplest radical form:<br> 25

Gre4nikov [31]

Answer:

<h3> $\boxed{ \bold{24}}$ </h3>

Step-by-step explanation:

$\mathsf{given}$

$\mathsf{hypotenuse(h) = 25}$

$\sf{perpendicular (p) = 7}$

$\sf{base(b) = }$ ?

Now, Using Pythagoras theorem

$\sf{{h}^{2} = {p}^{2} + {b}^{2} }$

plug the values

⇒ $\sf{ {25}^{2} = {7}^{2} + {b}^{2} }$

Evaluate the power

⇒ $\sf{625 = 49 + {b}^{2} }$

Swap the sides of the equation

⇒ $\sf{49 + {b}^{2} = 625}$

Move constant to right hand side and change it's sign

⇒ $\sf{ {b}^{2} = 625 - 49}$

Calculate the difference

⇒ $\sf{ {b}^{2} = 576}$

Squaring on both sides

⇒ $\sf{b = 24}$

Hope I helped!

Best regards!

8 0

3 years ago