Find all the real square roots of 0.0064

Answers

Answer 1

Answer: √64 = 8

64÷1000 = 0.0064

8÷1000=0.0008

√0.0064 = 0.0008

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Use the given data to construct a confidence interval for the population standard deviation, σσ. Assume that the population has a normal distribution: The football coach randomly selected the following players and timed how long each player took to perform a certain drill. The times (in minutes) were:[10,10,15,10,11,7,5,5]

Find a 95.0 confidence interval for the population standard deviation σ

A) 2.6194049<σ<6.43192582.6194049<σ<6.4319258
B) 2.2194049<σ<6.83192582.2194049<σ<6.8319258
C) 2.6194049<σ<7.43192582.6194049<σ<7.4319258
D) None of These

Answers

Answer:

The confidence interval for the population standard deviation would be:

C) 2.6194049<σ<7.4319258

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

$\bar x$ represent the sample mean

n=8 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates.

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$((n-1)s^2)/(\chi^2_(\alpha/2)) \leq \sigma \leq ((n-1)s^2)/(\chi^2_(1-\alpha/2))$

On this case we need to find the sample standard deviation with the following formula:

$s=\sqrt{(\sum_(i=1)^8 (x_i -\bar x)^2)/(n-1)}$

And in order to find the sample mean we just need to use this formula:

$\bar x =(\sum_(i=1)^n x_i)/(n)$

The sample mean obtained on this case is $\bar x= 9.125$ and the deviation s=3.357

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=8-1=7$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,7)" "=CHISQ.INV(0.975,7)". so for this case the critical values are:

$\chi^2_(\alpha/2)=16.012$

$\chi^2_(1- \alpha/2)=1.690$

And replacing into the formula for the interval we got:

$((7)(3.357)^2)/(16.012) \leq \sigma ((7)(3.357)^2)/(1.690)$

$4.927 \leq \sigma^2 \leq 46.678$

Now we just take square root on both sides of the interval and we got:

$2.2194049 \leq \sigma \leq 6.8319258$

So the best option would be:

C) 2.6194049<σ<7.4319258

In 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars. Which of the following represents the national debt in scientific notation?

Answers

Answer: $1.3 * 10^(13)$

Explanation:

We are given, that in 2010, the United States national debt was estimated to be nearly 13,000,000,000,000 dollars.

We are required to find the national debt in scientific notation. The scientific notation is used to represent either very small number or very large number.

The scientific form of the given number is:

$1.3 * 10^(13)$

What is the missing coefficient of the x-term of the product (-x-5)2 after it has been simplified

Answers

Answer:

we have

(-x -5) to the power of 2

we know that

(-x -5) to the power of 2 = (-x -5) x (-x -5)

To multiply two binomial I can use the FOIL method

(-x -5) x (-x -5) = (-x) x (-x) + (-x) x (-5) + (-5) x (-x) + (-5) x (-5)

= X to the power of 2 + 5x +5x + 25

= x to the power of 2 +10x +25

therefore

the answer is

the missing coefficient of the x-term is 10

Answer:

Step-by-step explanation:

Lana and Ron each opened a separate bank account with $1000. They were both offered a 4.5% interest rate for 2 years. After 2 years, Lana’s account had more money than Ron’s. What could explain the difference?A.Lana’s account earned simple interest; Ron’s account earned compound interest.

B.Lana invested funds for a longer time period.

C.Lana’s account had a higher interest rate.

D.Lana’s account earned compound interest; Ron’s account earned simple interest.