Which is the best way to solve the equation x2 = n?

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow p

Ede4ka [16]

Answer:

1) The mean calculated for this case is $\bar X=61.5$

2) $61.5-5.4=56.1$

3) $61.5+5.4=66.9$

4) B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.

Step-by-step explanation:

Previous concepts

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part 1

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (a)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (b)

The mean calculated for this case is $\bar X=61.5$

The sample deviation calculated $s=5.143$

$\mu$ population mean (variable of interest)

n=6 represent the sample size

Part 2

The confidence interval for the mean is given by the following formula:

$\bar X \pm ME$ (1)

So if we have the margin of error 5.4mm we can find the lowr limit like this:

$61.5-5.4=56.1$

Part 3

$61.5+5.4=66.9$

Part 4

B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.

4 0

3 years ago

Read 2 more answers

What is the area of the following trapezoid in square feet?

tangare [24]

Answer:

82.5 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = $\frac{1}{2}$ h (b₁ + b₂)

where h is the perpendicular height and b₁, b₂ the parallel bases

Here h = 7.5, b₁ = 7 and b₂ = 15 , then

A = $\frac{1}{2}$ × 7.5 × (7 + 15) = 0.5 × 7.5 × 22 = 82.5 ft²

4 0

2 years ago

Read 2 more answers

Unknown angle problems with algebra <br> Solve x in the diagram below

Alina [70]

Answer:

35

Step-by-step explanation:

Alright this is like a linear pair. All three angles add up to 180; so this is the set up:

40 + 2x + 30 + 40 = 180

2x + 110 = 180

2x = 70

x=35

8 0

3 years ago

HELP! Find the value of sin 0 if tan 0 = 4; 180 < 0< 270

BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

$\large \boxed{sin \theta = tan \theta cos \theta} \\ \large \boxed{tan^{2} \theta + 1 = {sec}^{2} \theta}$

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

$\large{ {4}^{2} + 1 = {sec}^{2} \theta } \\ \large{16 + 1 = {sec}^{2} \theta } \\ \large{ {sec}^{2} \theta = 17}$

As we know, sec²θ = 1/cos²θ.

$\large \boxed{sec \theta = \frac{1}{cos \theta} } \\ \large \boxed{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta} }$

And thus,

$\large{ {cos}^{2} \theta = \frac{1}{17}} \\ \large{cos \theta = \frac{ \sqrt{1} }{ \sqrt{17} } } \\ \large{cos \theta = \frac{1}{ \sqrt{17} } \longrightarrow \frac{ \sqrt{17} }{17} }$