1/15 greater or less than 10/18

Calculate the sample standard deviation and sample variance for the following frequency distribution of heart rates for a sample

adelina 88 [10]

Answer:

$\sigma = 12.5$ ---- sample standard deviation

$\sigma^2 = 157.2$ ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

$x_1 = \frac{56 + 64}{2} = 60$

$x_2 = \frac{65 + 73}{2} = 69$

And so on

So, the table becomes:

$\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}$

Calculate the mean

$\bar x = \frac{\sum fx}{\sum f}$

$\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}$

$\bar x = \frac{4191}{55}$

$\bar x = 76.2$

The variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}$

$\sigma^2 = \frac{8488.8}{54}$

$\sigma^2 = 157.2$

The sample standard deviation is:

$\sigma = \sqrt{\sigma^2$

$\sigma = \sqrt{157.2$

$\sigma = 12.5$

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

$\sigma^2 = 157.2$

6 0

3 years ago

When do you know to use either the shell method or washer method and how do you know what to take it to respect to when it is ro

Marat540 [252]

Step-by-step explanation:

Let's first consider a rotation about a vertical axis (x=0 or x=a).

Using washer method, the volume is:

∫ᵧ₁ᵞ² π (x₂² − x₁²) dy

∫ᵧ₁ᵞ² π ((x₂ − a)² − (x₁ − a)²) dy

Using shell method, the volume is:

∫ₓ₁ˣ² 2π x (y₂ − y₁) dx

∫ₓ₁ˣ² 2π (x − a) (y₂ − y₁) dx

First, notice that with washer method, the differential dy is parallel to the axis of rotation. With shell method, the differential dx is perpendicular to the axis of rotation.

Also, notice that the limits of integration must match the differential.

Choosing the best method will depend on the function.

If x² can be written in terms of y, and integrated, then washer method is the one to use.

If y can be written in terms of x, and integrated, then shell method is the one to use.

In other words, use washer method if x = f(y) is simple to integrate. Use shell method if y = f(x) is simple to integrate.

If instead we rotate about a horizontal axis (y=0 or y=a), the volume with washer method is:

∫ₓ₁ˣ² π (y₂² − y₁²) dx

∫ₓ₁ˣ² π ((y₂ − a)² − (y₁ − a)²) dx

Using shell method, the volume is:

∫ᵧ₁ᵞ² 2π y (x₂ − x₁) dy

∫ᵧ₁ᵞ² 2π (y − a) (x₂ − x₁) dy

We choose washer method when y² = f(x) is easy to integrate.

We choose shell method when x = f(y) is easy to integrate.

So here's the takeaway:

If the axis of rotation is x = 0 or x = a, and x² = f(y) is easy to integrate, use washer method.

If the axis of rotation is y = 0 or y = a, and y² = f(x) is easy to integrate, use washer method.

Otherwise, use shell method.

7 0

3 years ago

How many atoms sodium would a 4 mole sample of Na3P have?

ioda

<h3>Answer:</h3>

2 × 10²⁴ atoms Na₃P

<h3>General Formulas and Concepts:</h3>

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Chemistry</u>

<u>Atomic Structure</u>

Using Dimensional Analysis
Avogadro's Number - 6.022 × 10²³ atoms, molecules, formula units, etc.

<h3>Step-by-step explanation:</h3>

<u>Step 1: Define</u>

4 mol Na₃P

<u>Step 2: Identify Conversions</u>

Avogadro's Number

<u>Step 3: Convert</u>

<u /> $\displaystyle 4 \ mol \ Na_3P(\frac{6.022 \cdot 10^{23} \ atoms \ Na_3P}{1 \ mol \ Na_3P} )$ = 2.4088 × 10²⁴ atoms Na₃P

<u>Step 4: Check</u>

<em>We are given 1 sig fig. Follow sig fig rules and round.</em>

2.4088 × 10²⁴ atoms Na₃P ≈ 2 × 10²⁴ atoms Na₃P

7 0

3 years ago

Use the rules for long divide 262 by 9

Lady bird [3.3K]

29.11 reccuring is the answer i got

3 0

4 years ago

A rectangle has a length of 8m and a width of 3m. If a similar rectangle has

jarptica [38.1K]

Answer:

8.25 m

Step-by-step explanation:

the scale is 2.75

Hope this helps UwU

3 0

3 years ago