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3 years ago

5

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 47.3 m

iles per hour.

1 answer:

Marta_Voda [28]3 years ago

6 0

Answer:

$\bar X = \frac{2276}{48}=47.417$

If we compare this value with the 47.3 proposed we have the following error

$Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%$

The computed mean is close to the actual mean because the difference between the means is less than 5%.

Step-by-step explanation:

Assuming the following dataset:

Speed 42-45 46-49 50-53 54-57 58-61

Freq. 21 15 6 4 2

And we are interested in find the mean, since we have grouped data the formula for the mean is given by:

$\bar X = \frac{\sum_{i=1}^n x_i f_i}{\sum_{i=1}^n f_i}$

And is useful construct a table like this one:

Speed Freq Midpoint Freq*Midpoint

42-45 21 43.5 913.5

46-49 15 47.5 712.5

50-53 6 51.5 309

54-57 4 55.5 222

58-61 2 59.5 119

Total 48 2276

And the mean is given by:

$\bar X = \frac{2276}{48}=47.417$

If we compare this value with the 47.3 proposed we have the following error

$Error = \frac{|Actual-real|}{real}*100 = \frac{|47.417-47.3|}{47.3}*100 =0.247\%$

The computed mean is close to the actual mean because the difference between the means is less than 5%.

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Answer:

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Step-by-step explanation:

5 0

3 years ago

Solve and graph the inequality |5 – v| < 6.

Jet001 [13]

5 - v < 6, 5 - v >= 0

-5 + v < 6, 5 - v < 0

1) - v < 6 -5 (move 5 to the right side and then multiply by -1 both sides of the inequality)
v > -1 (don't forget that here v <= 5)

2) v < 6 + 5 (move -5 to the right side)
v < 11 (here v should be more than 5)

so from 1) you get that v is from -1 to 5 inclusive (-1;5]
and from 2) you get that v is from 5 to 11 (5;11)

so by adding up results from 1) and 2) you get v is (-1; 11)

answer: (-1; 11)

3 0

3 years ago

Read 2 more answers

Help with num 3 please. thanks

Alja [10]

Answer:

a) $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 0} = -1$

b) $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = \frac{\pi}{2}} = -1$

General Formulas and Concepts:

<u>Pre-Calculus</u>

Unit Circle

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Trigonometric Differentiation

Logarithmic Differentiation

Step-by-step explanation:

a)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = ln \bigg( \frac{1 - x}{\sqrt{1 + x^2}} \bigg)$

<u>Step 2: Differentiate</u>

Logarithmic Differentiation [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{1}{\frac{1 - x}{\sqrt{1 + x^2}}} \cdot \frac{d}{dx}[\frac{1 - x}{\sqrt{1 + x^2}}]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{d}{dx}[\frac{1 - x}{\sqrt{1 + x^2}}]$
Quotient Rule: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{(1 - x)'\sqrt{1 + x^2} - (1 - x)(\sqrt{1 + x^2})'}{(\sqrt{1 + x^2})^2}$
Basic Power Rule [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \frac{-\sqrt{1 + x^2} - (1 - x)(\frac{x}{\sqrt{x^2 + 1}})}{(\sqrt{1 + x^2})^2}$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-\sqrt{x^2 + 1}}{x - 1} \cdot \bigg( \frac{x(x - 1)}{(x^2 + 1)^\bigg{\frac{3}{2}}} - \frac{1}{\sqrt{x^2 + 1}} \bigg)$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{x + 1}{(x - 1)(x^2 + 1)}$

<u>Step 3: Find</u>

Substitute in <em>x</em> = 0 [Derivative]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = 0} = \frac{0 + 1}{(0 - 1)(0^2 + 1)}$
Evaluate: $\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 0} = -1$

b)

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle y = ln \bigg( \frac{1 + sinx}{1 - cosx} \bigg)$

<u>Step 2: Differentiate</u>

Logarithmic Differentiation [Chain Rule]: $\displaystyle \frac{dy}{dx} = \frac{1}{\frac{1 + sinx}{1 - cosx}} \cdot \frac{d}{dx}[\frac{1 + sinx}{1 - cosx}]$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{d}{dx}[\frac{1 + sinx}{1 - cosx}]$
Quotient Rule: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{(1 + sinx)'(1 - cosx) - (1 + sinx)(1 - cosx)'}{(1 - cosx)^2}$
Trigonometric Differentiation: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - 1]}{sin(x) + 1} \cdot \frac{cos(x)(1 - cosx) - sin(x)(1 + sinx)}{(1 - cosx)^2}$
Simplify: $\displaystyle \frac{dy}{dx} = \frac{-[cos(x) - sin(x) - 1]}{[sin(x) + 1][cos(x) - 1]}$

<u>Step 3: Find</u>

Substitute in <em>x</em> = π/2 [Derivative]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = \frac{\pi}{2}} = \frac{-[cos(\frac{\pi}{2}) - sin(\frac{\pi}{2}) - 1]}{[sin(\frac{\pi}{2}) + 1][cos(\frac{\pi}{2}) - 1]}$
Evaluate [Unit Circle]: $\displaystyle \frac{dy}{dx} \bigg| \limit_{x = \frac{\pi}{2}} = -1$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

4 0

3 years ago

“Eighteen is equal to the product of a number (n) and 9.”

gregori [183]

Answer:

n=2

Step-by-step explanation:

Create an equation.

9n=18

Divide 9 from both sides.

9n/9=18/9

n=2

Hope this helps!

4 0

2 years ago

Read 2 more answers

What is the equation of the axis of symmetry for the parabola y=1/2(x-3)^2+5

Rus_ich [418]

The general vertex form equation of the parabola is

$y=a(x-h)^2+k$

The Axis of Symmetry is given by

x=h

For the given equation the Equation of the Axis of symmetry for the parabola y=1/2(x-3)^2+5 as x=3.

5 0

3 years ago