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2 years ago

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The mean number of words per minute (WPM) typed by a speed typist is 149 with a standard deviation of 14 WPM. What is the probab

ility that the sample mean would be greater than 147.8 WPM if 88 speed typists are randomly selected

1 answer:

Troyanec [42]2 years ago

6 0

Answer:

78.81%

Step-by-step explanation:

We are given;

Population mean; μ = 149

Sample mean; x¯ = 147.8

Sample size; n = 88

standard deviation; σ = 14

Z-score is;

z = (x¯ - μ)/(σ/√n)

Plugging in the relevant values;

z = (147.8 - 149)/(14/√88)

z = -0.804

From z-distribution table attached, we have; p = 0.21186

P(X > 147.8) = 1 - 0.21186 = 0.78814

In percentage gives; p = 78.81%

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Find the limit of the function by using direct substitution.

serg [7]

Answer:

Option a.

$\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1$

Step-by-step explanation:

You have the following limit:

$\lim_{x \to \frac{\pi}{2}{(3e)^{xcosx}$

The method of direct substitution consists of substituting the value of $\frac{\pi}{2}$ in the function and simplifying the expression obtained.

We then use this method to solve the limit by doing $x=\frac{\pi}{2}$

Therefore:

$\lim_{x \to \frac{\pi}{2}}{(3e)^{xcosx} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})}$

$cos(\frac{\pi}{2})=0\\$

By definition, any number raised to exponent 0 is equal to 1

So

$\lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}(0)}\\\\$

$\lim_{x\to \frac{\pi}{2}}{(3e)^{0}} = 1$

Finally

$\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1$

6 0

3 years ago

3. Sam and Tim each have savings accounts. Every month they each put in some of their

Setler [38]

Answer:

$y = 30x +50$ --- Sam

$y = 20x +80$ --- Tim

Step-by-step explanation:

Given

Sam Tim

х --- f(x) --------------- g(x)

1 --- 80 --------------- 100

2 --- 110 --------------- 120

3 --- 140 --------------- 140

4 --- 170 -------------- 160

Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,80)$

$(x_2,y_2) = (4,170)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{170 - 80}{4 - 1}$

$m = \frac{90}{3}$

$m = 30$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 80 = 30(x - 1)$

$y - 80 = 30x - 30$

Make y the subject

$y = 30x - 30 + 80$

$y = 30x +50$

Calculating the equation of Tim

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,100)$

$(x_2,y_2) = (4,160)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{160 - 100}{4 - 1}$

$m = \frac{60}{3}$

$m = 20$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 100 = 20(x - 1)$

$y - 100 = 20x - 20$

Make y the subject

$y = 20x - 20+100$

$y = 20x +80$

7 0

2 years ago

The population of a town is 6500 and is increasing at a rate of 4% each year. Create a function for this scenario. At this rate,

Stella [2.4K]

Answer:

$P_4 = 7604.08$

Step-by-step explanation:

If the population increases at a rate of 4% per annum, then:

In year 1:

$P_1 = P_0 + 0.04P_0$

Where $P_0$ is the initial population and $P_n$ is the population in year n

In year 2

$P_2 = P_1 + 0.04P_1$

It can also be written as:

$P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)$

Taking out common factor $P_0$

$P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)$

Taking out common factor (1 + 0.04)

$P_2 = (1 + 0.04) (P_0 + 0.04P_0)$

Taking out again common factor $P_0$

$P_2 = (1 + 0.04) (1 + 0.04) P_0$

Simplifying

$P_2 = P_0 (1 + 0.04) ^ 2$

So

$P_n = P_0 (1 + 0.04) ^ n$

This is the equation that represents the population for year n

Then, in 4 years, the population will be:

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3 years ago

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Answer:

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4 0

2 years ago

ONLY answer if you know what the answer is. If you are not sure DONT FREAKING ANSWER.

Bogdan [553]

Answer:

5 = |-5|

Step-by-step explanation:

Think of it as a number line, like in the picture below. The absolute value is how far a number is from zero (0). If 5 is 5 away from zero, then the opposite of 5 (-5) is also 5 away from zero.

Refer to the picture below for an illustration:

8 0

2 years ago

Read 2 more answers