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2 years ago

15

A lawyer owns 4 pairs of pants, 5 dress shirts and 6 ties. How many days can the lawyer go without wearing the same combination

of three items?

2 answers:

SIZIF [17.4K]2 years ago

4 0

4 ways to wear all pants
5 ways to wear shirts
6 ways to wear ties
4*5*6=120 different combos
think of it like this

eample
2 pairs of pants and 3 pairs of shirts
a,b are the pants, and c,d,e are the shirts
the ways are below
ac
ad
ae
bc
bd
be
2*3=6, 6 ways

answer is 120 days

stiv31 [10]2 years ago

3 0

I believe that to calculate this, you do 4x5x6 and then divide it by 3, to get 40

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The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the act

stealth61 [152]

Answer: 0.2551

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.

Significance level : $\alpha=1-0.95=0.05$

The critical z-value for 95% confidence : $z_{\alpha/2}=1.960$ (1)

Since , $z=\dfrac{x-\mu}{\sigma}$ (where x be any random variable that represents the temperature reading from a thermocouple.)

Then, from (1)

$\dfrac{x-\mu}{\sigma}=1.96\\\\ x-\mu=1.96\sigma$ (2)

Also, all readings are within 0.5° of μ,

i.e. $x-\mu$

i.e. $1.96\sigma$ [From (2)]

i.e. $\sigma$

i.e. $\sigma\approx0.2551$

The required standard deviation : $\sigma=0.2551$

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2 years ago

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At <em>x</em> = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at <em>x</em> = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at <em>x</em> = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago

In a survey of a town, 56% of residents own a car, 21% of residents now a truck, and 4% of residents own both a car and a truck.

Vesna [10]

The conditional probability is 80

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2 years ago

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea

andrew11 [14]

Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{23}{12} = 1.92$

b) standard deviation for this population

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences = 126.92

$\sigma = \sqrt{\frac{126.92}{12}} = 3.25$

c) median change score

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

$\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5$

d) change score that is 2.2 standard deviations below the mean.

$x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23$

4 0

2 years ago

given the area of a rectangle is 14,628 square millimeters and the width is 12 millimeters find the length

HACTEHA [7]

A= l times w. A=14628 and w=12 so length equals 1219 millimeters

8 0

2 years ago

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