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2 years ago

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University graduates have a mean job search time of 38.1 weeks, with a standard deviation of 10.1 weeks. The distribution of job

search times is not assumed to be symmetric. Between what two search times does Chebyshev's Theorem guarantee that we will find at least 89% of the graduates

1 answer:

Lera25 [3.4K]2 years ago

5 0

Answer:

7.1 weeks to 68.4 weeks

Step-by-step explanation:

Chebyshev's Theorem states that:

75% of the measures are within 2 standard deviations of the mean.

89% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 38.1

Standard deviation = 10.1

Between what two search times does Chebyshev's Theorem guarantee that we will find at least 89% of the graduates

Between 3 standard deviations of the mean.

So from 38.1 - 3*10.1 = 7.8 weeks to 38.1 + 3*10.1 = 68.4 weeks

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Let e1= 1 0 and e2= 0 1 , y1= 4 5 , and y2= −2 7 , and let T: ℝ2→ℝ2 be a linear transformation that maps e1 into y1 and maps

Furkat [3]

Answer:

The image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is $\left[\begin{array}{c}24&-8\end{array}\right]$

Step-by-step explanation:

We know that $T:$ $IR^{2}$ → $IR^{2}$ is a linear transformation that maps $e_{1}$ into $y_{1}$ ⇒

$T(e_{1})=y_{1}$

And also maps $e_{2}$ into $y_{2}$ ⇒

$T(e_{2})=y_{2}$

We need to find the image of the vector $\left[\begin{array}{c}4&-4\end{array}\right]$

We know that exists a matrix A from $IR^{2x2}$ (because of how T was defined) such that :

$T(x)=Ax$ for all x ∈ $IR^{2}$

We can find the matrix A by applying T to a base of the domain ( $IR^{2}$ ).

Notice that we have that data :

$B_{IR^{2}}=$ { $e_{1},e_{2}$ }

Being $B_{IR^{2}}$ the cannonic base of $IR^{2}$

The following step is to put the images from the vectors of the base into the columns of the new matrix A :

$T(\left[\begin{array}{c}1&0\end{array}\right])=\left[\begin{array}{c}4&5\end{array}\right]$ (Data of the problem)

$T(\left[\begin{array}{c}0&1\end{array}\right])=\left[\begin{array}{c}-2&7\end{array}\right]$ (Data of the problem)

Writing the matrix A :

$A=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]$

Now with the matrix A we can find the image of $\left[\begin{array}{c}4&-4\\\end{array}\right]$ such as :

$T(x)=Ax$ ⇒

$T(\left[\begin{array}{c}4&-4\end{array}\right])=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]\left[\begin{array}{c}4&-4\end{array}\right]=\left[\begin{array}{c}24&-8\end{array}\right]$

We found out that the image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is the vector $\left[\begin{array}{c}24&-8\end{array}\right]$

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2 years ago

Which statements accurately describe the function f(x) = 3(16) Superscript three-fourths x? Select three options.

zzz [600]

Answer:

The initial value is 3.

The range is y greater than 0.

The simplified base is 8.

Step-by-step explanation:

The given function is $f(x) = 3(16)^{\frac{3}{4}x }$ ......... (1)

Therefore, the initial value of the function at x = 0 is $f(0) = 3(16)^{0} = 3$

Now, the domain can be any real value, since for all real value of x, y exists.

But, for no value of x the function has value < 0.

Therefore, y greater than 0 is the range of the function f(x).

Now, simplifying the equation (1) we will have

$f(x) = 3(16)^{\frac{3}{4}x } = 3(16^{\frac{3}{4} } )^{x} = 3(8)^{x}$

Therefore, the simplified base is 8. (Answer)

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Answer:

Leon is correct. (Option 1)

Step-by-step explanation:

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Step 1: Find the greatest common factor of the given lengths: 7

Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5

Step 3: Verify that the lengths found in step 2 form a Pythagorean triple.

we have to explain whether or not Leon is correct.

As, 3,4,5 forms a Pythagorean triplet i.e satisfies the Pythagoras theorem

$Hypotenuse^2=Base^2+Perpendicular^2$

⇒ $5^2=3^2+4^2$

Let a, b, c forms a Pythagorean triplet

$a^2+b^2=c^2$

Multiplied by 4 on both sides

⇒ $4a^2+4b^2=4c^2$

⇒ ${2a}^2+{2b}^2={2c}^2$

Hence, we say 4a, 4b and 4c also forms a Pythagorean triplet.

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Hence, Leon is correct.

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2 years ago

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Makovka662 [10]

Answer:

The answer is C) $197,263.70

Step-by-step explanation:

It's losing 6% PER year for the last 3 year.

You can do what I did and take $237,500 and times it 0.06. Which should give you 14,250, that is how much is lost in year one.

So subtract 14,250 from 237,500, you should have $223,250 now.

Repeat the first step with $223,250 now, you times it by 0.06 again and you should get 13,395, you subtract that from $223,250.

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It's a long, simple method and I'm sure there is another method of solving this question, but this is an easy way to get the answer.

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