All categories

3 years ago

Rational Exponent

Mathematics

2 answers:

liq [111]3 years ago

4 0

Answer:

Sample Response:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

lara [203]3 years ago

3 0

The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it.

When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical.
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).

Let's say we wanted to write the cubed root of x squared, in exponential form.
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2).
Therefore, it would be x^(2/3), or x to the 2 thirds power.

Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator.

You might be interested in

Which statement is true of an appropriate sample of a population?

Ulleksa [173]

The first statement!

4 0

3 years ago

Read 2 more answers

Is 18/54 equivalent to 3/9?

viva [34]

Yessssssssssssssssssssssss

4 0

3 years ago

Can you please help me find the area? Thank you. :)))

Phoenix [80]

The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.

The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

$A=w\cdot l$

For our rectangle w=12 in and l=20 in, the area is:

$\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}$

The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

You can determine the value of x as follows:

$\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}$

x=4 in → this means that the base of the triangle is 4in long.

The area of the triangle is equal to half the product of the base by the height, following the formula:

$A=\frac{b\cdot h}{2}$

For our triangle, the base is b=4in and the height is h=6in, then the area is:

$\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}$

Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:

$\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}$

The area of the figure is 228in²

8 0

1 year ago

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, port

GrogVix [38]

Answer:

$a=49.5 -1.28*15=30.3$

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.

If the score is lower than 30.3 we consider this score as risk averse

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(49.5,15)$

Where $\mu=49.5$ and $\sigma=15$

We are interested in the bottom 10% of the data.

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.9$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-1.28$

And if we solve for a we got

$a=49.5 -1.28*15=30.3$

So the value of height that separates the bottom 10% of data from the top 90% is 30.3.

If the score is lower than 30.3 we consider this score as risk averse

7 0

3 years ago

A student in the Construction Trades program at the Cecil County School of Technology has 4 1/2gallons of paint. If he uses 2.75

Andrew [12]

Answer:

1.75 gallons of paint

Step-by-step explanation:

A student in the construction trades program has 4 1/2 gallons of paint

If the student uses 2.75 gallons in one room then the gallons of paint that are left can be calculated as follows

= 4 1/2 - 2.75

= 9/2 - 2.75

= 4.5 - 2.75

= 1.75

Hence 1.75 gallons of paint are left

3 0

3 years ago