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3 years ago

Simplify the radical expression by rationalizing the denominator 4/√21

Mathematics

2 answers:

Tcecarenko [31]3 years ago

4 0

$\frac{4}{\sqrt{21}} =\frac{4\sqrt{21}}{\sqrt{21}\sqrt{21}} =\frac{4\sqrt{21}}{21}$

Lynna [10]3 years ago

3 0

I think

$\dfrac{4}{\sqrt{21}}$

is about as simple as this is going to get. For some reason teachers like the radicals in the numerator, so we multiply top and bottom by $\sqrt{21}$ and get

$\dfrac{4}{\sqrt{21}} \times \dfrac{\sqrt{21}}{\sqrt{21}} = \dfrac{4\sqrt{21}}{21}$

Answer: $\dfrac{4\sqrt{21}}{21}$

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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (6, 1280)(6,1280).

Phoenix [80]

Answer:

$y=20(2)^x$

Step-by-step explanation:

We want to write an exponential function that goes through the points (0, 20) and (6, 1280).

The standard exponential function is given by:

$y=ab^x$

The point (0, 20) tells us that y = 20 when x = 0. Hence:

$20=a(b)^0$

Simplify:

$20=a(1)\Rightarrow a=20$

So, our exponential function is now:

$y=20(b)^x$

Next, the point (6, 1280) tells us that y = 1280 when x = 6. Thus:

$1280=20(b)^6$

Solve for b. Divide both sides by 20:

$64=b^6$

Therefore:

$b=\sqrt[6]{64}=2$

Hence, our function is:

$y=20(2)^x$

8 0

2 years ago

Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-

soldi70 [24.7K]

Answer:

Jaime's. Interval not centered around the point estimate.

Step-by-step explanation:

When constructing a confidence interval based on a point estimate, the obtained point estimate must be the central value of the interval.

For Jaime's interval

Lower bound = 0.078

Upper Bound = 0.193

$Central = \frac{0.078+0.193}{2} =0.1355$

For Mariya's interval

Lower bound = 0.051

Upper Bound = 0.189

$Central = \frac{0.051+0.189}{2} =0.12$

For a point estimate of 0.12, only Mariya's interval is adequate since Jaime's is not centered around the point estimate.

4 0

2 years ago

A city block is a square with each side measuring 98 yards. Find the length of the diagonal of the city block.

vlabodo [156]

To find the answer to this, we can use the formula for the diagonal of a square,

a $\sqrt{2}$ , with a being the length of the side. That meaans that the length of the diagonal is 98 $\sqrt{2}$ , which is approximately equal to 138.59.