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3 years ago

Which of the following is true for most distributions? Group of answer choices

Mathematics

1 answer:

Drupady [299]3 years ago

8 0

Answer:

Step-by-step explanation:

The standard deviation is a measure that tells us how far measures tend to be from the mean. A low standard deviation gives us values closer to the mean than a high standard deviation. Usually 68% of the data falls within one standard deviation of the set.

Thus, the most accurate answer would be a) Around 70% of the scores will be located within one standard deviation of the mean

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Jake a plane and a 5 foot tree after one year he measured and found the tree had a grown by 20% of its original height how tall

Licemer1 [7]

Answer:

6.0'ft

Step-by-step explanation:

5 x 1.2 = 6

5 feet is how tall it is initially the 1.2 is the original height plus 20%

8 0

4 years ago

A pipe is leaking at 1.5 cups per day about how many gallons per week is the pipe leaking

yawa3891 [41]

1 U.S. CUP - 0.0625 U.S. GALLONS

So? Convert the cups to gallons.

7 DAYS/PER WEEK

1.5 x 7 = 10.5

So... half a cup is about 0.03125 gallons.

0.03125 + (10 x 0.0625) = ???

Drum roll please...

Plot twist: You can do it yourself.

:P

3 0

3 years ago

Simply the radical expression 189

Wittaler [7]

Answer

Step-by-step explanation:

3 0

3 years ago

How can the logarithmic expression be rewritten?

andrey2020 [161]

False
True
True.

I think?

7 0

3 years ago

Find the integral using substitution or a formula.

Nadusha1986 [10]

$\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx$

Derivative of the denominator:
$\rm (x^2+2x+5)'=2x+2$

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

$\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx$

and then split the fraction,

$\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx$

Based on our previous test, we know that a simple substitution will work for the first integral: $\rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx$

So the first integral changes,

$\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx$

integrating to a log,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx$

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

$\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2$

So we have this going on,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx$

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx$

Bringing all that stuff together as a single square,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx$

Making the substitution: $\rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx$

giving us,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du$

simplying a lil bit,

$\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du$

and hopefully from this point you recognize your arctangent integral,

$\rm ln|x^2+2x+5|+\frac52arctan(u)$

undo your substitution as a final step,
and include a constant of integration,

$\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c$

Hope that helps!
Lemme know if any steps were too confusing.

8 0

3 years ago