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Ipatiy [6.2K]
3 years ago
15

Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y grea

ter-than-or-equal-to 0 and z greater-than-or-equal-to 1 2 x squared z squared StartRoot 8 y cubed z EndRoot 4 x squared y z cubed StartRoot 2 x squared EndRoot 8 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot 64 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot
Mathematics
1 answer:
Nataly [62]3 years ago
6 0

Answer:

Option C.

Step-by-step explanation:

The given expression is  

\sqrt{128x^8y^3z^9}

It can be written as

\sqrt{(64\cdot 2)\cdot x^8\cdot y^{2+1}\cdot z^{8+1}}

=\sqrt{8^2\cdot 2\cdot (x^4)^2\cdot y^{2}\cdot y\cdot (z^{4})^2\cdot z}

=\sqrt{(8x^4yz^4)^2\cdot 2yz}

=8x^4yz^4\sqrt{2yz}

Therefore, the correct option is C.

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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati
just olya [345]

Answer:

Weights of at least 340.1 are in the highest 20%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 330, \sigma = 12

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

Z = \frac{X - \mu}{\sigma}

0.842 = \frac{X - 330}{12}

X - 330 = 12*0.842

X = 340.1

Weights of at least 340.1 are in the highest 20%.

3 0
3 years ago
If you had 11 dollars and spent 7 what fraction of the money did you spend
tatyana61 [14]

Answer:

7/11

Step-by-step explanation:

3 0
3 years ago
Calculate the radius of a circle that has a diameter of 190
Rasek [7]

Answer:

30.23944

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Prove that if b is a square matrix then b+b^t is symmetric
WARRIOR [948]
A matrix \mathbf X is symmetric if \mathbf X=\mathbf X^\top. We have

(\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top

and so \mathbf B+\mathbf B^\top is indeed symmetric.
6 0
3 years ago
15/40 in lowest term I need it so bad now
Vesnalui [34]

In order to reduce ANY fraction to lowest terms, find any common factors
of the numerator and denominator, and divide them both by it.  If they still
have a common factor, then divide them by it again.  Eventually, they won't
have any common factor except ' 1 ', and then you'll know that the fraction is
in lowest terms.

Do  15  and  40  have any common factors ?
Let's see . . .

The factors of  15  are  1,  3,  <em>5</em>, and  15 .
The factors of  40  are  1,  2,  4,<em>  5</em>,  8,  10,  20, and  40 .

Ah hah !  Do you see that ' <em>5</em> ' on both lists ?  That's a common factor.

So  15/40  is NOT in lowest terms.

Divide the numerator and denominator both by  5 :

       15 / 40  =<em>  3 / 8</em>

3  and  8  don't have any common factor except ' 1 '. 
So  3/8  is the same number as  15/40, but in lowest terms.


5 0
3 years ago
Read 2 more answers
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