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podryga [215]
3 years ago
8

Sarah has a solid wooden cube with a length of 4/5 centimeter. From each of its 8 corners, she cuts out a smaller cube with a le

ngth of 1/5centimeter. What is the volume of the block after cutting out the smaller cubes?
Mathematics
1 answer:
kobusy [5.1K]3 years ago
5 1
The answer would be the first one and the fourth one.
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45 Points! <br> Please help with this it's either B or C
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It's C I'm pretty sure and this in English not math
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3 years ago
A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down du
Mariana [72]

Answer:

4.01% probability that the battery will break down during the warranty period

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

\mu = 45, \sigma = 12

a. What is the probability that the battery will break down during the warranty period

Warranty of 2 years = 24 months. So this is the pvalue of Z when X = 24.

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

Z = \frac{24 - 45}{12}

Z = -1.75

Z = -1.75 has a pvalue of 0.0401

4.01% probability that the battery will break down during the warranty period

7 0
3 years ago
hi:) I’m not sure if this is correct. For the justifying part , must I still use the discriminant or can I just say that since t
labwork [276]

You did it right (almost, I got 21 instead of 19) but didn't finish.  You need to show your discriminant is never negative.

x² + (p+1)x = 5-2p

x² + (p+1)x +(2p-5) =0

Real roots mean a positive (or at least non-negative) discriminant:

D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20

D =  p² - 6p + 21

It's not totally obvious that D>0; we prove that by completing the square by noting

(p-3)² = p² - 6p + 9

so

p² - 6p = (p-3)² - 9.

D =  p² - 6p + 21

D =  (p-3)² - 9 + 21

D = (p-3)² + 12

Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12.   We always get two distinct real roots.

3 0
3 years ago
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