√10 Multiple √15 is equal to

Mathematics

1 answer:

icang [17]3 years ago

5 0

Answer:

a). 5√6

$\sqrt{10} \times \sqrt{15} \\ = ( \sqrt{5} \times \sqrt{2} ) \times ( \sqrt{5} \times \sqrt{3} ) \\ = {( \sqrt{5}) }^{2} \times ( \sqrt{2} \times \sqrt{3} ) \\ = 5 \times ( \sqrt{6} ) \\ = 5 \sqrt{6}$

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Solve the given triangles by finding the missing angle and other side lengths.

coldgirl [10]

Answer:

a ≈ 27.65; B = 28°; c ≈ 19.17
a ≈ 163.30; B = 120°; c ≈ 59.77
A = 13°; b ≈ 0.3874; c ≈ 1.3737

Step-by-step explanation:

As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.

Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...

B = 180° -A -C = 28°

The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...

side = sin(opposite angle)×<em>((reference side)/sin(reference angle))</em>

Note that the factor in italics remains the same for both remaining sides.

In the first problem, this becomes ...

a = sin(112°)·14/sin(28°) ≈ 27.65

c = sin(40°)·14/sin(28°) ≈ 19.17

The remaining problems are worked in similar fashion.

_____

<em>Comment on triangle solutions</em>

These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.

8 0

3 years ago

Read 2 more answers

andrezito [222]

Answer:

a) 0.27% probability that the mean is less than 1995 milliliters.

b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.

Step-by-step explanation:

To solve this problem, it is important to understand the normal probability distribution and the central limit theorem

Normal probability distribution

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.

Central Limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$