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3 years ago

A. B. C. D. ????????????

Mathematics

1 answer:

qaws [65]3 years ago

4 0

$n^{16}$ and 9 are the squares of, respectively, $n^8$ and 3.

So, using

$a^2-b^2=(a+b)(a-b)$

we have

$n^{16}-9=(n^8+3)(n^8-3)$

You might be interested in

Two ships leave a harbor together, traveling on courses that have an angle of 135°40' between them. If they each travel 402 mile

mario62 [17]

Answer:

Therefore they are 734.106 miles apart.

Step-by-step explanation:

Given that ,

Two ships have a harbor together. The angle between two ships is 135°40'. Each of two ships travel 402 miles.

It forms a isosceles triangle whose two sides are 402 miles and one angle is 135°40'. Since it is isosceles triangle then other two angles of the triangle is equal.

Let ∠B= 135°40', and AB = 402 miles , BC = 402 miles

Then the distance between the ships = AC

We know

The sum of all angles = 180°

⇒∠A+∠B+∠C=180°

⇒∠A+135°40'+∠C=180°

⇒2∠A= 180°- 135°40' [ since ∠A=∠C]

⇒2∠A=44°60'

⇒∠A= 22°30'

Again we know that,

$\frac{AB}{sin\angle C}=\frac{BC}{sin \angle A}=\frac{AC}{sin \angle B}$

Taking last two ratio,

$\frac{BC}{sin \angle A}=\frac{AC}{sin \angle B}$

Putting the value of BC , AC ,∠A,∠B

$\frac{402}{sin 22^\circ30'}=\frac{AC}{sin 135^\circ40'}$

$\Rightarrow AC=\frac{402 \times sin135^\circ40'}{sin 22^\circ30'}$

≈734.106 miles

Therefore they are 734.106 miles apart.

3 0

3 years ago

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$