Find the difference:

Mathematics

1 answer:

VLD [36.1K]3 years ago

6 0

Answer: The difference cannot be found because the indices of the radicals are not the same.

Step-by-step explanation:

To find the difference you need to subtract the radicals. But it is important ot remember the following: To make the subtraction of radicals, the indices and the radicand must be the same.

In this case you have these radicals:

$\sqrt[ {8ab}^{3} ]{{ac}^{2} }- \sqrt[ {14ab}^{3}]{{ac}^{2} }$

You can observe that the radicands are the same, but their indices are not the same.

Therefore, since the indices are different you cannot subtract these radicals.

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The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.

maks197457 [2]

Answer:

195.25

Step-by-step explanation:

Consider geometric series S(n) where initial term is a

So S(n)=a+ar^1+...ar^n

Factor out a

S(n)=a(1+r+r^2...+r^n)

Multiply by r

S(n)r=a(r+r^2+r^3...+r^n+r^n+1)

Subtract S(n) from S(n)r

Note that only 1 and rn^1 remain.

S(n)r-S(n)=a(r^n+1 -1)

Factor out S(n)

S(n)(r-1)=a(r^n+1 -1)

The formula now shows S(n)=a(r^n+1 -1)/(r-1)

Now use the formula for the problem

4 0

3 years ago

The speeds of cars on a given i street we are normally distributed with a mean of 72 miles per hour and a standard deviation of

Ostrovityanka [42]

Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Step-by-step explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

$P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278$