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2 years ago

What is

" alt="3^{x} = \frac{1}{9}" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Makovka662 [10]2 years ago

8 0

$~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 3^x=\cfrac{1}{9}\implies 3^x=\cfrac{1}{3^2}\implies 3^x=3^{-2}\implies x = -2$

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Help meee pleaseeeee

Wittaler [7]

Answer:

1 x 10^21

Step-by-step explanation:

The initial number (2 x 10^4) is in scientific notation. Scientific notation must be written as: a X 10^n, where 0<a<10 and n is an integer. In this case, the number in scientific notation is being raised to the power of 5. When we raise a power by another power, we must multiply the power of all the terms by the additional power. In this case, we would get 2^5 x 10^20, this would be 10 x 10^20. Since the value of 'a' needs to be greater than 0 and less than 10, we need to move the decimal to the left and add another power to our 10: 1 x 10^21.

7 0

3 years ago

A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obta

Andru [333]

Answer:

Step-by-step explanation:

According to the given question, a tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 37,000 miles and a standard deviation of 3,887 miles.

Let us define X be the random variable shows that the mileages tires normally distributed with

mean

μ = 37000

standard deviation

σ =3, 887

Therefore

X ~ (μ = 37000, σ =3,887)

The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. Therefore the guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage is determined as:

P(X < k) = 0.02

$\Rightarrow P\left ( \frac{X-\mu }{\sigma }\leq \frac{k-\mu }{\sigma } \right )=0.02
\\\\P\left ( Z \leq \frac{k-37,000 }{3,887 } \right )=0.02$

From the standard normal curve 2% area is determined as -2.0537 and hence

$\frac{k-37,000}{3,887}=-2.0537\\\\k=37000-7982.7319\\\\k=29017.2681\\\\\Rightarrow k=29018$

If we consider z value at two decimal places then

$\frac{k-37,000}{3,887} =-2.05\\\\\Rightarrow k=29032
$

Therefore the guaranteed 29032 mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage.

The area under the standard normal curve is determined as:

6 0

4 years ago

Name one expression that is equivalent to 5x-6y+7

IceJOKER [234]

Y=5/6x+7/6

i dont know if thats the answer your looking for but here

5 0

3 years ago

Line AB has endpoints A(-4,5) and B(3,5). What is the x-coordinate of a point C such that B is the midpoint of line AC

Ipatiy [6.2K]

Easy peasy

the midpoint between $(x_1,y_1)$ and $(x_2,y_2)$ is
$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
just average them

so given that (3,5) is the midpoint of (-4,5) and (x,y)
$(\frac{-4+x}{2},\frac{5+y}{2})=(3,5)$
so by logic
$\frac{-4+x}{2}=3$ and $\frac{5+y}{2}=5$
times both sides by 2 for everybody
-4+x=6 and 5+y=10
add 4 to both sides for left one and minus 5 from both sides for right
x=10 and y=5

the coordinate of point C is (10,5)
the x coordinate is 10

7 0

4 years ago

How Much Weight Does An Average 17 Year Old Bench

maxonik [38]

It should be 185 pounds. Have a GREAT day!!!!! :)

8 0

3 years ago