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3 years ago

What value of n solves the equation 2^n =1/8

1 answer:

5 0

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\
2^n=\cfrac{1}{8}\qquad \boxed{8=2^3}\qquad 2^n=\cfrac{1}{2^3}\implies 2^n=2^{-3}
\\\\\\
\textit{the base is the same, the exponents must also be the same}\quad n=-3$

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melisa1 [442]

First one is 2 ft because 12 inches in one foot. Other people will probably help out on rest!! I’m little busy rn so :D

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3 years ago

Read 2 more answers

In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviatio

muminat

Answer:

15.87%

Step-by-step explanation:

First thing here is that we calculate the z-score which corresponds to 76

mathematically;

z-score = (x-mean)/SD

mean = 71 and SD = 5

plugging these values, we have;

z = (76-71)/5 = 5/5 = 1

Now, we want to firstly get the probability that we have a student shorter than 76 inches

The probability we want to calculate is P(z<1)

we can get this using the z-score table directly

That would be 0.15866

In percentage that is 15.866% which is 15.87% to the nearest tenth

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3 years ago

For the function in the graph, find the values of f(-4), f(-1), and f(1).

Ray Of Light [21]

Answer:

f(-4) = -1

f(-1) = -4

f(1) = 4

Step-by-step explanation:

We need to find the y value for the x values

f(-4) means find the y value for x= -4

f(-4) = -1

f(-1) = -4

f(1) = 4

6 0

3 years ago

Given two vectors a⃗ = 4.60 i^+ 7.20 j^ and b⃗ = 5.10 i^− 2.70 j^ , find the scalar product of the two vectors a⃗ and b⃗ .

grin007 [14]

A=<4.60,7.20>
b=<5.10,2.70>
The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions,
a.b=4.6*5.1+7.2*2.7
=23.46+19.44
=42.9

6 0

3 years ago

Let X denote the time from the present until the stock market hits 25,000. If X ≤ 1, you win $10, 000X. If X > 1, you win not

const2013 [10]

Answer: $6321

Step-by-step explanation:

Expected value is given as exactly what you might think it means intuitively, the return you can expect for some type of action.

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens:(P(x) * n).

he formula for the Expected Value for a binomial random variable is:

P(x) * X.

X is the number of trials and P(x) is the probability of success.

The formula for calculating the Expected Value where there are multiple probabilities is:

E(X) = ∑X * P(X)

The equation is basically the same, but here you are adding the sum of all the gains multiplied by their individual probabilities instead of just one probability.

Calculating the expected value of winning as follows:

Given,

Fx= e^-x, x is greater or equal to 0

Now, P less than or equal to zero =

[-e^-x] ^1

e^-0 - e^-1

= 1 - e^-1

= 0.6321

and P(x>1) = 1-0.6321= 0.3679

Therefore,Let y= amount of winnings.

Based on the above given information,

y= $10000 0

P(y)= 0.6321 0.3679

The expected value of winning:

E(y) = ΣyP(y)

E(y) = 10000 × 0.6321 + 0 × 0.3679

E(y) = $6321

Therefore, the expected value of winning is $6321

5 0

3 years ago