All categories

3 years ago

Log base 32 of 2 Help

Mathematics

1 answer:

blagie [28]3 years ago

4 0

Answer:

$log_{32}(2)=0.2$

Step-by-step explanation:

Recall that the unknown (x) here is the log base 32 of 2, so we can write this as the equation:

$log_{32}(2)=x$

The above equation can be solved by the "change of base formula":

$x=\frac{log(2)}{log(32)} \\x=0.2$

We can also answer this by trying to solve the exponential equation:

$32^x=2$

Where we are asked what is the exponent (x) at which we need to raise the base (32) in order to obtain the answer "2"?

Notice that since

$2^5=32$

Then $32^{1/5} = 2$

And 1/5 = 0.2 which also agrees with our previous answer

You might be interested in

A cylindrical container has a base area of 100 m2 and is 12m high. if the container is one-third filled with water, what's the v

docker41 [41]

Volume of water= $\frac{1}{3}*BA*H$
V= $\frac{1}{3} *100 m^{2} *12m$
V= $400m^{3}$

5 0

3 years ago

Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviat

drek231 [11]

Answer:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 0*0.031 +1*0.156+ 2*0.313+3*0.313+ 4*0.156+ 5*0.031 = 2.5$

We can find the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 0^2*0.031 +1^2*0.156+ 2^2*0.313+3^2*0.313+ 4^2*0.156+ 5^2*0.031 =7.496$

And we can calculate the variance with this formula:

$Var(X) =E(X^2) -[E(X)]^2 = 7.496 -(2.5)^2 = 1.246$

And the deviation is:

$Sd(X) = \sqrt{1.246}= 1.116$

Step-by-step explanation:

For this case we have the following probability distribution given:

X 0 1 2 3 4 5

P(X) 0.031 0.156 0.313 0.313 0.156 0.031

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

We can verify that:

$\sum_{i=1}^n P(X_i) = 1$

And $P(X_i) \geq 0, \forall x_i$

So then we have a probability distribution

We can calculate the expected value with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i) = 0*0.031 +1*0.156+ 2*0.313+3*0.313+ 4*0.156+ 5*0.031 = 2.5$

We can find the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i) = 0^2*0.031 +1^2*0.156+ 2^2*0.313+3^2*0.313+ 4^2*0.156+ 5^2*0.031 =7.496$

And we can calculate the variance with this formula:

$Var(X) =E(X^2) -[E(X)]^2 = 7.496 -(2.5)^2 = 1.246$

And the deviation is:

$Sd(X) = \sqrt{1.246}= 1.116$

6 0

3 years ago

In 2009, a town's population was about 9,000 residents. In 2014, the population was about 12,500 residents. Which linear model r

jek_recluse [69]

Answer:

The linear function that discribes the size of the population in function of the t in years is p = 700t - 1,397,300

Step-by-step explanation:

A linear function is defined by a line, so in order to determine the linear function we can use the two points that were given to us to create a line equation and use that as our linear function. The points given to us were (2009; 9000) and (2014; 12500), in this case the year is our value of "x" and the size of the population is our value of "y". The first step is to find the slope of the line which is given by:

m = (y2 - y1)/(x2 - x1)

m = (12500 -9000)/(2014 - 2009) = 3500/5 = 700

Then we can use the slope and the first point to build the equation:

p - 9000 = 700*(t - 2009)

p = 700t - 1406300 + 9000

p = 700t - 1397300

5 0

3 years ago

At Maxx Middle School, there are 30 times as many students as teachers. If there are 450 students, how many teachers are there?

vredina [299]

30 times as many students than teachers
Equation = 450/30 = 15 teachers

8 0

3 years ago

Read 2 more answers

How do i solve this? and what’s the answer?

Vika [28.1K]

Im pretty sure x y should be 30, I hope this helps.

6 0

3 years ago