All categories

2 years ago

Which is equivalent to log Subscript 2 Baseline n = 4?

Mathematics

2 answers:

Marrrta [24]2 years ago

7 0

Answer:

n = 16

Step-by-step explanation:

Given the expression;

$log_2 n = 4$

If $log_a b = c, then;\\a^c = b$

Applying this to the question;

2⁴⁴= n

16 = n

Swap'

n = 16

Hence the value of n is 16

Brrunno [24]2 years ago

6 0

For Edg. it was A for me

You might be interested in

Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable wi

Mandarinka [93]

The moment generating function (mgf) of y is given by

$M_y(t)=E(e^{ty})=E(e^{2pxt})=M_x(2pt)=p(1-e^{2pt}(1-p))^{-1}$

Since the momoent generating function of x is given by $M_x(t)=p(1-e^{t}(1-p))^{-1}$

When p tends to 0, we have

$\lim_{p \to 0} M_y(t)= \lim_{p \to 0} \frac{p}{1-e^{2pt}(1-p)} = \frac{0}{0}$

Applying L'Hopital's rule we have:

$\lim_{p \to 0} M_y(t)=\lim_{p \to 0} \frac{1}{e^{2pt}+2te^{2pt}+2pte^{2pt}} = \frac{1}{1+2t} , \ \ \ t\ \textless \ \frac{1}{2}$

This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.

5 0

3 years ago

What have the Mars rovers discovered about Mars?

fomenos

Answer:D. The atmosphere of Mars is twice as thick as scientists predicted it would be.

Step-by-step explanation:

6 0

2 years ago

Please help me with my math

Natasha_Volkova [10]

Answer:

The answer is C

Step-by-step explanation:

the y-intercept is going through 0 therefore there would be no "b" in the y=mx+b formula

3 0

2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

2 years ago

I need some help on this if possible

Sophie [7]

where C is the circumference, d is the diameter and r is the radius.

The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. The radius of the circle is a line segment from the center of the circle to a point on the circle. The diameter of a circle is twice the length of its radius.

If you are given the diameter then use the formula C = πd

If you are given the radius then use the formula C = 2πr

Step-by-step explanation:

4 0

3 years ago