Expand the expression 3(-2a+3b)

Which expressions are equivalent to 2 ln a + 2 ln b - ln a?

ycow [4]

Answer:

Choices 2, 3, and 5 are correct.

Step-by-step explanation:

Complete question is:

Check all that apply.

1. ln ab² - ln a

2. ln a + 2 ln b

3. ln a² + ln b² - ln a

4. 2 ln ab

5. ln ab²

ANSWER:

The given expression is : 2 ln a + 2 ln b - ln a

It simplifies to: ln a + ln b² = ln ab²

Checking the given options.

1. ln ab² - ln a = ln (ab²)/a = ln b²

FALSE

2. ln a + 2 ln b = ln ab²

TRUE

3. ln a² + ln b² - ln a = ln (a²b²)/a = ln ab²

TRUE

4. 2 ln ab = ln a²b²

FALSE

5. ln ab²

TRUE

4 0

3 years ago

A square has an area of 64 m². What is the length of each side?

anygoal [31]

Answer:

8m

Step-by-step explanation:

The area of a square is length*width.

We can square root the area to get the length of each side. Since the shape is a square, the lengths are the same.

$\sqrt{64}$ =8

One side is 8m.

7 0

2 years ago

Allen wants to have a mean of 90 on his math quizzes. So far, he has scored 86, 94, 88, 95, and 89. What is the least score that

viva [34]

Answer:

88

Step-by-step explanation:

$\frac{86 + 94 + 88 + 95 + 89 + x}{6} = 90$

The mean would be the sum of all the math quiz grades divided by the number of quizzes taken.

Solve for x:

$86 + 94 + 88 + 95 + 89 + x = 540$

$452 + x = 540$

$x = 88$

Thus, Allen needs at least an 88 to obtain a mean of at least 90.

3 0

3 years ago

What is the value of n in this equation?(2.4 x 10^3) x (3 x 10^n) = 7.2 x 10^9

Burka [1]

The model below represents an equation. Which value of x makes the value true?

x=

The model below represents an equation. Which value of x makes the value true?

x=

7 0

2 years ago

Read 2 more answers

Let represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of is as follows.

Sindrei [870]

Answer:

a) $P(X=3) = 0.1$

b) $P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

c) $P(X=4) = 0.3$

d) $P(X=0) = 0.2$

e) $E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

f) $E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

Step-by-step explanation:

We have the following distribution

x 0 1 2 3 4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

$P(X=3) = 0.1$

Part b

We want this probability:

$P(X\geq 3) =1-P(X$

And replacing we got:

$P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4$

Part c

For this case we want this probability:

$P(X=4) = 0.3$

Part d

$P(X=0) = 0.2$

Part e

We can find the mean with this formula:

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

And replacing we got:

$E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2$

Part f

We can find the second moment with this formula

$E(X^2)= \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4$

And the variance would be:

$Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4$

And the deviation:

$\sigma =\sqrt{2.4} = 1.549$

4 0

3 years ago