Expand the following logarithmic expressions: a. In(AB2 C3) b. In(xVx2 + 1) c. logo

Answer

3.9 round to 4 ish

Step-by-step explanation:

hey, I'm not sure if I did this right but the way I did it it's what I'm learning so if you get it wrong I apologize.

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

3(2a+4b+7)+6a = 12a+12b+21

Answer:

B) 45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

45 + 90 = 135

180 - 135 =

45

Answer:

The pattern is that each time, 8 is added. The next 2 numbers are 47, 55.

Step-by-step explanation:

7+8=15

15+8=23

23+8=31

31+8=39

39+8=47

47+8=55

Answer:

The symbol 'n,' represents the total number of individuals or observations in the sample.

Answer:

The principal quantum number, n, describes the energy of an electron and the most probable distance of the electron from the nucleus. In other words, it refers to the size of the orbital and the energy level an electron is placed in. The number of subshells, or l, describes the shape of the orbital.

Answer:

72.

Step-by-step explanation:

Number of strings with exactly 2 1's

= 9C2

= 9*8/2*1

= 36.

Same for  2 0s

= 36.

Answer:

(- 3, 7 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

Here (x₁, y₁ ) = (0, 11) and (x₂, y₂ ) = (- 6, 3) , then

midpoint = ( \(\frac{0-6}{2}\), \(\frac{11+3}{2}\) ) = ( \(\frac{-6}{2}\), \(\frac{14}{2}\) ) = (- 3, 7 )

Answer:

(-3,7)

hope it helps........

The value of the variable c in the given expression is; c = d - e - 17

We are given the expression;

d - c - e = 17

The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign. For example, in the formula for the area of a rectangle A = b h ( area = base × height ), the subject of the formula is A.

Now, to find c, we have to isolate it. Thus;

Add c to both sides to get;

d - e = 17 + c

Subtract 17 from both sides to get;

d - e - 17 = c

Thus, the value of the variable c in the given expression is; c = d - e - 17

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Answer:

h > 1600

Step-by-step explanation:

Since the elevation at which it is difficult for Matt to breathe (h) has to be *higher* than 1600, h is greater than 1600.

Answer:

8

Step-by-step explanation:

40% is also .4, or you could do 40 divided by 100. Which will get you 0.4, 100 multiplied by .4 is 40, so if you multiply 20 by .4 you should get 40% of 20. (8)

Answer:

B. 7 1/2 hours

Step-by-step explanation:

5/6 times 9 can be written as 5/6 times 9/1. Then, you just multiply the numerators (the top numbers), and then multiply the denominators (the bottom numbers). 5x9=45, and 6x1=6, so 5/6 times nine is 45/6, or 7 1/2.

Answer:

about $0.13

Step-by-step explanation:

Answer:

13 cents

Step-by-step explanation:

1.59 divided by 12

Answer:

7 years

Step-by-step explanation:

Use the formula I=Prt

Convert 4% to a decimal. 4% = 0.04

1428  = 5100(.04)t

1428 = 204t

1428/204 = 204t/204

t = 7 years

In a 2 x 3 factorial design, the numbers 2 and 3 represent the levels of the first and second factors, respectively. Therefore, there are 2 levels in the first factor and 3 levels in the second factor.

In a factorial design, the numbers 2 and 3 do not directly represent the levels of the factors. The numbers indicate the number of levels present in each factor.

In a 2 x 3 factorial design, the "2" represents the number of levels in the first factor, and the "3" represents the number of levels in the second factor.

For example, let's say the first factor is "A" and it has two levels: Level 1 and Level 2. The second factor, "B," has three levels: Level 1, Level 2, and Level 3. The design would then involve combinations of these levels such as A1B1, A1B2, A1B3, A2B1, A2B2, and A2B3.

So, in a 2 x 3 factorial design, there are 2 levels in the first factor and 3 levels in the second factor, leading to a total of 6 unique combinations or cells.

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Step-by-step explanation:

All the explanation in the photo

Answer:

198 m³

Step-by-step explanation:

Find the area of the triangular prism.

3 × 4 × 1/2 × 9

= 54

Find the area of the rectangular prism.

4 × 4 × 9

= 144

Add their areas.

144 + 54 = 198

The area of the composite shape is 198 m³.

Answer:

10 square units.

Step-by-step explanation:

It is given that triangle ABC has its vertices A, B, and C on the sides of a rectangle 4 units by 5 units.

Height of triangle = 4 units

Base of triangle = 5 units

We need to find the area of triangle.

Area of triangle \(=\dfrac{1}{2}\times base \times height\)

Substitute base = 5 and height = 4 in the above formula.

Area of triangle \(=\dfrac{1}{2}\times 5\times 4\)

Area of triangle \(=\dfrac{20}{2}\)

Area of triangle \(=10\)

Therefore, the area of triangle ABC is 10 square units.

Answer:

9

Step-by-step explanation:

The smallest possible value of is 2, which is the greatest common divisor of the side lengths of the parallelograms bounded by the given lines.

To find the smallest possible value of , we need to determine the common divisor of the areas of the two parallelograms. Let's denote the lengths of the sides of the parallelogram bounded by the lines , , , and as 'a' and 'b', and the lengths of the sides of the parallelogram bounded by the lines , , , and as 'c' and 'd'.

The area of a parallelogram is given by the formula A = base × height. In this case, the bases of the parallelograms are 'a' and 'c', and the heights are 'b' and 'd', respectively.

We are given that the area of the first parallelogram is 18, so we have ab = 18.

Similarly, the area of the second parallelogram is 72, so we have cd = 72.

To find the common divisor of the two areas, we need to find the values of 'a', 'b', 'c', and 'd' that satisfy both equations.

Let's factorize 18 and 72:

18 = 2 × 3²

72 = 2³ × 3²

To minimize , we need to assign the lowest possible values to 'a', 'b', 'c', and 'd' such that the product ab = 18 and cd = 72.

The possible values are:

a = 2, b = 9 (2 × 9 = 18)

c = 4, d = 18 (4 × 18 = 72)

Therefore, the smallest possible value of is the greatest common divisor (GCD) of 'a' and 'c', which is GCD(2, 4) = 2.

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a. The average rate of change of h on the interval [40,000, 55,000] is -0.1533 dollars per mile.

b. The interpretation of h'(55,000) = -0.147 dollars per mile is that at 55,000 miles, the car's value drops/depreciates by 0.147 dollars.

a. The average rate of change of h on the interval [40,000, 55,000] can be calculated by finding the difference in the function values and dividing it by the difference in the input values.

Average rate of change = (h(55,000) - h(40,000)) / (55,000 - 40,000)

Substituting the given values, we have:

Average rate of change = (13,200 - 15,500) / (55,000 - 40,000)

                     = -2,300 / 15,000

                     = -0.1533

The units on this value are dollars per mile, as it represents the change in the value of the automobile per mile driven.

b. The statement "h'(55,000) = -0.147 dollars per mile" indicates the derivative of the function h(m) at m = 55,000. The negative value of the derivative indicates a decrease or depreciation in value.

The best interpretation among the given choices is iii. This value states that at 55,000 miles the car's value drops/depreciates by 0.147 dollars per mile.

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Answer:

Step-by-step explanation:

r32

Answer:

A) H+4

Step-by-step explanation:

I do this in a different way, but i'll do it in both

Mine:

30 ÷ 2 = 15

4 ÷ 2 = 2

15+2, 15 -2

17, 13

Kristen Has 17

Yours:

h+(h+4)=30

     -4   -4

h+h = 26

2h = 26,

h = 13, Back to the equation, use 13 as a sub. for all the h's

13+(13+4) = 30

13 + 17 = 30

Hope this helps!

Answer:

Step-by-step explanation:

The number of headbands Nikki has is represented by h, since it is an unknown value. To create a solvable equation, we can only have one variable. Since we know that Kristen has 4 more than Nikki has (4 more than h), we can represent this as h + 4, and solve for h. By doing this, we can then add to h to number 4 and determine how mnay headbands Kristen has.

The type of sampling method used in this survey is snowball sampling. Snowball sampling is a type of non-probability sampling approach.

In this technique, the initial group of study participants refers additional participants, and those participants lead to more referrals, and so on, like a snowball rolling down a hill. This technique can be used when the population of interest is unknown or challenging to access.

Debra wants to conduct a sex study on individuals who enjoy sadomasochism. She contacts a few of her friends who engage in sadomasochistic behavior. In turn, they contact others whom they know are sadomasochists or attend s/m parties. Eventually, a sample of 200 participants is obtained.

This technique is used when the population of interest is challenging to access or when the researchers lack information about the population. Here, the initial group of study participants refers additional participants, and those participants lead to more referrals, and so on, like a snowball rolling down a hill.

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Answer:

Erick's payment was late by 11.2 days.

Answer:

3y

Step-by-step explanation:

Therefore, one way the drama club could achieve its objective of earning  inequality at least $990 from ticket sales is by selling 60 student tickets and 80 adult tickets.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Thus, disparity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two values are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both parts' negative values are divided or added. Exchange the left and the right.

Let's first establish the disparities system:

Income equals 5.5x + 9 years

x + y ≤ 140

5.5x + 9y ≥ 990

We can first rephrase these inequality in the slope-intercept form before graphing them:

It is possible to rewrite x + y  140 as y  -x + 140.

It is possible to rewrite 5.5x + 9y  990 as y  -5/9x + 110.

These inequality can now be plotted on the same coordinate plane:

Graph of a system of inequalities

It is accurate to say that 60 + 80 equals 140, and that 5.5(60) + 9(80) equals 990.

Therefore, one way the drama club could achieve its objective of earning at least $990 from ticket sales is by selling 60 student tickets and 80 adult tickets.

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