What is the quotient of the rational expressions shown below? Make sure
your answer is in reduced form.
x2 - 16 x2 - 8x + 16
x+5 2x +10

Answer:

x=2.83

Step-by-step explanation:

The solution to the equation, rounded to two decimal places, is x = 2.83.

The correct answer is option B: x = 2.83.

To solve the equation 5 + 6·log2(x) = 14 and round the answer to two decimal places, we can follow these steps:

1. Subtract 5 from both sides of the equation: 6·log2(x) = 9.

2. Divide both sides of the equation by 6: log2(x) = 9/6.

3. Simplify the right side: log2(x) = 1.5.

To find the value of x, we need to rewrite the equation in exponential form.

Remember that log2(x) = y is equivalent to [tex]2^y= x[/tex].

4. Rewrite the equation in exponential form: [tex]2^{1.5} = x[/tex].

5. Calculate the value of [tex]2^{1.5}[/tex] using a calculator or by approximating: x ≈ 2.83.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ4

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that [tex]p = 0.9[/tex]

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when [tex]n = 4[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486[/tex]

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that [tex]n = 8[/tex]

It will operate if at least 4 components are working correctly, so we want:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0[/tex]

[tex]P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex]

[tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0[/tex]

[tex]P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004[/tex]

Then

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004[/tex]

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996[/tex]

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Answer:

6 1/2 quarts I think

Step-by-step explanation:

So sorry if I'm wrong! Have a nice day! Owa Owa!

Answer:

100

Step-by-step explanation:

it gives you the formula for simple interest

Answer:

6

Step-by-step explanation:

Volume of Rectangular Prism: (l)(w)(h)

8 x 4 x ? = 192

32 x ? = 192

/32        /32

height = 6

To check work:

(8)(4)(6) = 192

Answer:

sorry, I think u got yr question incomplete.

To find the median:

- Arrange the data points from smallest to largest.

- If the number of data points is odd, the median is the middle data point in the list.

- If the number of data points is even, the median is the average of the two middle data points in the list.

Answer:

{0, 1, 2, 3, 4} --> 96 5-digit numbers possible with this set.

Step-by-step explanation:

i dunno, i kinda just searched it up

link:   https://gmatclub.com/forum/how-many-five-digit-numbers-can-be-formed-using-digits-91597.html#:~:text=If%200%20is%20included%3A,numbers%20possible%20with%20this%20set.

Answer:

120

Step-by-step explanation:

using the equation 5P5, you find that the total number of ways these 5 digits can be arranged to form 5 digit numbers if each is only used ONCE.

Answer:

The answer is linear.

Step-by-step explanation:

The x int is being added by 1 while the y int is subtracting 1

Answer:

10³ = l

Step-by-step explanation:

Answer:

Step-by-step explanation:

To start this is a ratio, and the goal is to get at least 1 to be a whole number so first lets get the number below 1 to 1.

0.75 : 2 5/16 ---> (x1.3333 on both sides) ---> 1 : 3 1/12.

Next, if needed for your answer, lets get the other number to be a whole number as well. We can do this my multiplying both sides by 12 since the fraction on 3 1/12 is 1/12.

1 : 3 1/12 --> (x12 on both sides) ---> 12 : 37

Your final answer will either be 1 : 3 1/12 or 12 : 37, depending on the formatting expected for your homework assignment.

Answer:

2/B

Step-by-step explanation:

The base is 9 and the height is 4.

Answer:

50%

Step-by-step explanation:

Suppose you have a fair coin; this means it has a 50% chance of landing heads up. Suppose you dip it three times, these flips are independent. What is the probability that it lands heads up, then tails up and then heads up again. so the answer is 1/8 or 12.5%

(hope I wasnt late!!)

Answer:

(x+2)2+(y-1)2=25

Step-by-step explanation:

x2+y2+4x-2y+4+1=20+4+1

Answer:

!! , ' !!!

Step-by-step explanation:

ꜰɪʀꜱᴛ! ᴄᴏᴍʙɪɴᴇ ᴍᴜʟᴛɪᴘʟɪᴇᴅ ᴛᴇʀᴍꜱ ɪɴᴛᴏ ᴀ ꜱɪɴɢʟᴇ ꜰʀᴀᴄᴛɪᴏɴ:

        / = /

   / = /                 ᴊᴜꜱᴛ ʟɪᴋᴇ ᴛʜᴀᴛ!

ꜱᴇᴄᴏɴᴅ! ᴍᴜʟᴛɪᴘʟʏ ᴀʟʟ ᴛᴇʀᴍꜱ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴠᴀʟᴜᴇ ᴛᴏ ᴇʟɪᴍɪɴᴀᴛᴇ ꜰʀᴀᴄᴛɪᴏɴ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ!! ᴇᴀꜱʏ ᴘᴇᴀꜱʏ:

                    / = /

                  9⋅/= 9⋅/     ꜱᴇᴇ ᴇᴀꜱʏ ᴘᴇᴀꜱʏ!!

! :

          9⋅/=!!!

                                   ᴀʟᴍᴏꜱᴛ ᴅᴏɴᴇ!!

ꜰᴏᴜʀᴛʜʟʏ!! ᴍᴜʟᴛɪᴘʟʏ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ (ᴊᴜꜱᴛ ᴛʜᴀᴛ ꜱɪᴍᴘʟᴇ!):

                9⋅/  

           ˜”*°•.˜”*°• Which Would equal 60=10x!! •°*”˜.•°*”˜

ꜰɪꜰᴛʜ!! ᴅɪᴠɪᴅᴇ ʙᴏᴛʜ ꜱɪᴅᴇꜱ ᴏꜰ ᴛʜᴇ ᴇQᴜᴀᴛɪᴏɴ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴛᴇʀᴍ:

               60/10 = 10x/10

ʟᴀꜱᴛʟʏ!!! ꜱɪᴍᴘʟɪꜰʏʏ:

         =6

ᴛʜᴇɴ ʏᴏᴜ ɢᴇᴛ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀʀ!!

              x=6  ʕ ˵• ₒ •˵ ʔ  

ᴀɴʏᴡᴀʏꜱ ᴛᴏᴏᴅʟᴇꜱ!!

    ʜᴀᴠᴇ ᴀɴ ᴀᴍᴀᴢɪɴɢ ɴɪɢʜᴛ ᴏʀ ᴅᴀʏ!

ꜰʀᴏᴍ ʏᴏᴜʀ ᴏɴᴇ ᴀɴᴅ ᴏɴʟʏ ᴘɪɴᴋʏ  ʕ ﾟ ● ﾟʔ

Answer:

36

Step-by-step explanation:

1×36

36×2

36×16

aaaaaaaaaaaaaaaaaaaaaa

Answer:

HI!!

Step-by-step explanation:

What's your numerator and denominator value?

Answer:

B

Step-by-step explanation:

Angle 1 is an exterior angle, while angle 6 is an interior angle and so they are not congruent

Answer:

125 inches cubed

Step-by-step explanation:

First, you find the volume of the full square, and then you divide your answer by 2, since the figure is a triangle.

So,

10 x 10 x 2.5 = 250

250 ÷ 2 = 125 inches cubed

Answer:

b.)36

Step-by-step explanation:

Formula for area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]

where a and b = bases and h = height

The sign has the following dimensions

Base 1 = 6ft

base 2 = 12ft

height = 4ft

Using these dimensions we plug in the values into the formula

[tex]A=\frac{6+12}{2} 4\\6+12=18\\\frac{18}{2} =9\\9*4=36[/tex]

Hence the area of Mr. Wash's sign is 36 square feet.

Answer:

b) 36 sq ft.

Step-by-step explanation:

6 x 4 = 24 (multiply to find the square after splitting it)

12 - 6 = 6 x 4 = 24 / 2 = 12 (you divide by two because it's a triangle)

24 + 12 = 36

hope this helps :)

Hereaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answer:

1. x=16

2. x=35

3. x=10

4. x=30

5. x=3

Step-by-step explanation:

intercepted arcs are 2* the angle measure

1. x= 1/2( 32)=16 x=16

2. the intercepted arc is 360-110-180=70

1/2(70)= 35

3. 2x=x+10  subtract x from both sides

x=10

4. 2(x+30)=4x

2x+60=4x

60=2x

30=x

5. 2(3x)=12x-18

6x=12x-18

-6x=-18

x=m

Answer:

C

Step-by-step explanation:

Answering your question so it will not get removed.

The correct option for the question is C.  [tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]

If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the series is referred to as a geometric progression. (GP), while the constant value is called the common ratio.

Conclusion: The nth term from the end of the GP with the last term l and common ratio r = l/ [r(n – 1)]. The sum of infinite, i.e. the sum of a GP with infinite terms is S∞= a/(1 – r) such that 0 < r < 1.

[tex]a_{n}[/tex] = 5[tex](3/4)^{n}[/tex]

[tex]S_{n}[/tex]= Σ[tex]a_{n}[/tex]

[tex]S_{n}[/tex] = ∑5[tex](3/4)^{n}[/tex]

  = 5∑[tex](3/4)^{n}[/tex]

  = 5 [ 3/4 + [tex](3/4)^{2}[/tex] + ......+ [tex](3/4)^{n}[/tex]]

 =5 [ 3/4 * { 1- [tex](3/4)^{n}[/tex]} / 1 - 3/4 ]

[tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]

learn more about geometric sequence here https://brainly.com/question/1509142

#SPJ2

Answer:

They have 11 inches of rope left.

Step-by-step explanation:

First we do the 6 foot rope minus the 4 foot cut. That leaves us with 2 feet, or 24 inches.

24-13 = 11

[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = \lim_{h\to0}\frac{(9+h)^4-9^4}h[/tex]

Carry out the binomial expansion in the numerator:

[tex](9+h)^4 = 9^4+4\times9^3h+6\times9^2h^2+4\times9h^3+h^4[/tex]

Then the 9⁴ terms cancel each other, so in the limit we have

[tex]\displaystyle \lim_{h\to0}\frac{4\times9^3h+6\times9^2h^2+4\times9h^3+h^4}h[/tex]

Since h is approaching 0, that means h ≠ 0, so we can cancel the common factor of h in both numerator and denominator:

[tex]\displaystyle \lim_{h\to0}(4\times9^3+6\times9^2h+4\times9h^2+h^3)[/tex]

Then when h converges to 0, each remaining term containing h goes to 0, leaving you with

[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = 4\times9^3 = \boxed{2916}[/tex]

or choice C.

Alternatively, you can recognize the given limit as the derivative of f(x) at x = 9:

[tex]f'(x) = \displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h \implies f'(9) = \lim_{h\to0}\frac{f(9+h)-f(9)}h[/tex]

We have f(x) = x ⁴, so f '(x) = 4x ³, and evaluating this at x = 9 gives the same result, 2916.