Bus A and Bus B leave the bus depot at 6 pm. Bus A takes 20 minutes to complete its route once and bus B takes 45 minutes to complete its route once. If both buses continue to repeat their route, at what time will they be back at the bus depot together? Assume the buses have no breaks in between routes. Give your answer as a 12-hour clock time

Answer:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Step-by-step explanation:

We are given:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)[/tex]

And we want to evaluate it using L'Hopital's Rule.

First, using direct substitution, we will acquire:

[tex]=(1-1)^\ln(1)}=0^0[/tex]

Which is indeterminate.

In order to apply L'Hopital's Rule, we first need to manipulate the expression. We will let:

[tex]y=(x-1)^\ln(x)[/tex]

By taking the natural log of both sides:

[tex]\ln(y)=\ln(x)\ln(x-1)[/tex]

And by taking the limit as x approaches 1 from the right of both functions:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\lim_{x\to 1^+}\ln(x)\ln(x-1)[/tex]

Rewrite:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{\ln(x-1)}{\ln(x)^{-1}}[/tex]

Using direct substitution on the right will result in 0/0. Hence, we can now apply L'Hopital's Rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}\frac{1/(x-1)}{-\ln(x)^{-2}(1/x)}\Big(\frac{-x\ln(x)^2}{-x\ln(x)^2}\Big)[/tex]

Simplify:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-\frac{x\ln(x)^2}{x-1}[/tex]

Now, by using direct substitution, we will acquire:

[tex]\displaystyle \Rightarrow -\frac{1\ln(1)^2}{1-1}=\frac{0}{0}[/tex]

Hence, we will apply L'Hopital's Rule once more. Utilize the product rule:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)= \lim_{x\to 1^+}-(\ln(x)^2+2x\ln(x))[/tex]

Finally, direct substitution yields:

[tex]\Rightarrow -(\ln(1)^2+2(1)\ln(1))=-(0+0)=0[/tex]

Thus:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=0[/tex]

By the Composite Function Property for limits:

[tex]\displaystyle \lim_{x\to 1^+}\ln(y)=\ln( \lim_{x\to 1^+}y)=0[/tex]

Raising both sides to e produces:

[tex]\displaystyle e^{\ln \lim_{x\to 1^+}y}=e^0[/tex]

Therefore:

[tex]\displaystyle \lim_{x\to 1^+}y=1[/tex]

Substitution:

[tex]\displaystyle \lim_{x\to 1^+}(x-1)^\ln(x)}=1[/tex]

Answer:

Rotations, Reflections

Step-by-step explanation:

This is going to be our answer because we know that a figure has some kind of rotation.

A rotation is when a shape can be rotated in some way. A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection map every point of a figure to an image across a fixed-line.

So our answer would be Rotations, Reflections!

Hope this helps!

If it is correct please mark as Brainllest!

Have a good Day!

Answer:

(2/3,2)

Step-by-step explanation:

3*2/3+4

simplify  2=2

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2^6 = 2\times2\times2\times2\times2\times2}\\\mathsf{2\times2\times2\times2\times2\times2}\\\mathsf{2\times2=4}\\\mathsf{4\times4\times4}\\\mathsf{4\times4=16}\\\large\mathsf{16\times4=64}\\\mathsf{2^6 = \bf{64}}[/tex]

[tex]\mathsf{4^4=4\times4\times4\times4}\\\mathsf{4\times4\times4\times4}\\\mathsf{4\times4=16}\\\mathsf{16\times16}\\\mathsf{16\times16=256}\\\mathsf{4^4=\bf{256}}[/tex]

[tex]\boxed{\boxed{\mathsf{Answer: 64\neq 256}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

hard to read, can you take another picture please?

Step-by-step explanation:

Answer:

8(3y-4)

hope this help :)

Answer:

5,006 :)

Step-by-step explanation:

Answer:

3√3−x=3√2x

Graph each side of the equation. The solution is the x-value of the point of intersection.

x≈0.46567646

image of graph

Step-by-step explanation:

Hope it is helpful.....

Answer:

Its red becasue 1/2 is greater than all of them

The most likely color of the marble that will be chosen is red.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Number of red marbles in the bag=1/2

Number of blue marbles in the bag=1/4

Number of green marbles in the bag=1/6

Number of yellow marbles in the bag=1/12

Now,

To determine the most likely color of the marble that will be chosen, we need to calculate the probability of selecting each color. The probability of selecting a red marble is 1/2, the probability of selecting a blue marble is 1/4, the probability of selecting a green marble is 1/6, and the probability of selecting a yellow marble is 1/12.

To compare the probabilities, we need to find a common denominator. The common denominator for 2, 4, 6, and 12 is 12. So, we can rewrite the probabilities as:

Probability of selecting a red marble = 6/12

Probability of selecting a blue marble = 3/12

Probability of selecting a green marble = 2/12

Probability of selecting a yellow marble = 1/12

Since the probability of selecting a red marble is the highest among all the colors, it is the most likely color to be chosen.

Therefore, by probability the answer will be red marble.

Learn more about probability here;

https://brainly.com/question/9326835

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Answer:

it would be the third one ( 0,3)

Answer:

x = 11

Step-by-step explanation:

3(11 - 10) + 7 =

3 + 7 = 10

hope this helped

Answer:

50 units.

Step-by-step explanation:

Answer:

7x+77

Step-by-step explanation:

7(x+11)

=(7)(x+11)

=(7)(x)+(7)(11)

=7x+77

The equivalent expression from the distributive property is 7x+77.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is 7(x + 11). From the distributive property, the expression will be calculated as:-

E = 7(x+11)

E=(7)(x+11)

E=(7)(x)+(7)(11)

E=7x+77

Therefore, the equivalent expression from the distributive property is 7x+77.

To know more about an expression follow

https://brainly.com/question/29083959

#SPJ6

Step-by-step explanation:

its too blurry I can't see the numbers

Answer:

Hong Wu means...

Step-by-step explanation:

The last one

Answer:

Its D

Step-by-step explanation:

Answer:

l x w do the the math

Step-by-step explanation:

there

Answer:

u said free poinstt on that persons answer so Hi

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

x=2

Answer:

b

Step-by-step explanation:

Given:

Ratio of 40 centimeters to 2 metre.

To find:

The ratio in its simplest form.

Solution:

We know that,

1 m = 100 cm

2 m = 200 cm

We have, ratio of 40 centimeters to 2 metre.

[tex]Ratio=\dfrac{40\ cm}{2\ m}[/tex]

[tex]Ratio=\dfrac{40\ cm}{200\ cm}[/tex]

[tex]Ratio=\dfrac{40}{200}[/tex]

[tex]Ratio=\dfrac{1}{5}[/tex]

[tex]Ratio=1:5[/tex]

Therefore, the required ratio in the simplified form is 1:5.

Answer:

x = 3

Step-by-step explanation:

Answer: x = 3

Step-by-step explanation:

Answer:

D. 1.47

Step-by-step explanation:

Answer:

1.47

Step-by-step explanation:

Answer:

3h-9

Step-by-step explanation:

you can't fit it into an equation because 1, i dont  a image of it and 2, you can't subtract a number from a coefficient/variable

Answer:

2

Step-by-step explanation:

por que el le dio 5 manzanas a jose y le quedaron 2

Answer:

52

Step-by-step explanation:

Give Brainlest

Answer:

15

Step-by-step explanation:

8^2 + b^2 = 17^2

64 + b^2 = 289

289 - 64 = 225

square root of 225 = 15

Answer:

its the first one

Step-by-step explanation:

if the fractions have the same denominator, all you have to do is add the numerators across.

Answer:

A

Step-by-step explanation:

Slow down, take a breath.

All of the fractions have the denominator of 12 so you dont need to worry about finding a common denominator.

this is simple addition:

1+5+5=11, simple as that

i hope this helps u!

remember to stop and think,

pls give thx and brainliest

Answer:

eight hundred seventy-five thousand six hundred eighty-seven

hope this helps :)