When divding numbers with the same base you________ the exponents

Answer:

  -1

Step-by-step explanation:

The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.

  d(log(x))/dx = 1/(x·ln(10))

  d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))

Then the ratio of these derivatives is ...

  lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x

__

At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.

  d(-sin(x)cos(x))/dx = -cos(2x)

  dx/dx = 1

so the limit is ...

  lim = -cos(2x)/1

  lim = -1 when evaluated at x=0.

_____

I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.

Answer:

I think if you haven't hung out with her a lot, you should start hanging out with her, getting along, until you have built up courage to tell her you have feelings for her.

We want to see if the first selection is dependent on the second selection, we will see that no, the first selection can not depend on a selection that did not happen yet.

So the situation is:

We have a group of puppies, some are black, some are white.

Let's say that there are N puppies in total, n₁ are black, n₂ are white, such that:

n₁ + n₂ = N

Now we have that the first selection, event A, is a black puppy. The probability is just the quotient between the number of black puppies and the total number of puppies:

q = n₁/N

Then now we have:

Now for the second selection, event B, the probability of selecting a white puppy is:

P = n₂/(N - 1)

Notice that because there are fewer black puppies than before (because we took one) the denominator decreases, thus, the probability of getting a white puppy increases.

So clearly event B depends on event A.

Now the question is:

Is A dependent on B?

No, A can not depend on event B, because event A happens first. The probability of the first event is always q = n₁/N.

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Answer:

6x - 6

Step-by-step explanation:

(2x + 6) + (4x - 12) ← remove parenthesis

= 2x + 6 + 4x - 12 ← collect like terms

= (2x + 4x) + (6 - 12)

= 6x + (- 6)

= 6x - 6

Answer:

x=16.9+34.6

x=51.5

.............................

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Answer:

$1,270

Step-by-step explanation:

let x be the total amount of ice cream sold without tax

x + (x*0.0635)=21270

1.0635x=21270

x=20,000

so the amount he needs to send to state is

21270-20000

1,270

Total cost of icecream without cost be x

[tex]\\ \sf\longmapsto x+0.0635x=21270[/tex]

[tex]\\ \sf\longmapsto 1.0635x=21270[/tex]

[tex]\\ \sf\longmapsto x=21270/1.0635=20000[/tex]

Amount to be paid

[tex]\\ \sf\longmapsto 21270-20000=1270[/tex]

Answer:

Well lucy has a 50/50 chance to get a odd card so that is it

Step-by-step explanation:

The ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.

Let's denote the number of even cards as "x" and the number of odd cards as "y".

The probability of choosing an even card is given as [tex]\frac{3}{7}.[/tex]

The probability of choosing an even card is calculated by dividing the number of even cards by the total number of cards:

Probability of choosing an even card = Number of even cards / Total number of cards

Therefore, we have:

[tex]\frac{3}{7} = \frac{x}{x+y}[/tex]

To find the ratio of even cards to odd cards, we can set up the equation:

[tex]\frac{x}{y} = \frac{3}{4}[/tex]

Therefore, the ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.

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Answer:A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour.

Step-by-step explanation:

had this question

Answer:

Step-by-step explanation:

total # of families=15

families that own 0 cars=2

families that own 1 cars=5

families that own 2cars=4

families that own 3 cars=3

families that own 4 cars=1

so 2+5+4+3+1=15

total# of families/ sum of cars = 15/15=1

Answer:

C is my answer

You cam correct me if im wrong in the comments

Answer:

333

666

Step-by-step explanation:

333 / 9 = 37

666 / 9 = 74

yeah-ya...... right?

Answer:

333

Step-by-step explanation:

we see that all three digits are the same so heres a list of numbers it could be 222 333 444 555 666 777 and we know that numbers divisible by nine mean all the digits added up have to be divisible by nine and we can see that 333 equals 9 when the digits are added together so this is the answer.

Answer:

130542

Step-by-step explanation:

FV=48000(2.7196)

FV=130542

Answer:

12

Step-by-step explanation:

[tex]1/3(3)(12)[/tex]

The 1/3 and 3 cancel and you are left with

[tex]12[/tex]

Answer:

lines are perpendicular

Step-by-step explanation:

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines = - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the given equations into this form and extract the slope

3x - 2y = - 6 ( subtract 3x from both sides )

- 2y = - 3x - 6 ( divide through by - 2 )

y = [tex]\frac{3}{2}[/tex] x + 3 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

----------------------------------

4x + 6y = 2 ( subtract 4x from both sides )

6y = - 4x + 2 ( divide through by 6 )

y = - [tex]\frac{4}{6}[/tex] x + [tex]\frac{2}{6}[/tex] , that is

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

--------------------------------------

[tex]\frac{3}{2}[/tex] ≠ - [tex]\frac{2}{3}[/tex] , then lines are not parallel

[tex]\frac{3}{2}[/tex] × - [tex]\frac{2}{3}[/tex] = - 1

Thus the lines are perpendicular to each other

Answer:

Diagram B

Step-by-step explanation:

A line of best fit is a line drawn through a set of points that fits it best. You can see in diagrams A and C that the lines cross through or near most of the points. However, in diagram B, it crosses through 2 points, and misses quite a lot. Your answer is B :) hope this helped!

Answer:

First, we will change dissimilar fractions into similar fractions by finding the least common denominator. Second, add them like similar fractions. And then finally, convert the answer in the lowest term. Example No.6 Subtract 3/4 from 4/5. What will be our least common denominator? The least common multiple of 5 and 4 is 20. That was an Example

Step-by-step explanation:

Answer:

44 home runs

Step-by-step explanation:

550 ÷ 25

= 22

22 x 2

= 44

Answer:

i think its 16 but im not sure

Step-by-step explanation:

6+6+2+2= 16 but im not sure if that how u do it or not

it's been so long since i've done that stuff. 12 in i think

Answer:

A trust could protect them. Buying liability insurance or an umbrella policy will also help protect assets in case you get sued.

Step-by-step explanation:

Answer:

16.4% quick maths, ya dig?

Answer:

17/4

Step-by-step explanation:

add the fractions

Answer:

the 1 one

Step-by-step explanation:

Answer:

the answer is the first graph :)

Step-by-step explanation:

lmk if you need and explanation

hope this helps!❄︎

Answer:

6x + 13 = 12x - 20

Step-by-step explanation:

6x + 13 = 12x - 20

Answer: The cost of renting a car from Company A be the same as renting a car from company B in 17.5 miles

Step-by-step explanation:

y=2.30x +15

y=1.90x +22

0.4x +7 Divide 0.4 from both sides

x=17.5

y=2.30(17.5)+15

y=40.25+15

y=40.25-15

y=25.25

Answer:

New eq: 11x + 1. The line will become steeper.

Step-by-step explanation:

Slope is rise over run. In the original equation, y increased 4 times everytime x increased by one. In the new equation, y increased 11 times everytime x increased by one making it steeper.

Answer:

Perimeter: 4x+14

Step-by-step explanation:

The Formula for perimeter is P = 2L + 2W

So apply it:

L = x+7

W = x

[tex]P=2x+2\left(x+7\right)[/tex]

[tex]P=4x+14[/tex]

Answer:

2/3

Step-by-step explanation:

You go over 2 and down 3

Answer:

A ≈ 5.8 cm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 4.6 and h = 2.5 , then

A = [tex]\frac{1}{2}[/tex] × 4.6 × 2.5 = 2.3 × 2.5 ≈ 5.8 cm² ( to 1 dec. place )

Answer:

Step-by-step explanation: