The function, f(x), is plotted below.
Evaluate the following limits:
N
lim f(x)
-1
lim f(x) =
x -1
What is the value of the function at x = 1?
f(1) =

Recall the series expansion of the exponential function,

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

By comparison, the given sum is [tex]e^x[/tex] evaluated at x = ln(2), so

[tex]\displaystyle 1 + \ln(2) + \frac{\ln^2(2)}{2!} + \cdots = \sum_{n=0}^\infty \frac{\ln^n(2)}{n!} = e^{\ln(2)} = \boxed{2}[/tex]

Hello! :D

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ANSWER:

SOLUTION :

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Correct me if im wrong.

Answer:

252 cm is the anwer......

Answer:

(x-8)² + (y-5)² = 400

Step-by-step explanation:

general equation of a circle : (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

here we are given the center as well as a point on the circle

first we will need to identify the radius by  finding the distance between the center and the point on the circle using using the distance formula ( we know this is the radius because the radius is a line that goes on the center of the circle to any point on the circle )

Identifying the radius using the distance formula

Distance formula : [tex]d=\sqrt{(x_2-x1)^2+(y_2-y_1)^2}[/tex]

where the x and y values are derived from the two given points

Given points are (8,5) and (-4,21)

Assigning variables we get (x1,y1) = (8,5) , so x1 = 8 and y1 = 5

and (x2,y2) = (-4,21) so x2 = -4 and y2 = 21

Plugging this into the formula we get

[tex]d=\sqrt{(-4-8)^2+(21-5)^2}[/tex]

==> subtract values inside of parenthesis

[tex]d=\sqrt{(-12)^2+(16)^2}[/tex]

==> evaluate exponents

[tex]d = \sqrt{144+256}[/tex]

==> add 144 and 256

[tex]d=\sqrt{400}[/tex]

==> take the square root of 400

[tex]d=20[/tex]

so the radius is 400

Finding the equation of the circle

again we have the general equation of a circle as (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

here the center is at (8,5) and the radius is 20

so (h,k) = (8,5) so h = 8 and k = 5 and radius is 20 so r = 20

plugging these values into the general equation of a circle we get

(x-8)² + (y-5)² = 20²

==> evaluate exponent

(x-8)² + (y-5)² = 400

and we are done!

For more validation check the attached image :)

Answer:

a=79, b=101

Step-by-step explanation:

the consecutive angles are supplementary angles, and the opposite ones are congruent.

Answer:

Probably A?

Step-by-step explanation:

Answer:

5x+27 > -24

Don't forget the greater than or equal to sign, I just don't know how to type it. If you're not sure, it's the symbol I have typed above with a line underneath.

Hope this helps :)

Answer:

27 5/8

Step-by-step explanation:

12 5/8 + 2(7 1/2) = 12 5/8 + 15 = 27 5/8

The amount of space needed by John will be 27⁵/₈ inches.

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 John must mount a box which is 12⁵/₈ inches wide. He wants to leave 7¹/₂ inches on each side of the box.

The amount of space needed by John will be calculated as below:-

E = 12⁵/₈ + 2(7¹/₂)

E = 12⁵/₈ + 15

E = 27⁵/₈ Inches

Hence, the amount of space needed by John will be 27⁵/₈ inches.

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Answer:

# Points / Questions ❔

200

# Wrong ❌

54

# Correct ✔️

146

Percentage

73%

Grade

C

Step-by-step explanation:

Answer: 84%

Step-by-step explanation:

Teachers average out your grades. In order to average numbers, you add all the numbers and divide by the number of numbers you just averaged. If you add 200 to 54 you get 254. 254 divided by 3 is 84. You will probably get higher then a 84 if those two 100's are majors but you should get around a 84% overall grade!

Answer:

x = 18

Step-by-step explanation:

the square on the angle means the angle is 90 degrees

4x + x = 90

5x = 90

x = 18

Answer:

[tex]\boxed{\bf x = 1 {8}^{o} }[/tex]

Step-by-step explanation:

In the given figure....

[tex]\boxed{\bf m\angle BOA = 9 {0}^{o}} [/tex]

[tex]\bf m\angle BOA + m\angle COA = 9 {0}^{o} [/tex]

Combine like terms. 4x + x = 5x

Divide both sides by 5.

The probability that the next person will purchase no costume is 7/166 if the 7 visitors purchased no costume.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Total number of visitors = 7+143+16 = 166

Number of visitors purchased no costume = 7

The probability that the next person will purchase no costume:

= 7/166

Thus, the probability that the next person will purchase no costume is 7/166 if the 7 visitors purchased no costume.

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C. Two-thirds vote

To help with checks and balances, the consitution allows congress to override a presidential veto with a two-thirds vote; also known as a constitutional majority.

Intial Vote

When Congress first votes on a normal bill (not a consitutional change) all that is required is a simple majority. A simple majority means more than 50 percent.

Presidential Veto

Just because something is passed by Congress does not mean that it will be a law. The President still has to sign the bill into law. However, the President has the option to veto the bill.

Overriding a Veto

If a bill is overridden, Congress can move to override the veto. If they want to override the veto, there must be a 2/3's majority that agrees to pass the bill again.

Additionally, when overriding a veto any votes that are not affirmative, this includes abstentions and absent voters, are considered opposing votes. For example, if 2 congressmen did not show up to vote, then their votes would automatically be counted against the bill.

Answer:

2.5

Step-by-step explanation:

Radius is half way of the Diameter. so all you have to do is divde half.

Answer:

ex:  25+25 (square numbers) = 50 (not a perfect square)

Step-by-step explanation:

all in the example

Answer:

4/8

Step-by-step explanation:

Considering the situation described above, what would be the present value of this loan is $1,000.

This is explained below:

Given that the loan interest rate is $85 85/1000 = 8.5

Then the market interest rate is => 8.5 percent

Therefore, given that there is no difference between the market rate and the loan rate, then the loan is expected to be sold at $1,000 which is the face value of the loan.

To prove it, we have the following:

PV of the annuity of $85 during 8 years at an 8.5% market rate

C => 85

Time => 8

Rate => 0.085

C × { [1 - ( 1+ r ) ] ^-time } ÷ rate = PV

85 × [1 - (1 + 0.085)^-8] ÷ 0.085 = PV

PV =. $479.3306

Present value of the maturity date:

Maturity 1000

Time => 8

Rate => 0.085

Maturity ÷ (1+rate)^rate = PV

1000 ÷ (1+0.085)^8 = PV

PV => $520.6694

Therefore, the Total present value

=> PV c $479.3306 + PV m $520.6694

=> Total $1,000.

Hence, in this case, it is concluded that the correct answer is $1,000.

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Answer:

below

Step-by-step explanation:

Mathematically there cant be 150 student though since 85 + 70 = 155  

Answer:

3x+6

x+x+2+x+4

» You can group the like terms, in this case, the x's and the numbers.

x+x+x+2+4

3x+6

Answer:

A,C,E

Step-by-step explanation:

All three use double negative signs which cancel out into a plus sign. Moving the parentheses doesn’t change the value in these problems.

Answer:

<-8,-12,-9>

Step-by-step explanation:

got it right on edge

Using the permutation formula and the combination formula, it is found that:

a) There are 24,024 ways to appoint the officers.

b) There are 1,001 ways to appoint the committee members.

c) [tex]p = \frac{1}{1001}[/tex] probability that the four youngest members are appointed to the committee.

The number of possible permutations of x elements from a set of n elements is given by:

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

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

Item a:

For the officers, the order is important, as there are different roles, and 4 officers will be appointed from a set of 14 qualified candidates, hence we use the permutation formula to find the number of ways they can be appointed.

[tex]P_{14,4} = \frac{14!}{10!} = 24024[/tex]

Item b:

For the committee, the order is not important, as there are no different roles, and 4 members will be appointed from a set of the 10 remaining candidates, hence we use the combination formula to find the number of ways they can be appointed.

[tex]C_{14,4} = \frac{14!}{4!10!} = 1001[/tex]

Item c:

The four youngest is only one possible outcome, hence the probability they are appointed to the committee is given by:

[tex]p = \frac{1}{1001}[/tex]

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C) without an external energy source, fiction stops the car

Sure hope this helps you

Answer:

C

Step-by-step explanation:

The friction stops the car because there is no more energy pushing the car forward. Also this should be in the science section.

The distance traveled by the ray will be 26 inches. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

In a science experiment, a student concluded that a ray has to travel a distance from one corner at the top of the rectangular prism to the opposite side where the surface touching the floor is intersected.

If the length, width, and height of the prism are given as 24 inches and 8 inches, 6 inches respectively.

Then the distance traveled by the ray will be

We know the formula

D² = L² + W² + H²

We have

L = 24 in

W = 6 in

H = 8 in

Then the distance will be

D² = 24² + 6² + 8²

D² = 576 + 36 + 64

D² = 676

D = 26 in

Thus, the correct option is B.

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Answer:

135.5

Step-by-step explanation:

F(2) means the value of x is 2. Replace x with 2 then solve for b:

3(2) + b = 12

6 + b = 12

Subtract 6 from both sides

B = 6

answer: b = 6

Answer:

I will guess C because a matrix can only have 3 pivot positions.

[tex]\text{Given that,}~f(x) = 3x^2 -15~~ \text{and}~~ g(x) = 1- \dfrac 23 x\\\\(f \circ g)(-6)\\\\=f(g(-6))\\\\=f\left(1- \dfrac 23\cdot (-6)\right)\\ \\=f(1+4)\\\\=f(5)\\\\=3(5)^2 -15\\\\=75 -15\\\\=60\\\\\text{Hence the answer is B.}[/tex]

Since ∠A and ∠B forms a straight line, ∠A and ∠B are a linear pair.

Linear pair:

A linear pair is the sum of two angles that forms a straight line (180°).

⇒ ∠A + ∠B = 180°

Measure of ∠A:

Subtract the measure of ∠B from 180 to determine the measure of ∠A.

⇒ ∠A = 180 - ∠B

Measure of ∠B:

Subtract the measure of ∠A from 180 to determine the measure of ∠B.

⇒ ∠B = 180 - ∠A

*Let us take a few examples to understand the concept better.

Let the measure of ∠B (In the triangle shown) be 105°.

What is the measure of ∠A?

Solution:

Substitute the measure of ∠B in the equation ∠A = 180 - ∠B:

Simplify the equation:

Therefore, the measure of ∠A is 75°.

Let the measure of ∠A (In the triangle shown) be 60°.

What is the measure of ∠B?

Solution:

Substitute the measure of ∠A in the equation ∠B = 180 - ∠A:

Simplify the equation:

Therefore, the measure of ∠B is 120°.

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Answer:

Sin(45) = [tex]\frac{\sqrt{2} }{2}[/tex] , therefore Letter E is the answer ..

Step-by-step explanation:

Sin(45) = [tex]\frac{\sqrt{2} }{2}[/tex] , therefore Letter E is the answer ..

Answer:

take sin 45

Step-by-step explanation:

A graph is a way to represent a lot of data in such a visual format. The graph for the given situation can be drawn as shown below.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The graph for the given situation can be drawn as shown below.

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The slant height of the cone is = 15.6m. To calculate the slant height is further described below.

The radius of the cone is = 6m

The volume of the cone = 542.87m³

The height of the cone can be determined using the formula below;

V=πr²h/3

542.87 = 22/7×6²×h/3

542.87= 3.14×36×h/3

542.87= 113.04× h/3

Make h the subject of formula,

h = 542.87×3/113.04

h = 1628.61/113.04

h= 14.4m

Therefore the slant height ,

l=√r²+h²

l = √6²+14.4²

l= √36+207.36

l=√243.36

l= 15.6m

Therefore, the slant height of the cone is = 15.6m.

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