Find the largest integer not greater than the following expression :
[tex]\displaystyle \large \boldsymbol{} \frac{2150}{2005} +\frac{2150}{2006} +\frac{2150}{2007 } + ...+\frac{2150}{2020}[/tex]

Answers

Answer 1

Answer:

17

Step-by-step explanation:

The number of terms:

2020 - 2004 = 16

Each term is greater than 1, so the expression is greater than 16:

2150/2005 = 1 + 145/20052150/2006 = 1 + 144/2006...2150/2020 = 1 + 130/2020

It's easy to note each of the numbers getting smaller like 145/2005 > 144/2006 etc. Taking the smallest fraction.

The sum is:

S > 16 + 16*130/2020 = 16 + 2080/2020 > 16 + 1 = 17

So the largest integer not greater than S is 17.


Related Questions

Find the median of :- 25, 37, 27, 38, 29, 20, 39​

Answers

Answer: The median is 29

Step-by-step explanation:

I started by arranging the data points from smallest to largest to get 20, 25, 27, 29, 37, 38, 39. Then I found the middle number in the data set and got 29.

Answer:

Median: 29

Step-by-step explanation:

Median: middle number

•••••••••••••••••••••••••••••••

Sort the numbers from least to greatest

20, 25, 27, 29, 37, 38, 39

Then calculate the median

The median would be 29

7. If the supplement of an angle is 69, then find its complement.​

Answers

Answer:

no solution

Step-by-step explanation:

Supplementary angles add to 180

Let x be the supplement

x+69 = 180

x = 180-69

x =111

The complement of an angle means they add to 90

111+y = 90

y = 90-111

y =-21

But an angle cannot be negative so there is no solution

Answer:

21 degrees.

Step-by-step explanation:

To find the complementary angle you have to subtract the given angle from 90.

so,

90 - 69 = 21.

Extra info: if you need to find the supplementary angle you need to subtract the given angle from 180.

Integrate the following.[tex]\int\limits^a_b {sin(x)} \, dx[/tex]

Answers

Answer: -cos(a)+cos(b)

Step-by-step explanation:

To integrate is the same as saying to find the antiderivative.

[tex]\int\limits^a_b {sin(x)} \, dx[/tex]         [antiderivative of sinx is -cosx]

[tex]-cos(x)|_b^a[/tex]           [include boundaries]

[tex]-cos(a)+cos(b)[/tex]

Therefore, the integral would be -cos(a)+cos(b).

What is the vertex of the function f(x) = -|x + 7| − 4?

A.
(-7,-4)
B.
(7,4)
C.
(-7,4)
D.
(7,-4)

Answers

Answer:

it would be

D.

(7,-4)

Mark me as brainliest pleases

Answer:

it would be A (-7,-4)

Step-by-step explanation:

Which expression is equivalent to

Answers

Answer:

[tex]\frac{(x+2)}{(x-1)}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + x -2}{x^2 -2x+1}[/tex] =

[tex]\frac{(x+2)(x-1)}{(x-2)(x-1)}[/tex] =

[tex]\frac{(x+2)}{(x-1)}[/tex]

What is the exponential form of log3 2187 = 7?

Answers

Answer:

2187 = [tex]3^{7}[/tex]

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex] , then

[tex]log_{3}[/tex] 2187 = 7

2187 = [tex]3^{7}[/tex]

Answer:

3 ^7 = 2187

Step-by-step explanation:

log3 2187 = 7

log a (b) = c

a^c = b

3 ^7 = 2187

Solve the system of equations using substitution.
y = x + 6
y = –2x – 3

Answers

Answer:

x = -3

y= 3

Step-by-step explanation:

y =  x + 6 -----------------------(I)

y = -2x - 3 ---------------------(II)

Substitute y =x +6 in equation (II)

x + 6  = -2x - 3

Add 2x to both sides

x + 2x +6 = -3

Combine like terms

3x + 6 = - 3

Subtract 6 from both sides

3x = - 3 - 6

3x = -9

Divide both sides by 3

x = -9/3

x = -3

Plug in s = -3 in equation (I)

y = -3 + 6

y = 3

hope this helps! feel free to clarify

(06.04 MC) Dennis drew the line of best fit on the scatter plot shown below: What is the approximate equation of this line of best fit in slope-intercept form?

Answers

Answer:

Step-by-step explanation:

In order to write the equation of this line, we need to pick 2 points on the graph where the line goes right through the intersection of the grids. Actually, you only need 1 of these, because the line goes through at (0, 15). Another point then can be (6, 6). Locate this point so you know what I means when I say that the line goes right through where the grids intersect at x = 6 and y = 6 (as opposed to somewhere in the middle of one of these grids). Find the slope between these 2 points:

[tex]m=\frac{6-15}{6-0}=-\frac{9}{6}=-\frac{3}{2}[/tex]

Since there's only one choice with that slope, that is the choice you want.

Please Solve:
x^2-4x-5=0

Answers

The quadratic equation answer is: x^1 = -1; x^2=5 and the number of solutions are 2 real solutions. Hope this helps :)

would appreciate the help please!

Answers

Answer:

I think SAS is the correct Ans

find the scale factor

Answers

Answer:

I think its 1.4

Step-by-step explanation:

if you divide 42 by 1.4 it makes 30 and if u multiply 30 by 1.4 it makes 42

Answer:

the scale factor is 7/5

Step-by-step explanation:

42/30=

42/30=

then you find a common factor between the two is 6, so you divide both sides of the fraction by 6 to get 7/5. and because they both are the same you know that they both have the same scale factor. Which is 7/5. I am not quite sure if you need to find the missing side length but in case you do multiply 40 by 7/5 so it looks like 40/1 x 7/5. 40 x 7 = 280. 280/5 = 56. so your side length is 56.

Omg who can help me? Its due tomorrow

Answers

I could help ! But the light kinda makes some of the words hard to read

{(5,2), (-2,4), (2, -7)}

Domain:

Range:

Answers

Answer:

Step-by-step explanation:

The domain are all the x values in order, no repeats allowed:

D = {-2, 2, 5}

Same thing for the range, except these are the y values:

R = {-7, 2, 4}

The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.

Answer:

Domain : {-2,2,5}

Range:{ -7,2,4}

Step-by-step explanation:

The domain is the inputs

Domain : {-2,2,5}

The range is the outputs

Range:{ -7,2,4}

its given that s=n(a+c)/2


Express c in terms of s, n and a ​

Answers

This is the step by step solutions, hope u understand

A particular strain of bacteria triples in population every 45 minutes Assuming you start with 50 bacteria in a Petri dish how many bacteria will there be in 4.5 hours

Answers

Answer:

4.5 hours in minutes = 270

Every 45 minutes, bacteria triples

You start with 50

Divide 270 (total time) by 45 (every time bacteria triples)

270/45 = 6

36,450 bacteria

Solve the equation 5x + 2(2x -23) = -154

Answers

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

5x+2(2x-23)=-154

5x+4x-46=-154

9x-46=-154

9x=-154+46

9x=-108

x=[tex]\sf{\dfrac{-108}{9} }[/tex]

x=-12

Answer:

x = -12

Step-by-step explanation:

5x + 2(2x - 23) = -154

Distribute;

5x + 4x - 46 = -154

Collect like terms

9x - 46 = -154

Add 46 to both sides;

9x = -108

Divide both sides by 9

x = -12

Which of the following is the number of sides for a regular polygon that will
not form a regular tessellation?

A. 6
B. 4
C. 7
D. 3

Answers

Answer:

A

Step-by-step explanation:

A

The number of sides for a regular polygon that will not form a regular tessellation is 7. The correct option is C.

What is a polygon?

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

A tessellation or tiling is the seamless covering of a surface, frequently a plane, with one or more geometric shapes, known as tiles. One regular polygon can be used to create a single regular tessellation. Two or more regular polygons are used in a semi-regular tessellation.

Triangles, squares, and hexagons are the only three regular tessellations.

Now, the name of the polygon having 3, 4, and 6 sides is triangle, square, and Hexagon. Therefore, the only regular polygon that will not form a regular tessellation is heptagon, which has 7 sides.

Hence, the number of sides for a regular polygon that will not form a regular tessellation is 7.

Learn more about Polygon here:

https://brainly.com/question/10441863

#SPJ2

THIS QS with explanation sum

Answers

Answer:

X = 276°

Step-by-step explanation:

Divide X into x1 and x2

then then using the trick of co-interior angles, find the answer of x1 and x2 . then add x1 and x2

Please help 50 points! ​

Answers

d=10

Answer:

Solution given:

[tex]\sqrt{25+3x}=d+2x[/tex]

squaring both side

25+3x=(d+2x)²

when x=-3

25+3*-3=(d+2*-3)²

25-9=(d-6)²

16=(d-6)²

[tex]\sqrt{16}=d-6[/tex]

4=d-6

d=4-6

d=10

Answer:

d = 6

Step-by-step explanation:

[tex] \sqrt{25 + 3( - 3)} = d + 2( - 3) \\ 4 = d - 6 \\ d = 10[/tex]

hopefully this makes sense

:)

Please help me with this (geometry)

Answers

Answer:

∠ 6 = 55°

Step-by-step explanation:

∠ 6 and 125° are same- side interior angles and sum to 180° , then

∠ 6 = 180° - 125° = 55°

Instructions: Find the measure of the indicated angle to the nearest degree.
29 and 17

Answers

Answer:

30º

Step-by-step explanation:

because it is a right triangle, we can use trig functions to solve

tan^{-1}=17/29=30.379

When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?

5x + 2 – 3x2

Answers

Answer:

leading coefficient -3

constant 2

Step-by-step explanation:

Standard from is from largest power to smallest power

-3x^2 +5x +2

The leading coefficient is the number in front of the largest power of x

-3

The constant is the number without a power of x ( or x^0)

2

Nick works part-time at a bookstore. His pay varies directly with the number of hours worked. In one week, he earned $120 for 8 hours of work.

a) Define two variables for this relation.



b) Describe the rate of change in words.


c) Determine an equation to represent the relation:


d) Use the equation to determine how many hours Nick must work to earn $345

Answers

Answer:

23 hoiurs

Step-by-step explanation:

Given data

a. The two variables are

1. Number of hours worked

2. The amount earned

b. The rate is given as

=120/8

=$15 per hour

c. The equation is given as

rate=Amount earned/ number of hours worked

15= 345/hours

make hours subject of the formula we have

hours= 345/15

hours= 23 hours

Hence he must work for 23 hours

If f(x)f(x) is an exponential function where f(1.5)=5f(1.5)=5 and f(7.5)=79f(7.5)=79, then find the value of f(3)f(3), to the nearest hundredth.

Answers

Answer: [tex]7.93[/tex]

Step-by-step explanation:

Given

[tex]f(x)[/tex] is an exponential function. Suppose [tex]f(x)[/tex] is [tex]ae^{bx}[/tex]

[tex]f(1.5)=5\ \text{and}\ f(7.5)=79[/tex]

[tex]\Rightarrow 5=ae^{1.5b}\\\Rightarrow \ln 5=\ln a-1.5b\quad \ldots(i)[/tex]

Similarly,

[tex]\Rightarrow 79=ae^{7.5b}\\\Rightarrow \ln(79)=\ln a+7.5b\quad \ldots(ii)[/tex]

Subtract (i) and (ii)

[tex]\Rightarrow \ln (79)-\ln (5)=9b\\\Rightarrow \ln (\frac{79}{5})=9b\\\\\Rightarrow b=\dfrac{\ln (\frac{79}{5})}{9}\\\\\Rightarrow b=0.3066[/tex]

Insert the value of [tex]b[/tex]

[tex]\Rightarrow 5=ae^{0.46}\\\Rightarrow a=5\times 0.6312\\\Rightarrow a=3.156\approx 3.16[/tex]

So, the function becomes

[tex]\Rightarrow f(x)=3.16e^{0.3066b}[/tex]

[tex]\Rightarrow f(3)=3.16e^{0.3066\times 3}\\\Rightarrow f(3)=7.927\approx 7.93[/tex]

Answer:

7.93

General Exponential Form: y=ab^x

Plug in both points

divide the equations

cancel out a, subtract exponent of b

Will it matter if I don’t get accelerated pre algebra in 7th grade and get into normal pre algebra? Will it make me less likely to get into top colleges?

Answers

Answer:

Maybe, there is a chance, but I don't know for sure.

It might matter, but I wouldn't worry or stress about it too much.

My only advice to you is do not procrastinate and if you need help don't be afraid to ask.

Answer:

It matters but not like you think.

GPA, extracurricular activities, and SAT/ACT are the biggies. Truthfully it won't change a thing if you took accelerated pre-algebra versus normal. In fact, spoiler alert, the SAT/ACT (I'm assuming your american) will matter more than your courses ever did. I took two years of college physics in highschool and i made more off my SAT. Not only that, but an A in an easy class looks better than a C in a hard one on transcripts.

My advise is slow down, relax, and learn it well. Better to learn the concept fully in normal so that you can apply it, than half learn it in advance and struggle in future applications. After all, math ALWAYS builds. Take it slow, take it easy.

I would recommend talking to a school guidance counselor about your academic stress. Im sure their professional insight will help put you at ease. It may also help to get you going in the right direction so that you achieve your goals.

Good luck. Enjoy life

How do you solve this step-by-step?

Answers

Answer:

7 1/20

OAmalOHopeO

Make six prime numbers using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 once each.


~can you plz explain?!

Answers

Answer:

2, 3, 5, 7, 11, 13.

Step-by-step explanation:

A prime number is a number that you don't get a whole number when divided by 2 but you do get a whole number when divided by prime numbers such as 3,5,7,11... Basically a number with two factors, it can only be divided by 1 or themselves. for example:

9/2 = 4.5 (this is not a whole number so it might be a prime.

9/3 = 3 (it works when divided by a prime number.

another:

8/2 = 4 (it gives a whole number when divided by 2 therefor, it can't be a prime number.

Answering:

There are 6 prime numbers at the top^^^^.

One possible answer is  2, 3, 5, 41, 67, 89

Another possible answer is  2, 3, 5, 47, 61, 89

Other answers may be possible.

=============================================================

Explanation:

This is a trial and error type of problem. Though with practice it's not as blind of randomly guessing.

We have 9 values here. If we paired them up, then we can form at most 4 pairs (since 9/2 = 4.5 rounds down to 4). That means we won't be able to form six two-digit primes. Some of the primes must be single digits.

We can have 3 single digit primes and 3 two-digit primes since 3+2*3 = 9.

The single digit primes are: 2, 3, 5, 7

Let's say 2 and 5 are definitely locked down to be the single digit group. I'm doing this since we can't have 2 or 5 as the units digit. If the units digit is 2, then 2 is a factor and it's not prime. Similarly, if 5 is the units digit, then 5 is a factor and that two digit value is not prime.

For good measure, we'll throw 3 in there as well and see what happens.

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

The digits we have left are: 1, 4, 6, 7, 8, 9

The number 14 isn't prime, but 41 is prime

67 is prime so that's another two values off the list

lastly, 89 is prime so that works as well.

So one possible sequence is 2, 3, 5, 41, 67, 89

Notice how we can swap the 1 and 7 to go from 41,67 to 47,61; this gets us two other primes. So another possible answer is 2, 3, 5, 47, 61, 89

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

Side note: having the list of primes on a reference sheet is a handy recommendation. You only need to go up as high as 97 which is the largest two digit prime.

For each relation, decide whether or not it is a function.

Answers

Answer:

Step-by-step explanation:

Relation 1 is a function

Relation 2 is not a function

Relation 3 is a function

Realation 4 is not a function

at a post office always charges a flat one-time fee for any order. One time, Michael sent 35 letters and paid 26 dollars. The next time, he send 18 letters and paid $14.10. How much does the post office charge to send one letter? What is the flat fee?

Answers

Answer:

The post office charges $0.7cents to send one letter, and the fee is $1.5

Step-by-step explanation:

simplify m√p + n√p - √p

Answers

Answer:

[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]

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