Question 10: If the product of all the numbers from 1 to 100 is divisible by 2^n, then what is the maximum possible value for n: A. 128; B. 87; C. 64; D. 97; E. 70.

Answers

Answer 1

Answer: D

Step-by-step explanation:

100!=2*3*4*...*100

Counting which numbers are divisible by 2:

2,4,6,8,10,12,14,...,96,98,100 : 50 numbers (100/2=50)

Counting which numbers are divisible by 4=2²:

4,8,12,16,20,...96,100: 25 numbers (100/4=25)

Counting which numbers are divisible by 8=2³:

8,16,24,32,40,...,96: 12 numbers (100/8=12.5 ==> 12)

Counting which numbers are divisible by 16=2⁴:

16,32,48,...,96: 6 numbers (100/16=6.25 ==> 6)

Counting which numbers are divisible by 32=2⁵:

32,64,96 : 3 numbers(100/32=3.125 ==>3)

Counting which numbers are divisible by 64=2⁶:

64 : 1 number (100/64=1.5625 ==>1)

Sum of those numbers= 50+25+12+6+3+1=97

100! is divisible by 2⁹⁷.

Answer D

Answer 2
There are 50 even numbers - divisible by 2
There are 25 multiples of 4
There are 12 multiples of 8
There are 6 multiples of 16
There are 3 multiples of 32
There is one multiple of 64
Each of these is also counted in the line above

So the unique multiples are (1 x 64) x (2 x 32) x (3 x 16) x (6 x 8) x (13 x 4) x (25 x 2)
= (1 x 2^6) x (2 x 2^5) x (3 x 2^4) x (6 x 2^3) x (13 x 2^2) x (25 x 2^1)
So n = 6 + 10 + 12 + 18 + 26 + 25 = 97

The slow (but easier way) to see this is to write down all the even numbers in factors of 2 and count the number of 2S
Eg 2, 2x2, 2x3, 2x2x2, 2x5, 2x2x3, 2x7, 2x2x2x2, 2x9, 2x2x5, 2x11, 2x2x2x3, 2x13, 2x2x7, 2x15 etc
(This only got to 30 but you should get the idea - there are 26 twos up to there)

This is a tough question to explain simply

Related Questions

Including a 7% sales tax, an inn charges $125.19 per night. Find the inn's nightly cost before tax is added.

Answers

The inn's nightly cost before tax is added is $23.54

Taxes are prices added on top of goods and services

Let the normal price be x

Price including tax = x + 0.07x (note that the tax iss 7%)

Given that Price including tax = $125.19, then;

$125.19 = x + 0.07x

Find the value of x

125.19 = 1.07x

Swap

1.07x = 125.19

x = 125.19/1.07

x = $23.54

This shows that the inn's nightly cost before tax is added is $23.54

Learn more here: https://brainly.com/question/14889413

what is the answer for this Evaluate 3|-3|.

Answers

Answer: 9

Concept:

Here, we need to know the idea of absolute value.

The absolute value of a number or integer is the actual distance of the integer from zero, in a number line.

There are no negatives in absolute value. So in practice "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive.

Solve:

Given

3 |-3|

Expand absolute value sign, which means making [-3] positive

= 3 × (3)

Simplify by multiplication

= [tex]\boxed{9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

3|-3| = 9

Because absolute value sign |-3|
That mean 3
3*3 = 9
So answer is 9

List three different properties of a square

Answers

Answer:

All four sides of a square are equal in length, all interior angles of a square are right angles, all sides are parallel to an opposite side

Step-by-step explanation:

These are just 3 simple properties of many properties of a square. Obviously, a square is a quidrilateral that has four equal sides. Therefore, it makes all interior angles of the shape the same. And it is also a parallelogra, meaning that opposite sides are parralell to one another.

can someone help me plz

Answers

Answer:

The length is from -5 to +7, so the length answer is 12, The midpoint would be that divided by 2, so six.

Step-by-step explanation:

Answer:

Length = 12

Midpoint = 1

Step-by-step explanation:

to find the length u cancount from left to right of the segment and u can see that it is 12 units long. To find the mid point just take half of the the length, which is 6, and count that many units from either side of the segment. you'll stop at 1 do that is the mid point of the graph.

Use the domain and range of each of the following relations to determine which is a function. a. {(7,5), (-6,0), (2,3)} b. {(7,5), (-6,0), (-6,-2), (2,3)} c. {7,-6,2,-7} d. {(7,5), (-6,0), (7,3)}

plz hurry its timed

Answers

Answer:

A.  {(7,5), (-6,0), (2,3)}

Step-by-step explanation:

All of the x values do NOT repeat

I hope this helps!

pls ❤ and mark brainliest pls!

Three men build a wall in 10 days. How long will it take five men

Answers

Answer:

Step-by-step explanation:

By proportion it takes

3/5 * 10

= 6 days.

Grant has 12 roses, 15 tulips and 20 azaleas. Grant wants to use all of his flowers to create bouquets that are identical to each other. If Grant creates the maximum number of bouquets possible, how many of each flower will be in each bouquet? *

Answers

Answer:

5

Step-by-step explanation:

Can someone give me the answer and also explain it to me on how you got it so I can understand?

Question 26.

Answers

Answer:

150

Step-by-step explanation:

1km is 1000m

0.15km=0.15*1000 =150m

Using static equilibrium calculations, calculate the length from the fulcrum to the
resistance force.

Answers

Answer:

kdfbfnfffjjjjjjjjjjskslosksndbdd

PLS HELP WILL MAKE FIRST RIGHT ANSWER GETS BRAINLIEST ​

Answers

Answer:

B

Step-by-step explanation:

A line with a positive slope is indicated by

The line sloping up from left to right

This is shown in graph B

plz help me i need help
part A inputs: 7 8 9 10 11 outputs: 8 9 10 11 12






What is the rate of change of the equation from Part A?


Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different?




Is the relation in your data a function? Why or why not? Could the equation in the input and outputs represent a function? Why or why not? Explain your answer.

Answers

Answer:

inputs:outputs

7:8

output is equal to input plus one

Step-by-step explanation:

award brainliest

does anyone understand this? i need help

Answers

Answer:

[tex]81^{1/4}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{81} = 81^{1/4}[/tex]

a square root can be equivalently written as a fractional exponent. All the other options can be ruled out as they are simply incorrect.

-5^2(3)-4(-6)
ILL GIVE YOU POINTS JUST SOLVE

Answers

the answer to this is -51

Answer:

The answer foe the problem is -51

What is the shape of the distribution shown below?
Choose 1 answer:
The distribution is symmetrical.
B
The distribution is not symmetrical.
Age of each intramural volleyball participant
PLEASE HELP❌❌❌

Answers

Answer:

B. The distribution is not symmetrical.

Step-by-step explanation:

In order for the distribution to be symmetrical, the median line (line in the box) should be in the center. This box plot is more positvely skewed.

The answer for the question is b

bantu jawab ya guy's ​

Answers

Hey, i dont know what bantu jawab ya guys mean

reduction:
6 + 7x - 4x - 2x - 4

-3 + 2x +5 - 8x

x + 3x - 7 - 6x - 3

Answers

Answer:

1: x + 2

2: -6x + 2

3: -2x - 10

Your deposit $2513.45 into a savings account. The interest on the account is
compounded annually at 4.35%. How much will be in the account after 3 years?
CORRECT ANSWER GETS MARKED AS BRAINLYEST

Answers

Answer:

£2,855.93

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

1. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that δABD ≌ ΔBAC.

Answers

Step-by-step explanation:

ABCD is a quadrilateral triangle,where AD=BC and <DAB =<CBA.

In ∆ABD and ∆BAC

•AD=BC. (given)

•<DAB=<CBA (given)

•AB=BA. (common side)

Therefore, ∆ABD ≌ ΔBAC. {SAS congruence rule}

the shopkeeper sold a camera for 2570 and made a loss of rs180 at what price did he/she purchasr the camera​

Answers

purchase they sold it for: $2570

loss= $180

They purchased it for= loss + selling cost

=2570+180

=$2750


A segment has endpoints R(3. 8) and S(15,8). What are the coordinates of the midpoint M of the segment?

Answers

Answer:

(9, 8)

3 + 6

9 + 6

15

8 + 0

8 + 0

8

What is the like terms on this equation

3+5–2x–54-7

Answers

Answer:

3, 5, -54, and -7 are like terms while -2x stays alone.

Step-by-step explanation:

3+5-2x-54-7=0

3+5-2x-61=0

5-2x=61-3

5-2x=59

-2x=59-5

-2x=54

(-x)=54/2

(-x)=27

x=-27

ALGEBRA II! i need help with #2 with the same steps i took on #1

Answers

there you go!!!!!!!!!!!!:o

please help me with this math is for my homework​

Answers

Answer:

3 9/40 is the answer The decimal form of that is 3.225

Step-by-step explanation:

Explanation is on image, using calculator.

Answer:

it is 3 9/40 or 129/40

Step-by-step explanation:

hope that helps

Simplify:
mathematics​

Answers

[tex]\\ \rm\longmapsto \sqrt{x^2\sqrt{x^2\sqrt{x^2}}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^2\sqrt{x^2\times x^{2\times \dfrac{1}{2}}}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^2\sqrt{x^2x}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^2\sqrt{x^3}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^2\times x^{3\times \dfrac{1}{2}}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^2\times x^{\dfrac{3}{2}}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^{2+\dfrac{3}{2}}}[/tex]

[tex]\\ \rm\longmapsto \sqrt{x^\dfrac{7}{2}}[/tex]

[tex]\\ \rm\longmapsto x^{\dfrac{7}{2}\times\dfrac{1}{2}}[/tex]

[tex]\\ \rm\longmapsto x^{\dfrac{7}{4}}[/tex]

(HELP ASAP PLEASEE!!)
How much interest would u pay on a $930 loan at 6% simple interest rate at the end of 18 months

Answers

Answer:

18month=1.5 year

Interest = 0.06*930*1.5=$83.7

write each fraction number as a decimal write each fraction number as a decimal -7 8/45

Answers

[tex]\\ \sf\longmapsto -7\dfrac{8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{45(-7)+8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{315+8}{45}[/tex]

[tex]\\ \sf\longmapsto \dfrac{323}{45}[/tex]

[tex]\\ \sf\longmapsto 7.1[/tex]

find EF given E (-7, -2) and B (11, 3)
how do i solve this?

Answers

Answer:

EF ≈ 18.68

Step-by-step explanation:

Based on the info I am given I believe they are asking for the distance between E and F (i think you wrote B by mistake). (d = distance)

d =√ (x2 - x1)² + (y2 - y1)²   -->   (this is the distance formula)

d =√ (11 - (-7))² + (3 - (-2))²

d =√ (18)² + (5)²

d =√ 324 + 25

d =√ 349

d ≈ 18.68

answer needed asap :)))

Answers

Answer:

Even

Step-by-step explanation:

let A= 2 and B= 5(A + 2) (B + 3) = even number(2 + 2) (5 + 3) = ?4 × 8 = 32 32 is an even number2AB 2 (2) (5) = 2020 is an even number.I therefore conclude that 2AB is even.

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

−9+x ≤ 4
what is x

(so it passes:iuyhtgfghuytg)

Answers

Answer:

[tex]x \leqslant 13[/tex]

Step-by-step explanation:

[tex] - 9 + x \leqslant 4 \\ x \leqslant 4 + 9 \\ x \leqslant 13[/tex]

Hello!

For this type of problem, treat the “less than or equal to” sign as an equal sign!

So, -9+x=4

Now, it is as simple as solving for “x” just like a regular algebra problem. Add 9 to both sides to get “x” by itself:

-9+x+9=4+9

Now you have:

X= 13

Plug the “less than or equal to” sign back into the equation:

X ≤ 13

PLS HELP ME ITS URGENT

Answers

The answer is 72 because you have to add all sides including the ones you don’t know

Step-by-step explanation:

find the area of each square or rectangle

l*w

4 rectangles=4×(3×6)=72

2 squares=2×(3×3)=18

72+18=90cm^2

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