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+11

0

Hello,

To form an odd 4-digit number using 1, 2, 3, and 4, the units digit must be 1 or 3.

Case 1: The units digit is 1. We have 3 choices for the thousands digit (2, 3, or 4) and 2 choices for the hundreds digit (the remaining digits after the thousands digit and the units digit have been chosen). After the thousands and hundreds digits have been chosen, there is only 1 choice for the tens digit. Therefore, there are 3×2×1 = 6 ways to form an odd 4-digit number with 1 as the units digit.

Case 2: The units digit is 3. We have 3 choices for the thousands digit (2, 3, or 4) and 2 choices for the hundreds digit. After the thousands and hundreds digits have been chosen, there is only 1 choice for the tens digit. Therefore, there are 3×2×1 = 6 ways to form an odd 4-digit number with 3 as the units digit.

In total, there are 6+6=12 distinct odd 4-digit numbers that can be formed using the digits 1, 2, 3, and 4 if no digit may be used more than once. Nexusiceland.co.uk

wisdom321Mar 30, 2023

#1

+37193

+1

Parabola with vertex at 2, 22

Find her initial vertical speed (she only goes up 2 feet against gravity)

vf = 0 = v0 + at a = - 32.2 ft/s^2

0 = vo - 32.1 t shows vo = 32.1 t

then d = do + vo t - 16.1 t^2 <===== Use this to find 't'

22 = 20 + (32.1 t) ^t - 16.1 t^2

2 = 16.1 t^2

t = .3525 seconds her horizontal speed is then 2 ft / .3525 s = 5.675 f/s and vertical speed is 32.1 * .3525 = 11.31 f/s

Find a point on the parabola

at t = 1 sec x = 5.675 ft and y = d = do + vo t + 1/2 at^2 = 20 + 11.31(1) - 16.1 (1^2) = 15.21 ft

vertex form of the parabola

y = a ( x-2)^2 + 22 and when x = 5.675 y = 15.21

shows a = -.503

a) Trajectory equation becomes y = -.503 (x-2)^2 + 22

b) when she hits the water y = 0 = -.503 ( x-2)^2 + 22 shows x = 8.6 ft

Here is a graph that shows this:

ElectricPavlovMar 30, 2023

#2

+660

0

Sorry, its incorrect! I appreciate your help though!

KeihakuMar 30, 2023

#1

+1

\(\sqrt{36x^{36}} = 6x^6\)

.

GuestMar 30, 2023

#3

+37193

+1

27^2 + 2/3 * 27 * 2/3 * 27 + .......

= 27^2 + (2/3 * 27)^2 + (2/3)^4 * 27^2 + (2/3)^6 27^2 + (2/3)^8 * 27^2 =

(2/3^0 + 2/3 ^2 + 2/3 ^4 + 2/3 ^6 ) * 27^2 = 1289 4/9 units^2

Double check:

27^2 + 18^2 + 12^2 + 8^2 + (5 1/3)2 = 1289 4/9 <===CHECK !

ElectricPavlovMar 30, 2023

#2

+37193

+1

Fctors of 8

1 2 4 8

factors of 12

1 2 3 4 6 12 Common factors are 1 2 and 4

ElectricPavlovMar 30, 2023

#2

+37193

+1

There are 6 x 6 = 36 possible rolls

for a 1 2 or 3 you need 1 1 1 2 2 1 1 3 3 1 ===> five rolls out of 36 = 5/36

ElectricPavlovMar 30, 2023

#3

+37193

+1

4 choices for first digit

3 choices for second digit

2 choices for third digit

1 choice for last digit 4 * 3 * 2* 1 = 24 combos TOTAL ===> Half of these will be odd so 12 odd numbers can be made.

ElectricPavlovMar 30, 2023

#1

+37193

0

This question needs an edit.....is there some info missing? How many students bring 'both' ?

ElectricPavlovMar 30, 2023

#1

+37193

0

Can you read this post again and edit it so it has the correct information?

ElectricPavlovMar 30, 2023

#1

0

" The resulting product is less than.....?", what? Without that number, you haven't gotten a prayer of getting your question answered !!!! Understood ?

GuestMar 29, 2023

#1

0

" and the product of her rolls is......?", what? Without that number, you haven't gotten a prayer of getting your question answered !!!! Understood ?

GuestMar 29, 2023

#2

+1

4! ==24 permutations

Each permutation begins and ends with one of the 4 digits this many times:

24 / 4 ==6 permutations

Since you have two odd numbers (1 and 3), therefore you should have:

6 x 2 ==12 Odd and distinct permutations as follows: