Skipper follows a path along the grid shown, always moving either up orto the right. How many paths from A to C do not pass through B?

Answers

Answer 1

Answer: We can use complementary counting. First we can count ALL the ways we can get from A to C. Then we can count the ways we can get from A to C, where we DO pass through B. Then we do the total minus the number of ways we DO pass through B.

Number of TOTAL ways from A to C.
First we can imagine fake, dotted lines around the top left and bottom right "corners" so we can make a complete square.
Once we have this "complete" square with the dotted line corners, we can easily find the number of paths from A to C. It is just $(8!)/(4!*4!)$ = 70. If you don't know how this was derived, just comment.
HOWEVER, of the 70 paths we just counted, 2 of them are not possible using the original picture. Remember those dotted corners we drew? We cannot create paths using those corners; they were just there so we could use a formula. So, we actually have 70-2 = 68 total paths.

Now we find the number of paths from A to C that DO pass through B.
Well, first we have to find the number of paths from A to B and then from B to C. This will guarantee we move through B. From A to B, there is $(4!)/(2!*2!) =6$ ways. From B to C, there is also $(4!)/(2!*2!) =6$ ways. 6*6 = 36

68-36 = 32 FINAL ANSWER

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F(x) = 3x+2
What is f(5)?

Answers

Answer:

f(5) = 17

Step-by-step explanation:

f(x) = 3x+2

Let x =5

f(5) = 3(5) +2

f(5) = 15+2

f(5) = 17

615.44 to the nearest hundredth

Answers

When rounding, look to the next place to the right of what you are rounding to... for example if you are rounding to the nearest hundredth, look to the thousandths place to see if the hundredths place rounds up or down. Since your number, 615.44 stops on the hundredths place, the thousandths place is automatically zero, so your number stays the same.

615.44

PLEASE HELP I GIVE THANKS 1. What is atomic mass? (Points : 1)
only the neutrons in the atomic nucleus

only the protons in the atomic nucleus

the sum of all protons and neutrons in the atomic nucleus

the sum of all electrons in the atomic nucleus

Question 2. 2. Which term describes elements with different atomic masses due to varying numbers of neutrons? (Points : 1)
atomic mass units

isotopes

atoms

nuclei

Question 3. 3. If a carbon isotope has 6 protons and 7 neutrons, what is its atomic mass? (Points : 1)
6 amu

7 amu

13 amu

not enough information to calculate

Answers

Answer 1 : Atomic mass is the sum of all protons and neutrons in the atomic nucleus.

Answer 2 : The term that describes elements with different atomic masses due to varying numbers of neutrons is "isotopes". Isotope elements have same number of protons but different number of neutrons.

Answer 3 : As stated in the answer 1, atomic mass of an atoms is the sum of all protons and neutrons in it's nucleus. So, this carbon isotope has 6 protons and 7 neutrons in its nucleus so : 7+6=13 . It's atomic mass is 13 atomic mass unit.(amu)

Answer:

1. the sum of all protons and neutrons in the atomic nucleus

2. isotopes

3. 13 amu

You have $2,675.00 on a credit card with a 15.75% apr. you miss your minimum payment and there is a late fee of $29.00. how much is your balance at the beginning of the second month?a 2,814.31
b 2,739.11
c 3,125.31
d 2,710.11

Answers

The solution is Option B.

The balance amount at the second month is $ 2,739.11

What is Annual Percentage Yield?

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.

Given data ,

Let the initial amount be represented as A

The value of A = $ 2,675

Now , the annual percentage rate is given by r

The value of r = 15.75 %

So , the rate r in monthly basis is given by

Rate R = annual percentage rate / 12

Substituting the values in the equation , we get

Rate R = 15.75 / 12

Rate R = 1.3125 %

Now , the late fee of the credit card = $ 29.00

So , the amount balance at the end of second month = ( initial amount + Rate R x initial amount + late fee )

Substituting the values in the equation , we get

Amount balance at the end of second month = ( 2675 + ( 1.3125/100 ) x 2675 + 29 )

Amount balance at the end of second month = 2675 + 35.109 + 29

Amount balance at the end of second month = $ 2,739.109

Amount balance at the end of second month = $ 2,739.11

Therefore , the final balance amount is $ 2,739.11

Hence , The balance amount at the second month is $ 2,739.11

To learn more about Annual percentage yield click :

brainly.com/question/28495077

#SPJ2

Answer:

b. $2,739.11. You have $2,675.00 on a credit card with a 15.75% APR. You miss your minimum payment and there is a late fee of $29.00. Your balance at the beginning of the second month is $2,739.11.

Step-by-step explanation:

What is 20 more than 3 fish tanks

Answers

20+3 = 23 fish tanks

23 fish tanks
That is the answer

keith and michelle went out to dinner. the total cost of the meal,including the tip,came to $53.70. if the combined tip came out yo 9.60,and each friend spent and equal amouny,how much did each friend pay not including the tip?

Answers

Answer:

23.45

Step-by-step explanation:

53.70-9.60 is 46.90

46.90 divided by 2 is 23.45