I just need #10 answered please. Incase you can’t see it it says “what is the solution to the inequality for #9

Which situation will have the greatest number of permutations?

Anton [14]

Answer:

Option C will have greatest number of permutations.

Step-by-step explanation:

A.

The number of license plates with 4 letters followed by 3 numbers, where letters and digits cannot be repeated.

We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter

25 letters options for 2nd letter

24 letter options for 3rd letter

23 letter options for 4th letter.

So total options for 4 letters 26*25*24*23 = 358800

Now, 3 numbers are required. We have total 10 numbers (0-9)

10 number options for 1st number

9 number options for 2nd number

8 number options for 3rd number

Total options for 3 numbers= 10*9*8 = 720

total options for 4 letters and 3 numbers will be: 358800 * 720 = 258,336,000

B.

The number of license plates with 3 letters followed by 4 numbers, where letters and digits cannot be repeated.

We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter

25 letters options for 2nd letter

24 letter options for 3rd letter

So total options for 3 letters= 26*25*24 = 15600

Now, 4 numbers are required. We have total 10 numbers (0-9)

10 number options for 1st number

9 number options for 2nd number

8 number options for 3rd number

7 number options for 4th number

Total options for 4 numbers = 10*9*8*7 = 5040

total options for 4 letters and 3 numbers will be: 15600 * 5040 = 78,624,000

C. The number of license plates with 4 letters followed by 3 numbers, where letters and digits can be repeated.

Now, the letters and digits can be repeated. So we have 26 options for each 4 letters and 10 options for each 3 numbers

26*26*26*26 *10*10*10 = 456,976 * 10,00 = 456,976,000

total options for 4 letters and 3 numbers will be: 456,976,000

D.

The number of license plates with 3 letters followed by 4 numbers, where letters and digits can be repeated.

Now, the letters and digits can be repeated. So we have 26 options for each 3 letters and 10 options for each 4 numbers

26*26*26 *10*10*10*10 = 17,576 * 10,000 = 175,760,000

total options for 3 letters and 4 numbers will be: 175,760,000

So, Option C will have greatest number of permutations.

7 0

3 years ago

Plz look at pic !!!! Plz Help!!! Use proportion to solve

soldi70 [24.7K]

Answer:

It takes 26 2/3 gallons to make a 400 mile trip.

Step-by-step explanation:

This question is simply asking for the number of miles per gallon . In math, per means this is meant to be written as a fraction.

"If a trip of 270 miles required 18 gallons of gas" is actually saying "270 miles per 18 gallons." This can be written as a fraction like so: 270/18.

If we're looking for the amount of gas used for a 400 mile trip, we have the fraction: 400/g, g being the amount of gallons it took to make that trip.

Now we can set up the proportion: $\frac{270}{18} =\frac{400}{g}$

Cross multiply and solve accordingly.

$\frac{270}{18} =\frac{400}{g}$

400 $270g = 400 *18\\ 270g = 7200\\g=26\frac{2}{3}$ /g

So the answer is:

It takes 26 2/3 gallons to make a 400 mile trip.

6 0

3 years ago

If 5X - 4.3 =3X + 5.7 Then X=5 True OR FALSE

coldgirl [10]

True
Solution,5X-4.3-3X =5.7
or,5X-3X=5.7+4.3
or ,2X=10
or,X=10/2
or,X=5

3 0

3 years ago

What is the answer to 10-(8p+3)=9(2p-5) ?

aniked [119]

Use distribution.
10 - (8p + 3) = 10 - 8p - 3 = 7 - 8p
9(2p - 5) = 18p - 45

So...
-8p + 7 = 18p - 45
Subtract 7 from both sides
-8p = 18p - 52
Subtract 18p from both sides
-26p = 52
Divide both sides by -26.
p = -2

There's your answer :D

6 0

3 years ago

Read 2 more answers

What is the domain of this graph?

Salsk061 [2.6K]

$\rm{\pink{\underline{\underline{\blue{TO\:FIND:-}}}}}$

The domain of the attachment graph .

$\rm{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}$

The method to identify the domain and range of functions is by using graphs :-

⚡ The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis .

⚡ The range is the set of possible output values, which are shown on the y-axis .

See the attachment figure .

[NOTE :- Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values .]

✍️ So, we can observe that the graph extends horizontally from -3 to the right with +10 .

✯ Hence, the domain is [-3 , 10] .

5 0

3 years ago