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3 years ago

13

Lila forgot the security code for her apartment building. The code is two different digits followed by a capital letter. How man

y different possible codes are there?
A. 2,106
B. 2,340
C. 2,600

2 answers:

Yanka [14]3 years ago

5 0

Answer:B. 2,340

Step-by-step explanation:

The number of digits = 10 [0,1,2,3,4,5,6,7,8,9]

The number of alphabets = 26

Now we are given that the code is two different digits followed by a capital letter.

Therefore, the number of different possible codes there are :-

$=\ ^{10}P_2\times26=10\times9\times26=2340$

Hence, there are 2340 different possible codes.

Nataly [62]3 years ago

4 0

<span>10*9*26=2,340
B.2,340

</span>

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63.09 ÷ .00008<br><br>No rush on this, but if you know please respond, it will be appreciated.

mart [117]

Answer is 788, 625. Hope this helped!

3 0

3 years ago

Calculus hw, need help asap with steps.

nikdorinn [45]

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

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

Explanation:

Let $f(n) = \frac{(-1)^{n+1}}{n!}$

The summation given to us represents the following

$\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\$

There are infinitely many terms to be added.

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

The partial sums only care about adding a finite amount of terms.

The partial sum $S_1$ is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say $S_1 = f(1) = 1$

I'm skipping the steps to compute f(1) since you already have done so.

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

The second partial sum is when things get a bit more interesting.

We add the first two terms.

$S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\$

The scratch work for computing f(2) is shown in the diagram below.

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

We do the same type of steps for the third partial sum.

$S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\$

The scratch work for computing f(3) is shown in the diagram below.

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

Now add the first four terms to get the fourth partial sum.

$S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\$

As before, the scratch work for f(4) is shown below.

I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.

This means something like $S_3 = S_2 + f(3)$ and $S_4 = S_3 + f(4)$

In general, $S_{n+1} = S_{n} + f(n+1)$ so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.

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

Let's use that recursive trick to find $S_5$

$S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333$

The scratch work for f(5) is shown below.

7 0

3 years ago

Joe bought g: gallons of gasoline for $2.85 per gallon and c: cans for oil for 3.15 dollars.

OlgaM077 [116]

A) 2.85g+3.15c
B)2.85(8.4)+3.15(6)=$42.84

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3 years ago

1.)12.5+(-31.5)=<br>2.)-31.91+(-16.7)=<br>3.)1/6+(-11/12)+2/3=<br>4.)29+(-15.7)+(-31.05)=

Xelga [282]

1. = Step 1. Simplify Brackets and you get $12.5 - 31.5$ Step 2. Simplify and you get $-19
$ which is your answer.

2. = Step 1. Simplify Brackets and you get $-31.91-16.7$ Step 2. Simplify and you get $-48.61$

3. = Step 1. Simplify Brackets and you get $\frac{1}{6} - \frac{11}{12} + \frac{2}{3}$ Step 2. Simplify and you get $- \frac{1}{12}$

4. Step 1. = Simplify Brackets and you get $29-15.7-31.05$ Step 2. Simplify and you get $-17.75$

5 0

4 years ago

A tennis instructor chargers $40 for each one hour lesson and $25 for each half hour lesson if the instructors I come from 35 le

kaheart [24]

X = 1 hr lessons and y = 1/2 hr lessons

x + y = 35......y = 35 - x
40x + 25y = 1115

40x + 25(35 - x) = 1115
40x + 875 - 25x = 1115
40x - 25x = 1115 - 875
15x = 240
x = 240/15
x = 16 <=== there are 16 one-hr lessons
and 19 half-hr lessons

7 0

4 years ago