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tensa zangetsu [6.8K]
2 years ago
10

A product code consists of four letters followed by five digits. Only the letters X, Y, and Z can be used ( and any of the digit

s 0,1,2,3,4,5,6,7,8,9 can be used). For example, XYXZ31513, ZYZZ90654, YYYY44444 are possible product codes.
If one such product code is chosen at random, what is the probability it includes the letter Y?
Mathematics
1 answer:
Morgarella [4.7K]2 years ago
7 0

Answer:

\frac{49}{81}, 60.494%

Step-by-step explanation:

I am going to try to tackle this. I might miss a step as I am currently taking discrete mathematics.

We want to find all the possibilities with 1y, 2ys, 3ys, and 4ys, out of all total possibilities.

_ _ _ _   _ _ _ _ _

For the letters, in each spot, we have 3 choices. For the numbers, we have 10 choices in each spot

so

3*3*3*3 * 10*10*10*10*10

= 81*100000

= 8100000

The number of Y's will never affect the number of permutations of the numbers.

So:

For 1 y, we have

Y _ _ _ * 10*10*10*10*10

But we also have

_ Y _ _

_ _ Y _

and

_ _ _ Y

So we can multiply the number we get in one calculation by 4

4 *

Y _ _ _ * 10*10*10*10*10

2*2*2 * 10*10*10*10*10

= 800000 * 4  = 3200000

For 2 y's, we have

YY _ _

_ YY _

__ YY

3*

YY 2*2 * 10^5

4 * 100000

400000 * 3 = 1200000

For 3 y's, we have

YYY _

_ YYY

2 *

YYY 2 * 10^5

200000 * 2

= 400000

For 4 y's, we have

YYYY * 10^5

100000

Now we can add them all up and divide it by our original number 8100000

\frac{100000 + 400000 + 1200000 + 3200000}{8100000} = \frac{49}{81}

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It is known that 1.4< square root of 2 <1.5. Find all possible values of the expression 2-square root of 2. How do I find
horsena [70]

Answer:

0.5<2-√2<0.6

Step-by-step explanation:

The original inequality states that 1.4<√2<1.5

For the second inequality, you can think of 2-√2 as 2+(-√2).

Because of the "properties of inequalities", we know that when a positive inequality is being turned into a negative, the numbers need to swap and become negative. So, the original inequality becomes -1.5<-√2<-1.4. (Notice how the √2 becomes negative, too). This makes sense because -1.5 is less than -1.4.

Using our new inequality, we can solve the problem. Instead of 2+(-√2), we are going to switch "-√2" with both possibilities of -1.5 and -1.6. For -1.5, we would get 2+(-1.5), or 0.5. For -1.4, we would get 2+(-1.4), or 0.6.

Now, we insert the new numbers into the equation _<2-√2<_. The 0.5 would take the original equation's "1.4" place, and 0.6 would take 1.5's. In the end, you'd get 0.5<2-√2<0.6. All possible values of 2-√2 would be between 0.5 and 0.6.

Hope this helped!

4 0
3 years ago
5. Katie makes and sells scarves. Her monthly profit is given by P(s) = -s2 + 25s - 100, where "s" is the selling price. For wha
Marat540 [252]

Answer: s > 5

Step-by-step explanation:

-s² + 25s - 100 > 0

Coefficient of s² is -1, multiply the equation through by -1.

-1 × (-s² + 25s - 100)

s² — 25s + 100

ax² + bx + c

Then you get the factors x and y that gives x + y = b and xy = c

b = -25 and c = 100, x = -20 and y = -5

-20 × -5 = 100 and -20 + -5 = -25

Then

s² — 20s — 5s + 100 > 0

Factorising,

s (s — 20) — 5(s — 20) > 0

(s — 5)(s — 20) > 0

(s — 5) > 0 and (s — 20) > 0

s>5 and s>20

s > 5

Hope this Helps?

4 0
3 years ago
HELP PLEASE ASAP !!!
Zepler [3.9K]

Answer:

X = 6.25 ft.

Step-by-step explanation:

From the figure:

∵ Two angles in the small flag = the corresponding angles in the large flag

∴ Two flags are similar

∴ Their sides are proportional

∴ \frac{4}{5}=\frac{5}{x} \\ x=\frac{(5)(5)}{4}=6.25

∴ x = 6.25 ft

8 0
3 years ago
Does anyone know the Answer for this
Klio2033 [76]
Y= -6, hope this helps
8 0
3 years ago
Read 2 more answers
Question 9 of 13
blondinia [14]

Answer:

Actually, you have the correct answer. I think you are confused as to what the exact answer might be.

4 0
2 years ago
Read 2 more answers
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