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Varvara68 [4.7K]
3 years ago
12

How many solutions does the equation have? 5(w−1)−2=5w+7A.0 B.1 C.infinitely many

Mathematics
2 answers:
kotegsom [21]3 years ago
7 0

there are 0 solutions for this equation

bogdanovich [222]3 years ago
6 0
5(w - 1) - 2 = 5w + 7
5w - 5 - 2 = 5w + 7
5w - 7 = 5w + 7
5w - 5w = 7 + 7
0 = 14 (incorrect)

there are no solutions to this system...0 solutions
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A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
Maurinko [17]

Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

5 0
3 years ago
Amy earned a gross income of $51,750 last year. She made $644.28 in IRA contributions, donated $713 to her
VikaD [51]

Answer:

41,755.72

Step-by-step explanation:

6 0
3 years ago
write the 2 digit numbers that matches the clues my number has tens digit that 8 more that one's digit. zero is not one my digit
Natalka [10]
The answer is 91 because the tens place has to be 8 more so in the 80's, 8 would be 8 more than 0 and 0 is not one of the digits and it's a 2 digit number so it can't go to the 100's so 91 is the best answer. I hope this helped you
7 0
3 years ago
The table shows ordered pairs of the function y = 16 0. 5x. A 2-column table with 6 rows. The first column is labeled x with ent
zvonat [6]

Option 3 is the correct answer. The missing values of (x, y) is (8, 20).

<h3>How do you find out the values?</h3>

Given that the function is,

y = 16 + 0.5x

The function is a linear equation that can be solved graphically. The values of both variables x and y can be found on different points along with the straight-line graph.

Also, for every value of x, there is a corresponding value of y.

For the given options, we put the values of x to find the corresponding value of y.

For option 1, put x = 0 in the given function,

y = 16 + 0.5\times 0\\y = 16

But for x=0, y= 18, hence option 1 is not correct.

For option 2, put x = 5 in the given function,

y = 16 + 0.5\times 5\\y = 18.5

But for x=5, y= 19.5, hence option 2 is not correct.

For option 3, put x = 8 in the given function,

y = 16 + 0.5\times 8\\y = 20

But for x=8, y= 20, hence option 3 is the correct answer.

Hence we can conclude that option 3 is the correct answer. The missing values of (x, y) is (8, 20).

To know more about the function, follow the link given below.

brainly.com/question/5245372.

7 0
2 years ago
Factor the polynomial by grouping. 12x^x+x−13
tekilochka [14]

Answer:

  (x -1)(12x +13)

Step-by-step explanation:

You are looking to rewrite the middle term as the sum of terms that have factors of (12)(-13) that have a total of +1. Those factors are -12 and +13, so the expression you are factoring by grouping is ...

  12x^2 +13x -12x -13

  = x(12x +13) -1(12x +13)

  = (x -1)(12x +13)

5 0
3 years ago
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