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Verdich [7]
2 years ago
9

A number is chosen uniformly at random from among the positive integers less than $10^8$. Given that the sum of the digits of th

e number is 9, what is the probability that the number is prime
Mathematics
1 answer:
Reil [10]2 years ago
3 0

Answer:

 

If the sum of the digits of a number is divisible by 9, then that number is divisible by 9. An..... sorry if this does not help :(

Step-by-step explanation:

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factor the polynomial completely and SHOW WORK i’ve been on it for the past 30 minutes and I want to cry 24x^3-78x^2+45x NO LINK
Svetllana [295]

9514 1404 393

Answer:

  3(x)(4x -3)(2x -5)

Step-by-step explanation:

First of all, recognize that all coefficients are multiples of 3, and all terms have x as a common factor. This means your first factorization is ...

  (3x)(8x^2 -26x +15)

Now, you can use the "X-method" or similar to factor the quadratic. Start by looking for factors of (8)(15) = 120 that have a total of -26. Both will be negative. Here is a list of the positive factor pairs.

  120 = 1·120 = 2·60 = 3·40 = 4·30 = 5·24 = 6·20 = 8·15 = 10·12

The sums of these factor pairs are ...

  121, 62, 43, 34, 29, 26, 23, 22

The pair with a sum of 26 is highlighted.

Using this information, you can complete the X-method diagram, or you can use these numbers to rewrite the quadratic x-term to have 2 parts:

  8x^2 -20x -6x +15

Now, the quadratic can be factored by grouping:

  =  (8x^2 -20x) +(-6x +15)

  = 4x(2x -5) +3(-2x +5)

Recognizing the sign difference between the parentheses contents, we can factor the quadratic to be ...

  = (4x -3)(2x -5) . . . . . note the sign gets attached to the 3

So, the complete factorization of the original expression is ...

  24x^3-78x^2+45x = 3(x)(4x -3)(2x -5)

3 0
3 years ago
Use the area of the rectangle to find the area of the triangle.
tatyana61 [14]

Answer:

Answer is A

Step-by-step explanation:

Area of triangle = \frac{bxh}{2}

                          =\frac{10x5}{2}

                         =25

Area of rectangle = bxh

                             =10x5

                             = 50

6 0
2 years ago
Read 2 more answers
What is the volume of the composite figure? 1,200 units3 4,400 units3 5,040 units3 6,000 units3
swat32

Answer:

6000

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
How do you simplify a fraction?
attashe74 [19]
You simplify a fraction by finding it's greatest common factor. A greatest common factor is what both numbers are divisible by. If they can both be divided by two, then you've simplified them a little bit. Keep going until you can't find a common number that can be divided by the two, and you've got your simplified fraction. For example, 10/5 = 1/2 since both 10 and 5 is divisible by 5.
5 0
3 years ago
The 20% tip on a $8 sandwich ​
melamori03 [73]

Answer:

Tip of $1.60

The total is $9.60

Step-by-step explanation:

(20% × $8) + $8

$1.60 + $8

$9.60

5 0
3 years ago
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