MATHEMATICS HIGH SCHOOL

A bag has five red marbles, six blue marbles, and four black marbles. What is the probability of picking a blue marble, replacing it, and then picking another blue marble?A. 1/15
B. 8/75
C. 4/25
D. 1/9

Answers

Answer 1
Answer: The total number of marbles is 15. The probability of picking a blue marble is 6/15. After putting the marble back, the probability of picking another blue marble is probably 1/9. 

Answer: the probability of picking two blue marbles in a row is 1/9.
Answer 2
Answer:

Answer:

4/25 is the answer guys!

Step-by-step explanation:

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What is the next value 1I 2L 3F4

Answers

Answer:

The next value in the given pattern of digits and numbers is:

                      E

Step-by-step explanation:

  • Since, if we see the first pair:

                   1 I

Then we see that the alphabet I requires just one vertical line to get formed.

  •  The next pair is:

                    2 L

Hence, from this we could claim that L is formed with the help of one vertical and one horizontal line.

  •   The next pair is:

                   3 F

Again the alphabet F could be formed with the help of 3 lines one vertical and two horizontal line.

  • Hence, from the above three pairs we may infer that the next pair will be:

                   4 E

because E is formed with the help of four lines 1 vertical and three horizontal lines.

Final answer:

The next term in the sequence is 4U.

Explanation:

The given sequence seems to follow a pattern where the 1st term is the number itself, and the 2nd term is the last letter of the number. The 3rd term is the 1st letter of the next number, and so on.

  1. 1I
  2. 2L
  3. 3F
  4. 4U

Therefore, the next term in the sequence would be 4U.

Learn more about sequence here:

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Is y=5x+4 proportional?

Answers

Its proportional. 

(I need 20 characters but thats all really.)

Use Gauss-Jordan elimination to solve the following linear system.x – 6y – 3z = 4
–2x – 3z = –8
–2x + 2y – 3z = –14

Answers

\begin{cases}x-6y-3z=4&(1)\n-2x-3z=-8&(2)\n-2x+2y-3z=-14&(3)\end{cases}

First eliminate y by adding (1) to three times (3). This gives

(x-6y-3z)+3(-2x+2y-3z)=4+3(-14)\iff -5x-12z=-38

This reduces the system of one of two equations and two unknowns:

\begin{cases}-5x-12z=-38&(1)^*\n-2x-3z=-8&(2)^*\end{cases}

You can eliminate z by subtracting (1)^* and four times (2)^* to get

(-5x-12z)-4(-2x-3z)=-38-4(-8)\iff3x=-6\implies x=-2

Back-substitute to find z and y. You should end up with (x,y,z)=(-2,-3,4).

Answer:

(-2,-3,4)

Step-by-step explanation:

Expand the logarithmic expression log(8) a/2

Answers

log _(8) (a)/(2) = \n log _(8)a - log_(8) 2 = \n log _(8)a - (1)/(3)log _(2)2= \n log _(8)a - (1)/(3)

Final answer:

The given logarithmic expression log(8a/2) can be expanded as 2 log 2 + log a by using the properties of logarithms.

Explanation:

The question is asking to expand the logarithmic expression log(8a/2). The properties of logarithms can be applied in order to simplify it. There are two key properties that will be used. First, the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which can be represented as log xy = log x + log y. Second, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, represented as log (a/b) = log a - log b.

With these properties in mind, we can start simplifying the given logarithmic expression. The expression log(8a/2) can be represented as log 8 + log a - log 2. Simplifying further, we get log 2^3 + log a - log 2, which simplifies further to 3 log 2 + log a - log 2. Simplifying one more step gives 2 log 2 + log a.

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Scott has $500 in the bank. He withdraws the same amount of money each week for 12 weeks, at which point he has $20 left in the bank. How much money did he withdraw each week?

Answers

Scott knew that the only chance we would have to answer this problem would be if he kept his money in a bank that pays no interest, so that's what he did.  The bank simply stored his money in a mayonnaise jar under a tightly-guarded mattress, and he was allowed to come in and take some out of it each week.

He started with $500. He withdrew (500 - 20) = $480 in 12 weeks.

So he must have come in and picked up 480/12 = $40 each week.

Enter the correct value so that each expression is a perfect-square trinomial.x2 – 10x +_____

Answers

Answer:

A = 25 so that the expression x^2-10x+A is a perfect-square trinomial.

Step-by-step explanation:

  Given : expression  x^2-10x+A

We have to find the value of A so that  each expression is a perfect-square trinomial.

perfect-square is the term in the form of (a+b)^2 \ or\ (a-b)^2

Since , we know the algebraic identity,

(a+b)^2=a^2+b^2+2ab\n\n (a-b)^2=a^2+b^2-2ab

Given expression x^2-10x+A is of the form of (a-b)^2=a^2+b^2-2ab

Thus, comparing , we get,

a= x ,

-2ab = -10x

⇒ b = 5

Thus adding b² term to get perfect-square trinomial.

b² = 25

Thus, the perfect-square trinomial becomes x^2-10x+25=(x-5)^2

So, A = 25

the answer is x2-10x+25 because that is half of -10 (5) squared
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