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Vladimir79 [104]
3 years ago
13

A single standard six sides die is rolled. what is the probability the roll is a multiple of three given that it is an even numb

er
Mathematics
1 answer:
tankabanditka [31]3 years ago
5 0
33.3%

Since we are given that it is an even number, we know there is only 3 options (2, 4, 6). Since only one of them is an even number, we know that we need the fraction 1/3 or 33.3% for a probability. 
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J is the midpoint of HK¯¯¯¯¯¯¯ . What are HJ, JK, and HK?
lana [24]
Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.

1) You are told that the m<span>easure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
</span>9x-2 = 4x+13
5x = 15
x = 3

2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = <span>9x-2 
</span>HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25

JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25

3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.

-----

Answer: HJ = 25, JK = 25, HK = 50
4 0
3 years ago
A line's y-intercept is 8, and its slope is 2. What is its equation in slope-intercept form? Write your answer using integers, p
lisov135 [29]
The correct answer is y=2x+8
6 0
2 years ago
Read 2 more answers
What is the sum of the sequence 152,138,124, ... if there are 24 terms?
N76 [4]

Answer: -216

Step-by-step explanation:

To solve the exercise you must use the formula shown below:

Sn=\frac{(a_1+a_n)n}{2}

Where:

a_1=152\\a_n=a_{24}

You should find  a_{24}

The formula to find it is:

a_n=a_1+(n-1)d

Where d is the difference between two consecutive terms.

d=138-152=-14

Then:

a_{24}=152+(24-1)(14)=-170

Substitute it into the first formula. Therefore, you obtain:

S_{24}=\frac{(152-170)(24)}{2}=-216

3 0
3 years ago
Read 2 more answers
What is the answer to 8=56, 7=42, 6=30, 5=20, 3=?
ozzi
8(7) = 56
7(6) = 42
6(5) = 30
5(4) = 20
4(3) = 12
3(2) = 6
∴ 3 = 6
7 0
3 years ago
The roots of a quadratic equation ax2+bx+c=0 are 3+sqrt2 and 3−sqrt2. Find the values of b and c assuming that a=1.
slamgirl [31]

Answer:

b=-6\\c=7

Step-by-step explanation:

we know that

The general equation of a quadratic function in factored form is equal to

y=a(x-x_1)(x-x_2)

where

a is a coefficient of the leading term

x_1 and x_2 are the roots

we have

a=1\\x_1=3+\sqrt{2}\\x_2=3-\sqrt{2}

substitute

y=(1)(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))

Applying the distributive property convert to expanded form

y=x^2-x(3-\sqrt{2})-x(3+\sqrt{2})+(3+\sqrt{2})(3-\sqrt{2})

y=x^2-(3x-x\sqrt{2})-(3x+x\sqrt{2})+(9-2)

y=x^2-3x+x\sqrt{2}-3x-x\sqrt{2}+7

y=x^2-6x+7

therefore

b=-6\\c=7

7 0
2 years ago
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