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3 years ago

If you roll a die 30 times how many times would you expect to roll a 1 why

Mathematics

2 answers:

ivolga24 [154]3 years ago

5 0

5 times because 30/6 is 5 and there is one one 1 side of the six sided die (1/6)

Julli [10]3 years ago

4 0

If it's a fair die, and there are 6 possible outcomes out of 30 throws, it becomes a fraction. 30/6 which = 5. So you are expecting every number to come out 5 times. The answer is 5 :)

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Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope. We don't have to bother to take the square root. We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6). slope=-6/-1=6 AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1). slope=1/-6=-1/6. BC²=(-6)²+1²

CD=D-C=(1, 6). slope=6/1=6 CD²=1²+6²=37

DA=A-D=(6,-1) slope=-1/6 DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides. We see they all have squared distance 37. Equal perpendicular sides proves its a square.

If we do these problems enough we learn: There's no point taking the square root. In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides: (-1, -6) (-6, 1) (1, 6) (6,-1)

5 0

3 years ago

A cinema has three screens last Saturday there were 500 visitors 40% went to screen 1 ,25% went to screen 2 the rest went to scr

ratelena [41]

Answer:

200 visitors went to screen 1.

125 visitors went to screen 2.

175 visitors went to screen 3.

Step-by-step explanation:

We will find number of visitors who went to screen 1 by finding 40% of 500 as we are told that 40% of 500 visitors went to screen 1.

$500*\frac{40}{100} =5*40=200$

Therefore, 200 visitors went to screen 1.

Now we will find number of visitors who went to screen 2. We are told that 25% of 500 visitors went to screen 2.

$500*\frac{25}{100} =5*25=125$

Therefore, 125 visitors went to screen 2.

Now we will find the number of visitors who went to screen 3 by subtracting combined number of visitors who went to screen 1 and screen 2 from total number of visitors.

$500-(200+125)$

$500-325=175$

Therefore, 175 visitors went to screen 3.

7 0

3 years ago

Can someone please help me on this one question?

Katyanochek1 [597]

A+30 = 60
a = 30

a + 2b = 60
30+2b = 60
2b = 30
b = 15

5b - 5c = 60
5(15) - 5c = 60
5c = 15
c = 3

10c + d = 60
10(3) + d = 60
30 + d = 60
d = 30

2d + 6e = 180 - 60
2(30) + 6e = 120
6e = 60
e = 10

4f + 4e = 120
4f + 4(10) = 120
4f = 80
f = 20

5 0

3 years ago

Express p in terms of q if

Irina-Kira [14]

$p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)$

$q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}$

8 0

2 years ago

Claris was asked the expression 6 times y plus y times 4

lianna [129]

6y+y(4)
7y(4)
y=4/7

Youre welcome

3 0

3 years ago

Read 2 more answers