Four books, one each on physics, chemistry, mathematics, and biology are about to be stacked on a shelf. If the books are stacked randomly, what is the probability the mathematics book is on top?

Answers

Answer 1

Answer: There are 4 books.
The math book can either be top, second from top, third from top, or on the bottom.
The probability of being in any single given position is 1/4 = 25% .

Answer 2

Answer: Since each book can be put on the top, and there are 4 books, the chances of a math book going on the top is 1/4, while the other 3 chances are the other books. So your answer is 1/4 or 0.25

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One of diagonals of a parallelogram is its altitude. What is the length of this altitude, if its perimeter is 50 cm, and the length of one side is 1 cm longer than the length of the other?

Answers

The length of that altitude is 5 cm.

Explanation

According to the below diagram, $ABCD$ is a parallelogram with diagonal $\overline{AC}$ as its altitude.

Suppose, the length of side $\overline{AB}$ is $x$ cm.

As the length of one side is 1 cm longer than the length of the other, so the length of side $\overline{BC}$ will be: $(x+1) cm$

Given that, the perimeter of the parallelogram is 50 cm. So, the equation will be.....

$2[x+(x+1)]=50\n \n 2(2x+1)=50\n \n 4x+2=50\n \n 4x=48\n \n x= 12$

So, the length of $\overline{AB}$ is 12 cm and the length of $\overline{BC}$ is (12+1)= 13 cm.

Suppose, the length of the altitude( $\overline{AC}$ ) is $h$ cm.

Now, in right angle triangle $ABC$ , using Pythagorean theorem....

$(AC)^2+(AB)^2= (BC)^2\n \n h^2+(12)^2= (13)^2\n \n h^2+144= 169\n \n h^2= 25\n \n h= √(25)= 5$

So, the length of that altitude is 5 cm.

Do you know the answer for this math excercise: $6^(2) * (2)/(3) : √(9)$ Please help me :)

Answers

Well, if you simplify both sides of the ratio, you get
24:3
which, in its simplified version, is
8:1
Hope it Helps! :)

· If the value of +/= , find the value of + /

Answers

if x/y=0 and we're finding x,

you would multiply y on both sides so x=0

If this wasn't the answer you were looking for, tell me and I can edit my answer

For each quadratic function, find the axis of symmetry of its graph. Y=x^2+ 4x-7 Y=2x^2+3x-4

Answers

first find the vertex
the x coordinate of the vertex is the axis of symmetry

the vertex of an equation in form
y=ax^2+bx+c is
-b/2a=x coordinate

y=1x^2+4x-7
vertex=-4/2=-2
axis of symmetry is x=-2

y=2x^2+3x-4
ertex=-3/(2*2)=-3/4
axis of symmetry is x=-3/4

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