GYanggg

The smallest prime number is 2. 

We can check if \(3^{12}+5^{13}+7^{14}+11^{15}\equiv0\pmod2\)

Since the product of any amount of odd numbers is odd:

3 is odd

3² is odd

3³ is odd

...

We know that the expression is:

odd + odd + odd + odd = even 

Since the expression is even, it must be divisible by 2. 

Hey oscar.a1551!

The area cross section of ABC is equal to the are of ABC.

Since ABC is a right triangle, we can calculate its area. 

We know that the hypotenuse is 17, and the height is 8, but we need to figure out the base. 

Using the Pythagorean Theorem: a^2 + b^2 = c^2 

In a right triangle, the sum of the square of the two legs is equal to the square of the hypotenuse. 

If the base is x, 8^2 + x^2 = 17^2 , x = 15

The area of the triangle is half of the base times height.

8 * 15 / 2 = 60.

I hope this helped,

Gavin

Hey oscar.a1551!

The area of a cross section that is parallel to face ABCD has the equal area of ABCD.

Assuming ABCD is a rectangle, we can use calculate the area of ABCD.

Given 6 and 12, the area of the rectangle is 6*12 = 72 

Since the cross section has equal area to ABCD, its area is also 72. 

I hope this helped,

Gavin

Hello lysxsa!

The standard equation for a circle with center (a,b) and radius of c is:

\((x-a)^2+(y-b)^2=r^2\)

Using this, we can create our equation necessary to answer the question. 

Since we already know the center and the radius, we can just plug in our values. 

\((x+8)^2+(y+13)^2=13^2=169\)

I hope this helped,

Gavin

Pequino and I have answered these questions:

For your convenience, here is the solutions copied and pasted:

1.  (Peqino)

in decimal form im pretty positive it would be .30 or .3

now in percentage form the answer would be 30%

if you want it in fraction form it would be 30/100 or 3/10

2. (Me)

Hey Hev!

There are a total of 4*4 = 16 different outcomes. 

Only the product of:

(2, 6) ; (3, 4) ; (3, 5) ; (4, 3) ; (5, 3) is satisfactory to \(P(12\le{X}\le15)\)

5 out of the 16 outcomes work, 

5/16 is your final answer. 

I hope this helped,

Gavin

Hey Hev!

There are a total of 4*4 = 16 different outcomes. 

Only the product of:

(2, 6) ; (3, 4) ; (3, 5) ; (4, 3) ; (5, 3) is satisfactory to \(P(12\le{X}\le15)\)

5 out of the 16 outcomes work, 

5/16 is your final answer. 

I hope this helped,

Gavin

Hey Hev123!

I’m not familiar with this form of representing data, but I can try. 

If the right side is the amount of outcomes, one can draw this conjecture:

A total of 4 + 12 + 21 + 32 + 12 = 80 trials have been made. 

A total of 32 attempts have been satisfactory to be placed in the 4th row. 

Therefore the probability of another attempt being in the 4th row is:

32/80 = 0.4 = 2/5 = 40%

I hope this helped,

Gavin

Hey GAMEMASTERX40!

In a quadratic equation, there is sometimes two roots, or solutions. 

This happens when the discriminant, b^2-4ac is greater than zero. 

When it is equal to zero, the quadratic will have two identical roots. 

When it is less than zero, the quadratic will have no real solutions. 
 

Therefore, the larger root means the root with the larger value of the two. 

I hope this helped,

Gavin

Once again, this is a basic trigonometry relationship problem. 

In this case, we can use tangent or cotangent. 

Tangent is opposite over adjacent

Cotangent is adjacent over opposite.

Let’s just say we use tangent.

\(\tan{x}=\frac{26}{53}\)

I hope this helped,

Gavin

Hey layla!

Once again, we use the formula:

\(S_{abc}=AB\sin{c}\)

Where A and B are the adjacent sides to the angle c. 

We could apply the formula in this problem:

\(\text{area}=13\cdot13\sin{44.8}\)

After solving the right side, you got the area. 

I hope this helped,

Gavin