7y+3=10y+9
-3 -3
7y=10y+6
-10y -10y
3y=6
Y=2
Step-by-step explanation:
(3a-7a+6)-(4a-3a+4)
(-4a+6)-(1a+4)
Add the remaining a's together, as well as the 6 and 4.
you get,
-3a+10
Step-by-step explanation:
It is given that,
An aquarium is in the shape of a rectangular prism. The area of the base of the aquarium is 250 square inches.
We need to find the volume of the aquarium.
The formula for the volume of the rectangular prism is given by :
V = lbh
Where, l is length, b is width and h is height
Let the height of the prism is h inches. So,
V = A × h (As Area, A = lb)
V = 250× h
= (250h) inch³
By substituting the value of h, we can find its volume.
Hence, the volume of the aquarium is (250h) inch³.
Answer:
Option (C)
Step-by-step explanation:
Given sides of a triangle are 2, 
and 
.
Option (A).
If the triangle is a right triangle.
By Pythagoras theorem,
(Longest side)² = (Leg 1)² + (Leg 2)²
19 = 4 + 12
19 = 16
Not true.
Therefore, its not a right triangle.
Option (B).
If it is a triangle following conditions will be followed.
1). a + b > c
2). b + c > a
3). a + c > b
For the given sides of the triangle,
1). 2 + √12 > √19 [True]
2). 2 + √19 > √12 [True]
3). √12 + √19 > 2 [True]
Therefore, the given measures of the sides will form a triangle.
Option (C)
By Pythagorean inequality theorem,
If c² = a² + b² → Right triangle
If c² > a² + b² → Obtuse triangle
If c² < a² + b² → Acute triangle
Since, (√19)² > 2² + (√12)² → 19 > 4 + 12
Therefore, the given triangle is an Obtuse triangle.
Option (D).
Not true. It's an obtuse triangle.
Answer:
Step-by-step explanation:
In a deck of 52 cards there are 4 aces.
Therefore the probability of obtaining an ace is:
P (x) = 4/52
The probability of not getting an ace is:
P ('x) = 1-4 / 52
P ('x) = 48/52
In this problem the number of aces obtained when extracting cards from the deck is a discrete random variable.
For a discrete random variable V, the expected value is defined as:
Where V is the value that the random variable can take and P (V) is the probability that it takes that value.
We have the following equation for the expected value:
In this problem the variable V can take the value V = 9 if an ace of the deck is obtained, with probability of 4/52, and can take the value V = -1 if an ace of the deck is not obtained, with a probability of 48 / 52
