Answer:
The probability of getting a black pen from the bag is 13.5%.
Step-by-step explanation:
To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:
12 + 20 + 5 = 37
37 = 100%
5 = X
(5 x 100) / 37 = X
500/37 = X
13.5 = X
Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.
Therefore, the probability of getting a black pen from the bag is 13.5%.
The population is increasing every year. so we use exponential growth function
Where 'a' is the initial population
r is the rate of increase
x is the years
y is the final population
In 2015, the population of a small town in Florida is 95
Initial population a= 95
r= 15%= 0.15
x = 2023 - 2015 = 8 years
Plug in all the values and find out y
y = 290.607
The population in 2023 is 291
Answer:
x = 3
y = 2
Step-by-step explanation:
Diagonals of a parallelogram bisect each other into two equal segments. Therefore:
3x - 1 = 2(x + 1)
Solve for x
3x - 1 = 2x + 2
Collect like terms
3x - 2x = 1 + 2
x = 3
Also:
5y + 1 = 6y - 1
Collect like terms
5y - 6y = -1 - 1
-y = -2
Divide both sides by -1
y = -2/-1
y = 2
<h3>
Answer: 2x(x^2-2)(x+1)</h3>
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Explanation:
First factor out the GCF 2x
2x^4+2x^3-4x^2-4x
2x*x^3+2x*x^2-2x*2x-2x*2
2x(x^3 + x^2 - 2x - 2)
Then let's factor the expression inside the parenthesis using the factor by grouping method
x^3 + x^2 - 2x - 2
(x^3 + x^2) + (- 2x - 2)
x^2(x + 1) - 2(x + 1)
(x^2 - 2)(x+1)
We see that x^3 + x^2 - 2x - 2 factors to (x^2-2)(x+1)
Overall, the original expression fully factors to 2x(x^2-2)(x+1)
length = 2x
width = x^2-2
height = x+1
The order of length, width, and height doesn't matter.
