Given:
a.) The population of Arizona is estimated to increase by 6.2% every year.
b.) The population was 4.18 million in 2016.
For us to be able to determine the population in 2022, we will be using the following formula:
![\text{ P = P}_0e^{rt}](https://tex.z-dn.net/?f=%5Ctext%7B%20P%20%3D%20P%7D_0e%5E%7Brt%7D)
Where,
P = Total population after time (t)
P₀ = Starting population = 4.18 million
r = Growth rate (in decimal form) = 6.2%/100 = 0.062
t = time (in years) = 2022 - 2016 = 6 years
e = Euler's number = 2.71828182845
We get,
![\text{ P = P}_0e^{rt}\text{ = (4,180,000)(}2.71828182845)^{0.062(6)}](https://tex.z-dn.net/?f=%5Ctext%7B%20P%20%3D%20P%7D_0e%5E%7Brt%7D%5Ctext%7B%20%3D%20%284%2C180%2C000%29%28%7D2.71828182845%29%5E%7B0.062%286%29%7D)
![\text{ P = 6,063,645.861797897 }\approx\text{ 6,063,646}](https://tex.z-dn.net/?f=%5Ctext%7B%20P%20%3D%206%2C063%2C645.861797897%20%7D%5Capprox%5Ctext%7B%206%2C063%2C646%7D)
Therefore, the population in 2022 will be approximately 6,063,646.
Answer:
![x = \sqrt 6](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%206)
Step-by-step explanation:
Given
The attached triangle
Required
Find x
Considering angle 30 degrees,
![Opposite = \sqrt{2](https://tex.z-dn.net/?f=Opposite%20%3D%20%5Csqrt%7B2)
![Adjacent = x](https://tex.z-dn.net/?f=Adjacent%20%3D%20x)
Using the tangent formula:
![tan\ 30 = \frac{\sqrt 2}{x}](https://tex.z-dn.net/?f=tan%5C%2030%20%3D%20%5Cfrac%7B%5Csqrt%202%7D%7Bx%7D)
Make x the subject
![x = \frac{\sqrt 2}{tan\ 30}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Csqrt%202%7D%7Btan%5C%2030%7D)
![x = \frac{\sqrt 2}{1/\sqrt 3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Csqrt%202%7D%7B1%2F%5Csqrt%203%7D)
![x = \sqrt 2 * \sqrt 3](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%202%20%2A%20%5Csqrt%203)
![x = \sqrt 6](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%206)
Answer:
5 bags of brand x and 6 bags of brand y.
Step-by-step explanation:
Nutrient requirement for the garden:
39 pounds of nutrient a and
16 pounds of nutrient b
Component of each bag of brand x:
3 pounds of nutrient a and 2 pounds of nutrient b
Therefore, 5 bags of brand x will contain 15 pounds of nutrient a and 10 pounds of nutrient b
Component of each bag of brand y:
4 pounds of nutrient a and 1 pound of nutrient b
Therefore, 6 bags of brand y will contain 24 pounds of nutrient a and 6 pounds of nutrient b
Altogether, she should buy 5 bags of brand x and 6 bags of brand y to meet the nutrient requirement of the garden
Answer:
3,672
Step-by-step explanation:
Given the sequence 6, 9, 12...
The sequence is an arithmetic sequence
first term a = 6
common difference d = 9 - 6 = 12 - 9 = 3
number of terms n = 48
Sn = n/2[2a+(n-1)d]
Substitute the given values
S48 = 48/2[2(6)+(48-1)(3)]
S48 = 24(12+(3*47))
S48 = 24(12+141)
S48 = 24(153)
S48 = 3,672
Hence the sum of the first 48terms is 3,672
Here's what I got for the first question.
Did you want answers for the second one? I couldn't read that part of the image very well, if you did.