Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Reading a coordinate plane
- Coordinates (x, y)
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify points from graph</em>
Point (0, -1)
Point (-3, 1)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>
- Substitute in points [Slope Formula]:
- [Fraction] Subtract:
- Rewrite:
Answer:
c = 68 m
Step-by-step explanation:
<h2>Pythagorean theorem:</h2>
To find the hypotenuse 'c' use Pythagorean theorem
hypotenuse² = base ² + altitude²
c² = 60² + 32²
= 3600 + 1024
= 4624
Answer:
698 fishes
Step-by-step explanation:
Generally, we can represent an exponential growth function as;
y = a•(1 + r)^t
originally, there were 3 fishes
The original value in this case means a = 3
After 6 weeks, there were 31
31 in this case is y
r is the increase percentage or rate
t is the time
So, we have it that;
31 = 3•(1 + r)^6
31/3 = (1 + r)^6
10.33 = (1 + r)^6
ln 10.33 = 6 ln (1 + r)
ln 10.33/6 = ln (1 + r)
e^0.3892 = (1 + r)
1 + r = 1.476
r = 1.476-1
r = 0.476 or 47.6%
So the growth percentage or rate is 47.6%
For 14 weeks, we simply have the value of t as 14;
So ;
y = 3•(1 + 0.476)^14
y = 3(1.476)^14
y = 698 fishes
Answer:
10.58
Step-by-step explanation:
Answer:
Probability that in a random sample of six cities, the sample mean would be more than 40 is 0.3372.
Step-by-step explanation:
We are given that the percent of births to mothers with less than a college education in all of the most populated cities in the U.S. has an average of 39.3 with a standard deviation of 4.1.
Assuming the data follows distribution. Also, a random sample of six cities is selected.
<em>Firstly, Let </em><em> = sample mean of six cities</em>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = average percent of births = 39.3
= standard deviation = 4.1
n = sample of cities = 6
Probability that in a random sample of six cities, the sample mean would be more than 40 is given by = P( > 40)
P( > 40) = P( > ) = P(Z > 0.42) = 1 - P(Z 0.42)
= 1 - 0.66276 = 0.3372
Therefore, probability that the sample mean would be more than 40 is 0.3372.