Answer:
Correct Choice: Second Option
Step-by-step explanation:
<u>Standard Form of Quadratic Function</u>
The standard representation of a quadratic function is:
where a,b, and c are constants.
Solving with the quadratic formula:
We have the following equation to solve:
Rearranging all the terms to the left side:
Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:
Correct Choice: Second Option
Answer:
<u>Activity</u> <u>1:-</u>
1) Pi (π) is the ratio of circumference and the diameter of the circle which is 22/7. So
where circumference is directly proportional to diameter (d).
2) Area of a parallelogram = Altitude × Base
Base = 10 cm. So ,
where area (A) is directly proportional to altitude (a).
3) Let the fare of 1 unit distance be f
So, for distance d , total fare (F) will be where total fare (F) is directly proportional to distance (d).
4) Let the distance be 'D' , speed be 's' & time be 't' .
We know that where speed (s) is directly proportional to distance (D) & inversely proportional to time (t).
5) We know that area of a square (A) = side² (s²)
where area(A) is directly proportional to side(s).
<u>Activity</u> <u>2:-</u>
1) p is directly proportional to sum of u & w.
⇒ p ∝ u + w
⇒ p = k (u + w)
Putting the values of p , u & w
⇒ 14 = k(4 + 3)
⇒ 7k = 14
⇒ k = 14/7 = 2
2) r is directly proportional to square of t.
⇒ r ∝ t²
⇒ r = k × t²
Putting the values of r & t
⇒ 16 = k × 16²
⇒ k = 16² ÷ 16 = 16
3) y is directly proportional to cube root of x.
⇒ y ∝ ∛x
⇒ y = k × ∛x
Putting the values of x & y ,
⇒ 2 = k × ∛27
⇒ 3k = 2
⇒ k = 2/3
4) z is directly proportional to cube of d.
⇒ z ∝ d³
⇒ z = k × d³
Putting the values of d & z ,
⇒ 5 = k × 2³
⇒ 8k = 5
⇒ k = 5/8
5) Total Surface Area (SA) is directly proportional to square of the sides (s).
⇒ SA ∝ s²
⇒ SA = k × s²
Putting the values of SA & s ,
⇒ 96 = k × 4²
⇒ 16k = 96
⇒ k = 96/16 = 6
Answer:
CI ≈ (173.8 < μ < 196.2)
Step-by-step explanation:
We are told that laboratory tested twelve chicken eggs. Thus;
n = 12
Mean; x¯ = 185 mg
S.D; s = 17.6 mg
DF = n - 1 = 12 - 1 = 11
We have a 95% confidence level. Thus; α = 0.05
Since n < 30, we will use t-sample test.
Thus, from t-table attached at 95% Confidence level and DF = 11, we have;
t = 2.201
Thus,formula for Confidence interval is;
CI = (x¯ - t(s/√n)) < μ < (x¯ + t(s/√n))
CI = (185 - 2.201(17.6/√12)) < μ < (185 + 2.201(17.6/√12))
CI = (185 - 11.1825) < μ < (185 + 11.1825)
CI = (173.8175 < μ < 196.1825)
CI ≈ (173.8 < μ < 196.2)
