The correct slope is -5/2.
The formula for slope is
m = (y₂-y₁)/(x₂-x₁)
The y-coordinate of the second point is 0, and the y-coordinate of the first point is 2. The x-coordinate of the second point is 0.8 and the x-coordinate of the first point is 0:
m = (0-2)/(0.8-0) = -2/0.8 = -2 ÷ 8/10 = -2 × 10/8 = -2/1 × 10/8 = -20/8 = -5/2
Answer:
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
-1. 34
0.1837
Step-by-step explanation:
Full time :
n1 = 125
x1 = 2.7386
s1 = 0.65342
Part time :
n2 = 88
x2 = 2.8439
s2 = 0.49241
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Test statistic :
The test statistic :
(x1 - x2) / sqrt[(s1²/n1 + s2²/n2)]
(2.7386 - 2.8439) / sqrt[(0.65342²/125 + 0.49241²/88)]
−0.1053 / sqrt(0.0034156615712 + 0.0027553)
-0.1053 /0.0785554
= - 1.34
Test statistic = - 1.34
The Pvalue :
Using df = smaller n - 1 = 88 - 1 = 87
Pvalue from test statistic score ;
Pvalue = 0.1837
Pvalue > α ; We fail to reject the null and conclude that the GPA does not differ.
At α = 0.01 ; the result is insignificant
Standard equation: (x-h)^2 + (y-k)^2 = r^2
Here, (0-[-6])^2 + (0-[-8])^2 = r^2
Find r: 36 + 64 = 100, so r = 10
Then the desired equation is (x+6)^2 + (y+8)^2 = 10^2
Answer:
Yes
Step-by-step explanation:
The formula for area of a triangle is A = (1/2)bh,
For the first triangle we can leave it in general terms, so it's area is
A = (1/2)bh, depending on what b and h are, but it doesn't matter here...
The second triangle has base that is twice the other triangles base. Bases being multiples of each other is the definition of being proportional so the bases are proportional, an the area of the second triangle is
A = (1/2)(2b)h, which simplifies to
A = bh
Comparing the 2 areas, you can see that one has a multiplier of (1/2), so their areas are proportional
x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
<u>Explanation:</u>
We know
(x+y)ⁿ = ∑ ⁿCₐxⁿ⁻ᵃyᵃ
and ⁿCₐ = n! / ( a! ) . ( n-a )!
So,
(x+6)⁸ = ⁸C₀x⁸ + ⁸C₁(x)⁸⁻¹(6)¹ + ⁸C₂(x)⁸⁻²(6)² + ⁸C₃(x)⁸⁻³(6)³ + .......+ ⁸C₈(x)⁸⁻⁸(6)⁸
= ₓ⁸ + 8x⁷ₓ 6 + 28x⁶ₓ 36 + 56x⁵ₓ 216 + 70x⁴ₓ 1296 + 56x³ₓ 7776 + 28x²ₓ 46656 + 8x . 279936 + 1679616
= x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
Thus, the expansion of ( x+6)⁸ using binomial theorm is
x⁸ + 48x⁷ + 1008x⁶ + 12096x⁵ + 90720x⁴ + 435456x³ + 1306368x² + 2239488x + 1679616
