Answer:
x = -4
Step-by-step explanation:
Solve for x:
(5 x)/4 = x/2 - 3
Put each term in x/2 - 3 over the common denominator 2: x/2 - 3 = x/2 - 6/2:
(5 x)/4 = x/2 - 6/2
x/2 - 6/2 = (x - 6)/2:
(5 x)/4 = (x - 6)/2
Multiply both sides by 4:
(4×5 x)/4 = (4 (x - 6))/2
(4×5 x)/4 = 4/4×5 x = 5 x:
5 x = (4 (x - 6))/2
4/2 = (2×2)/2 = 2:
5 x = 2 (x - 6)
Expand out terms of the right hand side:
5 x = 2 x - 12
Subtract 2 x from both sides:
5 x - 2 x = (2 x - 2 x) - 12
5 x - 2 x = 3 x:
3 x = (2 x - 2 x) - 12
2 x - 2 x = 0:
3 x = -12
Divide both sides of 3 x = -12 by 3:
(3 x)/3 = (-12)/3
3/3 = 1:
x = (-12)/3
The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:
Answer: x = -4
Answer:
Step-by-step explanation:
Hello!
a.
The objective is to study the relationship between the shape of an ibuprofen tablet and its dissolution time.
For these two independent samples of tablets from different shapes where taken and their dissolution times measured:
Sample 1: Disk.shaped tablets
n₁= 6
X[bar]₁= 255.8
S₁= 8.22
Sample 2: Oval-shaped tablets
n₂=8
X[bar]₂= 270.74
S₂= 11.90
Assuming that the population variances are equal and both samples come from normal distributions you need to test if the average dissolution time of the disk-shaped tablets is less than the average dissolution time of the oval-shaped tablets, symbolically:
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
α: 0.05
Considering the given information about both populations, the statistic to use for this test is a Student t for independent samples with pooled sample variance:
Sa²= 110.76
Sa= 10.52
This test is one-tailed to the left, meaning that you will reject the null hypothesis to small values of t, the p-value has the same direction and you can calculate it as:
P(t₁₂≤-2.63)= 0.0110
Since the p-value= 0.0110 is less than the significance level α: 0.05, the decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average dissolution time of the disk-shaped ibuprofen tablets is less than the average dissolution time of the oval-shaped ibuprofen tablets.
b.
(X[bar]₁-X[bar]₂)+Sa
(255.8-270.74)+ 10.52*
(-∞;-4.815)
I hope it helps!
Answer:
≈ 5.8 units
Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (5, 5) and (x₂, y₂ ) = (10, 2)
d =
=
=
= ≈ 5.8 units ( to the nearest tenth )
Answer: area of square 64 cm^2 minus area of circle pir^2
4^2 =16pi cm^2
64-16pi=64-50.64= 13 + 36/100 or 13.36
Unchecked
Step-by-step explanation: