For unorganized data, median is the middle value when the numbers are arranged in ascending order.
Let's proceed ~
In ascending order :
12, 13, 23, 26, 26, 35, 38, 44, 47
So, for given data... median is 26
Measure of the following
1 answer:
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Answer:
a. θ = 30°
b. μ = √3 / 15 ≈ 0.115
Step-by-step explanation:
Draw a free body diagram for each scenario (see attached figure). The body has four forces acting on it:
- Weight pulling down
- Normal force perpendicular to the incline
- Applied force parallel up the incline
- Friction force parallel to the incline
Remember that friction opposes the direction of motion. So when the body is sliding up, friction points down the incline. And when the body is sliding down, friction points up the incline.
Now apply Newton's second law to each scenario, first in the normal direction, then in the parallel direction.
For sliding up, sum of the forces normal to the incline:
∑F = ma
N − mg cos θ = 0
N = mg cos θ
Sum of the forces parallel to the incline:
∑F = ma
P₁ − f − mg sin θ = 0
P₁ − Nμ − mg sin θ = 0
Substituting the expression for normal force:
P₁ − mgμ cos θ − mg sin θ = 0
Now for sliding down, sum of the forces normal to the incline:
∑F = ma
N − mg cos θ = 0
N = mg cos θ
And sum of the forces parallel to the incline:
∑F = ma
P₂ + f − mg sin θ = 0
P₂ + Nμ − mg sin θ = 0
Substituting the expression for normal force:
P₂ + mgμ cos θ − mg sin θ = 0
We know that P₁ = 6 kg.wt, P₂ = 4 kg.wt, and mg = 10 kg.wt.
So we have two equations and two unknowns (μ and θ):
P₁ − mgμ cos θ − mg sin θ = 0
P₂ + mgμ cos θ − mg sin θ = 0
Let's start by adding the equations together:
P₁ + P₂ − 2 mg sin θ = 0
P₁ + P₂ = 2 mg sin θ
sin θ = (P₁ + P₂) / (2 mg)
Plugging in the values:
sin θ = (6 + 4) / (2 × 10)
sin θ = 1/2
θ = 30°
Now we can plug this into either equation and find μ.
P₁ − mgμ cos θ − mg sin θ = 0
6 − (10 cos 30°) μ − 10 sin 30° = 0
6 − 5√3 μ − 5 = 0
1 = 5√3 μ
μ = √3 / 15
μ ≈ 0.115
Question is Incomplete; Complete question is given below;
Mr. Lin hires a moving company to help transport furniture to his new home. The bill from the moving company is $400. Mr. Lin includes a 15% tip with his payment.
What is Mr. Lin’s total payment, including tip?
Answer:
Mr. Lin made a Total payment of $460 including the Tip.
Step-by-step explanation:
Given:
Total bill = $400
Percentile amount paid in tip = 15%
We need to find the total payment, including tip.
Solution:
First we will find the amount paid in Tip.
amount paid in Tip can be calculated by Percentile amount paid in tip multiplied by Total bill and then divided 100.
amount paid in Tip =
Now we know that;
Total payment made by Mr.Lin is equal to sum of Total bill and amount paid in Tip.
framing in equation form we get;
Total payment made by Mr.Lin =
Hence Mr. Lin made a Total payment of $460 including the Tip.