Answer:
= 28.5 units^2
Step-by-step explanation:
To find the area of the figure, we can add the area of the rectangle plus the area of the triangle
Area of the rectangle is length times width
The length is 8 and the width is 3
A = 8*3 = 24 units ^2
The area of a triangle is 1/2 the base times the height
The base is 3 and the height is 3
A = 1/2 (3*3)
A = 9/2
A = 4.5 units^2
The total area of the figure is the sum
A = 24 +4.5
= 28.5 units^2
Answer:
there is no sufficient evidence to prove that viscosity is not 3000
Step-by-step explanation:
Let's state the hypothesis.
Null hypothesis; H0: μ = 3000
Alternative hypothesis; μ ≠ 3000
The sample mean is;
x = (2781 + 2900 + 3013 + 2856 + 2888)/5 = 2887.6
Standard deviation σ = √variance = √[(2781 - 2887.6)² + (2900 - 2887.6)² + (3013 - 2887.6)² + (2856 - 2887.6)² + (2888 - 2887.6)²)(1/(5 - 1))]
σ = √((1/4)(11363.56 + 153.76 + 15725.16 + 998.56 + 0.16)
σ = 84.026
Formula for test statistic is given as;
t = (x - μ)/σ
t = (2887.6 - 3000)/84.026
t = -1.338
From online p-value calculator from t value attached, using DF = 5 - 1 = 4, two tail and a significance level of 0.05,we have;
The p-value is 0.251896.
This is greater than the significance level of 0.05.
Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to prove that viscosity is not 3000
Answer: False
Step-by-step explanation:
Answer: 0.44mm
Step-by-step explanation:
In this problem we are asked for the height of a single playing chip. We know the volume of a cylinder is 25120 mm^3.
V=πr²h
25120=πr²h
The problem also gives the diameter of the case: 40mm.
To find radius, you divide the diameter in half.
d=2r
40=2r
r=20
With the radius, we can add that to the volume equation.
25120=(20)^2h
25120=400πh
All we have left is to find the height.
h=25120/(400π)
h≈20mm
Now that we know the height, we can find the height of a single chip. The problem states about 50 chips can fit in a case. To find the height of a single chip, you would divide 20 by 50.
20mm/50 chips=0.4mm/chip.
Question # 2 Solution
Answer:
The truth table for the Boolean expression ¬a ∨ ¬b ↔ c is given below.
Step-by-step explanation:
As the given Boolean expression is
¬a ∨ ¬b ↔ c
<em />
<em>Truth Table:</em>
a b c ¬a ¬b ¬a ∨ ¬b ¬a ∨ ¬b ↔ c
0 0 0 1 1 1 0
0 0 1 1 1 1 1
0 1 0 1 0 1 0
0 1 1 1 0 1 1
1 0 0 0 1 1 0
1 0 1 0 1 1 1
1 1 0 0 0 0 1
1 1 1 0 0 0 0
Question # 4 Solution
Answer:
The truth table to determine whether ¬(k ∧ L) = ¬k ∧ ¬L is given below.
Step-by-step explanation:
Lets construct the truth table to determine whether ¬(k ∧ L) = ¬k ∧ ¬L is true or not.
<em />
<em>Truth Table:</em>
k L ¬k ¬L (k ∧ L) ¬(k ∧ L) ¬k ∧ ¬L
0 0 1 1 0 1 1
0 1 1 0 0 1 0
1 0 0 1 0 1 0
1 1 0 0 1 0 0
From the truth table, it is clear that ¬(k ∧ L) is not equal to ¬k ∧ ¬L
Therefore, ¬(k ∧ L) ≠ ¬k ∧ ¬L
<em>Keywords: truth table, logical reasoning</em>
<em>
Learn more about logical reasoning and truth table from brainly.com/question/12971991</em>
<em>
#learnwithBrainly</em>