An injection-molded part is likely to be obtained from any one of 8 cavities on a mold. Round your answers to three decimal plac
1 answer:
Answer:
(b) The probability is 0.375
(c) The probability is 0.750
Step-by-step explanation:
The probability is calculated as a division between the number of options that satisfy a condition and the total number of options.
For part (b), we have 8 cavities or options for obtain the part but we want to obtain the part from cavity 1, 2 or 3, so we have 3 options. Therefore, the probability is:
For part (c), We have 8 cavities or options for obtain the part and we want to obtain the part from any cavity except cavity 3 or 4, so we have 6 options. These options are cavity 1, cavity 2, cavity 5, cavity 6, cavity 7 and cavity 8. Then, the probability is:
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1. Ans: Option (B) 
Explanation:
Given:
Take the common out:
=>
Hence: =>![[tex]-6x^4](https://tex.z-dn.net/?f=%5Btex%5D-6x%5E4)
[/tex] (Option B)
2. Ans: Option (D)
Explanation:
Given:
Take the common term(s) out:
=>
Hence: => (Option D)
3. Ans: Option (B)
<span> quadratic trinomial
Explanation:
</span>Given:
The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.
=>
=> (Option B)
4. Ans: Option (C)
Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:
</span>Common guppies:
<span>
Endler's guppies: </span>
(add both)
-----------------------------------------------------------------
Total number:
-----------------------------------------------------------------
Hence the ans is Option(C)
5. Ans: Option (D)
Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x =
Now the area of the circular fountain:
Area of the Circular Fountain =
Since, r=6x
Therefore,
Area of the Circular Fountain =
Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard = - 
=> Final area of the Yard =
(Option D)
6. Ans: Option (A)
Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x =
Now the area of the stadium:
Area of the stadium = 1x * 4x =
Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot= -
=> Final area of the lot = (Option A)
-i
Explanation:
Given:
Take the common out:
=>
Hence: =>
2. Ans: Option (D)
Explanation:
Given:
Take the common term(s) out:
=>
Hence: =>
3. Ans: Option (B)
Explanation:
</span>Given:
The standard form of polynomial function must have the highest powered value at the start, then the second highest and so on.
=>
=>
4. Ans: Option (C)
Explanation:
In order to find the total number of C<span>ommon and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:
</span>Common guppies:
Endler's guppies: </span>
(add both)
-----------------------------------------------------------------
Total number:
-----------------------------------------------------------------
Hence the ans is Option(C)
5. Ans: Option (D)
Explanation:
First let's find the total area of the yard:
Total Area of the Yard = 14x * 19x =
Now the area of the circular fountain:
Area of the Circular Fountain =
Since, r=6x
Therefore,
Area of the Circular Fountain =
Now the final Area of the yard would be:
Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain
Final area of the Yard =
=> Final area of the Yard =
6. Ans: Option (A)
Explanation:
First let's find the total area of the lot:
Total Area of the lot= 6x * 10x =
Now the area of the stadium:
Area of the stadium = 1x * 4x =
Now the final Area of the lot would be:
Final area of the lot= Total Area of the lot - Area of the stadium
Final area of the lot=
=> Final area of the lot =
-i
Answer:
Given: ABCD is a parallelogram.
Prove: Angle A and B are supplementary and C and D are supplementary.
That is, m∠A + m∠B = 180° and m∠C + m∠D = 180°
Statement Reason
1. ABCD is a parallelogram 1. Given
2.m∠A=m∠C and m∠B=m∠D 2. Definition of parallelogram.
3.m∠A+m∠B+m∠C+m∠D=360° 3. Definition of quadrilateral
4. m∠A+m∠B+m∠A+m∠B=360° 4. By substitution
⇒ 2( m∠A + m∠B ) = 360°
⇒ m∠A + m∠B = 180°
Similarly, m∠C + m∠D = 180°
5.∠A and ∠C are supplementary, 5. Def. of Supplementary
∠ B and ∠D are supplementary
