Answer:
![P(x \le -3) =0.30](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29%20%3D0.30)
Step-by-step explanation:
Given
The attached probability distribution of x
Required
Find ![P(x \le -3)](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29)
To do this, we consider all values of x less than or equal to-3.
So, we have:
![P(x \le -3) =P(x=-5) + P(x = -3)](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29%20%3DP%28x%3D-5%29%20%2B%20P%28x%20%3D%20-3%29)
From the table:
![P(x=-5) = 0.17](https://tex.z-dn.net/?f=P%28x%3D-5%29%20%3D%200.17)
![P(x = -3) = 0.13](https://tex.z-dn.net/?f=P%28x%20%3D%20-3%29%20%3D%200.13)
So, the equation becomes
![P(x \le -3) =P(x=-5) + P(x = -3)](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29%20%3DP%28x%3D-5%29%20%2B%20P%28x%20%3D%20-3%29)
![P(x \le -3) =0.17 + 0.13](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29%20%3D0.17%20%2B%200.13)
![P(x \le -3) =0.30](https://tex.z-dn.net/?f=P%28x%20%5Cle%20-3%29%20%3D0.30)
Answer:
x=17/3, y=10/3. (17/3, 10/3).
Step-by-step explanation:
4x-5y=6
2x+5y=-28
-----------------
4x-5y=6
-2(2x+5y)=-2(-28)
--------------------------
4x-5y=6
-4x-10y=56
------------------
-15y=-50
15y=50
y=50/15
y=10/3
4x-5(10/3)=6
4x-50/3=6
4x=6+50/3
4x=18/3+50/3
4x=68/3
x=(68/3)/4
x=(68/3)(1/4)=68/12=17/3
Answer:
Type of angle - Obtuse
Key information - 180° - 82° = 98° (missing angle)
Equation -
![y=17.2](https://tex.z-dn.net/?f=y%3D17.2)
Step-by-step explanation:
Let's solve for the missing angle first! 180° - 82° = 98°. 180 represents the total among the angles so we use 180 degrees.
then use the statement to solve for y and make it equal to 98°
![(5y+12)=98](https://tex.z-dn.net/?f=%285y%2B12%29%3D98)
= -12 subtract 12 from both sides
= 86 Now solve for y by dividing 86 ÷ 5
y = 17.2
If
is a factor of a polynomial
then,
is its root.
So
is a root of ![x^3-19x-p](https://tex.z-dn.net/?f=x%5E3-19x-p)
![(-2)^3-19\cdot(-2)-p=0\\-8+38-p=0\\p=30](https://tex.z-dn.net/?f=%28-2%29%5E3-19%5Ccdot%28-2%29-p%3D0%5C%5C-8%2B38-p%3D0%5C%5Cp%3D30)
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