Response:
The probability that a student has a pet, given they do not have any siblings is:
Option: D ( 60%)
Step-by-step breakdown:
Let A represent the situation where a student lacks a sibling.
Let B signify the occurrence that a student has a pet.
Consequently, A∩B refers to the event in which a student is without siblings but possesses a pet.
Let P denote the chance of an event happening.
We need to determine:
P(B|A)
From our knowledge:
From the data provided:
P(A)=0.25
and P(A∩B)=0.15
Thus,
which expressed as a percentage is:
Therefore, the probability is:
60%
Response:
The fence's length is expressed as 6.28x - 150 cm.
Detailed Breakdown:
Assuming the circular pool has a radius (r) of x cm.
As the pool is circular, its circumference represents the length of the fence. Additionally, subtracting the 150 cm for the gate gives us the actual length of the fence.
Length of fence = Circumference of pool – gate's width.
Length of fence = 2 π r – 150
Length of fence = 2 × 3.14 × x – 150
Therefore, the fence length is 6.28x – 150 cm.
Answer:
Step-by-step explanation:
Considering the equation
Sin(5x) = ½
5x = arcSin(½)
5x = 30°
Then,
The general formula for sin is
5θ = n180 + (-1)ⁿθ
Dividing throughout by 5
θ = n•36 + (-1)ⁿ30/5
θ = 36n + (-1)ⁿ6
The solution range is
0<θ<2π which means 0<θ<360
First solution
When n = 0
θ = 36n + (-1)ⁿθ
θ = 0×36 + (-1)^0×6
θ = 6°
When n = 1
θ = 36n + (-1)ⁿ6
θ = 36-6
θ = 30°
When n = 2
θ = 36n + (-1)ⁿ6
θ = 36×2 + 6
θ = 78°
When n =3
θ = 36n + (-1)ⁿ6
θ = 36×3 - 6
θ = 102°
When n=4
θ = 36n + (-1)ⁿ6
θ = 36×4 + 6
θ = 150
When n=5
θ = 36n + (-1)ⁿ6
θ = 36×5 - 6
θ = 174°
When n = 6
θ = 36n+ (-1)ⁿ6
θ = 36×6 + 6
θ = 222°
When n = 7
θ = 36n + (-1)ⁿ6
θ = 36×7 - 6
θ = 246°
When n =8
θ = 36n + (-1)ⁿ6
θ = 36×8 + 6
θ = 294°
When n =9
θ = 36n + (-1)ⁿ6
θ = 36×9 - 6
θ = 318°
When n =10
θ = 36n + (-1)ⁿ6
θ = 36×10 + 6
θ = 366°
When n = 10 surpasses the θ range
Thus, the solutions range from n =0 to n=9
Therefore, there are 10 solutions within the interval 0<θ<2π
Detailed explanation:
Information provided:
Tran possesses a credit card that allows up to $2000 in spending with an APR of 12%.
In the initial month, Tran incurred charges of $450 and settled $150 within that billing period.
The formula to determine the interest that will accrue for Tran in the first month is (0.012)(300)
Here, 0.01 signifies the monthly interest rate.
The 300 reflects the outstanding balance, as Tran charged $450 but only paid back $150.
Answer:
10,088 pounds
Step-by-step explanation:
Provided data
103 bushels of apples
102 bushels of grapes
101 bushels of oranges
With the respective weight per bushel:
Apples = 32 pounds
Grapes = 25 pounds
Oranges = 42 pounds
The total weight can be calculated by summing the products of each type:
Total Weight: 103(32) + 102(25) + 101(42) = 10,088 pounds
