Assuming a maximum rental duration of 8 days, if we apply this to the equation, Happy Harry's Rentals costs $500, while Smilin' Sam's charges $600. Therefore, for the 7th and 8th days, Happy Harry's Rentals is a better option, while Smilin' Sam's is preferable for the first six days.
The result is 10/117. We have three distinct letters and four unique non-zero digits. For letters, we have 26 options from A to Z. For digits, there are 9 choices from 1 to 9. As all selections must be distinct, we find the total number of codes as 26 × 25 × 24 × 9 × 8 × 7 × 6. For the specified code, we focus on the combinations with 5 vowels and 4 even digits, leading to a calculation of 5 × 25 × 24 × 8 × 7 × 6 × 4. Probability can thus be expressed as the ratio of these outcomes, yielding: 5 × 25 × 24 × 8 × 7 × 6 × 4 divided by 26 × 25 × 24 × 9 × 8 × 7 × 6.
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
Please take a look at the graph provided.
It’s stated that Ben is snacking on some pretzels along with a complete small pack of mustard. Our task is to determine the equation that illustrates the correlation between the quantity of pretzels Ben consumes, denoted as x, and the overall sodium content in his snack, y.
To start, we’ll calculate the slope of the line using the points (1,80) and (5,140).
Next, we will apply the point-slope formula 
, where the slope m is what we calculated, and the coordinates of point 
lie on the line.
We will input along with the coordinates of point (1,80) into the previously mentioned formula.
Consequently, the equation signifies the relationship between the number of pretzels that Ben eats and the total sodium present in his snack.
