Answer:
Step-by-step explanation:
Assuming a fair die is rolled.
- The sample space comprises 1, 2, 3, 4, 5, 6, with all results being equally probable.
Let X represent the collection of all outcomes. Let A represent a specific outcome.
<pThus, the probability of event A occurring is:
Considering that the set of all possible outcomes for a singular die roll is:
Notably,
Here,
since 8 is not included in the sample space. Therefore, rolling an 8 is impossible within the defined outcomes.
<pThis leads to the conclusion that the probability is zero.
In other terms,
<pAs a result,
Answer: £164.50
Reducing 175 by 6% results in 164.5.
The absolute change is:
164.5 - 175 = -10.5
Step-by-step explanation:
The calculation is as follows:
175 - Percentage decrease =
175 - (6% × 175) =
175 - 6% of 175 =
(1 - 0.06) × 175 =
0.94 × 175 =
94 ÷ 100 × 175 =
94 × 175 divided by 100 =
16,450 ÷ 100 =
164.5
So, the final amount is £164.50
Answer:
y=4x+7.75; continuous
Step-by-step explanation:
Let’s first establish the equation. Julie requires one segment of yarn measuring 7.75 inches: that's already known.
y = 7.75
Now, for the four pieces of yarn, each will be of equal length x. If she wants them to measure 1 inch, she'd need 4 inches of yarn. Therefore, the calculation would be:
y = 7.75 + 4x
Now, is this graph discrete or continuous? Continuous indicates there's a smooth line without gaps, while discrete has interruptions or spaces. In this scenario, x is continuous, as Julie can cut the yarn to any size for the four pieces. She is not limited to whole numbers; each piece could be, for instance, 2.5 inches or 3.1415 inches.
The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.
An airplane flying at a speed of 950 kilometers per hour would take 0.0010526 hours to travel 1.00 kilometer.
