I estimate that a total of 50 students participated in the survey
and 18 expressed a desire to learn Spanish.
Solution:
Reflect the parent function across the x-axis and then shift it 8 units left.
Step-by-step clarification:
The function in question is

The parent function can be described as

Due to the negative multiplier applied to the transformed function, a reflection occurs along the x-axis.
As the value 8 is added within the square root, it indicates a horizontal shift of 8 units left.
Therefore, to accurately graph the given function, reflect the parent function over the x-axis and translate it to the left by 8 units.
Answer: the likelihood of a randomly selected tire lasting exactly 47,500 miles is 0.067
Step-by-step explanation:
Since the expected lifespan of this tire brand follows a normal distribution, we will use the normal distribution formula:
z = (x - µ)/σ
Where
x = lifespan of the tire in miles.
µ = mean
σ = standard deviation
The given figures include,
µ = 40000 miles
σ = 5000 miles
The probability that a tire will last precisely 47,500 miles
P(x = 47500)
For x = 47500,
z = (40000 - 47500) / 5000 = -1.5
According to the standard normal distribution table, the probability associated with this z score is 0.067
The function

represents a parabola positioned at the vertex (5, 3).
Attached here is the graph depicting this function.
Answer:
Step-by-step explanation:
Delivery charge = $7.50
Cost per pizza = $14
Budgeted total = $60
7.50 + 14p < 60
First, subtract 7.50 from both sides
14p < 60 - 7.50
14p < 52.50
Now divide both sides by 14
p < 52.50 / 14
p < 3.75
Each pizza consists of 8 slices
Therefore, the total number of slices she can buy = 3.75 × 8
= 30 slices