Answer:
The 50th term is 288.
Step-by-step explanation:
A sequence that each term is related with the prior by a sum of a constant ratio is called a arithmetic progression, the sequence in this problem is one of those. In order to calculate the nth term of a setence like that we need to use the following formula:
an = a1 + (n-1)*r
Where an is the nth term, a1 is the first term, n is the position of the term in the sequence and r is the ratio between the numbers. In this case:
a50 = -6 + (50 - 1)*6
a50 = -6 + 49*6
a50 = -6 + 294
a50 = 288
The 50th term is 288.
Answer: P(22 ≤ x ≤ 29) = 0.703
Step-by-step explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703
Jaime is incorrect, the angle does not depend on the radius of the circles.
<h3>Is Jaime correct?</h3>
Remember that an angle that defines an arc on a circle, does not depend on the radius of the circle.
So, if we have an angle with a measure of π/3 radians in a circle with a radius of 3 inches and an angle with a measure of π/3 radians in a circle with a radius of 6 inches, these two angles are exactly the same thing.
The radius of the circle only has an impact on the length of the arc defined by the angle.
So Jaime is clearly incorrect.
If you want to learn more about angles:
brainly.com/question/17972372
#SPJ1
If two similar triangles have side lengths 3cm and 7cm then we can determine that the scale factor for the lengths is: 7/3
Now, we have to work out the area scale factor !
This is simple, since area is given in cm² then all we have to do is square our original scale factor!
So,
7/3² = 49/9
So, we can say that the ratio of the area would be:
x : 49/9x
Hope this helps! <3
