6) Stacie was solving the triangle below. Can you find her mistake?
1 answer:
Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
Solution is supposed to be
Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.
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This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The value of x is 6.
<h3>What are directly proportional and inversely proportional relationships?</h3>Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
p ∝ q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Let the days to set up with entries be represented by a, while the number of concerts is represented by b. Now, It is known that the days to set up with entries and the number of the concert are in a relationship. Therefore, we can write the relationship as,
a ∝ b
a = k b
Now, if we substitute the values from the first row, we will get,
1.5 = k × 1
1.5 = k
Thus, the value of k is 1.5.
Now, if we substitute the entries from the 4th row, we will get,
a = k × b
x = 1.5 × 4
x = 6
Hence, the value of x is 6.
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Answer:
90% confidence interval for the true percent of students that are registered voters is [0.56 , 0.64].
Step-by-step explanation:
We are given that for a class project, a political science student at a large university wants to estimate the percent of students that are registered voters.
He surveys 500 students and finds that 300 are registered voters.
Firstly, the pivotal quantity for 90% confidence interval for the true proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of students who are registered voters =
= 0.60
n = sample of students = 500
p = true percent of students
<em>Here for constructing 90% confidence interval we have used One-sample z proportion test statistics.</em>
So, 90% confidence interval for the true proportion, p is ;
P(-1.6449 < N(0,1) < 1.6449) = 0.90 {As the critical value of z at 5%
level of significance are -1.6449 & 1.6449}
P(-1.6449 < < 1.6449) = 0.90
P( <
<
) = 0.90
P( < p <
) = 0.90
<u>90% confidence interval for p</u> =[ ,
]
= [ ,
]
= [0.56 , 0.64]
Therefore, 90% confidence interval for the true percent of students that are registered voters is [0.56 , 0.64].
Interpretation of the above confidence interval is that we are 90% confident that the true percent of students that are registered voters will lie between 0.56 and 0.64.