Answer:
30 2/3
Step-by-step explanation:
Answer:
58.6*14=820.4 miles
Step-by-step explanation:
Let us assume the common ratio to be = x
Then
(1 * x) + (4 * x) = 50
x + 4x = 50
5x = 50
x = 50/5
= 10
So from the above deduction, we get the common ratio to be equal to 10
Then
The smallest number = 1 * x
= 1 * 10
= 10
Answer:
a

b

c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is 
The number that complained about dirty or ill-equipped bathrooms is 
The number that complained about loud or distracting diners at other tables is 
Given that the the confidence level is 95% then the level of significance is mathematically represented as


Next we obtain the critical value of
from the normal distribution table , the value is

Considering question a
The sample proportion is mathematically represented as

=> 
=> 
Generally the margin of error is mathematically represented as



The 95% confidence interval is



Considering question b
The sample proportion is mathematically represented as

=> 
=> 
Generally the margin of error is mathematically represented as



The 95% confidence interval is



Answer:
These lines will be perpendicular when m = ³⁄₂
Step-by-step explanation:
Two lines are perpendicular when the product of their gradients equal to -1. So:
m₁ * m₂ = -1
Let's get the first equation in gradient-intercept form (same as equation two).
2x + 3y = 4
3y = -2x + 4
y = -⅔x + ⁴⁄₃
We know the first gradient, and now we can find the gradient of the second line (which when multiplied will result in -1 as these lines are perpendicular). So:
-⅔ * m₂ = -1
m₂ = ³⁄₂