Answer:
For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
= 2 (g(x)) + 3
= 2( -x 2 + 1 ) + 3
= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)
Step-by-step explanation:
We know that
The MAD is <span>the mean absolute deviation of the data
step 1
</span><span>To find the mean absolute deviation of the data, start by finding the mean of the data set.
</span><span>Find the sum of the data values, and divide the sum by the number of data values
</span>sum of the data values=[130+150+190+100+175+120+165+140+180+190]
sum of the data values=1540
number of data=10
Mean=1540/10-----> 154
step 2
<span>Find the absolute value of the difference between each data value and the mean: |data value – mean|.
</span> |130 – 154|=24
|150 – 154|=4
|190 – 154|=44
|100 – 154|=54
|175 – 154|=21
|120 – 154|=34
|165 – 154|=11
|140 – 154|=14
|180 – 154|=26
|190 – 154|=44
step 3
<span>Find the sum of the absolute values of the differences.
</span>=[24+4+44+54+21+34+11+14+26+44]------> 276
step 4
<span>Divide the sum of the absolute values of the differences by the number of data values.
</span>276/10-----> 27.6
the answer is
27.6
Equate real part and imaginary part:
LHS:
real part -- 12
imaginary part -- 5y
RHS:
real part = 4x
imaginary part = 25
Equating::
12 = 4x
x = 12/4
x = 3
Again:
5y = 25
y = 25/5
y = 5
So,
x = 3
y = 5
10 degrees Celsius is 50 degrees Fahrenheit.
The equation for C to F is below.
C(9/5)+32= F
Multiply C by 1.8 (or 9/5) then add 32.
10(9/5)+32= 50 F
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


