Use the Distributive Property to rewrite each of the expressions below. Then simplify.
2 answers:
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Answer:
The calculated value z = 9.4451 > 1.96 at 5% level of significance.
Null hypothesis is rejected at 5% level of significance
yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance
Step-by-step explanation:
<u>Explanation</u>:-
<u>Step:- (1)</u>
The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart.
A student asked a random sample of teachers in 2018 and found 165 had smart-phones, 80 had a cell phone
The first sample proportion
A student asked a random sample of teachers in 2018 and found 165 had smart-phones,5 had no cell phone
The second sample proportion
<u>Step :-(ii)</u>
<u>Null hypothesis :H₀</u>: Assume that there is no difference in the distribution of types of cell phones for the teachers in 2018
H₀ : p₁ = p₂
<u>Alternative hypothesis :H₁</u>
H₁ : p₁ ≠ p₂
<u>Level of significance : ∝=0.05</u>
The tabulated value z=1.96
<u>Step:-(iii)</u>
The test statistic
where
q = 1-p
In given data n₁ = n₂ = n
on calculation , we get p = 0.2655
q =1-p = 1-0.2655
q = 0.7345
Z = 9.4451
The calculated value z = 9.4451 > 1.96 at 5% level of significance.
<u>Conclusion:</u>-
Null hypothesis is rejected at 5% level of significance
yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance
Answer:
1) Function; Linear Function (y=x)
2) Function; Exponential Function (y=bˣ)
3) Not a function.
Step-by-step explanation:
So, let's go through each table of values. I'm also going to graph them (see attached graphs) because it will make things simpler and provide a visual.
First, also recall what the definition of a function is. A function is a function if and only if an x only has <em>one</em> distinct y-value. No x can have two or more y-values. For instance, (1,2) and (1,3) is <em>not</em> a function between the x repeats. So, let's go through the choices:
1)
We have the table as shown. Let's plot the points. See TABLE 1:
First, there are no repeating x-values, so we can be sure that this is indeed a function.
Looking at the graph, we can see that this resembles a linear graph. So, the parent function of this is a line.
The parent function of a line is:
So, table 1 is associated with a linear function.
2)
Let's again plot the points. See TABLE 2.
Again, there are no repeating x-values, so this is also a function.
Looking at the graph, this resembles an exponential function. The function increases slowly at first but starts increasing increasingly fast. The parent function is thus an exponential function.
So, table 2 is associated with an exponential function.
3)
First, notice how all the x-coordinates are repeating. And since they do <em>not</em> equal the same thing, this is not a function.
Table 3 is not a function and so has no corresponding family function.
