-π/2 < arctan(x) < π/2
So cos(π/2) < cos(arctan(x)) < cos(0)
0 < cos(arctan(x)) < 1
Answer:
x=-1.83
Step-by-step explanation:
1-2x=4(x+3)
1-2x=4x+12
-2x=4x+12-1
-2x=4x+11
-2x-4x=11
-6x=11
x=11÷-6
x=-1.83
Answer:
Null hypothesis:
Alternative hypothesis:
A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.
Solution to the problem
On this case we want to test if the proportion of children diagnosed with Autism Spectrum Disorder (ASD) is different from 0.0147, so the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).
Answer:
A: 1/22
B: 3/44
C: 41/44
D: 3/11
Step-by-step explanation:
Hope this help : )
Answer:
0.833
Step-by-step explanation:
1. locate which vertical column of the graph we are referring to:
2. calculate the total number of trials student 7 did:
- if in 5 trials the tack landed point-up, and in 1 trial the tack did not land point-up, the total number of trials is 6
- 5 + 1 = 6
3. refer back to the question:
- the question states: "what is the experimental probability that the tack lands point-up"
4. interpret the graph:
- of the 6 trials student 7 underwent, the graph tells us that 5 landed point-up.
- therefore the experimental probability of a tack landing point up is 5/6 (in 5 out of the 6 trials, the tack landed point-up)
5. converting from fraction to decimal:
- all the given answers are given in decimal form, whilst our current answer (5/6) is in fraction form.
- to convert to decimal form, simply divide the top number by the bottom number
- 5 ÷ 6 = 0.833
therefore, the experimental probability that the tack will land point-up, is 0.833
hope this helps :)