Given right triangle ABC. To the nearest degree, find the measure of angle B.
1 answer:
Answer:
Step-by-step explanation:
We have the length of AC which is opposite angle B; we also have the length of the hypotenuse. We will use trig here to solve for angle B. The sin ratio is the one that fits.
sin(B) = side opposite / hypotenuse:
so
sin(B) = .9411764706
Now we will use the 2nd button on our calculators. This will give us the missing angle value. Press 2nd then sin and you will see on your screen:
Enter that decimal after the open parenthesis and hit "enter" to get
B = 70.25 or 70°
You might be interested in
- Slope Formula:
So remember that <u>perpendicular lines have slopes that are negative reciprocals to each other</u> and <u>parallel lines have the same slope.</u> To find out if they are either parallel or perpendicular, plug the pair of points into the slope formula to find their slopes:
Since these slopes aren't the same nor are they negative reciprocals to each other, <u>the lines are neither parallel nor perpendicular.</u>
Answer:
We conclude that there is no difference in the proportion of cockroaches that died on each surface.
Step-by-step explanation:
We are given that a study investigated the persistence of this pesticide on various types of surfaces.
After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On the glass, 18 cockroaches died, while on plasterboard, 25 died.
<em>Let </em><em> = proportion of cockroaches that died on glass surface.</em>
<em /><em> = proportion of cockroaches that died on plasterboard surface.</em>
So, Null Hypothesis, :
= 0 {means that there is no difference in the proportion of cockroaches that died on each surface}
Alternate Hypothesis, :
0 {means that there is a significant difference in the proportion of cockroaches that died on each surface}
The test statistics that would be used here <u>Two-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of cockroaches that died on glass surface =
= 0.50
= sample proportion of cockroaches that died on plasterboard surface =
= 0.694
= sample of cockroaches on glass surface = 36
= sample of cockroaches on plasterboard surface = 36
So, <u><em>test statistics</em></u> =
= -1.712
The value of z test statistics is -1.712.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that there is no difference in the proportion of cockroaches that died on each surface.