HELP 100 PointsIf △NMK ≅ △TRP, then answer the following questions:
a. Complete the congruence statement: △MNK ≅ △_______
b. What side is congruent to ≅ ______
c. Solve for x. _____

Simplify the expression- 3 - 5/6 / 5/2

What is the transformations of f(x) = - 2lx - 3| + 1 from the parent function f(x) =|x|

( 5n 3 + n 4 - 5 ) - ( -5 - 6n 3 - 4n 4 ) A) 5n 4 + 11n 3 B) 5n 4 + 11n 3 + 2 C) 4n 4 + 11n 3 + 2 D) 4n 4 + 19n 3 + 2

Right or leftMost people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13–70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​




The symbol π represents the long-run proportion of all the couples that lean their heads
leftright

while kissing.



Which of the following best describes the null hypothesis and the alternative hypothesis using π?



null: π ≠ 0.5, alternative: π > 0.5
null: π = 0.5, alternative: π < 0.5
null: π = 0.5, alternative: π > 0.5
null: π ≠ 0.5, alternative: π < 0.5



Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275)
p^=

the absolute tolerance is +/-0.001




Determine the standardized statistic from the data. ​(Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)
z =

the absolute tolerance is +/-0.02




Interpret the meaning of the standardized statistic.



The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50.
The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50.



Select the best conclusion that you would draw about the null and alternate hypotheses.



We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%.
We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%.

A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the number of points the athlete scored was 1.2 standard deviations below his mean. How many points below average was this value?

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.