# What is the value of x? Enter your answer in the box. x=  Question
Right triangles and trigonometry What is the value of x? Enter your answer in the box. x=  2021-01-24
By the Pythagorean theorem (for right triangles): $$c^{2}= a^{2} + b^{2}$$ where a and b represent the lenght of the legs and c represents the lenght of hypotenuse. $$a = 7, b = 24, c = x$$ $$x^{2} = 7^{2} + 24^{2} = 49 + 576 = 625$$ Next, we obtain the value of x by taking the square root: $$x = \sqrt x^{2} = \sqrt625=25$$
$$x = 25$$

### Relevant Questions Is statistical inference intuitive to babies? In other words, are babies able to generalize from sample to population? In this study,1 8-month-old infants watched someone draw a sample of five balls from an opaque box. Each sample consisted of four balls of one color (red or white) and one ball of the other color. After observing the sample, the side of the box was lifted so the infants could see all of the balls inside (the population). Some boxes had an “expected” population, with balls in the same color proportions as the sample, while other boxes had an “unexpected” population, with balls in the opposite color proportion from the sample. Babies looked at the unexpected populations for an average of 9.9 seconds (sd = 4.5 seconds) and the expected populations for an average of 7.5 seconds (sd = 4.2 seconds). The sample size in each group was 20, and you may assume the data in each group are reasonably normally distributed. Is this convincing evidence that babies look longer at the unexpected population, suggesting that they make inferences about the population from the sample? Let group 1 and group 2 be the time spent looking at the unexpected and expected populations, respectively. A) Calculate the relevant sample statistic. Enter the exact answer. Sample statistic: _____ B) Calculate the t-statistic. Round your answer to two decimal places. t-statistic = ___________ C) Find the p-value. Round your answer to three decimal places. p-value = If $$\displaystyle{m}∠{1}+{m}∠{5}={100}$$, find the measure of $$\displaystyle∠{2}$$. $$\displaystyle{A}{\left(\frac{{1}}{{3}}\right)}{2}{\left(\frac{{4}}{{7}}\right)}={\left(\frac{{8}}{{7}}\right)}{8}$$
$$\displaystyle{m}∠{2}=□=\frac{{1}}{{9}}$$ Type the correct answer, then press Enter. Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank
A . $$\displaystyle{\tan{{\left({\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}$$
B . $$\displaystyle{\cos{{\left({a}{r}{\sin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}$$
C. $$\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}{\sin{{\left({2}{\arcsin{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}$$
D. $$\displaystyle{\sin{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}$$
E. $$\displaystyle{\cos{{\left({\arctan{{\left({\frac{{{x}}}{{{8}}}}\right)}}}\right)}}}$$ Find the values of the variables in each right triangle.  Find the values of the variables in each right triangle.  Unusual points Each of the four scatterplots that follow shows a cluster of points and one “stray” point. For each, answer these questions:
1) In what way is the point unusual? Does it have high leverage, a large residual, or both?
2) Do you think that point is an influential point?
3) If that point were removed, would the correlation be- come stronger or weaker? Explain.
4) If that point were removed, would the slope of the re- gression line increase or decrease? Explain  Straight Lines Graph the straight lines in Exercises 1–3.
Then find the change in y for a one-unit change in x, find the point at which the line crosses the y-axis, and calculate the value of y when x 52.5.
1. y x 5 1 2.0 0.5
2. y x 5 1 40 36.2
3. y x 5 25 6
Scatterplots For the scatterplots in Exercises 5 describe the pattern that you see. How strong is the pattern? Do you see any outliers or clusters?  In this exercise, you will use the correlation and regression applet to create scatter plots with 10 points that have a correlation close to 0.7. The lesson here is that many models may have the same correlation. Always compile your data before trusting correlations. (a) Stop after adding the first two points. What is the value of correlation? Label the words of this 30,60,90 right triangle $$\displaystyle{S}{L},{2}{S}{L},{\quad\text{and}\quad}{S}{L}\sqrt{{2}}$$  Label the words of this 30,60,90 right triangle $$\displaystyle{S}{L},{2}{S}{L},{\quad\text{and}\quad}{S}{L}\sqrt{{2}}$$ 