Clare says, “We know that if we dilate a cube by a factor of `k`, the cube’s volume is multiplied by `k^{3}`. It seems like that must apply to all solids, but I’m not sure how to prove it.” Elena says, “Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by `k^{2}` when we dilate a figure by `k` applies to all shapes, not just rectangles. Can we do something similar here?”

Use Elena’s line of reasoning to argue that for any solid, if it’s dilated by a factor of `k`, the volume is multiplied by `k^{3}`.

Lucy and donavan measured the length of the school garden. lucys measurement is 11.3m and donavans measurement is 113 cm. could both be correct? explain

Which line is parallel to the line that passes through the points (2, –5) and (–4, 1) a. y=-x+5 b. y=-2/3x+3 c. y=2/3x-2 d. y=x+5

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.