Use complete sentences to describe the domain of the cosine function.

The length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

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.

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x â’ 1 , y = 0, x = 5; about the x-axis v = sketch the region. sketch the solid, and a typical disk or washer.