Carl is trying to determine the length of segment MN using the Pythagorean theorem. On a coordinate plane, line M N has points (negative 3, 1) and (4, negative 4).

Step 1: Find the vertex of a possible right triangle. V(4, 1)

Step 2: Find the leg lengths of the right triangle. NV = 7, MV = 5

Step 3: Substitute the values into the Pythagorean theorem. 7 squared + 5 squared = c squared

Step 4: Solve for c. 7 squared + 5 squared = c squared. 49 + 25 = c squared. 74 = c squared. StartRoot 74 EndRoot = c.

Which best describes the accuracy of Carl’s solution?

Carl’s work and answer are both entirely correct.

Carl’s answer is correct, but he incorrectly labeled the leg lengths in step 2.

Carl’s work and answer are incorrect. He choose a vertex, V, that does not make a right triangle with MN.

Carl’s work and answer are incorrect. He substituted and solved incorrectly.

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?