Final answer:
The correct number in the equation 5.90 - 42 is -36.10. For the quiz probability, the student must calculate the binomial probability of getting 7 out of 10 correct when guessing. To find an actual height from a scale model, set up a proportion and cross-multiply.
Step-by-step explanation:
To determine the number that makes the equation 5.90 - 42 true, we simply perform the subtraction. Subtracting 42 from 5.90 gives us an answer of -36.10.
In regards to the probability question, when a student takes a 10-question true/false quiz and guesses randomly, the probability of each question being correct is 0.5 (since there are two possible answers: true or false). To pass with at least a 70 percent, the student needs to answer at least 7 out of 10 questions correctly. The probability of this is calculated using the binomial probability formula," which accounts for the number of ways to choose the 7 correct answers out of 10 and the likelihood of each combination occurring.
For the proportion problem, given the scale model of 42 inches, you can use a proportion to find the actual height by setting 1.5 inches over 10 feet equal to 42 inches over 'x' feet, and then cross-multiplying to solve for 'x'. Using this method, you can determine the actual height of the building represented by the scale model.