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Substance A decomposes at a rate proportional to the amount of A present. It is found that 1414 lb of A will reduce to 77 lb in 4.24.2 hr. After how long will there be only 1 lb​ left?

Use direct substitution to verify that the function

is a solution to the differential equation

a. Substitute the function into the left-hand side of the differential equation and enter your result in the answerbox provided below.

b. Substitute the function into the right-hand side of the differential equation and enter your result in the answer box provided below.

c. Are the two sides equal? No

Yes

For each of the scenarios, determine if the ionic strength of the solution would increase, decrease, or not change. Ignore any ffects caused by the change in volume. Ifra solution of

were added to a solution of KOH , the ionic strength of the KOH solution would not change. decrease. increase. If a dilute solution of KOH were added to a solution of is formed), the ionic strength of the

solution would

( 5 points) A cable that weighs 1.3 pounds per foot is used to lift 840 pounds of coal up a mineshaft that is 766 feet deep. Find how much work was done. Your answer must include the correct units. (You may enter lbf or lb*ft for

.) Work =

_ is best described as people's tendency to avoid an undertaking because they expect to be criticized and humiliated if they are not successful.

7.6 A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data are presented here.56.1 57 .0 53.9 50.2 54.2 47 .9 78.1 60.2 47 .4 68.845.5 63.3 59.7 74.3 61.4 58.7 61.2 64.7 64.3 48.257 .7 72.1 72.0 67 .6 47 .6 65.9 72.3 55.7 55.0 75.262.8 47 .0 48.1 62.9 64.0 80.6 51.2 53.7 53.3 58.368.2 69.5 51.8 68.8 63.8 61.8 59.3 63.6 54.7 59.9 a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses? b. Estimate the standard deviation in the speeds of the vehicles traveling on the interstate using a 95% confidence interval. c. Do the data indicate that the standard deviation in vehicle speeds exceeds 10 mph? Use a 5 .05 in reaching your conclusion. d. To what population can the inferences obtained in parts (b) and (c) be validly applied?

A 2-year-old boy presents with painless rectal bleeding and a history of intermittent abdominal pain. linaging reveals a blind outpouching in the ileum coetairing alt layers of the bowel wall. What is the most likely diagnosis? Answers: A-D A Hirschsprung disease B Intussusception Meckel diverticulum D Volvulus

Sicphen has a tense, difficult relationship with his parents bocause they do not support the way he has chosen to live his life. Due to this lack of support, Siephen socks oat a therapist. If this therapist ascribes to Carl Roger's homanistic approach, how will he ragbet coenecting the condlict caused by Stephen's fractured relationahip with his parents? He will provide Stephes with unconditional positive rogand to resolve the self-discrepancy be fiels. responaes. He will motivate Siephen to correct the relarionchip oirl bie parents so that he will be able so gain self-discrepancy. He will akk Stephen to change his pernonaliry and alope characteristics found ie exceptional people.

1 2

The graph of

is given. Solve the inequalities. Write the solution sets in interval notation if possible. Part 1 of 4 (a)

The solution set is

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 − 32x2 + 2 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down.(Enter your answer using interval notation.)