Math Answers

Find the perimeter of loop of the curve 3ay²=x²(a-x)

1. The average score in the entrance examination in Mathematics at Sto.

Rosario National High School is 80 with a standard deviation of 10.A

random of 40 students was taken from this year's examinees and

was found to have a mean score of 84.

Is there a significant difference between the known mean and the

sample mean? Test at a= 0.05

Solution :

Step 1. H0: = 80 : There is no significant difference

hypothesized and the sample mean.

H1: "\\neq" 80 :

Step 2. Level of significance. a = 0.05.

Step 3. two tailed test, find the critical value. Zt =

4. Compute the test-statistic value:

5. Step :

6. Conclusion:

. Consider Interest centers on the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is 0.42. Suppose also that the probability that the component survives no longer than 4000 hours is 0.04. Determine the Probability that;

(a) The life of the component is less than or equal to 6000 hours?

(b)The life is greater than 4000 hours? 

According to a genetics theory,a certain cross of guinea pigs will result in red,black, and white offspring in the ratio 8:4:4.Find the probability that among 8 offspring,5 will be red,2 black, and 1 white.

A thermometer is removed from a room where the

temperature is 70° F and is taken outside, where the air

temperature is 10° F. After one-half minute the thermometer reads 50° F. What is the reading of the thermometer at t  1 min? How long will it take for the

thermometer to reach 15° F?

A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 10° F. After one-half minute the thermometer reads 50° F. What is the reading of the thermometer at t  1 min? How long will it take for the thermometer to reach 15° F?

Off-road motorbike racing can be dangerous, especially when it rains. It has been found that it rains during

18% of races. When it does not rain, there is a 5% chance that Dwayne (a rider) will get hurt. However, when it

rains, the chance that he gets hurt increases to 35%. Dwayne has just finished a race and is hurt. What is the

probability that it rained during the race?

The second term of an arithmetic progression is four times the fifth term, and the first term is 10. Find the common difference, and hence the sum of the first 12 terms.

Find the derivatives of each of the following functions:

a. 𝑦 = 5𝑥²+7𝑥−8

b. 𝑓(𝑥) = 7/𝑥⁴

c. 𝑦 = 15/√𝑥

d. 𝑓(𝑥) = 2𝑥^7/2−𝑥^-1/3

e. 𝑦 = (4𝑥²−7𝑥)/𝑥

f. 𝑓(𝑥) = 7𝑥³/√𝑥

Are there any values of p such that p²+48 is equal to -14p?