Math Answers

The following are the age of 8 jeepney passengers in a waiting shed: 12, 15, 18, 19, 21, 23, 35, and 40. A sample with size 7 is chosen to ride in the current jeepney. Find the standard error of the sample mean.

The average weight of 52 senior high school students is 50 kg with a standard deviation of 2.5 kg. If 25 students are randomly selected, find the mean, standard deviation, and variance of the corresponding sampling distribution of sample means.

Which of the following sets of polynomials span P2 ?

a. {t²+1, t-1, t²+t}

B. {t²+ 2, 2t²- t+1, t + 2 , t²+t+4}

Let V = set of all 3x1 matrices.

Define

+ to be the matrix addition

⦁ to be the matrix multiplication by a number

We know that V is a vector space. If W [a, b, 1] , a, b element of R then W is a subspace of V.

Let V be the set of all positive real numbers; define + by u+v = uv (+ is ordinary multiplication) and define • by c•v = . Prove that V is a vector space.

the possible values of the number of rainy days in may

The equation for the instantaneous voltage across a discharging capacitor is given by 𝑣 = 𝑉𝑂𝑒 − 𝑡 𝜏 , where 𝑉𝑂 is the initial voltage and 𝜏 is the time constant of the circuit. The tasks are to: a) Draw a graph of voltage against time for 𝑉𝑂 = 12𝑉 and 𝜏 = 2𝑠, between 𝑡 = 0𝑠 and 𝑡 = 10𝑠. b) Calculate the gradient at 𝑡 = 2𝑠 and 𝑡 = 4𝑠. c) Differentiate 𝑣 = 12𝑒 − 𝑡 2 and calculate the value of 𝑑𝑣 𝑑𝑡 at 𝑡 = 2𝑠 and 𝑡 = 4𝑠. d) Compare your answers for part b and part c. e) Calculate the second derivative of the instantaneous voltage ( 𝑑 2 𝑣 𝑑𝑡2 ).

Kagiso wants to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Kagiso to have R40 000 available is

A.

28 quarters.

B.

41 quarters.

C.

40 quarters.

D.

12 quarters.

Kagiso wants to buy a new gaming computer for R40 000. He decides to save by depositing an amount of R400 quarterly into an account earning 16% interest per year, compounded quarterly. The approximate number of quarters it will take Kagiso to have R40 000 available is

Sbusiso needs R150 000 on 17 November 2022 to upgrade his restaurant. On 8 January 2022 he deposited an amount into an account earning 13,45% interest per year, compounded monthly, and being credited on the 1st of every month. If fractional compounding is used for the full term, then the amount that Sbusiso deposited on 8 January 2022 was