Math Homework: Calculations, Problem Solving, and Formula Applications

This document presents a detailed solution to a math homework assignment. The solution covers various mathematical concepts, including calculations involving exponents, roots, and order of operations. It addresses word problems related to time, rates, and proportions, as well as financial calculations involving percentages and VAT. The assignment also includes questions on combinations and formula applications. Each problem is solved step-by-step, providing a clear understanding of the solution process. This homework assignment is a valuable resource for students seeking to understand mathematical concepts and improve their problem-solving skills. The solutions are presented in a clear and concise manner, making it easy for students to follow and learn from the examples. This document is ideal for students looking for extra practice and guidance in mathematics.

Task 1:
a) 1.88
= Step 1: Press 1.8 on calculator
Step 2: Click on Xy function on calculator
Step 3: Press 8
Step 4: Press ‘=’ and the answer is 110.19960576
b) ) 5√243
Step 1: Enter 5
Step 2: Press y√X function
Step 3: Enter 243
Step 4: Press ‘=’ and the answer will be 1.0066451831867605210379005716012
c) 1 / (1+0.07)3
Step 1: Press 1
Step 2: Press ÷
Step 3: Press ((then 1; then +; then 0.07 ; then Xy function; then ); then 3; and finally closing the
bracket with )
Step 4: Press ‘=’, and the answer is 0.81629787689085199458304728895231
d) 2500 x 5-3
Step 1: Press 2500
Step 2: Press ÷
Step 3: Press (; then 5; then Xy function; then 3; and finally press )
Step 4: Press ‘=’, and the answer is 20
e) 34.18 + √79 /0.4375−2.28
Step 1: Press (; then 34.18

Step 2: Press +
Step 3: Press ( ; then √ ; then 79; then ) and finally close bracket with )
Step 4: Press ÷
Step 5: Press (
Step 6: Press 0.4375
Step 5: Press –
Step 6: Press 2.28; and close the bracket by pressing)
Step 7: Press ‘=’; and the answer is 30.205402161066254287270456489476
Task 2
a) £6.38
b) 17 minutes
Task 3
a) 5 people can paint a fence in 3 hours.
1 people can paint same fence in = 5 × 3 = 15 hours
Time taken by 6 people to paint the same fence = 15÷6 = 3.5 hours
b) 12 men can build 100m long road in 5 days
To build 400m which is 4 times greater than 100m; the number of days will also increase by 4
times; thus number of days taken by 12 men to build 400m long road will be = 5 × 4 = 20 days.
Hence, one men can build 400m long road in = 20 × 12 = 240 days
Therefore, time taken by 20 men to build 400m long road will by = 240/20 = 12 days
c)
i) Red 112 liters; and Blue 32 liters
ii) 10 liters

Task 4
a) £13,530
b)
i) VAT = £19
ii) £114
c) 8 units
Task 5
In this situation; combination is applicable;
C (n,r) = n !
r !× ( n−r ) !
Where, C is the number of combinations
n is the total number of objects in the set = 30
r is the number of choosing objects from the set = 5