8 Three friends, Cleopatra, Dalila and Ebony go shopping.
The money they each have is in the ratio
Cleopatra : Dalila : Ebony = 5:7:8.
Cleopatra has $17.
(a) How many dollars do they have in total?
(b) Dalila spends $12 on a hat.
How many dollars does she have left?
(CIE Paper 1, Nov 2005)

Total number of parts = 5 + 7 + 8 = 20

Let the sum of the money with them be = x

Cleopatra has =

= 5/20 of x = $17

= 5/20x = 17

= 1/4x = 17

= 1x = 17 × 4 ( transposing ÷4 from LHS to RHS changes ÷4 to ×4 )

= x = 68

Therefore , they have $68 in total .

Total number of parts = 5 + 7 + 8 = 20

Parts with Dalila = 7/20

Money with Dalila =

= 7/20 of 68

= 7/20 × 68/1

= 476/20

= 23.8

Dalila has $23.8 with her .

Money she spends on a hat = $12

Money left with her =

= 23.8 - 12

= 11.8

Therefore , Dalila has $11.8 left with her , after she buys a hat .

Solution to the problems in the comment box :-

Ratio of cement to sand to aggregate to water = 2:5:8:1

Total parts = 2 + 5 + 8 + 1 = 16 parts

Number of parts for aggregate = 8/16

Then the aggregate needed by Bobbie =

= 8/16 × 1.2

= 1/2 × 1.2

= 1.2 as a fraction will be 6/5

= 1/2 × 6/5

= 6/10

6/10 as a decimal = 0.6

Therefore , Bobbie needs 0.6 cube of meter .

Cement : sand : aggregate : water = 2:5:8:1

Total parts = 16

Number of parts for cement = 5/16

Let the quantity of concrete be = x

Then ,

Cement =

= 5/16 of x

= 5/16x = 0.25 meter cube

= x = 0.25 × 16/5

= x = 25/100 × 16/5

= x = 1/4 × 16/5

= x = 16/20

= x = 4/5

4/5 as decimal = 80/100 = 0.08

Cement needed by Eddie = 0.08 cubic meter .

Quantity of water Eddie will need =

= 1/16 × 0.08

= 1/16 × 80/100

= 1/16 × 8/10

= 8/60

= 0.13

Water needed by Eddie = 0.13 cubic meter .

Quantity of aggregate needed by Eddie =

= 8/16 × 80/100

= 1/2 × 8/10

= 8/20

= 40/100

= 0.04

Aggregate needed by Eddie = 0.04 cubic meter .

Quantity of sand Eddie will need =

= 5/16 × 80/100

= 5/16 × 8/10

= 40/160

= 0.25

Quantity of sand needed by Eddie = 0.25 cubic meter .

Therefore , Eddie will need 0.25 cubic meter of sand , 0.04 cubic meter of aggregate ,0.13 cubic meter of water along with 0.25 cubic meter of cement to make concrete .

When water and aggregate has been added the quantity of concrete =

= 0.13 + 0.04

= 0.07

Therefore , when water and aggregate has been added the quantity of concrete will be 0.07 cubic meter .

answer: a rhombus has two lines of symmetry that run through one vertex to the one directly across it. unlike a square, planes through the center of each edge of a rhombus do not yield mirrored sides.

step-by-step explanation:

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: