MATHEMATICS HIGH SCHOOL

1 poinA catering assistant mixes 4 parts of cordial to 12 parts of water. Express
this as a ratio in its simplest form.*
1:1/3
O 1:2
O 1:3
O 14

Answers

Answer 1
Answer: 1:3

4 goes into 12 three times.

4/12 = 1/3 = 1:3

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complete the t-table

Answers

Answer:

See attached

Step-by-step explanation:

The answer is on the picture attached

Tables on the top filled in

The error on the bottom is the columns mixed up, just need to exchange x with y

A card is drawn at random from a standard pack of playing cards. Then a fair coin is flipped. What is the probability of selecting a 10 and the coin landing on tails

Answers

Answer:

1/26

Step-by-step explanation:

There are 4 packs in a regular card deck. Hence, we have four 10s.

The probability of selecting a 10 is thus 4/52 = 1/13

The probability of getting the coin to land on its tail is 1/2.

The probability of getting a 10 and a tail flip = 1/2 * 1/13 = 1/26

Ex 2.68. find the stationary points on the curve y=3x^4 -4x³ -12x² +1 and determine whether they are maximum or minimum turning points

Answers

y=3x^4 -4x^3 -12x^2 +1\ny'=12x^3-12x^2-24x\n\n12x^3-12x^2-24x=0\n12x(x^2-x-2)=0\n12x(x^2+x-2x-2)=0\n12x(x(x+1)-2(x+1))=0\n12x(x-2)(x+1)=0\nx=0 \vee x=2 \vee x=-1\n\n\forall{x\in(-\infty,-1)\cup(0,2)}\ y'<0\Rightarrow y\searrow\n\forall{x\in(-1,0)\cup(2,\infty)}\ y'>0\Rightarrow y\nearrow\n\Downarrow\ny(0)=1=y_(max)\ny(2)=3\cdot2^4-4\cdot2^3-12\cdot2^2+1=48-32-48=-32=y_(min)
y(-1)=3\cdot(-1)^4-4\cdot(-1)^3-12\cdot(-1)^2+1=3+4-12+1=-4=\n=y_(min)

What.is the product 2x(x- 4)

Answers

Answer:

2x(x−4)

=(2x)(x+−4)

=(2x)(x)+(2x)(−4)

=2x^2−8x

Answer:

2x²-8x

Step-by-step explanation:

you first multiply the 2x by the thus 2x times x or 1x giving you 2x² and positive 2x times -4 will give you -8x

What is the highest common factor of 12 and 49?

Answers

12|2\n.\ 6|2\n.\ 3|3\n.\ 1|\n==========\n49|7\n.\ 7|7\n.\ 1|\n==========\n\nHCF(12;\ 49)=1
Factors of 12 . . . . . 1, 2, 3, 4, 6, 12

Factors of 49 . . . . . 1, 7, 49

Common factors . . . 1

Highest common factor . . . 1

Which property justifies the following statement if a=b then a/d=b/d?

Answers

Division property of equality.
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