Samira and Sonia each have a bag containing 20 sweets. In each bag, there are 5 red, 6 green and 9 yellow sweets.
(a)
(b)
Samira chooses one sweet at random from her bag.
Write down the probability that she chooses a yellow sweet.
[1] Sonia chooses two sweets at random, without replacement, from her bag.
(i) Show that the probability that she chooses two green sweets is 3 . 38
(ii) Calculate the probability that the sweets she chooses are not both the same colour.

Answers

Answer 1

Step-by-step explanation:

there must be some typos here. but I try to address the right issues.

there is nothing under (a). so, really nothing to answer.

(b)

there are 20 sweets in her bag. 9 if the 20 are yellow.

so, the probability is the ratio of desired possibilities vs. total possibilities.

that is, tada! 9/20

that is the probabilty for Samira to pick a yellow sweet.

[1] (i)

again, 20 sweets to start with.

6 are green.

when she picks the first one, her probability to pick a green one is 6/20 = 3/10 = 0.3

and now, under the assumption that this came true, she picks another sweet.

this time she had only 19 left, and 5 of them are green.

so, this probabilty is 5/19

now both events need to happen for the case we are discussing. there is no overlapping, no ors, ifs and buts. it is just the product of both probabilities.

3/10 × 5/19 = 15/190 = 3/38

I think that is what the description asks for.

(ii)

that probability is

first selection is red and second is not red +

first selection is green and second is not green +

first selection is yellow and second is not yellow

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

so, now assuming up all 3 possibilities ("or" = sum) gives us the general possibility of selecting two different colors

= 0.7316


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Answer:

Step-by-step explanation:

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Oscar bought 15 gallons of water at $1.98 per gallon. He wants to divide this water in bottles of 1/8 gallon each. What is the cost of a bottle of water?

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Answer:

Step-by-step explanation:

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Answers

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What is the recursive formula for this geometric sequence?
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lan
ar = 2n-1.4

Answers

Answer:

a1 = -4

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Step-by-step explanation:

-4, -24, -144, -864, ...

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

• • •

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Answers

Solution :

Given :

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Step-by-step explanation:

Answer with explanation is in the attachment

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Answers

Answer:

The 1 liter bottle is better value

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Answers

Answer:

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James will be able to drive [tex]=4\frac{1}{2}[/tex] days.

What is arithmetic maths ?

Arithmetic is the fundamental of mathematics that includes the operations of numbers like addition, subtraction, multiplication and division.

We have,

James' truck uses gas per day [tex]=8[/tex] gallons

Tank has gas [tex]=36[/tex] gallons

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According to the question,

Number of days James will drive [tex]= \frac{Total\ gas}{Gas\ used\ per\ day}[/tex]

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Hence, we can say that James will be able to drive [tex]=4\frac{1}{2}[/tex] days.

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Answer:

(-3,-6) and (-3,2)

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A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3

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Answers

Answer:

<XYZ is equal to 49°

Step-by-step explanation:

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Answers

Answer:

The numbers you're looking for are 54, 55, and 56.

Step-by-step explanation:

x + (x + 1) + (x + 2) = 5 * (x + 1 - 22)

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x + 1 = 55

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Show Workings.
Question is in attached image.​

Answers

Answer:

A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.

Solution given;

diameter [d]=40cm

centre angle [C]=70°

(a) Find the perpendicular distance be tween the chord and the centre of the circle.

Answer:

we have

the perpendicular distance be tween the chord and the centre of the circle=[P]let

we have

P=d Sin (C/2)

=40*sin (70/2)

=22.9cm

the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.

(b) Using = 3.142, find the length of the minor arc.

Solution given;

minor arc=[tex]\frac{70}{360}*πd=\frac{7}{36}*3.142*40[/tex]

=24.44cm

the length of the minor arc. is 24.44cm.

B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.

If XY = 12 cm, find the area of triangle XYZ.

Solution given:

XY=12cm

XO=15/2cm

XZ=2*15/2=15cm

Now

In right angled triangle XOY [inscribed angle on a diameter is 90°]

By using Pythagoras law

h²=p²+b²

XZ²=XY²+YZ²

15²=12²+YZ²

YZ²=15²-12²

YZ=[tex]\sqrt{81}=9cm[/tex]

:.

base=9cm

perpendicular=12cm

Now

Area of triangle XYZ=½*perpendicular*base

=½*12*9=54cm²

the area of triangle XYZ is 54cm².

Answer:

Question 1

a)

d = 40 cm ⇒ r = 20 cm

Let the perpendicular distance is x.

Connecting the center with  the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.

From the given we get:

x/20 = cos 35°x = 20 cos 35°x = 16.383 cm (rounded)

b)

The minor arc is 70° and r = 20

The length of the arc is:

s = 2πr*70/360° = 2*3.142*20*7/36 = 24.437 cm (rounded)Question 2

Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.

r = 15/2 cm ⇒ XZ = d = 2r = 2*15/2 = 15 cm

Find the missing side, using Pythagorean:

[tex]YZ = \sqrt{XZ^2 - XY^2} = \sqrt{15^2-12^2} = \sqrt{81} = 9[/tex]

The area of the triangle:

A = 1/2*XY*YZ = 1/2*12*9 = 54 cm²

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Step-by-step explanation:

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