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marusya05 [52]
3 years ago
9

Let p and q be rational. Prove that p+q is rational

Mathematics
1 answer:
Contact [7]3 years ago
4 0

Let p and q rational numbers (what does it means?), then, p and q coul be written as

p = \frac{a}{b},a, b \in \mathbb{Z}, b \neq 0\\\\q = \frac{c}{d}, c,d \in \mathbb{Z}, d \neq 0

then,

p +q = \frac{a}{b} + \frac{c}{d} = \frac{ad +bc}{bd}

and we know that ad+bc is an integer, so, p +q is a rational number.

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You find 13,406,190 pennies which is $134,061.90 and weighs 118,222.45 lbs. Now assume a movie ticket costs $9.00, how many movi
inn [45]

Answer:

14895.6

Step-by-step explanation:

4 0
3 years ago
naveed makes 6.5litres of soup,correst to the nearest 0.5 litre he serves portions of his soup in 330ml cups correct to the near
Karolina [17]

Answer:

Number of Cups = 19

Step-by-step explanation:

Given

Size of Soup = 6.5 litres

SIze of cup = 330 ml

Required

Number of Cups.

First, it'll be assumed that the size of cups are uniform (the same).

The number of cups needed is calculated by dividing the size of soup by the size of the cup;

Number of Cup = Size of Soup/Size of Cup

Number of Cup = 6.5 litres/ 330 ml

<em>Convert units;</em>

<em>1 litres = 1000 ml</em>

<em>So,</em>

<em>6.5 litres = 6.5 * 1,000 ml</em>

<em>6.5 litres = 6,500 ml</em>

<em></em>

So,

Number of Cups = 6500 ml/330 ml

Number of Cups = 19.696969697

From the solution above, Naveed will definitely be able to serve 19 cups. The remaining fractional part won't fill a cup;

Hence, Number of Cups = 19

3 0
3 years ago
What is -14 divided by -2
Svetradugi [14.3K]
A negative divided by a negative is a positive, so -14/-2 = 7
Hope this helped!
5 0
4 years ago
Read 2 more answers
A famous Premier-league footballer was quoted on Match of the Day to have a goal-scoring statistic of 0.36
stepan [7]

Answer:

13a.\  The \ probability\ of \ scoring\ a\  goal\  in\  a\  game\  is\  0.36\\\\b. 3 \ games

14.

a. \ \£90\\b. \ 26 \ weeks\\c. \ \£4,860

15. This is not possible since p(yellow)=0.10 which is less than the stated 0.35

Step-by-step explanation:

13 a. -A goal-scoring statistic is the probability of a player scoring one goal in any given game played.

-A 0.36 goal scoring statistic means that the player has a 0.36 or 36% chance of scoring a goal in any game that he is involved in.

b. To determine the number of games it takes to score a whole goal, we divide the probability by 1 goal:

Games=\frac{1 \ game}{p(goal)}\\\\=\frac{1}{0.36}\\\\=2.778\approx 3

Hence, it takes approximately 3 games to score a full goal.

14.-The cost of a GCSE retake is £600 and attracts a 15% deposit

#The 15% equivalent in actual pounds is calculated by multiplying the percentage by the total cost as:

C_g=0.15\times 600\\\\=\£90

Hence, the 15%  deposit amount equals £90

b.#The student pays the balance in a £20 per week scheme,the total number of weeks is calculated as:

t=\frac{Balance}{Rate}\\\\=\frac{600-90}{20}\\\\=\frac{510}{20}\\\\=25.5\approx 26

Hence, it takes 26 weeks to clear the balance.

c. Given that 10% is the equivalent of £450

-We divide this amount by 10% to get the 100% equivalent

#We know that 10%=0.10

100\%=\frac{540}{0.1}\\\\=\£5400

#Alternatively, 100% divided by 10% is 10. Multiply this value by £540:

=540\times 10\\\\=\£5400

We subtract the discount amount for the per-discount price:

Cost=Total -discount\\\\=5400-540\\\\=\£4860

Hence, it will cost £4,860 without the discount.

15. Since we are not given the proportion of colors in the bag, we assume that all the 10 beads have different colors.

-As such, the sample space is 10 and each color has an equal chance of being picked:

P(Each \ Color)=P(Yellow)=\frac{1}{10}\\\\\therefore P(Yellow)

Hence, this is impossible since 0.10<0.35

7 0
4 years ago
Simplify the expression (6^2)^4.
Vlada [557]

Answer:

1679616

Step-by-step explanation:

36^4

7 0
3 years ago
Read 2 more answers
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