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2 years ago

Make a conjecture about the rules these patterns follow.

Mathematics

2 answers:

lora16 [44]2 years ago

7 0

Make a conjecture about the rules these patterns follow.

1. 3, 6, 9, 12, 15

2. 9, 3, 1, 1/3, 1/9

3. a, c, e, g, i, k, m

4. 0, 5, -2, 3, -4, 1, -6

5. 4, 8, 16, 32, 64, 128

6, 0.1, 0.01, 0.001, 0.0001

mihalych1998 [28]2 years ago

6 0

Step-by-step explanation:

1) 3, 6, 9, 12, 15

6 - 3 = 9 - 6 = 12 - 9 = 15 - 2
Each term is 3 more than the previous term.

2) 9, 3, 1, 1/3, 1/9

3/9 = 1/3 = (1/3)/1 = (1/9)/(1/3) = 1/3
Each term is 3 times less then the previous term.

3) a, c, e, g, i, k, m

a = 1, c = 3, e = 5, g = 7, i = 9, k = 11, m = 13
Each letter is 2 places right from the previous letter of English alphabet

4) 0, 5, -2, 3, -4, 1, -6

5 - 0 = 5, -2 - 5 = -7
3 - (-2) = 5, -4 - 3 = -7
1 - (-4) = 5, -6 - 1 = - 7
Each odd numbered term is 7 less than the previous term, each even numbered term is 5 more than the previous term

5) 4, 8, 16, 32, 64, 128

8/4 = 16/8 = 32/16 = 64/32 = 128/64 = 2
Each term is twice the previous term

6) 0.1, 0.01, 0.001, 0.0001

0.1/0.01 = 0.01/0.1 = 0.001/0.01 = 0.0001/0.001 = 0.1
Each term is 10 times less than the previous term

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qaws [65]

Answer:

The expected net winnings for the bet are -$1.0526

Step-by-step explanation:

P(x =+$20) = P(Black outcome) = 18/38

P(x =-$20) = P(red outcome) + P(green outcome)

= 18/38 + 2/38 = 20/38

Hence the probability distribution of x = $20 , P(x) = 18/38

x = -$20, P(x) = 20/38

Expected value of the random variable x is given by ;

miu = Summation [xP(x)] = 20(18/38) - 20( 20/38)

= -$1.0526

hence, the expected net winnings for the bet are -$1.0526

This implies that if a player bet on a very large number of games, the player would on the average lose $1.0526 per single bet

8 0

3 years ago

PLEASE HELP ME IM STRUGGLING!!!

Kitty [74]

Answer:

The required answer is $c=7\sqrt{3}$

Therefore the number in green box should be 7.

Step-by-step explanation:

Given:

AB = 7√2

AD = a , BD = b , DC = c , AC = d

∠B = 45°, ∠C = 30°

To Find:

c = ?

Solution:

In Right Angle Triangle ABD Sine identity we have

$\sin B = \dfrac{\textrm{side opposite to angle B}}{Hypotenuse}\\$

Substituting the values we get

$\sin 45 = \dfrac{AD}{AB}= \dfrac{a}{7\sqrt{2}}$

$\dfrac{1}{\sqrt{2}}= \dfrac{a}{7\sqrt{2}}\\\\\therefore a=7$

Now in Triangle ADC Tangent identity we have

$\tan C = \dfrac{\textrm{side opposite to angle C}}{\textrm{side adjacent to angle C}}$

Substituting the values we get

$\tan 30 = \dfrac{AD}{DC}= \dfrac{a}{c}\\\\\dfrac{1}{\sqrt{3}}=\dfrac{7}{c}\\\\\therefore c=7\sqrt{3}$

The required answer is $c=7\sqrt{3}$

8 0

3 years ago

Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plu

Lostsunrise [7]

The domain of the composite function is given as follows:

[–3, 6) ∪ (6, ∞)

<h3>What is the composite function of f(x) and g(x)?</h3>

The composite function of f(x) and g(x) is given as follows:

$(f \circ g)(x) = f(g(x))$

In this problem, the functions are:

$f(x) = \frac{1}{x - 3}$ .

$g(x) = \sqrt{x + 3}$

The composite function is of the given functions f(x) and g(x) is:

$f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}$

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:

$x + 3 \geq 0$

$x \geq -3$

The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:

$\sqrt{x + 3} - 3 \neq 0$

$\sqrt{x + 3} \neq 3$

$(\sqrt{x + 3})^2 \neq 3^2$

$x + 3 \neq 9$

$x \neq 6$

Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:

[–3, 6) ∪ (6, ∞)

More can be learned about composite functions at brainly.com/question/13502804

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2 years ago

Gustavo created a four-part spinner to represent the four prizes that he had an equal chance of winning: a video game system, a

cestrela7 [59]

What data? - I would say that his "data" showed that each prize has a likelihood of 1/4 to be won

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3 years ago

Simon spends £28 over 7 days. Each day, he spends 50p more than the previous day.

garik1379 [7]

This is about conversion of currencies.

He spent £25 on the first day.

We are told he had spent £28 over 7 days.

Each day, he spends 50 pence more than the previous day. This means that;

From conversion,

1 pound = 100 pence

Thus, 50 pence = (50 × 1)/100 = £0.5

If the money he spent on the first day is £x.

On second day, he would have spent a total of; £(x + 0.5)

On third day; x + 0.5 + 0.5= x + 1

On fourth day; x + 1 + 0.5 = x + 1.5

On fifth day; x + 1.5 + 0.5 = x + 2

On sixth day; x + 2 + 0.5 = x + 2.5

On seventh day; x + 2.5 + 0.5 = x + 3

Thus; x + 3 = 28

x = 28 - 3

x = £25

Read more at; brainly.com/question/22398109

3 0

3 years ago