Topic E: Expressing Operations in Algebraic Form

I NEED THE ANSWER AS SOON AS POSSIBLE

Answer:

I'm not sure if this is right, but I got 3/4. (0.75 as a decimal) I hope this helps!

Step-by-step explanation:

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Explanation:

H = heads

T = tails

Something like HHT means we get two heads in a row at first, followed by one tail. The order matters. Since there are 2 sides per coin, and 3 coins, this leads to 2^3 = 8 different possible ways to flip three coins.

Those 8 outcomes are:

Again the order matters.

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Now let's define the following events

There's only one way to get three heads, and that's HHH. So P(A) = 1/8.

There are three ways to get exactly two heads. Those three ways are: HHT, HTH, THH. This means P(B) = 3/8.

From those two probabilities, we then know that P(C) = 4/8 = 1/2 since there are 1+3 = 4 ways to get two or more heads, leaving 8-4 = 4 ways to get the other situations.

Now let's define function notation V(A) to mean "the net value of event A occurring". It's the number of points you receive if event A happens. We are given the following info:

From here, multiply the probability values with their corresponding net values

Finally, add up those results to get the expected value: 0.5+0.75+(-0.5) = 0.75

Each time a turn happens, we expect on average to get 0.75 points

Imagine a scenario where you play the game 10,000 times. If you record the result of each turn and then compute the arithmetic mean, you should get somewhere close to 0.75; it likely wont be 0.75 exactly due to the nature of theoretical probability and empirical probability not being perfectly aligned. However, due to the law of large numbers, the two should be very close when you do a large number of trials.

Because we're dealing with averages, it is possible to get a decimal value as the answer even though the point values of events A,B,C are integers.

Answer:

2n +14 = 30 I can use inverse operations and solve for n.

Step-by-step explanation:

twice means 2 so twice a number,n, means 2 times n thus 2n.

sum means add  so, 2n + 14

is means equal so 2n + 14 = 30

If you solve it you will find n = 8

Answer:

rectangle

7x + 4 = 36/2

7x + 4 = 18

7x = 14

x = 2

there is no y

Answer:

The radius is 20 units.

Step-by-step explanation:

(r)^2 + 21^2 = (r+9)^2

r^2 + 441 = r^2 + 18r + 81

360 - 18r = 0

360 = 18r

20 = r

-3,4. i adding this cause this answer needs atleast 20 characters

Answer:

2500 ( nearest hundred)

Step-by-step explanation:

Given that :

Number of stickers collected per week = 89

Number of weeks for which stickers were being collected = 28

To obtain the total number of stickers collected, we take the product of the number of weeks for which the stickers were beug vcilled and the number of stickers collected per week

The number of stickers collected :

89 * 28 = 2492

2492 = 2500 ( nearest hundred)

Answer:

There are 30240 possible codes.

Step-by-step explanation:

For the first digit, there are 10 number choices possible:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

For the second digit, 9 number choices, because one of the digits cannot be repeated.

For the third, 8 number choices, because two of the digits cannot be repeated.

For the fourth, 7 number choices, because three of the digits cannot be repeated.

For the fifth, 6 number choices because four of the digits cannot be repeated.

Now multiply all the numbers, and you can see that there are 10*9*8*7*6, or 30240 codes possible.

Answer:

1. 0.0469 (4.d.p)

2. 0.05

Step-by-step explanation:

1. First we'll find the probability of drawing a blue marble.

P = (No. favourable events)/(Total events)

In this case it's:

P = (No. blue marbles)/(Total Marbles)

Therefore P(Blue) = 4/16 = 0.25

Now we find the probability of drawing a yellow marble:

The total number will be the same because the blue marble will have been put back.

P(Yellow) = 3/16 = 0.1875

Now, since we are calculating the probability of both happening we multiply together the two individual probabilities to get the combined probability of both:

0.25 x 0.1875 = 0.0469 (4.d.p)

2. The probability of drawing a blue marble is still the same so we can keep that: P(Blue) = 0.25

But this time, the marble is not replaced. This means that the total number of marbles has changed when drawing the yellow marble:

P(Yellow) = 3/15 = 0.2

Now we multiply them together again to find the combined probability of both happening:

0.25 x 0.2 = 0.05

Hope this helped!

Answer:

His paycheck was $62.

Step-by-step explanation:

3/4 x = 46.5

x = 46.5 * 4/3

x = 62

Equation: 3/4 x = 46.5

Solution: x = 62

Answer:

Mean = 109.4

Step-by-step explanation:

Mean = (Sum of all values)/(Number of values)

Mean = (100 + 121 + 105 + 113 + 108)/(5)

Mean = (547)/5

Mean = 109.4

Answer:

109

Step-by-step explanation:

Mean is just finding the average of the data set.

100+121+105+113+108=547, first add up all the numbers

547/5=109.4, then divide that sum by the amount of numbers in the set

Answer:

f(3)= 33

Step-by-step explanation:

hello :

f(x) =8x+9

put x = 3    you have : f(3) =8(3)+9 = 24 + 9 =33

Answer: 9 L

Step-by-step explanation:

Given

The dimension of the rectangular container is [tex]40\times 30\times 25\ cm^3[/tex]

It is filled with [tex]\frac{3}{5}[/tex] of the height

Water present in the container

[tex]\Rightarrow 40\times 30\times 25\times \dfrac{3}{5}\\\\\Rightarrow 18000\ cm^3[/tex]

Also, [tex]1\ L=1000\ cm^3[/tex]

[tex]\therefore 18,000\ cm^3=18\ L[/tex]

Now, half of the water is poured out

So, half is left

[tex]\Rightarrow \dfrac{18}{2}=9\ L[/tex]

Thus, 9 L of water is left in the container

Answer:

x=8.17

Step-by-step explanation:

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Answer:

x = 8.17

Step-by-step explanation:

We will be using pythagoras theorem:

[tex]a^{2} + b^{2} = c^{2}[/tex]

=> [tex]4.25^{2} + x^{2} = 9.21^{2}[/tex]

=> [tex]x^{2}[/tex] = 84.8241 - 18.0625 = 66.7616

=> x = [tex]\sqrt{66.7616}[/tex] = 8.17077719.. = 8.17 (3 s.f)

Answer:

area = 432 ft²

Step-by-step explanation:

area = 1/2(B1 + B2)(H)

area = 1/2(20 + 16)(24) = 432 ft²

Answer: 17/19

Step-by-step explanation:

Number of red rocks = 6

Number of orange rock = 1

Number of blue rocks = 4

Number of white rock = 1

Number of yellow rocks = 7

Total number of rocks = 19

Probability of not getting a orange the first time will be (1 - 1/19) = 18/19.

Probability of not getting an orange the second time will be: (1 - 1/18) = 17/18

Probability of not getting an orange on both occasion will be:

= 18/19 × 17/18

= 17/19

Answer:

[tex]3(x - 6) = - 12 \\ 3x - 18 = - 12 \\ 3x = - 12 + 18 \\ 3x = 6 \\ x = \frac{6}{3} \\ x = 2[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

Answer:

x = 2

3 (x-6) = -12

3x - 18 = -12

3x - 18 + 18 = -12 + 18

3x = 6

3x/3 = 6/3

Hence,  x= 2

Step-by-step explanation:

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hope it helps u

Answer:

a) (0,5)

Step-by-step explanation:

Answer:

$1,020.71

Step-by-step explanation:

Solving the equation:

A = 1000(1 + (0.07 × 0.29589)) = 1020.7123

A = $1,020.71

Answer: n= -9

Step-by-step explanation:

5n-7=-52

5n = -52+7

5n=-45 (divide both sides)

n= -9

Answer:

it would be 18 in 1 minute

Answer:

1) The function is decreasing exponentially at a rate of 15% every decade.

2) The function is increasing exponentially at a rate of 20% every year.

Step-by-step explanation:

1) 1–0.85 = 0.15

0.15 x 100 = 15%

2) 1.2–1 = 0.2

0.2 x 100 = 20%

Answer:

No ;

Step-by-step explanation:

Given ;

s2 = 10 ; n2 = 10 ; s1 = 12 ; n1 = 12

Hypothesis :

H0 : σ1² = σ2²

H1 : σ1² ≠ σ2²

The test statistic :

Ftest = s1² / s2² = 12² / 10² = 144 / 100 = 1.44

The Pvalue using the Pvalue from Ftest calculator :

Numerator df = 12 - 1 = 11

Denominator df = 10 - 1 = 9

Pvalue = 0.2969

At α = 0.1

If Pvalue > α ; Fail to reject H0

0.2969 > 0.1 ; Hence, we fail to reject the Null

Hence, we cannot conclude that variation exists

Answer:

1114 ft

Step-by-step explanation:

tan 22°=450/d

==>d=450/tan 22°=1113.7890... ≈1114 (ft)

Answer:

p + 2c = 3.25 Start with these two equations

3p + 4c = 7.25

p = -2c + 3.25 Solve for one variable

3(-2c +3.25) + 4c = 7.25 Substitute

-6c + 9.75 + 4c = 7.25

-2c = -2

c = 1

p + 2(1) = 3.25 Substitute

p + 2 = 3.25

p = 1.25

A bag of chips costs $1

A pickle costs $1.25

Step-by-step explanation:

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