evaluate the following using identity
1 (a+4) ( a-4)
2. (1/p + 1/q) ( 1/p - 1/q )
3. ( 6x - 5) (6x + 5)​

Part A

p = 0.32 = probability of someone voting by internet

n = 13 = sample size

x = 10 = number of people who voted by internet

Apply the binomial probability formula.

[tex]P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(10) = (_{13} C _{10})*(0.32)^{10}*(1-0.32)^{13-10}\\\\P(10) = (286)*(0.32)^{10}*(0.68)^{3}\\\\P(10) \approx 0.0010124942242\\\\P(10) \approx \textbf{0.00101}\\\\[/tex]

Note: the [tex]_n C_x[/tex] refers to the combination formula.

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Part B

We could apply the binomial theorem for the following values of x: {10,11,12,13}. Then would add up the results.

However, such a task is fairly tedious and it's more efficient to use computer software (or a graphing calculator). Also, there's the element of limited time that you'll need to consider. I showed the steps for part A above because your teacher may have wanted you to list them. Usually it's better to rely on software for that task as well. At the very least, it's useful to have software to check your answer.

Whichever method you use, you should find the following:

The last value isn't exactly 0, but it's so small that it's effectively zero. This is because we only have 5 decimal places to work with.

Add up those four values to get:

[tex]P(x \ge 10) = P(10)+P(11)+P(12)+P(13)\\\\P(x \ge 10) \approx 0.00101+0.00013+0.00001+0\\\\P(x \ge 10) \approx 0.00115\\\\[/tex]

A faster shortcut is to use your calculator's binomCDF function.

This result of 0.00115 is fairly small. The usual distinction we make between whether a probability is small or not is to set up some kind of threshold. This threshold is known as the significance level. By default, it's set to 0.05 unless your teacher specifies otherwise. Another common significance level is 0.01, but it's usually mentioned.

Since 0.00115 is smaller than 0.05, and even 0.01, we consider the probability of getting 10 or more internet voters to be a significant event. It's fairly unusual to get 10 or more people voting by internet in this sample of n = 13 people.

=============================================================

Part C

Like with part B, we could find the binomial probability values for x = {1,2,3,...,11,12,13}. We could add up the values like I did, or use the binomCDF function which is faster.

Another approach is to use the complement of the event "at least 1". If x is some number in the set {0,1,2,..,12,13}, then either [tex]x = 0[/tex] or [tex]x \ge 1[/tex]

From this, we can say

[tex]P(x=0) + P(x \ge 1) = 1\\\\P(x \ge 1) = 1-P(x=0)\\\\P(x \ge 1) \approx 1-0.00665\\\\P(x \ge 1) \approx 0.99335\\\\[/tex]

This then rounds to 0.993

Answer:

34 trophies

Step-by-step explanation:

1348.25/3.95 = 34.24

Answer:

35

Step-by-step explanation:

138.25 / 3.95 will give you 35

Answer:

Using formula to calculate the circumference of wheel:

where

D is the distance bike travel

n is the number of times rotation

C is the circumference of the wheel

As per the statement:

Lin’s bike travels 100 meters when her wheels rotate 55 times.

here, n = 55 rotation and D = 100 meter.

then by definition:

meter

Therefore, the circumference of her wheel is, 1 9/11

Step-by-step explanation:

Answer:

190

Step-by-step explanation:

Attached picture...

Answer:

$1.10

Step-by-step explanation:

5.50 divided by 5, take a way the decimal in order to divide. 550/5=110

55 divided by 5 is 11 just add a zero

Step-by-step explanation:

the group of x friends is SPLITTING the cost of $50. Therefore to find the amount each person pays after the split, you will divide 50 by the amount fo friends (x). Each person is also paying an extra $5 for dessert. Therefore, you will be adding that 5 to everyone's total after splitting.

So the equation you will get is

[tex]a(x) = \frac{50}{x} + 5[/tex]

Answer:

A(x)= (50/x)+5

Step-by-step explanation:

50 bucks divided by the number of people in the group which is X and each must also pay 5 bucks for dessert.

Answer:

im pretty sure the answer is 90°

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find this, lets make a equation.

We have the expression 8b - 27, lets set this equal to -11 and solve:

8b -27 = -11

Now lets solve.

Lets add 27 to both sides to get 8b alone:

8b = 16

Now lets divide by 8:

b = 2

So our answer is 2.

Hope this helps!

Step-by-step explanation:

it has only 1 root

This shows how much you would make per day for both choices.

Total earned in 31 days for $10,000 per day: $310,000

Explanation

$10,000 every day in 31 days.

Total earned in 31 days for penny: 21,474,836.47

Explanation:

Day 1: $0.01

Day 2: $0.02

Day 3: $0.04

Day 4: $0.08

Day 5: $0.16

Day 6: $0.32

Day 7: $0.64

Day 8: $1.28

Day 9: $2.56

Day 10: $5.12

Day 11: $10.24

Day 12: $20.48

Day 13: $40.96

Day 14: $81.92

Day 15: $163.84

Day 16: $327.68

Day 17: $655.36

Day 18: $1,310.72

Day 19: $2,621.44

Day 20: $5,242.88

Day 21: $10,485.76

Day 22: $20,971.52

Day 23: $41,943.04

Day 24: $83,886.08

Day 25: $167,772.16

Day 26: $335,544.32

Day 27: $671,088.64

Day 28: $1,342,177.28

Day 29: $2,684,354.56

Day 30: $5,368,709.12

Day 31: $10,737,418.24

En la reunión semanal había 24 personas.

Los asistentes, hoy, a la reunión semanal de un club social se pueden agrupar por parejas para bailar, por tríos para hacer manualidades, y de 4 en 4 para jugar bingo, y en ninguno de esos casos queda nadie sin grupo, para determinar cuántas personas son si casi llegan a 25 se debe realizar el siguiente cálculo, obteniendo el múltiplo común entre estos números:

Por lo tanto, en la reunión semanal había 24 personas.

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[tex] \huge \bf༆ Answer ༄[/tex]

The distance between points can be solved using Distance formula (similar to Pythagoras theorem)

[tex] \boxed { \sf D = \sqrt{(x2 - x1) {}^{2} + {(y2 - y1) {}^{2} } }}[/tex]

Put the values : -

Distance between the points = 3√13 units

[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

If you are trying to find the line, simply use a graph.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(3x+2)(2x-5)

Brainliest?

Answer:

$97.20

Step-by-step explanation:

97.20 x 0.15 = 14.58

Multiply the total by 15 percent, giving you the $14.58 tip, proving it to be correct.

The responses for the quotient given to the nearest thousandths are

presented in the order of the of the questions as follows;

[tex]Question \ 4) \ \displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}}[/tex]

[tex]Question \ 2) \ \displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

[tex]Question \ 5) \ \displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

[tex]Question \ 3) \ \displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

[tex]Question \ 6) \ \displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

Reasons:

4. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{93}{9}}= \frac{90 + 3}{9} = 10 + \frac{1}{3} = 10.\overline 3[/tex]

Given that we have;

[tex]\displaystyle \frac{1}{3} = 0.\frac{10}{3} =0.3 \frac{10}{3} = 0.3333[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{93}{9} = 10.3333 \approx 10.333}[/tex]

2. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{77}{9}} = \frac{72 + 5}{9} = 8 + \frac{5}{9} = 8. \frac{50}{9} = 8.5\frac{50}{9} = 8.55\frac{50}{9} = 8.555\frac{50}{9} = 8.5555[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{77}{9} = 8.5555 \approx 8.556}[/tex]

5. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{88}{7}} = \frac{85 + 3}{7} = 12 + \frac{3}{7} = 12. \frac{30}{7} = 12.4\frac{20}{7} = 12.42\frac{60}{7} = 12.428\frac{40}{7} = 12.4285\frac{5}{7}[/tex]

[tex]\displaystyle \underline{\frac{88}{7} = 12.4285 \approx 12.429}[/tex]

3. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{81}{7}} = \frac{77 + 4}{7} = 11 + \frac{4}{7} = 11. \frac{40}{7} = 11.5\frac{5}{7} = 11.57\frac{10}{7} = 11.571\frac{30}{7} = 11.5714\frac{20}{7}[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{81}{7} = 11.5714\approx 11.571}[/tex]

6. The division is presented as follows;

[tex]\displaystyle \mathbf{\frac{55}{8}} = \frac{48 + 7}{8} = 6 + \frac{7}{8} = 6. \frac{70}{8} = 6.8\frac{60}{8} = 6.87\frac{40}{8} = 6.875\frac{0}{8} =6.8750[/tex]

Therefore;

[tex]\displaystyle \underline{\frac{55}{8} = 6.8750\approx 6.875}[/tex]

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Answer:

7+18n

might be the answer sorry if I am wrong

Given:

This is a horizontal parabola.

Canonical form of horizontal parabola is:

Focus is:

Directrix is:

Convert the equation:

We got:

Focus is:

Directrix is:

Given:

This is a vertical parabola.

Canonical form of vertical parabola is:

Focus is:

Directrix is:

Convert the equation:

We got:

Focus is:

Directrix is:

Answer:

Step-by-step explanation:

Non linear and varies

Answer:

linear because the pine is not straight it has to be straight to be proportional

Answer:

D

Step-by-step explanation:

We could plug x into the equation but to make it easier we simplify it first

[tex]\frac{1}{x} -\frac{1}{x+1}[/tex]

[tex]-\frac{1}{x+1} + \frac{1}{x}[/tex]

[tex]-\frac{1}{2x+1}[/tex]

x = -1/2

-2-2 = -4

Answer:

m=-5/2 b=2

Step-by-step explanation:

It goes over 2 times ever time it goes down 5 times. and when the y is 0 the x is 2

Answer:

x^2 + 7x- 3/x - 3/x^2 -16

Step-by-step explanation:

Key:  ( ^ ) means exponent

= x^2 + 2x- 3/x -2x^2 + 5x- 3/x^2 -16

= x^2 - 2x^2 + 2x+5x - 3/x- 3/x^2 -16

= x^2 - 2x^2 = -x^2

=  -x^2 + 2x + 5x- 3/x- 3/x^2-16

As you see you add 2x and the 5x and got 7x

= Answer : x^2 + 7x- 3/x - 3/x^2 -16

Answer:

I think the answer is x^2+3x-4/2x-1

Answer:

x = -2

Step-by-step explanation:

g(x) = 5

-2x + 1 = 5

-2x  = 5 - 1

-2x = 4

x = 4/-2

x = -2

_________

[tex]\:[/tex]

g(x) = 5

5 = -2x + 1

5 - 1 = -2x

4 = -2x

x = -2

The smaller the angle subtended by a side, the smaller the length of the

side.

The correct responses are;

Question 1: The list of sides from shortest to longest are;

From the given diagram, we have, the measure of the third angle, ∠O, is

found as follows;

∠O = 180° - 54° - 61° = 65°

Therefore, ∠O = The largest angle

We get;

The longest side is opposite the largest angle, which gives;

The shortest side is the side opposite ∠N (54°)= [tex]\overline{MO}[/tex]

The next shortest side is the side opposite ∠M(61°) = [tex]\overline{NO}[/tex]

The longest side is the side opposite ∠O(65°) = [tex]\overline{MN}[/tex]

a) The time spent training on Tuesday = 60 + 10 = 70 minutes

The time spent training on Thursday = 50 + 30 = 80 minutes

The time spent training on Friday = 45 + 40 = 85 minutes

Therefore, the day the athlete spent the longest total amount of time training is on Friday

b) The time spent training on Monday = 10 + 20 = 30 minutes

The time spent training on Wednesday = 20 + 15 = 35 minutes

Therefore, we get;

30, 35, 70, 80, and 85

The median total number of minutes the athlete spent training each day =

70 minutes

c) The time spent strength training = 20 + 10 + 15 + 30 + 45 = 120

The total number of minutes the athlete spent training = 70 + 80 + 85 + 30

+ 35 = 300

[tex]\mathrm{The \ percentage \ spent \ on \ strength \ training} = \dfrac{120}{300} \times 100 = \underline{40 \%}[/tex]

d) The mean number of minutes spent on strength training is found as follows;

[tex]Mean_{strength} = \dfrac{120}{5} = 24[/tex]

The mean number of minutes spent on aerobic training is found as follows;

[tex]Mean_{aerobic} = \dfrac{10 + 60 + 20 + 50 + 40}{5} = 36[/tex]

[tex]Mean_{strength} +Mean_{aerobic} = 24 + 36 = 60[/tex]

The mean total number of minutes spent training, [tex]Mean_{total}[/tex] = [tex]\dfrac{300}{5}[/tex] = 60

Therefore;

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Answer:

8.4 pontos

Step-by-step explanation:

4.2/5

multiplique o numerador e o denominador por 2

8.4/10

Answer: Each box of candy would contain 13.1 pounds of candy.

Step-by-step explanation:

Divide 65.5 by 5. Hope this helps!