Consider the following game: You reach into a jar of money, and select a single bill at random to keep. There are 9 five-dollar bills, 5 ten-dollar bills, and 3 twenty-dollar bills in the jar. What should the cost of this game be in order for the game to be fair

Recall the double angle identity for cosine:

cos(x) = cos(2×x/2) = 1 - 2 sin²(x/2)

Then the equation can be rewritten as

sin(x/2) + (1 - 2 sin²(x/2)) - 1 = 0

sin(x/2) - 2 sin²(x/2) = 0

sin(x/2) (1 - 2 sin(x/2)) = 0

sin(x/2) = 0   or   1 - 2 sin(x/2) = 0

sin(x/2) = 0   or   sin(x/2) = 1/2

[x/2 = arcsin(0) + 360n °   or   x/2 = 180° - arcsin(0) + 360n °]

… …   or   [x/2 = arcsin(1/2) + 360n °   or   x/2 = 180° - arcsin(1/2) + 360n °]

x/2 = 360n °   or   x/2 = 180° + 360n °

… …   or   x/2 = 30° + 360n °   or   x/2 = 150° + 360n °

x = 720n °   or   x = 360° + 720n °

… …   or   x = 60° + 720n °   or   x = 300° + 720n °

(where n is any integer)

We get only three solutions in 0° ≤ x < 360° :

720×0° = 0°

60° + 720×0° = 60°

300° + 720×0° = 300°

Answer:

B: (0, 60, 300)

Step-by-step explanation:

right on edge

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

Answer:

40% depreciation over the 4 years

10% depreciation per year

Step-by-step explanation:

The number of years between buying and selling is:

2020 - 2016 = 4

4 years

The amount of depreciation in the 4 years is:

AED 1,500 - AED 900 = AED 600

The percent depreciation for the 4 years is:

(1500 - 900)/1500 * 100% = 40%

The percent depreciation per year is:

40%/4 = 10%

Answer:

17 days

Step-by-step explanation:

as you see, 4=2^2

and 8=2^3

so we have a number sequence:

2+2^2+2^3+...+2^n=260000 (1)

multiply (1) by 2 we have:

2^2+2^4 +...+2^(n+1)=520000 (2)

(2) minus (1) we have:

2^(n+1)-2=260000

2^n*2=260002

2^n=130001

and we have 2^17=131072 >130001

so it will take her at least 17 days to buy the car

It will take her about 17 days to buy the car worth 260000 cents

If a student decides she wants to save money to buy a used car that cost $2600 (260,000 cents)

If she saves 2 cents the first day and doubles the amount thereafter, the sequence of savings will be:

2, 4, 8...

This sequence is geometric in nature

In order to determine how long it will take her to save 260,000, we will use the sum of a GP formula expressed as:

[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]

Given the folowing

a = 2

r = 4/2 = 8/4 = 2

Sn = 260,000

Substitute into the formula the given parameters

[tex]260000= \frac{2(2^n-1)}{2-1}\\260000/2=2^n-1\\130000 = 2^n - 1\\2^n = 130000 + 1\\2^n = 130001\\nlog 2=log130001\\n = \frac{log130001}{log2} \\n \approx 17[/tex]

This shows that it will take her about 17 days to buy the car worth 260000 cents

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Answer:

25 cm.

Step-by-step explaination:

Given,

Two sides of a triangle:

a = 7cm

b = 24 cm

To find,

Third side:

c = ?

By Pythagorean Theorem;

a² + b² = c²

[where c is the longest side,hypotenuse]

Putting the value of a and b;

we get,

7² + 24² = c²

49 + 576 = c²

625 = c²

25² = c² (square root)

25 = c

c = 25

Therefore, the length of the third side will be equal to 25 cm.

The lengths of two sides of the right triangle ABC shown in the illustration given

a= 7cm and b= 24cm

> a= 7cm

> b= 24cm

Side c (third side)

Using Pythagoras theorem,

▶️ a² + b² = c

▶️ 7cm ² + 24cm² = c²

▶️ 49cm + 576cm = c²

▶️ 625cm = c²

▶️ 25² = c² (25×25 = 625)

▶️ c = 25

The value of c is 25 cm.

Answer:

There are 60 permutations.

Step-by-step explanation:

Arrangements formula:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

With repetition:

For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:

[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]

In this question:

Apple has 5 letters.

P appears two times. So

[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]

There are 60 permutations.

Answer:

it is 2 te he

Step-by-step explanation:

ONCE THE 5 6 = 7 10 .. ?% =1 x 7 =2 te he

Answer:

máy ...

xác suất để một máy tính bảng có hệ điều hành B sử dụng ổn định trong 2 năm đầu tiên. Add answer

Answer:

BONANA MY NANA

Step-by-step explanation:

Answer:

y = 3/4 x - 3

Step-by-step explanation:

the slope of a line is the factor of x in the equation and is expressed as ratio of y/x : defining how many units y changes, when x changes a certain number of units.

in our graph here we can see that when increasing x from e.g. 0 to 4 (the x-axis intercept point, a change of +4), y changes from -3 to 0 (a change of +3).

so, the slope and factor of x is y/x = 3/4

and for x=0 we get y=-3 as y-axis intercept point.

so, the line equation is

y = 3/4 x - 3

9514 1404 393

Answer:

  π = 2A/r²

Step-by-step explanation:

Multiply by the inverse of the coefficient of π.

  A = π(r²/2)

  π = 2A/r²

Answer:

20 girls

Step-by-step explanation:

boys: girls

3          5

There are 12 boys

12/3 = 4

Multiply each side by 4

boys: girls

3*4      5*4

12         20

Answer:

20 girls

Step-by-step explanation:

Divide 12 by 3 : 12/3 = 4

Multiply 4 by 5 : 4*5 = 20

Answer:

b x=5

Step-by-step explanation:

20x+10=110

20x+10-10=110-10

20x/20=100/20

x=5

Answer:

x=5

Step-by-step explanation:

20x + 10 = 110

Subtract 10 from each side

20x +10-10 = 110-10

20x = 100

divide by 20

20x/20 =100/20

x= 5

Answer:

a) The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Step-by-step explanation:

Question a:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{1892}{\sqrt{25}} = 781[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 14381 - 781 = $13,600

The upper end of the interval is the sample mean added to M. So it is 14381 + 781 = $15,162

The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) Interpret the confidence interval you have computed.

We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Answer: 1.28571428571. This number is infinite.

Step-by-step explanation:

Answer:

1.29 rounded

Step-by-step explanation:

9514 1404 393

Answer:

  20

Step-by-step explanation:

A whole can be divided into two pieces that are each 1/2 of the whole.

 (10 wholes) × (2 pieces per whole) = 20 pieces

Answer:

BELOW

Step-by-step explanation:

242: multiply it by 2 to get 484 and its square root is 22

1280: multiply it by 5  to get 6400 and its square root is 80.

245: multiply it by 5 to get 1225  and its square root is 35.

968: multiply it by 2 to get 1936 and its square root is 44.

1728: multiply it by 3 to get 5184 and its square root is 72

4851: multiply it by 11 to get 53361 and its square root is 231.

HOPE THIS HELPED

Answer:

Neal

Step-by-step explanation:

13.01 < 13.89

Answer:

B) 62 is the answer. I'm sure

Answer:

x = 25

Step-by-step explanation:

x : (x+10) = 5:7

Fractional form

x / x+10 = 5/7

Cross multiply:

x * 7 = (x+10) * 5

7x = 5x + 50

7x - 5x = 5x + 50 - 5x

2x = 50

x = 25

Check:

25 : 25 + 10

25 : 35

25/35 = 5/7

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

13.99 x 2 = 27.98 dollars

now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents

Step-by-step explanation:

Answer:

Each group has 1 fiction book and 2 nonfiction book(s).

Damaris needs to save 10.46% of his net pay each week to purchase the new pair of shoes by the end of his break.

Given:

To find: The percentage of his net pay that Damaris needs to save each week to purchase the shoes by the end of his break

Let us assume that Damaris needs to save x% of his net pay each week to buy the shoes by the end of his break.

Then, savings per week is x% of $167.30, that is,

[tex]\frac{x}{100}\times 167.30[/tex]

Then, his savings for 10 weeks is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Since the summer break is for 10 weeks, Damaris' savings for the entire summer break is,

[tex]10 \times \frac{x}{100}\times 167.30[/tex]

Damaris wants to buy the new pair of shoes by then end of the break. Then, his savings for the entire summer break should equal the cost of the new pair of shoes.

It is given that the cost of the new pair of shoes is $175.

Then, according to the problem,

[tex]10 \times \frac{x}{100}\times 167.30 =175[/tex]

[tex]x=\frac{175\times 100}{10\times167.30}[/tex]

[tex]x=10.460251[/tex]

Rounding to the nearest hundredth, we have,

[tex]x=10.46[/tex]

Thus, Damaris needs to save [tex]10.46[/tex]% of his net pay each week to buy the shoes by the end of his break.

Learn more about percentage here:

https://brainly.com/question/22400644

Answer:

(f + g)(x) = 5x + 5

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x + 3

g(x) = 3x + 2

Step 2: Find

Answer:

a) 0.0749 = 7.49% probability that the student makes more than $15,000.

b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Full-time Ph.D. students receive an average of $12,837 per year.

This means that [tex]\mu = 12837[/tex]

Standard deviation of $1500

This means that [tex]\sigma = 1500[/tex]

a. The student makes more than $15,000.

This is 1 subtracted by the p-value of Z when X = 15000.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{15000 - 12837}{1500}[/tex]

[tex]Z = 1.44[/tex]

[tex]Z = 1.44[/tex] has a p-value of 0.9251.

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the student makes more than $15,000.

b. The student makes between $13,000 and $14,000.

This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.

X = 14000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14000 - 12837}{1500}[/tex]

[tex]Z = 0.775[/tex]

[tex]Z = 0.775[/tex] has a p-value of 0.7708.

X = 13000

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13000 - 12837}{1500}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

0.7708 - 0.5438 = 0.227

0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that:

Mean = $12837, standard deviation = $1500

a) For >15000:

z = (15000 - 12837)/1500 = 1.44

P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749

b) For >13000:

z = (13000 - 12837)/1500 = 0.11

For <14000:

z = (14000 - 12837)/1500 = 0.78

P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Find out more on z score at: https://brainly.com/question/25638875

Hi,

AxB = 0 means A=0. or B=0

so 2 solutions :

4x-3= 0

4x=3

x = 3/4

and x+2 = 0.

x= -2

solutions are : -2 +and 3/4

2 answers

1) -2

2) -3/4

Step-by-step explanation:

4x + 19 + 3x = - 5

4x + 3x + 19 = - 5 collect the like terms

7x + 19 = - 5

7x = - 5 - 19 bring 19 to the right

7x/ 7x = - 24/ 7

x = - 3.4

I hope this answers your question