You flip a fair coin 3 times, and get a different amount of money depending on how many heads you get. • For O heads, you get $0. • For 1 head, you get $2. • For 2 heads, you get $4. Another piece of information is also flashing at you as you stand before the lights: • Overall, across all possible outcomes your expected winnings from the game are $6. 1. (3 points) How much do you get paid if the coin comes up heads 3 times? 2. (3 points) Write down a complete expression for the cumulative probability function for your winnings from the game.

The linear equation on the graph is:

y = x + 3

Here we have a linear equation.

Remember that the general one is y = a*x + b where b is the y-intercept, here we can see that the line intercepts the y-axis at y = 3

y = a*x + 3

And it passes through the point (-3, 0), replacing these values we get:

0 = a*-3 + 3

3a =  3

a = 3/3 = 1

The linear equation is:

y = x + 3

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Answer:I.65

Step-by-step explanation:

Answer: The probability that a randomly selected individual is experiencing hypertension can be calculated by taking the ratio of the number of individuals with hypertension to the total number of individuals:

P(hypertension) = (21 + 36 + 30) / 180 = 87 / 180 = 0.4833

Given that a heavy smoker is selected at random, the probability that the person is experiencing hypertension can be calculated by taking the ratio of the number of heavy smokers with hypertension to the total number of heavy smokers:

P(hypertension | heavy smoker) = 30 / (30 + 19) = 30 / 49 = 0.6122

To determine if the events "hypertension" and "heavy smoker" are independent, we can compare the joint probability of both events happening to the product of their individual probabilities:

P(hypertension and heavy smoker) = 30 / 180 = 0.1667

P(hypertension) * P(heavy smoker) = 0.4833 * (30 / 180) = 0.1083

Since P(hypertension and heavy smoker) ≠ P(hypertension) * P(heavy smoker), we can conclude that the events "hypertension" and "heavy smoker" are not independent.

Step-by-step explanation:

Answer: 12 feet

Step-by-step explanation: If the length of the garden is 20 feet then that means 40 feet of fence was used to make both lengths of the garden. So we subtract 40 from 64 which leaves us with 24 feet and then we divide 24 by 2 to get 12 because there are 2 widths.

Hope this helps!

The sum of the series b 2 b 4 b 6 b 8 b {10} is [tex]$\dfrac{180}{3}$[/tex] since it is a geometric series with a common ratio of [tex]$\dfrac{7}{4}$[/tex].

Since the given series [tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] has a sum of 180, it can be deduced that the series is a geometric series with a common ratio of[tex]$\dfrac{7}{4}$[/tex]. This means that the ratio of any two consecutive terms in the series is a constant, [tex]$\dfrac{7}{4}$[/tex]. Therefore, the sum of the series b 2 b 4 b 6 b 8 b {10} can be calculated as follows:

[tex]$S = b2 + b4 + b6 + b8 + b_{10}$[/tex]

[tex]$= b2\left(\dfrac{7}{4}\right)^0 + b2\left(\dfrac{7}{4}\right)^2 + b2\left(\dfrac{7}{4}\right)^4 + b2\left(\dfrac{7}{4}\right)^6 + b2\left(\dfrac{7}{4}\right)^8$[/tex]

[tex]$= b2 \left[1 + \left(\dfrac{7}{4}\right)^2 + \left(\dfrac{7}{4}\right)^4 + \left(\dfrac{7}{4}\right)^6 + \left(\dfrac{7}{4}\right)^8\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{1-\left(\dfrac{7}{4}\right)^2}\right]$[/tex]

[tex]$= b2 \left[\dfrac{1-\left(\dfrac{7}{4}\right)^{10}}{\dfrac{3}{4}}\right]$[/tex]

[tex]$= \dfrac{4b2}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Since the sum of the series[tex]$b 1 b 2 b 3 \cdots b {10}$[/tex] is 180, we can substitute $b2$ with [tex]$\dfrac{180}{3}$[/tex]nd calculate the sum of the series $b 2 b 4 b 6 b 8 b {10}$:

[tex]$S = \dfrac{4\left(\dfrac{180}{3}\right)}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

[tex]$= \dfrac{180}{3} \left[1-\left(\dfrac{7}{4}\right)^{10}\right]$[/tex]

Therefore, the sum of the series [tex]$b 2 b 4 b 6 b 8 b {10}$ is $\dfrac{180}{3}$[/tex].

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The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 [tex]ft^3[/tex].

What is the volume of an object?

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Given that the top of a silo is a hemisphere

radius(r) = 12 ft.

Then,

the volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] =  [tex]\frac{2}{3} * 3.14* 12^3 = 10851.84[/tex] [tex]ft^3[/tex]

And, the bottom of the silo is a cylinder with

height (h) = 40ft.

the volume of a cylinder =[tex]\pi r^{2} h = 3.14*12^2*40=18095.57 ft^3[/tex]

So, the total volume is

V = 10851.84 + 18095.57 = 28947.41 [tex]ft^3[/tex]

Then, total volume = total number of cubic feet of grain

Hence, the required answer is  28947.41 [tex]ft^3[/tex].

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The number of 17 cars have clocks but no radios.

Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.

Given:

Out of 53 cars,41 had clocks,30 had radios and 6 had neither.

That means,

53-6 = 47 cars have either clocks or radios or both.

47 - 30 = 17 cars have no radio.

47 - 41 = 6 cars have no clocks.

Hence, 17 cars have clocks but no radios.

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Answer:

d^3-2d^2-5d+6

Step-by-step explanation:

Step 1: (d-1)(d+2)=d^2+d-2

Step 2: (d-3)(d^2+d-2) = d^3+d^2-2d-3d^2-3d+6 = d^3-2d^2-5d+6

Answer: The product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].

Step-by-step explanation:

When multiplying the binomials, you can break it down and multiply two expressions first then multiply that last expression:

(d−1)(d+2)(d+3)

first: (d−1)(d+2)

when multiplying expressions you can multiply using the 'box method' where you would draw a box and put each part of the expression on the top and the left side of the box, multiplying each on into the box and adding like terms.

You can also multiply it by first taking the expression, (d−1)(d+2) and multiplying the variable 'd' to the (d + 2) and then multiplying the '-1' to the (d+2) and then adding like terms:

(d−1)(d+2)

[tex]d^{2} + 2d - d - 2[/tex]

'd' is the only like term in this expression so lets add 2d and -d together

[tex]d^{2} + d - 2[/tex]

finally, we need to multiply the (d + 3) to expression, [tex]d^{2} + d - 2[/tex]

We will treat this multiplying process the same as before.

[tex](d + 3)(d^{2} + d - 2)[/tex]

[tex]d^3 + d^2 -2d + 3d^2 + 3d - 6[/tex]

now lets add like terms

[tex]d^3 + 4d^2 +d - 6[/tex]

So the product of the binomials (d-1)(d+2)(d+3) is [tex]d^3 + 4d^2 +d - 6[/tex].

Here's how I will do it:

1. Recite the Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]

2. Substitute the variables of a and b, so the equation will look like this [tex]3^{2} +6^{2} =c^{2}[/tex] now.  

3. Simplify the equation which gives you, [tex]9+36=c^{2}[/tex]. Simplifying more would give you [tex]45=c^{2}[/tex].

4. Solve for the c value :

[tex]c=\sqrt{45}[/tex]
Plug this into a calculator and it will give you 6.70820....
Rounding to the nearest tenth will give you, about 6.7.

The length of the hypotenuse of a right triangle can be calculated using the Pythagorean theorem: c^2 = a^2 + b^2.

Given that a = 3 meters and b = 6 meters, we can substitute those values into the equation:

c^2 = 3^2 + 6^2

c^2 = 9 + 36

c^2 = 45

c = sqrt(45)

c = 6.7 meters

Rounding to the nearest tenth, c = 6.7 meters becomes c = 6.7 meters.

Answer:

D

Step-by-step explanation:The proportional relationship between x and y is;

x 7 14 28 35

y 1 2 4 5

The correct option is D.

Proportional relationships;

Proportional relationships between x and y satisfy the following equation;

Where k is some constant.

Rearranging the equation;

Then,

The proportional relationship between x and y is;

Hence, the proportional relationship between x and y is the correct option is D.

The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).

A set is a graphical function of many object classes. One of the terms or elements that compose a set could include any kind of mathematical object. Symbols, digits, lines, other geometrical features, space-based points, variables, and even other quantities. In mathematics, a proposition is a structured set of components that can be written as a list or a hypothesis builder. To designate sets, curly brackets are usually applied. A = 1, 2, 3, and 4 is an illustration of a set. Basically, a set is an assortment of objects that are displayed together. A set's components or elements are the components that make up the set. Any object might make up a set's components, but for the purposes of the discussion,

given

Mean is the sum of all numbers divided by the amount of numbers. That means the sum of the first set would be 8*-2=-16.

With that in mind, you can simply have the first set be eight -2s (-2, -2, -2, -2, -2, -2, -2, -2).

Now we need to calculate the sum of the second set. This set has 9numbers, and the mean is 2. 9*2=18. To find the number to add to your set, take 48–63. Your set becomes (-2, -2, -2, -2, -2, -2, -2, -34).

The new set that follows has a mean that is 4 more than the mean of the previous set: (-2, -2, -2, -2, -2, -34).

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For a variety of reasons, files on your computer shouldn't be destroyed. One, you might have to keep them since your work is crucial. Two, I should have them just in case.

A computers is a piece of electrical equipment used to manipulate data or information. It has the ability to store, retrieve, and process data.You may already be aware of the fact you are able to use a computers to surf the Internet, send emails, type documents, and play games.

Modern computers are given their names after the jobs that they replaced. The term "computer" was first used in the English language in the 17th century to refer to a person who performed mathematical computations. It made its first mention of a calculator in 1897. The "human" computer is now outdated in the age of the "machine."

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The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note to solve this question, we can assign 2 variables to the 2 conditions stated in the question, and solve them simultaenously.

The publisher nedds to produce 2414 books and sell so that production cost will equal the money from sales.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A small publishing company is planning to publish a new book.

The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing).

The one-time fixed costs will amount to $27,160.

The variable costs will be $8.75 per book.

The publisher will sell the finished product to bookstores at a price of $20.00 per book.

Let x be the number of books.

Cost = 8.75x + 27160

Revenue = 20x

Revenue = cost

20x = 8.75x + 27160

11.25x = 27160

x = 2414.2

x ≈ 2414 books.

Therefore, the required number of books are 2414 books.

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At 0.05 alpha level, your claim is not significant.

In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct.

Given is that a friend read online that 37% or less Americans have a gun in their household. I claim that the percent of Americans that have a gun in their household is actually greater than 37%. To test this claim, I survey 200 random Americans and find that 86 of them have a gun in their household. The alpha level is at .05.

We can write -

P{E} % = 86/200 x 100

P{E} % = 86/2

P{E} % = 43%

We can find the p - value using the formula -

[tex]$Z = \frac{\hat{p}-p 0}{\sqrt{\frac{p 0(1-p 0)}{n}}}[/tex]

where -

[tex]$\hat{p}=[/tex] Sample Proportion

[tex]$p_{o}[/tex] = Assumed population proportion in the null hypothesis.

It can be calculate to find that the p value is less than 0.05. So, we can conclude that the null hypothesis is rejected.

Therefore, at 0.05 alpha level, your claim is not significant.

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In normal scientific notation, round off each integer to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form. Scientific notation is a method of writing extremely big or extremely tiny integers. When a number between 1 and 10 is multiplied by a power of 10, it is expressed in scientific notation.

Here,

a. 422.65 times 10⁻³ = 4.227 x 10⁻²

b. 71.246 times 10⁵ = 7.125 x 10⁶

c. 0.00044515 = 4.452 x 10⁻⁴

d. 22.9987 times 10⁻⁵ = 2.300 x 10⁻⁴

e. 9.7222 times 10⁵ = 9.722 x 10⁵

f. 0.0048545 times 10⁵ = 4.855 x 10³

The following numbers in standard scientific notation, rounding off each to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

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Answer:

  3.75%

Step-by-step explanation:

You want to know the semiannual interest rate if the annual rate is 7.5%.

The rate of interest for a period is the annual rate divided by the number of periods in a year.

Interest compounded semiannually is compounded 2 times per year. The semiannual rate is ...

  7.5%/2 = 3.75% . . . . semiannual rate

Answer:

6

Step-by-step explanation:

The growth in balance from year 20 to year 25 is $274.57.

A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Molly's claim is correct.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

A table is given below:

Animals     Weight of the animals,   The weight of food packages

Cat                  6 Kg                                    300 grams.

Dog                 12 Kg                                  900 grams.

From the table:

The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Therefore, Molly's claim is correct.

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Answer: Kaia is not correct

Step-by-step explanation: A function works as long as there is only one 'output' for every 'input', or for every x value, only one y value works. (There can be multiple x values for any y value). If you do the verticle line test on this graph, the line won't pass through two points at the same time anywhere. Therefore, Kaia is incorrect.

Answer:

Step-by-step explanation: 3

7

9

0

7

5

Answer:

Below

Step-by-step explanation:

Start at -8... you have to go 8 units to reach 0

  then you have to go another 9 to reach 9     total = 8 + 9 = 17

Answer:

-3550x - 12y + 20

Step-by-step explanation:

50x+ 20 - 60(1/5y+60x)

50x + 20 - 12y - 3600x

-3550x - 12y + 20

Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:

(1/3 * 50) + (2/3 * -5) = 16.67

So, if you rolled the die 100 times, you would expect to gain or lose:

100 * 16.67 = 1667 points

The answer is: a gain of about 1,667 points.

Step-by-step explanation:

Step-by-step explanation:

Median IJK = IM = PN + 2

Median PQR = PN

Therefore, IM = PN + 2

IM = PN + 2

PN = IM - 2

IM = (15 + 9 + PN)/2

PN = (15 + 9 + IM - 2)/2

15 + 9 + PN = 2IM

15 + 9 + IM - 2 = 2PN

25 + PN = 2IM

25 + IM - 2 = 2PN

PN = 2IM - 25

PN = 2PN - 25

3PN = 25

PN = 25/3

IM = PN + 2

IM = 25/3 + 2

IM = 29/3

Therefore, IM = 29/3 and PN = 25/3.

Answer:4/3

Step-by-step explanation: rise over run when finding slope, and the first point i can find (-3,-5) is 4 up and 3 right away from (0,-1)