A coin is loaded so that the probability of heads is 0.9 and the probability of tails is 0.1. Suppose that the coin is tossed twice and that the results of the tosses are independent. For i = 1 and 2, let H; be the event that the result of toss i is heads, and let T; be the event that the result of toss i is tails. (a) What is the probability (as a %) of obtaining exactly two heads? 81 % (b) What is the probability (as a %) of obtaining exactly one head? The probability of obtaining exactly one head is P((H, NT, U (H, NT,)) v U which equals %. Enter an exact number. (C) What is the probability (as a % of obtaining no heads? % (d) What is the probability of obtaining at least one head? % Use the binomial theorem to expand the expression.

Using Counting principle,

The black center square contains total 330 small squares.

We start with lowest one i.e 1 × 1

Let’s consider any one face out of six faces of cube ,

as one face of grid or cube is made up of 25 small squares.

If we are facing difficulty in visualising then

simply we draw a 5× 5 board on paper, just as seen in above picture :

and now check 2× 2 squares.

By using R1, R2 and all columns we shall be able to draw 4 such blocks.

Again, R2,R3 and R3, R4 and R4,R5 we can easily draw 4 squares each cash .

Thus, total square count of 2× 2 squares will be

= 16

similarly, we do it for 3× 3 and 4×4 and we will get 9 & 4 respectively.

For final one 5× 5 there is one big square

So, total squares for one face will be

= 25+16+9+4+1=55

Since, there are 6 such faces for a cube then

=>55× 6= 330

Hence, total squares contain the black center square is 330.

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Answer:

6

Step-by-step explanation:

90/7 divided by 1 3/4 is 7.34 so the closest one to it is 6

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list.

When an individual places their phone number on the Do Not Call (DNC) Registry, it remains there permanently, and telemarketers are prohibited from making unsolicited calls to that number until the individual requests to be removed from the list. This list is managed by the Federal Trade Commission (FTC), which enforces the Telephone Consumer Protection Act (TCPA) in the United States. If someone's phone number is on the DNC registry, the registry rules apply indefinitely. This means that even if the individual's phone number is still listed after a period of time, telemarketers are prohibited from calling that number. If the individual wishes to receive telemarketing calls again, they must remove their phone number from the list by dialing the DNC registry's phone number, which is 1-888-382-1222. The process of removing a phone number from the list is a simple one. Dial the number on your phone, and then follow the instructions that the voice prompt gives you. Furthermore, it is important to know that calls from organizations that you have given permission to call you are still allowed even if your number is on the DNC registry.

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Answer:

What is the gear ratio

The gear ratio is the ratio of the number of teeth in the gear to the number of teeth in the pinion, the pinion being the smaller of the two gears in mesh.

What is the great reduction

reduction refers to the rewriting of an expression into a simpler form

what is the simplified gear reduction

If you count up the number of teeth on gear one, and on gear X (the last one) and set them in a ratio (1:X), this is the gear ratio. If the number can be reduced, you should reduce it, for example a ratio of 100 teeth:40 teeth reduces to 5:2

Answer:

eighty four 84 84 84 84 84

Answer:

84

Step-by-step explanation:

Answer:

0,-11

Step-by-step explanation:

-p^2 − 11p = 0

Factor out -p

-p( p+11) =0

Using the zero product property

-p =0    p+11 =0

p =0      p = -11

The American Housing Survey is conducted annually by the Bureau of the Census to gather data on the distribution of occupied housing units in the United States.

Using data from the 2003 survey, the distribution of occupied housing units by the number of rooms can be found. To visualize this data, histograms can be drawn separately for owner-occupied and renter-occupied units.

It is important to note that "10 or more" mean 10 or 11, as very few units have more than 11 rooms.

(a) The This could be due to rounding errors or differences in sample sizes between the two groups.

(b) The percentage of one-room units is much smaller for owner-occupied housing. This is not necessarily because there are more owner-occupied units in total, but could be due to differences in the length preferences and financial means of renters versus owners.

(c) It is unclear which group, on the whole, has larger units without additional information about the distribution of rooms.

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Empirical probability is a method of estimating probabilities based on observed data.

An event A occurred 30 times. The empirical probability of event A can be calculated by dividing the number of occurrences of event A by the total number of trials:

Empirical Probability of A = Number of occurrences of A / Total number of trials

In this case, the empirical probability of event A would be:

Empirical Probability of A = 30 / 100 = 0.3 or 30%

The empirical probability is an estimate of the true probability based on observed data. It is often used when the outcomes of an experiment or event cannot be easily determined theoretically or when there is limited information available.

It is important to note that empirical probability is based on the assumption that the observed data is representative of the underlying probability distribution. Therefore, it becomes more reliable and accurate as the number of trials or observations increases.

By collecting more data and conducting more trials, we can refine our estimates of empirical probability and approach the true probability of an event. However, it is essential to ensure that the data collection process is unbiased and the observations are independent and identically distributed to obtain valid empirical probabilities.

Empirical probability is commonly used in fields such as statistics, economics, and social sciences to analyze and make inferences based on observed data. It allows researchers to draw conclusions and make predictions about the likelihood of events based on real-world observations.

It is worth noting that empirical probability is a useful tool, but it has its limitations. It does not provide a guarantee of the true probability and is subject to sampling variability. Additionally, it may not accurately represent the probability of rare events if the sample size is small.

In summary, it is calculated by dividing the number of occurrences of an event by the total number of trials or observations. While it provides a practical approach when theoretical probabilities are unavailable, it should be used with caution and in conjunction with other statistical methods.

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Answer:

slope m = 1   y-intercept b = 3

Step-by-step explanation:

to double check you can do use the formula y=mx+b

-3*1= -3 +3= 0

so the coordinates would be (-3,0)

Answer:

the domain of the function is y-2vx-5 is 0x25

The domain of the function  x≥ 5.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

The domain takes all of the potential input values from the set of real numbers, while the range takes all of the function's output values.

We have the function y = √(x- 5)

The domain is the x values operate, often known as the horizontal axis.

The Range is y values on the vertical axis.

As, the radical never gives Negative Value.

So, x- 5 ≥ 0

and, x≥5

Thus, the domain is x≥ 5.

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The  entire area under the standard normal distribution curve is always positive even if the z value is negative.

The normal distribution, it's useful to think of the standard deviation as being steps away from the mean. One step to the right or one step to the left is considered one standard deviation away from the mean. Two steps to the left or two steps to the right are considered two standard deviations away from the mean. Likewise, three steps to the left or three steps to the right are considered three standard deviations from the mean.

The probability of the outcome of an experiment is never negative, although a quasi probability distribution allows a negative probability, or quasi probability for some events. These distributions may apply to unobservable events or conditional probabilities.

Therefore,

The value can be negative can be any positive value can be any positive value larger than 1.

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Answer:

31 years

Step-by-step explanation:

65000*(1.07) ^31 is around $529000

however, 65000*(1.07) ^30 is around $491000

so you would need 31 years to gain more than $500,000.

It will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

To determine the number of years it will take to reach $500,000 in savings with an investment that earns an average of 7% per year, we can use the given investment model equation: y = 65000(1.07)ˣ.

We need to find the value of x, which represents the number of years.

Setting y = $500,000, we can solve for x:

500,000 = 65,000(1.07)ˣ

500,000/65,000 = (1.07)ˣ

100/13 = (1.07)ˣ

To solve for x, we take the logarithm of both sides:

ln 100/13 = ln (1.07)ˣ

ln 100/13 = x ln (1.07)

x = (ln 100/13)/(ln (1.07))

x = 30

Therefore, it will take approximately 30 years to reach $500,000 in savings with an investment that earns an average of 7% per year.

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Answer:

0.025

Step-by-step explanation:

Answer: 0-1hr

Step-by-step explanation: lollll

If f(x, y, z) = xyzi + yj + zk, the divergence of the curl of the vector field f is zero.

To find the divergence of the curl of the vector field f(x,y,z) = xyzi + yj + zk, we first need to compute the curl of f, which is given by:

curl f = (∇ × f) = ∂(zk)/∂y - ∂(yj)/∂z + (∂(yj)/∂x - ∂(xyzi)/∂y)k + (∂(xyzi)/∂z - ∂(zk)/∂x)j + (∂(zk)/∂x - ∂(yj)/∂y) i

Simplifying this expression, we get:

curl f = (-z)i + xj + yk

Next, we need to find the divergence of the curl of f, which is given by:

div(curl f) = ∇ · (∇ × f) = ∂(∂(zk)/∂y - ∂(yj)/∂z)/∂x + ∂(∂(yj)/∂x - ∂(xyzi)/∂y)/∂y + ∂(∂(xyzi)/∂z - ∂(zk)/∂x)/∂z

Substituting the values from the curl f expression, we get:

div(curl f) = ∂(-z)/∂x + ∂(x)/∂y + ∂(y)/∂z

Simplifying this expression, we get:

div(curl f) = 0

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Answer:

the answer is C. 180°clockwise

The chocolate bar has a length of 10.5ft and width of 5.7ft

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

In the question, we were given the l is equal to 0.9 less than 2 times the width of the rectangle.

let;

A = l * w

l = 2w - 0.9

A = l * w

59.85 = w * (2w - 0.9)

59.85 = 2w² - 0.9w

2w² - 0.9w - 59.85 = 0

Solving for w

w = 5.7ft

The width of the bar is 5.7ft

The length will be (2 * 5.7) - 0.9

L = 10.5ft.

The length and width of the bar is 10.5ft and 5.7ft respectively

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

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65 min by riding her bike

x min by boarding a bus

since the time taken to get to the dentist with a bus is 5min shorter than twice the time taken with a bike, it can be written as

(2x) - 5 = 65

2x = 65 + 5

2x = 70

x = 35 min. (A)

Step 1

Given;

Step 2

Thus it is increasing at;

It is decreasing at;

Answer;

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

Pythagorean Theorem

Step-by-step explanation:

Because they give you the hypotenuse and the adjacent angle.

Answer:

Pythagorean Theorem

Step-by-step explanation:

Because they give you the hypotenuse and the adjacent angle.

Answer:

96 pizzas

Step-by-step explanation:

Allan can make 8 pizzas in 15 minutes at the pizza restaurant where he works.

We are told that;

If the number of pizzas varies directly with minutes,

P ∝ M

P = kM

Hence:

8 = 15k

k = 8/15

How many pizzas can Allan make in 3 hours?

Convert 3 hours to minutes

1 hour = 60 minutes

3 hours = x

x = 3 × 60

x = 180 minutes

Hence,

M = 180 minutes

k = 8/15

P = kM

P = 8/15 × 180

P = 96 pizzas

Therefore, Allan can make 96 pizzas in 3 hours

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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If x = 0, then the value of the function f(0) will be negative 15. And if the value of the function f(x) is 27. Then the value of x will be 3.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The table is given below.

If x = 0, then the value of the function f(0) will be

f(0) = -15

And if the value of the function f(x) is 27. Then the value of x will be

x = 3

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Answer:

if x = 0, then f(0) = -15 and if f(x) = 27, then x = 3

Step-by-step explanation:

i look at the table for 0 and 27 and then look at the numbers next to it

The expected value for your profit is -$2.57.

To calculate the expected value, you need to multiply the probability of winning each prize by the amount of money you will receive if you win that prize.

Probability of winning the grand prize: 1/900 = 0.0011

Probability of winning a second prize: 3/900 = 0.0033

Probability of winning a third prize: 11/900 = 0.0122

Expected value of winning the grand prize: (0.0011)($2000) = $2.20

Expected value of winning a second prize: (0.0033)($300) = $0.99

Expected value of winning a third prize: (0.0122)($20) = $0.24

Total expected value: $2.20 + $0.99 + $0.24 = $3.43

Expected cost of buying a ticket: $6

Expected profit: $3.43 - $6 = -$2.57

Therefore, the expected value for your profit is -$2.57. However, since this is a negative value, it means that, on average, you will lose money by buying a ticket.

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Answer:

16

Step-by-step explanation:

area of square = side * side

side = 4u

so area = 4*4 = 16 units

Answer:

16

Step-by-step explanation:

4x4=16

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