in three flips of an unfair coin the probability of getting three heads is the same as the probability of getting exactly two tails. what is the ratio of the probability of flipping a tail to the probability of flipping a head?

The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:

a)sinθ=0.5

b)cosθ=0.866

c)tanθ=0.577

What is trigonometric-ratios ?

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.

Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]

hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]

                  =[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]

                  =[tex]\sqrt{16+48}[/tex]

                  =8

a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]

Sin θ=[tex]\frac{4 }{8}[/tex]

Sin θ=[tex]\frac{1}{2}[/tex]

Sin θ=0.5

b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]

            =[tex]\frac{4\sqrt{3} }{8}[/tex]

            =[tex]\frac{\sqrt{3} }{2}[/tex]

            =[tex]\frac{1.732}{2}[/tex]

Cos θ=0.866

c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]

            =[tex]\frac{4}{4\sqrt{3} }[/tex]

            =[tex]\frac{1}{\sqrt{3} }[/tex]

tan θ=0.577

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Three distances that are equivalent to 1/2 mile are:

880 yards

1,609.34 meters

2,640 feet

The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.

To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.

Using the formula, we get:

V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3

Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.

Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99

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Answer:

40.8°

Step-by-step explanation:

SohCahToa

use tan

tan^-1(19/22)

=40.81508387

=40.8

Answer:

Step-by-step explanation:

Here,

Opposite side is 19

Adjacent side is 22

To find : The value of Angle A, that is X°.

Formula

Tan X° = Opposite side/Adjacent side

Tan X° = 19/22 = 0.863 ( approximately )

X° = Tan inverse (0.863)

X° = 40.79° ~ 40.8°

Rounding off this to nearest tenth is 41°.

Hence,

X° = 41°

That is,

Angle A is 45°.

Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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Answer:

-5d + 5.5 < 17

-5d < 11.5

d > -2.3

A is the correct solution.

The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B

To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.

The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.

However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.

To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.

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Answer:

8c^2 + 24c - 6

Step-by-step explanation:

I got it right on edmentum

Answer: 2 girls to 3 non-girls

Step-by-step explanation:

80 are girls

120 are boys (200-80)

80:120

simplify

2:3

The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.

Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.

Here,

Let's figure out how many issues of the magazine are still available in the store.

Given: There were 90 copies in all when the bookstore opened.

1/6 of the total copies were sold at the bookstore yesterday.

=> 15 copies were sold yesterday = (1/6) * 90.

=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale

=> 2/5 of the remaining copies were sold in the bookstore today.

30 copies were sold today, which

=>  (2/5) * 75.

The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:

=>  75 - 30 = 45

45 copies of the magazine are still available at the bookstore.

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The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,

To solve this problem, we can use the formula for permutations, which is:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).

Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:

52P52 = 52! / (52 - 52)! = 52!

Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.

Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.

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There are  [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.

The problem you are describing is a classic example of a combination problem, specifically choosing a certain number of items from a larger set without regard to the order in which they are arranged.

The formula to calculate the number of ways to choose "r" items from a set of "n" items without replacement is given by the combination formula, also known as "n choose r" or denoted as C(n, r). The formula is:

[tex]C(n, r) = n! / (r! \times (n - r)!)[/tex]

where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

In your case, you are choosing 4 members from a family of 5 for a photo shoot, and the order in which they line up does not matter. So you need to find C(5, 4).

Plugging the values into the formula:

[tex]C(5, 4) = 5! / (4! \times (5 - 4)!) = 5! / (4! \times 1!) = (5 \times 4 \times 3 \times 2 \times 1) / ((4 \times 3 \times 2 \times 1) \times 1) = 5[/tex]

Therefore,  there are  [tex]5[/tex] ways to choose 4 members from a family of 5 to line up for a photo shoot.

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Answer:

  -3

Step-by-step explanation:

You want the graphical solution to x² +6x +9 = 0.

The graph of the expression on the left shows it has a value of 0 when x = -3.

The solution is x = -3.

__

Additional comment

A graphing calculator is very helpful when you want a graphical solution.

If you want to graph this by hand, you can rewrite it as ...

  (x +3)² = 0

The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.

Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.

GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.

Seasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

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Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.

Given data:

Area of triangle = 1/2* base * height

Ratios:

area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)

area of larger triangle / area of smaller triangle = B*H / b*h

area of larger triangle / area of smaller triangle = 10*5 / 5*2

area of larger triangle / area of smaller triangle = 50 / 10

area of larger triangle / area of smaller triangle = 5/ 1 = 5:1

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

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Complete question:

what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.

Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

The next four equivalent fractions of 8/13 are:

Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.

In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.

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To estimate the sample size required for estimating the proportion of college students who are working while going to school with a desired accuracy of 4% at a 90% confidence level, we can use the following formula:

n = (Z^2 * p * (1-p)) / (E^2)

where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645)

p is the estimated proportion (or expected proportion) of the population

E is the desired margin of error

Given:

Desired accuracy (E): 4% or 0.04

Confidence level (Z-score): 1.645 (corresponding to 90% confidence level)

Estimated proportion (p): 0.40 (or 40%)

Plugging the values into the formula, we get:

n = (1.645^2 * 0.40 * (1-0.40)) / (0.04^2)

n = 0.1239 / 0.0016

n ≈ 77.4375

Rounding up to the nearest whole number, the estimated sample size required to achieve the desired accuracy is 78.

So, a sample size of at least 78 college students would be needed to estimate the proportion of college students who are working while going to school with a margin of error of 4% at a 90% confidence level, assuming an estimated proportion of 40%.

The unit price for the first bag is $2.12 per kilogram and the unit price for the second bag is $2.09 per kilogram.

To find the unit price, we need to divide the total cost by the weight of the bag.

For the first bag

Unit price = Total cost / Weight

Unit price = $15.84 / 7.48 kg

Unit price = $2.12/kg

Therefore, the unit price for the first bag is $2.12 per kilogram.

For the second bag

Unit price = Total cost / Weight

Substitute the values in the equation

Unit price = $16.58 / 7.94 kg

Unit price = $2.09/kg

Therefore, the unit price for the second bag is $2.09 per kilogram.

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Answer:2/3

Step-by-step explanation:

its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD

Answer: 2/3

Step-by-step explanation:

The corresponding side of AD is A'D'.

AD = 30

A'D' = 20

Scale factor = 2/3 because AD * 2/3 = A'D'

If I'm wrong, please tell me.

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.

The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.

They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.

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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.

B. save time in arriving at solutions to problems . The correct answer is:

Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.

One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.

However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.

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Answer: Using the given information and the formula ab = cd, we can write:

d = (ab) / c

We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the unknown length we want to find. Substituting the given values, we get:

a^2 + 12^2 = 6^2

a^2 + 144 = 36

a^2 = -108 (which is not a possible solution)

This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.

Step-by-step explanation:

There are 216 possible outcomes for each trial of rolling three standard dice.

In probability theory, an outcome is defined as the result of a single experiment or trial. The total number of outcomes in a trial can be determined by the multiplication principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m x n ways to do both.

In this case, Michelle is rolling three standard dice simultaneously, which means that there are six possible outcomes for each die. Therefore, the total number of outcomes for a single trial is calculated by multiplying the number of outcomes for each die. Using the multiplication principle, we get:

Number of outcomes for each die = 6

Total number of outcomes for a single trial = 6 x 6 x 6 = 216

It is important to note that not all outcomes are equally likely, and the probability of getting a specific outcome can be calculated by dividing the number of favorable outcomes by the total number of outcomes.

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Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

Both computers working together can process the payroll in 2.4 hours.

Let's denote the time it takes for both computers working together to process the payroll as "t".

We can use the formula:

work done = rate x time

where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :

1/6 + 1/4 = 1/t

We can simplify the left-hand side of the equation:

2/12 + 3/12 = 1/t

5/12 = 1/t

Multiplying both sides by 12t:

5t = 12

t = 12/5

t = 2.4

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