A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely?
(i) H T H T H T H T H T H T
(ii) H T T H H T T H T H H T
(iii) H H H H H H H H H H H H
(iv) T T T H T H H H H T H H
A. (i) because there are an equal number of heads and tails.
B. (ii) because there are an equal number of heads and tails but in a random order
C. (iii) because heads are just as likely as tails
D. (iv) because you won’t necessarily get the same number of heads and tails with a fair coin
E. They are all equally likely.

Answer:

a. from A to B, a rotation by 90 degrees anti-clockwise about (0,0).

b. from B to C, a translation by vector (-3/4, -1/4).

c. from A to C, a rotation by 60 degrees, anti-clockwise about (0,0).

Hope this helps, I'm sorry if it doesn't. If you need more help, ask me! :]

Answer:

429

Step-by-step explanation:

Answer: To find the rational roots of f(d) = 5d^3 - 6d^2 + d - 8, we can use the Rational Root Theorem, which states that any rational root of a polynomial equation must be of the form p/q, where p is a factor of the constant term (in this case, -8) and q is a factor of the leading coefficient (in this case, 5).

The factors of -8 are ±1, ±2, ±4, and ±8, and the factors of 5 are ±1 and ±5. Therefore, the possible rational roots of f(d) are:

±1/1, ±2/1, ±4/1, ±8/1, ±1/5, ±2/5, ±4/5, and ±8/5

We can try these values one by one to see if they are roots of f(d). For example, when we try d = 1, we get:

f(1) = 5(1)^3 - 6(1)^2 + 1 - 8 = 5 - 6 + 1 - 8 = -8

Since f(1) is not equal to zero, d = 1 is not a root of f(d). We can continue this process until we find all the rational roots of f(d).

Step-by-step explanation:

Answer:

Step-by-step explanation:

angle

The statement "rotated an angle whose measure is more than halfway around a circle" is incorrect. An angle whose measure is 60 degree is rotated more than halfway around a circle.

A rotated angle is an angle that has been moved or transformed from its original position, while an angle that measures more than halfway around a circle is called a reflex angle. A reflex angle measures between 180 and 360 degrees, which means that it has rotated more than halfway around a circle.

In contrast, an angle that measures less than 180 degrees is called an acute angle, while an angle that measures exactly 180 degrees is called a straight angle. Understanding the different types of angles is important in geometry and mathematics.

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The rent of the apartment during the 9th year of living in the apartment would be approximately $3,510.45 per month.

If the rent starts at $1600 per month and increases by 9.5% each year, then we can use the formula for compound interest to calculate the rent after 9 years.

The formula for compound interest is:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the initial principal (the starting amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, P = $1600, r = 9.5% = 0.095, n = 1 (compounded once per year), and t = 9. We want to find A, the rent after 9 years.

A = 1600(1 + 0.095/1)^(1×9)

A = 1600(1.095)^9

A ≈ $3,510.45

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(15) The value of x is -588 (option A).

(16) The value of x makes the expression equal to 0 is -2i. (option B).

The value of x is calculated by solving the equation as follows;

(15) We have the equation:

√x = 14i√3

Squaring both sides, we get:

x = (14i√3)^2

x = -588

(16) Factoring the expression, we get:

x(x⁴ + 6x² + 8)

Setting each factor equal to 0, we get:

x = 0 or x⁴ + 6x² + 8 = 0

Let's solve for the second equation:

Let y = x²

Then we have:

y² + 6y + 8 = 0

Factorizing, we get:

(y + 2)(y + 4) = 0

So y = -2 or y = -4

Since y = x², this means:

x² = -2 or x² = -4

Taking the square root of both sides, we get:

x = ±√(-2) or x = ±√(-4)

Simplifying using imaginary numbers, we get:

x = ±i√(2) or x = ±2i

Thus, for the expression √x is equivalent to 14i√3,  the value of x is -588. And for the expression x⁵ + 6x³ + 8x, x = -2i.

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the distance from point C to line AB, you must find the length of the segment from C perpendicular to AB

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction. A ray has only one endpoint and an endlessly long another end, as opposed to a line segment that has two ends.

When the angle of inclination between two line segments is exactly equal, those two segments are said to be perpendicular.

The plus symbol is formed when two perpendicular line segments cross one other.

To find the distance from point C to line AB, you must find the length of the segment from C_______ to AB

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Answer:10ft

Step-by-step explanation:

we must use pythagorean theorem

[tex]which \ is \ a^{2} +b^{2} =c^{2} \\6^{2} + 8^{2} =36+64=100=10^{2}\\c=10--- > hypotenuse[/tex]

The expression 1÷2+2 3÷4-3÷8​ when simplified is 9/4

From the question, we have the following parameters that can be used in our computation:

1÷2+2 3÷4-3÷8​

Express the terms properly as fractions

So, we have the following

1/2 + 2 3/4 - 3/8

Express each term as proper/improper fraction

So, we have the following representation

1/2 + 11/4 - 3/8

Express the denominator as the same

So, we have

4/8 + 22/8 - 3/8

Evaluate the like terms

18/8

So, we have

9/4

Hence, the solution is 9/4

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The estimated life expectancy for someone born in 2005 is approximately 85.09 years.

Life expectancy is the average number of years that a person is expected to live, based on statistical data and various demographic factors such as age, gender, health status, lifestyle, and environmental conditions. It is usually calculated from birth and is a useful indicator of the overall health and well-being of a population.

Life expectancy can vary widely between different countries and regions, as well as between different demographic groups within a population. Factors that can influence life expectancy include access to healthcare, nutrition, education, economic development, social support, and public health policies.

To estimate the life expectancy for someone born in 2005, we need to use the line of best fit equation:

y = 0.40x - 716.91

where x is the birth year and y is the corresponding life expectancy.

To find the estimated life expectancy for someone born in 2005, we substitute x = 2005 into the equation:

y = 0.40(2005) - 716.91

y = 802 - 716.91

y = 85.09

Therefore, the estimated life expectancy for someone born in 2005 is approximately 85.09 years.

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The measurements in order of size, starting with the smallest are: 2.3 mm, 24 mm, 2.3 cm, 21 cm, and  0.2 m.

Given the measurements in the question;

2.3 cm, 24 mm, 0.2 m, 21 cm, 2.3 mm​

To arrange the measurements in order of size, we need to convert them to a common unit of measurement.

We can convert all the measurements to meters, as it is the largest unit given.

Hence;

2.3 mm = 2.3 ÷ 1000 =  0.0023 m

24 mm = 24 ÷ 1000 = 0.024 m

21 cm = 21 ÷ 100 = 0.21 m

2.3 cm = 2.3 ÷ 100 =  0.023 m

0.2 m = 0.2 m

Now that all the measurements are in meters, we can compare them:

0.0023 m < 0.024 m < 0.023 m < 0.21 m < 0.2 m

Therefore, the measurements in order of size, starting with the smallest, are:

2.3 mm < 24 mm < 2.3 cm < 21 cm < 0.2 m

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Answer:

The two teachers are approximately 4.1 meters apart.

Step-by-step explanation:

Let's use the following variables:

d = distance between the two teachers

Using the Pythagorean theorem:

d^2 = 4^2 + 1^2

d^2 = 16 + 1

d^2 = 17

d = sqrt(17)

d ≈ 4.1

Answer: 4.1

Step-by-step explanation:

[tex]\sqrt{1^2+4^2}[/tex]

evaluate the equation / expression

4.12311

round

4.12311 to the required place

4.1

Answer:0.27 miles

Step-by-step explanation:

Answer:

The answer to your question is 7040

Step-by-step explanation:

How many yards are in 1 mile:

So 1 mile = 1760 yards

Speed = 1760 yard per minute

= 1760 yd/min

Since we have 4 miles, we are gonna multiply 4 multiplied by 1760.

So 4 miles x 1760 = 7040

I hope this helps and have a wonderful day!

Step-by-step explanation:

To determine whether two lines are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

A) x − 5y = 10 can be rearranged to y = (1/5)x − 2, so its slope is 1/5.

y = 5x – 2 is already in slope-intercept form, so its slope is 5.

These two slopes are not equal, so the lines are not parallel.

B) x + y = 0 can be rearranged to y = −x, so its slope is −1.

y = x + 7 is already in slope-intercept form, so its slope is 1.

These two slopes are not equal, so the lines are not parallel.

C) 2x − 3y = 9 can be rearranged to y = (2/3)x − 3, so its slope is 2/3.

4y = 6x − 20 can be rearranged to y = (3/2)x − 5, so its slope is 3/2.

These two slopes are not equal, so the lines are not parallel.

D) 4x + 8y = 8 can be rearranged to y = −(1/2)x + 1, so its slope is −1/2.

y = 2x + 2 is already in slope-intercept form, so its slope is 2.

These two slopes are not equal, so the lines are not parallel.

E) 9x − 3y = 12 can be rearranged to y = 3x − 4, so its slope is 3.

y = 3x − 10 is already in slope-intercept form, so its slope is 3.

These two slopes are equal, so the lines are parallel.

Therefore, the pair of lines that are parallel is (E) 9x - 3y = 12; y = 3x - 10.

Answer:

e = - 10

Step-by-step explanation:

4e - 6e - 5 = 15

- 2e - 5 = 15 ( add 5 to both sides )

- 2e = 20 ( divide both sides by - 2 )

e = - 10

Answer: e = -10

Step-by-step explanation:

4e-6e-5=15

-2e-5=15

add 5 on both sides

-2e=20

divide 20 on both sides

e=-10

The probability that the second person chosen will also be a boy is roughly 0.872, or 87.2%.

Since the first person chosen is a boy, there are now 12 boys and 15 girls left in the class. We want to find the probability that the second person chosen is also a boy.

The probability of choosing a boy for the first selection is 13/28. Then, for the second selection, there are now 12 boys and 27 students left, so the probability of choosing a boy is 12/27.

Using conditional probability, we can calculate the probability that the second person chosen is also a boy given that the first person chosen is a boy:

P(Second person is a boy | First person is a boy) = P(Both are boys) / P(First person is a boy)

P(Second person is a boy | First person is a boy) = (12/27) / (13/28)

P(Second person is a boy | First person is a boy) ≈ 0.872

Therefore, the probability that the second person chosen is also a boy given that the first person chosen is a boy is approximately 0.872 or 87.2%.

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using graph f(x) is concave down on (-1,0), (1,∞).

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

f(x) is concave up where f'(x) is increasing and concave down where f'(x) is decreasing

So, using graph f(x) is concave down on (-1,0), (1,∞).

Hence, using graph f(x) is concave down on (-1,0), (1,∞).

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The missing measurements of the triangle given include:

The value of angle B can be found thanks to the knowledge that the interior angles of a triangle add up to 180 degrees and we have two of the angle measurements :

= 180 - angles measurements

= 180 - 27 - 90

= 63 degrees

The value of AB can be found by using the Sin theta operation such that:

Sin theta = Opposite / hypotenuse

Sin ( 27 degrees ) = 12 / hypotenuse which is AB

hypotenuse = 12 / ( Sin ( 27 degrees ))

= 26 .4 units

The value of AC measurement is:

Tan ( 27 degrees ) = 12 / AC

AC = 12 / Tan ( 27 degrees )

AC = 23. 6 units

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Answer:x=5/4

Step-by-step explanation:

you can take numbers with same variable(i mean x or y or other) in the same side:

2+3x=12-5x

2-12=-5x-3x

-10=-8x

x=10/8=5/4

Answer:

x = 5/ 4

Step-by-step explanation:

2 + 3x =12- 5x

3x + 5x = 12 - 2

8x = 10

x = 10/8

x = 5/4

Answer:

30mph

Step-by-step explanation:

We can use the concept of speed, distance, and time to solve the problem.

Let's assume that the bird was flying at a constant speed of "x" miles per minute.

When the bird passed the first building, Tim started the stopwatch. Let's say the time on the stopwatch was "t" minutes.

Therefore, the bird had flown a distance of "x*t" miles when Tim started the stopwatch.

In the next minute, the bird flew another 0.5 miles (the distance between the two buildings). So, the total distance traveled by the bird was:

x*t + 0.5 miles

We know that the total time elapsed was 1 minute. Therefore:

t + 1 = total time elapsed

Now, we can use these equations to solve for the speed of the bird:

x*t + 0.5 = distance traveled

t + 1 = total time elapsed

We want to find the value of x, so we can solve for t:

t = total time elapsed - 1

Substituting this value of t into the first equation, we get:

x*(total time elapsed - 1) + 0.5 = distance traveled

Simplifying, we get:

x*(total time elapsed) = distance traveled + 0.5

Substituting the given values, we get:

x*(1) = 0.5 + x*t

x = 0.5 + x*(total time elapsed - 1)

x = 0.5 + x*(59/60)

Solving for x, we get:

x = 30 miles per hour

Therefore, the bird was flying at a speed of 30 miles per hour.

The break-even point is 120 tickets, which is option A.

It is the income generated by a business, which includes all the money received from customers for the products or services sold, as well as any other sources of income. Revenue is calculated by multiplying the price of a product or service by the number of units sold. It is an important financial metric that helps businesses determine their profitability and growth potential.

Let's assume that x number of students are attending the party.

The cost for food per person is $15 and the revenue generated per person is $20, so the profit per person is $20 - $15 = $5.

The total cost of the party is $600 + $15x.

We need to find the number of tickets sold to cover the cost of the party, which is the break-even point.

So, we set the revenue generated equal to the cost of the party:

20x = 600 + 15x

5x = 600

x = 120

Therefore, the break-even point is 120 tickets, which is option A.

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Answer:

-3

Step-by-step explanation:

After answering the presented question, we can conclude that The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.

An equation is a mathematical statement that validates the equivalent of two expressions linked by the equal symbol '='. For example, 2x - 5 = 13. 2x-5 and 13 are two phrases. The character '=' is used to connect the two expressions. An equation is a mathematical formula that has two algebras on either side of an assignment operator (=). It illustrates the equivalency relationship between the left and middle formulas. In any formula, L.H.S. = R.H.S. (left side = right side).

The graph represents the following equation system:

[tex]y = x^2 + 3x + 2 x + y = 2[/tex]

This is due to the fact that the graph of a quadratic function intersecting a linear function at point (2, 0) is represented by a parabola and a straight line intersecting at that point (2, 0).

The equation [tex]y = x^2 + 3x + 2[/tex] represents an upward-opening parabola that goes through the point (-2, 0).

The equation x + y = 2 denotes a straight line that connects the locations (0, 2) and (2, 0).

The point of intersection of these two equations is (2, 0), which is the spot on the graph where the parabola and line intersect.

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The relationship is: number of dots = n + 1

The "number of dots" typically refers to the count or quantity of small, circular shapes that are arranged in a particular pattern or sequence. The term can be used in various contexts, such as in mathematical or geometric patterns, puzzles, games, or art.

Assuming you are referring to a specific pattern of dots that increases with each step, the equation to represent the relationship between the step number, n, and the number of dots at each step can be written as:

Number of dots = n + 1

In this equation, "n" represents the step number and "n + 1" represents the number of dots at each step. This equation assumes that the pattern starts with one dot at the first step, and the number of dots increases by one with each subsequent step.

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Answer:

the answer is y=-2/3x+6

The cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

We can use the fοrmula fοr the area οf a triangle, which is:

area = (base * height) / 2

We knοw that the base AB has a length οf 16 units, sο we can find the height by rearranging the fοrmula:

height = (2 * area) / base

height = (2 * 80) / 16

height = 10

Sο, pοint B is at (4, 0) and pοint C is at (x, y) where the height frοm A tο BC is 10 units and the length οf BC is 16 units.

We can use the Pythagοrean theοrem tο find the cοοrdinates οf pοint C:

[tex]x^2 + y^2 = BC^2[/tex]

[tex]x^2 + y^2 = 16^2[/tex]

[tex]x^2 + y^2 = 25[/tex]

Alsο, we knοw that the height frοm A tο BC is 10 units, sο the distance between pοint A and the line BC is 10 units. The slοpe οf the line BC is -y/x (rise οver run), sο the equatiοn οf the line BC is:

[tex]y = (-y/x) * (x - 4)[/tex]

[tex]y = (-y/x) * x + (y/x) * 4[/tex]

[tex]y + (y/x) * x = (y/x) * 4[/tex]

[tex]y(x/x + 1) = (y/x) * 4[/tex]

[tex]y + x = 4y/x[/tex]

[tex]x^2 + xy = 4y[/tex]

[tex]y = (x^2) / (4 - x)[/tex]

Nοw we can substitute this expressiοn fοr y intο the equatiοn[tex]x^2 + y^2 = 256:[/tex]

[tex]x^2 + ((x^2) / (4 - x))^2 = 256[/tex]

Sοlving this equatiοn gives twο pοssible values fοr x: x = 8 οr x = -4.

If x = 8, then y = 16/3, and if x = -4, then y = -16.

Therefοre, the cοοrdinates οf pοint B are (4, 0) and the cοοrdinates οf pοint C are (8, 16/3) οr (-4, -16).

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Answer:

-5 is your answer

Step-by-step explanation:

What do you mean leading coefficient of the following polynomial.

Look at the x^n and see who has the biggest values.

-5x^7 is the leading coefficient.