A, B, and C take turns flipping a coin. The first one to get a head wins. The sample space of this experiment can be defined by S= 1,01,001,0001, ..., 0000... (a) Interpret the sample space. (b) Define the following events in terms of S: (i) A wins = A. (ii) B wins = B. (iii) (A U B). Assume that A flips first, then B, then C, then A, and so on.

Answer:

Answer. = 176 m sq.

Step-by-step explanation:

Hope it helps you

Have a nice day

Answer: 882.96

Step-by-step explanation:

The product of -16.98 and 5.2 is -88.296.

The given expression is -16.98 multiplied by 5.2. To find the product, multiply the two numbers:

-16.98 * 5.2 = -88.296.

Therefore, the product of -16.98 and 5.2 is -88.296. The correct answer is -88.296, which matches the second option. When multiplying a negative number by a positive number, the result is negative. The calculation involves multiplying the absolute values (16.98 and 5.2) and then assigning the negative sign to the product. In this case, the product is -88.296, as it accurately represents the multiplication of -16.98 and 5.2.

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the answer is on the picture

Answer: x=8

Step-by-step explanation: Hope this help :D

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Answer:

i hope this helps

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

use the formula for slope       y2-y1 / x2-x1

(-3,5)   (2,15)

15-5 / 2-(-3)

we know 15-5=10 and 2-(-3)=5

10/5 = 2

Answer:

2

Step-by-step explanation:

Slope is:

\(\frac{rise}{run}= \frac{change.in.y}{change.in.x}\)

("." in second fraction as it has multiply words)

We can plug our numbers in, and solve to find the slope:

- Coordinates are (x, y) -

\(\frac{change.in.y}{change.in.x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{15-5}{2--3}= \frac{15-5}{2+3}=\frac{10}{5} =2\)

So our slope is 2.

Hope this helps, have a nice day! :D

The values of f(2) = 0 & f(3) = 2.

Here given that,

f(0) = f(1) = 1

f(n+1) = (n)/(n-1)

We have to solve the equation if n = 1:

putting the value of n = 1 in the given equation f(n+1) = (n)/(n-1)

= f(1+1) = 1/(1-1)

= f(2) = 0

In the same way we have to solve the equation if n = 2:

putting the value of n = 2 in the given equation f(n+1) = (n)/(n-1)

= f(2+1) = 2/(2-1)

= f(3) = 2/1

= f(3) = 2

Hence the answer is the values of f(2) = 0 & f(3) = 2.

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Answer:

$100

Step-by-step explanation:

1L has 1000ml, so 1000/20=50x$2.00=$100

I think

Hope this helps

:)

The tip of the pendulum travels approximately 2.62 feet as it swings through an angle of 30 degrees.

The distance traveled by the tip of a pendulum is equal to the length of the arc of the circle traced out by the pendulum as it swings through the given angle. The length of the arc can be calculated as a fraction of the circumference of the circle.

In this case, the pendulum has a length of 5 feet, so the radius of the circle it traces is also 5 feet. The circumference of this circle is 2πr = 2π(5 ft) = 10π ft.

To find the length of the arc traced out by the pendulum as it swings through an angle of 30 degrees, we need to calculate what fraction of the circle's circumference this angle represents. Since a full circle has an angle of 360 degrees, we have:

fraction of circle's circumference = (30 degrees) / (360 degrees) = 1/12

Therefore, the length of the arc traced out by the pendulum is:

length of arc = (1/12) x (10π ft) = (5/6)π ft ≈ 2.62 ft

So the tip of the pendulum travels approximately 2.62 feet as it swings through an angle of 30 degrees.

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Answer:

a = \(\frac{2b - 2cd}{d^2}\)

Step-by-step explanation:

Step 1: Write out equation

2b = 2cd + ad²

Step 2: Subtract 2cd on both sides

2b - 2cd = ad²

Step 3: Divide both sides by d²

a = \(\frac{2b - 2cd}{d^2}\)

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

t ≥ 75

Step-by-step explanation:

"at least 75" means 75 or higher.

The temperature is equal to 75 or greater than 75.

t ≥ 75

The L.C.M of c, 3c , 3 is 3c.

The L.C.M of c, 3c, and 3, we first need to factor each term:
c cannot be factored any further.
3c can be factored as 3 x c.
3 cannot be factored any further.
Next, we look for the highest common factors among the factors of these terms.

The only common factor is 3, which is included in both 3c and 3.
Therefore, the L.C.M of c, 3c, and 3 is 3c.
The L.C.M (Least Common Multiple) of c, 3c, and 3 can be found by analyzing the factors of each term.
For c, the only factor is c itself.
For 3c, the factors are 3 and c.
For 3, the only factor is 3.
Now, find the LCM by taking the highest power of each unique factor:
LCM(c, 3c, 3) = 3 * c = 3c

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Answer:

40g : 3g

Step-by-step explanation:

12 kg : 900 g

unit conversion so that we can have the same unit in both ratios,

1 kg = 1000 g

so, 12 kg = 12000g

thus,

12000 g : 900 g

by simplifyig in lowest terms,

120 g : 9 g

40g : 3g

The annual compound growth rate of the Redstone Castle price is 73.10%.

From the information given, the formula to calculate the annual compound growth rate will be:

g = (F/P)^(1/n) - 1

where g = growth rate

f = final value = 19750000

p = initial value = 2200000

n = period = 2020 - 2016 = 4

g = (F/P)^(1/n) - 1

g = (19750000/2200000)^(1/4) - 1

g = 73.10%

Therefore, the growth rate is 73.10%

The price of the house in 1902 will be calculated thus:

PV = F/(1 + g)^n

= 19750000/(1 + 73.10%)^4

= $4811

The year that is considered as the time point 0 in that problem is 1902.

When the average compound growth rate in the question #2 now is compounded daily, the price of the house in 1902 will be $4071. The difference in values will be:

= $4811 - $4071

= $740

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The circumference of a circle is given by:

where d is the diameter.

In this case the diameter is 20, therefore the exact circunference is given by:

Using a calculator a rounding to the nearest hundreth the cicunference is 62.83 cm

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

0

Step-by-step explanation:

Since the x coordinate is -1, 2+t = -1, and thus t = -3.

So, y = 1+(3/(-3)) = 0.

After answering the provided question, we can conclude that Therefore, circle the length of the minor arc AB is approximately 50.9 cm.

A circle appears to be an a double component that is defined as the collection of all points in a jet that are equidistant out from hub. A circle is typically depicted with a capital "O" for the centre and a bottom end "r" for the radius, which represents the distance from where it started to any point on the circle. The formula 2r gives the girth (the distance from the center of the circle), where (pi) seems to be a proportionality steady roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which is the quantity of space inside the circle. To calculate the length of the minor arc AB, we need to first find the central angle that it subtends.

C = 2πr

r = C/(2π)

r = 65/(2π) ≈ 10.34 cm

angle = (arc length / radius) x (180/π)

ADB = 360° - AOB

ADB = 360° - 72° = 288°

angle ADB = (arc length AB / 10.34) x (180/π) = 288°

arc length AB = (288° x 10.34 cm x π) / 180 ≈ 50.9 cm

Therefore, the length of the minor arc AB is approximately 50.9 cm.

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Answer:

Explanations:

Given the system of equations:

- 2x + y = 7 .................................... 1

- 2x + y = -6 .................................. 2

Subtract both equations from each other to have;

-2x-(-2x) + (y-y) = 7 - (-6)

0x = 7 + 6

0x = 13

Divide both sides by 0

0x/0 = 13/0

x = 13/0

x = ∞

This shows that the system of equations has no solution

Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

The support vector of the input dsolve('Dy = -3*y') is "dsolve(diff(y,t) == -3*y)".

A symbol is a mathematical object that represents a mathematical entity, such as a number, a variable, or a function. In mathematical software, symbols are used to represent variables, which can be used in mathematical expressions to perform computations.

In the past, character vectors or strings were used to represent symbols in certain mathematical software programs.

In the future release of this software, support for character vectors or strings will be removed. Instead, the program will require users to use the "syms" function to declare variables as symbols.

As an example of how this might be used in practice, consider the differential equation

=> "dy/dt = -3y".

In the past, this equation might have been entered into a mathematical software program using a character vector or string to represent the variable "y".

However, in the future release of this software, the user will need to use the "syms" function to declare "y" as a symbol. The equation would then be entered using the "diff" function, like this:

=> "dsolve(diff(y,t) == -3*y)".

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Answer:

114.29

Step-by-step explanation:

All of the outside angles added together are 360 so it would be 7x+49+6x+33+83=360

13x+165=360

13x=195

x=15

The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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Answer:

Yes

Step-by-step explanation:

Answer:

The probability of an event can only be between 0 and 1 and can also be written as a percentage. ... If P ( A ) > P ( B ) P(A) > P(B) P(A)>P(B)P, left parenthesis, A, right parenthesis, is greater than, P, left parenthesis, B, right parenthesis, then event A has a higher chance of occurring than event B.

so that means yes

To solve the problem find the value of (45)^2 at first

The answer is 25 with the remainder 75

You can simplify the fraction to be 25/26