From the given information provided, emily and john should drink 56.7 cups of water for 42 hours hiking.
If hikers should drink 2.7 cups of water for every 2 hours of hiking, then we can use a proportion to find how much water Emily and John should drink over their 42-hour hike:
2.7 cups / 2 hours = x cups / 42 hours
To solve for x, we can cross-multiply:
2.7 cups × 42 hours = 2 hours × x cups
113.4 cups = 2x
Finally, we can divide both sides of the equation by 2 to solve for x:
x = 56.7 cups
Therefore, Emily and John should drink a total of 56.7 cups of water during their 42-hour hike.
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Which of the following shows that the two composite figures cover the same area?
-7
5-
y
7
The two composite figures cover the same area, A = 4+2+2+1= 9 units²
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
we know that
The area for both composite figures is equal to the area of a square plus the area of two isosceles right triangles plus the area of a smaller isosceles triangle
So
Area of the square
A = 2² = 4 units²
Area of the isosceles right triangle
A = (1/2) (2) (2) = 2 units²
Area of the smaller isosceles triangle
A = (1/2)(2)(1) = 1 units²
The area of the composite figure is
A = 4+2+2+1= 9 units²
Hence, the two composite figures cover the same area, A = 4+2+2+1= 9 units²
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Write ^4√11^5 without radicals.
Answer: ^4√11^5 = 11^(5/4)
Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.
So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:
^4√11^5 = (11^5)^(1/4) = 11^(5/4)
Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.
Hope this helps, and have a great day!
5-1 Additional Practice 1. Look at the paper to the right. a. Write an equation to represent the description. 8 more than 4 times number 28 b. Describe a real-world situation the equation could represent.
HELP I CANT GET LUNCH DETENTION
linear Equation to represent the description "8 more than 4 times number 28" is: y = 4x + 8
What is linear equation ?
A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
The slope, m, represents the rate of change of y with respect to x, or how steep the line is. It is calculated as the change in y divided by the change in x between any two points on the line.
According to the question:
a. An equation to represent the description "8 more than 4 times number 28" is:
y = 4x + 8
where x represents the number 28, and y represents the result of multiplying 28 by 4 and then adding 8.
b. A real-world situation that this equation could represent is the cost of purchasing a certain number of items. For example, if the price of one item is $28, and there is a discount of 8 dollars for every four items purchased, the equation y = 4x + 8 could be used to calculate the total cost y of purchasing x items. The 4x term represents the cost of the items before the discount, and the +8 term represents the discount. For instance, if a customer wants to purchase 12 items, they would pay 4 * $28 = $112 for the first 12 items, minus $8 for the discount, resulting in a total cost of $104.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
According to the given information, the two equations that are true for x=-2 and x=2 are 4x²-16=0 and 2(x-2)²=0.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
The values of x=-2 and x=2 satisfy the equation 4x²=16, so 4x²-16=0 is true for both x=-2 and x=2.
The equation x²=-4 has no real solutions, so it is not true for either x=-2 or x=2.
The equation 3x²+12=0 is not true for either x=-2 or x=2 , because 3x²+12 is always positive for any real value of x .
The equation 2(x-2)²=0 is only true for x=2 , because plugging in x=-2 gives 2(-4)² =32 ≠0.
Therefore, the two equations that are true for x=-2 and x=2 are 4x²-16=0 and 2(x-2)²=0 .
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6. A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 3. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 4 meters, with an interval of 8 seconds between maximums. Based on the context of the problem, what are the values of a and b? = b a = 1 and 4 a = 1 and 8 = a = 2 and 4 = b a = 2 and 8
The values of a and b are a = 1 and b = π/4.
Explanation:
We know that the height of the innertube can be modeled by the function:
h = asinbx + 3
where h is the height in meters,
a is the amplitude of the wave,
b is the frequency of the wave in cycles per meter, and
3 is the average height of the wave.
We also know that the innertube's height fluctuates between 2 meters and 4 meters, so we can set up the following equation:
2 <= asinbx + 3 <= 4
Subtracting 3 from each term, we get:
-1 <= asinbx <= 1
Dividing by a, we get:
-1/a <= sinbx <= 1/a
Since the maximum value of sinbx is 1 and the minimum value is -1, we know that:
1/a >= 1 or -1/a <= -1
Simplifying, we get:
a <= 1 or a >= -1
However, a must be positive because it represents the amplitude of the wave. Therefore, we have:
a >= 1
Next, we can use the fact that the innertube reaches its maximum height every 8 seconds to find the value of b. Since the period of a sine function is given by:
period = 2π / b
and the period in this case is 8 seconds, we have:
8 = 2π / b
Solving for b, we get:
b = 2π / 8 = π / 4
Therefore, the values of a and b are:
a = 1 and b = π / 4
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what is the value of x?
Applying the triangle proportionality theorem, the value of x is calculated as: D. 15.
How to Apply the Triangle Proportionality Theorem?The Triangle Proportionality Theorem (also known as the Side-Splitter Theorem) states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally
Based on the triangle proportionality theorem, we have:
x - 6 / 3 = x / 5
Cross multiply:
5(x - 6) = 3x
5x - 30 = 3x
Combine like terms to find the value of x:
5x - 3x = 30
2x = 30
x = 30/2
x = 15
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Let triangle ABC be similar to DEF. Find the missing side EF.
The length of the side EF is equal to 18 units since the triangle DEF and triangle ABC are similar and DEF is bigger than ABC in the margin of 3 times.
Given, two triangles ABC and DEF.
The length of AB = 8 units
The length of its concurrent side DE = 24 units
Also given that the length of BC = 6 units
Here we can see that:
As both triangles are similar, their corresponding sides are in proportion.
This means that:
[tex]\frac{BC}{EF} = \frac{AE}{DE} =\frac{AC}{DF}[/tex]
Length of AB * 3 = Length of DE
Now the length of the side EF will be 3 times more than the side BC.
Length of EF = Length of BC * 3
Length of EF = 6 * 3
Length of EF = 18 units.
Therefore, the length of the side EF is equal to 18 units.
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what is the difference of (4m^2-5) -(5m-20)
Answer:
4m^2+15-5m
Step-by-step explanation:
Remove parentheses.
4m^2-5-5m+20
Collect like terms.
4m^2+(-5+20)-5m
Simplify
4m^2+15-5m
n/45 = 1/15 Please select the best answer from the choices provided
a. n= 1/3
b. n= 4
c. n= 675
d. n= 3
a spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 20 cm to 10 cm in 30 minutes. at what rate, in cm3 per minute, is the volume of the snowball changing at the instant the radius is 9 cm?
The volume of the snowball is decreasing at a rate of approximately 108π cubic centimeters per minute when the radius is 9 cm.
The volume V of a sphere with radius r is given by the formula V = (4/3)πr^3. To find the rate at which the volume is changing with respect to time, we need to take the derivative of V with respect to time t. Using the chain rule, we get:
dV/dt = (dV/dr) * (dr/dt)
Since the radius is changing at a constant rate, we can calculate dr/dt by dividing the change in radius by the time interval:
dr/dt = (10 cm - 20 cm) / (30 minutes) = -1/3 cm/min
To find dV/dr, we can take the derivative of the volume formula with respect to r:
dV/dr = 4πr^2
Substituting the given radius of 9 cm, we get:
dV/dr = 4π(9)^2 = 324π cm^2
Finally, we can substitute these values into the formula for dV/dt:
dV/dt = (dV/dr) * (dr/dt) = 324π cm^2 * (-1/3 cm/min) = -108π cm^3/min
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Add the additive inverse to the product of - 1 and - 4
The answer to this question is 0.
To add the additive inverse to the product of - 1 and -4, we must first find the product of -1 and -4. The product of -1 and -4 is 4. Now that we have found the product of -1 and -4, we can add the additive inverse to it. The additive inverse of 4 is -4, so we add -4 to 4. 4+ (-4) is equal to 0. Therefore, the answer to this question is 0.
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What is the base, rate of change (incr/decr), and is it growth or decay
Y=3000(0.72)^x
The key features of the function are Base = 0.72, Rate = decrement and it decays
identifying the key features of the functionGiven that
y = 3000 * (0.72)ˣ
The given equation is in the form of exponential decay:
Base: The base of the exponential function is the constant term that is being raised to a power. In this case, the base is 0.72.
Rate of change: The rate of change is the factor by which the function is being multiplied or divided as the input variable increases.
Since the base is less than 1, the function is decreasing as x increases. The rate of decrease is given by the base, which is 0.72.
Growth or decay: As the base is less than 1, the function is decreasing, which means it is a decay function.
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Find the linear measure of arc KML on OO, where line segment KM is a diameter, OM=36, and angle KOL-145. Use 3. 14 for pie and estimate your answer to two decimal places
The linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
Since KM is a diameter, angle KOM is a right angle. Therefore, angle KOL is a straight angle, which means that angle MOL is 180 - 145 = 35 degrees.
Now, we can use the fact that the measure of an arc is proportional to the measure of the angle it subtends. In particular, if the measure of an angle in degrees is θ and the radius of the circle is r, then the length of the arc it subtends is given by:
length of arc = (θ/360) * 2πr
In this case, the radius of the circle is half of the diameter KM, which is 36/2 = 18. So we have:
length of arc KML = (35/360) * 2 * 3.14 * 18
≈ 3.33
Therefore, the linear measure of arc KML on OO is approximately 3.33 units, rounded to two decimal places.
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you roll a 6 sided die.
What is P(not greater than 3)? Write your answer as a fraction or whole number.
Answer:
1/2
Step-by-step explanation:
options in a 6 sided die= 1,2,3,4,5,6
greater than 3 = 4,5,6
so three sides out of a 6 sided die is greater than three
P(not greater than 3) = [tex]\frac{6-3}{6} = \frac{1}{2}[/tex]
Answer:
1/2 or 0.5
Step-by-step explanation:
The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.
To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:
P(not greater than 3) = 1 - P(greater than 3)
P(not greater than 3) = 1 - 1/2
P(not greater than 3) = 1/2
Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.
Borachio eats at the same fast-food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4. 2 minutes and standard deviation 1. 3 minutes. A. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served. B. Find the probability that average time until he is served in eight randomly selected visits to the restaurant will be at least 5 minutes
The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is 0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.
Given that mean μ = 4.2 , standard deviation σ = 1.3
1. P(X >= 5) = P((X - μ)/σ >
= (5 - 4.2) /1.3
= P(Z ≥ 0.6154)
= 1 - P(Z < 0.6154)
= 1 - 0.7324
= 0.2676
The required probability is 0.2676.
2.Given that n = 8 then [tex]\bar x[/tex] = σ/[tex]\sqrt{(n)[/tex] = 1.3/√(8) = 0.4596
P(x-bar ≥ 5) = P(([tex]\bar x[/tex] - μ)/σx-bar ≥ (5 - 4.2)/0.4596)
= P(Z ≥ 1.7406)
= 1 - P(Z < 1.7406)
= 1 - 0.9591
= 0.0409
The required probability is 0.0409.
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Matt wants to buy a tie. The prices of similar ties offered by four different online retailers are listed. $15.50, $17.50, $16.00, $18.00 What is the mean absolute deviation of the prices of the ties?
Answer: mean-16.75
population size- 4
Step-by-step explanation:
A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Which of the following is the best interpretation of the interval? Five percent of the time, the time for response is less than 2.8 minutes or greater than 12.3 minutes. B The probability is 0.95 that a randomly selected time for response will be between 28 minutes and 12.3 minutes Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes. (D) We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.
The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct
A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.
Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.
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what is the modular inverse of $11$, modulo $1000$? express your answer as an integer from $0$ to $999$, inclusive.
The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.
To find the modular inverse of 11 modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].
One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.
We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.
Applying the extended Euclidean algorithm, we have:
1000= 11 *90 + 10
11 = 10 *1 + 1
Working backward, we can express 1 as a linear combination of 11 and 1000:
1 =11 - 10* 1
= 11 - (1000 - 11*90)
= 901 * 11 - 1 *1000
Therefore, the modular inverse of 11 modulo 1000 is 901, since
11*901=1 mod{1000}.
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What is the lcd of 2/5,1/2, and 3/4
The LCD of 2/5, 1/2, and 3/4 is equal to 20.
What is LCD?In Mathematics, LCD is an abbreviation for least common denominator or lowest common denominator and it can be defined as the smallest number that can act as a common denominator for a given set of fractions.
Next, we would determine the factors of the denominators for the given fraction 5, 2, and 4 as follows;
5 = 5 × 1
2 = 2 × 1
4 = 2 × 2 × 1
Therefore, the least common denominator (LCD) would be calculated as follows:
Least common denominator (LCD) = 5 × 2 × 2 × 1
Least common denominator (LCD) = 20.
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Please answer my question by the way the number 4 and 5 is FOIL.
Using FOIL method for the multiplication, we have:
1: 3x (5x - 4) = 15x² - 12x
2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²
3: (4x + 3)(4x -5) = 16x² - 8x - 15
4: (7x - 3)(4x - 5) = 28x² - 47x + 15
How to carry out multiplication using FOIL?
FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.
No. 1
3x (5x - 4) = 3x*5x + 3x*(-4)
= 15x² - 12x
No. 2
x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1
= 5x⁴ + 3x²y + x²
No. 3
(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)
= 4x*4x + 4x*(-5) + 3*4x + 3*(-5)
= 16x² - 20x + 12x - 15
= 16x² - 8x - 15
No. 4
(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)
= 7x*4x + 7x*(-5) - 3*4x - 3*(-5)
= 28x² - 35x -12x + 15
= 28x² - 47x + 15
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What is the area of the parallelogram
Base is 8 height is 5 and width is 5.1:
I NEED AN ASWER ASAP
Pls Help I am stuck on this and i don't know how to do this
Men will have completed oil changes in hours Therefore, Will and Gabriel will each have done 12 oil changes after 4 hours.
What is hours?Hours is a unit of time measurement. It is used to measure a specific amount of time and is usually denoted by the symbol “h”. There are 24 hours in a day, 60 minutes in an hour and 60 seconds in a minute. Hours are used to measure both short and long periods of time. Commonly, hours are used to measure the length of a workday, the length of a school day, or the length of a movie. Hours are also used to measure how long a person has been alive, how long an event has been going on, or how long an item has been in use.
Let W be the total number of oil changes Will has completed, and G be the total number of oil changes Gabriel has completed.
System of equations:
W = 8 + 2t
G = 3t
Since they will be tied at some point during the day, W = G.
Substituting W into G's equation:
8 + 2t = 3t
Solving for t:
2t = 8
t = 4
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If the ratio of the number of cats to dogs at an
animal shelter is 9 to 5, which of the following is
the possible number of cats to dogs at the animal
shelter?
Answer:
If the ratio of the number of cats to dogs at the animal shelter is 9 to 5, this means that for every 9 cats at the shelter, there are 5 dogs.
We can express this ratio as:
number of cats : number of dogs = 9 : 5
To find the possible number of cats to dogs, we need to look for pairs of numbers that have a ratio of 9:5. Here are some possible pairs:
9 cats : 5 dogs
18 cats : 10 dogs
27 cats : 15 dogs
36 cats : 20 dogs
45 cats : 25 dogs
54 cats : 30 dogs
...
We can see that there are infinitely many possible pairs of numbers that have a ratio of 9:5. To narrow down the possibilities, we need more information such as the total number of animals at the shelter or the number of cats or dogs at the shelter.
Two thirds of a number X subtracted from four times the sum of y and 5
Answer: 4y - (2/3)x + 20
Step-by-step explanation:
Write out problem: 4(y+5) - (2/3)x
Expand: 4y + 20 - (2/3)x
Reorder: 4y - (2/3)x + 20
A primary credit card holder has a current APR of 16.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent?
To calculate the monthly periodic interest rate from an annual percentage rate (APR), we need to divide the APR by 12 (the number of months in a year). We can use the following formula:
Monthly periodic interest rate = APR / 12
In this case, the APR is 16.75%, so we can plug it into the formula and simplify:
Monthly periodic interest rate = 16.75% / 12
Monthly periodic interest rate = 1.395833...%
Rounding to the nearest hundredth of a percent, we get:
Monthly periodic interest rate = 1.40%
Therefore, the monthly periodic interest rate for the primary credit card holder is 1.40%.
Please help work this out with workings out
You usually buy the same small bottle of shampoo.
There is a larger, 6.7
-ounce bottle that says it gives you 25%
more free.
What is the size in ounces of the original smaller bottle of shampoo?
Round your answer to the nearest tenth.
Answer:
If the larger bottle of shampoo gives 25% more for the same price, then it must contain 1.25 times the amount of shampoo in the smaller bottle. Let's represent the size of the smaller bottle as x ounces.
Thus, we can set up the following equation:
x * 1.25 = 6.7
Solving for x, we get:
x = 6.7 / 1.25
x ≈ 5.36
Therefore, the size of the original smaller bottle of shampoo is approximately 5.4 ounces (rounded to the nearest tenth).
How do I solve this challenging math problem?
Answer:
13/32
Step-by-step explanation:
You want the area of the shaded portion of the unit square shown.
CircumcenterPoints B, C, E are shown as equidistant from point F, so will lie on a circle centered at F. The center of that circle is at the point of coincidence of the perpendicular bisectors of BE, BC, and CE.
Without loss of generality, we can let line EF lie on the x-axis such that E is at the origin. Chord EB of the circle has a rise of 1/2 for a run of 1, so a slope of 1/2. Its midpoint is (1, 1/2)/2 = (1/2, 1/4). The perpendicular line through this point will have slope -2, so its equation can be written ...
y -1/4 = -2(x -1/2)
y = -2x +5/4
Then the x-intercept (point F) will have coordinates (0, 5/8):
0 = -2x +5/4 . . . . . y=0 on the x-axis
2x = 5/4
x = 5/8
TrapezoidTrapezoid EFCD will have upper base 5/8, lower base 1, and height 1/2. Its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(5/8 +1)(1/2) = (1/4)(13/8) = 13/32
The shaded area is 13/32.
__
Additional comment
The point-slope equation of a line through (h, k) with slope m is ...
y -k = m(x -h)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(9x-1)º
74°
62°
PLS HURRY!!
In the given triangle, the value of x = 5.
What is a triangle's definition?
A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.
Now,
As we know the property of a triangle that
sum of all angles of triangle=180°
given angles are (9x-1)°, 74° and 62°
then,
9x-1+74+62=180°
9x+135=180
9x=45
x=5
Hence,
the value of x is 5.
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You have the option to pick between an action, horror, or
romantic comedy movie. You can also go at either 5pm, 7pm,
8pm, or 9pm. What is the total number of possible outcomes?