The expected value of the number of points you get is 0.
To find the expected value of the number of points you get, we need to calculate the probability of getting each outcome (rolling a prime number or rolling a composite number) and multiply it by the corresponding points.
Here's how we can do that:
There are 10 possible outcomes when rolling the ten-sided die, each with an equal probability of 1/10.
Prime numbers on the die: 2, 3, 5, 7 (total 4 numbers)
Composite numbers on the die: 4, 6, 8, 9 (total 4 numbers)
For prime numbers (4 possible outcomes):
Probability of rolling a prime number = Number of prime numbers / Total possible outcomes = 4/10 = 2/5
Points gained for rolling a prime number = 1
For composite numbers (4 possible outcomes):
Probability of rolling a composite number = Number of composite numbers / Total possible outcomes = 4/10 = 2/5
Points lost for rolling a composite number = -1
Expected value = (Probability of prime number [tex]\times[/tex]Points gained) + (Probability of composite number [tex]\times[/tex] Points lost)
Expected value = (2/5 [tex]\times[/tex] 1) + (2/5 [tex]\times[/tex] -1)
Expected value = 2/5 - 2/5
Expected value = 0
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what are the properties of a diamond plane shape
Step-by-step explanation:
A diamond is a two-dimensional flat quadrilateral with four closed straight sides. A diamond is also called a rhombus because it's sides are of equal measure and because the inside opposite angles are equal. Diamonds are also considered to be parallelograms because their opposite sides are parallel to each other
Nora kicks a football. Its height in feet is given by h = -16t² +64t where t
represents the time in seconds after kick. What is the football's greatest height?
The football's greatest height is 341.33 feet
How to find the football's greatest height?For any quadratic function of the form, at² + bt + c, the greatest point can be determined using formula:
greatest point = c - b²/2a
where a, b and c are constant
Since the height of the football in feet is given by h = -16t² +64t.
Thus, a = -16, b = 64 and c = 0
substituting:
greatest point = 0 - (64)²/2*(-6)
greatest point = -4096/(-12)
greatest point = 341.33 feet
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3.a coin is tossed, and a die is rolled. what is the probability that the outcome is a head or an even number?
According to the statement the probability of getting either a head or an even number on the die is 3/4.
To calculate the probability of getting a head or an even number, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
In this case, A represents getting a head, and B represents getting an even number on the die.
P(A) = Probability of getting a head = 1/2 (since there are two sides of the coin: heads and tails)
P(B) = Probability of getting an even number on the die = 3/6 (since there are three even numbers out of six possible outcomes: 2, 4, and 6)
P(A ∩ B) = Probability of getting both a head and an even number. Since these two events are independent, we can find this probability by multiplying the individual probabilities: P(A) * P(B) = (1/2) * (3/6) = 1/4
Now, we can find the probability of the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (3/6) - (1/4) = 1/2 + 1/2 - 1/4 = 3/4
So, the probability of getting either a head or an even number on the die is 3/4.
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Polar Coordinates
4. Name two different representations of the
point on the interval of [-2π, 2π].
Given P = (2,π /4).
Please help me, I got it wrong.
Please refer to picture.
The polar coordinates are solved the point is P ( 2 , π/4 )
Given data ,
Given the point P = (2, π/4) on the interval [-2π, 2π], here are two different representations of this point:
Cartesian Coordinates: (2, π/4)
In the Cartesian coordinate system, the point P is represented by its x and y coordinates. The x-coordinate is 2, and the y-coordinate is π/4.
Polar Coordinates: (2, 45°)
In polar coordinates, the point P is represented by its radius (distance from the origin) and angle. The radius is 2, and the angle is π/4, which is equivalent to 45 degrees.
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Which composite figure is made up of a cylinder and a half sphere?
a cliff overlooking dover lake is experiencing erosion, losing elevation at a rate of 5% every millennium. the cliff's current elevation is 1,519 meters. what will its elevation be in 10 millennia?
To calculate the cliff's elevation in 10 millennia, we need to use a little bit of math.
Since the cliff is losing elevation at a rate of 5% every millennium, we know that after one millennium, the cliff's elevation will be 95% of its current elevation. Therefore, we can use this formula to calculate the cliff's elevation after three millennia:
1,519 meters * 0.95^10 = 601.83 meters
So, after 10 millennia, the cliff's elevation will be approximately 601.83 meters. This means that the cliff will have lost approximately 917 meters of elevation over the course of 10,000 years due to erosion.
Finally, by applying the formula, we can determine the cliff's elevation in 10 millennia. After doing the calculation, we find that the final elevation will be approximately 744.29 meters.
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what is the probability of a type i error for a sample of size 10? (round your answer to four decimal places.)
The probability of a type i error for a sample of size 10 depends on the significance level (α) chosen for the hypothesis test. Assuming a standard significance level of 0.05, the probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software.
A type i error occurs when a null hypothesis is rejected when it is actually true. In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. A common significance level used in statistical analysis is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.
The probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software. The calculation involves finding the critical value of t at the chosen significance level and degrees of freedom (df), which is equal to the sample size minus 1 (n-1). For a sample size of 10 and a significance level of 0.05, the critical value of t is approximately 2.306 (from a t-distribution table with 9 degrees of freedom).
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = - + 7.
The Equation for Table I is y= 1/3x + 5.
The solution of the Equation is (3, 6).
Equation for Table II
y= -1/3 x +7
Table I:
Slope = (6-5)/ (3-0)
slope = 1/3
and, using slope intercept form
y - 5 = 1/3 (x - 0)
y-5 = 1/3x
y = 1/3x + 5
Now, solving the equation for both table we get
x= 3 and y= 6
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Tommy opens a bank account with an initial amount of $650. The account has an annual
interest rate of 3.5%. What will the account balance (principle+interest) be after 8 years if
the account is compounded:
a) annually?
b) quarterly?
c) weekly?
d) daily?
e) continuously?
Annually: $822.49
Quarterly: $842.67
Weekly: $849.01
Daily: $850.98
Continuously: $853.39
snow is falling in syracuse ny on wednesday morning there was 3 inches of snow in the morning and it is falling at a constant rate of 2 inches per hour. on friday morning there was 5 inches of snow on the ground and it is falling at a constant rate of 1 inch per hour. after how many hours would the total snow on the ground on each day be equal?
To solve this problem, we need to use algebra. Let x be the number of hours that have passed since Wednesday morning. Then the total snow on the ground on Wednesday morning is 3 inches, and the total snow on the ground at any time x hours later is:
3 + 2x
Similarly, the total snow on the ground on Friday morning is 5 inches, and the total snow on the ground at any time x hours later is:
5 + 1x
To find out when these two totals are equal, we can set the expressions equal to each other and solve for x:
3 + 2x = 5 + 1x
Subtracting 1x from both sides, we get:
2x = 2
Dividing both sides by 2, we get:
x = 1
Therefore, the total snow on the ground would be equal after 1 hour.
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PQR is a tangent to circle QABCD. AB || QD. CB=CD. Let 2, -30° and D₂ =70°. P A 1.1 Calculate Q₁. 1.2 Prove that C=110 A 1.3 Calculate B1
Help with my math please
Answer:
Step-by-step explanation:
x+y=5; x-y=3Adding both equations, we get:
2x = 8
x = 4Substituting the value of x in any of the equations:
x+y=5
4+y=5
y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:
3x+x+3=11
4x=8
x=2Substituting x=2 in the second equation:
y=x+3
y=2+3
y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:
6x-3y=-21Adding both equations, we get:
7x=-21
x=-3Substituting x=-3 in the first equation:
x+3y=0
-3+3y=0
y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:
6x+2(-3x-2)=-4
6x-6x-4=-4
-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:
5x-30y=-10Adding both equations, we get:
x-4x+5y-30y=-2+27
-x-25y=25
25y=-x-25
y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:
-4x+5(-(1/25)x-1)=27
-4x-5/5x-5=27
-9x=32
x=-32/9Substituting x=-32/9 in the expression for y:
y=-(1/25)(-32/9)-1
y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
A. 0
B. 1
C. 2
D. 3
E. 4
The number of horizontal asymptotes that graph of y = f(x) can have is (c) 2.
As x approaches negative infinity, the function f(x) approaches the horizontal-asymptote y = 0 because the term 1/x becomes negligible compared to other terms. This occurs in the portion of the function defined as 1/x when x < 0.
As x approaches positive infinity, the function f(x) approaches the horizontal-asymptote y = 2 because the term 2x becomes dominant compared to other terms. This occurs in the portion of the function defined as 2x - 1 when x ≥ 0.
Therefore, the graph of y = f(x) has two horizontal asymptotes: y = 0 as x approaches negative infinity and y = 2 as x approaches positive infinity. The correct answer is (c) 2.
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The given question is incomplete, the complete question is
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
f(x) = {1/x , if x<0,
= {2x - 1 , if x≥0.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
a circular diaphragm 58.06 cm in diameter oscillates at a frequency of 15.69 khz as an underwater source of sound used for submarine detection. far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. take the speed of sound in water to be 1450. m/s, and find the angle (in degrees) between the normal to the diaphragm and a line from the diaphragm to the first minimum.
The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees
To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:
sin(θ) = λ / (diameter)
where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.
First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:
wavelength = speed of sound / frequency
wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)
wavelength = 0.09257 meters (rounded to five decimal places)
Next, we can substitute the values into the formula to find the angle:
θ = [tex]sin^{(-1)}[/tex] (0.09257 meters / 0.5806 meters)
θ ≈ 9.43 degrees (rounded to two decimal places)
Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.
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given f(x)=3x+2 and g(x)= √x-1, determine the following: f(g(17))=
The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.
We have,
A function is simply a relationship that maps one input to one output.
Given that:
f(x) = 3x + 2
g(x) = √( x - 1 )
g(f(x)) = ?
First, set up the composite result function:
Evaluate g( 3x + 2 ) by substituting in the value of f into g.
g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )
Simplify
g( 3x + 2 ) = √( 3x + 2 - 1 )
g( 3x + 2 ) = √( 3x + 1 )
Evaluate the result function by replacing the x with 8.
g( f(x) ) = √( 3(8) + 1 )
g( f(x) ) = √( 24 + 1 )
g( f(x) ) = √( 25 )
g( f(x) ) = 5
Therefore, the composite result function g( f(x) ) is 5.
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complete question;
Given f(x)=3x+2 and g(x)= √x-1, determine the following: g(f(8))=
Find the value of m if polynomial p(x) = 4x2 – 6x – m is exactly divisible by x – 3.
Answer:
Since p(x) is exactly divisible by x – 3, then p(3) = 0.
Plugging in x = 3 into p(x), we get
4(3)2 – 6(3) – m = 0
36 – 18 – m = 0
m = 18
Therefore, the value of m is 18.
Step-by-step explanation:
What is the probability that a randomly chosen college student exercises in the morning or the afternoon, but not both?
a spinner has five equal sections labeled a, b, c, d, and e. a fair coin has faces labeled heads and tails. carlos will spin the arrow of the spinner and flip the coin one time each. what is the probability the arrow will land on the section labeled a and the coin will land on heads?
The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.
To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.
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Which of the following inequalities has a solution set represented by the following graph?
There are two ways you could approach this.
The first is to solve each inequality separately and see which one ends up equal to x ≥ -1.
Another and faster option is to test 0 in each inequality, because 0 is in the solution set and 0 is easy to work with. (You could do this for any value in the solution set.)
A: Is 4(0) + 3 > 7 true? No. 3 > 7 is false. This eliminates A.
B. Is 0/3 - 2 ≥ 2 true? No. -2 ≥ 2 is false. This eliminates B.
C. Is -2(0) - 3 ≤ -1 true? Yes. -3 ≤ -1 is false. We cannot eliminate C.
D. Is 0 + 5 < 4 true? No. 5 < 4 is false. This eliminates D.
So based on using x=0, the only possible solution is C.
You can double check this by solving 2x - 3 ≤ -1 for x:
-2x - 3 ≤ -1
-2x ≤ 2 (by adding 3 to both sides)
Now when you divide by -2 to solve for x, remember to flip the inequality.
-2x ≤ 2
x ≥ -1
So this confirms that C is correc.
Directions: Find the volume of each figure. Round to the nearest hundredth.
2.
1.
3.
5.
8 m.
7.
34 m
3 km
** This is a 2-page
EXER
11 cm
P
4.
end 1601 02
6.
11 yd
Tw
10.8 ft
Directions: Find the surface area of each figure. Round to the nearest hundredth.
8.
0-
29 in
8.6 ft
boil Co
II in
3.
13.4 mm
5.
98
7.
1956
The calculated volumes of the figures are 2145.52 cubic meters, 697.19 cubic yards, 20587.81 cubic meters, 2639.40 cubic feet, 56.57 cubic km and 6387.60 cubic inches
How to find the volume of the figuresThe sphere 1
The volume is calculated as
V = 4/3πr³
Where
r = Radius = 8 meters
So, we have
V = 4/3 * 22/7 * 8³
Evaluate
Volume = 2145.52 cubic meters
The sphere 2
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (11/2) yards
So, we have
V = 4/3 * 22/7 * (11/2)³
Evaluate
Volume = 697.19 cubic yards
The sphere 3
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (34/2) meters
So, we have
V = 4/3 * 22/7 * (34/2)³
Evaluate
Volume = 20587.81 cubic meters
The hemisphere 4
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 10.8 feet
So, we have
V = 2/3 * 22/7 * 10.8³
Evaluate
Volume = 2639.40 cubic feet
The hemisphere 5
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 3 km
So, we have
V = 2/3 * 22/7 * 3³
Evaluate
Volume = 56.57 cubic km
The hemisphere 6
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 29/2 in
So, we have
V = 2/3 * 22/7 * (29/2)³
Evaluate
Volume = 6387.60 cubic inches
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[tex]\frac{2x-1}{3} -\frac{3x}{4} =\frac{5}{6}[/tex]
The value of the variable is -14
What are fractions?Fractions are simple defined as the part of a whole number or variable.
From the information given, we have that;
2x - 1/3 - 3x/4 = 5/6
Find the LCM, we have;
4(2x - 1) - 3(3x) /12 = 5/6
expand the bracket, we get;
8x - 4 - 9x/12 = 5/6
collect the like terms
-x - 4/12 = 5/6
cross multiply the values
-6x - 24 = 60
collect like terms
-6x = 84
make 'x' the subject
x = -14
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Choose the INCORRECT statement below.
Answer:
The thrid one
Step-by-step explanation:
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the test statistic for testing equality of proportions multiple select question. assumes when samples are large that p1 - p2 is normally distributed. uses a pooled proportion to calculate the standard error. is a t statistic. is a z score
The test statistic for testing equality of proportions is a z-score. It is calculated by dividing the difference in sample proportions by the standard error. The resulting z-score is then compared to critical values from the standard normal distribution to determine the statistical significance of the difference in proportions.
The correct options for the test statistic for testing the equality of proportions in a multiple-select question are:
Assumes when samples are large that p1 - p2 is normally distributed.
Uses a pooled proportion to calculate the standard error.
Is a z-score.
When the samples are large, the difference between two proportions (p1 - p2) can be approximated to follow a normal distribution. This assumption is based on the Central Limit Theorem.
To calculate the standard error in this scenario, a pooled proportion is used. The pooled proportion combines the proportions from both samples to estimate the common population proportion.
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1. If we had a large 16 inch pizza for $14, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
2. If we had a medium 14 inch pizza for $12, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
Answer: $0.07 and $0.08
Step-by-step explanation: 1. To find the price per square inch of a 16 inch pizza for $14, we need to first calculate the area of the pizza.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the radius is half of the diameter, which is 8 inches.
So, the area of the pizza is A = π(8)^2 = 64π square inches.
The price per square inch is the total price divided by the area of the pizza:
Price per square inch = Total price / Area
Price per square inch = $14 / (64π) square inches
Price per square inch ≈ $0.07
Therefore, the price per square inch of a 16 inch pizza for $14 is approximately $0.07.
Answer: $0.07
2. Following the same method as above, for a 14 inch pizza for $12, the radius is 7 inches and the area is A = π(7)^2 = 49π square inches.
The price per square inch is:
Price per square inch = Total price / Area
Price per square inch = $12 / (49π) square inches
Price per square inch ≈ $0.08
Therefore, the price per square inch of a 14 inch pizza for $12 is approximately $0.08.
Answer: $0.08
measuring the concentration of a certain pollutant in a lake results in the determination that observations are normally distributed with mean (expectation) 210 units, and that there is a probability of 0.05 that a given measurement will exceed 250 units. 1. what is the standard deviation? 2. assuming that the standard deviati
The standard deviation is approximately 24.28 units.
1. The standard deviation can be calculated using the formula for the normal distribution:
P(X > 250) = 0.05
Using a standard normal distribution table, we can find the corresponding z-score for a probability of 0.05, which is approximately 1.645.
z = (250 - 210) / σ
Solving for σ, we get:
σ = (250 - 210) / z = (250 - 210) / 1.645 = 24.28 units
Therefore, the standard deviation is approximately 24.28 units.
To determine the standard deviation of a normally distributed pollutant concentration in a lake, we first use the probability of exceeding 250 units (0.05) and a standard normal distribution table to find the corresponding z-score (1.645). Using this z-score and the given mean (210 units), we can solve for the standard deviation using the formula for the normal distribution. The resulting standard deviation is approximately 24.28 units.
The standard deviation is an important measure of variability in a dataset and can be calculated using the formula for the normal distribution. In this case, the standard deviation of a normally distributed pollutant concentration in a lake was calculated using the mean and probability of exceeding a certain value.
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If f(3x - 1) = -6x + 3, find f f (2).
Therefore, function of x f(f(2)) = f(-3) = 9
Function (X) calculationTo find function of f f (2) we need to find the function f(2).
Given f(3x - 1) = -6x + 3
Let 3x -1 = 2 we will get
3x =3
x =1
Therefore, let input x =1
f(3x - 1) = -6x + 3
f(3(1) - 1) = -(1) + 3
Therefore, we need to find function of f(-3) and get f f (2).
f f (2). =f(-3) =9
f(3x - 1) = -6x + 3
f(-3) = -6(-1) + 3 =9
Therefore, if f(3x - 1) = -6x + 3, function of f(f(2)) = f(-3) = 9
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Evaluate the following expression.
25
1/25
-25
-1/25
The expression is evaluated to 1/25. Option B
What are index forms?Index forms are simply described as distinct mathematical forms that are used in the representation of variables or numbers that are too large or too small in more convenient forms.
These index forms are also referred to as scientific notations or standard forms.
Some rules of index forms are;
Add the exponent value of variables or number that have the same bases and are being multipliedSubtract the exponent value of variables or number that have the same bases and are being dividedThe value of a number with negative power is its inverseFrom the information given, we have that;
1/5⁻²
Take the inverse power
1/25
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how many units is -1+(-4) from -1
The expression -1 + (-4) is 4 units away from -1.
How to find the unitsThis can be solved using the concept of number line.
A number line is a visual representation of all real numbers placed on a straight line with an arbitrary point as the origin the origin is usually represented as zero and the numbers increase from left to right or from right to left
Another way is to find how many units -1 + (-4) is from -1, we need to subtract -1 from -1 + (-4) this is done below
= -1 + (-4) - (-1)
= -1 - 4 + 1
= -4
we can say that, -1 + (-4 ) is 4 units away from -1.
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Use the organized list which shows the possible outcomes of flipping a fair coin three times, where H is heads and T is tails.
The correct probabilities given the sample space would be:
P ( one tails ) = 0. 375P ( at least two tails ) = 0. 125P ( at least one heads ) = 0. 875How to find the probabilities ?The number of outcomes with one tail :
HHT, HTH, THH which is 3.
The probability is :
= 3 / 8
= 0. 375
The number of outcomes with at least two tails :
HTT, THT, TTH, TTT which is 4 :
= 4 / 8
= 0. 50
The number of outcomes with at least one heads :
HHH, HHT, HTH, HTT, TTH, THT, TTH which is 7 outcomes:
= 7 / 8
= 0. 875
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please help me I dont know how to do this please I need it done ASAP!!!!!
All the solutions are as;
LJ = 18 feet
m GM = 77 deg
m QT = 142 deg
m ∠STR = 23 deg
m ST = 13 deg
m RQ = 38 deg
Now, We can formulate;
Since, KP = PL
Hence, HP = PJ
Then, Δ PKH ≅ Δ PLJ
By HL property.
As point K, L are midpoint of GH and GJ.
Then, KH ≅ LJ = 1/2(JH)
⇒ LJ = 1/2 (36) = 18 feet
As, GH ≅ GJ
Then,
m GM = 1/2 (1/2 (m GM) = 1/4 (360 - 52) = 77 deg.
As, m ∠QST = 71°,
So, m QT = 2 (m ∠QST) = 2 (71) = 142 deg
m ∠STR = 1/2 (m SR) = 1/2 (46) = 23 deg
As RT is a diameter then,
m ∠TSR = 90°
Then, m ∠SRT = 190 - 90 - m ∠STR
m ∠SRT = 67 deg
Hence, m ST = 2 m ∠SRT = 2 (67) = 134 deg
Since, m ∠RSQ = 90 - 71 = 19 deg
And, m RQ = 2 ( m ∠RSQ)
m RQ = 2 × 19 = 38 deg
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