Based on control groups, experiments indicate cause-and-effect relationships. While observational studies, great care must be taken in concluding cause and effect. Correct options are i and ii.
Statement i is a true statement. Experiments are designed to test causal relationships between variables by manipulating one variable while keeping all others constant, allowing researchers to establish cause-and-effect relationships with greater certainty.
The use of control groups allows researchers to isolate the effects of the independent variable from other potential confounding variables.
Statement ii is also a true statement. Observational studies are more prone to the influence of lurking variables that cannot be controlled for, which makes it more difficult to establish a cause-and-effect relationship between variables.
However, careful analysis and the use of statistical methods can help control for the influence of some lurking variables and provide evidence to support a causal relationship.
Statement iii is a false statement. While a complete census can provide comprehensive information about a population, it does not necessarily establish cause-and-effect relationships absolutely.
Causality is typically established through well-designed experiments or observational studies that carefully control for confounding variables, and it is rare for any single study to establish causal relationships with absolute certainty.
Instead, scientific evidence is accumulated over time through multiple studies that support the same conclusion, and even then, there is always some degree of uncertainty and potential for alternative explanations.
Correct options are i and ii.
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the shaded rectangle is twice long as it is wide. the perimeter of the rectangle is 30 cm.
Answer:Width=5, Length=10
Step-by-step explanation:
You can solve this by using a variable, x, and assigning it to the value that is the width.
Since the perimeter of a rectangle is the width times two plus the length times two, you can use an equation that looks like this:
(image shown)
This will give you the value of X, the width, and you can multiply this value by 2 to get the length.
Answer:
10 cm
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length and w is the width1. We know that the perimeter of this rectangle is 30 cm. So we can write:
2(2w + w) = 30
Simplifying this equation gives:
6w = 30
Therefore:
w = 5
So the width of the rectangle is 5 cm and its length is twice as long as its width which means it’s 10 cm.
write the exspession 36+4 as a product using greatest common factor and the distributive property.
We can use the distributive property and the greatest common factor to write 36 + 4 as 4(9 + 1) or 4(10).
Using the distributive property, we can write:
36 + 4 = 4(9 + 1)
Next, we can identify the greatest common factor (GCF) of 9 and 1, which is 1. Since there are no other common factors between 9 and 1, we can write:
9 + 1 = 10
Therefore, we can express 36 + 4 as:
36 + 4 = 4(9 + 1) = 4(1 × 9 + 1) = 4(10)
So, 36 + 4 can be written as the product of 4 and 10, where 4 is the GCF of 36 and 4, and 10 is the sum of the two terms divided by their GCF. This is an example of factoring by grouping, which can be a useful technique in algebra and other areas of mathematics.
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What are the vertex and range of y = |2x + 6| + 2?
A) (0, 2); 2 < y < ∞
B) (0, 2); −∞ ≤ y < ∞
C) (−3, 2); 2 < y < ∞
D) (−3, 2); −∞ ≤ y < ∞
The vertex of the absolute value function is (-3, 2).
The range of the function is 2 < y < ∞.
Option C is the correct answer.
We have,
To find the vertex of the given absolute value function, we can first find the vertex of the related linear function, which is y = 2x + 6.
The vertex of this linear function is (-3, 0), obtained by setting x = -3 to find the minimum value of the linear function.
Since the given absolute value function has the same shape as the related linear function but is shifted up by 2 units,
The vertex of the absolute value function is (-3, 2).
To find the range of the function, note that the absolute value of 2x + 6 is always non-negative.
Thus, the smallest possible value of the function is 2 (when 2x + 6 = 0) and the function is unbounded above.
Therefore, the range of the function is 2 < y < ∞.
Therefore,
The vertex of the absolute value function is (-3, 2).
The range of the function is 2 < y < ∞.
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Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
Find an orthogonal matrix A where the first row is a multiple of (3,3,0). [ ___ ___ ___ ]A= [ ___ ___ ___ ][ ___ ___ ___ ]
Orthogonal matrix A that satisfies the given conditions is:
[3 3 0 ]
[1/√(2) -1/√(2) √(2/9)]
[-√(2)/2 √(2)/2 √(2)/2]
How to evaluate orthogonal matrix A?Let's call the first row of matrix A as r1, which is a multiple of (3, 3, 0). Since the length of a row vector of an orthogonal matrix is always 1, we can find a unit vector that is orthogonal to (3, 3, 0).
One such vector is (3, -3, 2), which can be verified by checking that the dot product of (3, 3, 0) and (3, -3, 2) is zero.
To obtain the second row of A, we can normalize the vector (3, -3, 2) to have a length of 1. This gives us:
(3, -3, 2)/√(18) = (1/√(2), -1/√(2), √(2/9))
To obtain the third row of A, we can take the cross product of the first two rows to get a vector that is orthogonal to both. This gives us:
(3, 3, 0) x (1/√(2), -1/√(2), √(2/9)) = (-2√(2)/3, 2√(2)/3, 2√(2)/3)
We can then normalize this vector to obtain the third row of A:
(-2√(2)/3, 2√(2)/3, 2√(2)/3)/√(8/9) = (-√(2)/2, √(2)/2, √(2)/2)
Therefore, the orthogonal matrix A that satisfies the given conditions is:
[3 3 0 ]
[1/√(2) -1/√(2) √(2/9)]
[-√(2)/2 √(2)/2 √(2)/2]
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Mark sells 15 pieces of artwork. He spent a total of $175 on supplies to create the art. He sold 6 of the pieces of artwork for $70 each. The remaining pieces were sold for $85 each. Mark plans to set aside 40% of his total profit for more supplies. How much money does Mark set aside for more supplies?
Mark sets aside $404 for more supplies.
Mark spent $175 on supplies, so his total cost is $175.
Mark sold 6 pieces of artwork for $70 each, so he earned 6 * $70 = $420 from these pieces.
He sold 15 - 6 = 9 pieces of artwork at $85 each, so he earned 9 * $85 = $765 from these pieces.
His total revenue is $420 + $765 = $1185.
His profit is his revenue minus his cost: $1185 - $175 = $1010.
He plans to set aside 40% of his profit for more supplies, so he will set aside 0.4 * $1010 = $404.
Therefore, Mark sets aside $404 for more supplies.
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please help me answer this
Answer:
The parrot is 48 years old and knows 76 words.
Step-by-step explanation:
The outlier is far away from all the other points on the y-axis and the x-axis.
find an equation of the tangent line to the curve at the given point. y = sec(x), (π/6, 2 3 /3)
1. Identify the curve and the point: The curve is y = sec(x), and the point is (π/6, 2√3/3).
2. Calculate the derivative of the curve: The derivative of y = sec(x) is y' = sec(x)tan(x).
3. Evaluate the derivative at the given point: At x = π/6, we have y' = sec(π/6)tan(π/6). Since sec(π/6) = 2 and tan(π/6) = √3/3, we get y' = 2(√3/3) = 2√3/3.(4). Use the point-slope form of the line equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope (derivative).
5. Plug in the values: y - (2√3/3) = (2√3/3)(x - π/6). This is the equation of the tangent line to the curve y = sec(x) at the point (π/6, 2√3/3).
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(b) If the width of the rectangle is 21 inches, what is the length and the area? Use appropriate units and explain
how you found your answer.
is
The Aren of reclange
If the width of the rectangle is 21 inches, the length is 24.5cm and the area is 372cm²
How do we calculate?A rectangle is described as a quadrilateral with four right angles.
suppose we have the width of rectangle = 21 inches
therefore:
( x + 0.5) = 21
x = 20.5
Area of rectangle = we multiply the length of the rectangle by the width of the rectangle.
2x² + 9x + 4
Area of rectangle = 2(11.5)² + 9(11.5) + 4
= 372cm²
length of rectangle = x + 4
length of rectangle= 20.5 + 4
length of rectangle = 24.5cm
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Water flows through each of the pipes that fill a lake at the same rate.
It takes 4 of the pipes 12 hours to fill the lake.
Work out how many hours it would take 6 pipes to fill 1/4 of the lake.
The number of hours it would take 6 pipes to fill 1/4 of the lake is 4.5 hours
Working out how many hours it would take 6 pipesGiven that
It takes 4 of the pipes 12 hours to fill the lake.
This means that
Rate = 12 hours/4 pipes
So, we have
Rate = 3 hours/ pipe
For 6 pipes to fill 1/4 of the lake. we have
Time = 3 hours *6 * 1/4
Evalaute
Time = 4.5 hours
Hence, the time taken is 4.5 hours
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For this item, enter the answer in the space provided.
The value of z is 20 in.
What is triangle?
A polygon that has three sides and three angles is called triangle.
In triangle QWX, we have WX || RS, so by the intercept theorem, we have:
QW/WX = QR/RS
Substituting the given values, we get:
z/(3y) = 20/(20 + y)
Cross-multiplying, we get:
20z + 3y² = 60y
We also know that:
QW + WX = QX
Substituting the given values, we get:
z + 3y = 3y
Simplifying, we get:
z = 0
Substituting this value of z into the equation we derived earlier, we get:
20z + 3y² = 60y
0 + 3y² = 60y
Dividing both sides by 3y, we get:
y = 20
Therefore, the value of z is:
z = QW = QX - WX = 3y - 2y = y = 20
So, z = 20
Therefore required value of z is 20 in.
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How do I do this math problem?
The length of line AC of the given quadrilateral ABCD would be = 13.7cm
How to calculate the missing length of the quadrilateral?To calculate the length of line AC is to calculate the length of CE and AE separately and add up the lengths afterwards.
The length of CE can be calculated using Pythagorean formula;
That is C² = a² +b²
where C = 8cm
a = 5cm
b = CE = ?
b² = 8²-5²
b = 64-25
b² = 39
b =√39
b = 6.2
For AE;
b² = AE = 9²-5²
= 81-25
= 56
b = √56
= 7.5
Therefore the length of AC = 6.2+7.5 = 13.7cm
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Mavis has 33 nickels, 67 dimes, 19 quarters, and 14 fifty-cent pieces. How much money does she have?
A. $18.40
B. $21.35
C. $20.10
D. $27.30
The total amount of money that Mavis with 33 nickels, 67 dimes, 19 quarters, and 14 fifty-cent pieces has is C. $20.10.
How is the total amount determined?The total amount that Mavis has can be determined by the multiplication of the cents based on their unit values.
Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
33 nickels = $1.65 (33 x $0.05)
67 dimes = $6.70 (67 x $0.10)
19 quarters = $4.75 (19 x $0.25)
14 fifty-cents = $7.00 (14 x $0.50)
Total amount = $20.10
Thus, Mavis has a total amount of $20.10.
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URGENT
The hypotenuse of a right triangle measures 13 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
13*
Step-by-step explanation:
Use the Pythagorean theorem.
a=1
b=x
c=13
so, [tex]1^2 + x^2 = 13^2[/tex]
[tex]x^2 = 169 - 1 = 168[/tex]
[tex]x = \sqrt{168}[/tex]
[tex]\sqrt{168} = 12.961481396815720461931934872176[/tex] = 13
*If we round to the nearest tenth, we get 13. Because of this rounding, the other leg is the hypotenuse, but it is actually different.
Can someone explain?
The proof is completed using the properties of equality
How to write the two column proofThe two column proof is completed as below
Statement Reason
angle 2 ≅ angle 4 Given
angle 1 + angle 2 = 90 deg definition of right triangle
angle 3 + angle 4 = 90 deg definition of right triangle
angle 1 + angle 2 = angle 3 + angle 4 substitution property of equality
angle 1 + angle 4 = angle 3 + angle 4 substitution property of equality
angle 1 = angle 3 addition property of equality
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Which fraction below represents a repeating decimal?
A.) 1/4
B.) 6/4
C.) 19/2
D.) 22/12
A sailboat sail is triangular with a height 3 feet greater than its base. If the sail's area is 90 square feet, find its base
and height.
←
The base of the sail is
and the height is
Answer:
Height 15 feet
Base 12 Feet
Step-by-step explanation:
The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.
A=(.5) x 12 x 15
A=(.5) x 180
A= 90
Find side BC in the given triangle
Answer: BC = 8.94
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem. a and b are the triangle legs and c is the hypotenuse.
a² + b² = c²
19² + b² = 21²
361 + b² = 441
b² = 80
b = [tex]\sqrt{80}[/tex]
b ≈ 8.94
BC = 8.94
What is 7/14 in its simplest form?
Answer quick !!!!
Answer:
7/14 in simplest form is 1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
4. Blair has a box of candy to sell. She has 4
chocolate bars, 4 fruit chews, 1 pack of
bubble gum and 3 sour candies. If she
chooses a piece of candy at random, how
many possible outcome are there?
Give the number of favorable outcomes for
each event.
a) choosing a pack of gum
b) not choosing a sour candy
c) choosing a chocolate bar or pack of gum
d) choosing anything other than fruit chews
Gina Wison JAI Things Algebra C), 2018
Answer:
a)1/12
b)3/4
c)5/12
d)2/3
Step-by-step explanation:
let chocolate bar be C
let fruit chew be F
let Pack of buble gum be =B
1let sour Candie be S
C=4
F=4
B=1 pack
S=3
T=4+4+1+3=12
a) 1/12
b)9/12=3/4
c)4/12+1/12=1/3+1/12=5/12
d)8/12=2/3
A chord, 20cm long, is 12cm from the centre of the circle. Calculate, correct to one decimal place, the: (a) angle subtended by the chord at the centre of the circle; (b) perimeter of the minor segment cut off by the chord. [Take
[tex]\pi[/tex]
3.142]
Step-by-step explanation:
there are 2 formulas to calculate the length of a chord, depending on what pieces of information we have.
here now we have the length of the chord, which we need to find the radius, which we need to find the angle at the center.
chord length = 2×sqrt(r² - d²)
chord length = 2×r×sin(c/2)
r is the radius, d is the distance of the chord from the center of the circle, c is the angle of the chord at the center of the circle.
20 =2×sqrt(r² - 12²) = 2×sqrt(r² - 144)
10 = sqrt(r² - 144)
100 = r² - 144
244 = r²
r = 15.62049935... cm
20 = 2×r×sin(c/2) = 2×15.62049935...×sin(c/2)
10 = 15.62049935...×sin(c/2)
sin(c/2) = 10/15.62049935... = 0.6401844...
c/2 = 39.80557109...°
c = 79.61114218...° ≈ 79.6°
(a) the angle subtended by the chord at the center of the circle is about 79.6°.
(b)
the arc length of a segment is 2pi×r × c/360
in our case
2×3.142×15.62049935...×79.61114218.../360 =
= 21.70713182... cm
the whole perimeter of the segment is then arc length + chord length =
= 21.70713182... + 20 = 41.70713182... ≈ 41.7 cm
the perimeter of the minor segment cut off by the chord is about 41.7 cm.
the global business travel association reported the domestic airfare for business travel for the current year and the previous year. below is a sample of flights with their domestic airfares shown for both years. do not round intermediate calculations. current year previous year current year previous year 558 219 417 312 480 489 375 276 342 276 624 303 603 612 288 324 477 543 294 534 339 348 348 369 a. formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period.
With a significance level of 0.05 for a one-tailed test, the critical value is 1.761. Since -1.86 is less than -1.761, we reject the null hypothesis.
To test for significant increases in average domestic business charges over a one-year period, you can use a paired-sample t-test.
This is good because the two sets of observations (current year and previous year) are paired on the same flight.
The null hypothesis (H0) states that the average domestic fares for business travel are not significantly different from the previous year.
The alternative hypothesis (Ha) indicates that average domestic fares for business travel will increase significantly this year compared to the previous year.
This can be written as:
H0:
µd = 0
teeth:
µd > 0
where μd is the population mean of the differences in domestic fares between the current year and the previous year.
To do the test, to begin with, calculate the contrast between the residential passages for the current year and the past year.
At that point calculate the mean and standard deviation of these contrasts.
d = (558-219) + (417-312) + ... + (348-369) / 15
= -15.2
s = sqrt([(558-219+15.2)^2 + ... + (348-369+15.2)^2] / (15-1))
= 134.8
The t-statistic for the test is
t = (d - 0) / (s / sqrt(n))
= (-15.2 - 0) / (134.8 / square(15))
= -1.86
Using a one-sided test with 14 (n-1) degrees of freedom and a t table with a significance level of 0.05, the critical value is 1.761. -1.86 is less than -1.761, so we reject the null hypothesis.
It can in this manner be concluded that there's adequate proof to back the claim that the normal household airfare for trade travel has expanded essentially over the years.
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Find the measure of the angle in standard position
The angle in standard position is 150°
How to find the angle in standard position?The angle of any position (x, y) on a graph is given by Ф = tan⁻¹(y/x).
Now given the position (-√3, 1) on the graph, to find the angle in standard position, we proceed as follows.
To find the angle, we substitute the values of the variables into the equation. so, we have that
Ф = tan⁻¹(y/x)
Given that
x = -√3 and y = 1. so, we have thatФ = tan⁻¹(y/x)
Ф = tan⁻¹(1/-√3)
= tan⁻¹(-1/√3)
= 180° - tan⁻¹(1/√3)
= 180° - 30°
= 150°
So, the angle is 150°
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The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling tickets, the members would like to raise $2,050 every night to cover all expenses. Letdrepresent the number of adult tickets sold at $6.50. Let's represent the number of student tickets sold at $3.50 each.
a.If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly$2,050?
b.At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that performance, how much below the goal of$2,050 did ticket sales fall?
The type of ticket that must have been sold are 100 adults and 400 students
Also, they were short by $360
How many of each type of ticket must have been soldGiven that tickets are sold for adults and students
Let d = adults
Let s = students
So, we have
6.5d + 3.5s = 2050
d + s = 500
When solved graphically, we have
d = adults = 100
s = students = 400
How much below the goal of$2,050 did ticket sales fall?Here, we have
s = 3d
s + d = 480
So, we have
4d = 480
Evaluate
d = 120
s = 360
So, we have
Total = 6.5 * 120 + 3.5 * 260
Total = 1690
Difference = 2050 - 1690
Evaluate
Difference = 360
They were short by $360
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Please help. Answer as soon as possible!!!
Answer:
Step-by-step explanation:
A. Variability means the spread of the range for between the 3rd and 1st quartile meaning the actual box. The actual box is wider with South Middle so the difference is greater and therefore greater variability
B. North Middle has greater distance in general because the box has bigger numbers. That's where the majority of the kids are, so in general North Middle has kids that are further away
drag the graphs to match each inequality to its solution
The graphs to match each inequality to its solution are added as an attachment
Matching the graphs to the inequalitesAnalyzing the inequalities from the question, we have the following explanations
f < 5: The number line points to the left of 5f > 5: The number line points to the right of 5f ≤ 5: The number line points to the left of 5 and 5 is inclusivef ≥ 5: The number line points to the right of 5 and 5 is inclusiveNext, we match the number lines and the inequalities
See attachment for number lines
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Leroy's total job benefits were $50,150 last year. His total job expenses for traveling and for professional development for the year were $3,500. Which of the following represents his total employment compensation?
a.
$46,650
b.
$47,650
c.
$50,150
d.
$53,650
Leroy's total employment compensation last year was $46,650. Hence, the correct answer is option a, $46,650.
To find Leroy's total employment compensation, we need to consider his total job benefits and his total job expenses for traveling and professional development.
Leroy's total job benefits last year were $50,150. His total job expenses for traveling and professional development were $3,500. To calculate his total employment compensation, we need to subtract the job expenses from the job benefits.
Total employment compensation = Total job benefits - Total job expenses
Total employment compensation = $50,150 - $3,500
Total employment compensation = $46,650
The correct option is a. $46650.
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if one of the zeroes of cubic polynomial x^3+ax^2+bx+c is 2 then the product of other two zeroes is:
a)c/2
b)-2/c
c)-c/2
d)2/c
Answer:
The answer is d) 2/c.
Explanation :
If one of the zeroes of cubic polynomial x^3+ax^2+bx+c is 2, then the product of the other two zeroes can be found by dividing the polynomial by (x-2), which gives:
x^3+ax^2+bx+c = (x-2)(x^2+(a+2)x+(c-2a))
We can solve the quadratic equation x^2+(a+2)x+(c-2a) to find the other two zeroes. By Vieta's formulas, the product of the roots of a quadratic equation ax^2+bx+c=0 is c/a. Therefore, the product of the other two zeroes is:
pq = (c-2a)/1 * 1/(a+2) = (c-2a)/(a+2)
Substituting the value of c/2a from the cubic polynomial gives:
pq = (c-2a)/(a+2) = (2c-4a)/(2a+4) = -2(c/2a) + 2
Therefore, the answer is d) 2/c.
What is the perimeter? If necessary, round to the nearest tenth.
a=24
b=45
c=?
Answer:
Step-by-step explanation:
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with sides a = 24, b = 45, and c = ?, we need to add up the lengths of the known sides:
Perimeter = a + b + c
Plugging in the values, we get:
Perimeter = 24 + 45 + c
Simplifying, we get:
Perimeter = 69 + c
We still need to find the length of the third side, c. However, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:
a + b > c
24 + 45 > c
69 > c
Therefore, we know that c must be less than 69.
On the other hand, we can also use the fact that the difference between the lengths of any two sides of a triangle must be less than the length of the third side. In other words:
|a - b| < c
|24 - 45| < c
21 < c
Therefore, we know that c must be greater than 21.
Putting these two inequalities together, we have:
21 < c < 69
So the perimeter is:
Perimeter = 69 + c
And we know that:
21 < c < 69
Therefore, we can say that the perimeter is somewhere between:
69 + 21 = 90
and
69 + 69 = 138
Rounding to the nearest tenth, we get:
Perimeter ≈ 90.0 - 138.0
Therefore, the perimeter is somewhere between 90.0 and 138.0, depending on the actual length of the third side, c.
a player wins a minimum award of $10000 by correctly matching four numbers, of the five, drawn from the white balls (1 through 56) and matching the number on the gold ball (1 through 46). what is the probability of winning this minimum prize?
The probability of winning the minimum prize is approximately 0.00014
To calculate the probability of winning this minimum prize, we need to first find out the total number of possible combinations of numbers that can be drawn.
There are 56 white balls, and 5 balls are drawn from them, so the total number of possible combinations of white balls is
56 choose 5 = 56! / (5! (56-5)!) = 3,819,816
There are 46 gold balls, and only 1 is drawn from them. Therefore, the total number of possible combinations of gold balls is simply 46.
To win the minimum prize, we need to correctly match 4 out of the 5 white balls drawn, and we also need to match the gold ball.
The number of ways to choose 4 white balls out of 5 is
5 choose 4 = 5! / (4! (5-4)!) = 5
So, the total number of ways to win the minimum prize is the product of the number of ways to choose 4 white balls and the number of ways to choose 1 gold ball
Total number of ways to win the minimum prize = 5 × 46 = 230
Therefore, the probability of winning the minimum prize is
Probability = number of ways to win the minimum prize / total number of possible combinations
Probability = 230 / (3,819,816 × 46) = 0.00014
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