The game called lotto sponsored by the louisiana lottery commission pays its largest prize when a contestant matches all 4 of the 41 possible numbers. assume there are 41 ping-pong balls each with a single number between 1 and 41. any number appears only once, and the winning balls are selected without replacement.
a. the commission reports that the probability of matching all the numbers are 1 in 101,270. what is this in terms of probability
Final answer:
The reported probability of 1 in 101,270 for matching all four lotto numbers is equivalent to a decimal probability of approximately 0.00000987.
Explanation:
The Louisiana Lottery Commission's lotto game entails participants matching all 4 numbers out of a pool of 41. The reported probability of achieving this feat is 1 in 101,270. To express this probability, we utilize the ratio of successful outcomes to total possible outcomes. Consequently, the probability of matching all four numbers is 1/101,270, equivalent to approximately 0.00000987 in decimal form. This minute probability underscores the challenging nature of the lotto game, highlighting the rarity of successfully predicting and matching the specified set of numbers within the given range.
if f(x) = 5x^3-2 and g(x)= 2x+1, find (f+g) (x).
The expression for (f + g)(x) is [tex]\rm 5x^3+2x-1[/tex] and this can be determined by using the arithmetic operations and the given data.
Given :
[tex]\rm f(x) = 5x^3-2[/tex][tex]\rm g(x) = 2x + 1[/tex]The following steps can be used in order to determine the value of (f + g)(x):
Step 1 - Write the given functions.
[tex]\rm f(x) = 5x^3-2[/tex] --- (1)
[tex]\rm g(x) = 2x + 1[/tex] --- (2)
Step 2 - Now, to determine the value of (f + g)(x), add both function f(x) and g(x).
f(x) + g(x) = (f + g)(x)
Step 3 - Substitute the value of f(x) and g(x) in the above expression.
[tex]\rm (f + g)(x) = 5x^3-2+2x+1[/tex]
Step 4 - Simplify the above expression.
[tex]\rm (f + g)(x) = 5x^3+2x-1[/tex]
For more information, refer to the link given below:
https://brainly.com/question/5245372
The volume of a rectangular prism is (x3-3x2+5x-3), and the area of its base is (x -2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
To find the height of the rectangular prism, divide the volume by the area of the base.
Explanation:To find the height of the rectangular prism, we need to divide the volume by the area of the base. The formula for the volume of a rectangular prism is V = lwh, where l, w, and h represent the length, width, and height, respectively. The formula for the area of the base is A = lw.
In this case, the volume is given as (x3-3x2+5x-3) and the area of the base is (x -2). So, we need to divide the volume by the area of the base, which gives us:
(x3-3x2+5x-3)/(x -2).
Learn more about rectangular prism height here:https://brainly.com/question/16027067
#SPJ12
what is the greatest common factor (gcf) of the numerator and denominator in the rational expression below? 7x+14/2x^2+x-6
a. -6
b. 7
c. x+2
d. 2x-3
Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational expression (7x+14)/(2x²+x-6) is x+2. Thus, option C is correct.
Explanation:
To find the greatest common factor (GCF) of the numerator and denominator of the given rational expression (7x+14)/(2x²+x-6), we need to factor both the numerator and the denominator separately.
For the numerator 7x+14, we can factor out a 7:
7x + 14 = 7(x + 2)
For the denominator 2x² + x - 6, we need to factor it as a quadratic expression. This can be done by finding two numbers that multiply to give -12 (the product of the coefficient of x² and the constant term) and add up to 1 (the coefficient of x). These numbers are 3 and -4, so the denominator can be factored as:
2x² + x - 6 = (2x - 3)(x + 2)
Now we can see that the common factor between the numerator and the denominator is x + 2. Therefore, the GCF is x + 2, which corresponds to option (c).
H + 9.7 = -9.7 what is this answer
How many three-letter codes can we make using only vowels, a, e, i, o, or u?
Answer and explanation:
Given : Vowels a,e,i,o or u.
To find : How many three-letter codes can we make using only vowels ?
Solution :
1) If we assume that repetition is allowed then
The three letter code can form
[tex]5\times 5\times 5=125[/tex] ways
Number of three-letter codes can we make using only vowels is 125.
2) If we assume that repetition is not allowed then
The three letter code can form
[tex]5\times 4\times 3=60[/tex] ways
Number of three-letter codes can we make using only vowels is 60.
Where is the point of concurrency of the angle bisectors of a triangle?
A) outside the triangle
B) inside the triangle
C) on the triangle
Answer:
B) inside the triangle
Step-by-step explanation:
That point of concurrency is called the "incenter" as it is the center of the largest circle that can be inscribed in the triangle. It is always located inside the triangle.
Each angle bisector must be inside the triangle, so their point of intersection must be inside the triangle.
Final answer:
The point of concurrency of the angle bisectors of a triangle called the incenter, is always located inside the triangle.
Explanation:
The point of concurrency of the angle bisectors of a triangle is known as the incenter. This point is where all three angle bisectors of a triangle intersect, and it is always inside the triangle.
No matter what type of triangle it is—scalene, isosceles, or equilateral—the incenter is always located within the interior of the triangle, serving as the center of the triangle's incircle, which is a circle that is tangent to all three sides of the triangle. Thus , the correct option is B.
A basketball player makes 60% of his shots from the free throw line. suppose that each of his shots can be considered independent and that he throws 4 shots. let x = the number of shots that he makes. what is the probability that he makes all 4 shots?
Using the binomial distribution, it is found that there is a 0.1296 = 12.96% probability that he makes all 4 shots.
-------------------------------
For each throw, the player either makes it or misses it. The probability of making each throw is the same, independent of other throws, thus, the binomial distribution is used to solve this question.
Binomial probability distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, with X having two possible outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
Makes 60% of the shots, thus [tex]p = 0.6[/tex]4 shots, thus [tex]n = 4[/tex].The probability of making all of them is P(X = 4), thus:[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,4}.(0.6)^{4}.(0.4)^{0} = 0.1296[/tex]
0.1296 = 12.96% probability that he makes all 4 shots.
A similar problem is given at https://brainly.com/question/9000732
Which statements are true about thecordered pair (7,19) and the system of equations 2x-y=-5
The population of a small town decreased from 983 to 901. What is the percent decrease, to the nearest tenth of a percent?
The population of the small town percent decreased by approximately 8.4%.
To find the percent decrease in the population of the small town, we can use the formula for percent decrease:
Percent Decrease = [(Initial Value - Final Value) / Initial Value] * 100
Given that the initial population was 983 and the final population was 901, we can plug these values into the formula:
Percent Decrease = [(983 - 901) / 983] * 100
Now, calculate the numerator:
Percent Decrease = [82 / 983] * 100
Divide and multiply:
Percent Decrease = 0.0835 * 100
Now, calculate the percent decrease to the nearest tenth of a percent:
Percent Decrease ≈ 8.4%
So, the population of the small town decreased by approximately 8.4%.
To know more about percent decrease click here :
https://brainly.com/question/2913116
#SPJ2
Ming says that 0.24 > 14 because 0.24 = 24. Which best explains Ming's error?
Answer:
Ming says that 0.24 > 14
1
4
because 0.24 = 24
2
4
. Which best explains Ming's error?
Step-by-step explanation:
Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove?
The function f(x) is an arithmetic sequence.
The function f(x) is a geometric sequence.
The function f(x) is not a sequence.
This does not prove anything.
Answer:-The function f(x) is an arithmetic sequence.
Explanation:-
Let [tex]a_1[/tex] be the initial value
According to the question
[tex]a_2=a_1+4[/tex]
[tex]a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2\times4\\\Rightarrow\ a_3=a_1+(3-1)4[/tex] and so on
Thus, we can write a formula for the term n of an arithmetic sequence in the form:
[tex]a_n=a_1+(n-1)4[/tex]
where, n=1,2,3,4,....
4= common difference
Therefore, the function f(x) is an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.Which relation defined by a set of ordered pairs is a function?
A {(2, 6), (3, 6), (4, 5), (6, 6), (6, 7)}
B {(6, 2), (6, 3), (5, 4), (6, 6), (7, 6)}
C {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}
D {(–2, 6), (3, –6), (–4, 5), (6, –6), (6, –7)}
Answer:
Step-by-step explanation:
Two secant segments intersect outside a circle as shown. What is the value of x?
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24 cubic units what is the height of the cylinder
the answer is c.6 i just took the test.
Consider a game in which a coin will be flipped three times. for each heads you will be paid $100. assume that the coin comes up heads with probability 4/5.
IF YOU ANSWER WITHOUT A PROPER ANSWER AND YOU JUST WANT POINTS YOUR ANSWER WILL BE REPORTED! 99 POINT QUESTION! So I want a full explanation, best answer gets to be the brainliest. How much is 457 - (-54) + 7700 * 325 = ? I feel generous today so I'm making this 99 points. Btw, this is my first question asked here on brainly.
What set of reflections would carry triangle ABC onto itself?
Two years ago Carol's living expenses were $ 1200 $ 1200 per month. This year the same items cost Carol $ 1400 $ 1400 per month. What was the annual inflation rate for the past two years?
What are the solutions to the equation? x2−12x+36=4 Enter your answers in the boxes. x1= x2=
Answer:
4 and 8
Step-by-step explanation:
x1 = 4
x2 = 8
How do you solve 7(2-j)-5??
How many numbers must be selected from the set $\{1, 3, 5, 7, 9, 11, 13, 15\}$ to guarantee that at least one pair of these numbers add up to 16?
At a concession stand, one person purchased 3 drinks and 3 soft pretzels for a total of $9.00. Another person purchased 4 drinks and 2 soft pretzels for a total of 8.50. What was the price of one soft pretzel
The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle? A. length = 20 inches, width = 17 inches B. length = 17 inches, width = 14 inches C. length = 10 inches, width = 7 inches D. length = 34 inches, width = 10 inches
To find the length and width of a rectangle given its area and the relationship between its dimensions, set up and solve an equation by following the step-by-step process.
Explanation:Given: The width of a rectangle is 3 inches less than its length and the area is 340 square inches.
To solve: Let the length be 'x' inches, then the width is 'x - 3' inches. Set up the equation 'x(x - 3) = 340', solve for 'x' to find the length and width.
Step-by-step:
Express the area as a product of the length and width: 'x(x - 3) = 340'.Expand and rearrange the equation: 'x^2 - 3x - 340 = 0'.Factor the quadratic equation: '(x + 17)(x - 20) = 0'.Solve for 'x': 'x = -17' or 'x = 20'. Since length cannot be negative, the length is 20 inches.Calculate the width: '20 - 3 = 17 inches'.Please help me with questions 26 and 27
Hudson worked two jobs last summer to start saving for a car. He mowed lawns during the day and worked at a pizza place in the evenings. In one month, Hudson earned a total of $1,400. If he earned $360 more at the pizza place than mowing lawns how much did he earn at each job?
Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
What is a system of linear equation?A System of Linear Equations is when we have two or more linear equations working together.
Given that, Hudson mowed lawns during the day and worked at a pizza place in the evenings. Hudson earned a total of $1,400. also he earned $360 more at the pizza place than mowing lawns
Let he earn x at deliveries and y at mowing,
Therefore, establishing a system of equations,
x+y = 1400
x-y = 360
Adding both the equations,
2x = 1760
x = 880
y = 1400-880
y = 520
Hence, Hudson earned $880 at pizza deliveries and $520 at mowing the lawn.
Learn more about system of equations, click;
https://brainly.com/question/12895249
#SPJ3
The ratio of boys to girls at the beach cleanup was 7:8. If there are 42 boys, how many girls are there?
that ratio means for every 7 boys there are 8 girls
so 42 boys / 7 = 6
now 6*8 = 48
there are 48 girls
I need help please I’m confused
Make a box-and-whisker plot for the data. What is the upper quartile value? 56 32 48 52 51 53 48 38 35 42 40 46 54 50
Answer:
Step-by-step explanation:
The given data is:
56 32 48 52 51 53 48 38 35 42 40 46 54 50
In order to get the value of the upper quartile, first arrange he given data in ascending form, we get
32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56
The upper quartile is:48, 50, 52, 53, 54, 56
The value of upper quartile is given as:
[tex]\frac{52+53}{2}[/tex]
=[tex]\frac{105}{2}[/tex]
=[tex]52.5[/tex]
Thus, the value of the upper quartile will be 52.5.
EXPERTS/ACE/GENIUSES HELP PLZ!!:)
( only #2 )
Explain as well!! Best answer will get brainlist... but make ur answer short and sweet plz.
(a) Volume of 1st cup = (1/3)pi *(4/2)^2 * 8 = 32/3 pi in^3
scoops = (2000/3)pi / ( 32/3) pi = 2000/32 = 62.5 = 63
(b) Volume of 2nd cup = (1/3)pi *(8/2)^2 * 8 = 128/3 pi in^3
scoops = (2000/3)pi / ( 128/3) pi = 2000/128 = 15.625 = 16