In a state's lottery, you can bet $3 by selecting three digits, each between 0 and 9 inclusive. If the same three numbers are drawn in the same order, you win and collect $500. Complete parts (a) through (e).
Answers
Using the Fundamental Counting Theorem, it is found that:
a) 1000 combinations are possible.
b) The probability of winning is of 0.001.
c) If you win, the net profit is of $497.
d) The expected value of a $3 bet is of -$2.5.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, each thing independent of the other, the number of results is given as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In the context of this problem, three digits that can be repeated are chosen, hence the parameters are:
[tex]n_1 = n_2 = n_3 = 10[/tex]
Hence the number of combinations is:
N = 10³ = 10 x 10 x 10 = 1000.
The order also has to be correct, hence the there is only one winning outcome and the probability is:
p = 1/1000 = 0.001.
You bet $3, and if you win you collect $500, hence the net profit is of:
500 - 3 = $497.
Then the distribution of earnings are as follows:
P(X = -3) = 0.999 -> losing.P(X = 497) = 0.001. -> winning.Hence the expected value is:
E(X) = -3 x 0.999 + 497 x 0.001 = -$2.5.
Missing informationThe problem is given by the image at the end of the answer.
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Related Questions
When the internet first launched, it was slow, clogged up phone lines and was most certainly not cheap. In fact, most Internet service providers (ISP) charged a flat rate access fee that included 20 hours a month of internet time. After twenty-hours of use, the ISP’s charged an additional per-hour fee. Suppose in 1995, Charter charged a flat rate of $39.95 for the first twenty hours of service and an additional per-hour charge of $5.99.a. How much would a Charter bill for 18 hours of internet used be in 1995? b. How much would a Charter bill for 28 hours of internet used be in 1995?
Answers
from the question, we were told in 1995, Charter charged a flat rate of
$39.95 for the first twenty hours.
and an additional per hour charge of $5.99
if,
for 20 hours = 39.95
therefore for 1 hour = 39.95/20
so for 18 hours = 39.95/20 X 18.95/20
so for 18 hours = 9
so,
to get the amount Charter bill for 18 hours in 1995 is,
39.95 x 18/20
= 39.95 x 0.9
= $35.955
so Charter bill for 18 hours of internet used in 1995 is $35.955
ould bill for 28 hours is
so, what Charter would
Ariel dropped a golf ball from her second story window. The ball starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the golf ball.
Answers
The average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².
Given in the question is:
Since the ball started from rest
Initial velocity; u= 0m/s
Final velocity; v = 14.7 m/s
Time taken for the golf ball to hit the sidewalk; t = 1.5 s
Average Acceleration; g =?
To determine the average acceleration of the golf ball, we use the First Equation of Motion:
v = u + at
The Equation will be :
v = u + gt
Plug the all values in above equation:
14.7m/s = 0 + g x 1.5 s
g = 14.7 / 1.5
g = 9.8m/[tex]s^2[/tex]
Therefore, the average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².
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Write the sentence as an equation.
y decreased by 283 is equal to 48
Answers
Answer:
y - 283 = 48
Step-by-step explanation:
y decreased by 283 means that 283 is subtracted from y. All set equal to 48.
283 is being subtracted from y therefore y-283 is equal to 48
The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy. The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
Which equation could you use to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet?
Answers
The equation which can be used to find the area of the place where guests wait for the ride if the area of the canopy is 7600 square feet is:
2a+100=7600.
Given, The rectangular waiting area for a popular amusement park ride is covered by a large sun canopy.
The total area of the canopy, in square feet, is 100 square feet more than twice the area where guests wait.
let the area of the place where guests wait be represented by 'a'.
the canopy covers the area = 2a + 100
total area of the canopy = 7600
equation used to find the area of the place where guests wait for the ride if the area of the canopy is 7,600 square feet = ?
⇒ 2a + 100 = 7600
arrange the like terms.
⇒ 2a = 7600 - 100
calculate the difference.
⇒ 2a = 7500
⇒ a = 7500/2
⇒ a = 3750
Hence the area of the place where guests wait is 3750 square feet.
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What is the equation of a line that passes through the point (5, −3) and is parallel to 6x+3y=−12?
Enter your answer in the box.
Answers
Answer: Slope= -2.000
x-intercept= -2
y-intercept= -4.000
Hope this helps !
Find the perimeter of the polygon with the vertices J(-5, 3), K(-2, 1) and L(3, 4). Round your answer to the nearest tenth.
The perimeter of JKL is about____
units.
Answers
The perimeter of the polygon with the vertices is: 17.5 units.
How to Find the Perimeter of a Polygon?The perimeter of a polygon is the sum of all the sides of the polygon. To find the perimeter of a polygon with coordinates given for its vertices, we have to apply the distance formula to find the length between each of the vertices of the polygon.
The distance formula is d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Given:
J(-5, 3)
K(-2, 1)
L(3, 4)
Find JK:
JK = √[(−2−(−5))² + (1−3)²]
JK = √13
JK = 3.6 units
Find KL:
KL = √[(−2−3)² + (1−4)²]
KL = √34
KL = 5.8 units
Find JL:
JL = √[(−5−3)² + (3−4)²]
JL = √65
JL = 8.1 units
Perimeter = 3.6 + 5.8 + 8.1
Perimeter = 17.5 units.
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Directions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.Solve for x.( + 0.5) + 5.24 = = + ( + 2.2)The value of x is
Answers
1/5 (x+0.5) +5.24 = 3/2x + 7/10 (x+2.2)
First, apply the distributive property to solve the parentheses
1/5(x)+ 1/5 (0.5) +5.24 = 3/2x + 7/10(x) + 7/10 (2.2)
1/5x +0.1 +5.24 = 3/2x + 7/10 x + 1.54
Combine like terms
1/5x +5.34 = 11/5x +1.54
Move the x terms to the left side of the equation:
1/5x-11/5x = 1.54-5.34
-2x = -3.8
Divide both sides by -2
-2x/-2 = -3.8/-2
x = 1.9
An online furniture store sells chairs and tables. Each day, the store can ship no more than 19 pieces of furniture. Write an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint.
Answers
An inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint is (c + t) ≤ 19
In this question, we have been given the online furniture store can ship not more than 19 pieces of chairs and tables each day.
If the possible number of chairs they can ship each day is represented by c and the possible number of tables they can ship each day is represented by t, then the inequality equation can be written as
(c + t) ≤ 19
Therefore, an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint is (c + t) ≤ 19
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у
0
1
1
3
2
9
3
27
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In a quadrilateral, two angles are x°, two angles are (3x+8)°. What is x and the measures of the angles?
Answers
Step-by-step explanation:
the sum of all angles in any quadrilateral is 360°.
so,
x + x + 3x + 8 + 3x + 8 = 360
8x + 16 = 360
8x = 344
x = 344/8 = 43°
3x + 8 = 3×43 + 8 = 129 + 8 = 137°
so, the angles are
43°
137°
43°
137°
32+40+…+120=? Someone help PLEASE
Answers
Answer:
912
Step-by-step explanation:
the assumption is that this is an arithmetic progression
the nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
use this to find which term 120 is in the sequence
with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then
32 + 8(n - 1) = 120 ( subtract 32 from both sides )
8(n - 1) = 88 ( divide both sides by 8 )
n - 1 = 11 ( add 1 to both sides )
n = 12
given the first and last terms in the sequence then sum is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)
S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912
In today's recording, the first example was the function
f(x) = x² + 5x³ + 10x² + 20x + 24
After depressing our function twice and getting a quotient (depressed polynomial), which was the
resulting quadratic equation that we needed to solve?
O x²+4=0
O x²-4=0
O x² + 4x + 4 = 0
O x² + 4x = 0
Answers
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
How can you locate a polynomial's root?Set the equation's value to zero to get the polynomial's roots. Completely factor the polynomial expression. Then, in order to find the variable, set each factor equal to zero. The formula isx^4+5x^3-10x^2-20x+24Finding polynomial roots (zeroes) is the focus of this solution.((((x4)+(5•(x3)))-(2•5x2))-20x)+24
((((x4) + 5x3) - (2•5x2)) - 20x) + 24
Find the roots (zeroes) of F(x) = x4 + 5 x 3 x 10 x 2 x 20 + 24.The Polynomial Roots Calculator is a collection of techniques for identifying x values where F(x)=0.One of the tools discussed above is the rational roots test. Only numbers x that can be written as the quotient of two integers would be considered rational roots.According to the Rational Root Theorem, P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient if a polynomial zeroes for a rational integer P/Q.The Leading Coefficient in this situation is 1 and the Trailing Constant is 24.The element(s) are: of the Trailing Constant: 1, 1, 2, 3, 4, 6, 8, 12, and 24 of the Leading Coefficient: 1.According to the Factor Theorem, if P/Q is a polynomial's root, then q*x-p can be used to divide the polynomial. Keep in mind that q and p come from P/Q in its simplest form.In our situation, this means that 4 different polynomials, including x-2, can divide x4+5x3–10x2–20x+24.To Learn more about polynomial refer to:
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A recent math test had an average score of 75, with a standard deviation of 10. What percentage of people scored an 85 or higher?16%34%50%, 13.5%
Answers
Answer:
16%.
Explanation:
In a recent math test:
• The average score = 75
,• Standard Deviation = 10
To find: The percentage of people who scored an 85 or higher, P(X>85).
First, find the z-score when X=85.
[tex]z-score=\frac{X-\mu}{\sigma}[/tex]Substitute the given values:
[tex]z=\frac{85-75}{10}=\frac{10}{10}=1[/tex]The people who scored an 85 or higher are 1 standard deviation away from the mean.
[tex]13.5\%+2.35\%+0.15\%=16\%[/tex]The percentage of people who scored an 85 or higher is 16%.
Write an equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
Please help and Thank you.
Answers
h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
What is Translation?Translation is the process of reworking text from one language into another to maintain the original message and communication.
The parent function is: g(x)=|x|
we stretch the parent function y = |x| by a factor of 3.
h= |x/3|
If the constant is between 0 and 1, we get a horizontal stretch
if the constant is greater than 1, we get a horizontal compression of the function.
Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
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A and B are supplementary angles. If mA = (3x - 28)° and
m/B = (x − 4)°, then find the measure of A.
Answers
Answer:
A = 131°
Step-by-step explanation:
Supplementary angles sum 180°
A + B = 180°
(3x - 28) + (x - 4) = 180
4x - 28 - 4 = 180
4x - 32 = 180
4x = 180 + 32
4x = 212
x = 212/4
x = 53
Then:
A = 3x - 28
A = 3*53 - 28
A = 159 - 28
A = 131°
B = x - 4
B = 53 - 4
B = 49°
Check:
131° + 49° = 180°
Answer:m∠A=33
Step-by-step explanation:
Consider the function y=(x−1)2+3.(a) Give the coordinates of the vertex of the graph of the function.(b) Graph the function on a window that includes the vertex.
Answers
Given function is
[tex]y=(x-1)^2+3[/tex]The vertex of the graph is at (1,3).
pls answer the question i need it to day 20 points
Answers
Answer:
Step-by-step explanation:
See attached worksheet
Determine whether the table of values represents a linear function. If so, write the function.
PLEASE HELP!!
Answers
a) is a function y = -1/3x + 5
b. Is NOT a function, the slope / rate changes so it won’t be a straight line
Step by step
a. Rate is proportional -1/3 slope so it is a function
To write a linear function, you need the slope and the y-intercept.
We will use slope formula for two pairs to find slope
y2-y1 over x2-x1
(-2, 5 2/3) and (0, 5)
5 - 5 2/3 over 0 - -2
-2/3 over 2
Divide
-2/3 * 1/2 = -1/3
(2, 4 1/3) and (4, 3 2/3)
3 2/3 - 4 1/3 over 4 - 2
-2/3 over 2
Divide
-2/3 * 1/2 = -1/3
We found slope is -1/3
Now we can find our equation by using point slope form and points (0, 5)
y - 5 = -1/3 (x - 0)
y -5 = -1/3x
add 5 to both sides to solve for y
y -5 +5 = -1/3x + 5
Combine
y = -1/3x + 5 your answer
- - - - - -
b. Reason, use slope formula for two pairs
y2-y1 over x2-x1
(-5, -27) and (0, -2)
-2 - -27 over 0 - -5
25 over 5, slope is 5
(5, 20) and (10, 48)
48 - 20 over 10 - 5
28 over 5, slope is 5 3/5
Slope of 5 and slope of 5 3/5 are not the same so the line will not be a straight line and it won’t be a linear function
Determine whether there is enough information to conclude that the triangles are congruent. If so, select the theorem
you used.
Given: TR intersects NP, TU RU, NU - PU
Is ATUN ARUP?
N
No. There is not enough information to conclude that the triangles are congruent.
SAS
Yes. There is enough information to conclude that the triangles are congruent.
ASA
SSS
Previous
Answers
Answer:
SAS
Step-by-step explanation:
Whats the Point-Slope Equation for the line that goes through
(-3, 5) and (-7, 4)
Answers
Step by step
The point slope formula is y − y1 = m (x − x1 )
First we need to find “m” or slope
Slope formula is (y2 - y1) over (x2 - x1)
4-5 over -7 - -3
-1 over -4 or 1/4
Now for point slope formula using (-3, 5)
y - 5 = 1/4 (x + 3) (x - -3 is same as x + 3)
Distribute
y -5 = 1/4x + 3/4
add 5 to both sides to solve for y
y -5 +5 = 1/4x + 3/4 + 5
Combine
y = 1/4x + 5 3/4 is your answer
2/7×7/10 reduced to the smallest fraction
Answers
Answer:
1/5
Step-by-step explanation:
I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.
what isss 1+2
please help im so confused
Answers
Answer:
3
Step-by-step explanation:
1 + 2 = 3
please mark this answer brainliest if it helped you in any way:)
Answer:
3
Step-by-step explanation:
1 + 2 = 3
Let break it down.
Lets say you have 1 apple
Your friend has 2 apples
All together you have 1 + 1 + 1 = 3 apples
7x+12=x-6 please answer
Answers
Answer:
x=-3
Step-by-step explanation:
The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Answers
Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.
For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.
In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):
P(x ≤ 21) = 50%
P(x ≤ 21) = 50/100
P(x ≤ 21) = 0.5.
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jim is six feet tall, and his shadow is $16$ feet long. the flagpole he is standing next to casts a shadow that is $72$ feet long. how tall is the flagpole, in feet?
Answers
The height of the flagpole is 27 feet.
Given,
If two triangles are similar, sides of these triangles will be proportional.
Height of the flagpole = h feet
Shadow castes by the flagpole = 72 feet
Height of the person = 6 feet
Shadow casted by the person = 16 feet
By using the property of similar triangles,
Hence, h/6 = 72/16
h = (6×72)/ 16
h = 27 feet
Therefore, The height of the flagpole is 27 feet.
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find the 2 points if the (x,-1) which are 4 units from the pooint (3,2)
Answers
The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)
How to calculate the coordinates of the two points?From the question, we have
Points = (3, 2) and (x, -1)Distance = 4 unitsWhere (x, -1) represents the other points
The distance between the points is the number of units between them
It is calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y represent the coordinates of the given points
Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
So, we have
d = √[(3 - x)²+ (2 + 1)²]
Evaluate the expression
d = √[(3 - x)²+ 9]
Recall that d = 4
So, we have
√[(3 - x)²+ 9] = 4
Square both sides
(3 - x)²+ 9 = 16
This gives
(3 - x)² = 7
So, we have
3 - x = ±√7
Solve for x
x = 3 ± √7
Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)
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Answer the question below
Answers
A) 4/5 or 0.8
B)7
C)1/81
y=−3x+9
3y=−9x+9 how many solutions
Answers
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.
A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.
The linear equations are given below.
y = -3x + 9 ...1
3y = -9x + 9 ...2
Divide the equation 2 by 3, then the equation will become.
y = -3x + 3
The slope of the lines is the same but the lines are separated by a distance.
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
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Find the derivatives of the following using increment method.1.y = 6x² +10x - 3
Answers
Given
[tex]y=6x²+10x-3[/tex]Find
derivatives using increment method.
Explanation
Given
[tex]y=6x²+10x-3[/tex]replace x and y by
[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]so ,
[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]now divide by
[tex]\Delta x[/tex]so ,
[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]now taking limit
[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
400 x 600x 800x150x120
Answers
Answer:
3.456e+12
or
3,456,000,000,000
Step-by-step explanation:
400 x 600 = 240,000
240,000 x 800 = 192,000,000
192,000,000 x 150 = 28,800,000,000
28,800,000,000 x 120 = 3,456,000,000,000
hope this helps you :D
