Answer: The player expects to lose 184.21 dollars.
=========================================================
Explanation:
X = net winnings in dollars
Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.
If the player wins, then they walk away with 7+245 = 252 dollars
If the player loses, then their "winnings" is -7
So either X = 252 or X = -7 are the only two options.
Let's form a table showing those options with their corresponding probabilities.
[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]
Now multiply each X value and P(X) value across the rows.
252*(1/38) = 6.631579
-7*(37/38) = -6.815789
These values are approximate.
[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]
Add up the results of the third column
6.631579 + (-6.815789) = -0.18421
This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.
Do this 1000 times and the player should expect to lose about
1000*(0.18421) = 184.21 dollars
Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.
Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21
a. What are the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps?
The distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
Missing informationWhen you walk with a normal stride, the average distance covered in 2 steps is about 5 feet
How to determine the distances?From the question, we have:
Rate = 5 feet per 2 steps
This gives
Rate = 5/2 feet per step
So, we have:
Rate = 2.5 feet per step
The distance is then calculated as:
Distance = Rate * Steps
This gives
Distance = 2.5 * Steps
So, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are
Distance = 2.5 * 4 = 10 feet
Distance = 2.5 * 6 = 15 feet
Distance = 2.5 * 12 = 30 feet
Distance = 2.5 * 30 = 75 feet
Hence, the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps are 10 feet, 15 feet, 30 feet and 75 feet.
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ING DROPS
1. The total volume to be given is 30 ml.
The time over which this is to be given is 30 minutes.
The drop factor is 15.
How many drops per minute will be delivered ?
Answer:
15 drops per minute
Step-by-step explanation:
(drops per minute) flow/drip rate: volume ÷ time × drop factor
note:
volume (mL)
time (minutes)\
30 / 30 = 1
1 * 15 = 15
so, 15 drops per minute will be delivered
hope this helps!! have a lovely day :)
Answer:
15 drops/minute
Step-by-step explanation:
30 ÷ 30 = 1
1 · 15 = 15
hope this is helpful :)
Work out the height of this triangle with base, b = 4.7mm and area, A = 137.475mm2.
Step-by-step explanation:
hope you can understand
The height of the triangle will be;
⇒ 58.5 mm
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The base of the triangle = 4.7 mm
The area of triangle = 137.475 mm²
Now,
We know that;
⇒ The area of triangle = 1/2 × Base × Height
Substitute all the values, we get;
⇒ 137.475 = 1/2 × 4.7 × h
⇒ 137.475 = 2.35 × h
⇒ h = 137.475 / 2.35
⇒ h = 58.5 mm
Thus, The height of the triangle = 58.5 mm
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Graph the following non-linear system of equations and identify the two solutions. y=2x −7x+3y=3 What type of function is the equation y=2x ? Linear [ ] Quadratic [ ] Exponential [ ] What type of function is the equation −7x+3y=3 ? Linear [ ] Quadratic [ ] Exponential [ ] Use your graph below to identify the two solutions to this non-linear system of equations. Note: All solutions to this problem are whole numbers. None of the answers are decimals or fractions. List the solution, (x,y), with the smallest x value below. x= __________ y= __________ List the solution, (x,y), with the largest x value below. x= __________ y= __________
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
What is a Equation ?An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.
The equations given in the question is
y = 2ˣ
This is an exponential function
-7x +3y = 3
This is a linear function
The equations have been plotted and the solution to the non linear system of equation has been determined
The point at which the graphs intersect is the solution to the system of non -linear equations.
(0,1) and (3,8)
x = 0 , y = 1 ; x = 3 , y = 8
The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value x = 3 , y = 8 .
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Hakim, Edmund and Paul share a bag of guppies. There are 132 guppies in the bag. The ratio of Hakim's share to Edmund's share is 2:3. The ratio of Edmund's share to Paul's share is 1:2. How many guppies does each boy get? Hakim , Edmund and Paul share a bag of guppies . There are 132 guppies in the bag . The ratio of Hakim's share to Edmund's share is 2 : 3 . The ratio of Edmund's share to Paul's share is 1 : 2 . How many guppies does each boy get ?
Answer:
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Step-by-step explanation:
We will have Hakim's share as the base unit.
Hakim : Edmund = 2:3
Edmund : Paul = 1:2
Hakim : Edmund : Paul = 2:3:3x2 = 2:3:6
Total units = 2+3+6 = 11 units
11 units = 132 guppies
1 unit = 132/11 = 12 guppies
Hakim's share = 2 x 12 = 24 guppies
Edmund's share = 3 x 12 = 36 guppies
Paul's share = 6 x 12 = 72 guppies
Work out the bearing of D from C.
(Hint: bearings are written with three digits.)
Answer:
050°
Step-by-step explanation:
The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.
From the diagram, the angle is 050°
PLS HELP PLS In the diagram below, ΔABC ≅ ΔDEF. Complete the statement ∠A ≅
Answer:
∠A ≅ ∠D
Step-by-step explanation:
When writing a triangle congruency like ΔABC ≅ ΔDEF, the angles are congurent based on the orders listed. For example the first angle A is congruent with the first angle of the other triangle D.
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Find the equation of a line passing through the points (-1,5) and (3,17).
Answer:
y=3x+8
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
you find the slope by using this formula:
then we figure out it is 3
then graph to find the y-intercept which is 8
Answer:
y = 3x + 8
Step-by-step explanation:
Below is the image for the formula of the slope.
1. Subtract y values:
17 - 5 - 12
2. Subtract x values:
3 - (-1) = 4
3. Divide y/x
12 / 4 = 3
Therefore, the slope is 3.
Next, you need to find the y-intercept. This is our equation so far:
y = 3x + b
We can substitute any of the points given to us from the problem. I will use the first point: (-1, 5).
When substituting, you get:
5 = 3 ( -1 ) + b
5 = -3 + b
b = 8
Therefore, the equation is y = 3x + 8
What is the measurement of this angle?
I NEED HELP ASAP!!!!
Samuel entered the following key strokes on his calculator.
5 EE (-) 9 divided by 2 EE 4
What did Samuel's calculator display?
A. 2.5E - 13
B. 2.5E - 4
C. 2.5E5
D. 2.5E14
Whoever gets this CORRECT may get MARKED BRAINLIEST.
In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
What is the calculation about?The function was [tex]\frac{5E (-9) }{2E(4) }[/tex] :
We know that, E implies 10 to rise to power.
So, The equation above is Converted from scientific notation into standard form.
[tex]\frac{5 x 10^-9 }{2 x 10^ 4 }[/tex]
= 5/2 x 10 ⁻⁹⁻⁴
=2.5 x 10⁻¹³
Therefore, In the case above about Samuel, one can say that Samuel's calculator has display option A. 2.5 E (- 13)
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A car is purchased for 28,000 after each year, the resale value decreased by 25% what will be the resale value be after 3 years?
Answer:
11,812.5
Step-by-step explanation:
25% = 0.25
(YEAR ONE)
[tex]28,000*0.25 -- > 21,000[/tex]
↓ (why?)
28,000 * 0.25 = 7,000
[tex]28,000 - 7,000 = 21,000[/tex]
(YEAR TWO)
[tex]21,000 * 0.25 -- > 15,750[/tex]
↓ (why?)
[tex]21,000 * 0.25 = 5250[/tex]
[tex]21,000 - 5,250 = 15,750[/tex]
(YEAR THREE)
[tex]15,750 * 0.25 -- > 11,812.5\\[/tex]
↓ (why?)
[tex]15,750 * 0.25 = 3,937.5\\15,750 - 3,937.5 = 11,812.5[/tex]
Answer = 11, 812.5
Please explain and i need it urgently... One fifth of marked price of a watch is given as discount. What is the discount percent?
Answer:
1/5 times 100= 20%
Step-by-step explanation:
brainliest????????!!!!!!!
1/a + 1/b = 1/2 (solve for a)
Answer:
1/a+ 1/b = 1/2
Adding the fractions we get
b+a/ab=1/2
cross Multiplying the denominator we get,
b+a=ab/2
a= ab/2 -b
Answer:
a = 1/(1/2 + 1/b)
Step-by-step explanation:
1/a + 1/b = 1/2
1/a = 1/2 - 1/b
1 = a(1/2 - 1/b)
1/(1/2 + 1/b) = a
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml
PLEASE HELP
If k and r are constants, the graph of y = (x-r)²(x - k)4 does which of the following?
A)Passes through the x-axis at k and 'bounces off' the x-axis at r
B)Bounces off' the x-axis at r and k
C)Passes through the x-axis at r and 'bounces off the x-axis at k
D)Passes through the x-axis at r and k
Answer:
D
Step-by-step explanation:
Passes through the x-axis at r and k
What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
O {x|x=-5, -4, -2, 0, 2}
Oy | y=-9, -3, 0, 5, 7}
{x|x = -9, -5, -4, −3,−2, 0, 2, 5, 7}
{y | y=-9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the function will be (-9, 7). Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given in the form of the pair of points.
{(-2, 0), (-4,-3), (2, -9), (0, 5), (-5, 7)}
Then the range of the function will be (-9, 7).
Then the correct option is D.
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non homogeneous recurrence relation
2fn - 6fn-1 = (n+1)(3^n)
Answer:
Non-Homogeneous Recurrence Relation and Particular Solutions
A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.
Find the equation of the tangent line to the curve:
y = ( 1 + 2x)
at the point (2, 25).
Answer:
the first answer y = 20x - 15
Step-by-step explanation:
since the correct tangent line must share the same point with the originated function, only a line function that delivers y = 25 for x = 2 can be correct.
only the first answer option provides this (20×2 - 15 = 25).
so, we know, this line goes through the given point, but does it have the correct slope for the tangent ?
the correct slope we get from the first derivative of the original function.
f(x) = (1 + 2x)² = 1 + 4x + 4x²
f'(x) = 4 + 8x
for x = 2 we get the tangent slope at that point as
4 + 8×2 = 20
and the provided line is again
y = 20x - 15
with the slope being the factor of x (20).
so, it fits, and indeed, answer 1 is correct.
A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
Answer:
[tex]\boxed {f(x) = x^{2} - 6x + 1}[/tex]
Step-by-step explanation:
Substituting each x value and checking it corresponds to the table :
x = -6
⇒ f(-6) = (-6)² - 6(-6) + 1
⇒ f(-6) = 36 + 36 + 1
⇒ f(-6) = 73
x = -2
⇒ f(-2) = (-2)² - 6(-2) + 1
⇒ f(-2) = 4 + 12 + 1
⇒ f(-2) = 17
x = 2
⇒ f(2) = (2)² - 6(2) + 1
⇒ f(2) = 4 - 12 + 1
⇒ f(2) = -7
x = 6
⇒ f(6) = (6)² - 6(6) + 1
⇒ f(6) = 36 - 36 + 1
⇒ f(6) = 1
x = 10
⇒ f(10) = (10)² - 6(10) + 1
⇒ f(10) = 100 - 60 + 1
⇒ f(10) = 41
Help me with this please!!!!
Answer:
3
Step-by-step explanation:
Cardinalities are the number of elements in a set.
(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.
Calcular cuántos números enteros diferentes de tres dígitos se pueden formar con los dígitos 2, 3 ,4 ,5 ,6 ,7 , 8 si los dígitos no pueden repetirse
There are 210 different three-digit whole numbers that can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated.
To calculate how many different three-digit whole numbers can be formed with the digits 2, 3, 4, 5, 6, 7, 8 if the digits cannot be repeated, we need to use the permutation formula.
The number of permutations of n objects taken r at a time, where order matters and objects cannot be repeated, is given by:
P(n,r) = n! / (n-r)!
In this case, we have 7 digits to choose from, and we want to form a three-digit number, so r = 3. Therefore, the number of different three-digit whole numbers that can be formed is:
P(7,3) = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210
Each of these numbers will be unique, as we are not allowed to repeat any of the digits.
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What is the inverse of the function f(x) = 2x + 1?
Answer:
[tex]h(x)=\frac{1}{2}x -\frac{1}{2} .[/tex]
Step-by-step explanation:
if the initial function is f(x)=2x+1, then
x=2*h(x)+1;
2h(x)=x-1;
[tex]h(x)=\frac{x}{2} -\frac{1}{2}.[/tex]
PS. change design according the local requirements.
Answer:
[tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
Step-by-step explanation:
To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.
So, given f(x)=2x+1, its inverse would give,
x=2y+1.
Solve for y,
2y=x-1 -> y=(x-1)/2 -> y=[tex]\frac{1}{2} x-\frac{1}{2}[/tex]
Therefore, [tex]y^{-1} =\frac{1}{2} x-\frac{1}{2}[/tex]
In a board game, you gain 1.5x the number of coins in your purse every time you pass start. However, you max out at 300 coins. If you have 5 coins in your purse, how many times must you pass until you reach maximum?
Answer:
6
Step-by-step explanation:
The requried number of passes to reach the maximum is given as 10 passes.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
We have 5 coins in your purse,
We Gain 1.5x the number of coins in your purse every time you pass the start. The maximum number of coins is 300.
According to the quesiton,
5 . 1.5ˣ = 300
Where x is the number of passes,
1.5ˣ = 60
x ≈ 10
Thus, the requried number of passes to reach the maximum is given as 10 passes.
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Need help with this geometry question
Answer: B
Step-by-step explanation:
In triangles ABC and CED, CE=AC and AB=ED, but CD>BC, meaning the angle E is smaller than angle A.
Find the area of the triangle.
Answer:
take 1/2 multiply by sin 91°×2×8
The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
The equation that represents the given data is [tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
What is a Function ?It is a statement where two variables , one dependent and one independent are related.
It is given that
a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
The equation given in the options are
[tex]\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}[/tex]
The function goes through (8,2)
Substituting the values
f(x) = -2
f(x) = [tex]\sqrt[3]{7}[/tex]
f(x) = -3
f(x) = 2
The equation that represents the given data is
[tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
1) (b + a) = 4; use a = 1 and b = 3
2) c(b + b); use b = 1 and c = 5
3) 4+ pm; use m = 4 and p =3
4) 5+ pm; use m = 4 and p = 2
5) m(p + 2); use m = 5 and p = 2
6) h+j²; use h = 1 and j = 4
7) y-(x - 5); use x = 5 and y = 6
8) 4xy; use x = 5 and y = 2
9) n(p + 3); use n = 2 and p = 2
10) y +x+x; use x = 3 and y = 5
11) 6+ a-b; use a = 4 and b = 4
Step-by-step explanation:
1). (3+1)=4
2).5(1+11)
5(2)=103).4+3(4)
4+12=16.4).5+2(4)
5+8=135).5(2+2)
5(4)=206).1+4^2
1+16=177).6-(5-5)
6-0=68).4×5×2=40
9).2(2+3)
2(5)=1010).5+3+3=11
11)6+(4-4)
6+0=6.I hope this helps. Pls mark as brainliest like and follow me
Please help me find the area of this trapeziod.
Answer:
37.5 m
Step-by-step explanation:
Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.
((8+7)/2)*5
(15/2)*5
7.5*5=37.5
Now we add the unit, "m" to get 37.5 m!
Round 7,485 to the nearest hundred.
Answer:
7,500
Step-by-step explanation:
When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500
Every row and every column of this 3 x 3 square must contain
each of the numbers 1, 2 and 3.
What is the value of N + M?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
=========================================================
Reason:
We have "1" in the upper left corner and "2" in the direct middle. This means "3" goes to the left of the "2" since each row and column cannot use repeats. Just below that "3" will go "2".
In summary so far, the first column has 1, 3, 2 in that order when moving from top to bottom. Refer to the values in green in the diagram below.
For identical reasoning, the first row has 1, 3, 2 in that order when moving from left to right. These are the values in light blue.
Once the first row is filled out, we can determine the middle entry of the bottom row, which is "1" marked in pink. This item helps us determine that M = 3 which in turn leads to N = 1.
Therefore, N+M = 1+3 = 4 is the final answer.
Side note: This square has symmetry along the northwest diagonal
