You'll lose on average $22 per roll.
====================================================
Explanation:
Normally there is a 1/6 chance to land on any given side of a standard die, but your friend has loaded the die in a way to make it have a 40% chance to land on "1" and an equal chance to land on anything else. Since there's a 40% chance to land on "1", this leaves 100% - 40% = 60% for everything else.
Let's define two events
A = event of landing on "1".B = event of landing on anything else (2 through 6).So far we know that P(A) = 0.40 and P(B) = 0.60; I'm using the decimal form of each percentage.
The net value of event A, which I'll denote as V(A), is -100 since you pay $100 when event A occurs. So we'll write V(A) = -100. Also, we know that V(B) = 30 and this value is positive because you receive $30 if event B occurs.
To recap things so far, we have the following:
P(A) = 0.40P(B) = 0.60V(A) = -100V(B) = 30Multiply the corresponding probability and net value items together
P(A)*V(A) = 0.40*(-100) = -40P(B)*V(B) = 0.60*30 = 18Then add up those products:
-40+18 = -22
This is the expected value, and it represents the average amount of money you earn for each dice roll. So you'll lose on average about $22. Because the expected value is not zero, this means this game is not mathematically fair.
This does not mean that any single die roll you would lose $22; instead it means that if you played the game say 1000 or 10,000 times, then averaging out the wins and losses will get you close to a loss of $22.
A number cube has faces 1 through 6. How many of the number on the cube are composite?
A. 1
B. 2
C. 3
D. 4
Answer:
B) 2 numbers
Step-by-step explanation:
composite #'s: 4, 6
prime #'s: 2, 3, 5
neither composite nor prime: 1
Suppose there are three routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from Beaver Dam to Star Lake, and two routes directly from Boulder Creek to Star Lake. (Hint: Draw a sketch. Assume each route can pass through a city at most one time.) (a) How many routes from North Point to Star Lake pass through Beaver Dam? To answer this question, think of creating a route from North Point to Star Lake that passes through Beaver Dam as a 3-step process. Step 1: Choose a route from North Point to Boulder Creek . Step 2: Choose a route from Boulder Creek to Beaver Dam. Step 3: Choose a route from Beaver Dam to Star Lake. There are choices for step 1, choices for step 2, and choices for step 3. Thus, the answer is . (b) How many routes from North Point to Star Lake bypass Beaver Dam?
Answer:
(a) 36 routes
(b) 6 routes
Step-by-step explanation:
Given
[tex]North\ Point \to Boulder\ Creek = 3[/tex]
[tex]Boulder\ Creek \to Beaver\ Dam = 4[/tex]
[tex]Beaver\ Dam \to Star\ Lake= 4[/tex]
[tex]Boulder\ Creek\to Star\ Lake= 2[/tex]
Solving (a): From [tex]North\ Point[/tex] to [tex]Star\ Lake[/tex] through [tex]Beaver\ Dam[/tex]
To do this, we consider the following routes;
[tex]North\ Point \to Boulder\ Creek \to Beaver\ Dam \to Star\ Lake[/tex]
Taking a pair of routes, we have:
[tex]North\ Point \to Boulder\ Creek = 3[/tex]
[tex]Boulder\ Creek \to Beaver\ Dam = 4[/tex]
[tex]Beaver\ Dam \to Star\ Lake= 4[/tex]
By multiplication route, we have:
[tex]Routes = 3 * 4 * 3[/tex]
[tex]Routes = 36[/tex]
(b) From [tex]North\ Point[/tex] to [tex]Star\ Lake[/tex] bypass [tex]Beaver\ Dam[/tex]?
To do this, we consider the following routes
[tex]North\ Point \to Boulder\ Creek \to Star\ Lake[/tex]
Taking a pair of routes, we have:
[tex]North\ Point \to Boulder\ Creek = 3[/tex]
[tex]Boulder\ Creek\to Star\ Lake= 2[/tex]
By multiplication rule, we have:
[tex]Routes = 3 * 2[/tex]
[tex]Routes = 6[/tex]
Hence factorize completely the expression
9x³y² - 4xy⁴
Step-by-step explanation:
[tex]9 {x}^{3} {y}^{2} - 4x {y}^{4} \\ = x {y}^{2} (9 {x}^{2} - 4 {y}^{2} )[/tex]
A store pay $120 for a bicycle. The store has a 60% markup policy. What is the selling price of the bicycle?
Answer:
$192
Step-by-step explanation:
can u plz help me it’s for a test!! PLZ ANSWER 1 &2
Answer:
Step-by-step explanation:
number one is 10
number two is (c) they have the same median
Answer:
C/B
Step-by-step explanation:
test 1: 90 - 50 = 40
test 2: 100 - 40 = 60
60 - 40 = 20
test 1 is 60 and test 2 is 80
If
the
mean of A and B is 20. The mean of B and c is 24 and the
mean of A,B,C is 18. what is the mean of
A and c?
Answer:
Mean of a and c is a+c/2=6+14/2=10
Cómo saco el volumen de un cilindro?:(
Step-by-step explanation:
La fórmula para hacer este cálculo es muy sencilla, ya que el cilindro es una forma geométrica simple. Se trata de V = hπr2, lo que significa que hallaremos el volumen al tener la altura (h) y el radio (r). Los dos círculos son del mismo tamaño, así que puedes utilizar cualquiera de ellos como base
Please Help Me ASAP.
Answer:
C
Step-by-step explanation:
cuz itz IRRATIONAL
help me 5⋅f(1)+5⋅g(9)
Answer:
-50
Step-by-step explanation:
5f(1) +5g(9) = 5(-5) + 5(-5) = -25 +(-25) = -50
Answer:
5f+45g
Step-by-step explanation:
Help plz if u can i would really like it
Answer:
you would subtract thoose numbers
Step-by-step explanation:
Find $m\angle1$ and $m\angle2$ .
Answer:
m<1 = 125°
m<2 = 55°
Step-by-step explanation:
Okay, so we're dealing with alternate interior angles and all that sorta stuff, so I'll try to explain it best I can, if I'm too confusing let me know, let's go:
So the angle labeled 125° and angle 1 are alternate interior angles, so they're equal (yes, we're ignoring the fact that that might not me right because the other line isn't straight, I don't have another solution okay) anyways, so that means that:
1 = 125°
Now we know what 1 and 2 are on the same plane or axis or something like that, so basically, 1 and 2 HAVE TO add up to 180°, so that means that:
125 + x = 180
And now we just have to do the inverse operations thing:
180 - 125 = 55
So, m<1 = 125° and m<2 = 55°
tell me if this is wrong so I can fix it
hope this helps:)
3x (7+8)x2+6 = ? HM?
Answer96
Step-by-step explanation:
3x (7+8)x2+6=96
Answer:
SHORTYYYYYYYYYYYYYYYYYYYYYYYYYYY ANSWER MEH YOU PRECIOUS CHILD
Step-by-step explanation:
It's meh Min you better not have forgotten who I am-
6. Simone was timing John, Johnny and
James to see who could hold their breath
the longest. John held his breath for 10
seconds, Johnny held his breath for 15
seconds and James for 25 seconds. For how
much longer than John and Johnny did
James hold his breath?
Answer:
hgyjhudhehd
Step-by-step explanation:
(2.4 x 10^4)(4.5 x 10^3)
2.4x104(4.5x103)
Simplifies to:
10.8x11000
=10.8x11000
Please help! Due today
Answer:
-4 5/12
Step-by-step explanation:
URGENT!!! Help pls. U could literally just give me the equations
Answer:
Step-by-step explanation:
Terminal points of vector u has been given as (4, 0), (9, 4).
Therefore, vector u can be represented by,
[tex]\vec{u}=\vec{u_2}-\vec{u_1}[/tex]
[tex]\vec{u}=(9i+4j)-(4i)[/tex]
[tex]\vec{u}=5i+4j[/tex]
And the magnitude of the vector u will be,
|| u || = [tex]\sqrt{5^2+4^2}[/tex]
= [tex]\sqrt{41}[/tex]
Slope of vector passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the expression,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of vector u will be,
Slope = [tex]\frac{4-0}{9-4}[/tex]
= [tex]\frac{4}{5}[/tex]
Similarly, terminal points of vector v are (-7, 1) and (3, 9).
So the vector v will be,
[tex]\vec{v}=(3i+9j)-(-7i+1j)[/tex]
[tex]\vec{v}=(3i+7i)+(9j-1j)[/tex]
[tex]\vec{v}=10i+8j[/tex]
Therefore, magnitude of vector v will be,
|| v || = [tex]\sqrt{10^2+8^2}[/tex]
= [tex]\sqrt{164}[/tex]
= [tex]2\sqrt{41}[/tex]
Slope of vector v = [tex]\frac{9-1}{3+7}[/tex]
= [tex]\frac{8}{10}[/tex]
= [tex]\frac{4}{5}[/tex]
HELP ME PLEASE I AM STUCK
Answer:
-9.8 > -11.3, and -9.8 is located to the right of -11.3.
Step-by-step explanation:
On a number line, the larger value of numbers always increase towards the right side, becoming more positive.
Same, the numbers which have smaller values decrease towards the left.
The larger the negative number, the smaller the value it has.
hewo the whole world that i hate^^
Royston plays a video game 7 times. His scores are 60, 65, 66, 74, 69, 72, and 63. Which is the best measure of center of Royston's performance?
median
middle number
mean
mode
Answer:
Mean: 67
Median: 66
Mode: no mode
Range: 14
Step-by-step explanation:
Answer:
mean
Step-by-step explanation:
THIS WORK IS DUE!!! I MARK BRAINLIEST! The following table shows the number of fire hydrants in each neighborhood overseen by Fire District 9. (LOOK AT IMAGE BELOW) If the mean of the data set is 15 fire hydrants, find the number of fire hydrants in Prairie Pass.
Answer:
10 fire hydrants
Step-by-step explanation:
(15)(5)= 17+15+21+12+x
x= 10
-------------------------
hope it helps...
have a great day!!
Answer:
10
Step-by-step explanation:
A student has been tracking his progress in French class. He notes each
grade he receives along with the date he received it. At the end of the
semester, he decides to create a data display to illustrate how his grades
have improved over time. What kind of display is his best choice?
O A. Stem-and-leaf plot
O B. Line graph
O C. Bar graph
D. Circle graph
Answer:
B) Line graph
Which expression is equivalent to 1/5(150x - 80y + 50 - 50x - 25y + 20)?
Answer:
20x - 21y + 14
1/5(150x - 80y + 50 -50x - 25y + 20)
30x -16y + 10 - 10x - 5y + 4
30x -10x -16y - 5y + 10 + 4
20x -21y + 14
Answer:
20x-21y+14
Step-by-step explanation:
add up like terms and divide them by 5
Hey morning help please thanks
Answer:
metaphor
Step-by-step explanation:
Answer:
Metaphor!
Step-by-step explanation:
Kites are described as "colorful fishes swimming in the sky".
Metaphors don't use like or as but still compare.
A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80. Suppose also that exactly 15% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
Answer:
The mean score is of 617.4.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80.
This means that [tex]\sigma = 80[/tex]
Suppose also that exactly 15% of the scores exceed 700.
This means that when X = 700, Z has a pvalue of 0.85. So X when X = 700, Z = 1.033. We use this to find [tex]\mu[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.033 = \frac{700 - \mu}{80}[/tex]
[tex]700 - \mu = 80*1.033[/tex]
[tex]\mu = 700 - 80*1.033[/tex]
[tex]\mu = 617.4[/tex]
The mean score is of 617.4.
Mother combined 7/4 cups of pancake mix and 3/4 cups of water to make pancake butter if she uses 1/4 of a cup of battte to make each pancake
how many pacakes can johny make
Answer:
10
Step-by-step explanation:
add the 7/4 and 3/4 which is 2 1/2. then divide 2 1/2 by 1/4
write the following rational numbers in their lowest terms:
1. 24/192
2. 12/168
3. 21/49
Answer:
The Answer is gonna be 1. 24/192
Answer:
24/192 = 1/8
12/168 = 1/14
21/49 = 3/7
Step-by-step explanation:
Using first principle find derivatives of x2
Answer:
[tex]\displaystyle f'(x) = 2x[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationDefinition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = x^2[/tex]
Step 2: Differentiate
Substitute in function [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h}[/tex]Expand: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{x^2 + 2hx + h^2 - x^2}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2hx + h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h(2x + h)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} 2x + h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
A basketball team won 80% of the games played.if the team played 25 games,how many games did they lose?
Answer:
5
Step-by-step explanation:
Simplify the following expression.
-20 + (-15)
O A 5
OB. -35
O C.
-5
OD. 35
Reset
Submit
Answer:
B) -35
Step-by-step explanation:
Which of the following functions have a domain of ( -infinity, infinity) and a range of
(-2, infinity)?
Check all that apply.
A. f(x) = 0.25^x- 2
B. f(x) = 0.25^x+2
c. f(x) = 3^x – 2
D. f(x) = 3^x +2
Answer:
It would be answers A and C
Step-by-step explanation:
Notice both end in negative 2, matching your range, so you can't get that correct using either B or D
The functions having domain (-∞,∞) and range (-2,∞) are f(x)=[tex]0.25^{x}-2[/tex] and f(x)=[tex]3^{x}-2[/tex].
What is function?A function is relationship between two or more variables expressed in equal to form .In a function each value of x must have a corresponding y value. The value of x is known as domain of the function and the value of y is known as range of function.
How to find function?We have been given four functions and we have to find the functions having domain (-∞,∞) and range (-2,∞).
Taking f(x)=[tex]0.25^{x}-2[/tex]
f(0)=1-2
=-1
f(1)=0.25-2
=-1.75
f(2)=0.50-2
=-1.50
f(-2)=1/0.50-2
=1-1/0.50
=0
So this function has domain (-∞,∞) and range (-2,∞) because the value of function increases from -2 as the value of x increases.
Taking f(x)=[tex]0.25^{x}+2[/tex]
Because the above function is opposite of the first function so it behaves opposite as the function.
Taking f(x)=[tex]3^{x} -2[/tex]
f(0)=1-2
=-1
f(1)=3-2
=1
f(-2)=1/9-2
=(1-18)/9
=-17/9
=-1.8
This function also has domain (-∞,∞) and range (-2,∞) because the value of increases from -2 as the value of x increases.
Next function is opposite from the third function so it behaves opposite to third function
Hence the functions having domain (-∞,∞) and range (-2,∞) are f(x)=[tex]0.25^{x}-2[/tex] and f(x)=[tex]3^{x}-2[/tex].
Learn more about function at https://brainly.com/question/10439235
#SPJ2
Which graph represents the following piecewise defined function?
Answer: is B
Step-by-step explanation:
on edge 2020
The graph that represents the following piecewise defined function is graph D (Image attached).
What is piecewise defined function?A piecewise function is known to be a type of function that is known to be formed or created from scratch (pieces) of different functions over different intervals.
An example, a person can make a piecewise function f(x) where f(x) = -9 when -8 < x ≤ -4, f(x) = 5 when -4 < x ≤ -1, and f(x) = -6 when -1 <x ≤ 9. Looking at the graph attached, you can see that it tells us more about piecewise defined function.
Learn more about piecewise defined function from
https://brainly.com/question/24313105