Answer:
you expect to win on average $1.33 per round
Step-by-step explanation:
The expected value is the sum of products of probability and value:
2/6×$8 + 4/6×(-$2) = $8/3 - 4/3 = $4/3 ≈ $1.33
The expected value of the gambling game is calculated by taking into account the probability of winning $8 and losing $2. The final expected value is $1.33, which means on average, you would gain $1.33 per game played.
Explanation:To calculate the expected value for the gambling game where you roll a die, you need to account for the different outcomes and their associated probabilities. In this game, rolling a 1 or 2 means you win $8, and there are two outcomes out of six that result in a win, giving a probability of 2/6 or 1/3 for each of these outcomes. Rolling any other number (3, 4, 5, or 6) results in losing $2, with a probability of 4/6 or 2/3 for each of these losing outcomes.
The expected value (EV) can be calculated using the formula:
EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)
Substituting the values into the formula:
EV = (1/3 × $8) + (2/3 × -$2)
EV = ($2.67) + (-$1.33)
EV = $1.33
This means that the average gain per game, after many plays, is expected to be $1.33.
For each trial of a binomial experiment, there are two mutually exclusive outcomes:------------------------or------------
Answer:
The underlying assumptions of the binomial distribution are that there is only one outcome for each trial, that each trial has the same probability of success, and that each trial is mutually exclusive, or independent of each other.
Step-by-step explanation:
Express the following relationship as a rate. Washing 24 cars in 4 hours
A.) 4 cars per minute
B.) 8 cars per hour
C.) 6 cars per minute
D.) 6 cars per hour
Answer:
D.) 6 cars per hour
Step-by-step explanation:
6 cars washed on each our which we got 4 hours
Multiply it 6 x 4= 24
Answer:
D.) 6 cars per hour
Step-by-step explanation:
You invest $2000 in an account that is compounded annually at an interest rate of 5% . You never withdraw money from the account. How much money will be in the account after 4 years?
$2,431 is the answer to this problem I think
What are the coordinates of the center of the ellipse shown below?
[tex]\frac{(x-7)^2}{4} + \frac{(y+3)^2}{16} = 1[/tex]
A. (-7,3)
B. (4,16)
C. (2,4)
D. (7,-3)
Answer:
Option D (7, -3)
Step-by-step explanation:
We know that the general equation of an ellipse has the form:
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1[/tex]
Where the point (h, k) are the coordinates of the center of the ellipse
In this case the equation of the ellipse is:
[tex]\frac{(x-7)^2}{4} + \frac{(y+3)^2}{16} = 1[/tex]
Then
[tex]h=7\\\\k = -3[/tex]
So The coordinates of the center of the ellipse are (7, -3)
Answer:
D. (7,-3)
Step-by-step explanation:
This equation is for vertical Ellipse;
For vertical Ellipse;
center of ellipse is given by (h,v)vertices for ellipse is given by (h, v ± a)co-vertices for the ellipse is given by (h ±b, v)where the equation is (x-h)²/b² + (y-v)²/a²
In this question;
h=7 and v= -3
center= (7,-3)
Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches. What is the smallest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. square inches What is the largest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. square inches
Answer: The smallest possible area of the tabletop=[tex]113\text{ square inches}[/tex]
The largest possible area of the tabletop =[tex]1662\text{ square inches}[/tex]
Step-by-step explanation:
Given: The minimum radius of the tabletop = 6 inches
The maximum radius of the tabletop = 23 inches
We know that the area of circle is given by :-
[tex]A=\pi r^2[/tex], where r is the radius of the circle.
Now, the smallest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (6)^2=113.097335529\approx113\text{ square inches}[/tex]
The largest possible area of the tabletop that will fit on Timothy’s table is given by :-
[tex]A_s=(3.14159265359) (23)^2=1661.90251375\approx1662\text{ square inches}[/tex]
Answer:
113 square inches
1,662 square inches
Step-by-step explanation: Have a good day :)
I need help with these 2 questions on geometry PLEASE!!
Answer:
13. 26
14. The answer is 71
find any points of discontinuity for y=x^2/x^2+1
Answer:
The function is continuous for all real numbers
Step-by-step explanation:
We have the following function
[tex]y=\frac{x^2}{x^2+1}[/tex]
Note that the denominator of the function is:
[tex]x^2 +1[/tex]
This expression is different from zero for all real numbers, since for [tex]x^2 +1[/tex] then [tex]x^2 =-1[/tex], there is no number in the real numbers whose square root is equal to -1.
For this reason the function is defined for all real numbers and has no discontinuity.
This function is always positive, continuous and has horizontal asymptote
[tex]y = 1[/tex]
Observe the attached image
Which expression is equivalent to root 2/cubed root 2
Answer:
It's the second choice ⁶√2.
Step-by-step explanation:
Convert to fractional exponents:
√2 = 2^1/2
∛2 = 2^1/3
√2 / ∛2
= 2^1/2 / 2^1/3 = 2^(1/2-1/3)
= 2^(1/6)
Now change back to radicals:
= ⁶√2.
Please help!!!!!!!!!!!!!!!
86 which equals 90 and then you divide by two
Answer:
x = 53.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8}{10}[/tex]
x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{10}[/tex] ) ≈ 53.1°
What is the solution of the inequality x^2-9x+18 less then or equal to zero? Graph solution.
ANSWER
[tex]3\le x\le6[/tex]
EXPLANATION
The given inequality is
[tex] {x}^{2} - 9x + 18 \leqslant 0[/tex]
This is the same as
[tex](x - 3)(x - 6) \leqslant 0[/tex]
The corresponding equation is
[tex](x - 3)(x - 6)= 0[/tex]
By the zero product principle,
[tex]x = 3 \: or \: x = 6[/tex]
We now plot the boundaries and test for the region that satisfies the inequality.
See attachment.
From the graph the solution is
[tex]3\le x\le6[/tex]
Verify each identity.
I need help with the Precalculus.
1)
[tex]\bf \cfrac{cot(x)}{sin^2(x)}=\cfrac{csc^2(x)}{tan(x)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{cos(x)}{sin(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{cos(x)}{sin(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the left-hand-side} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~\frac{1}{sin^2(x)}~~}{\frac{sin(x)}{cos(x)}}\implies \cfrac{1}{sin^2(x)}\cdot \cfrac{cos(x)}{sin(x)}\implies \cfrac{cos(x)}{sin^3(x)}~\hfill \textit{doing the right-hand-side}[/tex]
2)
[tex]\bf \cfrac{cos^2(x)+tan(x)}{sec(x)}=cos^3(x)+sin(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~cos^2(x)+\frac{sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}\implies \cfrac{~~\frac{cos^3(x)+sin(x)}{cos(x)}~~}{\frac{1}{cos(x)}}~\hfill \textit{doing the left-hand side} \\\\\\ \cfrac{cos^3(x)+sin(x)}{\underline{cos(x)}}\cdot \cfrac{\underline{cos(x)}}{1}\implies cos^3(x)+sin(x)[/tex]
Gabriella bought a pile of brick wall. Yesterday , she used 5/8 of the bricks. Tommrow she plans to use another 1/4 of the brick wall. what fraction of brick pile will she have left after tommrow
You could turn the 1/4 into 2/8 to make it have a common denominator. When you add 2/8 and 5/8 you’ll obviously get 7/8. She’ll only have 1/8 left.
Hoped this helped
Please help me fill in the blank with the correct word from each statements' parentheses:
1. In an observational study, randomization of subjects _____ (occurs, does not occur).
2. A survey makes inferences about a population from_____ (a sample, a study, an experiment) of the population.
3. In an experiment, a treatment is imposed on those being studied to discern any differences in____ (a control, a response, an independent) variable.
Answer:
1. does not occur
2. a sample
3. an independent
Step-by-step explanation:
The correct answer for this question would be Occurs, Sample and an independent variable.
What is meant by survey?A survey is a type of research that involves gathering data from a predetermined group of people in order to get knowledge and insights about a variety of issues.
1) In an observational study, randomization of subjects has to occur to get a lot of diverse information from all the participants.
2) In a survey, randomly a sample is chosen from the population and all the inferences about the population are made from studying this sample only.
3) In a survey a treatment is imposed on all the participants so as to neutralize all the qualities they have which are quite different from the others.
Learn more about survey on:
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#SPJ2
(Economics) Real Gross Domestic Product is adjusted for _____ changes.
a. price
b. time
c. government
(will mark brainliest)
C.Government is the answer
Answer:A-Price
Step-by-step explanation:
Real Gross Domestic Product is adjusted for Price changes.
Unlike Nominal GDP Real GDP accounts for the change in prices and provides a better figure than nominal GDP. Real GDP differentiate GDP in different years more significant because it permits comparisons of the real volume of services and goods without taking inflation.
The quotient of a numder and -5 is 6. what is the number?
Answer:
B
Step-by-step explanation:
Make an equation.
[tex]\frac{x}{-5}=6[/tex]
[tex]x=-30[/tex]
Answer:
B, -30
Step-by-step explanation:
Suppose you were designing a line graph that was going to be printed in Time magazine. Your editor has warned against misleading your audience in any way. What items will you try to avoid when creating your graph?
I would try to avoid unclear statements about the graph and make sure it's clear enough for audience. Also not to use items that bleed through paper.
Answer: Always avoid doing unnecessary things. like changing the zero or using logarithmic scale (and if you use them, mention it), if the graph contains more than one line, then use different colors or dots and label every line.
Also, comparative graphs should always be in the same scale.
At the foootball game 8 1/5 of the fans wore team T-shirts.Of those wearing team T-shirts,1/4 also wore team hats.Wgat fraction of the fans at the football game wore both a team T-shirts and team hat?
Answer:
The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]
Step-by-step explanation:
Let
x----> total fans
we know that
[tex]8\frac{1}{5}x[/tex] ----> wore team T-shirts
Convert to an improper fraction
[tex]8\frac{1}{5}x=8\frac{8*5+1}{5}=\frac{41}{5}x[/tex]
Multiply by 1/4
[tex]\frac{41}{5}x*\frac{1}{4}=\frac{41}{20}x[/tex]
convert to mixed number
[tex]\frac{41}{20}x=\frac{40}{20}+\frac{1}{20}=2\frac{1}{20}x[/tex]
therefore
The fraction of the fans at the football game that wore both a team T-shirts and team hat is [tex]2\frac{1}{20}[/tex]
In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K. Find the measure of angle K and angle L.
The measure of angle K and angle L is 35 degrees and 105 degrees
Given information:In Triangle JKL the measure of angle J = 40 and the measure of angle L is 3 times the measure of angle K.
Calculation of measure of angle K and angle L:here we assume the angle K be x
So Angle L be 3x
Now
J + K + L = 180
40 + x + 3x = 180
40 + 4x = 180
4x = 180 - 40
4x = 140
x = 35 degrees
So, the angle K be 35 degrees
And, angle L should be 3(35) 105 degrees
learn more about the triangle here: https://brainly.com/question/11067716
The area of the shaded triangles in the fractal shown form a geometric sequence. The area of the largest triangle (not shaded) is 1 square unit. Find the areas of these shaded triangles. Orange: 1/4 square units Blue: _____ square units Green: _____ square units
Answer:
Blue: 1/16 square units
Green: 1/64
yes
1/3
Step-by-step explanation:
The areas of these shaded triangles. Orange: 1/4 square units, Blue: 1/16 square units, Green: 1/64 square units
What is a fraction?A fraction represents a part of a whole number of equal parts.
The area of the largest triangle is given as 1 square unit.
The area of the triangle is colored and follows a geometric sequence with the common ratio of 1/4.
The area of the non-shaded triangle is given by 1 square unit.
The area of the orange triangle
1 × 1/4 = 1/4 square units.
The area of the blue triangle
1/4 × 1/4 = 1/16 square units.
The area of the green triangle
1/16 × 1/4 = 1/64 square units.
Learn more about fractions:
https://brainly.com/question/10354322
A computer room has 12 computers. The room is open for 4 hours each day. 25 students sigh up for computer time. Each student gets the same number of minutes. What is the graetest whole number of minutes each student can get?
Answer:
155 minutes
Step-by-step explanation:
1. Find the total available "computer time": 4 hours * 12 computers= 48 hours
2. Split this among all of the students: 48 hours/25 students= 1.92 hours
3. Convert to minutes: 1.92 hr/student * 60 minutes ≈ 155 minutes/student
Which value is the best estimate for the correlation coefficient of the data set?
Answer: The answer is D -0.5
Step-by-step explanation:
First off you can cross out A and B because they are zero and a positive because the line has a negative slope. So that leaves you with C, D, and E. C is close to zero so the plot would be pretty scattered about. D is an in between answer because it isn’t quite a strong correlation or a weak one. Finally E is close to -1 so it is a strong correlation.
Answer: The answer is D -0.5
Step-by-step explanation:
First off you can cross out A and B because they are zero and a positive because the line has a negative slope. So that leaves you with C, D, and E. C is close to zero so the plot would be pretty scattered about. D is an in between answer because it isn’t quite a strong correlation or a weak one. Finally E is close to -1 so it is a strong correlation.
which of the following describes the graph of
y = -x^2 + 3x + 10
A| The graph has zeroed at x = -2 and x= 5 and it opens downward.
B| The graph has zeros at x = 2 and x = -5 and it opens upward
C| The graph has zeroed at x = 2 and x = -5 and it opens downward
D| the graph has zeroed at x = -2 and x = 5 and it opens upward
The answer is D because that’s the answer lol
need help now will mark brainlyst answer quick
Describe how to use unit pricing to decide which is the better buy between 5 lbs of chicken for $14.95 or 8 lbs for $23.36.
Answer:
The 8 lbs for 23.36
Step-by-step explanation:
First you divide the total cost by how many lbs
This will provide you with the cost per pound to get your answer
14.95 / 5 = 2.99 or $2.99 a pound
23.36 / 8 = 2.92 or $2.92 a pound
Therefore it is better to but the 8 lbs for 23.36
Answer:
All you have to do is divide 14.95 by 5 and divide 23.36 by 8.
Step-by-step explanation:
the first option is 2.99 per pound,
the second is 2.92 so the second choice is the better option.
PLZ brainliest!!
Find the solution set of this system:
y=−3x
x2−4=y
(4,12), (−1,3)
(−1,−3) only
(4,12) only
(−4,12), (1,−3)
Answer:
(−4, 12), (1, −3)
Step-by-step explanation:
y = −3x
x^2 −4 = y
so
x^2 −4 = −3x
x^2 + 3x - 4 = 0
(x + 4)(x - 1) = 0
x + 4 = 0; x = -4
x - 1 = 0; x = 1
when x = 1, y = -3(1) = -3
when x = -4, y = -3(-4) = 12
Answer
(-4 , 12), (1 , -3)
ANSWER
(−4,12), (1,−3)
EXPLANATION
The system has equations:
y=−3x
[tex] {x}^{2} - 4 = y[/tex]
We equate the two equations to get:
[tex] {x}^{2} - 4 = - 3x[/tex]
[tex]{x}^{2} + 3x - 4 = 0[/tex]
[tex]{x}^{2} + 4x - x - 4 = 0[/tex]
[tex]x(x + 4) - 1(x + 4) = 0[/tex]
[tex](x + 4)(x - 1) = 0[/tex]
[tex]x = - 4 \: or \: x = 1[/tex]
When x=1,
y=-3(1)=-3
when x=-4, y=-3(-4)=12
The solution is (1,-3) and (-4,12)
Describe the error(s) that occurred and show the correct solution.
Answer:
[tex]-x^{2}+4x[/tex]
Step-by-step explanation:
we have
[tex](x^{2}+x)-(2x^{2} -3x)[/tex]
step 1
Eliminate the parenthesis
[tex]x^{2}+x-2x^{2} +3x[/tex]
The symbol of the term 3x is incorrect, must be positive instead of negative
so
[tex]-(-3x)=+3x[/tex]
Group terms that contain the same variable
[tex](x^{2}-2x^{2})+(x+3x)[/tex]
Combine like terms
[tex]-x^{2}+4x[/tex]
128 + 0 = ?
128 - 0 = ?
128 x 0 = ?
128 / 0 = ?
Answer:
1.=128 2.= 128 3.= 0 4.= 0
Step-by-step explanation:
Answer:
128 + 0 = 128
128 - 0 = 128
128 x 0 = 0
128 / 0 = 0
A bicycle manufacturer uses the given expression to model the monthly profit from sales of a new model of bicycle, where x is the selling price of one bicycle, in dollars. At what selling prices for the bicycle will the manufacturer make neither a profit nor a loss?
Answer:
The manufacturer will have no profit or loss when the selling price equals $200 or $100.
Step-by-step explanation:
The expression to model the monthly profit from sales of a new model of bicycle is
-x^2 + 300x -20,000
Let
f(x) -----> the monthly profit in dollars
x -----> s the selling price of one bicycle in dollars
[tex]f(x)= -x^{2}+300x-20,000[/tex]
we know that
The manufacturer will make no profit nor a loss when the profit is equal to zero
so
f(x)=0
[tex]-x^{2}+300x-20,000=0[/tex]
Multiply by -1 both sides
[tex]x^{2}-300x+20,000=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]a=1\\b=-300\\c=20,000[/tex]
substitute in the formula
[tex]x=\frac{300(+/-)\sqrt{-300^{2}-4(1)(20,000)}}{2(1)}[/tex]
[tex]x=\frac{300(+/-)\sqrt{10,000}}{2}[/tex]
[tex]x=\frac{300(+/-)100}{2}[/tex]
[tex]x=\frac{300(+)100}{2}=200[/tex]
[tex]x=\frac{300(-)100}{2}=100[/tex]
therefore
The manufacturer will have no profit or loss when the selling price equals $200 or $100.
To find the selling prices at which the manufacturer will make neither a profit nor a loss, set the profit expression equal to zero and solve for x, giving a selling price of $5.
To determine the selling prices at which the manufacturer will make neither a profit nor a loss, we set the profit expression equal to zero:
0 = 100x - (500 + 20x)
Solving for x, we get x = 5. This means the selling price for the bicycle to break even is $5.
please solve!!!!!!!!! Thanks!
Answer:
a) 60°b) 80°c) 100°d) 50°e) 30°Step-by-step explanation:
The key here is that AB ║ EC. This makes arc AE have the same measure as arc BC. Since those have the same measure as AB and the three arcs together make a semicircle, each has measure 180°/3 = 60°.
Then the various arc measures are:
AB = 60°BC = 60°CD = 80° (given)DE = 100° . . . . . since CDE is 180°EA = 60°Then your answers are ...
a) AE = 60°
b) ∠ABD = (1/2)(DE +EA) = (1/2)(100° +60°) = 80°
c) ∠DFC = (1/2)(CD +EB) = (1/2)(80° + (60° +60°)) = 100°
d) ∠P = (1/2)(DA -AB) = (1/2)(100° +60° -60°) = 50°
e) ∠PAB = (1/2)(AB) = (1/2)(60°) = 30°
Amelia ran a total of 60 miles in the first 3 months of her new running program. She ran equal distances in the first and second months, but ran twice that distance in the third month. How far did she run in the third month?
15 miles
20 miles
40 miles
30 miles
she ran 15 miles in the first month and 15 in the second but because it doubled in the third month she ran 30 miles. 15+15+30=60 miles total
Identify the measure of arc BG◠. HELP ASAP!! I'm so confused!
Answer:
arc BG = 14°
Step-by-step explanation:
∠BMG = [tex]\frac{1}{2}[/tex] ( arc BG + arc JS) = 30
Multiply both sides by 2
arc BG + arc JS = 60, that is
arc BG + 46° = 60° ( subtract 46° from both sides )
arc BG = 14°
Answer:
arc BG= 14°
Step-by-step explanation:
It is given in the figure that mJS = 46∘ and m∠BMG = 30∘.
If two chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. So,
m∠BMG = 12 (mJS +mBG)
Substitute the given values and solve for mBG.
30∘ = 12 (46∘ + mBG)
Multiply by 2.
60∘ = (46∘ + mBG)
Subtract 46∘.
14∘ = mBG
Therefore, mBG = 14∘.