Given:
A fair die is rolled.
It pays off $10 for 6, $7 for a 5, $4 for a 4 and no payoff otherwise.
To find:
The expected winning for this game.
Solution:
If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.
The probability of getting a 6 is:
[tex]P(6)=\dfrac{1}{6}[/tex]
The probability of getting a 5 is:
[tex]P(5)=\dfrac{1}{6}[/tex]
The probability of getting a 4 is:
[tex]P(4)=\dfrac{1}{6}[/tex]
The probability of getting other numbers (1,2,3) is:
[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]
[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]
Now, find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.
[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]
[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]
[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]
On further simplification, we get
[tex]E(x)=\dfrac{10+7+4}{6}[/tex]
[tex]E(x)=\dfrac{21}{6}[/tex]
[tex]E(x)=3.5[/tex]
Hence, the expected winnings for this game are $3.50.
can you guys help me measure x
Step-by-step explanation:
everything can be found in the picture
Answer:
x = 102
Step-by-step explanation:
The angles form a straight line
Angles that form a straight line add up to equal 180
Hence, x + 78 = 180
Subtract both sides by 78
180 - 78 = 102
78 - 78 cancels out
Were left with x = 102
Can any one help me on this
point D is the answer
________
HELPPPPPP don't troll ima report
Answer:
The x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
Step-by-step explanation:
We have the function:
[tex]\displaystyle y=\frac{x^2 -1}{x}[/tex]
And we want to find the x-coordinates for which the gradient (or slope) at the point is 5.
The gradients of a curve at a point is given by its derivative. Find the derivative:
[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\frac{x^2-1}{x}\right][/tex]
Use the quotient rule:
[tex]\displaystyle \frac{dy}{dx}=\frac{(x^2-1)'(x)-(x^2-1)(x)'}{(x)^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{(2x)(x)-(x^2-1)(1)}{x^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{x^2+1}{x^2}[/tex]
Since the gradient is 5, substitute 5 for dy/dx and solve for x:
[tex]\displaystyle 5=\frac{x^2+1}{x^2}[/tex]Multiply both sides by x² (x ≠ 0):
[tex]5x^2=x^2+1[/tex]
Subtract x² from boths sides:
[tex]4x^2=1[/tex]
Solve for x:
[tex]\displaystyle x=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}\text{ or } -\frac{1}{2}[/tex]
So, the x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
Please answer this your award will be 20 points for the first answer and brainliest
Step-by-step explanation:
pool = 1600 sq.cm
1600 sq.sm = 50cm × 32cm
AB = 50cm
the area of the park of A'B' :
50cm×4=200 sq.cm
Please help it’s a riddle can you find the correct answer
what are the approximate measurements of each given measurement to the nearest centimetre, then find the sum: 16.4 cm + 12.8 mm + 9.6 cm + 14.6 mm
Answer:
54
Step-by-step explanation:
16.4= 16
12.8= 13
9.6= 10
14.6=15
16 + 13 +10 +15 = 54
NEED HELP ASAP! Which condition would prove JKL ~ XYZ?
A farmer has a rectangular field with length 1 mile and width 0.5 miles. How much fencing would it take to enclose his field?
Answer:
3 mi of fencing would be required to enclose this field.
Step-by-step explanation:
Here we are finding the perimeter of a field with given length and width. We apply the perimeter formula P = 2L + 2W. Substituting the given dimensions, we get:
P = 2(1 mi) + 2(0.5 mi), or
P = 2 mi + 1 mi = 3 mi
3 mi of fencing would be required to enclose this field.
Answer:
15840 feet of fencing = Perimeter = 15840ft
However, if fencing is 6ft or 10ft we need to divide by the length of each fence for panels.
See bold.
Step-by-step explanation:
6ft fencing = 5280/6 = 880 fences one length
880 x 2 = 1760 6ft fences 2 sides
0.5 x 1760 = 880
1760+ 880 = 2640 fences each 6ft
Total feet of fence = 2640 x 6 =15840 feet of fencing
What is the y-intercept of the graph of the line whose equation is y = -2/5x + 4?
1) - 5/2
2) - 2/5
3) 0
4) 4
I’ve been stuck on this question for so long I need help with it.
Answer:
4
Step-by-step explanation:
in y=mx+b, the "b" is the y-intercept
Answer:
4
it's in y = mx + b form, where b is the y-intercept
The storage space in a moving truck is shaped like a rectangular prism. It has a total volume of 16 cubic meters. The height and width are both 2 meters less than the depth. What are the dimensions of the storage space?
Answer:
The dimensions are four by two by two meters.
Step-by-step explanation:
The volume for a rectangular prism is given by:
[tex]V=\ell wh[/tex]
Where l is the length (or depth), w is the width, and h is the height.
Since the height and width are both two meters less than the depth, we can write that:
[tex]h=\ell -2\text{ and } w = \ell -2[/tex]
We are also given that the total volume is 16 cubic meters. Substitute:
[tex]16=\ell(\ell -2)(\ell -2)[/tex]
Expand:
[tex]16=\ell(\ell^2 -4\ell +4)[/tex]
Distribute:
[tex]16=\ell ^3-4\ell ^2+4\ell[/tex]
Isolate the equation. So:
[tex]\ell ^3-4\ell ^2+4\ell -16=0[/tex]
We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:
[tex]\ell ^2(\ell -4)+4(\ell -4)=0[/tex]
Factor:
[tex](\ell ^2+4)(\ell -4)=0[/tex]
Zero Product Property:
[tex]\ell ^2+4=0\text{ or } \ell - 4=0[/tex]
Solve for each case:
[tex]\ell^2=-4\text{ or } \ell =4[/tex]
Since we cannot take the square root of a negative number, we can ignore the first case.
Therefore, the length (or depth) of the storage space is four meters.
Thus, the dimensions are four by two by two meters.
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Pls show work I get different answers from people every time
To purchase $14.400 worth of machinery for his business, Greg made a down payment of $1400 and took out a business loan for the rest. After 2 years of
paying monthly payments of $576.18, he finally paid off the loan.
Answer:
below
Step-by-step explanation:
cost of the machinery = $14,400
he paid a deposit of $1400
then later paid $576.18 for two years
two years = 24 months
= $576.18 *24
=$13,828.32
total amount paid
= initial deposit + amount paid in two years
= $1,400 + $13,828.32
=$15,228.32
so he finally paid $15,228.32
interest = selling price - original cost
= $15,228.32 - $14,400
=$828.32
therefore interest = $828.32
(a)
There are 33 liters of orange juice at a school party. 1010 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get?
___liters
Enter your answer as a fraction or a mixed number.
(b)
Write a number sentence that represents the problem.
___________ = __________
In the first box write an equation like 1+11+11+1 . In the second box, write your answer.
PLS DON'T FOR GET TO DO PART B TOO I AM BEGING YOU!
Answer:
a) 30.60
b) 1010/33 = 30.60
Step-by-step explanation:
Use the distributive property to find a equivalent expression for 6(x+4)
Answer:
6x +24
Step-by-step explanation:
you factor out the 6 so 6x and 6*4 is 24
explanation please will give brainliest.
Answer:
[tex]AC = 28[/tex]
Step-by-step explanation:
Given
[tex]AB = 16[/tex]
[tex]BC = 12[/tex]
Required
Determine AC
Since A, B and C are collinear, then:
[tex]AC = AB + BC[/tex]
So, we have:
[tex]AC = 16 + 12[/tex]
[tex]AC = 28[/tex]
In the accompanying diagram, ABC is isosceles, BC is extended to D. AB = AC. and M
Answer:
m∠ACD = 130
Step-by-step explanation:
If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.
This is because angles in a triangle adds up to 180°.
180° - 80° = 100°/2 = 50°
∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:
50° + 80° = 130°
Or
Angles on a straight line adds up to 180°.
180° - 50° = 130°
A cooking teacher needs to give each student in his class three eggs to use in a recipe. There are 44 students in the class. How many dozens should the teacher buy?
Answer:
11
Step-by-step explanation:
Multiply 44 by 3 to get the amount of eggs you need total, then divide it by 12 for each dozen of cartons you’ll need to buy. The end result is 11.
What is 15 percent in 660
Answer:
99
Step-by-step explanation:
10% = 66
5% = 33
66+33=99
The Natural History Museum has a 1:60 scale model of a tyrannosaurus rex dinosaur. The length of the model is 20 centimeters. Find the
actual length (in meters) of a tyrannosaurus rex.
Answer:
12 meters
20cm*60 = 1200cm = 12 meters
100cm = 1m btw
Darrell builds and sells bookcases to earn money. He earns $20 for each bookcase he sells. The more bookcases he sells, the more money he earns. What is the dependent variable in this situation?
Answer: The total amount of money Darrell earns selling bookcases
Answer
Step-by-step explanation:
The dependent variable refers to the variable which is tested or measured or tested when an experiment is done. The dependent variable normally depends on the independent variable.
In this question, the independent variable is the bookcase while dependent variable is the total amount of money Darrell earns selling bookcases.
What is the thirteenth number in the Fibonacci sequence
Answer:
The 13th number in the Fibonacci sequence is 144.
Step-by-step explanation:
The sequence from the first to the 13th number is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
[tex]\huge\boxed{\sf 144}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
[tex]\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \boxed{144}, 233, 377,...[/tex]
Xác suất thống kê: Người ta tổng kết các phương pháp chẩn đoán dạ dày tá tràng. Trên lâm sàng chẩn đoán đúng 60%; X-quang 70%; nội soi 80%. Kết hợp cả 3 phương pháp thì khả năng chẩn đoán đúng là bao nhiêu?
Answer:
Step-by-step explanation:
iam a gay 345366e2673
Jenna just got done jumping at the Trampoline center. The total cost of the session was $15.23
She had to pay an entrance fee of $7.25 and $1.45 for every minute she was on the trampoline.
Answer:
≈ 5.5 minutes.
Step-by-step explanation:
Let m = number of minutes on the trampoline.
[tex]1.45m+7.25=15.23\\1.45m=7.98\\m=5.5[/tex]
She was on the trampoline for approximately 5.5 minutes.
Answer:
= 5.5 minutes
Step-by-step explanation:
1.45 + 7.25 = 15. 23
1. 45 = 15. 23 - 7. 25
1. 45 = 7 . 98
m = 5.5
Hope this answer helps you :)
Have a great day
Mark brainliest
Fill in the table of values so that this is a proportional relationship with k=3/2 X. Y. *blank*. 0 2. *blank*. *blank*. 6. -2. *blank*
Answer:
x => y
0 => 0
2 => 3
4 => 6
-2 => -3
Step-by-step explanation:
The equation of a proportional relationship is represented as y = kx,
where, k = y/x
We are given that k = ³/2
This means that, equation of the relationship therefore would be:
y = ³/2x
Use this equation to solve for each missing value on the table given:
✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:
0 = ³/2x
0 * 2 = 3x
0 = 3x
0/3 = x
x = 0
✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:
y = ³/2(2)
y = 3
✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:
6 = ³/2x
6 * 2 = 3x
12 = 3x
12/3 = x
x = 4
✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:
y = ³/2(-2)
y = -3
Jackson is making brownies. He uses the following ingredients.
Ingredients Amount for 1
Batch of Brownies
Flour 3 cups
Sugar 2 cups
Butter 1/3 cup
Cocoa Powder 1/4 cup
Jackson has 1 cup of butter. If he wants to use all the butter, how many batches of brownies can he make?
Part A
Which equation can you use to solve the problem?
A. 1 ÷ 3 = 3
B. 1 ÷ 13 = 3
C. 1 × 13 = 13
D. 1 + 13 = 13
Part B
Jackson used all the butter to make the brownies.
If each brownie is 1/9 of a batch, how many brownies did he make?
Enter your answer in the box.
Answer:
It's B (1÷13=3) for Part a
1 whole is equal to 3/3. One batch of brownies uses up to 1/3 of butter. So 1 ÷ 1/3 = 3.
Step-by-step explanation:
The question is on the picture
answer:
ABCD is not congruent to KLMN
ABCD cannot be mapped onto KLMN
HELP HELP HELP!!!!!!!!!!!!!!!!!!!
Answer: the top one
Step-by-step explanation:
Classify the following as discrete or continuous random variables.
1. The weight of bags of apples, with 10 apples in each bag.
2. The number of times required for a modem to dial an internet provider before connecting.
3. Out of 10 times connecting to an internet provider, the average number of attempts necessary before connecting.
4. A pair of dice is rolled, and the sum to appear on the dice is recorded.
Answer:
A discrete variable is a variable that can only take some selected given values from a given set, like x ∈ {x₁, x₂, ..., xₙ}
While a continuous variable can take any value in the range, like x ∈ {x₁, xₙ}.
1) The weight of bags of apples, with 10 apples in each bag.
Here the weight depends on the number of apples in the bag, and we can have only whole numbers of apples in the bag, so this is clearly a discrete variable.
2) The number of times required for a modem to dial an internet provider before connecting.
Same as before, here we can have only a whole number of attempts, so this set is discrete.
3) Out of 10 times connecting to an internet provider, the average number of attempts necessary before connecting.
Here we will have an average of 10 integer numbers:
[tex]M = \frac{x_1 + x_2 + ... + x_{10}}{10}[/tex]
so here we have a kinda dense set of possible values, so we can think of this as a continuous variable.
4) A pair of dice is rolled, and the sum to appear on the dice is recorded.
Here the possible values are whole numbers again, so we can not have values like 3.5, so again, this is a discrete variable.
PLS HELP ASAP! Find the Surface Area of the given figure.
THANK YOU!
Answer:
158 m^2
Step-by-step explanation:
l = 5 m, w = 3 m, h = 8 m
S.A. = [tex]2(lw+wh+lh)[/tex]
S.A. = 2{(5)(3) + (3)(8) + (5)(8)}
S.A. = 2(15 + 24 + 40)
S.A. = 2(79)
S.A. = 158 m^2
Hope this help!!!
Have a nice day!!!
Find the value of x to the nearest tenth.
Step-by-step explanation:
p^2+b^2=h^2
or, 16+9=h^2
or, 25=h^2
or h=5
again, p^2 +b^2=h^2
or, 25+b^2=36
or, b^2=11
or. b=√11 therefore b=x=√11