Mathematics High School

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

Answers

Answer 1

i would say about $10 about 1/6th the time

Answer 2

Answer:

$30

Step-by-step explanation:

To find the expected value, first we find the outcomes for the sample space.

Rolling a 6-sided die, we have

1, 2, 3, 4, 5, 6

There are 2 values that are whole number multiples of 3: 3 and 6.

There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.

There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.

Next we multiply the value won or lost by each probability.

If the player rolls a 3, they win 3(20) = 60. Multiplying it by its probability, we have

1/6(60) = 60/6 = 10

If the player rolls a 6, they win 6(20) = 120. Multiplying it by its probability, we have

1/6(120) = 120/6 = 20.

If the player rolls a 1, 2, 4 or 5, they win nothing. 0 times all of these will be 0.

Lastly, we add together these products:

10+20+0+0+0+0 = 30

Related Questions

How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?

I'm between 3 & 11.

Answers

The number of solutions of an algebraic equation equals the value of the exponent with the highest power.
Therefore, the answer is 11.

In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.
Find x. (accurate to 3 significant figures)
The value of x = .

Answers

To solve the value of x we use the sine rule that states.
a/sinA = b/sinB = c/sinC
Where a, b, and c are the opposite sides of angle A, B. and C respectively.

x/sin60 = 7/sin80

x =(7sin60)/sin80

= 6.062/0.9848
=6.155696691

To 3 significant figures the answer is 6.16

Using the law of the sine we have two possibilities:
Way 1:
x / sine (60) = 7 / sine (80)
Rewriting we have:
x = (7 / sine (80)) * (sine (60))
x = 6.16
Way 2:
x / sine (80) = 7 / sine (60)
Rewriting we have:
x = (7 / sine (60)) * (sine (80))
x = 7.96
Answer:
x = 6.16
or
x = 7.96
Note: it depends on the location of a and b in the triangle.

Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth?

Answers

Answer:

Step-by-step explanation:

A student invests $500 for 3 years in a savings account that earns 4% interest per year. No further deposits or withdrawals were made during this time. Which does NOT yield the correct balance in the account at the end of the 3 years? Please show work for the answer! A)500(1.04)^3 B)500(1-.04)^3 C)500(1+.04)(1+.04) D)500+500(.4)+520(.04)+540.8(04)

Answers

To get the balance after 3 years we use the formula:
A=P(1+r/100)^n
where:
A=future amount
r=rate
n=time
thus plugging in the values we obtain:
A=500(1+4/100)^3
A=500(1+0.04)^3
A=500(1.04)^3
The correct choices are A and B

The wrong choices are C and D

Answer:

he`s right its a or b

i'm going with b

Step-by-step explanation:

How many combinations with 3 numbers 0-6?

Answers

Assuming the digits can be repeated but cannot start with zero;

6x7x7=294

(5.4+3)×(6−2) help plzzz

Answers

The answer is 33.6. Hope that's what your looking for.

A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested area is shaded in green and the open field is the white space. Upon landing, the hang glider realizes she has dropped her keys.
What is the probability that her keys have landed within the forest?
The blacked out middle section of the pyramid is 20 acres
A 0.2
B 0.6
C 0.8
D 1.0

Answers

0.8 is the probability that her keys have landed within the forest

The probability that her keys have landed within the forest will be C. 0.8.

How to calculate probability?

From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:

= 20/100 = 0.2

Now, the probability that her keys have landed within the forest will be:

= 1 - 0.2

= 0.8

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Given:
CDKM is a parallelogram,

DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK

Answers

With the information given, the triangle CAD and KAD are both right angled triangle and they share the base AD.

So we can form 2 equation and solve them simultaneously.

(AD)²=(CD)²-(AC)²
(AD)² = (CD)² - 6² ...........(i)

(AD)² = (DK)² - (AK)²
(AD)² = (DK)² - 15² ..............(ii)

But DK - CD = 7. So, DK=7+CD
Now let CD=x
From the 2 equations above,
(AD)²=x²-36 .......(i)
(AD)²=(7+x)²-225 .......(ii)

x²-36=49+14x+x²-225
14x=140
x=10

CD = 10.

DK = 7+CD
= 7+10
= 17

In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

What is Pythagoras theorem?

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.

The difference of the side DK and CD is,

[tex]DK - CD = 7\\DK=7+CD[/tex]

The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,

[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex] ....1

Again by using the Pythagoras theorem

[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]

Put the value of (AD)², from equation 1 in the above equation as,

[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]

Put the value of DK in the above equation as,

[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]

Hence, the value of DK is,

[tex]DK=7+10DK=17[/tex]

Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.

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Quadrilateral ABCD is a parallelogram. DE = 6.1 cm and m∠DAB = 120°. What is BC? cm What is m∠BCD? ° What is AB? cm What is EB? cm

Answers

we know that

There are six important properties of parallelograms to know:

1) Opposite sides are congruent (AB = DC and AD=BC).
2) Opposite angles are congruent (D = B and A=C)
3) Consecutive angles are supplementary (A + D = 180° and D+C= 180°).
4) If one angle is right, then all angles are right.
5) The diagonals of a parallelogram bisect each other.
6) Each diagonal of a parallelogram separates it into two congruent triangles.

Part 1) What is BC?
BC=AD-----------> BC=10 cm--------> by Opposite sides are congruent

the answer Part 1) is
BC=10 cm

Part 2) What is m∠BCD?
m∠BCD=m∠DAB-----> m∠BCD=120°----> by Opposite angles are congruent

the answer part 2) is
m∠BCD=120°

part 3) What is AB?
AB=CD------> AB=5 cm----> by Opposite sides are congruent

the answer Part 3) is
AB=5 cm

Part 4) What is EB?
EB=DE-----> EB=6.1 cm----> by The diagonals of a parallelogram bisect each other.

the answer Part 4) is
EB=6.1 cm

Answer: check

Step-by-step explanation:

done

Conor buys 75 tokens for games at the arcade. the price to play each game is 3 tokens. if conor has already played x games, which expression is equivalent to the number of tokens that remain?

Answers

For this case we have the following variables:
x: number of games
y: number of remaining tokens
The expression that models the problem is given by:
y = -3x + 75
Answer:
the number of tokens that remain is:
y = -3x + 75

Answer:

y = 75 - 3x

Step-by-step explanation:

Let the number of token left = y

total number of token bought = 75

Number of games played by Conor = x

It is given for playing one game, the price = 3 token

Therefore for playing x games, the price is = 3x

Therefore, the number of tokens left with Conor is given by

y = 75 - 3x

Thus, the expression that is equivalent to the number of remaining tokens is

y = 75 - 3x

Quickly

Which coordinates represent a translation of B(–4, 1) 3 units to the right and 2 units down?

Answers

B(-4; 1)

3 units right → x + 3
2 units down → y - 2

B'(-4 + 3; 1 - 2) → B'(-1; -1)

To translate point B(−4, 1) 3 units to the right and 2 units down, you add 3 to the x-coordinate and subtract 2 from the y-coordinate, resulting in the new coordinates B' = (−1, −1).

The coordinates that represent a translation of B(−4, 1) 3 units to the right and 2 units down can be found by adding 3 to the x-coordinate and subtracting 2 from the y-coordinate of point B. The new coordinates will be:

B' = (−4 + 3, 1 − 2)

So, the new coordinates would be B' = (−1, −1).

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Answers

The derivatives tell you there are local extremes at (-2, 8) and (2, 0), a point of inflection at (0, 4). The curve is decreasing on the interval (-2, 2) and non-decreasing everywhere else. It is concave downward for x<0 and concave upward for x>0.

This is nicely done by a cubic function such as the one shown here.

The tax rate is 3.9%
What is the tax on 42$?
Round to the nearest hundredth

Answers

Final answer:

To calculate the tax on $42 at a 3.9% rate, first convert the percentage to a decimal (0.039) then multiply the amount by the tax rate. The result is approximately $1.64.

Explanation:

The problem involves calculating the tax on a certain amount using a specified tax rate. In this case, the tax rate is given as 3.9% and the amount is $42.

You calculate the tax by multiplying the tax rate by the amount.

First, convert the percentage into a decimal by dividing by 100: 3.9 ÷ 100 = 0.039.

Next, multiply the amount by the tax rate: $42 x 0.039 = $1.638.

Therefore, the tax on $42 at a rate of 3.9% is approximately $1.64, when rounded to the nearest hundredth.

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Final answer:

The tax on $42 with a 3.9% tax rate is approximately $1.64 when rounded to the nearest hundredth.

Explanation:

To find the tax on $42 with a tax rate of 3.9%, we need to multiply the total amount by the tax rate. First, turn the percentage into a decimal by dividing 3.9 by 100, which gives us 0.039. After that, you multiply $42 by 0.039. This results in approximately $1.64, which we round to the nearest hundredth as per the instructions, thus our answer is $1.64.

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Is -5/0 undefined. And why is it or why is it not.

Answers

yes -5/0 is undefined because having 0 of something means you cannot split that 0 into any number so the answer is undefined.

-5/0 is undefined.

The reason why division by zero is undefined is because there is no real number that can be multiplied by 0 to get -5.

In essence, the division operation asks how many times the denominator can be contained within the numerator. Since nothing times zero gives any number other than zero, this question has no answer.

Moreover, division by zero is not allowed in the real number system because it can lead to logical contradictions and undefined behavior.

In how many different ways can someone arrange 6 books on a shelf

Answers

Number of ways = 6!
Number of ways = 6 x 5 x 4 x 3 x 2 x 1
Number of ways = 720

------------------------------
Answer: 720 ways
------------------------------

You have to do 6!---- factorize 6

6x5x4x3x2x1---- this equals 720.

So, there are 720!

The mathematics department of a college has 1414 male professors, 99 female professors, 99 male teaching assistants, and 1111 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.

Answers

there are 1414+99=1513 professor
and 99 male assistant.

Probability is (1513+99)/(1414+99+1111+99)=1612/2723

I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723

Easy math problem, please help.

O is the center of the circle. Assume that lines that appear to tangent are tangent. What is the value of x?

A. 56
B. 62
C. 248
D. 304

Answers

The answer would be a. 56

Answer:

Option A is correct that is x° = 56°

Step-by-step explanation:

Let Given Lines are tangents.

So we use a result which states that Tangents are perpendicular with radius at point of contacts.

⇒ ∠ B = ∠ D = 90°

Angle sum property of Quadrilateral = 360°

⇒ ∠A + ∠B + ∠O + ∠D = 360

x + 90 + 124 + 90 = 360

x + 304 = 360

x = 360 - 304

x = 56

Therefore, Option A is correct that is x° = 56°

Express answer in exact form.

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.

Answers

Hello,
Please, see the attached file.
Thanks.

Can anybody help me with this question(#6)? It’s over systems word problems. ASAP!

Answers

Let S represent the cost of a small box, and L represent the cost of a large box.

Matt's sale can be represented by the equation
3S +14L = 203
Ming's sale can be represented by the equation
11S +11L = 220

There are a number of ways to solve a pair of equations. One is to graph them. The graph shows the costs to be ...
The cost of a small box of oranges is $7.
The cost of a large box of oranges is $13.

In the united states, 20 ounces of a beverage that is 25% ethanol contains __________ ounces of alcohol

Answers

20 x 25/100 = 5 ounces of alcohol

PLS HELP ME ASAP ON THIS,
YOU NEED TO FIND THE DOMAIN AND RANGE

AND CIRCLE WHAT BEST ANSWERS THEQUESTION

(Random answers gets moderated.)

Answers

1. The usable domain of the function is the time period from when the object was dropped (t=0) to when it hits the ground (h(t) = 0, at t=3). The appropriate choice for domain is ...
2) 0 ≤ t ≤ 3

The appropriate choice for range is the range of heights the object may have:
3) 0 ≤ h(t) ≤ 144

2. The domain is a count of people, ...
1) positive integers

The domain is an amount of money, ...
2) positive real numbers

If a square has a perimeter of 40 yards, what is the length of one side of the square?

Answers

10 yards because a square has 4 sides and all four sides are equal and so 40 divided by 4 equals 10

a - the length of the square

A perimeter of the square: P = 4a

therefore

4a = 40yd |:4

a = 10yd

Suppose that on a particular computer, it takes the merge sort algorithm a total of 60 seconds to sort an array with 60,000 values. approximately how long will it take the algorithm to sort an array with 120,000 values? round to the nearest second.

Answers

120 seconds is the answer. divide 120,000 by 60,000 get 2. 60 times 2 = 120

how do we find the volume ?

Answers

The volume of figure is 877.876 yd³

1. Volume of Cone

= 1/3πr²h

= 1/3 x 3.14 x 2 x 2 x 4

= 16.746

2. Volume of cylinder

= 3.14 x 2 x 2 x 8

= 100.48

3. Volume of Hemisphere

= 2/3πr³

= 7.065

4. Volume of cylinder

= 3.14 x 1.5 x 1.5 x 9

= 63.585

5. Volume of prism

= 1/2 x ( 6 x 6) x 12

= 216

6. Volume of Cuboidal prism

= l w h

= 6 x 6 x 12

= 432

7. Volume of pyramid

= 1/3 x 3 x 2

= 2

8. Volume of cuboidal prism

= 10 x 2 x 2

= 40

So, the volume of figure is

= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40

= 877.876 yd³

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Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units. What is the length of AC?

A. 5 units
B. 6 units
C. 10 units
D. 12 units

Answers

Answer:

D. 12 on edge

Step-by-step explanation:

How many permutations exist of the letters a, b, c, d taken four at a time?

Answers

Final answer:

There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.

Explanation:

The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.

In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.

Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.

HELPPPPPPPPPPPP and explain

Answers

Start by eliminating anything with a z in it. z to the zero power is 1. That means that the top one and the third one from the bottom is gone.

If you want to remove the power (3/4) the rule is that you multiply every power inside the brackets by 3/4.
2 has a power of 1
2^1 is the way you think of it.
(2^1)^3/4 = 2^(3/4). It would look like this.[tex]2^\frac{3}{4} [/tex]

(a ^2 ) ^(3/4) = 2^(6/4) which would look like this [tex]a^\frac{6}{4} [/tex]
which could be written as [tex]a^\frac{3}{2} [/tex] or a^1.5

x ^ (-5) can be written as [tex]x^\frac{-15}{4} [/tex] Notice that - 5 * 3/4 = - 15/4 It could also be written as 1/x^(15/4) That would get rid of the - sign.

(y ^ 8) ^(3/4) = y^(24/4) = y^6

On your page, number the questions from a to h

e is the only one I found to be correct. I will go through the errors. Sometimes I did not list them all. There's just too many of them. The key point is that all the powers are multiplied by 1/4. You need 4 letters or numbers to take 1 letter or number outside the root sign.

a
wrong because a should be 6/4 and not 5/4. As noted, this may not be the only error.

b
is because the y should be y^1 outside the root sign and y^2 inside the root.

c
is wrong because there should be a y^2 inside the brackets.

d
is wrong 2 should be 8 raised the the 1/4 power. 8^1/4

e
correct but I sure don't like z^0 sitting there.

f
has all kinds of problems. Start with the 268 That is wrong. If you are going to bring 36 inside the root sign, it should be 36^3 which is 44656. y is wrong and so is x. For x you will have to use the -15 somewhere.

g
is wrong. The 36 is not to be altered and if it is it must be done as it was in the above question
y should be to the 6/4

h
is wrong. You lost a y somewhere.

Remark
Up until now, the questions you have asked could have been answered and it would have cleared up any of the problems you have been having. This one is quite different.

It is extremely long and it supposes that you know the multiplication rule for powers. You must have been been taught something before you tackled this monster. You need to go to a help center if you are in school or ask a tutor if you are not. It is not you that's the problem. It's the question that's the problem. It is very long and there are all sorts of tricks in it. In my opinion, it's not really a fair question without a lot of help.

Rearrange the formula to calculate the diameter of a circle.

Answers

a=1/4pid^2
4a=pid^2
4a/pi=d^2
square both sides to get d
Answer: Square root of 4a over pi equals d.

To find your answer, you want to get everything but the variable "d," the diameter, onto one side of the equal sign, leaving d by itself.

1) Start by multiplying both sides by 4 to get rid of the 4 in the denominator on the right. bringing it to the other side:
[tex]A = \frac{1}{4} \pi d^{2} \\ 4(A) = 4(\frac{1}{4} \pi d^{2} )\\ 4A = \pi d^{2} [/tex]

2) Divide both sides by π to move the π to the other side of the equation (I put the d squared on the left, but you can keep it on the right):
[tex]4A = \pi d^{2} \\ d^{2} = \frac{4A}{ \pi } [/tex]

3) Finally, take the square root of both sides to get the value of d:
[tex]d^{2} = \frac{4A}{ \pi } \\ d = \sqrt{\frac{4A}{ \pi } } [/tex]

-----

Answer: [tex]d = \sqrt{\frac{4A}{ \pi } } [/tex]

What is the least common multiple (LCM) of 8 and 10?

Answers

Answer:

LCM (8,10) = 2 × 2 × 2 × 5 = 40

Step-by-step explanation:

Least common multiple is the smallest number that is multiple of both the given numbers.

Example: LCM of 2 and 3 is 6 .

6 is a multiple of both 2 and 3 .

Given numbers are 8 and 10

First write both in factor form,

⇒ 8 = 2 × 2 × 2

⇒ 10 = 2 × 5

We find LCM by writing common terms one times and multiplying all terms together,

Here, 2 is common to both 8 and 10 so we write it once only.

Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.

Write the equation in standard form for the circle with radius 3 centered at the origin

Answers

[tex]\text{The equation in standard forn of the circle with radius r and a center}\\\text{in A(a; b) is}\ (x-a)^2+(y-b)^2=r^2\\\\\text{We have: r=3 and A(0; 0)}\\\\\text{substitute:}\\\\(x-0)^2+(y-0)^2=3^2\to\boxed{x^2+y^2=9}[/tex]

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