To find out how much Mark should pay for one draw, calculate the expected value by multiplying the payouts for a heart, a jack, and the jack of hearts by their respective probabilities. Sum these values to find the amount Mark should pay per draw to make the game fair, which is $0.135.
To determine how much Mark should pay for one draw from the deck of 52 cards, we need to calculate the expected value (EV) of one draw. The EV is calculated by multiplying each outcome by its probability and summing these products.
The deck has 13 hearts, so the probability of drawing a heart (excluding the jack of hearts) is 12/52 or 3/13. Drawing any jack other than the jack of hearts has 3 possible outcomes in the remaining 51 cards; the probability is 3/52. The jack of hearts is a single card with a probability of 1/52. The remaining 36 cards are neither hearts nor jacks and yield no payout.
The EV is calculated as follows:
(12/52 × $0.35) for a heart
(3/52 × $0.55) for a jack
(1/52 × $0.85) for the jack of hearts
Adding these up we get: (3/13 × $0.35) + (3/52 × $0.55) + (1/52 × $0.85) = $0.13538. To ensure the game is fair and the host neither loses nor gains money in the long term, Mark should pay $0.135 per draw.
Simplify -4/7 + (-4/3)
24 divided by 2 find the qoutient
24/2 = 12
the quotient is 12
Answer: So your answer is 12 for 24 divided by 2 which gives you 12 I hope this helps
Step-by-step explanation:
24 divided by 2 = 12
12 times 2= 24
Or 2 times 12 = 24
Show that the statement is true. If GH has endpoints G(−2, 1) and H(4, −1), then the midpoint M of GH lies on the line y = −x + 1.
The midpoint M is ( , ). The midpoint does not lie or lies on the line y = −x + 1 since its coordinates satisfy or do not satisfy the equation.
How many even numbers can be formed from the digits 1,2,3,4,5?
A machine manufactures wheels with a diameter of 70 cm. It is acceptable for the diameter of a wheel to be within 0.02 cm of this value. Write and solve an absolute-value equation to find the minimum and maximum acceptable diameters.
To find the minimum and maximum acceptable diameters for wheels manufactured by a machine with a 70 cm diameter tolerance set within 0.02 cm, an absolute-value equation is used to determine the range of acceptable values.
The question is: A machine manufactures wheels with a diameter of 70 cm, and it can be within 0.02 cm of this value. To find the minimum and maximum acceptable diameters, we need to set up an absolute-value equation.
Let x be the diameter of the wheel.The absolute-value equation is |x - 70| ≤ 0.02.Solving this equation, the minimum acceptable diameter is 69.98 cm, and the maximum acceptable diameter is 70.02 cm.Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).
What is the y-value of P'?
Answer:
The answer is -10
Step-by-step explanation:
In combining like terms when adding or subtracting do you add the exponents together
Answer: If adding exponents, they have to the same value or same coefficient.
For example:
1) 2x^2+2x^2= 4x^2
what number fills in the blank to complete the factorization of 3x+24?
Answer:
Complete factorization of 3x+24 is:
3(x+8)
Step-by-step explanation:
we have to completely factorize:
3x+24
Taking 3 common in the above expression
3(x+8)
This cannot be factorized further
Hence, complete factorization of 3x+24 is:
3(x+8)
Which statements are true regarding the diagram
Answer:
A. AngleGNH and AngleHNJ are complementary.
C.AngleKNL and AngleLNM are complementary.
D.mAngleHNK + mAngleKNL = 180°
Step-by-step explanation:
Point M is the midpoint of LN. LM = 7x - 12 and MN = 3x + 16. Find LM.
Martha will be entering high school in a couple of years. Which steps should she take to ensure she has money to pay for college? Check all that apply. She should start or add to a college savings account so it can grow with deposits and earned interest. She should ask her parents if they have a college savings account set up for her. She should work to maintain high grades throughout school so she can qualify for scholarships. She should get involved in extracurricular activities like clubs and sports so she can discover what she enjoys and qualify for scholarships. She should fill out the FAFSA immediately so she does not miss grants or scholarships she qualifies for. She should ask all her friends and neighbors to contribute to her college savings account so it will grow faster.
Martha can ensure she has money to pay for college by starting or adding to a college savings account, maintaining high grades, getting involved in extracurricular activities, and filling out the FAFSA immediately.
Explanation:Martha can take the following steps to ensure she has money to pay for college:
Start or add to a college savings account: By saving money early, Martha can let it grow with deposits and earn interest.Work towards maintaining high grades: This will help her qualify for scholarships that can assist in paying for college.Get involved in extracurricular activities: Participating in clubs and sports can help Martha discover what she enjoys and also qualify her for scholarships.Fill out the FAFSA immediately: By submitting the FAFSA, Martha can ensure that she doesn't miss out on any grants or scholarships she may qualify for.
The steps Martha should take to ensure she has money to pay for college are as follows:
1. She should start or add to a college savings account so it can grow with deposits and earned interest. This is a proactive step that allows the money to benefit from compound interest over time.
2. She should ask her parents if they have a college savings account set up for her. It's important to know if there are existing funds that can be used for her education.
3. She should work to maintain high grades throughout school so she can qualify for scholarships. Many scholarships are merit-based, and good grades are often a key criterion.
4. She should get involved in extracurricular activities like clubs and sports so she can discover what she enjoys and qualify for scholarships. Participation in these activities can make her a well-rounded candidate for scholarships that value leadership and community involvement.
5. She should fill out the FAFSA (Free Application for Federal Student Aid) when she is eligible, which is typically during her senior year of high school. This form is crucial for accessing federal grants, loans, and work-study opportunities, as well as some state and college-specific aid.
6. While asking friends and neighbors to contribute to her college savings account could potentially help the account grow faster, it is not a conventional or reliable method for funding college education. Therefore, it is not a primary step she should take.
In summary, Martha should focus on saving money, exploring existing savings, maintaining good grades, engaging in extracurricular activities, and preparing to fill out the FAFSA. These steps will help her secure funding for college through savings, scholarships, and financial aid.
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). There may be more than one possible decomposition.
y = (x^3 + 1)^2
How many, and what type of, solutions does 6x2−2x+7=0 have?
A.) 2 nonreal solutions
B.) 2 irrational solutions
C.)2 rational solutions
D.) 1 rational solution
Answer:
Nope! The answer is 2 Nonreal Solutions i took the test! :)
Step-by-step explanation:
The given quadratic equation will have 2 nonreal solutions. The correct option is A.
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that the quadratic equation is 6x²−2x+7=0. The equation can be solved as below;-
6x²−2x + 7 = 0
The equation will have two non-real values for x. The correct option is A.
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If i was born in 2002 how old will i be in 2130
D: Region D help please .....
The equation h(t)=−16t2+78t+45 gives the height of a firework, in feet, t seconds after it is launched from a platform. What is the height of the platform? Enter your answer in the box.
The height of the platform is 45 feet.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation h(t)=−16t² +78t+45 gives the height of a firework
When a firework is launched from a platform, its height at time t=0 seconds is equal to the height of the platform.
To find the height of the platform, we can substitute t=0 into the equation:
h(0) = -16(0)² + 78(0) + 45
h(0) = 0 + 0 + 45
h(0) = 45
Therefore, the height of the platform is 45 feet.
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The sum of two even numbers is even. the sum of 6 and another number is even. what conjecture can you make about the other number?
Answer: We can say that the other number is even since the sum of two even numbers is even.
The required conjecture is given as the other number must be an even number.
What is an even number?An even number is defined as a number that is a multiple of 2 is called even number, such as 2, 4, 6, 12, and so on.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
here,
The sum of two even numbers is even. Following the statement,
If the sum of 6 and another number is even, that another number must be even to get the sum of 6 and another number to be even, while 6 it self is an even number.
Thus, the required conjecture is given as the other number must be an even number.
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an angle's measure is twice the measure of its complement. the larger angle is how many degrees greater than the smaller angle.
Which is a pair of vertical angles ?
The pair of angles that are vertical are <TRS and <VRW.
Determining vertical anglesTo calculate vertical angles, take the following actions:
Recognize the intersecting lines: Vertical angles are created when two lines cross.
Find the common vertex: The point where the two lines join is the common vertex for vertical angles.
Recognize the pairs of opposite angles: Two pairs of opposite angles cross the intersection point to generate vertical angles.
Hence the pair of angles that are vertical are <TRS and <VRW.
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The sum of three consecutive even integers is less than 84. find the set of these three integers with the greatest sum.
The admission fee at a small fair is $1.50 for children and $4.00 for adults. on a certain day, 2200 people enter the fair and $5050 is collected. how many children and how many adults attended that day?
Which function grows at the fastest rate for increasing values of x?
p(x)=5x3+3
f(x)=8x2−3x
h(x)=2x
g(x)=19x
The function which has the fastest rate for increasing values of x are:
[tex]p(x)=5x^3+3[/tex]
Step-by-step explanation:We are given four polynomial functions as:
[tex]p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x[/tex]
Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.
Hence, among the given options the function which has the fastest rate of increase is:
[tex]p(x)=5x^3+3[/tex]
( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )
Please answer me this equation
Keiko runs 10 miles in 75 minutes. at the same rate, how many miles would she run in 69 minutes?
If P is the midpoint of ST, SP = x + 4, and ST = 4x, determine the length of ST
Answer:
ST = 16.
Step-by-step explanation:
Given : P is the midpoint of ST, SP = x + 4, and ST = 4x,
To find : Determine the length of ST.
Solution : We have given P is mid point of ST.
It mean P divide the ST in to two equal parts .
So, SP = PT .
We can say
ST = 2 SP .
Plug the given values SP = x + 4, and ST = 4x,
4x = 2 ( x +4).
4x = 2x + 8.
On subtracting both sides by 2x
4x -2x = 8.
2x = 8
On dividing both sides by 2
x = 4.
ST = 4 * 4 = 16.
Therefore, ST = 16.
Solve the triangle. A = 46°, a = 31, b = 27
To solve the given triangle with A = 46°, a = 31, and b = 27, we use the Law of Sines to first find angle B, then use the sum of angles to find angle C, and finally, use the Law of Sines again to find side c.
Explanation:To solve the triangle with the given information A = 46°, a = 31, and b = 27, we need to use the Law of Sines or the Law of Cosines. Since we have one angle and the side opposite to it (a = 31), as well as another side (b = 27), we first need to find angle B using the Law of Sines:
\frac{\sin(A)}{a} = \frac{\sin(B)}{b}
By solving for sin(B), we get:
\sin(B) = \frac{\sin(46°) * 27}{31}
Next, we calculate the value of sin(B) and then angle B. After that, we can find angle C by using the fact that the sum of angles in a triangle is 180°:
A + B + C = 180°
Once we have angle C, we can use the Law of Sines again to find side c:
\frac{\sin(C)}{c} = \frac{\sin(A)}{a}
By rearranging and solving for c, we get:
c = \frac{\sin(C) * a}{\sin(A)}
This process will give us the lengths of all sides and the measurements of all angles, thus solving the triangle.
A pet-sitting company charges $25 to board a pet for one day. It also charges all customers an extra $7.50 to trim the pet's nails once per stay.
How much will it cost to board a dog for two weeks?
A.
$57.50
B.
$65.00
C.
$357.50
D.
$455.00
2 weeks = 14 days
14 * 25 = 350
350 + 7.50 = 357.50
Answer is C
What is the surface area of this cone ?
Jermaine’s father owes $6,300 in interest at the end of a 60-month car loan at a 7% simple annual interest rate. What was the original loan amount?
Answer:
$18,000
Step-by-step explanation:
It is given that the interest amount $6,300
We will calculate the principal amount.
So we use the formula
I = prt
P = Principal amount
r = rate of interest 7% ( 0.07 )
t = time in years 60 months ( [tex]\frac{60}{12}[/tex] years )
6,300 = P × 0.07 × [tex]\frac{60}{12}[/tex]
6,300 = P × 0.07 × 5
6,300 = 0.35P
[tex]\frac{6,300}{0.35}[/tex] = P
P = $18000
The original loan amount was $18,000.
In the expression 12 + 7, the values on the right and left of the + symbol are called _____ .
In the expression 12 + 7, the values on the right and left of the + symbol are called operands.
What are operands?A mathematical object upon which an operator acts.
Given that, an expression 12+7,
In maths, the values that an operator acts on are called operands. In this case, 12+7 are the operands.
Hence, the asked statement is operands.
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