consider the following quiz game. there are 2 questions. question 1 can be answered with probability 0.8 with reward $100 and question 2 can be answered with probability 0.5 with reward $200. if your first attempt in answering the question of your choice fails, the game is terminated. which question you should choose first to maximize your expected reward?

The balance of your investment account at any given point in time during the week can be calculated using the exponential growth formula:

N(t) = N0 * (1 + r)^t, where N0 is the initial balance (1,459 dollars), r is the growth rate per day (4.73/day), and t is the number of days since the week began (n).

For example, if it is the fourth day of the week (n = 4), then the balance of your investment account would be N(4) = 1,459 * (1 + 4.73/day)^4 = 2,719.37 dollars.

The exponential growth formula is a mathematical equation used to calculate the growth of a population over time. It is expressed as N(t) = N0 * (1 + r)^t, where N0 is the initial population size, r is the growth rate, and t is the time in days.

Learn more about The exponential growth formula

https://brainly.com/question/27207350

#SPJ4

Answer:

1 yard and 1 foot

Step-by-step explanation:

7-4=3

3-1 yd and 2 feet

there are three feet in a yard. you can subtract the yard first, leaving you with two yards, then subtract two feet. you will be left with 1 yard and 1 foot.

Answer:

$27

Cost = 20 + 1x = 20 + x

Step-by-step explanation:

Membership fee is $20 per month. This amount has to be paid whether he buys pizzas or not that month

If x is the number of pizzas, the total cost for 7 pizzas at discounted price of $1 is  20 + 7 x 1 = $27

For  x pizzas, the equation is

Cost = 20 + x

If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .

When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :

⇒ r × s = k, where k is a constant ;

the value of variable "r" = 7 when s = 6,

First , we have to find the value of k:

⇒ k = r × s = 7 × 6 = 42 ;

So, for any value of r and s, the product "rs" will always be equal to 42.

When r = 10, we can use the equation to find s:

⇒ s = k/r = 42/10 = 4.2

Therefore , when r = 10 , the variable "s" is 4.2.

Learn more about Proportionality here

https://brainly.com/question/599120

#SPJ4

Answer:

Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears,how many pounds of gummy bears did she buy?

1/8 pound

Step-by-step explanation:

The lengths of the diagonals of QRST is 14units.

In a rectangle, the diagonals are equal in length and bisect each other at 90 degrees. This means that the diagonals divide the rectangle into four congruent right triangles.

Since the diagonals of a rectangle are of equal length. then

QS = RT

4x + 2 = 5x - 1

Simplify and solve for the value of x.

4x + 2 = 5x - 1

x = 3

Substitute the value of x in any of the expression for the length of the diagonal.

QS = 4x + 2

length of diagonal = 4(3) + 2 = 14

Hence, the length of the diagonals QS and RT is 14 units.

The problem seems unreadable, it must have been...

"In rectangle QRST, QS = 4x + 2 and RT = 5x - 1. Find the lengths of the diagonals of QRST."

Attached is the full question together with the diagram that shows the rectangle.

Learn more about diagonal here: https://brainly.com/question/23008020

#SPJ4

The distance between two raisins will increase by a factor of the square root of 2.

As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.

However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.

This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.

To know more about Distance click here:

https://brainly.com/question/15172156#

#SPJ11

Answer:

the two coefficients are 2/3 and -1/6

the sum of the expressions are = 1 /2 q−r+ −3 /4

hope this helps :)

Answer:

(8, -8)

x = 8

y = -8

Step-by-step explanation:

-4x - 5y = 8

7x + 5y = 16

-----------------------

3x = 24

÷3   ÷3

----------------

x = 8

7x + 5y = 16

7(8) + 5y = 16

56 + 5y = 16

-56          -56

----------------------

5y = -40

÷5    ÷5

------------------

y = -8

(8, -8)

I hope this helps!

Answer: See below

Step-by-step explanation:

First, we will use the conversions that you provided to find how many feet are in 3 miles. Since we know that one mile = 5,280 feet, all we have to do is multiply that number by 3 to find the conversion.

5,280 * 3 = 15,840 feet

Now, we can use the value found above to find how many inches are in 3 miles. We know that 12 inches are in one foot, so we have to multiply 12 by 15,840. This equals 190,080 inches.

I hope this helps, and if you need me to show you the step-by-step work for multiplication, let me know!

Kyle spending on this shirt at end up is, $63.07.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Kyle is looking to buy a shirt that normally costs $85.

Here, Lucky for Kyle, the store selling the shirt is having a 30% off sale for all items.

Hence, The discount price is,

⇒ 30% of 85

⇒ 30/100 × 85

⇒ $25.5

So, The price of shirt after discount = $85 - %25.5

                                                       = $59.5

Since, After the discount, Kyle must pay 6% sales tax on the shirt.

Hence, The sales tax is,

⇒ 6% of 59.5

⇒ 6/100 × 59.5

⇒ $3.57

Thus, The amount to pay at endup by Kyle = $59.5 + $3.57

                                                                  = $63.07

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

Using the properties of triangle, the value of x = 10.5 and y = 8.75.

A polygon with three vertices and three sides is called a triangle. The triangle's angles are created by joining its three sides end to end at a single point. The sum of the three angles of the triangle is 180 degrees.

The sum of the angles of the triangle is 180 degrees.

A triangle's exterior angles add up to 360 degrees.

The shortest side of a triangle is always on the opposite side of its smallest angle.

From the given figure,

If we consider the line measuring 4, divides the triangle into 2 equal halves,

The sides of triangle will be in equal ratio,

⇒ [tex]\frac{5}{y} = \frac{6}{x} = \frac{4}{7}[/tex]

⇒ x = 10.5

⇒ y = 8.75

To learn more about triangles from given link

https://brainly.com/question/1058720

#SPJ1

Answer:

D

Leah spent y

15 times ryan's

ryan spent x

y = 15x

Step-by-step explanation:

A -  Leah spent x

      15 times more than

      Ryan spent y

x = 15 * y

B - Leah spent y

     15 more

     Ryan spent x

y = x + 15

C- Leah spent x

    15 less

    Ryan spent y

x = y-15

Answer:

f = 4/7 * 4/5 = 16 / 35      Fraction of spool used

4/7 of spool was originally present and Frank used 4/5 of the yarn left on the spool

According to the problem,The area of the figure is approximately 34 square units.

A square is a four-sided plane figure where all sides are equal length and all angles are right angles. It is a two-dimensional shape with four equal-length sides and four equal angles of 90°. Squares are often used in designs and architecture, and are an important part of Euclidean geometry. They are also found in nature, such as in a honeycomb, in a checkerboard pattern, and in tessellations.

To calculate this, we need to calculate the area of the square and the area of the circle's segment. The side of the square is 4 units, so the area of the square is 4 x 4 = 16 square units. The radius of the circle is also 4 units, so the area of the circle's segment is (1/2)πr^2, which is (1/2)π(4^2) = 16π/2 = 16 x 3.14/2 = 24.96 square units.

Therefore, the area of the figure is 16 + 24.96 = 40.96 square units, which is approximately 34 square units to the nearest whole number.

To learn more about square

https://brainly.com/question/620307

#SPJ1

Answer:

Prisms

Step-by-step explanation:

The only two associated are rectangles and prisms

The required probability for the number of phone calls more than two in next 30 minutes is equal to ( 18 / 5)e⁻⁶.

Number of phone calls between 6pm and 8.00 pm 'n' = About 6 calls

Using Poisson's distribution we have,

P ( X = x ) = ( e⁻ⁿ nˣ ) / x!

Probability of receiving more than 2 phone calls in next 30 minutes

= P( X > 2 )

= P ( X = 3 ) + P ( X = 4 ) + P ( X = 5) + P( X = 6)

= ( e⁻⁶ 6³ ) / 3! +  ( e⁻⁶ 6⁴ ) / 4! +  ( e⁻⁶ 6⁵) / 5! +  ( e⁻⁶ 6⁶ ) / 6!

=  ( e⁻⁶ 6³ ) / 3! [ 1 +  (6 / 4) + (6² / 5× 4 ) + ( 6³ / 6 ×5× 4) ]

= ( e⁻⁶ 6³ ) / 3! [ ( 20 + 30 + 72 ) / 20 ]

= ( 18 / 5)e⁻⁶.

Therefore, the probability of more than two phone calls is  ( 18 / 5)e⁻⁶.

learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

Becca's birthday is June 10th, which is a Wednesday this year. November 10th is exactly 6 months after June 10th, so the friend's birthday is also a Wednesday this year.

The increase in the area of the circle is 64π, not 39π. If the original circle had an area of 25m, then the original radius was 5. The new radius would be 5 + 3 = 8. The new area would be 8^2 * pi = 64 * pi = 64π.

Let X be the number of 4 point scores that Hunter made and Y be the number of 9 point scores. X + Y = total number of scores and 4X + 9Y = 755. Substituting Y = 100 + X, we get 4X + 900 = 755. Solving for X, we get X = 41. Therefore, Hunter made 41 4 point scores.

Answer:

see explanation

Step-by-step explanation:

solving the inequality

- 13t ≤ 78

divide both sides by - 13, reversing the symbol as a result of dividing by a negative quantity.

t ≥ - 6

this means that any value of t greater than 6, including 6, is a solution.

listing the solutions from - 10 through to 10 that are solutions when substituted for t

- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6

Step-by-step explanation:

add it and the answer is 2,453

Answer:

PR = 3.6

Step-by-step explanation:

Triangles PQR and STR are similar figures. PQ is the base of triangle PQR just like ST is of triangle STR. PR is parallel to SR and RQ is parallel to RT.

[tex]\frac{Side PQ}{Side ST} =\frac{Side PR}{Side SR}[/tex]

=[tex]\frac{1.8}{1.2} = \frac{PR}{2.4}[/tex]

Cross-multiplying:

=(1.8)(2.4) = (1.2)(PR)

= PR = [tex]\frac{(1.8)(2.4)}{(1.2)}[/tex]

= PR = 3.6

Opposite angles of a parallelogram are congruent.

[tex]9x-13=14+6x \\ \\ 3x-13=14 \\ \\ 3x=27 \\ \\ x=9[/tex]

This means [tex]m\angle ADC=68^{\circ}[/tex].

Answer: B- 7, 24, 25

Hope this helps :)

Step-by-step explanation:

Use the Pythagorean Theorem

a^2 + b^2 = c^2

49 + 576 = 625

625 = 625

The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is,  =  integral. 1 0 s7 cos(s8) dt ds

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

= f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus,  ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

=  integral. 1 0 s7 cos(s8) dt ds

Integrate the given iterated integral.

We get:

=   integral. 1 0 s7 cos(s8) dt ds

= t       when s = 0

= 6         t = 0  

=   ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

=  cos(t)

=   cos(t) dt

=  [sin(t)]

=  [ sin(1) - sin(0) ]

= 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

To learn more about Integration  visit :

brainly.com/question/13981661

#SPJ4

The solution of the expression is Z/57

A ring is a mathematical structure that combines the properties of an additive group with the properties of a multiplicative group.

When we look at solutions to the equation x² = 7 in different rings, we are asking "In what mathematical structures can we find numbers which, when squared, equal 7?"

(a) In the ring Z/19, the solutions are the residue classes modulo 19 that satisfy x² = 7. This means that we only consider the integers 0, 1, 2, ..., 18, and we take their remainders after dividing by 19. In this ring, we use the operations of addition and multiplication modulo 19.

(b) In Z/21, the equation x² = 7 has no solutions. This is because none of the remainders 0, 1, 2, ..., 20 after dividing by 21 can be squared to give 7.

(c) In Z/57, the equation x² = 7 has exactly 2 solutions. This is because there are exactly two residue classes modulo 57 that, when squared, give 7. To find these two solutions, we would need to perform a bit of calculation to determine which residues satisfy x² = 7.

To know more about expression here.

https://brainly.com/question/14083225

#SPJ4

(a)Tax Schedule Notation:

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.

What is the inequality notation?

An inequality is a mathematical statement that represents the relationship between two quantities but states that they are not exactly equal. The four symbols of inequality notation are. ≥,>,<,and≤

(a) Tax Schedule Notation:

Income Tax = Tax bracket rate * (Income - Bracket Lower Bound) + Fixed Amount

Example:

Income = $172,876.99

Tax bracket rate = 37% (for 2022 taxes, 37% applies to taxable income over $518,400 for singles)

Bracket Lower Bound = $518,400

Fixed Amount = $208,725 + 37% * ($172,876.99 - $518,400)

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation:

The interval notation for the income $172,876.99 would be $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation:

The compound inequality notation for the income $172,876.99 would be $518,400 < $172,876.99 < ∞.

Hence,  (a)Tax Schedule Notation:

Income Tax = 37% * ($172,876.99 - $518,400) + $208,725

(b) Interval Notation: $172,876.99 ∈ [$518,400, ∞)

(c) Compound Inequality Notation: $518,400 < $172,876.99 < ∞.

To learn more about the inequality notation visit,

https://brainly.com/question/28485020

#SPJ1

Answer:

$174,850.10

Step-by-step explanation:

the future value of $7000 at the end of 5 periods at 8% compounded interest is

$10,285.30

so you multiply $10,285.30 x 17 = 174,850.10 that's the amount you have to invest. After thirty years you will have $1,049,100.60

Answer:

slope = 1/2

y-intercept = -1

Step-by-step explanation:

Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept?

The equation given is: y= 1/2x - 1

y = mx + b

where m = slope and b = y-intercept, so:

slope = 1/2

y-intercept = -1