a game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar. would you play this game or not and why?

Answer:

81

Step-by-step explanation:

First find the amount decrease

90 * 10 %

90 * .10

9

90 decreased by 9

90 -9

81

the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

What is Laplace Transform?

The Laplace transform is an integral transform that is widely used in mathematics and engineering to solve differential equations. It allows us to convert a function of time, typically denoted as f(t), into a function of a complex variable s, denoted as F(s), where s = σ + jω (σ is the real part and ω is the imaginary part).

To apply the Laplace transform to the initial value problem (IVP) y'' - 3y' + 2y = sin(2t), with initial conditions y'(0) = 4 and y(0) = -1, we follow these steps:

Take the Laplace transform of both sides of the differential equation, utilizing the properties of the Laplace transform.

L{y''} - 3L{y'} + 2L{y} = L{sin(2t)}

The Laplace transform of the derivatives y'' and y' can be expressed as follows:

L{y''} = s²Y(s) - sy(0) - y'(0)

L{y'} = sY(s) - y(0)

Here, Y(s) denotes the Laplace transform of y(t).

Substitute the initial conditions into the Laplace-transformed equation:

s²Y(s) - s(-1) - 4 - 3(sY(s) + 1) + 2Y(s) = L{sin(2t)}

Simplify the equation:

s²Y(s) + s - 4 - 3sY(s) - 3 + 2Y(s) = L{sin(2t)}

Combine like terms:

(s² - 3s + 2)Y(s) + (s - 7) = L{sin(2t)}

Express the Laplace transform of sin(2t):

L{sin(2t)} = 2/(s² + 4)

Rearrange the equation to solve for Y(s):

(Y(s) = (s - 7) / ((s² - 3s + 2))

Apply the inverse Laplace transform to find y(t):

y(t) = L⁻¹{(s - 7) / ((s² - 3s + 2))}

Perform partial fraction decomposition on the right side:

y(t) = L⁻¹{(s - 7) / ((s - 2)(s - 1))}

Using the inverse Laplace transform table or software, we find:

y(t) = e^(2t) - e^t + 7

Therefore, the solution to the given IVP is y(t) = e^(2t) - e^t + 7.

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The sum of all the numbers on the chessboard is 4036, obtained by summing the values in the top row, leftmost column, and the products in the remaining squares.

The sum of all the numbers on the chessboard can be found by summing the values in the top row, the values in the leftmost column, and the products in the remaining squares.

The sum of the values in the top row is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.

The sum of the values in the leftmost column is 1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 = 3270.

The sum of the products in the remaining squares can be calculated by finding the sum of the geometric series 1 + 2 + 4 + ..... + 128. Using the formula for the sum of a geometric series, this sum is 2⁸⁺¹ - 1 = 2⁹ - 1 = 511.

Therefore, the sum of all the numbers on the chessboard is 255 + 3270 + 511 = 4036.

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Step-by-step explanation:

\((x - 2)(x + 3) = \\ {x}^{2} + x - 6\)

standard form

\( {x}^{2} + x - 6 = 0\)

function form

\(f(x) = {x}^{2} + x - 6\)

y-intercept = -6

Answer:

(9 x 100) + (5 x 10) +  (0 x 1) + (9/10) + (5/100)

hope this helps brainliest <3

Answer:

Step-by-step explanation:

in this case, we are assuming that the series \(cn xn\)and \(dn xn\) are both convergent, and thus their product series (cn dn)xn will also converge within a radius of 5.

The radius of convergence for the series \((cn dn)xn\) can be determined by considering the product of the radii of convergence for the individual series \(cn xn\)and \(dn xn\). In this case, the series \(cn xn\)has a radius of convergence of 5 and the series dn xn has a radius of convergence of 6.

To find the radius of convergence for the product series (cn dn)xn, we take the minimum of the two radii. In other words, we choose the smaller radius between 5 and 6.

Therefore, the radius of convergence for the series\((cn dn)xn\) is 5, since it is the smaller of the two radii.

It's important to note that the product of two convergent power series may not always converge.

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The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

i think is 50

Step-by-step explanation:

The approximate probability that the driver will be fined is 0.25.

If the driver of a truck loaded with 900 boxes of books will be fined if the total weight of the boxes exceeds 37,350 pounds, then the weight of each box of book must not exceed 41.5 pounds.

37,350 pounds / 900 boxes = 41.5 pounds

Suppose that distribution of the weight is a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 41.5

μ = mean = 41.1

σ = standard deviation = 6

z-score = (41.5 - 41.1) / 6

z-score = (0.4) / 6

z-score = 0.06667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 0.06667,     p = 0.7472

Since the fine will be given if the load exceeds 41.5, we have to consider the values greater than 41.5. Subtract the answer from 1.

probability = 1 - 0.7472 = 0.25

Hence, the approximate probability that the driver will be fined is 0.25.

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Answer:

(a) 152.5

(b) -45.4

(c) 750

(d) -87.5

Step-by-step explanation:

To calculate the percentage increase:

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number.

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

I hope this helps! :)

Answer:8.4

explanation:

it just is the answer

Answer: 8.4

Step-by-step explanation:

Hope it helps!

Answer:

First you need to make the denominators equivalent so you can add them.

× =

× =

Then you can add them together

+

=

They walked \( \frac{13}{20} \) of a mile altogether

Step-by-step explanation:

Step-by-step explanation:

8-3 = 5,

3-5 = -2 = the x coordinate of B

-2-4 =-6,

-2-6 =-8 = the y coordinate of B

(-2,-8) is the point B

A is 5 to the right of the midpoint, so B is 5 to the left of the midpoint

A is 6 up from the midpoint so B is 6 down from the midpoint

The measurement of angle b is 523 degree.

We know that,

Lines are divided into numerous categories in geometry, including parallel, perpendicular, intersecting, and non-intersecting lines, among others. We may draw a particular line called a transversal that meets non-intersecting lines at different locations.

Since

Corresponding angles are one of the types of angles created when the transversal intersects two parallel lines. These are produced in the transversal's matching or equivalent corners.

Now from figure we can see that,

Angle a and Angle c are corresponding angles

And it is given that,

angle a = 127 degree

Therefore,

Angle c = 127 degree

Since we know that angle of line  = 180 degree

So,

Angle b = 180 - 127

             = 53 degree

Thus,

∠b = 53 degree

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The complete question is attached below:

The probability of choosing a purple flower at random from a garden with 10 purple flowers and 40 total flowers is 1/4 or 25%.

To calculate the probability of an event, we divide the number of ways that event can occur by the total number of possible outcomes. In this case, we need to determine the number of purple flowers in the garden and divide it by the total number of flowers in the garden.

Let's say there are 10 purple flowers and 40 total flowers in the garden. The probability of choosing a purple flower at random would be:

Number of ways to choose a purple flower = 10

Total number of flowers = 40

Probability of choosing a purple flower = 10/40

Simplifying this fraction, we get:

Probability of choosing a purple flower = 1/4 or 25%

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Complete Question:

10 flower is chosen at random number of 40 from the garden. what is the probability that the flower is purple?

\(y = 4^{-2}\) = \(\frac{1}{16}\)

\(y = 4^ {1}\) = \(\\ 4\)

\(y = 4^{3}\) = \(\\ 64\)

The engineer measuring the western rod with a sample size of 20 is expected to have a more precise (narrower) confidence interval compared to the engineer measuring the eastern rod with a sample size of 25.

The engineer who measures the length of the western rod 20 times and calculates the average is expected to have a more precise (narrower) confidence interval compared to the engineer who measures the length of the eastern rod 25 times.

In statistical terms, the precision of a confidence interval is influenced by the sample size. The larger the sample size, the more precise the estimate tends to be. In this case, the engineer measuring the western rod has a sample size of 20, while the engineer measuring the eastern rod has a sample size of 25. Since the sample size of the western rod is smaller, it is expected to have a narrower confidence interval and therefore a more precise estimate of the true length of the rod.

A larger sample size provides more information and reduces the variability in the estimates. It allows for a more accurate estimation of the population parameter. Therefore, the engineer with a larger sample size is likely to have a more precise interval.

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The value of angle ADO in the rectangle is 62°.

From the information, angle BOC = 56°

In a rectangle, there are two congruent diagonals.

Therefore DO = AO

angle ADO = angle DAO

angle DOA = 56° (vertical opposite angles)

sum of all three interior angles in a triangle = 180°

angle ADO + angle DAO + angle DOA = 180°

angle ADO + angle ADO + 56° = 180°

2angleADO = 180° - 56°

2angleADO = 124°

Divide

angle ADO = 124/2

angle ADO = 62°

Hence, the measure of angle ADO = 62°

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The probabilities are given as follows:

a) Both are even: 1/4.

b) One is even and one is odd: 1/2.

c) The same number is chosen twice: 1/40.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the 40 numbers between 20 and 40, we have that:

Hence the probability of both even is given as follows:

p = 1/2 x 1/2 = 1/4.

The probability of one even and one odd is given as follows:

p = 2 x 1/2 x 1/2 = 2/4 = 1/2.

(multiplied by two as the order can be even/odd or odd/even).

For the second number, there are 40 options, only one of which is equals to the first, hence the probability that the same number is chosen twice is given as follows:

p = 1/40.

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3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Answer:

-5/3

Step-by-step explanation:

The slope of a line is found by

m = (y2-y1)/(x2-x1)

   = (13- -12)/(-3 -12)

   = ( 13+12) / (-15)

     25/-15

    -5/3

The right answer is -5/3

please see the attached picture for full solution

Hope it helps..

Good luck on your assignment..

80 times farther from the Sun is Neptune than Mercury.

Given that, the distance between Mercury and Sun = 35,000,000 miles and the distance between Neptune and Sun = \(2.8\times10^9\).

An average distance is the average of the greatest and least distances of a celestial body from its primary.

Now, number of times farther from the Sun is Neptune than Mercury

= \(\frac{2.8\times10^9}{3.5\times10^7}\)

=0.8×10²

=80

Time taken for light to reach Neptune = 3×80=240 minutes

=4 hours

Therefore, 80 times farther from the Sun is Neptune than Mercury.

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Answer:

Its C.

Step-by-step explanation:

I had this and its C. trust me

Answer:

c=30

v=10

30+10=40

4*30=120

6*10=60

120+60=180

Answer:

perimeter=2(l+b)=2(16+24)=80

rate =$2per inch

total cost=perimeter ×rate=80×2=$160is your answer

Answer: \(x=-3/4\)

Subtract 36x from both sides

\(20x-2-36x=36x+10-36x\\-16x-2=10\)

Add 2 to both sides

\(-16x-2+2=10+2\\-16x=12\)

Divide both sides by -16

\(\frac{-16x}{16} =\frac{12}{-16} \\x=\frac{-3}{4}\)

Answer:

x = - \(\frac{3}{4}\)

Step-by-step explanation:

Given

20x - 2 = 36x + 10 ( subtract 36x from both sides )

- 16x - 2 = 10 ( add 2 to both sides )

- 16x = 12 ( divide both sides by - 16 )

x = \(\frac{12}{-16}\) = - \(\frac{3}{4}\)

As a check

Substitute this value into the equation and if both sides are equal then it is the solution.

left side = 20 × - \(\frac{3}{4}\) - 2 = - 15 - 2 = - 17

right side = 36 × - \(\frac{3}{4}\) + 10 = - 27 + 10 = - x17

Since both sides are equal then x = - \(\frac{3}{4}\) is the solution

Answer:

tan Q = 15/8

Step-by-step explanation:

tan Q = opp/adj

tan Q = OP/8

OP² + PQ² = OQ²

OP² + 64 = 289

OP² = 225

OP = 15

tan Q = 15/8

By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.

Given two equations are;

5x+3y=30..........(1)

−5x−2y=−25.........(2)

Now , from (2)

−5x−2y=−25

⇒ 5x +2y = 25 (multiply both sides with '-' sign)

⇒ y = \(\frac{(25 -5x)}{2}\)

Solving the system;

substitute the above vale of y in eq (1)

5x + 3y = 30

⇒ 5x + 3 ( \(\frac{(25 -5x)}{2}\)) = 30

⇒  5x + (\(\frac{(75 - 15x)}{2}\)) = 30

⇒  \(\frac{10x+75-15x}{2}\) = 30

⇒ -5x + 75 = 60

⇒  -5x = -5

⇒ x = 1

∴ x = 1

Now substitute the value of x in (1)

5x + 3y = 30

⇒ 5 × 1 + 3y = 30

⇒ 3y = 25

⇒ y = 25/3

∴ y = 25/3

Now using the value of x and y , we can find the value of x - y

x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3

∴ x - y = -22/3

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Answer:

Step-by-step explanation:

The standard form of an equation for a straight line is y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

We can calculate the slope from the two given points, (6,-3) and (-6,-5).  Slope is Rise/Run, where Rise is the change in y and Run is the change in x.

From the two given points, starting at (-6,-5) and going to (6,-3):

Rise = (-3 - (-5)) = +2

Run = (6 - (-6)) = 12

Rise/Run (slope) = 2/12 or 1/6

The equation becomes y = (1/6)x + b

We can find b by enterieng either of the two given points and solving for b.  I'll pick (6,-3):

y = (1/6)x + b

-3 = (1/6)*(6) + b

-3 = 1 + b             [Now you can see why I chose (6,-3)]

b = -4

The equation is y = (1/6)x - 4

Check this with a DESMOS graph (attached).

Answer:

12

Step-by-step explanation:

A profit, or money you have, or money you deposit in a bank account is usually positive.

A debt, or money you withdraw from a bank account, or money you give away is usually negative.

Answer: 12