a turn consists of rolling a standard die and tossing a fair coin. the game is won when the die shows a $1$ or a $6$ and the coin shows heads. what is the probability the game will be won before the fourth turn? express your answer as a common fraction.

Answer:

192

Step-by-step explanation:

The probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

We are required to find the probability of having 90 or more wins in the next three hours of playing a mobile phone game similar to Pokémon, given that the number of successive win follows a Poisson distribution with a mean of 27 wins per hour.

The given mean of Poisson distribution is λ = 27.

The Poisson distribution formula is:P(X = x) = (e^-λ λ^x) / x!

We need to calculate the probability of having 90 or more wins in 3 hours.

We can combine these three hours and treat them as one large interval, for which λ will be λ1 + λ2 + λ3= (27 wins/hour) * 3 hours= 81 wins.

P(X ≥ 90) = 1 - P(X < 90)

To calculate P(X < 90), we can use the Poisson distribution formula with λ = 81.P(X < 90) = Σ (e^-81 * 81^k) / k!, k = 0, 1, 2, ....89= 0.9494

Using the above formula and values, we get P(X ≥ 90) = 1 - P(X < 90)= 1 - 0.9494= 0.0506

Therefore, the probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

Hence, the probability of having 90 or more wins in the next three hours of playing is 0.0506 or 5.06% (approx).

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The appropriate way to state the conclusion of the given statement is:

The results of the statistical test suggest that women have a shorter mean nose length than men (p = 0.04, α = 0.05).

Given:

A null hypothesis is that the mean nose lengths of men and women are the same.

The alternative hypothesis is that women have a shorter mean nose length than men.

Alpha for the problem is.05.

A statistical test is done and the p-value is 0.04.

Hence based on the condition we frame it as:

The results of the statistical test suggest that women have a shorter mean nose length than men (p = 0.04, α = 0.05).

Hence we get the required answer,

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The perimeter of the non-shaded region in the figure can be calculated to be 14 inches.

Given a figure.

The middle portion of the figure is not shaded.

It is required to find the perimeter of the non-shaded region.

It is given that:

The whole area of the shaded region = 78 inches²

The area of the small square which is situated at the bottom is:

Area of small square = 2 × 4

                                  = 8 inches²

So, the area of the rest of the shaded area = 78 - 8

                                                                       = 70 inches²

Now, the area of the whole region without the small square is:

Area = 10 × (10 - 2)

        = 80 inches²

So, the area of the non-shaded region = 80 - 70

                                                                = 10 inches²

The width of the non-shaded rectangle is 2 inches.

So, length = 5 inches.

So, the perimeter is:

P = 2(5 + 2)

  = 14 inches

Hence, the perimeter is 14 inches.

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The figure is given below.

Answer:

x^2+6x+9

Step-by-step explanation:

(x+3)^2

(x+3)(x+3)

x^2+3x+3x+9

x^2+6x+9

Answer:

r^5/a^3

Step-by-step explanation:

r^8(ra)^-3

r^8/(ra)^3

r^8/r^3a^3

r^8-3/a^3

r^5/a^3

The accumulated amount after 25 years is , $70,702.80.

Now, We can use the formula for compound interest to find the accumulated amount after 25 years:

A = P(1 + r/k)^(kt)

Where A is the accumulated amount, P is the principal , r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period.

In this case, we have:

P = $25,300

r = 0.045 (

k = 12 (monthly compounding)

t = 25

Substituting these values into the formula, we get:

A = $25,300(1 + 0.045/12)^(12 x 25)

A ≈ $70,702.80

Therefore, the accumulated amount after 25 years is ,

$70,702.80.

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Answer:

There are 35 red marbles

Your selections are correct.

The coefficients of the x terms are opposites, so x will be eliminated when we add these two equations for both examples.

××1=× 123 =×/1= the value of x is one

Answer:

The answer would be -1/3.

Step-by-step explanation:

If you plug the coordinates into slope formula (y 2 - y 1 )/ (x 2 - x 1) , you'd have 3-5 over 8-2, and once you solve that, you'll have -1/3 as your slope. Hope this helps ! :D

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A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The length of Jk can be either 10 or 26.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Since in a rectangle the opposite sides are equal, therefore, the sides NM and JK will be equal.

JK = MN

8x - 14 = x² + 1

0 = x² - 8x + 15

x = 5, 3

Hence, the length of Jk can be either 10 or 26.

The complete questions are:

Quadrilateral JKMN is a rectangle, if NM= 8x - 14 and JK= x squared + 1, find JK.

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1. The value of h(1) is 24.5 m

2. The maximum height of the balloon is 39.59 m.

3. The balloon burst  after  5.5979 sec it hits the ground

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

h(t) = –4.9t² + 27t + 2.5.

1. For t= 1 hour

h(1) = –4.9(1)² + 27(1) + 2.5.

h(1) = 24.5m

2. Vertex formula (-b/2a, h(-b/2a))

Vertex = -27/ 2(4.9) = 2.755

So, h(2.755) = 39.59 m

3.–4.9t² + 27t + 2.5. = 0

solving the above equation for t we get

t= -0.877 sec

t = 5.5979 sec

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Answer:

y + 8 = - 1(x - 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (2, - 8) , thus

y - (- 8) = - 1 (x - 2) , that is

y + 8 = - (x - 2)

The expression that is an element of AxBxB is (1,2,3)

The given data is A= (a, b}, B = {1,2,3}

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined.

\(& \ A \times B=\left\{\begin{array}{c}(a, 1),(a, 2),(a, 3),(b, 1) \\(b, 2),(b, 3)\end{array}\right. \\\)

\(& A \times B \times B=\left\{\begin{array}{l}(a, 1,1),(a, 1,2),(a, 1,3), \\(a, 2,1),(a, 2,2),(a, 2,3),\end{array}\right. \\& (a, 3,1),(a, 3,2),(a, 3,3) \\ & (b, 1,1),(b, 1,2),(b, 1,3) \\& \left.\begin{array}{l}(b, 2,1),(b, 2,2),(b, 2,3) \\(b, 3,1),(b, 2),(b, 3,3)\end{array}\right\} \\\)

\(& \therefore(b, 2,3) \in D \times B \times B \\\\& (a, a, 1) \notin A \times B \times B \\\\& \left(b, 2^2\right) \quad \forall A \times B \times B \\\\& (2,1,1) \notin A \times B \times B \\\\&=(b, 2,3) \in \cap \times B \times B \\&\end{aligned}\)

The union of two sets X and Y is equal to the set of elements that are present in set X, in set Y, or in both the sets X and Y.

The intersection of sets can be denoted using the symbol ‘∩’. As defined above, the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B.

Therefore, the expression that is an element of AxBxB is (1,2,3).

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Answer:

2.5x-1.5x=21

2.5x-1.5x=21

1x=21

x=21 ANSWER.

Step-by-step explanation:

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\(\bold{Hello~!}\)

\(2.5x~-~1.5x~=21:~x = 21\)

\(\sf{Add~similar~elements:~2.5x~ -~ 1.5x = x\)

\(\sf{x = 21}\)

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Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

The given function is-

To graph this linear function, we just need two points. Let's find the corresponding values of y when x = 0 and x = 5.

For x = 0.

So, the first point is (0, 8).

For x = 5.

The second point is (5, 5).

Then, we graph these points to draw a straight line through them.

The image below shows the graph.

The perimeter are given by the sum of the expressions of the lengths of

the sides which are each equal to 4·x + 6.

Response:

Part A

Part B

Part A

Given parameters;

Perimeter of the rectangular garden = Perimeter of the triangular garden

Therefore;

Perimeter of the rectangular garden = 2 × (x + 2) + 2 × (x + 1) = 4·x + 6

Perimeter of the triangular garden = x + 3 + 2·x + 1 + x + 2 = 4·x + 6

The equation that sets the perimeters equal is therefore;

4·x + 6 = 4·x + 6

The solution of the above equation is therefore;

x = x

Part B

The values of x that make the first part of the equation true are;

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Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

Answer:

T=1280

Step-by-step explanation:

T / 16=80

multiply 80 by 16

t= 1280

so if we divide 1280 by 16 we get 80

Answer:

\( \longmapsto \sf \: t \div 16 = 80\)

\( \longmapsto \sf \: t = 80 \times 60\)

\( \longmapsto \sf \: t = 1280\)

Answer:

The answer will be A

hope this helps :)

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

I assume that QP = 18 cm and m∠Q = 72°

Answer:

\(\fbox {P = 6.76 cm}\)

Step-by-step explanation:

Finding the missing angle :

Applying the Law of Sines :

\(\boxed {\frac{sin P}{P} = \frac{sin R}{PQ}}\)

Substituting the known values :

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The area of the Trapezium given in the question is 28ft²

The area of a trapezium is calculated using the relation :

Using the parameters given for our compuation:

height, h = 4

b1 = 9

b2 = 5

Inputting the parameters into our formula :

Area = 4/2(5 + 9)

Area = 2(14)

Area = 28ft²

Therefore, the area of the Trapezium is 28ft²

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Answer:

y = 4/3x + 1.

Step-by-step explanation:

The equation of the lines passing through (2,1) and (6,7) is:

y - 7 = (7-1)/(6- -2)(x - 6)

y - 7 = 6/8(x - 6)

y = 3/4(x - 6) + 7

y = 3/4x + 5/2.

So the line perpendicular to it has slope -1/3/4 = -4/3:

y - 9 = -4/3(x  + 6)

y = -4/3 x  - 8 + 9

y = 4/3x + 1.