Rationalise the denominator 7/2-root 5

If there are multiple coins in a row we call them a streak , the expected number of streaks here are 224

Attempt: I interpreted the number of streaks as the number of switch between either H to T or T to H in the sequence + 1.

The problem has a markov chain structure and so we can  obtain the following equations, given S(n)

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.

number of strike in sequence with n coins:

                 S(n|H) = 0.2s(n-1) + 0.8 (1+s(n-1))

                  S(n|T) = 0.8s(n-1) + 0.2(1+s(n-1))

This implies S(n) = S(n|T)p(T) + S(n|H)p(H)

                           = S(n-1) + 8/25

Therefore,  E[S(700)] = 224.

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She buys 15 bags of candy.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Given that the number of bags of taffy was 5 more than the number of bags of caramels.

The Taffy bags weigh 8 ounces each, and the caramel bags weigh 16 ounces each.

The total weight of the bags of candy was 400 ounces.

Consider c be the total number of Carmel candy bags and t the total number of taffy bags that Ariel bought.

t = 5 + c

Then, we have:

8t + 16c = 400

8(5 + c) + 16c = 400

40 + 8c + 16c = 400

24c = 360

c = 15.

Hence, she buys 15 bags of candy.

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Answer: CP = 1418.34

Step-by-step explanation: We've to calculate the cost price (CP)

Selling price (SP) = 1546,  Profit% = 9%

According to the formula,

Profit%= [tex]\frac{SP-CP}{CP} * 100[/tex]

9 = [tex]\frac{1546-CP}{CP} *100[/tex]

9*CP = (1546-CP)*100

109CP = 154600

CP = 154600/109

CP= 1418.34

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The probability that valley 1 is also infected is 15%

The math term probability is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Here we have know that two valleys are sometimes infected with tree rot.

The probability of rotting valley 1 = 35%

The probability of rotting valley 2 = 60%

And the probability that at least one is infected = 80%

When we convert these values into decimal then we get,

The probability of rotting valley 1 = 0.35

The probability of rotting valley 2 = 0.6

And the probability that at least one is infected = 0.8

Then the probability that valley 1 is also infected is

=> P = 0.35 + 0.6 - 0.8

=> P = 0.15

When we convert it into percentage then we get,

=> P = 15%.

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The percent of increase from 45 to 72 is 60%.

Using this formula to find the percent of increase

Percent of increase= End value - Start value /Start value  

Where:

End value = 72

Start value = 45

Let plug the formula

Percent of increase =(72 - 45) /45

Percent of increase =27 /45  × 100

Percent of increase = 60%

Therefore we can conclude that the percent of increase is 60%.

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Step-by-step explanation:

a = 16

b = 3

because only the factor 3 gets repeatedly added every year (x).

the rest (the starting value that gets tripled and then tripled and then tripled ... every year) is constant.

f(x) = 16×3^x

as you know, exponents have the higher priority to multiplications.

if you want to be save you can use brackets like

f(x) = 16×(3^x)

Null hypothesis: H₀ : μ = 55

Alternative hypothesis: H₁: μ [tex]\neq[/tex] 55

Given,

Rating = 55 mpg

For a two-tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis. In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.

the claim is the jeep has a 55 mpg rating and we want to test whether the rating is correct or incorrect. So, it is a two-tailed hypothesis because the rating can be less than or more than 55 mpg.

Therefore, H₀ : μ = 55

H₁: μ [tex]\neq[/tex] 55

These are the required null and alternative hypotheses.

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Relative frequencies are calculated by dividing the count by the total count in the column or row.

Joint relative frequencies show the proportion of individuals in a specific category of two variables.

They are calculated by dividing the count of individuals in a specific category by the total number of individuals surveyed.

In a two-way table, they are represented by the cells and give a sense of how the two variables are related to each other.

For example, in the given table, the joint relative frequency of males who plan to go to college is 0.35, which means 35% of the surveyed males plan to go to college.

Joint relative frequencies can be used to identify patterns and relationships between two variables, such as how gender and college plans are related.

joint relative frequencies:

Yes No Total

M 0.35 0.23 0.58

F 0.33 0.19 0.52

1

Marginal relative frequencies:

Yes No Total

M 0.58 0.42 1

F 0.52 0.48 1

1

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This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To determine if sending teachers to the summer training on mentor groups is a good decision, the committee needs to calculate the break-even point. This is the point at which the cost of sending the teachers is equal to the cost of not sending them. The break-even point can be calculated by dividing the advanced payment by the difference between the cost at registration and the advanced payment.

In this case, the break-even point is: $1,250 ÷ ($175 - $1,250) = $1,250 ÷ -$1,075 = 7 teachers.

Hence, This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

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The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric equation is given below.

sin 2x − √3/2 = 0

Simplify the equation, then we have

sin 2x − √3/2 = 0

sin 2x = √3/2

sin 2x = sin 60°, sin 120°

2x = 60°, 120°, 420°, 480°

x = 30°, 60°, 210°, 240°

The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.

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Plans for what to do after high school and three ways to protect yourself from the effects of inflation are mentioned below.

To take into account a recovering economy with scarce jobs and low salaries when making plans for after high school, one could consider the following:

To protect oneself from the effects of inflation, one could consider the following:

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Answer: He can buy 4 pants for $120 and 4 shirts for $80

Answer: Roger wants to buy at least 6 items, so he needs to buy at least 6 pants or 6 shirts or a combination of both.

Step-by-step explanation:

The cost of 6 pants is $30 x 6 = $180.

The cost of 6 shirts is $20 x 6 = $120.

If Roger wants to buy both pants and shirts, he can buy 3 pants and 6 shirts for a total cost of $90 + $120 = $210.

Another option would be 4 pants and 5 shirts for a total cost of $120 + $100 = $220.

Thus, Roger can buy either 6 pants, 6 shirts or a combination of 3 pants and 6 shirts or 4 pants and 5 shirts with his $200.

If Nick spends $4.89 and Riley spends 3 times as much as Nick and Clay spends $12.73 more than Riley , then the total amount spent by Clay is $27.4 .

The amount Nick spends to buy School Supplies is = $4.89 ,

the amount spent by Riley is 3 times of amount spent by Nick ,

that means , Riley spent = 3 × 4.89 = $14.67 ,

the amount spent by Clay is $12.73 more than the amount spent by Riley , which means ;

Clay spent is = $14.67 + $12.73 = $27.4 .

Therefore , Clay spent $27.4 to buy school supplies .

The given question is incomplete , the complete question is

Some friends go to the store to buy school supplies. Nick spends $4.89  Riley spends 3 times as much as Nick. Clay spends $12.73 more than Riley. How much did Clay spend ?

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Statement "B. the median is a negative number" will be correct among these options.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  that A set of data contains 10 negative numbers and 4 positive numbers.

Since the value of data is not given it can be any positive or negative numbers

mode:

A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.

Range:

When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.

Median:

The median is the value that's exactly in the middle of a dataset when it is ordered.

Thus, the Median will be negative.

Therefore, Statement "B. the median is a negative number" will be correct among these options.

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Complete question:

A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?

A. The mean is a negative number.

B. The median is a negative number.

C. The mode is a negative number.

D. The range is a negative number.

The domain of the relation is 0 ≤ x ≤ 4 and the range of the relation is all real numbers  (-∞, ∞)

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We know that Domain : the set of possible x-values (the "input" values)

And also, we know that Range : the set of y-values (the "output" values)

In the given graph we have attached below, the domain of the relation is 0 ≤ x ≤ 4

The range = all real numbers (-∞, ∞)

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Answer: 26 units

Step-by-step explanation:

Let's label the left side as side a, the bottom as side b, and the hypotenuse (the diagonal side) as side c.

As you can see, side a is 8 units, and side b is 7 units. To calculate side c, you need to plug both a and b in to the Pythagoras' theorem, which states that a² + b² = c².

> 8² + 7² = c²

> 64 + 49 = c²

> 113 = c²

> c = 10.63 which would round up to 11.

Now adding up all the sides together, a + b + c = 7 + 8 + 11 = 26 units

It will take 2/3 minutes to run 1 mile.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Amal can run 1/8 mile in 1/12 minutes.

If Amal can maintain that pace,

it will take him to run 1 mile,

= 1/12 ÷ 1/8

= 1/12 x 8/1

= 8/12

= 2/3 minutes.

Therefore, the required time is  2/3 minutes.

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[tex]~~~~~~ \stackrel{\textit{\LARGE Bank 1}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.25\%\to \frac{5.25}{100}\dotfill &0.0525\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.0525)(3) \implies I = 3937.5 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \stackrel{\textit{\LARGE Bank 2}}{\textit{Simple Interest Earned}} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (25000)(0.085)(3) \implies I = 6375 \\\\[-0.35em] ~\dotfill\\\\ 3937.5~~ + ~~6375\implies \text{\LARGE 10312.5}[/tex]

0.266… is the answer.

I hope this helps even a bit :]

Violet's money tripled Dylan's money to triple= 23,249.95.

Dylan invested $6,100 in an account paying an interest rate of 2% compound.

Violet invested $6,100 in an account paying an interest rate of 2%

compound.

The formula for compound amounts is A = P(1 + r/n)^(nt),

where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.

Here,

A = ($6100)(1 + 0.02/4)^(12*4)

Evaluating this we get:

A = ($6100)(1.005)^48, or

A  = ($6100)(`1.2704)

A = $7,749.98

Violet's money to triple than for Dylan's money to triple

=3(A)=3*7749.98=23249.95.

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The shortest possible height of the vase rounded to the nearest tenth of a centimetres is 45.650.

The concept of rounding the numbers will be used here to find the answer. Concerning this, we must know, that a number will be rounded to next digit, if the subsequent number if 5 or more than 5.

We know 6 preceedes 7 and the number is rounded to nearest tenth. So, the just possible number will be 45.69. However, as mentioned, it will be rounded to 45.7. The same will happen for till 45.65. Proceeding before this, we get 45.64 which will not be rounded to 45.7. Thus, the smallest possible number is 45.65 centimetres.

Similarly, the 1 at hundredths place will be the smallest number. This is because, rounding off 5 will eventually lead to rounding off to 45.7.

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Varun takes 4 rotis per meal and Rosa takes 2 per meal

Varun wastes 40 rotis in 20 days

Let's call the number of rotis Varun takes per meal "V".

We know that Rosa takes half the amount of rotis as Varun, so Rosa takes V/2 rotis per meal.

Together, they take V + V/2 = 1.5V rotis per meal.

If they consume 120 rotis in 20 days, that means the amount they consume is

Amount = 120/20 = 6 rotis per day.

So, 1.5V = 6, and V = 4.

Varun takes 4 rotis per meal and wastes 4/2 = 2 rotis per meal.

Over 20 days, Varun would waste 2 * 20 = 40 rotis.

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In triangle UVT, the missing length, i.e., UV is 37. It is applicable in the case when triangle UVT ≈ triangle DEF.

Two triangles that are identical in size and shape are said to be congruent triangles. They share the same number of vertices, angles, and sides—three. The matching sides and angles of the two triangles must match in size for them to be considered congruent. In other words, when the two triangles are positioned next to one another, they must match.

The Pythagorean theorem may be used to determine the length that is lacking if the other three lengths are known. According to the Pythagorean theorem, the square of the longest side of a right triangle is equal to the sum of the squares of the two shorter sides. By computing the square root of the sum of the squares of the other three lengths, it is possible to determine the missing length.

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The quadratic equation 3x² + 2x - 5 = 0 is solved to give x = 1 and -5/3

From the information given, we have the quadratic equation as;

3x² + 2x - 5 = 0

Using the factorization method of solving quadratic equation, we have to take the following steps

Multiply the coefficient of x² by the constant -5

Find the pair factors of the product of their multiplication that sums up to 2

The pair factors are +5 and -3

Substitute the values

3x² + 5x - 3x - 5 = 0

Add parentheses

(3x² + 5x) - (3x - 5) =0

factorize the values

x(3x +5) - 1(3x + 5) = 0

The values of x are;

x= 1 and x = -5/3

Thus, the values are 1 and -5/3

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The complete question:

Solve the quadratic equation 3x2 + 2x - 5 = 0 using factorization method

Answer:The mathematical expression -4(-3t-10t-7)-t can be simplified to -4( -13t - 7 ) - t . This can be simplified even further by combining like terms to -4( -13t - 7) - 1t .

Step-by-step explanation:

Robel's age will be 15 and Father's age will be 45, which is three times as old as Robel.

Robel's current age = x

Father's current age = 4x

After 5 years,

Robel's age = x + 5

Father's age = 4x + 5

After 5 years, father will be three times a old a Robel

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

x = 10

Therefore, Robel's current age is 10 years and father's current age is 40 years.

Let x represent the current age of Robel and 4x represent the current age of Robel's father.

We can use the formula 4x + 5 = 3(x + 5) to solve for x.

We rearrange the equation to get x = 10.

Robel's current age is 10 years and father's current age is 40 years.

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By polar form properties, the product of complex numbers (5 · cos 225° + i 5 · sin 225°) and (2 · cos 135° + i r₂ · sin 135°).

In this question we find the case of the product of two complex numbers in rectangular form but including features of polar form (magnitude, direction). Then, we have the following situation:

(r₁ · cos θ₁ + i r₁ · sin θ₁) · (r₂ · cos θ₂ + i r₂ · sin θ₂)

Result can be found easily by transforming the expression into polar form:

(r₁, θ₁) · (r₂, θ₂) = (r₁ · r₂, θ₁ + θ₂)

[r₁ · r₂ · cos (θ₁ + θ₂) + i r₁ · r₂ · sin (θ₁ + θ₂)]

If we know that r₁ = 5, r₂ = 2, θ₁ = 225° and θ₂ = 135°, then the product of the complex number is:

10 · [cos 360° + i sin 360°]

10 · (1 + i 0)

10

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The money Nicole that he owes by selling the 36 quarts of lemonade is $ 54.

As per the given data, Nicole is selling the lemonade at her stand.

She charges $0.75 per pint.

Mr. Terry buys 36 quarts of lemonade.

Here we have to determine how much money he owes Nicole by selling the 36 quarts of lemonade.

Convert the quantity from quarts to pints.

As we know that 1 quart = 2 pints

1 quart = 2 pints

36 quarts = 2 × 36 pints

36 quarts = 72 pints.

The 36 quarts are equal to 72 pints.

The cost of one pint is $0.75.

We have to find the cost of 72 pints.

1 pint = $0.75

72 pints = ( 0.75 × 72 pints ) $

72 pints = 54 $.

Therefore the money owned by Nicole is $ 54.

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The lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

Now, According to the question:

In two-dimensional geometry, a cylinder has two circles as its bases so that both the bases are parallel and congruent.

In a cylinder, there is a lateral surface that is between the bases.

Let us suppose d is the diameter of the base of a cylinder, and h is the height of the cylinder then:

Radius of the cylinder (r) = [tex]\frac{d}{2}[/tex]

Lateral surface area of the cylinder(S) = [tex]2\pi rh[/tex]

Total surface area(A) = lateral area + total area of the bases

Given that the diameter of the above cylinder is 12cm, and the height of the cylinder is 3.5cm.

d = 12cm

and,

h = 3.5cm

Now the radius of the cylinder:

(r) = [tex]\frac{d}{2}[/tex] = 12/2 = 6cm

Now the total surface area of the cylinder:

A = [tex]2\pi r(h +r)[/tex]

A = [tex]2\pi (6)(3.5+6)[/tex]

A = [tex]12\pi (9.5)[/tex]

A = 114[tex]\pi[/tex]

We use [tex]\pi[/tex] = 3.14

A = 114(3.14)

A = 357.96[tex]cm^2[/tex]

Hence, the lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

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