flips a fair coin five times, what is the probability that there are 3 heads in a row somewhere in the sequence of five flips.

Answer:2x^3+3x^2-11x-6

Step-by-step explanation:

Therefore, the numerator of the given equation comes out to be 4x+6

A fraction denotes a component of a whole or, more generally, any number of equal parts. In conversational English, a fraction, such as one-half, eight-fifths, or three-quarters, denotes the quantity of a specific size of portions.

Given

[tex]\frac{x}{x^{2} +3x+2} + \frac{3}{x+1}[/tex]

A common denominator must exist for the fractions before we can add them.

Factor the denominator of the first fraction

[tex]\frac{x}{(x+1) (x+2)} + \frac{3}{x+1}[/tex]

Subtract (x + 2) from the second fraction's numerator and denominator.

[tex]\frac{x}{(x+1) (x+2)} + \frac{3(x+2)}{(x+2)(x+1)}[/tex]  ← Currently, fractions share a common denominator.

Add the numerators leaving the denominators

= [tex]\frac{(x+2)(x+3)}{(x+2)(x+1)}[/tex]  

= [tex]\frac{x^{2} +3x+6}{(x+2)(x+1)}[/tex]

=  [tex]\frac{4x+6}{(x+2)(x+1)}[/tex]

simplified sum with numerator 4x + 6

Therefore the numerator of the given equation comes out to be 4x+6.

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Question 1

C. Congruent by ASA.

Question 2

The reason is 'definition of isosceles triangle'.

The probability that Lucia receives (Head, Tail, Head) within this order is 1/8.

A coin toss has a total of two possible outcomes.

Three coin flips have a total of eight outcomes possible: 2 x 2 x 2 = 8

Positive result = (Head, tail, Head) in that sequence

i.e., 1 is the number of favourable results.

As we well aware,

Probability = favourable outcome / total outcome

The needed probability follows as a result.

Probability (first head) = 1/2

Probability (second tail) = 1/2

Probability (third head) = 1/2

Thus,

Probability(Head, tail, Head) = 1/2 x 1/2 x 1/2

Probability (Head, tail, Head) = 1/8

Consequently, the likelihood that she receives (Head, Tail, Head) within this order is 1/8.

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If fox run at speed of 10 kmph and wolf run at 11 mph , then the animal that runs faster is  wolf  .

In the question ,

it is given that ,

the speed at which the fox runs is = 10 kmph

the speed at which the wolf runs is = 11mph ,

for comparison , the units should be same ,

So , we need to convert 11 mph to kmph .

we know  that , 1 mile per hour = 1.60934 kmph ,

So , 11 mph = 17.7028 kmph .

So , the speed at which the wolf runs is = 17.7028 kmph .

On comparison , we get that speed of wolf is greater than speed of fox .

Therefore , wolf runs faster than fox .

The given question is incomplete , the complete question is

A fox can run at a speed of 10 kmph, and a wolf can run at a speed of 11 mph. Which animal is faster ?

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Answer: the Answer is wolf

Step-by-step explanation:

the wolf can peed so it is fater

Using the concept of probability, the probability of not landing on yellow or red at all is 1/4.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Creating a square model of the two spins :

Red(R) ; Blue(B) ; Green(G) ; Yellow(Y)

___ R ___ B ___ G ___ Y

R_ RR __ RB __ RG __ RY

B_ BR __ BB __ BG __ BY

G_ GR __GB __ GG __GY

Y_ YR __ YB __ YG __ YY

Sample space = 4² = 16

Combinations without red and yellow :

{BB, BG, GB, GG}

Number of selections without red or yellow = 4

Recall :

Probability = required outcome / Total possible outcomes

P(without Red or Yellow) = 4/16 = 1/4

Hence, the probability of not landing on yellow or red at all is 1/4.

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See steps below for proving n = 2m:

An equation is formed of two equal expressions. n=2m can be proved by solving the two of the given equation for h and then equating them together as shown below.

An equation is formed when two equal expressions are equated together with the help of an equal sign ''=''.

Given the two equations, 2n=m+h, and h=n+m. Now, solve the two of the equations for h as shown below:

Equation 1.

2n = m + h

2n - m = h

h = 2n - m

Equation 2.

h = n + m

Further, equate the value of h from both the equation,

h = h

2n - m = n + m

Bring the like terms on the same side of the equation,

2n - n = m + m

n = 2m

Hence, proved n=2m.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The house value is decreased by $33840 and the current value of the house is $342160

Here, we have been given a house on the market was valued at $376,000.

The value decreased by 9% .

We need to find the amount by which the house value decreased in dollar and the current value of the house.

The 9 percent of $376,000

376,000 * (9/100) = 33840

This means, the house value is decreased by $33840

So, the current value would be,

376,000 - 33840 = 342160

Therefore, the house value is decreased by $33840.

The current value = $342160

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Answer:

$ 7.2

Step-by-step explanation:

½ pound = $3.60

1 pound = x

just cross multiply.

½x = $ 3.60

0.5x = $ 3.60

x = $3.60/0.5

x = $7.2

Answer:

[tex]\huge\boxed{\sf \$ 7.20}[/tex]

Step-by-step explanation:

Given that,

1/2 pound of cheese = $3.60

Multiply 2 to both sides

1 pound of cheese = $3.60 × 2

[tex]\rule[225]{225}{2}[/tex]

The factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

y =x³-4x²-17x+60x

Let us assume that the factors are

(x−a), (x−b) and (x- c)

So, if x is either equal to a or b or c, y=0

and a⋅ b⋅ c=−60, which means a or b and c are factors of 60.

Thus, which factor of 60 (such as 2, 3, 5, 6, 10 etc.) makes y=0.

It is given that (x−3) is a factor of y

and, When we divide y by (x−3), we get x²−x−20

Similarly x=5 makes x²−x−20 equal and Dividing x2−x−20 by (x−5), we get (x+4)

Hence, the factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

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here's your answer hope it helps :D

Answer: He planted 5/42 acres

Step-by-step explanation:

First, find the common of 7 and 6, which is 42

5/7 - 5/6

= 30/42 - 35/42

= -5/42

As a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree

What is Trigonometric Ratios ?

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions.

                  The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

The expression given is

(2tan(10 degrees))/(1 - tan² (10 degrees))

By the property of Tan 2x

Tan 2x = 2tanx /(1 - tan² x)

Therefore from the formula ,

x = 10 in the given expression

Therefore as a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree

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Answer: yes tan(20°) option 4

Step-by-step explanation:

Answer:

x^3y^2√xy

Step-by-step explanation:

First, you calculate what's in the square root. x^2 becomes x and y^4 becomes y^2.

Then you distribute the 1/2 to the x^5 and the y so they become x^5/2 and y^1/2.

Next, you combine the like terms. x and x^5/2 becomes x^7/2. y^2 and y^1/2 become y^5/2.

So you have x^7/2 y^5/2

To get rid of the 2 on the bottom of the exponents you square root both variables.

So you get √x^7 y^5 (square rooted x^7 and y^5)

Simplify the square rooted problem to x^3 y^2 √xy

You get x to the third power y to the second power and square rooted xy.

Answer: Z=35(4)^7

Step-by-step explanation:b = multiplier = 4b = multiplier = 4a = starting amount = 35a = starting amount = 35t = time = 7 hourst = time = 7 hours. a⋅b^t

35(4)735(4)7Equivalent forms:Equivalent forms:35(4)(4)(4)(4)(4)(4)(4)35(4)(4)(4)(4)(4)(4)(4)

Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.

What is an equation?

An equation is written in the form of variables and constants separated by the operation of multiplication and division.

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

According to the given question:

Hugo decided to pay $2 a week to his brother to buy a bicycle.

The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.

To pay back to the brother he must owe no money which is y = 0.

∴ The weeks needed is,

0 - 10 = -2(x - 10).

- 10 = -2x + 20.

2x = 30.

x = 15.

He needs 15 weeks to pay back completely.

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Julius's Schedule C gross profit is $72,000

($97,000 sales - $2,000 returns - $25,000 cost of goods sold = $70,000 gross profit).

income from trade or business after covering the costs of generating and disbursing goods and services: Selling scraps to textile businesses brings her a sizable profit.

A business's primary goal should be to earn a profit. Understanding where your business is producing money and where you are spending it can help you assess your level of success. Calculating your profit can also provide you this information.

Income less all costs. As an illustration, Sam's Bakery collected $900 yesterday, but its expenses, including salaries, food, and power, were $650. Profit was therefore $900 divided by $650 to equal $250.

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a) The equation for the volume of the cube after t hours is of: V(t) = (0.5t + 2)³.

b) The equation for the surface area of the cube after t hours is of: S(t) = 6(0.5t + 2)².

c) The surface area will be of 216 in² after 8 hours.

Considering a cube of side length s, the surface area and the volume are given as follows:

In this problem, the side length is a function of the time, as follows:

s(t) = 0.5t + 2.

Hence the equations are given as follows:

The surface area will be of 216 in³ when:

6(0.5t + 2)² = 216

(0.5t + 2)² = 216/6

(0.5t + 2)² = 36.

Taking the square root from both sides, the time is given as follows:

0.5t + 2 = 6

0.5t = 4

t = 4/0.5

t = 8 hours.

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Answer:

144 + 64 =208

Step-by-step explanation:

you see the 12th square number is 12 × 12 which is 144 then the 4th cube number is 4 × 4 ×4 make it 64 and the sum of all of this is 204

The taxable income in marginal tax rates for 2016 is $44964.

What is marginal tax rate?

Gross income = $88000

Adjustments = $2000

Deductions interest = $27000

Property taxes = $4036

Charitable contribution = $2000

Taxable income = 88000 - (2000 + 27000 + 4036 + 2000)

= 88000 - 35036

= 44964

Hence, the taxable income in marginal tax rates for 2016 is $44964.

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Answer:

As the age of your car increases the value of that car decreases

Step-by-step explanation:

hope this helps

The trains leaving atlanta for new york every 30 minutes....it takes 10 hours   so there is 20 trains on the track when YOUR

NY to ATL train leaves......during the 10 hour trip ANOTHER 20 trains will launch from ATL going to NY

  so you will pass 40 trains that are going from ATL to NY    while you are travelling to ATL  

This assumes that the trains go every 30 minutes around the clock.

If they do not go around the clock , you will only pass trains that launch for the 10 hours after your departure from NY

  that would be 20 trains

The average speed for the whole journey is 24.3 km per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

It should be noted that:

Speed = Distance / Time

Distance = 32km + 41km

= 73km

Time = 1 hour + 2 hours

Time = 3 hours

Speed = Distance / Time

Speed = 73 / 3

Speed = 24.3 km per hour.

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The 20% Tony spends from his monthly salary on the wallet, the bag which cost $20 more than the wallet and the ratio of the wallet to shoe cost of 5:6, which expressed as a fraction is 5/6, indicates;

(a) Tony's monthly salary is $2,400

(b) The amount spent on the pair of shoes is (6/25) of his monthly salary

A fraction is a part of a whole item, expressed as a quotient.

Let x represent Tony's salary, from the details of the question, we get;

The amount Tony spent on the wallet = 20% of his salary

The cost of the bag Tony bought = $20 + The cost of the wallet

Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6

The amount Tony had left = $844

Therefore;

The amount Tony spent on the wallet = 20% of x = 0.2·x

Amount spent on the bag = 20 + 0.2·x

Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6

Therefore;

Cost of the pair of shoes = (6/5)×(0.2·x)

Therefore;

x - 0.2·x - (20 + 0.2·x) - (6/5) ×(0.2·x) = 844

0.36·x - 20 = 844

x = (844 + 20)/0.36 = 2400

(b) The amount Tony spends on the pair of shoes = (6/5) × (0.2·x)

(6/5) × (0.2·x) = (6/5) × (2/10) × x = (12/50)·x = (6/25)·x

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Answer:

the answer to this should be no solution

Step-by-step explanation:

the first step would be adding seven to both sides, but all that does is leave a zero on the other side, so the equation ends up being 9x=0.

The value of x in the expression is 0.

We have,

Expression: 9x - 7 = -7

To solve for x.

Add 7 on both sides.

9x - 7 + 7 = -7 + 7

9x = 0

x = 0

Thus,

The value of x in the expression is 0.

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Answer:125=n

Step-by-step explanation: 375 divided by 3 is 125

Answer:

DG = √[tex]2x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex] + [tex]x^{2}[/tex] = 2[tex]x^{2}[/tex]

DG = √[tex]2x^{2}[/tex]

The demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.

Define Marginal revenue

Marginal revenue is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit.

Given expression is,

R′(x) = 0.06x² − 0.05x + 138

To make R'(x) to R(x) just integrate R'(x),

R(x) = ∫ R'(x) dx

      = ∫ (0.06x² − 0.05x + 138) dx

      =  0.06x³/3 − 0.05x²/2 + 138 x  + C

We get, R(x) = 0.02x³ − 0.025x² + 138 x  + C

It's given, the revenue is 0 means no items sold so R(0) = 0.

Now, put x = 0 and find C

R(0) = 0.02(0)³ − 0.025(0)² + 138 (0)  + C

   0 = 0 + C

C = 0

So, R(x) = 0.02x³ − 0.025x² + 138 x, since C = 0

Now, take x common from R(x) will give us,

R(x) = x( 0.02x² − 0.025x + 138 )

so, R(x) = x p(x)

so, p(x) = 0.02x² − 0.025x + 138

Hence, the demand function for the marginal revenue function is p(x) = 0.02x² - 0.025x + 138.

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Answer:

x = 6 or x = 0 or x = -8

Step-by-step explanation:

Solve for x over the real numbers:

2 x^3 - 4 x^2 - 96 x = -8 x^2

Add 8 x^2 to both sides:

2 x^3 + 4 x^2 - 96 x = 0

The left-hand side factors into a product with four terms:

2 x (x - 6) (x + 8) = 0

Divide both sides by 2:

x (x - 6) (x + 8) = 0

Split into three equations:

x - 6 = 0 or x = 0 or x + 8 = 0

Add 6 to both sides:

x = 6 or x = 0 or x + 8 = 0

Subtract 8 from both sides:

Answer: x = 6 or x = 0 or x = -8