Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-
angled triangle.
Give your answer in centimetres (cm) to 1 d.p.
6 cm
2.5 cm

Answer:

rise = 4, run = 5. The slope would be 4/5

Step-by-step explanation:

You go up by four then right by 5

The probability that the number of heads obtained from flipping the two fair coins is the same is 35/128.

Probability:

Probability means the fraction of favorable outcome and the total number of outcomes.

So it can be written as,

Probability = Favorable outcomes / Total outcomes

Given,

The coin a is flipped three times and coin b is flipped four times.

Here we need to find the probability that the number of heads obtained from flipping the two fair coins is the same.

We know that,

There are 4 ways that the same number of heads will be obtained;

0, 1, 2, or 3 heads.

The probability of both getting 0 heads is

[tex]$\left(\frac12\right)^3{3\choose0}\left(\frac12\right)^4{4\choose0}=\frac1{128}$[/tex]

Probability of getting 1 head,

[tex]$\left(\frac12\right)^3{3\choose1}\left(\frac12\right)^4{4\choose1}=\frac{12}{128}$[/tex]

Probability of getting 2 heads is,

[tex]$\left(\frac12\right)^3{3\choose2}\left(\frac12\right)^4{4\choose2}=\frac{18}{128}$[/tex]

And the probability of getting 3 heads is,

[tex]$\left(\frac12\right)^3{3\choose3}\left(\frac12\right)^4{4\choose3}=\frac{4}{128}$[/tex]

Therefore, the probability that the number of heads obtained from flipping the two fair coins is the same is,

=> (1/128) + (12/128) + (18/128) + (4/128)

=> 35/128.

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Answer:

Step-by-step explanation:

i know

Answer:

Step-by-step explanation:

In the plane, there is exactly one perpendicular line to a line from a particular point.

We can see CD is marked as perpendicular segment and there are no more such possible segments.

Correct choice is B.

Answer:

b) Segment CD only

Step-by-step explanation:

Now we have to,

→ find the segment perpendicular to AB.

The segment will be,

→ CD (only)

* As it is 90° from the segment AB, we can say that it is perpendicular to AB.

Hence, option (b) is correct answer.

The electric potential energy is 5.0 × 10^(-9) J

The formula to calculate the electric potential energy in a capacitor is;

E = 1/2 * C * V²

Where;

E = electric potential energy

C = capacitance = charge

V = voltage applied

We are given;

Voltage applied; V = 100 V

Capacitance (Charge) = 1 × 10⁻¹⁰ C

Plugging in the relevant values gives

E = 1/2  * 1 × 10⁻¹⁰ *  100

E = 1/2 * 1 × 10⁻⁸

E = 0.5  × 0⁻⁸ volts

E = 5.0 × 10^(-9) J

Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J

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Answer: 5.218*10^8 ==> Option 4

Step-by-step explanation:

(5.3 x 10^8) − (8.2 x 10^6)=

(5.3*10^2 x 10^6) − (8.2 x 10^6)=

(5.3*100*10^6)-(8.2*10^6)=

(530*10^6)-(8.2*10^6)=

(530-8.2)*10^6=

(530.0-8.2)*10^6=

521.8*10^6=5.218*10^8 ==> Option 4

Answer:

190

Step-by-step explanation:

(120*2) - 10 = 190

hope this helped !!

The value of m∠1 is 158° as the two line x and y are parallel.

Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.

In the given figure it is given that x║y and m∠2 = 22°.

Now let us use the above principles to solve the value of the other angles.

m∠2+m∠1 = 180°(linear pair)

or, m∠1= 180°-22°

or, m∠1=158°

m∠2+m∠3 = 180°(co-interior angles are supplementary)

or,m∠3=158°

m∠2=m∠4(Corresponding angles are equal)

or, m∠4=22°

m∠2=m∠5 (vertically opposite angles are equal)

or, m∠5=22°

m∠6=m∠1 (vertically opposite angles are equal)

or, m∠6=158°

m∠2=m∠7(alternate angles are equal)

or, m∠7=22°

m∠3=m∠8 (vertically opposite angles are equal)

or, m∠8=158°

Hence all the above angles are calculated using the properties of parallel lines.

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Answer:

8

Step-by-step explanation:

$ 42 / 5.25 $ / box = x  = 8 boxes

The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

According to the statement

We have to find that the ice creams that neither are fat-free nor contain nuts.

So, For this purpose, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

From the given information:

There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.

Contain nuts = 25

Are fat free = 12

Are both = 8

Then

Contain nuts or are fat free = 25+12-8 = 29

Total = 35

Neither contain nuts nor are fat free = 35-29 = 6.

So, The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

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Answer:

48

because. Of the time

Answer:

Step-by-step explanation

10 cm

Answer: unknwon

Step-by-step explanation:

because height of pillar not given

Answer: The LCD is 2

Step-by-step explanation: I think that because 2, 4, 6 but I'm not sure. (please don't get mad if I'm wrong)

Answer:

6.

Step-by-step explanation:

Factorise 2 and 6:

2 = 2

6 = 2*3

In calculating the LCM we only use the 2 once, as it is duplicated in the 2 lists of factors.

The LCM = 2 * 3 = 6.

(Note LCM = LCD.)

Vernon put 16 liters of gas in his tank. 21 miles per gallons of gas are consumed each mile that is driven.

Given that,

Vernon put 16 liters of gas in his tank.

The table depicts the linear relationship between the mileage driven and the amount of gas in his tank.

We have to find how many gallons of gas are consumed each mile that is driven.

From the table we can say

The total Distance is 336

The total gallons of gas is 16

Rate= Total distance/Total gallons

Rate=336/16

Rate=21 miles per gallons

Therefore, 21 miles per gallons of gas are consumed each mile that is driven.

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 z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]   is the value of z in linear equation.

What in mathematics is a linear equation?

a ) Simplify using exponent rule with same base  = a[tex]a^{n} . a^{m} = a^{n + m}[/tex]

Based on the given conditions, corresponding exponents are equal                                                                              = [tex]3^{2 + x} = 3^{7}[/tex]

Rearrange unknown terms to the left side of the equation                                                                           = 2 + x = 7

 Calculate the sum or difference                                                                               x = 5

b) Calculate the power 5764801 + [tex]7^{y}[/tex] = 117649

Rearrange unknown terms to the left side of the equation

         7^{y} = 117649 - 5764801

The equation is not defined.

c)  the equations  z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

   answer    z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

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Answer:

4/x+x-7

Step-by-step explanation:

1. 4/x

2. x-7

3. adding the two steps

Sorry in my keyboard there is no symbol for squareroot

200 gallons of regular gas and 80 gallons of premium gas were sold.

Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).

Now, forming the equation using the given information, to find the amount of each type of gallon.

Equation -

2.10x + 2.90(280 - x) = 652

Performing multiplication with values inside bracket in Left Hand Side

2.10x + 812 - 2.90x = 652

Rewriting the equation -

812 - 652 = 2.90x - 2.10x

Performing subtraction

160  = 0.8x

Rewriting the equation according to x

x = 160÷0.8

Performing division to find the value of x

x = 200

So, 200 gallons of regular gas was sold.

Amount of premium gas sold = 280 - 200

Performing subtraction

Amount of premium gas sold = 80 gallons

Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.

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Answer:   Let the length and breadth of a rectangle are x and y units , its area is x.y units^2

Step-by-step explanation: sorry no explanation

9.665 x 10^5

966500.0

Move the dot to the right 5 times

Answer:

-0.2667

Step-by-step explanation:

m =y2 - y1

x2 - x1

=14 - (10)

-7 - (8)

=14 - 10

-7 - 8

=4

-15

Answer:

7 months to pay it off.

Step-by-step explanation:

see attached for details.

Answer:26 eggs

Step-by-step explanation: yes

The market woman bought 60 eggs.

The market woman bought n eggs at the rate of 12 eggs for €60.

So, the cost price of each egg is given by:

Cost price per egg = €60 / 12 = €5

The total cost of n eggs is the cost price per egg multiplied by the number of eggs (n):

Total cost = €5 * n = 5n

After buying n eggs, 8 of them were broken.

So, the market woman had (n - 8) eggs left to sell.

She sold the remaining eggs at the rate of 4 eggs for €24.

The selling price of each egg is given by:

Selling price per egg = €24 / 4 = €6

The total selling price of the remaining (n - 8) eggs is the selling price per egg multiplied by the number of remaining eggs (n - 8):

Total selling price = €6 * (n - 8) = 6n - 48

The profit is the difference between the total selling price and the total cost:

Profit = Total selling price - Total cost

Since the problem states that the market woman made a profit of €12, we can set up the equation:

6n - 48 - 5n = 12

Solve for n.

Combine like terms:

n - 48 = 12

Add 48 to both sides:

n = 60

So, the market woman bought 60 eggs.

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The following ingredients are needed to make 6 brownies:

Cups of butter needed  is 1/4 cups

Ounces of chocolate needed is 1 7/8

Cups of sugar needed is 9/16

Ounces of vanilla needed is 3/4

Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero. An example of an integer is -1.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator.

Cups of butter needed = (2/3 x 6) / 16

4 / 16 = 1/4 cups

Ounces of chocolate needed = (5 x 6) / 16

= 30 / 16 = 1 14/16 = 1 7/8

Cups of sugar needed = ( 1 1/2 x 6) / 16

(3/2 x 6) / 16 = 9/16

Ounces of vanilla needed = ( 2 x 6) / 16

= 12 / 16 = 3/4

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Answer:

7y + 13x

Step-by-step explanation:

Let's simplify step-by-step.

7y+5x+8x

Combine Like Terms:

=7y+5x+8x

=(5x+8x)+(7y)

=13x+7y

The expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x which is correct answer would be option (B).

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

⇒ (7y + 5x) + 8x

Open parenthesis and combine like terms to get the solution,

⇒ 7y + 5x + 8x

⇒ (5x + 8x) + (7y)

⇒ 13x + 7y or

⇒ 7y + 13x

Therefore, the expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x.

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It is found that Ken will have run 3 laps and Hamid will have run 4  around a track.

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.  Prime factorization is when all those factors are prime numbers.Thus, prime factorization expresses an integer in terms of multiples of prime numbers.

Prime factorization is unique for each integer.

To determine the number of seconds that will have passed when they meet again.  We will use the LCM, or least common multiple, for this.

Thus the prime factorization of each number:

80 = 10(8)

10 = 5(2)

8 = 2(4)

4 = 2(2)

80 = 2(2)(2)(5)(2)

60 = 10(6)

10 = 5(2)

6 = 2(3)

60 = 2(2)(3)(5)

For the LCM,

2(2)(5)(2)(2)(3) = 240

This means every 240 sec; they will both be at the start line.

Since Ken completes a lap in 80 seconds, then he will completes

240/80 = 3 laps in 240 seconds.

Since Hamid completes a lap in 60 seconds, then he will completes 240/60 = 4 laps in 240 seconds.

Hence, It is found that Ken will have run 3 laps and Hamid will have run 4.

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Answer:  Choice C

This is the result of subtracting 3x from both sides. The inequality sign does not flip. It only flips if we multiply or divide both sides by a negative number.

The time plane will take to travel 1050 miles into the wind is 2.5 hours.

Speed is defined as the rate of change of position in unit time.

Mathematically,

Speed = Distance/Time

Now given that,

Speed of airplane in still air = 450 mph

Speed of wind = 30 mph

Distance to travel = 1050 miles

So, Actual speed of wind = 450 mph - 30 mph

⇒ Actual speed of wind = 420 mph

So, since Speed = Distance/Time

⇒ Time = Distance/Speed

⇒ Time = 1050/420

⇒ Time = 2.5 hours

Thus, the time plane will take to travel 1050 miles into the wind is 2.5 hours.

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The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.

To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.

Given:

f(x) = 2(3 - x) - 2x, we have:

-10 = 2(3 - x) - 2x

Let's simplify the equation step by step:

-10 = 6 - 2x - 2x

-10 = 6 - 4x

-10 - 6 = -4x

-16 = -4x

To solve for x, divide both sides by -4:

x = (-16) / (-4)

x = 4

Therefore, when f(x) = -10, the value of x is 4.

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Answer: x=5

Good luck :)