Two players take turns removing a ball from a jar that initially contains m white and n black balls. The rst player to remove a white ball wins. Find the probability that the starting player wins.

Answer:

D. x = 7

Step-by-step explanation:

NOTE : there should be an equal sign somewhere in the given expression.

suppose the equation is the following:

3(x-4)-5 = x-3

………………………………………………………

3(x - 4) - 5 = x - 3

⇔ 3x - 12 - 5 = x - 3

⇔ 3x - 17 = x - 3

⇔ 3x - 17 + 17= x - 3 + 17

⇔ 3x = x + 14

⇔ 2x = 14

⇔ x = 14/2

⇔ x = 7

Answer:

50 miles per hour

Step-by-step explanation:

Step 1: We subtract 600 from 1000. That gives us 400 miles for the second day.

Step 2: Now we divide that by 8, giving us 50 miles per hour. We have our answer!

Answer:

60466176

Step-by-step explanation:

By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.

In this problem we assume that the first angle is measured with respect to the east side and that the second angle is counterclockwise and measured with respect to the direction of the first vector. First, we need to determine the resulting vector by using trigonometric and vectorial formulas:

(x, y) = (240 · cos 290°, 240 · sin 290°) + (50 · cos 320°, 50 · sin 320°)

(x, y) = (120.387, - 257.666) [mi]

The magnitude is found by Pythagorean theorem:

[tex]r = \sqrt{(120.387\,mi)^{2}+(-257.666\,mi)^{2}}[/tex]

r ≈ 284.403 mi

The direction of the boat is obtained by inverse trigonometric functions:

θ = tan⁻¹ (- 257.666/120.387)

θ ≈ 295.043°

By Pythagorean theorem and trigonometric functions, the magnitude and direction of the boat are approximately 284.403 miles and 295.043° with respect to the east.

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Step-by-step explanation:

I have solve all the questions and your work is to match with that option

The number of weeks by which the students in both classes will know how to write the same number of letters will be 4 weeks.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. McMillan and Ms. Burke are teaching their classes how to write in cursive.

Mr. McMillan has already taught his class 8 letters.

The students in Ms. Burke's class, who started the unit later, currently know how to write 12 letters.

Mr. McMillan plans to teach his class 4 new letters per week.

Ms. Burke intends to cover 3 new letters per week.

Eventually, the students in both classes will know how to write the same number of letters.

Then the number of weeks by which the students in both classes will know how to write the same number of letters will be

Let x be the number of the weeks and y be the total number of the letters.

Then the equation will be

y = 4x + 8 …1

y = 3x + 12 …2

Then by solving the equations 1 and 2, we have

x = 4 and y = 24

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Answer:

6 Slices

Step-by-step explanation:

Total units = 1 + 3 + 2 = 6 Units

6 Units = 18 Slices of Pizza

Iris shared 2 units.

1 Unit = 18/6 = 3 Slices of Pizza

2 Units = 2 * 3 = 6 Slices of Pizza

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.

A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,

a₂ = -3(a₁) = -3(9) = -27

a₃ = -3(a₂) = -3(-27) = 81

a₄ = -3(a₃) = -3(81) = -243

a₅ = -3(a₄) = -3(-243) = -729

Hence, the value of a₅ is -729.

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The values of the angles based on the information will be:

From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.

In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.

Angle 3 will be:

= 180° - 110° = 70° (angle on a straight line).

Angle 4 will also be 70° as opposite angle to angle 3.

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The simplified expression of (-2 - c)(-1) is 2 + c

We have:

(-2 - c)(-1)

Express as product

(-2 - c) * (-1)

Evaluate the product

2 + c

Hence, the simplified expression of (-2 - c)(-1) is 2 + c

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Answer:

The function is even because of symmetry over x axis

Answer:

Question 1 : -2 3/4 × 3 1/5 . Change the fractions to improper fraction and multiply .

= -11/4 × 16/5

= -176/20

= -44/5

= -8 4/5

Question 2: -4.6/-2

= -4.6/-2

= 2.3

Question 3: - 7/8 ÷ (-2)(-4)

= 7/6(-4)

= -7/4

Question 4 : -4 27/30

= -147/30

= -4.9

Question 5 : -3 13/20

Answer:

x = 60

Step-by-step explanation:

The sum of the angles of a triangle is 180

95+25 +x = 180

120 +x = 180

Subtract 120 from each side

120+x-120 = 180-120

x = 60

The given reaction is considered as nuclear reaction instead of chemical reaction as the change is coming in the nucleus.

A nuclear reaction is one in which the number of protons or neutrons changes as a result of collisions between two nuclei or an atom and a subatomic particle.

In the given reaction also which is superscript 1 subscript 1 h plus superscript 1 subscript 0 n right arrow superscript 2 subscript 1 h.

A neutron is added to the nucleus of a hydrogen atom here. As a result, it is a nuclear reaction.

A chemical reaction involves the acquisition or loss of electrons, which leads in the synthesis of a new molecule while leaving the nucleus of an atom unchanged.

Thus, we can give a conclusion that because a change in a nucleus happened, the described event is categorised as a nuclear reaction rather than a chemical reaction.

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Answer:

? = 26

Step-by-step explanation:

Challenge accepted!

For the bottom left corner:

[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]

Now, 10 - 6 = 4

136 / 4 = 34

For the top left corner:

[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]

Now, 7 - 5 = 2

74 / 2 = 37

For the top right corner:

[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]

Now, 8 - 4 = 4

80 / 4 = 20

For the bottom right corner:

[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]

Now, 6 - 4 = 2

52 / 2 = 26

Another method:

5×6+7=37

7×6-5=37

6×4+10=34

10×4-6=34

4×3+8=20

8×3-4=20

So, 4×5+6=26

6×5-4=26

Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question

See the graph in the image.

A function is a relationship between inputs where each input is related to exactly one output.

The graph of f(x) = (4x² - 16) / (2x - 4) is given below.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function:

f(x) = (4x² - 16) / (2x - 4)

This can be written as,

f(x) = (2x)² - 4² / (2x - 4)       [ a² - b² = (a + b)(a - b) ]

f(x) = (2x - 4)(2x + 4) / (2x - 4)

f(x) = 2x + 4

Now,

We will find the coordinates from the function f(x) = 2x + 4

x = 0, f(x) = 4

(0, 4)

x = 1, f(x) = 6

(1, 6)

x = 3, f(x) = 10

(3, 10)

And so on.....

The graph is given below,

Thus,

The graph of f(x) = (4x² - 16) / (2x - 4) is given below.

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The matching of definitions and terms are done below.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Match the verbal expression (term) with its algebraic expression (definition).

Some number increased by two ⇒ b + 2

A variable decreased by two ⇒ x – 2

Product of an unknown value and two ⇒ 2z

Quotient of some number and two ⇒ a ÷ 2

An unknown value squared ⇒ y²

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Answer:

The squared root of 9 is 3

Why - Half of 9 is 3

Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.

5 Cubed is equal to 125

Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5

Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.

Answer:

2.3p – 10.1 = 6.49p – 4  [tex]\huge \checkmark[/tex]

230p – 1010 = 650p – 400 – p  [tex]\huge \checkmark[/tex]

Step-by-step explanation:

……………………………………………

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4

⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4

⇔ 2.3p – 10.1 = (6.49)p – 4

⇔ 2.3p – 10.1 = 6.49p – 4

_______________________

_______________________

2.3p – 10.1 = 6.5p – 4 – 0.01p

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)  multiply both sides by 100

⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)

⇔ 230p – 1010 = 650p – 400 – p

……………………………………………………

Answer:

Its the last option.

Step-by-step explanation:

The function will  rise from the left and descend to the right.

f(x) ---> -∝ as x ---> -∝ and f(x) ---> -∝ as x ---> ∝

The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.

In a right angled triangle, its side, such as hypotenuse, perpendicular and base  is Pythagorean triplets.

We have

Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.

[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]

and c = 13

Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.  

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Answer:

d

Step-by-step explanation:

- 5 (3x - 7) ← multiply each term in the parenthesis by - 5

= - 15x + 35

Answer: d.) -15x + 35

Given expression:

⇒ -5(3x - 7)

Apply distributive method: a(b + c) = ab + ac

⇒ -5(3x) -5(-7)

multiply the variables

⇒ -15x + 35

Answer:

A = -1

B = -3

C = -7

Step-by-step explanation:

See attached image.

Tony's coins in ascending order of value will be 5p, 10p, and 15p.

Definition of in Ascending order

Arranged in a series that begins with the smallest or least and ends with the largest or greatest The children were lined up in ascending order of height. Test score are listed in ascending order from lowest to highest.

How do depict the information?

Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.

In this case, 5p + 10p + 15p = 30p

10p + 15p + 15p = 40p

5p + 5p + 10p + 15p + 15p = 50p

Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.

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By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.

Herein we have a polynomials of the form y = a · x² - b. By algebra we find that two roots exists, which are described below according to the square root method:

[tex]y_{1} = +\sqrt{\frac{b}{a} }[/tex], [tex]y_{2} = -\sqrt{\frac{b}{a} }[/tex]

If we know that a = 25 and b = 100, then the two roots of the equation are:

y₁ = + 2, y₂ = - 2

By solving y = 25 · x² - 100 through the square root method, we conclude that the two roots of the quadratic formula are y₁ = + 2 and y₂ = - 2.

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