Juan, Carlos and Manu take turns flipping a coin in their respective order. The first one to flip heads wins. What is the probability that Manu will win

Answer:

28.31

Step-by-step explanation:

So in this case you're going to need to use the law of sines which essentially states that: [tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex] which should apply to any of the sides. the lowercase a and b are the opposite sides of the angles A and B. In this example the angle A is given and C is given, but not in the text. Since you have the right angle thing in the diagram, angle C is a right angle (90 degrees).

Given information:

[tex]\angle A = 32\\a=15\\\angle C = 90 \text{(the right angle symbol in the diagram of the triangle)}[/tex]

Law of sines equation:

[tex]\frac{a}{sinA}=\frac{b}{sinB} \text{ can be applied to any two sides }[/tex]

Plug in known information:

[tex]\frac{15}{sin(32)}=\frac{c}{sin (90)}[/tex]

since sin(90) = 1, simplify the fraction

[tex]\frac{15}{sin(32)} = c[/tex]

Calculate sin(32)

[tex]\frac{15}{0.530}\approx c[/tex]

Divide

[tex]28.306\approx c[/tex]

If you haven't learned law of sines yet and don't quite understand why it works you can also use the definition of tan to find what b equals and then use the Pythagorean Theorem to solve for c

tan is defined as: [tex]\frac{opposite}{adjacent}[/tex]

[tex]tan(32)=\frac{15}{b}[/tex]

now multiply both sides by b

[tex]b * tan(32)=15[/tex]

Divide both sides by tan 32

[tex]b = \frac{15}{tan(32)}[/tex]

[tex]b\approx 24.005[/tex]

Now use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

[tex](24.005)^2+15^2=c^2\\[/tex]

Square known values

[tex]576.241+225=c^2[/tex]

Add the values

[tex]801.241 = c^2[/tex]

take the square root of both sides

[tex]28.306\approx c[/tex]

Rounding to the nearest hundredth gives you 28.31

Answer:

14

Step-by-step explanation:

24/12=2

(2)7=14 hours

Answer:

A. 2640

Step-by-step explanation:

44 feet per second 30 miles per hour is 2640 feet per minute

A) The situation represents an arithmetic sequence because the successive y-values have a common difference of 210.

F(1) = 240 +210

F(2) = 240 +2(210)

F(3) = 240+3(210)

.

.

.

.

F(x)= 240 +210x.

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Answer:

[tex]\huge\boxed{\sf 9x^2+12x+4 \ units^2}[/tex]

Step-by-step explanation:

Given that,

Length of cube = l = 3x + 2 units

[tex]= l \times l\\\\= (3x+2)(3x+2)\\\\= 3x(3x+2)+2(3x+2)\\\\= 9x^2+6x+6x+4\\\\= 9x^2+12x+4 \ units^2\\\\\rule[225]{225}{2}[/tex]

Answer:

50 [tex]cm^{2}[/tex]

Step-by-step explanation:

Area of a trapezoid: [tex]\frac{a+b}{2} h[/tex]

[tex]\frac{a+b}{2} h[/tex]

= [tex]\frac{14+6}{2} (5)[/tex]

= [tex]\frac{20}{2} (5)[/tex]

= [tex]10(5)[/tex]

= 50 sq. cm

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given:

△QRS and △TUV is translated across SQ and then is shifted down and to the right to form △TUV.

So, translation mapping vertex Q to vertex T is done and a reflection across the line containing QS will map △QRS to △TUV.

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Answer:

B

Step-by-step explanation:

That's what the other person is saying

Evidence is used in proofs to support a claim.

It should be noted that evidence simply means a claim that's is used to support a proposition that's it's true.

In this case, evidence is used in proofs to support a claim. On the other hand, counterexample is used to disprove a theory.

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The rule of 72 is a rule of thumb that is used to determine the doubling time for an investment given the annual interest rate.

The equation Miguel needs to set up is r = 72/16.

The interest rate is 4.5%.

The rule of 72 is used to determine the time it would take an investment to double in value. The doubling time is determined by dividing 72 by the interest rate.

Number of years it would take an investment to double = 72 / interest rate

n = 72 / r

r = 72 / n

72 / 16 = 4.5%

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The point (0, 0) lies in the shaded region and satisfies the solution for the inequality y ≥ 3x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the inequality y ≥ 3x - 2, since the point (0, 0) lies on the shaded region, hence:

0 ≥ 3(0) - 2

0 ≥ -2

The point (0, 0) satisfies the solution for the inequality y ≥ 3x - 2

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Based on the relevant congruent theorems, all of the statements are correct except: D. △RST ≅ △UST by SAS.

Two triangles that have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles are proven to be congruent by the AAS congruence theorem.

Thus, △RWS ≅ △UWT by AAS because they have two pairs of corresponding congruent angles and a pair of corresponding non-included congruence angles.

△RST cannot be proven to be congruent to △UST by SAS because there is no sufficient information.

Based on the reflexive property, ST ≅ ST. Also, using the CPCTC, all parts of the two congruent triangles are equal, therefore, ∠WTU ≅ ∠WSR.

The only statement that is incorrect is: D. △RST ≅ △UST by SAS.

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Answer:

A, B, C and E

Step-by-step explanation:

Using the least common multiple, it is found that the least possible number of coins that each of them has is of 24.

They have the same number of coins, with Betty sorting the coins in groups of 6 and Jane sorting the coins in groups of 8, and none of them having coins remaining.

Thus, the least possible number of coins they have is the least common multiple of 6 and 8, found factoring both these numbers into prime factors, as is done below:

6 - 8|2

3 - 4|2

3 - 2|2

3 - 1|3

1

Hence the least common multiple of 6 and 8 is given by:

lcm(6,8) = 2 x 2 x 2 x 3 = 2³ x 3 = 24.

Thus, it is found that the least possible number of coins that each of them has is of 24.

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Answer:

Slope = 1/3

Step-by-step explanation:

  [tex]\sf \ x_1=-1 ; \ y_1=-2\\\\ x_2 = 2 ; \ y_2=-1[/tex]

      [tex]\sf \boxed{\bf \ Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                  [tex]\sf = \dfrac{-1-[-2]}{2-[-1]}\\\\ =\dfrac{-1+2}{2+1}\\\\= \dfrac{1}{3}[/tex]

Answer: 14.79

Step-by-step explanation:

[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]

The length of the segment AB will be equal to 9.848 units.

It states that in the right-angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

The length of segment AB will be calculated as:-

Points are A(1,7) and B(10,3)

AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

AB = [tex]\sqrt{(10-1)^2+(3-7)^2}[/tex]

AB = √(81+16)

AB = √97

AB = 9.848

Therefore the length of the segment AB will be equal to 9.848 units.

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The four powers have zero (0) in common

From the question, we are to determine what the four powers have in common

In the question, we can observe that the four powers have 0 in common.

The value of each of the expressions is 1.

Hence, the four powers have zero (0) in common.

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Answer:

7

Step-by-step explanation:

a^3 = 2^3 = 8

b^3 = -3^3 = -27

(8 - (-27))/5= (8+27)/5 =35/5=7

Answer:

Step-by-step explanation:

By taking the product between the number of boys and the number of rocks that each gets, we conclude that they collected 75 rocks.

We know that there are 3 boys, and each boy collected 25 rocks.

If we take the product between the number of boys and the number of rocks that each boy collected, we get:

R = 3*25 rocks = 75 rocks.

We conclude that the boys collected 75 rocks in total.

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The equation that relates x and y is y = 2.5x.

The values of x and y vary directly. Therefore,

y α x

where

Hence,

y = kx

where

Therefore,

x = 2

y = 5

5 = 2k

k = 5 / 2

k = 2.5

Hence, the equation that relates x and y are as follows;

y = 2.5x

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The equation that represents the situation are x = 1/2 y + 3 and x = 1/4y + 5

Let the first number be x and the second number be y.  If a number is equal to the sum of half a second number and 3, this is expressed as;

x = 1/2 y + 3

For the second equation;

The first number is equal to the sum of one- quarter of the second number and 5

x = 1/4y + 5

Hence the equation that represents the situation are x = 1/2 y + 3 and x = 1/4y + 5

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Answer:

[tex]\displaystyle{y=2\sqrt{x+4}}[/tex]

Step-by-step explanation:

We are given parametric equations of:

[tex]\displaystyle{x=t^2-4}[/tex] and [tex]\displaystyle{y=2t}[/tex]

Isolate t-variable in [tex]\displaystyle{x=t^2-4}[/tex] first by adding both sides by 4:

[tex]\displaystyle{x+4=t^2-4+4}\\\\\displaystyle{x+4=t^2}[/tex]

Square root both sides then write plus-minus:

[tex]\displaystyle{\sqrt{x+4}=\sqrt{t^2}}\\\\\displaystyle{t=\pm \sqrt{x+4}}[/tex]

Since the choice determines y-term as a function and only positive t-value exists, substitute only [tex]\displaystyle{t=\sqrt{x+4}}[/tex] in [tex]\displaystyle{y=2t}[/tex].

Therefore, the answer is [tex]\displaystyle{y=2\sqrt{x+4}}[/tex]

Answer:

c

Step-by-step explanation:

Answer:

A. Square

Step-by-step explanation:

Hope this helps!

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There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with [tex]0\leq r < d[/tex] such that [tex]a=dq+r[/tex]

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

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Answer:

(-4,-2)

Step-by-step explanation:

Isolate x:

2x - 5y = 2

2x = 5y + 2

x = 5/2y + 1

Substitute and solve for y:

3(5/2y + 1) + 2y = -16

15/2y + 3 + 2y = -16

7.5y + 2y = -16 - 3

9.5y = -19

y = -2

Substitute and solve for x:

2x - 5y = 2

2x - 5(-2) = 2

2x + 10 = 2

2x = -8

x = -4

The value of ST is 3

The given parameters are:

RT = 8

RS = 5

To calculate ST, we make use of the following straight line theorem

RT = RS + ST

This gives

8 = 5 + ST

Subtract 5 from both sides

ST = 3

Hence, the value of ST is 3

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Answer: f(n + 1) = (–0.5)f(n)

Step-by-step explanation:

This is a geometric series with common ratio -0.5.

Answer: B. G(x) = (x-5)^2

Step-by-step explanation:

This will shift the graph 5 units right

Answer: [tex]\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}[/tex]

Step-by-step explanation:

     We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.

     [tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

     [tex]\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}[/tex]

     [tex]\displaystyle d=\sqrt{(1)^2 +(-4)^2}[/tex]

     [tex]\displaystyle d=\sqrt{1 +16}[/tex]

     [tex]\displaystyle d=\sqrt{1 7}[/tex]