Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not, it becomes Bob's turn. On Bob's turn, he flips a coin. If he gets a tails, he wins. If not, it becomes Alice's turn. What is the probability that Alice wins the game?

Answer:

Step-by-step explanation:

1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...

[tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]

is the matrix ...

[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]

The first row can be interpreted as the equation ...

  x -y = 3

  x -3 = y . . . . . add y-3

The second row can be interpreted as the equation ...

  z = 0

Then the solution set is ...

  (x, y, z) = (x, x -3, 0) . . . . matches selection B

__

2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.

Answer:

No, because the reflection of ABC is not congruent to A’B’C’.

Step-by-step explanation:

we know that

The rule of the reflection across the line y=x is equal to

(x,y) -------> (y,x)

so

A(-6,6) -------> A'(6,-6) ----> is ok

B(-3,3) ------> B'(3,-3) ----> is ok

C(-8,2) ------> C'(8,-2) ----> is not ok ( is not a reflection acros the line y=x)

therefore

The triangles are no t congruent, because the reflection of ABC is not congruent to A’B’C’

Answer:

To remove 5x and create and linear equation

Step-by-step explanation:

5x+(-4)=6x+4

The equation can be solved by arranging terms so that numbers can be on one side and other constants will be on the other side.

This is given by the associative rule that states:

(-5x) + 5x + (-4) = 6x +4 - 5x

giving:

-4 = x + 4

this gives, x= -8

Hence a linear equation with a solution.

Answer:

a) decay factor is b = 0.9

b) y = 20,000(0.9)^x

c) y = $10,629

Step-by-step explanation:

a) What is the decay factor for the value of the car?

The formula used to find the decay factor is

y = a(b)^x

where y = future value

a = current value

b = decay factor

x = time

The decay factor is: b = 1-r

We are given rate r = 10% or 0.1

b = 1 - 0.1

b = 0.9

So, decay factor is b = 0.9

b) Write an equation to model the car’s value.

Using the formula:

y = a(1-r)^x

y = 20,000(1-0.1)^x

y = 20,000(0.9)^x

c) Use your equation to determine the value of the car six years after Kelly purchased it.

y = 20,000(0.9)^x

We need to find value after 6 years, so x=6

y = 20,000(0.9)^6

y = 10,628.82

y = $10,629

The correct answer would be: C. 5.02 x 10^18

Here's how you solve it!

Since the earthquake registered is 7.4 on the scale let it represent RS=7.4

The reference intensity is 2.0 x 10^11 so let it represent RI= 2.0 x 10^11

Now you need to use the formula.

[tex]RS=log(\frac{I}{I_{r} } )[/tex]

Then we need to plug in the values for the formula

[tex]7.4=log(\frac{I}{2.0 x 10^{11} } )[/tex]

[tex]I=10^{7.4}[/tex] x [tex]2.0[/tex] x [tex]10^{11}[/tex]

[tex]I= 5.02[/tex] x [tex]10^{18}[/tex]

Hope this helps! :3

Answer:

5.02×10^18

I got it right.

Answer:

  x° = 78°

Step-by-step explanation:

x° is the measure of external angle BHC of triangle BHD. As such, its measure is the sum of the opposite interior angles at B and D:

  47° + 31° = x° = 78°

Answer:1866

Step-by-step explanation:

Given

n=200

x=118

Population proportion P=[tex]\frac{118}{200}[/tex]=0.59

[tex]\alpha [/tex]=0.005

Realiability =99%

[tex]Z_{\frac{\alpha }{2}}=2.576[/tex]

Margin of erroe is given by [tex]\sqrt{\frac{p\left ( 1-p \right )}{N}}[/tex]

0.03= [tex]\sqrt{\frac{0.59\left ( 1-0.59 \right )}{N}}[/tex]

85.667=[tex]\sqrt{\frac{N}{0.6519}}[tex]

N=1865.88[tex]\approx 1866 Students[/tex]

To estimate the proportion of students receiving financial aid within 3% with 99% reliability, the dean needs to sample about 1846 students. This is calculated using the formula for the sample size in a proportion estimation with a 99% confidence level and a 3% margin of error.

The subject matter of your question involves using statistics to estimate a population proportion with a specified confidence level and margin of error. This can be calculated using the formula for the sample size in a proportion estimation: n = (Z² * p * (1-p)) / E², where Z is the Z-score, p is the preliminary estimate of the proportion, and E is the desired margin of error.

In this case, the Z-score for a 99% confidence level is approximately 2.58 (you can find this value in a standard normal distribution table). The preliminary estimate of the proportion (p) can be obtained from the initial sample: 118 in 200. So, p = 118/200 = 0.59. The desired margin of error (E) is 3%, or 0.03.

Putting these values into the formula, we get n = (2.58²* 0.59 * (1 - 0.59)) / 0.03² = approximately 1846. This means the dean would need to randomly sample about 1846 students to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability.

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Answer:

[tex]\frac{\pi}{2}[/tex] radians

Step-by-step explanation:

We can use the concept of proportion to answer this question.

The arc CD is given to be 1/4 in measure of the circumference of the circle. A complete circle is 360 degrees in measure which in radian measure is 2π

So, the arc which 1/4 in measure of the circumference will make an angle which is 1/4 of the angle of the entire circle.

i.e.

Angle formed by the arc =[tex]\frac{1}{4} \times 2 \pi =\frac{\pi}{2}[/tex] radians

Therefore, the radian measure of the central angle of arc CD is [tex]\frac{\pi}{2}[/tex] radians

Answer:

  $0.65

Step-by-step explanation:

When d increases by 1, A(d) increases by 0.65 dollars.

Thomas gets paid $0.65 for every mile of travel.

Answer:

  There are 10 packets of​ sweet-pepper seeds and 6 packets of​ hot-pepper seeds.

Step-by-step explanation:

Let h represent the number of packets of hot pepper seeds. Then 16-h is the number of packets of sweet pepper seeds. The total cost of a 16-packet mix is ...

  4.56h + 2.32(16 -h) = 3.16·16

  2.24h + 37.12 = 50.56 . . . . . . . simplify

  2.24h = 13.44 . . . . . . . . . . . . . . subtract 37.12

  13.44/2.24 = h = 6 . . . . . . . . . . divide by 2.24

  16 -h = 16 -6 = 10 . . . . . . . . . . . number of sweet pepper seed packets

There are 10 packets of​ sweet-pepper seeds and 6 packets of​ hot-pepper seeds.

Answer:

b) 4:3

Step-by-step explanation:

The point P is 4/7 of the distance from point M to point N. This means that moving from M to N, the total distance is divided into 7 equal parts and the point P lies after the 4 parts starting from M.

So, out of 7, 4 parts are present between M and P. and the remaining 3 parts are present between P and N. In other words we can say,when we move from M towards N, the line segment MP covers 4 out of 7 parts and the line segment PN covers the 3 parts.

So, we can conclude here that the point P partitions the directed line segment from M to N into a 4:3

Answer:

B. 4:3 is your answer

Answer:

50% is the answer.

Step-by-step explanation:

All three persons have different blood groups.

Mary has O blood type.

Her husband has B blood type.

Her father in law has A blood type.

As everyone has different blood groups and the child's group depends on parents blood groups so we have 2 options left.

Hence, the probability that the child will have type O blood is = [tex]\frac{1}{2}[/tex] =50%

Answer:

50/ 50

Step-by-step explanation:

The father's father blood doesn't really matter since the husband has type B. It's just a 50/50 chance between B and O.

Answer:

y = 3x

Step-by-step explanation:

y = mx + b

(x,y) = (1,3)

m = 3

3 = 3(1) + b

3 = 3 + b

3 - 3 = b

0 = b

y = 3x

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut-off point with the y axis

According to the data we have to:

[tex]m = 3\\(x, y) :( 1,3)[/tex]

So, the equation is of the form:

[tex]y = 3x + b[/tex]

We substitute the point and find b:

[tex]3 = 3 (1) + b\\3 = 3 + b\\b = 3-3\\b = 0[/tex]

Finally, the equation is of the form:

[tex]y = 3x[/tex]

Answer:

[tex]y = 3x[/tex]

Answer: 1088 :)

Step-by-step explanation:

The distance from San Juan to Miami is 1088 miles.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. Types of triangles include: scalene, right triangle, isosceles and equilateral triangle.

The law of sine would be used to determine the distance.

(a / sin a) = (b / sin b) = (c / sin c)

(a / sin 63) = [960 / (180 - 62 - 63)]

a / sin 63 = 960 / sin 54

a = (sin 63 x 960) / sin 54

a = 1088 miles

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Answer:

Δ ABC was dilated by a scale factor of 1/3, reflected across the y-axis

and moved through the translation (1 , -2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The similar triangles have equal ratios between their

  corresponding side

- So lets find from the graph the corresponding sides and calculate the

  ratio, which is the scale factor of the dilation

- In Δ ABC :

∵ The length of the vertical line is y2 - y1

- Let A is (x1 , y1) and B is (x2 , y2)

∵ A = (-6 , 0) and B = (-6 , 3)

∴ AB = 3 - 0 = 3

- The corresponding side to AB is FE

∵ The length of the vertical line is y2 - y1

- Let F is (x1 , y1) , E is (x2 , y2)

∵ F = (3 , -2) and E = (3 , -1)

∵ FE = -1 - -2 = -1 + 2 = 1

∵ Δ ABC similar to Δ FED

∵ FE/AB = 1/3

∴ The scale factor of dilation is 1/3

* Δ ABC was dilated by a scale factor of 1/3

- From the graph Δ ABC in the second quadrant in which x-coordinates

 of any point are negative and Δ FED in the fourth quadrant in which

 x-coordinates of any point are positive

∵ The reflection of point (x , y) across the y-axis give image (-x , y)

* Δ ABC is reflected after dilation across the y-axis

- Lets find the images of the vertices of Δ ABC after dilation and

 reflection  and compare it with the vertices of Δ FED to find the

 translation

∵ A = (-6 , 0) , B = (-6 , 3) , C (-3 , 0)

∵ Their images after dilation are A' = (-2 , 0) , B' = (-2 , 1) , C' = (-1 , 0)

∴ Their image after reflection are A" = (2 , 0) , B" = (2 , 1) , C" = (1 , 0)

∵ The vertices of ΔFED are F = (3 , -2) , E = (3 , -1) , D = (2 , -2)

- Lets find the difference between the x-coordinates and the

 y- coordinates of the corresponding vertices

∵ 3 - 2 = 1 and -2 - 0 = -2

∴ The x-coordinates add by 1 and the y-coordinates add by -2

∴ Their moved 1 unit to the right and 2 units down

* The Δ ABC after dilation and reflection moved through the

  translation (1 , -2)

The garden house takes 4 days, so that means it fills 1/4 of the pool per day ( 1/4 x 4 days = 1)

The larger hose takes 2 days, so this means it fills 1/2 the pool per day ( 1/2 x 2 days = 1)

Using both the garden hose and larger hose means 1/4 + 1/2 = 3/4 of the pool is filled in one day.

Now we need to find X ( the number of days to completely fill the pool.

Multiply the amount per day by the number of days to equal 1 ( 1 pool):

3/4 * x = 1

To solve for x, multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:

x = 4/3 *1

x = 4/3 = 1 and 1/3 days.

It will take 4/3 days or approximately 1.33 days to fill the pool when both hoses are used together.

To solve this problem, we need to understand the rate at which each hose fills the pool and then combine these rates to find the total rate when both hoses are used together.

Let's denote the fill rate of the first garden hose as 1/4 pool per day and the larger hose as 1/2 pool per day.

Using both hoses together, you add their rates to get the combined rate.

So, the combined rate of both hoses is:

1/4 + 1/2  = 3/4 pool per day.

This means three-quarters of the pool is filled in one day with both hoses working together.

To find the time (t) it takes to fill one entire pool, you can set up the equation:

3/4 * t = 1  (quantity is equal to 1 full pool)

t = 4/3 days

Therefore, it will take 4/3 days, or approximately 1.33 days, to fill the pool when both hoses are used together.

Answer:

  r = 3 + sin(θ)

Step-by-step explanation:

The curve extends below the x-axis, so the added constant must be larger than the coefficient of the sine function. There are two choices matching that description.

The extent in the -y (θ=-π/2) direction looks to be about 2/3 of the extent in the +x (θ=0) direction, so we expect the appropriate equation is ...

  r = 3 + sin(θ)

Answer:

2.

Step-by-step explanation:

is a geometric progression with common ratio of 1/4.

there, multiple 150 by 1/4 in 3 places. (4th, 5th and 6th day)

150 ÷ (4*4*4) = 150/64 = 2.3 ≈ 2

Using the formula for the n-th term of a geometric sequence, the number of mosquitoes killed on the sixth day is found to be approximately 2 when rounded to the nearest whole number.

The sequence representing the number of mosquitoes killed after spraying insecticide appears to decrease by a factor of 4 each day.

This pattern can be described as a geometric sequence. To find the number of mosquitoes killed on the sixth day, we will use the formula for the n-th term of a geometric sequence, which is an = a₁ × rⁿ⁻¹, where a1 is the first term, r is the common ratio, and n is the term number.

Day 1 (first term, a1): 2400 mosquitoes

Day 2: 2400 / 4 = 600 mosquitoes

Day 3: 600 / 4 = 150 mosquitoes

From this pattern, we identify the common ratio r as 1/4. To find the number of mosquitoes killed on the sixth day:

Let n = 6 for the sixth day.

Substitute a1 = 2400 and r = 1/4 into the formula: a6 = 2400 × (1/4)⁶⁻¹ = 2400 × (1/4)⁵.

Calculate the value: a6 = 2400 × (1/1024) ≈ 2.34, which rounds to 2 mosquitoes when rounded to the nearest whole number.

Therefore, approximately 2 mosquitoes were killed on the sixth day after the spraying.

Answer:

9 represents the initial height from which the ball was dropped

Step-by-step explanation:

Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

[tex]f(n)=9(0.7)^{n}[/tex]

The general formula for the geometric progression modelling this scenario is:

[tex]f(n)=f_{0}(r)^{n}[/tex]

Here,

[tex]f_{0}[/tex] represents the initial height i.e. the height from which the object was dropped.

r represents the percentage the object covers with respect to the previous bounce.

Comparing the given scenario with general equation, we can write:

[tex]f_{0}[/tex] = 9

r = 0.7 = 70%

i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.

Answer:

95.44% of hotels are with rate between 144 and 176 euros

Step-by-step explanation:

Given

Mean = μ = 160 euros

SD = σ = 8 euros

We have to find the z-scores for both values

So,

z-score for 144 = z_1 = (x-μ)/σ = (144-160)/8 = -16/8 = -2

z-score for 176 = z_2 = (x-μ)/σ = (176-160)/8 = 16/8 = 2

Now the area to the left of z_1 = 0.0228

Area to the left of z_2 = 0.9772

Area between z_1 and z_2 = z_2-z_1

= 0.9772-0.0228

=0.9544

Converting into percentage

95.44%

Therefore, 95.44% of hotels are with rate between 144 and 176 euros..

Using the Empirical Rule for a bell-shaped distribution, we find that approximately 95% of the hotel rates are between 144 and 176 euros.

The question asks for the percentage of hotels with rates between 144 and 176 euros given a bell-shaped and symmetrical distribution of nightly rates for a three-star hotel in Paris, with a mean of 160 euros and a standard deviation of 8 euros. To solve this, we can apply the Empirical Rule which states that approximately 95% of data within a bell-shaped distribution lies within two standard deviations of the mean.

Calculating two standard deviations from the mean (160 ± (2 × 8)), we get the range from 144 to 176 euros. Therefore, using the Empirical Rule, we can conclude that approximately 95% of the hotel rates fall within the given range.

[tex]25mn^2 +5mn =5mn(5n+1)[/tex]

The complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).

The given polynomial is 25mn^2 + 5mn. To find the complete factored form, we can factor out the GCF (Greatest Common Factor) from each term, which in this case is mn:

So, the complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).

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Answer:

y = 2

Step-by-step explanation:

I am assuming there was some info that got left out of this that states somewhere along the line that this is right triangle inscribed in a circle or something like that.  That means that angle R is a right angle.  Therefore,

53y - 16 = 90 so

53y = 106 and

y = 2

The value of y is 2.

Using the Inscribed angle theorem, in a semi-circle, the inscribed arc measures 180° for which inscribed angle in semi-circle will be half of 180° i.e. the inscribed angle in semi-circle will be right-angle i.e. 90°.

Here As PQ crosses the center of the circle M. so PQ ia the diameter.

the measure of the arc PRQ is 180°.

then using inscribed angle theorem, ∠PRQ will be half of 180°.

So, ∠PRQ =90°

Given, ∠PRQ= 53y-16°

⇒90°=53y-16°

⇒53y=90°+16°=116°

⇒y=116°/53°

⇒y=2

Therefore the value of y is 2.

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Answer:

50

Step-by-step explanation:

it is given that there is one variable with 1000 records

we have to find the records which is expected would be removed

it is given that one variable is missing with 5% that 0.05

we can find missing records by multiplying total number of records and the missing value with one variable

so the expected record removed will be =0.05×1000=50

Step-by-step explanation:

u.v=|u||v|cos60°

u.v=(2.5)(3.2)(1/2)

u.v=(8)(1/2)

u.v=4

Answer:

January

Step-by-step explanation:

A counterexample is something that proves the statement false.

January is a month that starts with J that is not a summer month.

That proves the statement false

[tex]\huge{\boxed{\text{January}}}[/tex]

A counterexample is an example that proves the statement wrong.

In this case, we are trying to prove that not all months that start with J are summer months. This means we need to find a month that starts with J that is also not a summer month.

[tex]\boxed{January}[/tex] is the only month that fits this criteria.  It begins with the letter J and is a winter month, which is not summer.

Answer:

D. 10.6

Step-by-step explanation:

Using Pythagoras' theorem

hyp² = side ² + side²

hyp² = 7² + 8²

hyp² = 49 + 64

hyp² = 113

hyp = sqrt of 113

hyp = 10.6

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)

The correct answer is option d. 10.6.

Given:

The hypotenuse is AC. Therefore, we use the formula:

AC² = AB² + BC²

Substituting the given values:

AC² = 7² + 8²
AC² = 49 + 64
AC² = 113

Now, take the square root of both sides to find AC:

AC = √113 ≈ 10.6

Thus, the missing length AC is approximately 10.6.

The correct answer is d. 10.6.

Complete question: Find the missing length on the triangle.  AB = 7, BC = 8 ∠B = 90°. Round your answer to the nearest tenth if necessary

a. 15

b. 113

c. 12

d. 10.6

Answer:

Step-by-step explanation:

In this problem, we will use ratios

60%------->120 guests

30%-------->60guests

10%---------->20guests

Multiply by 10 to both sides to get 200

100%--------> 200 guests

hope this helps!

Answer:

65.4

Step-by-step explanation:

Use the Law of Sines here.  The Law is as follows:

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

We only have need for 2 of those 3 proportions.  Since we can have only 1 unknown in a single equation, we have to use angle C as that unknown.  That means that other angle and side have to be given in the problem.  Angle B is given as 45 and side b is given as 7, so we will use those.

[tex]\frac{sinC}{9}=\frac{sin45}{7}[/tex]

We solve for sinC:

[tex]sinC=\frac{9sin45}{7}[/tex]

Doing that on our calculator gives us

sinC = .9091372901

Taking the inverse sin in degree mode gives you that angle C = 65.4

Answer:

x=-3 or x=3/2

Step-by-step explanation:

We are given the following equation:

2x^2+5x-9=2x

We are asked to find the roots.  That means just solve it for x.

2x^2+5x-9=2x

Subtract 2x on both sides:

2x^2+3x-9=0

Let's see if we can put this in factored form.

Compare

2x^2+3x-9=0

and

ax^2+bx+c=0.

a=2, b=3 , c=-9

We have to find two numbers that multiply to be ac and add up to be b.

ac=-18

b=3

What are two numbers that multiply to be -18 and add to be 3?

Say -3 and 6.

So we are going to factor 2x^2-3x+6x-9=0

The first two terms have a common factor of x.

The last two terms have a common factor of 3.

2x^2-3x+6x-9=0

x(2x-3)+3(2x-3)=0

Now we can factor the (x-3) out of those 2 terms there since they share that common factor:

(x+3)(2x-3)=0

(x+3)(2x-3)=0 implies x+3=0  or 2x-3=0.

So we must solve x+3=0   and 2x-3=0

x+3=0

Subtract 3 on both sides:

x=-3

2x-3=0

Add 3 on both sides:

2x=3

Divide both sides by 2:

x=3/2

The solutions are x=3 or x=-3/2

Answer:

-2B

Step-by-step explanation:

log₉ (1/16)

log₉ (16^-1)

log₉ (4^-2)

Using exponent property of logs:

-2 log₉ (4)

Substituting:

-2B

Answer:

-2B

(I guess this is what you are looking for; didn't need A or C).

Step-by-step explanation:

It seems like to wants us to to find [tex]\log_9(\frac{1}{16})[/tex] in terms of [tex]A,B,C[/tex].

First thing I'm going to do is rewrite  [tex]\log_9(\frac{1}{16})[/tex]  using the quotient rule.

The quotient rule says:

[tex]\log_m(\frac{a}{b})=\log_m(a)-\log_m(b)[/tex]

So that means for our expression we have:

[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]

Second thing I'm going to do is say that [tex]\log_9(1)=0 \text{ since } 9^0=1[/tex].

[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]

Now I know 16 is 4 squared so the third thing I'm going to do is replace 16 with 4^2 with aim to use power rule.

[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-\log_9(4^2)[/tex]

The fourth thing I'm going to is apply the power rule. The power rule say [tex]\log_a(b^x)=x\log_a(b)[/tex]. So I'm applying that now:

[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-2\log_9(4)[/tex]

So we are given that [tex]\log_9(4)[/tex] is [tex]B[/tex]. So this is the last thing I'm going to do is apply that substitution:

[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]

[tex]\log_9(\frac{1}{16})=-2\log_9(4)[/tex]

[tex]\log_9(\frac{1}{16})=-2B[/tex]