a₁ = 20, r=-3, n = 6
Oa. 4860
Ob. -4860
Oc. -300
Od. -360

Find An for each geometric sequence

The expected number of tosses until either a head comes up or four tails are obtained is 7/4

Let X be the random variable representing the number of tosses until either a head comes up or four tails are obtained.

Let's consider the first toss. There are two possible outcomes: heads or tails. If a head comes up on the first toss, then we stop and X = 1. If a tail comes up, we need to continue tossing until we get four tails in a row or a head.

Let Y be the random variable representing the number of additional tosses needed if the first toss is a tail. There are two possible outcomes for the second toss: heads or tails. If a head comes up, we stop and X = 2. If a tail comes up, we need to continue tossing until we get three tails in a row or a head.

Similarly, we can define Z as the random variable representing the number of additional tosses needed if the first two tosses are tails. There are two possible outcomes for the third toss: heads or tails. If a head comes up, we stop and X = 3. If a tail comes up, we need to continue tossing until we get two tails in a row or a head.

Finally, let W be the random variable representing the number of additional tosses needed if the first three tosses are tails. There are two possible outcomes for the fourth toss: heads or tails. If a head comes up, we stop and X = 4. If a tail comes up, we need to continue tossing until we get four tails in a row.

We can write X in terms of Y, Z, and W as follows

X = 1 + Y if the first toss is heads

X = 1 + 1 + Z if the first two tosses are tails and the third toss is heads

X = 1 + 1 + 1 + W if the first three tosses are tails and the fourth toss is heads

X = 1 + 1 + 1 + 1 if the first four tosses are tails

Now, we need to compute the expected values of Y, Z, and W.

If the first toss is a tail, the probability of getting another tail on the second toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Y] = 1/2(1) + 1/2(1 + Z)

If the first two tosses are tails, the probability of getting another tail on the third toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Z] = 1/2(1) + 1/2(1 + W)

If the first three tosses are tails, the probability of getting another tail on the fourth toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[W] = 1/2(1) + 1/2(4)

Note that the expected value of W is 2, not 3, because if we get three tails in a row, we stop and X = 4.

Putting it all together, we have:

E[X] = 1/2(1) + 1/2(1 + E[Z])

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + E[W]))

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + 2))

= 7/4

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Answer:

5°

Step-by-step explanation:

The three angles of a triangle add up to 180° (every triangle, always) Since this triangle is a right triangle, one of the angles is a right angle, 90°.

Another angle is given, 85°.

x + 85° + 90° = 180°

x + 175° = 180°

x = 5°

To do this question using mental math, if one angle is 90° the other two angles must add up to 90° (thats the total of 180°) One angle is 85° then the other is 5°

Answer:7,6,5

Step-by-step explanation:

So this is how I did it

So the theorem  is

a+b>c

a+c>b

b+c>a

---

Let's now substitute A= 6 and B =2 so It'll look something like

6+2> C

6+C> 2

2+C>6

From there I added like terms

8>C

4<C

2<C

Then from there I noticed the numbers 5,6,7 are the the only whole numbers between 4 and 8. So that's what I'm put as my answer.

mean temperature=sum of all the temperatures to the total number of temperatures:

Mean temperature = (71 + 75 + 74 + 80 + 83 + 86 + 90 + 85 + 81 + 80) / 10

Mean temperature = 805 / 10

Mean temperature = 80.5°F

Therefore, the mean temperature for the next 10 days is 80.5 degrees Fahrenheit.

The mean temperature in Fahrenheit for the next 10 days is 79.5.

The mean temperature in Fahrenheit for the next 10 days can be calculated as follows;

Add all the given temperatures together:

71 + 75 + 74 + 80 + 83 + 86 + 90 + 85 + 81 + 80 = 795

Divide the sum obtained by the total number of temperatures, which is 10: 795 ÷ 10 = 79.5.

Therefore, the mean temperature in Fahrenheit for the next 10 days is 79.5.

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Answer:  F(1) = 2. (1)^3 + (1)^2 + 3

                      = 2+1+3

                      = 7

Step-by-step explanation:

Answer:

45 times

Step-by-step explanation:

I hope this helps

The cost of one package of tulip bulbs is 11, and the cost of one package of crocus bulbs is 16.

To find the cost of one package of tulip bulbs and one package of crocus bulbs, follow these steps:

Write two equations based on the given information:

Equation 1 (James): 3T + 7C = 145

Equation 2 (Kim): 10T + 14C = 334

Solve the system of equations using the substitution or elimination method. In this case, we'll use the elimination

method by multiplying Equation 1 by 2 to make the coefficients of C the same:

Equation 1 modified: 6T + 14C = 290

Subtract Equation 2 from the modified Equation 1:

(6T + 14C) - (10T + 14C) = 290 - 334
  -4T = -44

Divide both sides by -4 to find the value of T (tulip bulbs):
  T = 11

Substitute the value of T back into Equation 1 to find the value of C (crocus bulbs):
  3(11) + 7C = 145
  33 + 7C = 145

Subtract 33 from both sides:
  7C = 112

Divide both sides by 7 to find the value of C:
  C = 16

So, the cost of one package of tulip bulbs is 11, and the cost of one package of crocus bulbs is 16.

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Answer:

y = - 2x + 12

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 1 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (6, 0 ) , the point it crosses on the x- axis into the partial equation.

0 = - 2(6) + c = - 12 + c ( add 12 to both sides )

12 = c

y = - 2x + 12 ← equation of perpendicular line

GIVEN EQUATION IS y = 1/2x + 1

NOW PERPENDICULAR EQUATION CAN BE WRITTEN AS

Since the line passes through the point (6,0) on the x-axis, we can substitute these values into the equation to solve for k:

Answer:

If 1 + 1 = 2, then we can say that 1 = 2 - 1. Now, if we have 3x + 5x, we can factor out the common term of x to get: 3x + 5x = (3 + 5)x = 8x So, 3x + 5x = 8x.

Answer: B

Step-by-step explanation: Answer choice B states, that same side interrior angles are supplementary so picture i shows parralel lines. This is trues, as line L and line M have interior angles that are supplementary, meaning that it ends up to 180. This concept is not true for ii, as 106 and 73 angles are not supplementary.

Angles are created by joining the extremities of two rays, with the joint vertex representing the common terminal of the two beams. The value of ∠c= 48.65.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

Given,

AC = 33 cm

AB = 35.75 cm

Hence, The value of ∠C = 48.65.

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Answer:

(C). 45.2

Step-by-step explanation:

Answer:

-16/5 divided by 12/25 is equal to -40/3.

Step-by-step explanation:

We can say that approximately 48 villagers (40% of 120) are under the age of 25. This means that just under half of the population in this village is under the age of 25.

According to the pie chart, we can see that the village of 120 people has 20% of its population over the age of 60. To determine the exact number of villagers over 60, we can multiply the total population by the percentage of people over 60:

120 x 20% = 24

So there are 24 villagers over the age of 60 in this village.

As for the percentage of villagers under the age of 25, we can see from the pie chart that 40% of the population falls into this category. However, it is important to note that the question mentions a village of 120 people, while the percentage given in the chart may not reflect this exact number. Therefore, we cannot determine the exact number of villagers under the age of 25 without additional information.

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The area of the given rectangle is [tex]32\dfrac{6}{20}[/tex] square feet

For better understanding check the calculation here.

Area of the rectangle is the space inside the given triangle.

Formula: Formula to find the area of the triangle is length times width

Length and width are given as mixed fractions

Lets convert mixed fractions into improper fractions

[tex]\text{Length}=6\dfrac{4}{5} =\dfrac{6\times5+4}{5} =\dfrac{34}{5}[/tex]

[tex]\text{Width}=4\dfrac{3}{4} =\dfrac{4\times4+3}{4} =\dfrac{19}{4}[/tex]

Now we find out the area

[tex]\text{Area}=\text{length}\times\text{width}[/tex]

[tex]\text{Area}=\dfrac{34}{5} \times\dfrac{19}{4}[/tex]

[tex]\text{Area}=\dfrac{646}{20}[/tex]

Now we divide the number and find out the quotient and remainder

[tex]\text{Area}=\dfrac{646}{4}[/tex]

[tex]\text{Quotient}=32[/tex]

[tex]\text{Remainder}=6[/tex]

[tex]\text{Area}=32\dfrac{6}{20}[/tex]

The area of the given rectangle is [tex]32\dfrac{6}{20}[/tex] square feet

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Answer:

B

Step-by-step explanation:

The perimeter of the triangle is 28.08 units, the area of the triangle is 8.49 square units, and the height of the triangle is 3.18 units.

The lengths of the triangle's sides must be determined using the distance formula in order to determine the triangle's perimeter:

Side X to Y length: [tex]\sqrt{(5-2)2 + (9-10)2}[/tex]]d(XY) equals sqrt[9+1] = sqrt (10)

Side Y to Z length: [tex]d(YZ) = \sqrt{[(1-9)2 + (6-5)2]} = \sqrt{65}[/tex]

Side Z to X length: [tex]\sqrt{(2-6)2 + (10-1)2]} = d(ZX) = \sqrt{16+81]} = \sqrt{97}[/tex]

Perimeter: (XY + YZ + d) (ZX)

Sqrt(10) + Sqrt(65) + Sqrt Equals the circumference (97)

Radius = 10.17 + 8.06 + 9.85

Diameter: 28.08

We can apply the following formula to determine the triangle's area:

(1/2) * Base * Height = Area

Every triangle side's length serves as the base. Using side YZ

sqrt = base (65)

We must drop a perpendicular from vertex X to side YZ in order to get the height. The height of the triangle equals the length of this perpendicular.

y - 9 = (1/5) is the equation of the line connecting points Y and Z. (x - 6)

y - 10 = (-5) is the equation for the line that is perpendicular to this line and passes through point X. (x - 2)

We may get the location of the perpendicular's intersection with side YZ by solving these two equations:

x = 3.08, y = 6.47

Hence, the distance between points X and the point of intersection on side YZ is the triangle's height:

height is equal to sqrt[(3.08-2)2 + (6.47-9)2] = sqrt[10.11] = 3.18.

Area = (1/2)*base*height*sqrt(65)*3.18 Area = (1/2)*base*height*area Area = 8.49

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Using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the central angle of degrees must first be converted to radians.

θ(rad) = 275/180 * π = 1.53 rad

Then, by multiplying the Central angle (in rad units) by the circle radius r, the arc length may be determined:

s = θ * r

Changing the θ and r values:

s = 1.53 * π * 12 ft

s = 57.60 ft

Therefore, using the radians we know that the length of the arc in terms of π is s = 1.53 * π * 12 ft or s = 57.60 ft.

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Correct question:

Find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. Express arc length in terms of π. Then round your answer to two decimal places.

Radius, r = 12 feet; Central angle, θ = 275

Answer:

It will take 3 days to runn total of 12 Kilometers

Step-by-step explanation:

12(1000) = 12,000 meters

400(10) = 4000 meters/day

12,000/4000 = 3 days

Answer:

3.375 hope this helps

Answer:

[tex]\dfrac{27}{8}[/tex]

Step-by-step explanation:

we have to find,

[tex]x = \left( -\dfrac{1}{4} -\dfrac{1}{2}\right) \div \left( - \dfrac{2}{9} \right)[/tex]

simplifying,

[tex]x = \left( -\dfrac{1}{4} -\dfrac{2}{4}\right) \div \left( - \dfrac{2}{9} \right)[/tex] (changed the base)

[tex]x = \left( -\dfrac{3}{4}\right) \div \left( - \dfrac{2}{9} \right)[/tex]

therefore,

[tex]x =\dfrac{27}{8}[/tex] (canceled negative sign and used division rule for fractions)

Hopefully this answer helped you!

Answer:

  17/6√3

Step-by-step explanation:

You want the simplified form of 9·sin(60°) -5/√3.

  [tex]9\sin(60^\circ)-\dfrac{5}{\sqrt{3}}=9\cdot\dfrac{\sqrt{3}}{2}-\dfrac{5\sqrt{3}}{\sqrt{3}\cdot\sqrt{3}}= \dfrac{3\cdot9\sqrt{3}}{3\cdot2}-\dfrac{2\cdot5\sqrt{3}}{2\cdot3}\\\\=\dfrac{(27-10)\sqrt{3}}{6}=\boxed{\dfrac{17}{6}\sqrt{3}}[/tex]

Answer:

Step-by-step explanation:

To find the inverse of the function y = 3x, we need to swap the positions of x and y and then solve for y.

Step 1: Swap the positions of x and y

x = 3y

Step 2: Solve for y

Divide both sides by 3

x/3 = y

So the inverse function of y = 3x is x/3.

We can also verify that this is the inverse function by plugging in x/3 for y in the original equation and confirming that we get x:

y = 3x

x/3 = 3x/3

x/3 = x

Therefore, the inverse function of y = 3x is x/3.

Answer:

Step-by-step explanation:

The given function is y = 3x.

To find its inverse, we start by swapping x and y in the equation to get:

x = 3y

Next, we solve this equation for y to isolate it:

y = x/3

Therefore, the inverse of y = 3x is y = x/3.

Answer:

y = 200·1.15^t The required function is y=1.047t + 199.12

Step-by-step explanation:

The ratio from one year to the next is 1.15, so the balance is a geometric sequence. Since t starts at zero, we can write the balance (y) after t years as ...

 y = initial value · (common ratio)^t

 y = 200·1.15^tThe given table shows the balance of a money market account over time.

Time (t)     Balance(y)

0  200

1  210

2  220.5

3  231.53

4  243.1

5  255.26

The function that represents the balance y(in dollars) after t years is linear regression line, because the value of y increased linearly.

The linear regression function is defined as

Where,

Put the values from the below table in the above formulas.

The value of b is 11.047 and the value of a is 199.12. Here, the variable is t.

Therefore the required function is the anser up top

Answer:

x = 189/4

Step-by-step explanation:

1 / 3x = 1/7x + 9

x / 3 = x / 7 + 9

4x / 21  = 9

x = 189/4

3120 different types of colorings are possible . Thus, Option C is the correct option. There are 3 cases involved

6! = 720 cases

No rotation is necessary because all permutation are already accounted for.

6 × 5 × 4 × 3 = 360

There are 5 different locations where the pair can be present.

360 × 5 = 1800 one pairs is possible

6 × 5 × 4 = 120

There are 5 rotations in the pentagon so the total number of possibilities is  

120 × 5 = 600 two pairs are possible

now, we add the 3 cases to find the total number of possibilities

720 + 1800 + 600 =  3120

3120 different types of colorings are possible. Thus, Option C is the correct option.

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the equation √x = -7 has no real solutions.

Why it is?

There is no real number x that satisfies the equation √x = -7.

The square root of a non-negative real number is always non-negative. Therefore, √x is non-negative for all real numbers x, including x = 0. However, -7 is negative, so the equation √x = -7 has no real solutions.

An equation is a statement that asserts the equality of two mathematical expressions. It generally consists of two sides, left-hand side (LHS) and right-hand side (RHS), which are separated by an equal sign (=). An equation is true when both the LHS and RHS represent the same value or expression.

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Complete question:

What is the solution to the equation √x = -7, where √x represents the square root of x and -7 is a negative number?

Answer: 16 girls

Step-by-step explanation:

Step 1: Calculate the total number of students in the school by multiplying 32 by the ratio of girls to all the students, which is 5:8.

32 x (5/8) = 20

Step 2: Subtract the result from 32 to get the number of girls in the school.

32 - 20 = 12

Step 3: Multiply the result by the ratio of girls to all the students, which is 5:8.

12 x (5/8) = 16

The false statement among the options is E. The power of a hypothesis test does depend on the sample size.

The power of a hypothesis test is indeed a measure of the test's ability to detect a difference between the estimated value and the true value of a parameter (Statement A). It represents the probability of correctly rejecting the null hypothesis when it is actually false.

Statement B is true as well. As the alpha level increases, the beta level of a hypothesis test decreases. Alpha (α) represents the probability of a Type I error (rejecting the null hypothesis when it is true), while beta (β) represents the probability of a Type II error (failing to reject the null hypothesis when it is false). Statement C is accurate, as beta is the measure of the probability of a Type II error, meaning the likelihood of failing to reject a false null hypothesis. Statement D is also true. The power of a hypothesis test increases as alpha increases because increasing the alpha level means that you are more likely to reject the null hypothesis when it is false, which ultimately increases the power of the test.

However, statement E is false. The power of a hypothesis test does depend on the sample size. As the sample size increases, the power of the test increases as well. Larger sample sizes provide more accurate estimates of the population parameters, which helps in better differentiating between the null and alternative hypotheses, leading to a higher power for the hypothesis test. Therefore, the correct option is E.

The question was incomplete, Find the full content below:

which of the following statements is false?

A. the power of a hypothesis test is a measure of the ability of the test to detect a difference between the estimated value and the true value of a parameter.

B. as the alpha level increases, the beta level of a hypothesis test decreases.

C.Beta is the measure of the probability of a type ii error.

D. the power of a hypothesis test increases as alpha increases.

E. the power of a hypothesis test does not depend on the sample size.

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f(w) = 100 + 15t is the function that represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

It is given to us that Jordan received $100 for a graduation present and deposited it in a savings account. Each week thereafter, he added $15 to the account but no interest was earned.

We need to write an equation represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account:

Graduation present = $100

Amount deposited per week = $15

Let, w be the number of weeks, and t, the total amount in the savings account, therefore, the function is:

f(w) = 100 + 15t

Therefore, f(w) = 100 + 15t represents the relationship between w, the number of weeks Jordan kept his money in the account, and t, the total amount in the savings account

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