(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) I equation editorEquation Editor 1. For all n>2, nn3−2<2n2, and the series 2∑1n2 converges, so by the Comparison Test, the series ∑nn3−2 converges. equation editorEquation Editor 2. For all n>2, 1n2−1<1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑1n2−1 converges. I equation editorEquation Editor 3. For all n>2, n+1−−−−−√n>1n, and the series ∑1n diverges, so by the Comparison Test, the series ∑n+1−−−−−√n diverges. I equation editorEquation Editor 4. For all n>2, ln(n)n2>1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑ln(n)n2 converges. I equation editorEquation Editor 5. For all n>1, 1nln(n)<2n, and the series 2∑1n diverges, so by the Comparison Test, the series ∑1nln(n) diverges. I equation editorEquation Editor 6. For all n>1, n7−n3<1n2, and the series ∑1n2 converges, so by the Comparison Test, the series ∑n7−n3 converges.

The question is incomplete. The complete question is as follows.

Juan, Carlos and Maria went to the museum. The entrance ticket cost $5 per person, but, as they are students, there is a discount of $1 per ticket. After, they bought: 3 combos of chicken and fries costing $4 each; 3 bottles of water costing $1 each; 3 vanilla cookies costing $1 each; How much money each student paid if they divided the costs in equal amount?

Answer: $10

Step-by-step explanation: As each students split the bill in equal parts, to find how much they spent, we can calculate how much one of the three spent.

For ticket: 5 - 1 (because of the students discount) = $4

Each combo of chicken and fries cost $4, so: combo = $4

Each bottle of water costs $1, so: water = $1

and each vanilla cookie costs $1: cookie = $1

Total spent is:

T = 4+4+1+1

T = 10

Each student spent a total of $10 for this outing.

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

1. Let's draw the trapezoids, then combine them. The first trapezoid has larger Base measuring 4.67 cm, parallel and minor base =2, an area of  4.98

2. Since the other one is a copy, same area, same base. The junction of both trapezoids generates a hexagon. We have another trapezoid with an area of 4.98. The hexagon has a total area of 9.96

3. So each trapezoid has exactly 1/2 of the area of the hexagon.

Final answer:

The expected value of the sample mean weight of watermelons, given a population mean of 21.3 pounds, is also 21.3 pounds.

Explanation:

Expected Value of the Sample Mean Weight of Watermelons

If we have a population in which the average watermelon weighs 21.3 pounds with a standard deviation of 1.07 pounds, and we consider the sample mean weight of 90 watermelons, we can calculate the expected value of this sample mean. In statistics, the expected value of the sample mean is the same as the population mean when the samples are drawn from the population independently. Thus, the expected value of the sample mean weight for the watermelons is 21.3 pounds.

The correct answer is 96 degrees for the circle.

Equation

Since angles KJL and KML are opposite angles of a cyclic quadrilateral, their sum is 180 degrees.

(7x - 8) + (3x + 8) = 180° is the equation.

10x = 172

x = 17.2

Therefore, angle KJL measures 7(17.2) - 8 = 115.4 degrees, and angle KML measures 3(17.2) + 8 = 52.6 degrees.

The measure of arc KL is equal to the sum of the measures of angles KJL and KML:

115.4 + 52.6 = 168

So the measure of arc KL is 168 degrees.

Therefore, the correct answer is 96 degrees, which matches one of the answer choices.

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Answer:

57 in³

Step-by-step explanation:

Area of cylinder= [tex]\pi {r}^{2} h[/tex]

Let's find the radius.

Radius= Diameter ÷2

Radius= 6 ÷2

Radius= 3 in.

Area of Rover's dog bowl

= 3.14(3)²(2)

= 56.52

= 57 in³ (nearest cubic inch)

Answer:

57 in3

Step-by-step explanation:

Answer:

68% of the diameters are between 7.06 cm and 7.78 cm

Step-by-step explanation:

Mean diameter = μ = 7.42

Standard Deviation = σ = 0.36

We have to find what percentage of diameters will be between 7.06 cm and 7.78 cm. According to the empirical rule, for a bell-shaped data:

So, we first need to find how many standard deviations away are the given two data points. This can be done by converting them to z-score. A z score tells us that how far is a data value from the mean. The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

x = 7.06 converted to z score will be:

[tex]z=\frac{7.06-7.42}{0.36}=-1[/tex]

x = 7.78 converted to z score will be:

[tex]z=\frac{7.78-7.42}{0.36}=1[/tex]

This means the two given values are 1 standard deviation away from the mean and we have to find what percentage of values are within 1 standard deviation of the mean.

From the first listed point of empirical formula, we can say that 68% of the data values lie within 1 standard deviation of the mean. Therefore, 68% of the diameters are between 7.06 cm and 7.78 cm

Approximately 68% of the apples have diameters between 7.06cm and 7.78cm.

To determine the percentage of apples with diameters between 7.06cm and 7.78cm, we can use the empirical rule which is based on the standard deviation. According to the empirical rule, approximately 68% of the apples will fall within one standard deviation of the mean, which in this case is between 7.42 - 0.36 and 7.42 + 0.36. In other words, between 7.06cm and 7.78cm. Therefore, approximately 68% of the apples have diameters between 7.06cm and 7.78cm.

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Answer:

  18%

Step-by-step explanation:

Of the 50 soccer players, 4 play soccer and lacrosse, and 5 play soccer and football. That is, 9 of the 50 players also play one of the other sports.

 9/50 × 100% = 18%

18% of soccer players also play another sport.

Answer:

THE ANSWER IS (6,-9)

Step-by-step explanation:

The solution to the equation is ( 6 , -9 )

The value of x = 6

The value of y = -9

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

y = x - 15   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = -2x + 3   be equation (2)

Substituting the value of equation (1) in equation (2) , we get

x - 15 = -2x + 3

On simplifying the equation , we get

Adding 2x on both sides of the equation , we get

x + 2x - 15 = 3

Adding 15 on both sides of the equation , we get

3x = 18

Divide by 3 on both sides of the equation , we get

x = 6

Therefore , the value of x is 6

Substitute the value of x in equation (1) , we get

y = x - 15

y = 6 - 15

y = -9

Therefore , the value of y is -9

Hence , the values of x and y of the equation is ( 6 , -9 )

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Final answer:

To simplify √72 by removing all perfect squares, you factor 72 into 2³ × 3², then take out the square root of 4 and 9 to get 6√(2) as the simplified result.

Explanation:

To simplify the square root of 72 and remove all perfect squares from inside the square root, you first need to factor 72 into its prime factors. The prime factorization of 72 is 2³ × 3². This can be rewritten as (2² × 3²) × 2, which simplifies to (4 × 9) × 2.

Since the square root of 4 and 9 are perfect squares, you can take them out of the square root, resulting in √(4) × √(9) × √(2) = 2 × 3 × √(2) = 6√(2).

Therefore, the simplified form of √72 is 6√(2), which removes all perfect squares from inside the square root.

Answer:

EX=-$1

Step-by-step explanation:

Expected Value of Probability Distribution

Assume a discrete probability distribution is

[tex]P=\{p1,p2,p3,...pn\}[/tex]

For

[tex]X=\{x1,x2,x3,...xn\}[/tex]

The expected value is

[tex]EX=\sum x_i.p_i[/tex]

We have two possible outcomes from our random experience: The sum of the die is 7 or different from 7. If it sums 7, the player wins $9, otherwise, they lose $3. Thus

[tex]x=\{9,-3\}[/tex]

We must find the probability of having a 7. Each dice can be a 1, 2, 3 ,4 , 5, or 6. The combinations to sum 7 are 1+6, 2+5, 3+4, 4+4, 5+2, and 6+1. That is 6 possibilities out of 36 in total. The probability of having a 7 is

[tex]\displaystyle p_1=\frac{6}{36}=\frac{1}{6}[/tex]

The probability of not getting 7 is the negation of the previous event

[tex]\displaystyle p_2=1-\frac{1}{6}=\frac{5}{6}[/tex]

The probability set is:

[tex]\displaystyle P=\left\{\frac{1}{6},\frac{5}{6}\right\}[/tex]

The expected value is:

[tex]\displaystyle EX=9\cdot \frac{1}{6}-3\cdot \frac{5}{6}[/tex]

[tex]\displaystyle EX=\frac{3}{2}-\frac{5}{2}=-1[/tex]

Therefore, the player can expect to lose $1

The expected value of the game "Under-or-Over-Seven" is a loss of $1, computed by considering the probabilities of winning $9 or losing $3 based on dice sums.

To compute the expected value of the game, we need to consider all possible outcomes and their associated probabilities.

1. The sum of two fair dice can range from 2 to 12.

2. The probability of each sum can be calculated by considering all possible combinations of the dice.

Here's the breakdown of the sums and their probabilities:

- Sum of 2: Probability = 1/36

- Sum of 3: Probability = 2/36

- Sum of 4: Probability = 3/36

- Sum of 5: Probability = 4/36

- Sum of 6: Probability = 5/36

- Sum of 7: Probability = 6/36

- Sum of 8: Probability = 5/36

- Sum of 9: Probability = 4/36

- Sum of 10: Probability = 3/36

- Sum of 11: Probability = 2/36

- Sum of 12: Probability = 1/36

Now, let's calculate the expected value:

[tex]\[ E(X) = (P(X=7) \times \$9) + (P(X\neq7) \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) + (\frac{30}{36} \times (-\$3)) \][/tex]

[tex]\[ E(X) = (\frac{6}{36} \times \$9) - (\frac{30}{36} \times \$3) \][/tex]

[tex]\[ E(X) = \frac{54}{36} - \frac{90}{36} \][/tex]

[tex]\[ E(X) = \frac{-36}{36} \][/tex]

E(X) = -$1

So, the expected value of the game is a loss of $1.

Answer: 3

Step-by-step explanation:

E2020 answer

Answer:

3

Step-by-step explanation:

answer on edge

Answer:

9x - 3y = -12

-9x +5y = -1

2y = -13

y = -13/2

-3x - 13/2 = 8/2

-3x = 21/2

-6x = 21

x = -21/6 = -7/2

(-7/2, -13/2)

Answer:

473 milliliters in 1 pint

Step-by-step explanation:

divide 946 by 2

Answer:

There are 473 milliliters in 1 pint so 5 pints would be 2,365

Step-by-step explanation:

Answer:

0.00198

Step-by-step explanation:

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

⁵²C₅ = 2,598,960 ways.

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

Note that of the 52 cards, each suit has 13 cards, So, ⁴C₁ represents selecting a suit out of 4 different suits and ¹³C₅ represents selecting 5 cards out of 13 cards thay a suit contains.

So, the probability of a flush

= 5148 ÷ 2,598,960 = 0.0019807923 = 0.00198 to 5 d.p

Hope this Helps!!!

The probability of  five cards of the same suit is 0.00198

Probability of any event happen is calculated by, divide favourable number of outcomes by total number of outcomes.

The number of total ways that 5 cards can be selected from a deck of 52 cards is given as

                    Total outcomes =     ⁵²C₅ = 2598960  

Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by

         Number of favourable outcomes =       ⁴C₁ × ¹³C₅ = 4 × 1287 = 5148

 ⁴C₁ represents selecting a suit out of 4 different suits .

¹³C₅ represents selecting 5 cards out of 13 cards that a suit contains.

Therefore, the probability that a five-card poker hand contains a flush,

                              =[tex]\frac{5148}{2598960}=0.00198[/tex]

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Answer:

Type of investigation = Experimental

Dependent variable = The reaction time of the controllers

Independent variable =  Controlled breaks

Step-by-step explanation:

A researcher is examining the effects of controlled breaks on reaction times of Air Traffic Controllers.

The controllers are randomly assigned to two groups.

Group 1 and Group 2

Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics.

Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices.

After the breaks, the reaction times of controllers in the two groups were measured.

Type of investigation?

This is clearly an experimental type of investigation where the researcher performs an experiment and after that measures the results.

Type of variables involved?

In this experimental investigation, we have both dependent as well as independent variable.

The controlled break is the independent variable since it can be manipulated by the researcher.

The reaction time of the controllers is the dependent variable since it is being measured and is expected to get affected when the independent variable is manipulated that is controlled breaks.

Final answer:

This is an experimental investigation where the effects of controlled breaks on reaction times of Air Traffic Controllers are examined. The independent variable is the type of break, and the dependent variable is the reaction times of the controllers.

Explanation:

The type of investigation used in this study is an experimental investigation. The independent variable in this study is the type of break given to the Air Traffic Controllers, with two levels: controlled breaks in a quiet room and breaks in a common area with allowed talking, TV, and electronic devices. The dependent variable is the reaction times of the controllers after their breaks. There are no extraneous variables mentioned in the given information.

Answer:

4, -4

Step-by-step explanation:

Take the  (+2)th  root of both sides of the  equation  to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

x  =  4 , − 4

The plane would travel approximately 4533.33 miles in 6 hours.

To find the distance the plane would travel in 6 hours, we can use the formula:

Distance = Speed × Time

Given that the plane travels at 3400 miles in 8 hours, we can substitute the values into the formula:

Distance = 3400 × 8/6

Simplifying the expression:

Distance = 4533.33 miles

Therefore, the plane would travel approximately 4533.33 miles in 6 hours.

Answer:

$2,520

Step-by-step explanation:

The simple Interest earned on an deposit, P at a rate of r% for a period of t years is calculated using the formula:

[tex]\text{ Simple Interest}=\dfrac{Principal*Time*Rate}{100}[/tex]

P=$10,500

R=6%

T=4 years

Therefore:

[tex]\text{ Simple Interest}=\dfrac{10500*4*6}{100}\\=\$2,520[/tex]

Sally will earn $2520 interest after 4 years.

Answer:

(1,1) is a solution of the system.

Step-by-step explanation:

Let's solve the system.

y = 2x - 1

5x - 4y = 1

In the first equation, y is already separated as a function of x. So we replace in the second equation;

5x - 4(2x - 1) = 1

5x - 8x + 4 = 1

4 - 1 = 8x - 5x

x = 1

y = 2x - 1 = 2(1) - 1 = 1

(1,1) is a solution of the system.

Answer:

See below.

Step-by-step explanation:

A year has 12 months and 365 days.

3 months: 3/12 year = 1/4 year

55 days: 55/365 year = 11/73 year

1 month: 1/12 year

7 months = 7/12 year

120 days = 120/365 year = 24/73 year

Answer:

3 months = 3/12 | 55 days = 55/365 | 1 month = 1/12 | 7 months = 7/12 | 120 days = 120/365

Step-by-step explanation:

All you have to do is write the numbers with the total underneath. With months, it is out of 12 because there are 12 months in a year. With days, it is out of 365 days because there are 365 days in total in a year.

If needed, simplify the answer to its simplest form

Answer:

choosing 1 red marble ; choosing 1 white marble, replacing it, and choosing another white marble ; and choosing 1 white marble

Step-by-step explanation:

There are 2+3+5 = 10 marbles.  The probability of choosing 1 blue marble is 2/10 = 1/5; this is not greater than 1/5.

The probability of choosing 1 red marble is 3/10; this is greater than 2/10, which is the same as 1/5.

The probability of choosing 1 red marble is 3/10; not replacing it and choosing a blue marble would then be a probability of 2/9.  Together this is a probability of 3/10(2/9) = 6/90 = 3/45; this is smaller than 9/45, which is the same as 1/5.

The probability of choosing 1 white marble is 5/10 = 1/2; replacing it and choosing another white marble would be 1/2.  Together this is a probability of 1/2(1/2) = 1/4; this is greater than 4/20, which is the same as 1/5.

The probability of choosing 1 white marble is 5/10 = 1/2.  This is greater than 2/10, which is the same as 1/5.

Answer:

b,d,e are the awnsers

Step-by-step explanation:

0.555555556 so that's it hope this helped

Answer:

0.5

Step-by-step explanation:

Because I said so

Answer:

-9

Step-by-step explanation:

Plug in 15 for x in the equation

you should get (1/5*15) -12

multiply 1/5 and 15 to get 3

then 3-12=-9

therefore the answer is -9

Step-by-step explanation:

The Length ,

L

=

284

f

t

.

Explanation:

Given:

Rectangle

Area,

A

=

8804

f

t

2

let W bet he width of the rectangle

L be the length of the rectangle

L

=

10

W

−

26

E

q

u

a

t

i

o

n

1

substitute to

e

q

u

a

t

i

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2

A

=

(

L

)

(

W

)

e

q

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a

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i

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2

A

=

(

10

W

−

26

)

(

W

)

8804

=

(

10

W

−

26

)

(

W

)

factor

8804

=

2

(

5

W

−

13

)

(

W

)

divide both sides by 2

4402

=

(

5

W

−

13

)

(

W

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4402

=

5

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W

transposing 4402 to the right side of the equation

0

=

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−

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W

−

4402

by quadratic formula

W

=

−

(

−

13

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+

√

(

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(

5

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(

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4402

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169

+

88040

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+

297

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310

10

W

=

31

ft

Thus ,

L

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10

W

−

26

=

10

(

31

)

−

26

L

=

284

f

t

.

answer

W

=

−

(

−

13

)

−

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this is discarded since this will yield a negative

To find the length of the rectangle, set up an equation using the given information. Solve the quadratic equation to find the width and substitute it back to find the length.

To find the length of the rectangle, we can set up an equation using the given information. Let's assume the width of the rectangle is 'w' meters. According to the problem, the length of the rectangle is 10 times its width minus 11 meters, so it can be represented as 10w - 11 meters. The area of the rectangle is given as 9888 square meters. We know that the formula for the area of a rectangle is length times width, so we can write the equation as:

w (10w - 11) = 9888

Expanding the equation and rearranging terms, we get:

10w^2 - 11w - 9888 = 0

Now, we can solve this quadratic equation for 'w' and find the width of the rectangle. Once we have the width, we can substitute it back into the expression for the length (10w - 11) to find the length of the rectangle.

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Answer: Obviously chose Pizza Hut, as no other pizza place can out pizza the hut.

Answer:

I devour the souls of the innocent

Step-by-step explanation:

XD what question is this???

Answer:

0.0498 = 4.98%

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.

Each minute has 60 seconds.

So a rate of 1 inquire each 4 seconds.

The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately

Mean of 1 inquire each 4 seconds, so for 12 seconds [tex]\mu = \frac{12}{4} = 3[/tex]

This probability is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

The probability that it takes more than 12 seconds for the first inquiry to arrive in a Poisson process at a rate of 15 inquiries per minute is calculated using the exponential distribution formula: e^{-15*0.2}.

The student is asking for the probability that it takes more than 12 seconds for the first inquiry to arrive at a record message device, with inquiries arriving according to a Poisson process with a rate of 15 inquiries per minute. Since the time between arrivals in a Poisson process follows an exponential distribution, we can calculate this probability using the exponential distribution's formula.

The mean interval between inquiries is the inverse of the rate, which for 15 inquiries per minute is 1/15 minute per inquiry, or 4 seconds per inquiry. To convert minutes to seconds, multiply by 60. Therefore, the average interval is 4 seconds.

The exponential distribution gives us the probability that the time until the first event (inquiry) exceeds a certain amount, t, which is P(T > t) = e-λ*t, where λ is the rate and T is the time. In this case, t is 12 seconds or 0.2 minutes. Therefore, the probability (P) that the time is more than 12 seconds is: P(T > 0.2) = e-15*0.2.

Answer: the volume is: 280.8

Step-by-step explanation:

volume= length x width x height

Answer:

140.4 cm^3

Step-by-step explanation:

The formula for calculating volume of a triangular prism : 1/2 × h × l × b

1/2 × 4 × 9 × 7.2 = 140.4 cm^3

Using a system of equations, it was determined there were 336 bottles worth 5 cents each and 82 bottles worth 10 cents each, summing up to a total of $25.

The local organization collected 418 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. The total value was $25.00. We need to find out how many bottles were worth 5 cents and how many were worth 10 cents.

We can set up two equations to solve this problem using algebra. Let's assume that the number of 5-cent bottles is x and the number of 10-cent bottles is y.

The first equation will represent the total number of bottles: x + y = 418.

The second equation will represent the total value of these bottles: 0.05x + 0.10y = 25.

To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals and then apply the method of substitution or elimination to find the values of x and y.

Rewrite the second equation without decimals: 5x + 10y = 2500.

Multiply the first equation by 5: 5x + 5y = 2090.

Subtract the modified first equation from the second equation: 5y = 410.

Divide both sides by 5 to find y: y = 82.

Substitute y = 82 into the first equation and solve for x: x = 418 - 82 = 336.

Therefore, there were 336 bottles or cans worth 5 cents each and 82 bottles or cans worth 10 cents each.

Answer:

The ratio is 2:1

Step-by-step explanation:

This is since there are 2 times the amount of hands as there are phones