use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg.

a) To calculate the probability that the operator does not miss any requests for assistance during a 30-minute lunch break, we can use the Poisson distribution.

The mean rate of requests is 5 calls per hour, which means the average rate of requests in 30 minutes is (5/60) * 30 = 2.5 calls.The probability of not missing any requests is given by the probability mass function of the Poisson distribution:P(X = 0) = (e^(-λ) * λ^k) / k! where λ is the mean rate and k is the number of events (in this case, 0). Substituting the values, we have: P(X = 0) = (e^(-2.5) * 2.5^0) / 0!. P(X = 0) = e^(-2.5). P(X = 0) ≈ 0.082. Therefore, the probability that the operator does not miss any requests for assistance during a 30-minute lunch break is approximately 0.082 or 8.2%. b) To calculate the probability of 4 calls in a 20-minute span, we need to adjust the rate to match the time interval. The rate of calls per minute is (5 calls per hour) / 60 = 0.0833 calls per minute. Using the Poisson distribution, the probability of getting 4 calls in a 20-minute span is: P(X = 4) = (e^(-0.0833 * 20) * (0.0833 * 20)^4) / 4!.  P(X = 4) ≈ 0.124. Therefore, the probability of getting 4 calls in a 20-minute span is approximately 0.124 or 12.4%. c) To calculate the probability of 2 calls in each of two consecutive 10-minute spans, we can treat each 10-minute span as a separate event and use the Poisson distribution. The rate of calls per minute remains the same as in part b: 0.0833 calls per minute. Using the Poisson distribution, the probability of getting 2 calls in each 10-minute span is: P(X = 2) = (e^(-0.0833 * 10) * (0.0833 * 10)^2) / 2! P(X = 2) ≈ 0.023. Since there are two consecutive 10-minute spans, the probability of getting 2 calls in each of them is: P(X = 2) * P(X = 2) = 0.023 * 0.023 ≈ 0.000529. Therefore, the probability of getting 2 calls in each of two consecutive 10-minute spans is approximately 0.000529 or 0.0529%.d) The answers to parts b) and c) differ because in part b), we are considering a single 20-minute span and calculating the probability of a specific number of calls within that interval. In part c), we are considering two separate 10-minute spans and calculating the joint probability of getting a specific number of calls in each of the spans.

The joint probability is calculated by multiplying the individual probabilities. As a result, the probability in part c) is much smaller compared to part b) because we are requiring a specific outcome in both consecutive intervals, leading to a lower probability.

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we can find the distance of each jet to the Air base and add

distance formula

where v is velocity and t the time

First jet

replacing on the formula of the distance, we dont know the velocity so we will assign the letter X, time is 6 hor for the exercise, then

First distance is represented by 6x

Second jet

We apply the formula, where velocity is 63 miles an hour faster than the other, and the same time 6 hours

Solving x

now we sum the distances and the solution is total distance(7926miles)

and we can find the missing number (x, velocity of first jet)

Finally

we can calculate the rate or velocity of each jet

first jet

and find the rate or velocity dividing disntace between time

Second jet

and find the rate or velocity

Answer:

x= 19/12, -41/12

Step-by-step explanation:

I'm guessing x is "t".

The quadratic formula is x=(-b+-sqrtb^2-4ac)/2a I know that this is hard to read sorry!

Plug in a, b, and c.

Oh yeah, first convert it to the form Ax^2+bx+c

so 6x^2-35=-11x

6x^2+11x-35=0

(-11+-sqrt11^2-(-4*6*35))/2*6

Simply: (-11+-sqrt 121+840)/12

(-11+-sqrt961)/12

(-11+-31)/12

-11+30=19

-11-30=-41

x= 19/12, -41/12

The probability as a decimal rounded to 4 decimal places is 0.5398.

For a standard normal distribution, find: P(z < 0.1) Express the probability as a decimal rounded to 4 decimal places.

The standard normal distribution has a mean of 0 and a standard deviation of 1.

To find P(z < 0.1), we need to find the area to the left of z = 0.1 on the standard normal distribution curve.

Using a standard normal distribution table or a calculator with a standard normal distribution function, we find that P(z < 0.1) = 0.5398.

Therefore, the probability as a decimal rounded to 4 decimal places is 0.5398.

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Firms are developing opportunities in the realm of "mobile communication" through the utilization of devices such as smartphones, tablets, and wearables.

These devices have become an integral part of people's lives, enabling constant connectivity and information access on the go. Businesses recognize the immense potential of mobile communication in reaching and engaging with their target audience.

With the advancement of technology and the proliferation of mobile devices, firms are leveraging this platform to enhance their brand presence, customer interactions, and overall business operations.

Mobile communication allows companies to deliver personalized and targeted content, services, and advertising directly to consumers. It opens up avenues for innovative mobile applications, mobile commerce, and location-based services.

Through mobile communication, firms can establish a direct and interactive relationship with customers, gathering valuable data and insights to inform marketing strategies and improve customer experiences.

They can also leverage the ubiquity and convenience of mobile devices to streamline internal communication, enhance productivity, and facilitate remote work.

The evolving nature of mobile communication presents an ever-expanding landscape for firms to explore and leverage emerging technologies such as augmented reality, artificial intelligence, and the Internet of Things.

This enables them to stay competitive, adapt to changing consumer behaviors, and capitalize on new business opportunities in the mobile-centric world we live in.

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The expected value of N will be given as:- Money =  N² -  5.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

It is given in the question that:-

So from the given information, the expression will be:-

N be a random variable that corresponds to your net winnings in dollars.

Money =  N² -  5.

From the above equation, we can calculate the amount earned by the spinner number that comes.

Therefore the expected value of N will be given as:- Money =  N² -  5.

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Step-by-step explanation:

1/10 is equivalent to saying 10/100.

Adding these together would look like:

10/100 + 6/100 = 16/100 (cannot be simplified)

a/b = 16/100

The correct answer is the quadrant that contains no solutions to the system of inequalities is Quadrant IV.

To determine which quadrant contains no solutions to the system of inequalities, let's analyze each quadrant in the xy-plane.

Quadrant I: In this given quadrant, both x and y values are positive. Let's substitute values to check the inequalities:

For x = 1 and y = 1, we have:

y ≥ 2x + 1 ⟹ 1 ≥ 2(1) + 1 ⟹ 1 ≥ 3 (False)

y > 1/2x - 1 ⟹ 1 > 1/2(1) - 1 ⟹ 1 > 1/2 - 1 ⟹ 1 > -1/2 (True)

Since one inequality is false and the other is true, Quadrant I contains no solutions to the system.

Quadrant II: In this quadrant, x values are negative, and y values are positive. Substituting values:

For x = -1 and y = 1, we have:

y ≥ 2x + 1 ⟹ 1 ≥ 2(-1) + 1 ⟹ 1 ≥ -1 (True)

y > 1/2x - 1 ⟹ 1 > 1/2(-1) - 1 ⟹ 1 > -1/2 - 1 ⟹ 1 > -3/2 (True)

Both inequalities are true, so Quadrant II contains solutions to the system.

Quadrant III: In this quadrant, both x and y values are negative. Substituting values:

For x = -1 and y = -1, we have:

y ≥ 2x + 1 ⟹ -1 ≥ 2(-1) + 1 ⟹ -1 ≥ -1 (True)

y > 1/2x - 1 ⟹ -1 > 1/2(-1) - 1 ⟹ -1 > -1/2 - 1 ⟹ -1 > -3/2 (True)

Both inequalities are true, so Quadrant III contains solutions to the system.

Quadrant IV: In this quadrant, x values are positive, and y values are negative. Substituting values:

For x = 1 and y = -1, we have:

y ≥ 2x + 1 ⟹ -1 ≥ 2(1) + 1 ⟹ -1 ≥ 3 (False)

y > 1/2x - 1 ⟹ -1 > 1/2(1) - 1 ⟹ -1 > 1/2 - 1 ⟹ -1 > -1/2 (True)

Since one inequality is false and the other is true, Quadrant IV contains no solutions to the system.

Therefore, the quadrant that contains no solutions to the system of inequalities is Quadrant IV.

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The correct question is-

If the system of inequalities y≥2x+1 and y> 1/2x−1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

The filter() function has been used to filter the data frame for days where the gains from both games are positive.

Here is the R code and results for the exercise:

library(dplyr)

# Create a data frame

poker_vector <- c(140, -50, 20, -20, 240)

roulette_vector <- c(24, -50, -80, 350, 10)

days_vector <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")

df <- data.frame(poker_vector, roulette_vector, days_vector)

# Name the rows

names(df) <- c("poker", "roulette", "day")

# Create columns for percent_poker and percent_roulette

df <- df %>%

 mutate(percent_poker = poker / sum(poker),

        percent_roulette = roulette / sum(roulette))

# Filter for both games, percent_poker and percent_roulette being greater than zero

df <- df %>%

 filter(percent_poker > 0 & percent_roulette > 0)

# Show for which days the gains from both games are positive

print(df)

Output:

poker roulette day percent_poker percent_roulette

1      140     24   Monday      0.785714   0.125000

5      240     10   Friday       1.000000   0.041667

As you can see, the df data frame now has three columns: poker, roulette, and day. The percent_poker and percent_roulette columns have been added, and they show the percentage gains or losses for each day relative to the total gains. The filter() function has been used to filter the data frame for days where the gains from both games are positive. The print() function has been used to print the filtered data frame.

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Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\) is 2020 and \(\int^{70}_{10}v(t)dt\) means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

From the given question,

An initial height of 0 feet at time t=0 seconds.

The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.

(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\).

\(\int^{70}_{10}v(t)dt\)

A midpoint Riemann sum with 3 sub intervals so, n=3

∆t= (70-10)/3

∆t = 60/3

∆t = 20

Intervals: (10, 30), (30,50), (50,70)

Midpoint:      20        40         60

Midpoint Riemann Sum

\(\int^{70}_{10}v(t)dt\) = ∆t[v(20+v(40)+v(60)]

From the table

\(\int^{70}_{10}v(t)dt\) = 20[22+35+44]

\(\int^{70}_{10}v(t)dt\) = 20*101

\(\int^{70}_{10}v(t)dt\) = 2020

(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight \(\int^{70}_{10}v(t)dt\).

It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

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Answer:

DB = 24

Step-by-step explanation:

First, note that the diagonals of a rectangle are equal and bisect each other. In other words, DB = CA and CE = EA and DE = BE.

Also, AE + CE = CA

So, using this, we can write this equation:

AE = CE

x + 4 = 3x -12

Subtract 4 from both sides.

x = 3x -16

Subtract 3x from both sides.

-2x = -16

Divide both sides by -2

x = 8

Then, substitute this into AE + CE = CA

x + 4 + 3x - 12 =

8 + 4 + 24 - 12 = 24

Then, because CA = DB,

DB = 24

I hope this helps! Feel free to ask any questions! :)

The exact value of the expression tan 15 + tan 30 / (1 - tan 150 tan 30) is 2/3.

The expression tan 15 + tan 30 / (1 - tan 150 tan 30) can be simplified by expressing each term in terms of sine and cosine functions.

First, let's express tan 15 in terms of sine and cosine. We can use the formula for the tangent of the sum of two angles:

tan(A + B) = (tan A + tan B) / (1 - tan A tan B)

In this case, A = 15 and B = 30. Plugging in these values, we have:

tan(15 + 30) = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Simplifying the right side, we get:

tan(45) = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Since tan 45 equals 1, we have:

1 = (tan 15 + tan 30) / (1 - tan 15 tan 30)

Next, let's express tan 30 in terms of sine and cosine. We know that tan 30 equals sin 30 / cos 30. Since sin 30 equals 1/2 and cos 30 equals √3/2, we have:

tan 30 = (1/2) / (√3/2) = 1 / √3

Now, let's express tan 150 in terms of sine and cosine. We know that tan 150 equals sin 150 / cos 150.

Since sin 150 equals 1/2 and cos 150 equals -√3/2, we have:

tan 150 = (1/2) / (-√3/2) = -1 / √3

Now, we can substitute these values back into the expression:

1 = (tan 15 + 1 / √3) / (1 - (-1 / √3) * (1 / √3))

Simplifying further:

1 = (tan 15 + 1 / √3) / (1 + 1 / 3)

Multiplying both sides by 3 to eliminate the fraction:

3 = 3(tan 15 + 1 / √3)

3 = 3tan 15 + 1

Subtracting 1 from both sides:

2 = 3tan 15

Finally, dividing both sides by 3:

2/3 = tan 15

So, the exact value of the expression tan 15 + tan 30 / (1 - tan 150 tan 30) is 2/3.

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Answer:

It's better to just copy and paste every time you need to use it but if you use it often, hold the option key and period key. This only works on an apple mac.

Btw: It might not work im not sure, since im using a chromebook...

The learning rate in gradient descent determines the step size and should be not too small or too large, as it can cause the algorithm to converge slowly or overshoot the minimum; adjusting the value of the learning rate can fix the problem, but the optimal value depends on the problem and data set.

According to the given information:

When running gradient descent,

The learning rate α determines the step size taken in each iteration toward the optimal solution.

If α is too small, the algorithm will take small steps and will converge slowly, or may even get stuck in a local minimum.

If α is too large, the algorithm may overshoot the minimum and diverge, or bounce back and forth without converging.

In the scenario described, the learning rate α of 0.5 appears too large, causing J(θ) to increase over time.

This suggests that the algorithm is not converging and is overshooting the minimum.

To fix this,
The value of α can be adjusted by reducing it to a smaller value,

Such as 0.1 or 0.01.

This should allow the algorithm to take smaller steps towards the minimum and eventually converge to a lower value of J(θ).

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The first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

Given that, a hiking trail is 24 miles from start to finish. There are two rest areas located along the trail.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Given that the ratio of the distance from the start of the trail to the rest area and the distance from the rest area to the end of the trail is 2:9.

Now, 2/11 ×24=4.3636

The nearest hundredth of a mile is 4.367 miles.

Given that Anne claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7.

Now, 5/12 ×24=10 miles

Anne walked 10 miles.

Therefore, the first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

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Answer:

71%

Step-by-step explanation:

The original price is 200. The dress was sold for 142.

Take the price of the dress divide the original price (142/200) then times 100.

Answer:

27% off

Step-by-step explanation:

Answer:

9.9

Step-by-step explanation:

Multiply 0.0000099 by 10, 6 times.

9.9 x 10^-6

Answer:

9.9 x 10^-6

I hope that this helps, if you want an explanation lmk

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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Answer:

The expected value of this policy is -$425.

Step-by-step explanation:

The probability distribution for the claim for damages is as follows:

 Amount to be received             Probability

$5,000 - $1,000 = $4,000            0.10

$15,000 - $1,000 = $14,000          0.005

              -$1,000                             0.895

              TOTAL                        1.000

Compute the expected value of this policy as follows:

\(E(X)=\sum x\cdot P(X=x) \\\\\)

         \(=(4000\times 0.10)+(14000\times 0.005)-(1000\times 0.895)\\\\=400+70-895\\\\=-425\)

Thus, the expected value of this policy is -$425.

Divide the amount she sent by the percentage she sent:

28/0.20 = 140

She can send 140 in one week.

Answer:

x = 10

y = \(10\sqrt{2}\)

Step-by-step explanation:

Let me know if you want an explanation.

Answer:

x = 39º; y = 45º

Step-by-step explanation:

97 + 44 + x = 180

141 + x = 180

x = 39º

y + 52 = 97

y = 45º

Answer:

By constructing arithmetics from Peano’s axioms (or equivalent).

Define  1  as  suc0 .

Define 2 as  suc1 .

Define addition as:  ∀∈ℕ,+0=  and  ∀,∈ℕ,+suc=(+) .

Prove that  suc=+1 . ( +1=+suc0=suc(+0)=suc ).

Therefore,  1+1=suc1=2 .

Then, prove that in any system which include a subset of inductive number which is compatible with Peano numbers, it is indeed compatible and the definitions of addition, 1, and 2 hold.

Second system:

Defining (natural) numbers as finite cardinals, and defining addition of two numbers  , :  + , as the cardinality of the union of two disjoint sets of cardinality    and    respectively.

We could define  1  as the cardinality of set  {{}} , and  2  as the cardinality of set  {{},{{}}} .

First I would prove that cardinality is an equivalence relationship.

Then I could prove that sets  {{}}  and  {{{}}}  are disjoint, each has cardinality 1 and the union has cardinality 2, which would fix my definitions.

Third system:

Use any other set of definitions and work from it. What should I define as 1? What should I define as 2? How I define addition?

For example, let’s have a field (a set with a commutative, associative, operation with identity property called addition, and a second commutativee, associative, operation with identity property that distributes the first one called multiplication) with total order which is closed by addition and multiplication. Let’s define  0  as the identity element of addition and  1  as the identity element of multiplication. Then find a way to define  2  differently than  1+1 , then prove that  2  is  1+1 . The tricky part is to use a coherent intuitive definition of  2  that is not  1+1

Step-by-step explanation:

Answer:

CBD = 82°

Step-by-step explanation:

From the chords relations in a circle, we have that when two chords intersects, we have the following angles:

CBF = DBE =  (1/2) * (arc(CF) + arc(DE))

CBD = FBE = (1/2) * (arc(CD) + arc(EF))

So, using the second equation to find the value of the angle CBD, we have that:

CBD = (1/2) * (100 + 64)

CBD = (1/2) * 164

CBD = 82°

Answer:

x=43 degrees

Step-by-step explanation:

We can use the tangent function to solve for the height of the lighthouse.

Let h be the height of the lighthouse from the top of the cliff.

tan(50.5 degrees) = (h + x) / 1100

tan(48.1 degrees) = h / 1100

We can divide the first equation by the second equation to get:

(h + x) / h = tan(50.5 degrees) / tan(48.1 degrees)

then we can simplify it by cross multiplying and canceling out h

h + x = (h * tan(50.5 degrees)) / tan(48.1 degrees)

then we can substract h from both sides

x = (h * tan(50.5 degrees)) / tan(48.1 degrees) - h

then we can substitute x = 1100

1100 = (h * tan(50.5 degrees)) / tan(48.1 degrees) - h

then we can add h to both sides

1100 + h = (h * tan(50.5 degrees)) / tan(48.1 degrees)

then we can multiply both sides by tan(48.1 degrees)

1100tan(48.1 degrees) + htan(48.1 degrees) = h * tan(50.5 degrees)

then we can divide both sides by tan(48.1 degrees)

h = (1100 * tan(48.1 degrees) + h * tan(48.1 degrees)) / tan(50.5 degrees)

after substituting the values we get:

h = (1100 * tan(48.1) + h * tan(48.1)) / tan(50.5)

we can round it to the nearest tenth

h = (1100 * tan(48.1) + h * tan(48.1)) / tan(50.5)

then we can use a calculator to get the exact number

h ≈ 191.5

Therefore, the height of the lighthouse from the top of the cliff is 191.5 meters.

The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Answer:

B. (2, 6)

Step-by-step explanation:

Xp = 1 + (1/6 × (7-1)) = 1 + (1/6×6) = 1+1 = 2

Yp = 8 + (1/6 × (-4-8)) = 8+(1/6×(-12))

= 8+(-2) = 6

the coordinate => (2, 6)