How many times must a fair coin be flipped in order to ensure that there is at least a 99% chance of
getting at least one tail?

Answer:

\(169\)

Step-by-step explanation:

\(13*13=13^2=169\)

The divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

To find the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k, you need to take the divergence operator (∇ · F).

The divergence of a vector field in Cartesian coordinates is given by the following formula:

∇ · F = (∂Fx/∂x) + (∂Fy/∂y) + (∂Fz/∂z),

where Fx, Fy, and Fz are the x, y, and z components of the vector field F, respectively.

In this case, we have:

Fx = (5x^2 + 7 - sin(xz)),

Fy = 0, and

Fz = (5x^2 + 7 - sin(xz)).

Taking the partial derivatives, we get:

∂Fx/∂x = 10x - zcos(xz),

∂Fy/∂y = 0, and

∂Fz/∂z = 10x - zcos(xz).

Now, substituting these derivatives into the divergence formula, we have:

∇ · F = (10x - zcos(xz)) + 0 + (10x - zcos(xz)).

Simplifying further, we get:

∇ · F = 20x - 2zcos(xz).

Therefore, the divergence of the vector field F(x, y, z) = (5x^2 + 7 - sin(xz))i + 0j + (5x^2 + 7 - sin(xz))k is 20x - 2zcos(xz).

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Answer:

x=51

Step-by-step explanation:

166=13+3x

153=3x

51=x

I hope this is correct and helps you!

Answer:

12 miles i think

Step-by-step explanation:

Because if you divide 48 by 4 it will equal to 12

To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.

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Complete question:

A combination of values that, when arranged correctly, result in a final value. true/false

Answer:

x(x-1)=72 x=9

Step-by-step explanation:

In a process with rework, we find the bottleneck as the resource with the highest implied utilization.

The above statement is True.

Bottleneck:

A bottleneck is a process in a process chain where the performance of the entire chain is degraded due to limited capacity. Bottlenecks lead to downtime, excess inventory, customer pressure and low employee morale.

Another example is a surface mount board assembly line with multiple pieces of equipment lined up. A common-sense strategy in general is to set and move the bottleneck until the end of the process, leading the better and faster machines to keep the printed circuit board (PCB) powered at all times, and preventing the slower machines from coming to a complete halt. Strategies that can lead to detrimental (or destructive) significant overall process drawbacks.

The product with the highest usage (again, the resource with the lowest capacity is not always the case) is the bottleneck. Defines the bottleneck as the resource with the highest specified usage in a process that involves rework. Better predictions can be identified by simply averaging the prediction errors. In the manufacturing process, each flow unit must have the same output. The recycling process requires only one turnaround time.

Rework also has a processing time different from that of a typical flow unit.

Complete Question:

In a process with rework, we find the bottleneck as the resource with the highest implied utilization. T/F?

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(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

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Answer: 12x + 8

Step-by-step explanation: 6x +2x + 7x - 3x + -8 + 10 +6

                                             15x - 3 + 8

                                             12x - 8

Answer:

Thats not a proper question

Step-by-step explanation:

Answer:

$5.24

Step-by-step explanation:

The 16 feet distance from Chase to his older brother and the 20 feet distance from his older brother to his younger sister, using Pythagorean, Theorem, indicates that the distance from Chase to his younger sister in the assembly is 12 feet

Pythagorean Theorem states how the length of the sides of a right triangle are related, that is the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.

The location of Chase, his younger sister, and his older brother forms a right triangle.

The distance from Chase to his older brother = A leg of the right triangle

The distance from Chase to his sister = A second leg of the right triangle

The distance from his older brother to his sister = The hypotenuse side of a right triangle

From the question, we get;

Distance between Chase and his older brother = 16 feet

Distance between Chase's older brother and his sister = 20 feet

According to Pythagorean Theorem, we get;

Distance between Chase and his younger sister = √(20² - 16²) = 12

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To find the value of the line integral, we need to integrate the dot product of the vector field F with the differential vector dr along path C.

(a) Using the parametric equation r1(t) = ti - (t-4)j, we can calculate dr/dt = i - j and substitute it into the line integral formula:

∫ F · dr = ∫ (yexyi + xexyj) · (i-j) dt

= ∫ (ye^(t-i) - xe^(t-i)) dt from t=0 to t=4

= [ye^(t-i) + xe^(t-i)] from t=0 to t=4

= (4e^3 - 4e^-1) + (0 - 0)

= 4e^3 - 4e^-1

(b) To use an alternative path for easier integration, we can check if the vector field F is conservative.

∂M/∂y = exy + xexy = ∂N/∂x

where F = M(x,y)i + N(x,y)j

Thus, F is conservative and we can use the path independence property of conservative vector fields.

Going from (0,4) to (0,0) to (4,0) to (0,4) is equivalent to going from (0,4) to (4,0) to (0,0) to (0,4) and back to the starting point.

Using Green's theorem, we have:

∫ F · dr = ∫ M dy - ∫ N dx = ∫∫ (∂N/∂x - ∂M/∂y) dA

= ∫∫ (exy + xexy - exy - xexy) dA

= 0

Therefore, the value of the line integral along the closed path is zero.

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To find the equation of a line in slope-intercept form (y = mx + b) that passes through the points (-2, 2) and (7, -4), we first need to determine the slope (m) of the line.

The slope (m) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates (-2, 2) and (7, -4) into the formula, we get:

m = (-4 - 2) / (7 - (-2)) = -6 / 9 = -2/3

Now that we have the slope (m), we can use it along with one of the given points to find the y-intercept (b).

Let's use the point (-2, 2) and substitute the values into the slope-intercept form:

2 = (-2/3)(-2) + b

2 = 4/3 + b

b = 2 - 4/3

b = 2/3

Therefore, the equation of the line in slope-intercept form is:

y = (-2/3)x + 2/3

By using the formula for slope, we calculate the slope of the line passing through the given points. Substituting one of the points into the slope-intercept form equation, we solve for the y-intercept. Finally, we combine the slope and y-intercept to obtain the equation of the line in slope-intercept form, which is y = (-2/3)x + 2/3.

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Answer:

4w + 12

Step-by-step explanation:

Perimeter of a rectangle = 2(length + width)

Let

Width of the rectangle = w feet

Length of the rectangle = (w + 6) feet

Perimeter of a rectangle = 2(length + width)

= 2{(w+6) + w}

= 2(w + 6 + w)

= 2(2w + 6)

= 4w + 12

Perimeter of a rectangle = (4w + 12) feet

Step-by-step explanation:

2x-6: 6x-4

Use any value to represent x

Let's use 1

2(1)-6: 6(1)-4

2-6 : 6-4

-4 : 2

Write in simplest form by dividing by 2

-2:1

Now do the same in all the answers above, use 1 for the value of x

1. - 2:1 is equivalent

2. 1-3 : 3(1)-2 = - 2:1 Equivalent

3. 3(1) : 1 = 3 :1 not equivalent

4. 4(1) - 12 : 12(1) - 8 = - 8 : 4 (

Simplify by dividing by 4, you get - 2 :1 equivalent

5. 1-1 : 1 - 2 = 0 : - 1 not equivalent

Less than half of the surveyed internet users have posted photos or videos online. To determine if less than half of internet users have posted photos or videos online based on the poll, we can follow these steps:

1. Calculate the proportion of users surveyed who have posted photos or videos online.
2. Compare the proportion to 0.5 (which represents half).

Step 1: Calculate the proportion
The poll surveyed 1,765 internet users, and 865 of them posted a photo or video online. To calculate the proportion, we can divide the number of users who posted (865) by the total number of users surveyed (1,765):

Proportion = 865 / 1,765 ≈ 0.49

Step 2: Compare the proportion to 0.5
Since 0.49 is less than 0.5, it appears that less than half of the surveyed internet users have posted photos or videos online.

However, we cannot conclude that this is true for all internet users, as the poll surveyed a limited sample size of 1,765 users. A larger, more representative sample may be needed to draw a more accurate conclusion.

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Complete Question:

a poll surveyed 1765 internet users and found that 865 of them had posted a photo or video online. can you conclude that less than half of internet users have posted photos or videos online? use the ∝ = 0.01 level of significance and the P value method with the TI-84 calculator.

The samples of size n = 2 that can be drawn from this population is 28

From the question, we have the following parameters that can be used in our computation:

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Answer:

Therefore, the integer that is congruent to 5 modulo 13 is 122.

Step-by-step explanation:

Answer:

(4\(\sqrt{3}\))/3

Step-by-step explanation:

From the diagram,

Applying

sinθ = Opposite/Hypotenuse................. Equation 1

From the diagram,

Given: θ = 60°, Opposite = 2, Hypotenuse = X

Substitute these values into equation 1

sin60°  = 2/X

make X the subject of the equation

X = 2/sin60°.................. Equation 2

But,

sin60° = \(\frac{\sqrt{3} }{2}\)

Therefore,

X = 2/( \(\frac{\sqrt{3} }{2}\))

X = (2×2)/\(\sqrt{3}\)

X = 4/\(\sqrt{3}\)

Rationalising the denominator,

X = (4/\(\sqrt{3}\))×(\(\sqrt{3}\)/\(\sqrt{3}\))

X = (4\(\sqrt{3}\))/3

The value of result in the following expression will be 0 if x has the value of 12:

result = x > 100 ? 0 : 1.

The expression given is known as a ternary operator.

It's a short form of if-else.

The ternary operator is written with three arguments separated by a question mark and a colon:

`variable = (condition) ? value_if_true : value_if_false`.

Here, `result = x > 100 ? 0 : 1;` is a ternary operator, and its meaning is the same as below if-else block.if (x > 100)  {  result = 0; }  else {  result = 1; }

As per the question, we know that if the value of `x` is `12`, then the value of `result` will be `0`.

Hence, the answer is `0`.

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Answer:

-2, -1

Step-by-step explanation:

Answer:

(-1 , -2)

Explanation:

Answer:

1km please brain list me pls

The distance between the end of the ramp and the bottom of the platform is about 15.87 feet. Therefore, the wheelchair ramp is 15.87 feet far from the end of the ramp to the bottom of the platform.

We will use the Pythagorean theorem (a²+b²=c²)

To solve,

Let's take that a and b are the legs, c is the hypotenuse

Insert, the given values in the Pythagoras theorem i.e. in the equation  (a²+b²=c²)

2² + x² = 16²

2² + x² = 16 × 16

Now we will solve for x

x² + 2² = 256

x² + 2×2 = 256

x² + 4 = 256

x² = 256-4

x²= 252

x= \(\sqrt{252}\)

x= 15.87

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Answer:

1/20

Step-by-step explanation:

\( \frac{3}{4} \div \frac{15}{1} \\ \frac{3}{4} \times \frac{1}{15} \\ \frac{3}{60} = \frac{1}{20} \)

Answer:

1/20

Step-by-step explanation:

For the given exercise

a. f(g(2)) = 67

b. f(g(x)) = 18x^2 - 30x + 16

c. g(f(x)) = 6x^2 + 2

d. (g∘g)(x) = 9x - 20

e. (f∘f)(-2) = 69

a. To find f(g(2)) of given function, we substitute x = 2 into g(x) first: g(2) = 3(2) - 5 = 1. Then we substitute this result into f(x): f(1) = 2(1)^2 + 1 = 3. Therefore, f(g(2)) = 3.

b. To find f(g(x)), we substitute g(x) into f(x): f(g(x)) = 2(g(x))^2 + 1 = 2(3x - 5)^2 + 1 = 18x^2 - 30x + 16.

c. To find g(f(x)), we substitute f(x) into g(x): g(f(x)) = 3(f(x)) - 5 = 3(2x^2 + 1) - 5 = 6x^2 + 2.

d. To find (g∘g)(x), we perform the composition of g(x) with itself: (g∘g)(x) = g(g(x)) = g(3x - 5) = 3(3x - 5) - 5 = 9x - 20.

e. To find (f∘f)(-2), we perform the composition of f(x) with itself: (f∘f)(-2) = f(f(-2)) = f(2(-2)^2 + 1) = f(9) = 2(9)^2 + 1 = 163. Therefore, (f∘f)(-2) = 163.

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Answer:

after working for at least 10 1/4 years

Step-by-step explanation:

After working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

A quadratic equation, \(ax^{2} +bx+c=0\) is solved by

\(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

Given function \(f(x)=x^4-10x^2+10000\)

Function that has monthly salary $20,000 will be \(x^4-10x^2+10000=20000\)

\(x^4-10x^2+10000-20000=0\)

\(x^4-10x^2-10000=0\)

Now using the formula \(x=\frac{-b \pm \sqrt{b^2-4ac} }{2}\)

\(x^2=\frac{10 \pm \sqrt{10^2+40000} }{2}\)

\(x^2=\frac{10 \pm \sqrt{40100} }{2}\)

\(x^2=\frac{10 \pm 200.2}{2}\)

\(x^2=5 \pm 100.1\)

\(x^2=105.1\)

\(x=\sqrt{105.1}\)

\(x=10.25\)

Hence, after working for at least  10 1/4 years  a project manager would be eligible for a $20,000 monthly salary.

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