Suppose that A, B and C are some events consisting of parts of the probability sample space. Which of the following relationships is NOT always true?
A. (A U B U C) = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)
B. (A U B U C) = Ac - Bc + (A U B) + (A ∩ B)c - (B U C) + (A ∩ B ∩ C)
C. (A U B U C) = Ac + (A ∩ B) + (A ∩ C) + (A ∩ (B U C)c ) - (A ∩ B ∩ C)

The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

To determine where the function f(x) = x^3 - 4x is decreasing, we need to find the intervals where the derivative is negative. Let's calculate the derivative of f(x) first:

f'(x) = 3x² - 4

To find where f'(x) < 0, let's solve the inequality:

3x² - 4 < 0

Adding 4 to both sides gives:

3x² < 4

Dividing both sides by 3 gives:

x² < 4/3

Taking the square root of both sides (and considering both the positive and negative square root) gives:

x < √(4/3) and x > -√(4/3)

Simplifying further, we have:

x < 2√(1/3) and x > -2√(1/3)

The largest open interval where f(x) is decreasing is (-2√(1/3), 2√(1/3)). In interval notation, this can be written as (-2√(1/3), 2√(1/3)).

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We need to investigate the behavior of the derivative of the feature. If the spinoff is negative inside a c program language period, then the quality is lowering over that c language.

Let's begin by finding the derivative of the function f(x) = x^3 - 4x:

f'(x) = 3x^2 - 4

we set f'(x) < zero:

3x^2 - four < zero.

Now, permit's remedy this inequality:

3x^2 < 4,

x^2 < four/three,

x^2 - 4/three < 0.

To find the critical points, we set x^2 - 4/three = zero:

x^2 = 4/three,

x = ±√(4/three),

x = ±2/√3.

We need to test the durations among the essential factors and beyond.

For x < -2/√3, allow's select x = -1. Plugging this cost into f'(x):

'(-1) = three(-1)^2 - four = -1.

Since f'(-1) < zero, the characteristic is decreasing for x < -2/√3.

For -2/√three < x < 2/√three, permits select x = zero. Plugging this price into f'(x):

f'(0) = 3(0)^2 - four = -four.

Since f'(0) < zero, the characteristic is lowering for -2/√three < x < 2/√3.

For x > 2/√three, permits choose x = 1. Plugging this cost into f'(x):

f'(1) = three(1)^2 - four = -1.

Since f'(1) < 0, the function is decreasing for x > 2/√3.

Therefore, the largest open c language in which the characteristic f(x) = x^3 - 4x is lowering is (-∞, 2/√three).

Since both of the flower will be y = 1 at x = 0, yes, the flowers will be the same​ height at x = 0. And (0,1) is the solution to the system of equation

To know the solution of a system of equation, the two equation can be solved simultaneously.

Given the 2 equations y = 1.5x + 1 and y = 1.2x + 1

Equate the two equations to get x

1.5x + 1 = 1.2x + 1

collect the like terms

1.5x - 1.2x = 1 - 1

0.3x = 0

x = 0

Substitute x in any of the equation.

y = 1.5(0) + 1

y = 1

Yes! The flower will be of the same height at x = 0.

Therefore, (0,1) is the solution to the system of equation. And the flower will be of the same height at x = 0.

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The another term for the average value of a distribution is "mean."

The mean is a commonly used measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in a dataset and dividing by the total number of observations. The mean is a useful tool for summarizing the general tendency of a dataset and is used as a basis for other statistical calculations such as variance and standard deviation.

However, the mean is sensitive to outliers, meaning that a few extreme values in a dataset can greatly affect the mean. For this reason, it's sometimes necessary to use other measures of central tendency, such as the median or mode, to get a better understanding of the central tendency of a dataset.

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Answer:

25x+125< 500 15 fewer seats

Step-by-step explanation

this is number 1

The probability that no births will occur today is 0.1353 (approximately) found by using the Poisson distribution.

Given that the number of births in a local hospital follows a Poisson distribution and averages λ per day.

To find the probability that no births will occur today, we can use the formula of Poisson distribution.

Poisson distribution is given by

P(X = x) = e-λλx / x!,

where

P(X = x) is the probability of having x successes in a specific interval of time,

λ is the mean number of successes per unit time, e is the Euler’s number, which is approximately equal to 2.71828,

x is the number of successes we want to find, and

x! is the factorial of x (i.e. x! = x × (x - 1) × (x - 2) × ... × 3 × 2 × 1).

Here, the mean number of successes per day (λ) is

λ = 2

So, the probability that no births will occur today is

P(X = 0) = e-λλ0 / 0!

= e-2× 20 / 1

= e-2

= 0.1353 (approximately)

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Answer:

0.5 = the square root of 1/4

Step-by-step explanation:

√1/4 = 0.5

But, I don't know if

it would be positive or negative for you since you asked for -1/4.

Answer:

-1

Step-by-step explanation:

because 1/4 is just a whole number just put a negative single

Sample of test statistic is 2.080 and p-value is 0.082.

From the given information,

α = 0.01;

H₀ : μ = 0

H₁ : μ ≠ 0.

Student's t,

d.f. = 6

d = 0.371

t = 2.08

0.050 < p-value < 0.100

on t graph, shade area to the left of -2.08 and to the right of 2.08.

From TI-84, p-value = 0.0823.

P-value interval > 0.01 for α; fail to reject H₀.

At the 5% level of significance, the sample data do not support the claim that the average HC for this patient is higher than 14.

The P-value means the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results.

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Answer:

x - 3

Step-by-step explanation:

Answer:

1) m<1=42°

2) m<3=42°

3 m<4=138°

Step-by-step explanation:

1) m<1=180-138=42

2) m<3=180-138=42

3 m<4=138  (Alternate Interior Angle Theorem)

The series ∑(1n² + 81n) diverges.

Here, we have,

To determine the convergence or divergence of the series, we examine the behavior of the individual terms as n approaches infinity. In this series, each term is represented by the expression 1n² + 81n.

As n increases, the dominant term in the expression is the n² term. When we consider the limit of the ratio of consecutive terms, we find that the leading term simplifies to 1n²/n² = 1.

Since the limit is a nonzero constant, this indicates that the series does not converge to a finite value.

Therefore, the series ∑(1n² + 81n) diverges.

This means that as n approaches infinity, the sum of the terms in the series becomes arbitrarily large, indicating an unbounded growth. In practical terms, no matter how large of a value we assign to n, the sum of the terms in the series will continue to increase without bound.

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Answer:

x = 5

Step-by-step explanation:

18 + 9 = 27

27/9 = 3

3x = x + 10

2x = 10

x = 5

Answer:

Option D is correct.

Value of x is, 10 units.

Step-by-step explanation:

Given that:  

From the given figure, we have;

AP = 3 units , PB = 6 units , QC = 20 units and AQ = x units.

then, by triangle proportionality theorem;

Substitute the given values, to find the value of x;

By cross multiply we have;

Divide both sides by 6 we get;

10 = x

Therefore, the value of x is, 10 units

The correct options for the parts of the circle are:

A circle is a spherical plane figure whose edge is made up of points spaced equally apart from a fixed point.

The fixed point from which every point on the circle's edge is equally distant is the center of the circle.

The parts of a circle include the following:

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The notations and the terms that correctly defines them is matched below:

1.)GCB = Major arc. Option I.

2.)CE = Chord. Option B.

3.)AB= Radius. Option C.

4.)CB= Minor arc. Option A.

5.)BAD= central angle. Option F.

6.)A = Center. Option J.

7.)DGC = Minor arc. Option A.

8.)CD = Diameter. Option G.

The circle has the following parts with their various properties described below;

Major arc: This is part of the circle that has an angle which measures more that 180°.

Minor arc: This is part of the circle that has an angle which measures less than 180°.

Diameter: This is defined as the distance across a circle which must pass through its central point.

Radius: This is defined as half the diameter of a circle.

Chord:. This is defined as the line that joins two point on the circumference of a circle.

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The signal x; is a discrete signal with N samples and taking values x(n) = &**/N for n = 0,1,...,N-1. The signal Xt is the discrete Fourier transform of x; and is given by:

Xt(k) = Σn=0N-1 x(n) exp(-i2πnk/N)

This means that the Fourier transform of x(n) gives us a set of coefficients, Xt(k), that represent the contribution of each frequency, k, to the original signal x(n). In other words, the relationship between the signals x; and Xt is that Xt is a frequency-domain representation of x;.

The relationship between x and x ¢ is that x ¢ is the complex conjugate of x. This means that if x(n) = a + bi, then x ¢(n) = a - bi. In terms of the Fourier transform, this means that if X(k) is the Fourier transform of x(n), then X ¢(k) is the complex conjugate of X(k). Mathematically, this can be expressed as:

X ¢(k) = Σn=0N-1 x(n) exp(i2πnk/N)

So, the relationship between x and x ¢ is that they are complex conjugates of each other, and the relationship between their Fourier transforms, X(k) and X ¢(k), is that they are also complex conjugates of each other.
Hi! I understand that you want to know the relationship between signals x and x_t, as well as x and x', given a parameter k and a discrete signal x of duration N with values x(n) = &**/N for n = 0, 1, ..., N-1.

1. Relationship between x and x_t:
Assuming x_t is the time-shifted version of the signal x by k units, we can define x_t(n) as the time-shifted signal for each value of n:

x_t(n) = x(n - k)

Mathematically, the relationship between x and x_t is represented by the equation above, which states that x_t(n) is obtained by shifting the values of x(n) by k units in the time domain.

2. Relationship between x and x':
Assuming x' is the derivative of the signal x with respect to time, we can define x'(n) as the difference between consecutive values of x(n):

x'(n) = x(n + 1) - x(n)

Mathematically, the relationship between x and x' is represented by the equation above, which states that x'(n) is the difference between consecutive values of the discrete signal x(n), approximating the derivative of the signal with respect to time.

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The equation of a circle whose center is (0,.-5) and radius is 7 as required is; (x - 0)² + (y + 5)² = 7².

It follows from circle equations that; (x - a)² + (y - b)² = r² represents the equation of a circle whose center is; (a, b) and radius is; r.

Hence, for the given circle whose center is (0,.-5) and radius is 7.

(x - 0)² + (y + 5)² = 7²

Therefore, it can be inferred that the equation of the circle in discuss is; (x - 0)² + (y + 5)² = 7².

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The length of side f is  8.38 in the triangle DEF.

In a triangle, the sum of the angles is always 180 degrees.

∠D + ∠E + ∠F = 180 degrees

∠D + ∠E + 166 degrees = 180 degrees

∠D + ∠E = 14 degrees

Now, we can use the Law of Cosines to find the length of side f:

f² = d² + e² - 2de cos(∠F)

f² = (5.2 inches)² + (6.8 inches)² - 2(5.2 inches)(6.8 inches) cos(166 degrees)

f² = 70.29 inches²

Taking the square root of both sides, we get:

f = 8.38 inches

Therefore, the length of side f is  8.38 in the triangle DEF.

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Answer:

Step-by-step explanation:

31 degreese

add 59 with 90 you get 149 then you subtract 149 with 180 a

nd then get 31

Answer:

the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.

Step-by-step explanation:

Let's denote the angles of the triangle as 3x, 4x, and 5x, where x is a constant.

Since the sum of the angles of a triangle is 180 degrees, we can write the following equation:

3x + 4x + 5x = 180

Simplifying this equation, we get:

12x = 180

Dividing both sides by 12, we get:

x = 15

Therefore, the angles of the triangle are:

3x = 3(15) = 45 degrees

4x = 4(15) = 60 degrees

5x = 5(15) = 75 degrees

So the angles of the triangle are 45 degrees, 60 degrees, and 75 degrees, and they are in the ratio of 3 : 4 : 5.

Answer:

\(\boxed {r = \frac{31}{3}}\)

Step-by-step explanation:

To find the value of \(r\), write an expression by using the following measurements of both \(\overline {DG}\) and \(\overline {GM}\), then you solve for \(r\):

\(\overline {DG} = r + 3\)

\(\overline {GM} = 4r - 28\)

\(r + 3 = 4r - 28\)

Solve for \(r\):

\(r + 3 = 4r - 28\)

\(x + 3 - 4r = 4r - 4r - 28\)

\(-3r + 3 = -28\)

\(-3r + 3 - 3 = -28 - 3\)

\(-3r = -31\)

\(\frac{-3r}{-3} = \frac{-31}{-3}\)

\(\boxed {r = \frac{31}{3}}\)

So, the value of \(r\) is \(\frac{31}{3}\).

Answer: the answer is 9 hours 45 minutes

The range of f(x) = 2x for any real number x will always be the set of all real numbers, regardless of what specific value of x is plugged in.

The range of a function is the set of all possible output values for the function. In this case, the function f(x) = 2x has a domain of the set of real numbers, meaning that any real number can be plugged in for x. The range of the function will be determined by what values of x are plugged in.

(a) If z is a real number, then f(z) = 2z. The range of f(z) will be the set of all real numbers since any real number can be plugged in for z and the output will also be a real number.

(b) Similarly, if n is a real number, then f(n) = 2n. The range of f(n) will also be the set of all real numbers since any real number can be plugged in for n and the output will also be a real number.

(c) Finally, if r is a real number, then f(r) = 2r. The range of f(r) will also be the set of all real numbers since any real number can be plugged in for r and the output will also be a real number.

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A student with a GPA of 2.57 is estimated to have worked approximately 15 hours each week.

To estimate the number of hours worked each week for a student with a GPA of 2.57, we can substitute the GPA value into the equation G = -0.0007h^2 + 0.011h + 3.01, where G represents the GPA and h represents the number of hours worked.

By substituting G = 2.57 into the equation, we get:

2.57 = -0.0007h^2 + 0.011h + 3.01

To find the approximate number of hours worked, we can solve this quadratic equation. However, since we are asked to round the answer to the nearest whole number, we can use estimation techniques or software to find the value.

Using estimation or a quadratic solver, we find that the approximate number of hours worked each week for a student with a GPA of 2.57 is around 15 hours. Please note that this is an estimate based on the given equation and the specific GPA value. The actual number of hours worked may vary depending on various factors and individual circumstances.

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Answer: Carlos started with 38 comic books.

Step-by-step explanation:

33 - 14 = 19

19 x 2 = 38

Answer:

the answer is C :) good luck

Answer:

Scale factor of \(\frac{1}{7}\).

Step-by-step explanation:

scale = \(\frac{scaled length}{actual length}\)

The rectangle has been scaled by a factor of seven implies that its real dimensions has been multiplied by seven. Therefore, to scale the copy back to its original size, its dimension should be multiplied by a scale factor of \(\frac{1}{7}\).

Example:

when the scale is 7;

2 x 7 = 14

3 x 7 = 21

when the scale is \(\frac{1}{7}\);

14 x \(\frac{1}{7}\) = 2

21 x \(\frac{1}{7}\) = 3

Answer:

3/7

Step-by-step explanation:

First, when dividing 6/7 by 2 you need to change the number 2 into a fraction. The number 2 as a fraction is 2/1. However, this is division so you need to reverse the fraction so it is 1/2 instead of 2/1. So, 6/7 x 1/2 = 6/14. You can simplify to get your the answer.

Hope this helped!

The  pilot is approximately 177.86 miles from the starting position.

To solve this problem, we can use trigonometry and the Pythagorean theorem.

First, let's find the distance traveled in the original straight path:

distance = speed x time
distance = 645 mph x 1.5 hours
distance = 967.5 miles

Next, let's find the distance traveled in the new direction:

distance = speed x time
distance = 645 mph x 2 hours
distance = 1290 miles

Now, let's use trigonometry to find the distance from the starting position to the final position. We can draw a right triangle with the original distance traveled as the adjacent side (because it is parallel to the ground) and the new distance traveled as the opposite side (because it is perpendicular to the ground due to the course correction). The hypotenuse of this triangle is the distance from the starting position to the final position.

To find the hypotenuse, we can use the tangent function:

tan(10 degrees) = opposite/adjacent
tan(10 degrees) = distance from starting position/967.5 miles

Solving for the distance from starting position:

distance from starting position = tan(10 degrees) x 967.5 miles
distance from starting position = 177.86 miles.

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Answer:

V = π r^2 h = π · 10^2 · 15 ≈ 4712.38898

Thus,  78% of the people surveyed,  shopped at a local grocery store.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Grocery Options:

                                Store           Online          Total

Women                     32                 9                  41

Men                           28                8                   36

Total                          60               17                  77

Total people = 77

Total people who shop at a local grocery store = 60

Thus,

Percentage = 60/77 *100  = 77.92% = 78%

Thus,  78% of the people surveyed,  shopped at a local grocery store.

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