Corrupted by their power, the judges running the popular game show America’s Next Top Mathematician have been taking bribes from many of the contestants. During each of two episodes, a given contestant is either allowed to stay on the show or is kicked off. If the contestant has been bribing the judges, she will be allowed to stay with probability 1. If the contestant has not been bribing the judges, she will be allowed to stay with probability 1/3, independent of what happens in earlier episodes. Suppose that 1/4 of the contestants have been bribing the judges. The same contestants bribe the judges in both rounds. (a) If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she was bribing the judges? (b) If you pick a random contestant, what is the probability that she is allowed to stay during both episodes? (c) If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she ge

The best prediction for the time to read 18 pages is 15 minutes

The table entry is given as:

Pages      Time

10               8

12               11

5                4

26              22

20              17

From the table, 18 pages is between 12 and 20 pages.

This means that, the time to read a chapter that has 18 pages must be between the time to read a chapter of 12 and 20 pages.

It takes 11 minutes to read 12 pages, and 17 minutes to read 20 pages.

So, the time to read 18 pages must be between 11 minutes and 17 minutes.

From the given options, 15 is between 11 and 17

Hence, the best prediction for the time to read 18 pages is 15 minutes

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The area of a square is given by the following formula:

To find the sidelength of the square, solve the equation for s:

Replace the given value in the equation to find the sidelength:

The sidelength is 4/7cm.

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

6 m/s

Step-by-step explanation:

divide the speed value by 3.6

Answer:

6m / s

Step-by-step explanation:

21600/3600

= 6m/s

Answer:

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They have a perimeter of 40 meters, and an area of 168 square meters. Therefore, either set of dimensions would work for Chase's fence.

Let's assume the rectangular plot of land has length L and width W. We can use the given information to set up the following system of equations:

2L + W = 40 (since there are three sides and the total length of fencing is 40 m)

LW = 168 (since the area of the land is 168 square meters)

Solving the first equation for W, we get:

W = 40 - 2L

we get:

L(40 - 2L) = 168

we get a quadratic equation:

\(2L^2\) - 20L + 84 = 0

Using the quadratic formula, we can solve for L:

L = (20 ± sqrt(\(20^2\) - 4(2)(84))) / (2(2))

L = (20 ± 4sqrt(11)) / 4

L = 5 ± sqrt(11)

Therefore, we have:

L = 5 + sqrt(11) or L = 5 - sqrt(11)

W = 30 - 2sqrt(11) or W = 30 + 2sqrt(11)

(5 + sqrt(11)) m by (30 - 2sqrt(11)) m

and

(5 - sqrt(11)) m by (30 + 2sqrt(11)) m

Note that both sets of dimensions satisfy the given conditions: they have a perimeter of 40 m (2L + W = 40) and an area of 168 square meters (LW = 168).

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Considering the three-place Boolean function f defined

(a) f(1, 1, 1) = (7(1) + 2(1) + 4(1)) and f(0, 0, 1) = (7(0) + 2(0) + 4(1))

(b) Using an input/output table f is an odd parity function.

A Boolean function is a mathematical function that takes input values and returns a binary output value. In the given problem, the three-place Boolean function f is defined by the rule (7x1 + 2x2 + 4x3) mod 2, where x1, x2, and x3 are binary inputs.
To find f(1, 1, 1), we substitute x1=1, x2=1, and x3=1 in the given function. Therefore, f(1, 1, 1) = (7(1) + 2(1) + 4(1)) mod 2 = 1.
Similarly, to find f(0, 0, 1), we substitute x1=0, x2=0, and x3=1 in the given function. Therefore, f(0, 0, 1) = (7(0) + 2(0) + 4(1)) mod 2 = 0.
To describe f using an input/output table, we consider all possible input combinations of x1, x2, and x3 and evaluate the function for each combination. The resulting input/output table is as follows:
Input Output
x1 x2 x3 f
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
From the input/output table, we can see that the function f returns 1 when the sum of 7x1, 2x2, and 4x3 is odd and returns 0 when it is even. Thus, we can conclude that f is an odd parity function.

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To find the radius of the spinner, we'll first find the total area of the spinner and then use the formula for the area of a circle. Radius is defined as the length between the center and the arc of circle.

Here are the steps:
1. Determine the proportion of the sectors that do not move the token: There are 3 such sectors (remaining sectors) out of a total of 9 sectors. So, the proportion is 3/9 = 1/3.

2. Calculate the total area of the spinner: Since 1/3 of the spinner has an area of 14.6 square inches, we can find the total area by multiplying the area of non-moving sectors by 3.
Total area = 14.6 * 3 = 43.8 square inches.

3. Use the formula for the area of a circle to find the radius: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. We'll solve for the radius (r) in this formula:
43.8 = πr^2

4. Divide both sides of the equation by π:
r^2 = 43.8 / π

5. Calculate r:
r = √(43.8 / π)

6. Round the result to the nearest tenth of an inch:
r ≈ 3.7 inches

So, the radius of the spinner is approximately 3.7 inches.

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Answer:

um a

Step-by-step explanation:

I'm pretty sure (98%) it is A.

Let me know if I'm wrong.

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

Step-by-step explanation:

Descending order:

6.21     ;           2.62   ;  2.612    ; 2.061    ;  0.66

First see the whole number. write the number with biggest whole number.

6.21

2) Then three numbers have 2 . So, now compare the tenth place.

Two numbers have same place value 2.62 and 2.612.

Compare the hundredth place value in these two numbers.

So, 2.62

3) 2.612

4) 2.061

5) 0.66 is the smallest

To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

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Answer: 29°

Step-by-step explanation:

(2x-2)° + (x+5)° + 90° = 180°

(2x-2)° + (x+5)° = 90°

(2x + x)° = 87°

(3x)° = 87°

x° = 29°

The absolute value function, when graphed, that would be wider than the graph of the parent function, f(x) = |x| is: C. f(x) = 1/3|x|.

In Mathematics and Geometry, the vertex form of an absolute value function can be modeled as follows;

y = a|(x - h)| + k

When the value of a is greater than 1, the graph of the parent absolute value function f(x) would be vertically stretched by factor of a, and if 0 < a < 1, the graph of the parent absolute value function f(x) would be vertically compressed vertically by a factor of 1/a.

In this context, only this absolute value function f(x) = 1/3|x| would be wider than the graph of the parent function, f(x) = |x|.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The distribution is skewed to the right.

Step-by-step explanation:

There are more data values to the left of the box plot, indicating that the distribution is skewed to the right.

Answer:

Composite Numbers.

To find two nonnegative numbers x and y such that xy = 162 and 4x +2y is minimized, we need to use the concept of the Arithmetic-Geometric Mean.The main answer is:x = 9√2y = 9/√2

Explanation: Arithmetic-Geometric Mean: Let a and b be positive numbers.The Arithmetic Mean (AM) is a + b / 2. The Geometric Mean (GM) is √ab.The Arithmetic-Geometric Mean is the following:a_n = (a_n−1 + b_n−1) / 2  b_n = √a_n−1 * b_n−1  a_0 = a  b_0 = b

Let's solve the problem using the Arithmetic-Geometric Mean.√(4xy) = √(4 * 162) = 36xy/36 = 162/36xy = 9√2 * 9/√2xy = 81The numbers that will minimize 4x + 2y are 4x = 36, and 2y = 18. Therefore, x = 9√2, and y = 9/√2

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Answer:

x=8

Step-by-step explanation:

5x-4=3x+12

-3x. -3×

2x-4=12

+4. +4

2×=16

÷2. ÷2

x=8

In order to find the value of N in the equation when T = 60, we just need to apply the value of T and then calculate the value of N.

So we have that:

So the number of chirps per minute is 80

Answer:

Step-by-step explanation:

By the Mean Value Theorem, there is at least one number, c, in the interval (1,6) such that

f'(c) = [f(6) - f(1)]/ (6 - 1)

So, f(6) - f(1) = 5f'(c).

Since 2 ≤ f'(c) ≤ 4, 10 ≤ 5f'(c) ≤ 20

So, f(6) - f(1) is between 10 and 20.  

The value of the 10% trimmed mean is approximately 1.3027. To calculate the 10% trimmed mean, we need to trim off the lowest and highest 10% of the data and then find the mean of the remaining values.

First, let's sort the data in ascending order:

0.2, 0.21, 0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26, 3.06, 3.24

Next, we calculate the number of values to trim from each end:

10% of 15 (total number of values) = 0.1 * 15 = 1.5

Since we can't remove half a value, we round up to the nearest whole number, which is 2.

Now, we remove the two lowest and two highest values:

0.26, 0.3, 0.33, 0.41, 0.54, 0.57, 1.41, 1.7, 1.84, 2.2, 2.26

Finally, we calculate the mean of the remaining values:

(0.26 + 0.3 + 0.33 + 0.41 + 0.54 + 0.57 + 1.41 + 1.7 + 1.84 + 2.2 + 2.26) / 11 = 14.33 / 11 ≈ 1.3027

Rounding to four decimal places, the value of the 10% trimmed mean is approximately 1.3027.

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Answer:

a. The common ratio is 0.5

b) The value of the first term is 29

c) The sum of the first 5 terms is 56.1875

Step-by-step explanation:

The nth term of the geometric sequence is a\(_{n}\) = a\(r^{n-1}\), where

The sum of the nth term is S\(_{n}\) = \(\frac{a(1-r^{n})}{1-r}\)

∵ The second term of a geometric sequence is 14.5

∴ n = 2

∴ a\(_{2}\) = 14.5

∵ a\(_{2}\) = ar

→ Equate the right sides of a\(_{2}\) by 14.5

∵ ar = 14.5 ⇒ (1)

∵ The fifth term is 1.8125

∴ n = 5

∴ a\(_{5}\) = 1.8125

∵ a\(_{5}\) = a\(r^{4}\)

→ Equate the right sides of a\(_{5}\) by 14.5

∵ a\(r^{4}\) = 1.8125 ⇒ (2)

→ Divide equation (2) by equation (1)

∵ \(\frac{ar^{4}}{ar}\) = \(\frac{1.8125}{14.5}\)

∴ r³ = 0.125

→ Take ∛ for both sides

∴ r = 0.5

a. The common ratio is 0.5

→ Substitute the value of r in equation (1) to find a

∵ a(0.5) = 14.5

∴ 0.5a = 14.5

→ Divide both sides by 0.5

∴ a = 29

b) The value of the first term is 29

∵ n = 5

∴ S\(_{5}\) = \(\frac{29[1-[0.5]^{5})}{1-0.5}\)

∴ S\(_{5}\) = 56.1875

c) The sum of the first 5 terms is 56.1875

a) Let's evaluate f(-1) and f(1): f(-1) = (-1)³ + 2(-1) - 2 = -1 - 2 - 2 = -5

f(1) = (1)³ + 2(1) - 2 = 1 + 2 - 2 = 1

Since f(-1) = -5 < 0 and f(1) = 1 > 0, by the Intermediate Value Theorem, there exists a value c in the interval (-1,1) such that f(c) = 0.

b) The function f(x) = x³ + 2x - 2 is a polynomial function, and polynomial functions are continuous over their entire domain. Therefore, the function f satisfies the continuity requirement of the Intermediate Value Theorem.

c) To show that there is exactly one solution to the equation f(x) = 0, we can analyze the behavior of the function using calculus techniques. For instance, by finding the derivative f'(x) = 3x² + 2 and observing its sign changes, we can conclude that there is a single root within the interval (-1,1). Additionally, we can apply the Mean Value Theorem, which guarantees that if a function is continuous on a closed interval and differentiable on the open interval, there exists at least one point in the open interval where the derivative is equal to the average rate of change over the closed interval. By analyzing the behavior of the derivative, we can show that there is exactly one solution within the interval (-1,1).

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Answer: If you look at the x axis 1 is less than $1 so if you follow the x axis to the right until you find a number of minutes that meets the y axis of $1 so x4, y1 that means  $.25 per minute if you divide 1 by 4. So 1 is the correct answer.

Step-by-step explanation:

1. Follow the x axis until the x and y axis meet. This is $1.00 on the y axis.

2. Then you would divide 1 by 4 and you get .25. Each minute would be $.25.

Therefore, the equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2) is y = -x + 2.

To find an equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2), we need to use the concept of differentiation.

First, we differentiate both sides of the equation with respect to x using the product rule and the chain rule:

(d/dx)[xe^y] + (d/dx)[ye^x] = (d/dx)[2]

e^y + xe^y(dy/dx) + e^x(dy/dx) + ye^x = 0

Simplifying this expression and evaluating it at the point (0, 2), where x = 0 and y = 1, we get:

e^1 + 0 + e^0(dy/dx) + 2e^0 = 0

dy/dx = -1

Therefore, the slope of the tangent line at the point (0, 2) is -1.

Next, we can use the point-slope form of a line to find the equation of the tangent line. We know the slope is -1 and the point (0, 2) lies on the line, so we can write:

y - 2 = -1(x - 0)

Simplifying this expression, we get:

y = -x + 2

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Answer:

A)  C (15:30)        B) D (16km)

Step-by-step explanation:

A)  

 Look along x-axis which is time the dotted whish is of bethan

journey finished between 14:00 to 16:00

The ending point is 3 boxes forwad to 14:00 and each box represent 30 min

So time is 15:00

B)

Look at y-axis which is distance

Journey start from 0 to 8 then take time and again start from 8 to final point

When addedup it equal t0  16km

Mark brainliest if you understand

The unit tangent vector t(1) at t = 1 is:

t(1) = (4 i + 6 j + 3 k) /\(\sqrt{(61)}\)

To find the unit tangent vector,

we need to calculate the derivative of the position vector r(t) with respect to the parameter t, and then normalize the resulting vector.

Given the position vector r(t) = 4t i + 3t^2 j + 3t k,

we can find the derivative:

r'(t) = d(r(t))/dt

     = 4 i + 6t j + 3 k

Now, we can evaluate r'(t) at t = 1:

r'(1) = 4 i + 6(1) j + 3 k

      = 4 i + 6 j + 3 k

To obtain the unit tangent vector,

we need to normalize r'(1):

t(1) = r'(1) / ||r'(1)||

where ||r'(1)|| represents the magnitude or length of r'(1).

The magnitude of r'(1) is given by:

||r'(1)|| = \(\sqrt{((4^2) + (6^2) + (3^2))}\)

       = \(\sqrt{61}\))

This is the normalized vector representing the direction of the tangent to the curve at the point where t = 1.

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Answer:

12

Step-by-step explanation:

average rate

\(=\frac{g(-1)-g(-7)}{-1-(-7)} \\=\frac{[12(-1)+1]-[12(-7)+1]}{-1+7} \\=\frac{[-12+1]-[-84+1]}{6} \\=\frac{-11+83}{6} \\=\frac{72}{6} \\=12\)