Manuel the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on monday there were 3 clients who did plan a and 8 who did plan b. manuel trained his monday clients for a total of 7 hours and his tuesday clients for a total of 6 hours. how long does each workout plans last?​

Answer:

B

Step-by-step explanation:

Answer:

n = 27

Step-by-step explanation:

n + 6 + 2n + 3 + 90 = 180

solve for n then n = 27

hope this helped

have a good day ^^

Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.

For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2/x³, 2y, 22] = [2, 2, 22].

The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].

Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2x, 2y, 2z] = [2, 2, 2].

As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.

Step-by-step explanation:

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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We can use the Taylor series formula to find the fourth-degree Taylor polynomial for f about x = 2.  The answer is d. 18

\(f(2) = f(2) = 405\)

\(f'(2) = 29\)

\(f''(2) = 28\)

\(f'''(2) = 168\)

The fourth-degree Taylor polynomial is:

P4(x) \(= f(2) + f'(2)(x-2) + (f''(2)/2!)(x-2)^2 + (f'''(2)/3!)(x-2)^3 + (f''''(c)/4!)(x-2)x^{2}\)^4

where c is some number between 2 and x.

Using the given third derivative, we can find the fourth derivative:

\(f''''(x) = (4x + 1) ^6 * 4\)

Plugging in x = c, we have:\(f''''(c) = (4c + 1) ^6 * 4\)

Therefore, the coefficient of \((x-2)^4\) in the fourth-degree Taylor polynomial is:\((f''''(c)/4!) = [(4c + 1) ^6 * 4] / 24\)

We need to evaluate this at c = 2:\([(4c + 1) ^6 * 4] / 24 = [(4*2 + 1) ^6 * 4] / 24 = 18\)

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Answer:

D 108

Step-by-step explanation:

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The probability that the team will win the sport is 77%.

Given that an area kicker in pro football incorporates a 77% probability of creating a field goal over 40 yards and every attempt field goal is independent.

Probability is how something is likely to happen. The probability of a happening is calculated by the probability formula by simply dividing the favorable number of outcomes by the overall number of possible outcomes.

So, his team will win the sport if he makes a goal otherwise loses.

Therefore, the Probability that his team will win the sport P[E] =P[making a field goal]

P[E]=77%

Hence, the probability that the team will win the sport when making a field goal is 77%.

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Step-by-step explanation:

20 - x = -5

-x = -25

x = 25

the temperature fell by 25°F.

Finite-state machines for given inputs: (a) 0s multiple of 3: 3-state machine. (b) At least four 1s: 4-state machine. (c) Exactly one 1: 2-state machine. (d) Begins with 000: 3-state machine. (e) Second is 0, fourth is 1: 4-state machine. (f) 01 pairs or 2 1s + 0s: 3-state machine. (g) Ends in 110: 3-state machine.

To construct finite-state machines that act as recognizers for the given inputs, we can follow these guidelines:

(a) For the set of all strings where the number of 0s is a multiple of 3, we can use a finite-state machine with three states. Start with the initial state, and transition to the next state whenever a 0 is encountered. After three transitions, go back to the initial state. If the machine ends in the accepting state, output 1.
(b) For the set of all strings containing at least four 1s, we can use a finite-state machine with four states. Start with the initial state, and transition to the next state whenever a 1 is encountered. If the machine enters the final state after four transitions, output 1.

(c) For the set of all strings containing exactly one 1, we can use a finite-state machine with two states. Start with the initial state and transition to the final state when the first 1 is encountered. Output 1 only if the final state is reached.

(d) For the set of all strings beginning with 000, we can use a finite-state machine with three states. Start with the initial state and transition to the next state whenever a 0 is encountered. If the machine reaches the final state after three transitions, output 1.

(e) For the set of all strings where the second input is 0 and the fourth input is 1, we can use a finite-state machine with four states. Start with the initial state and transition to the next state based on the inputs. Output 1 only if the machine reaches the final state.

(f) For the set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two 1s followed by any number (including none) of 0s, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

(g) For the set of all strings ending in 110, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

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Finite-state machines (FSMs) can be constructed to act as recognizers for specific patterns in input strings. These are examples of how to construct FSMs as recognizers for different patterns in input strings. Each FSM is designed to produce an output of 1 when the input received matches the description provided.

Let's consider the given cases and construct FSMs for each one.

(a) The set of all strings where the number of Os is a multiple of 3:
To construct an FSM for this, we can keep track of the number of Os encountered so far. Initially, set the count to zero. When an O is encountered, increment the count by one. If the count becomes a multiple of 3, the FSM outputs 1; otherwise, it outputs 0. Reset the count to zero whenever a 1 is encountered.

(b) The set of all strings containing at least four 1s:
To create an FSM for this, we can keep track of the number of 1s encountered so far. Initially, set the count to zero. When a 1 is encountered, increment the count by one. If the count becomes equal to or greater than four, the FSM outputs 1; otherwise, it outputs 0.

(c) The set of all strings containing exactly one 1:
To build an FSM for this, we can have two states: a "no 1 encountered" state and a "1 encountered" state. Initially, start in the "no 1 encountered" state. Whenever a 1 is encountered, transition to the "1 encountered" state. If another 1 is encountered in the "1 encountered" state, transition to a third "more than one 1 encountered" state. In this case, the FSM outputs 0. Otherwise, if no additional 1s are encountered, the FSM outputs 1.

(d) The set of all strings beginning with 000:
To create an FSM for this, start in an initial state. When a 0 is encountered, transition to a second state. If two consecutive 0s are encountered in the second state, transition to a third state. Finally, if a third 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

(e) The set of all strings where the second input is 0 and the fourth input is 1:
To construct an FSM for this, start in an initial state. When the first input is read, transition to a second state. In the second state, transition to a third state if the second input is 0. In the third state, transition to a fourth state if the third input is not 0. Finally, in the fourth state, if the fourth input is 1, the FSM outputs 1; otherwise, it outputs 0.

(f) The set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two Is followed by any number (including none) of Os:
To create an FSM for this, we can have multiple states to represent different scenarios. We start in an initial state and transition to a second state when a 0 is encountered. In the second state, transition back to the initial state if a 1 is encountered. If a 1 is encountered in the initial state, transition to a third state. In the third state, transition to a fourth state if an O is encountered. Finally, if an O is encountered in the fourth state, the FSM outputs 1; otherwise, it outputs 0.

(g) The set of all strings ending in 110:
To construct an FSM for this, start in an initial state. Transition to a second state if a 1 is encountered. In the second state, transition to a third state if a 1 is encountered again. Finally, if a 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

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The equation of a straight line passing through the given point and slope is y - y1 = m(x - x1).

What is the simple definition of slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Let the given point be (x1,y1).

slope be m.

we know that,

Line equation passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given point and slope is  y - y1 = m(x - x1).

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Step-by-step explanation:

60n=180

n=3

180(2-3)

360-540=-180

Answer:

$28

Step-by-step explanation:

original price = $40

discount = 30%

discount amount = 30% of original price

=30/100 * 40

=$1200/100

=$12

sale price = original price - discount amount

=$40 - $12

=$28

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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c. If all subsets of {A,B,C,D} are closed, every attribute determines itself and all other attributes. e. If only the closed subsets are {}, {B,C}, and {A,B,C,D}, it implies B and C determine themselves and each other, while A determines all attributes.

c. All subsets of {A,B,C,D} are closed.

If all subsets of {A,B,C,D} are closed, it implies that every attribute determines itself and all other attributes. This can be represented by the following set of functional dependencies:

{A → A, B → B, C → C, D → D, AB → AB, AC → AC, AD → AD, BC → BC, BD → BD, CD → CD, ABC → ABC, ABD → ABD, ACD → ACD, BCD → BCD, ABCD → ABCD}

d. The only closed subsets of {A,B,C,D} are {} and {A,B,C,D}.

If only the empty set {} and the set {A,B,C,D} are closed, it implies that no other attribute or combination of attributes determines any other attribute or combination of attributes. In this case, there are no non-trivial functional dependencies. Therefore, the set of functional dependencies consistent with this closure is:

{}e. The only closed subsets of {A,B,C,D} are {}, {B,C}, and {A,B,C,D}.

If only the empty set {}, the set {B,C}, and the set {A,B,C,D} are closed, it implies that the attribute B and C together determine themselves and each other, while the attribute A determines all attributes. This can be represented by the following set of functional dependencies:

{A → A, A → B, A → C, A → D, BC → B, BC → C, B → B, B → C, C → B, C → C, D → D}

These functional dependencies ensure that the only closed subsets are {}, {B,C}, and {A,B,C,D}.

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Using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

To find the distance of two points on a coordinate grid, the distance formula that is employed is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Given the points are on a coordinate grid:

(1, -2) = (x1, y1)

(-9, 3) = (x2, y2)

Plug in the  values into the distance formula:

d = √[(−9−1)² + (3−(−2))²]

d = √[(−10)² + (5)²]

d = √(100 + 25)

d = √125

d = 11.18034

d ≈ 11 units.

Therefore, using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

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Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.

In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).

Step-by-step explanation:

The fundamental questions of risk management that would benefit from using pairwise ranking are those related to prioritizing risks and deciding which risks to address first.

Pairwise ranking is a technique used to compare and prioritize items by comparing them in pairs and determining which one is more important or has a higher priority. This technique can be used to prioritize risks based on their likelihood and impact.
The risk management that would benefit from using pairwise ranking include:
- Which risks should be addressed first?
- Which risks have the highest likelihood of occurring?
- Which risks have the highest impact on the project or organization?
- Which risks should be given the most attention and resources?
By using pairwise ranking, risk managers can prioritize risks and make more informed decisions about which risks to address first and which risks to allocate the most resources to. This can help ensure that the most important risks are addressed first and that resources are used effectively to manage risks.

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Answer:

A≈78.54cm² Diamter= 10

Step-by-step explanation:

hope this helps

Answer:

A=78.54 cm sq

Step-by-step explanation:

Using the formulas

A=πr2

d=2r

Solving for A

A=1

4πd2=1

4·π·102≈78.53982cm²

The polynomial function f(x) = -4x⁵ + 15x⁴ - 17x³ + 6x² - 7x + 11 has a maximum of 2 positive real zeros and a maximum of 0 negative real zeros.

To determine the possible number of positive real zeros and negative real zeros of the polynomial function f(x) = -4x⁵ + 15x⁴ - 17x³ + 6x² - 7x + 11, we need to examine the signs of the coefficients.

For the positive real zeros:

- Count the number of sign changes in the coefficients or the sign changes in f(x) when substituting -x for x.

- The maximum number of positive real zeros is equal to the number of sign changes or less by an even number.

For the negative real zeros:

- Count the number of sign changes in the coefficients of f(-x) or f(x) when substituting -x for x.

- The maximum number of negative real zeros is equal to the number of sign changes or less by an even number.

Let's analyze the coefficients of the polynomial function: -4, 15, -17, 6, -7, 11

For the positive real zeros, there are 2 sign changes from negative to positive:

-4, 15, -17, 6, -7, 11

So, the maximum number of positive real zeros is 2 or less by an even number.

For the negative real zeros, there are no sign changes from positive to negative:

4, 15, 17, 6, 7, 11

Therefore, the maximum number of negative real zeros is 0.

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Answer:

D

Step-by-step explanation:

x + y = 30

65x + 80y = $2,200

The only option that matches this is D

Hope that helps!

-Sabrina

Answer: 700

Step-by-step explanation:

175 * 4 = 700

Answer:

700

Step-by-step explanation:

To solve this problem you multiply 175 by 100 and then divide the total by 25 as follows: (175 x 100) / 25

When we put that into our calculator, we get the following answer:

700

The probability that a randomly selected member of Congress who favours corporate tax reform is a Democrat is 0.4444, rounded to four decimal places.

To solve this problem, we can use Bayes' theorem. Let D represent the event that the selected member is a Democrat, and R represent the event that the selected member is a Republican, and I represent the event that the selected member is an Independent. Let F represent the event that the selected member favors some type of corporate tax reform. We are given the following probabilities:

P(R) = 0.28, P(D) = 0.50, P(I) = 0.22

P(F|R) = 0.34, P(F|D) = 0.35, P(F|I) = 0.31

We want to find P(D|F), the probability that the selected member is a Democrat given that they favor corporate tax reform. We can use Bayes' theorem:

P(D|F) = P(F|D)P(D) / [P(F|D)P(D) + P(F|R)P(R) + P(F|I)P(I)]

Plugging in the values we know, we get:

P(D|F) = 0.35 * 0.50 / [0.35 * 0.50 + 0.34 * 0.28 + 0.31 * 0.22]

P(D|F) = 0.4444 (rounded to four decimal places)

Therefore, the probability that the selected member is a Democrat given that they favour corporate tax reform is 0.4444.

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Answer:

A can with capacity 44 litres

Step-by-step explanation:

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Answer: A: y= 3x + 3

Step-by-step explanation:

The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.

Answer:

x=58 ; z=32

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Given that:

Sample space = {1, 2, 3, 4, 5,6}

Probability of obtaining an odd number in a single roll :

Probability = required outcome / Total possible outcomes

Required outcome = {1,3,5} = 3

Total possible outcomes = 6

P(odd number) = 3/6 = 1/2

Number of odds on 84 die rolls :

1/2 * 84 = 42 times

Answer:  y = (1/3)x - 5

This is the same as writing \(y = \frac{1}{3}x-5\)

======================================================

Explanation:

Assume we have a linear pattern matching the form y = mx+b.

The first row has x = 12 lead to y = -1

The second row has x = 3 lead to y = -4

This produces the two points (12,-1) and (3,-4)

Let's find the slope through those points.

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

m = (-4-(-1))/(3-12)

m = (-4+1)/(3-12)

m = -3/(-9)

m = 1/3

The slope is 1/3.

The y intercept is b = -5 since x = 0 leads to y = -5

We go from y = mx+b to y = (1/3)x - 5

--------------------------

To verify we have the correct equation, plug in each left side value as x values.

Let's try x = 12

y = (1/3)x - 5

y = (1/3)*12 - 5

y = 4 - 5

y = -1

This shows that the input x = 12 maps to the output y = -1

i.e.  12 ↦ −1 is the case here.

Repeat for x = 3

y = (1/3)x - 5

y = (1/3)*3 - 5

y = 1 - 5

y = -4

We can see that 3 ↦ −4 occurs.

I'll let you check the others, but you should find that the other mappings hold true as well. Therefore, the answer has been fully confirmed.

If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean then the minimum sample size that should be taken is 83.

Given:

the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels.

if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean

what is the minimum sample size that should be taken = ?

population standard deviation (σ) = 94

margin of error (E) = 17

for 90% confidence interval Zα/2 = 1.645

formula:

sample size (n) = [ zα/2 × σ/E]²

sample size (n) = [1.645×94/17]²

sample size (n) = 82.7

sample size (n) ≈ 83

Hence we get the required answer.

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The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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Answer:

138

Step-by-step explanation: