Tim celebrated his dental school acceptance by completing the seven days trek to Machu Pichu (Day 7: Aguas Calientes elevation 2,430 m). Tim is in good physical condition. He runs 3-5 miles per day, weight trains, and plays midfield in the local soccer club. (Review pages 527-the top of 531 in Guyton and Hall).

The L1 norm of vector A is greater than or equal to the L1 norm of vector B.

Basically, if the L2 norm of vector A is greater than the L2 norm of vector B, it is indeed always true that the L1 norm of vector A is greater than or equal to the L1 norm of vector B. The Lp norm is defined as follows:

\(||x||_p = (|x_1|^p + |x_2|^p + ... + |x_n|^p)^(1/p),\)

where x = [x₁, x₂, ..., xₙ] is a vector.

For the L2 norm (p = 2), the formula is:

\(||x||_2 = \sqrt(|x_1|^2 + |x_2|^2 + ... + |x_n|^2).\)

For the L1 norm (p = 1), the formula is:

\(||x||₁ = |x_1| + |x_2| + ... + |x_n|.\)

If ||A||₂ > ||B||₂, it implies that:

\(\sqrt(|A_1|^2 + |A_2|^2 + ... + |A_n|^2) > \sqrt(|B_1|^2 + |B_2|^2 + ... + |B_n|^2).\)

Squaring both sides of the inequality, we get:

\(|A_1|^2 + |A_2|^2 + ... + |A_n|^2 > |B_1|^2 + |B_2|^2 + ... + |B_n|^2.\)

Since the squares of the magnitudes are positive, we can conclude that:

\(|A_1| + |A_2| + ... + |A_n| > |B_1| + |B_2| + ... + |B_n|.\)

Therefore, the L1 norm of vector A is greater than or equal to the L1 norm of vector B.

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The populations from which the samples are obtained must be normally distributed.

Sampling is done correctly. Observations for within and between groups must be independent.

The variances among populations must be equal (homoscedastic).

Data are interval or nominal.

An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 27 - 4(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 27

Second term, a₂ = 31

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 31 - 27

Common difference, d = 4.

Substituting the parameters into the mathematical expression, we have;

aₙ = 27 + (n - 1)(4)

aₙ = 27 - 4(n - 1).

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The probability that all n flips are heads is (1/2)ⁿ.

The probability that the digit 1 doesn’t appear among n digits where each digit is one of (0-9) and all sequences are equally likely?The total number of possible n digit numbers that can be formed is 9ⁿ because 0 can not be the leading digit. So, the number of n digit numbers that does not contain 1 is 8ⁿ.The probability that the digit 1 does not appear in any n digit number is given by: P(no 1) = 8ⁿ/9ⁿ = (8/9)ⁿ

The probability that the number k ends up in the i-th position in the resulting permutation?The probability that a particular number is in the ith position is 1/n, since each of the n numbers is equally likely to appear in any given position.

A fair coin is flipped n times (each outcome in {H, T} n is equally likely). What is the probability that all heads occur at the end of the sequence?The probability that each of the n flips results in a head is 1/2ⁿ. Thus, the probability that all n flips are heads is (1/2)ⁿ.

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Answer:

Explanation:

Given the equation of the line as;

We can express y in terms of x by subtracting x from both sides of the equation;

Let the point on the line be P(x, y)

We'll use the below distance formula to determine the distance between point P(x, y) to the given point (6, 8) as seen below;

Answer: 15,600 different choices for initials

Step-by-step explanation:

26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.

Answer:

I think the answer is B

Step-by-step explanation:

The inequality that represents "all real number's 'x' greater than 2" is \(x > 2\) and the inequality that represents "6 more than a number 'k' is less than or equal to 12" is \(6 + k \leq 12\).

a)

Given :

All real number's 'x' greater than 2

So, the inequality that represents the given verbal expression is given below:

\(x > 2\)

where 'x' is the real number.

b)

Given :

6 more than a number 'k' is less than or equal to 12.

So, the inequality that represents the given verbal expression is given below:

\(6 + k \leq 12\)

where 'k' is the given number.

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Answer:

150-200

Step-by-step explanation:

Answer:

4 x 6 = 24 feet squared

Step-by-step explanation:

Answer:

       0.59 < 0.6

14.807 < 14.087

Step-by-step explanation:

all the bolded ones are correct

The correct comparisons are 0.59 < 0.6, 6.580 = 6.58 and 4.59 < 4.598.

Decimals are types of real numbers where the fractional number is simplified by base-10 number system. It involves a whole number part and a decimal part separated by a decimal point.

Any whole number 'a' can be written as decimal as a.00...

The first place value after the decimal point is called tenths, second value is called hundredths, third value is called thousandths and so on.

The comparison 0.59 < 0.6 is true, since the tenths of 0.59 is 5 which is less than the tenths of 0.6, which is 6.

The comparison 6.580 = 6.58 is also true, since the zeroes on the last after decimal point have no value.

The comparison 33.54 < 33.504 is false, because the hundredths of 33.54, 4, is greater than the hundredths of 33.504 which is 0.

The comparison 14.807 <14.087 is false, because tenths of 14.807 is 8 which is greater than the tenths of 14.087, which is 0.

The comparison 4.59 < 4.598, because the thousandth of 4.59 can be told as 0 which is less than the thousandths of 4.598, which is 8.

Hence  0.59 < 0.6, 6.580 = 6.58 and 4.59 < 4.598 are the correct comparisons given.

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The arithmetic mean is 59.

What is arithmetic mean?

It is the sum of collection of numbers divided by the count of the numbers.

Conider AB is the nuber satisfying the condition. Hence,

\(10A+B=A+B+A\times B\\9A=A\times B\\\)

Since AB is a two digit number hence, \(A\neq 0\\\). Hence, divide both sides by \(A\).

\(9=B\)

Hence, B is 9 and A can take any value from 1 to 9.

Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.

Now, calculate arithmetic mean as follows:

\(AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59\)

Hence, arithmetic mean of numbers is 59.

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Answer:

∠DEC = 83º

Step-by-step explanation:

∠BAC and ∠ABC combine is 105º.

∠ACB is 75º.

∠ECD is 75º.

180º-75º-22º=83º

Answer:

22/25

Step-by-step explanation:

it is 22/25 because 88/100 ÷2 = 44/50

and 44/50÷2= 22/25

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The expressions are solved below :

sinu = -3/5 3π/2 < u < 2π is [ 4th quadrant ]

Now we know that

By using trigonometric identities,

When there are trigonometric functions present in an expression or equation, trigonometric Identities come in handy. Every value of a variable appearing on both sides of an equation is valid in terms of trigonometric identities. These trigonometric functions of one or more angles, such sine, cosine, and tangent, are involved in these geometric identities.

sin²u + cos²u = 1

cos²u= 1-sin²u

cos²u = 1 -(-3/5)²

cos²u= 1 - 9/25

cosu = +4/5

:. u is in 4th quadrant

Now

1.  sin2u = 2 sinu cosu

= 2 (-3/5)(4/5) = -24/25

2. cos2u = 2cos²u- 1

       = 2(4/5)²- 1

       = 7/25

3. tan2u = sin2u /cos2u

              = -24/7

The exact values of the sine, cosine, and tangent of the angle are found.

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a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

hope it is helpful to you

Answer:

Step-by-step explanation:

 x - 3y = 5

2x +  y = 10  multiply by 3 to eliminate y and solve for x

 x - 3y = 5

6x + 3y = 30  then add

7x          = 35

simplify:

x = 35 / 7

x = 5  

substitute x = 5 back into the eq.2

 2x +  y = 10

2(5) +  y = 10

           y = 10 - 10

           y = 0

therefore the answer is ( 5, 0 )

Step-by-step explanation:

a)316/5 = 63.2

b)141/4= 35.25

c)268/8= 33.5

d)158/6 = 26.3333333

a decimal fraction in which a figure or group of figures is repeated indefinitely, so answer is d)

Answer: Triangle ABE is similar to triangle ACD.

Step-by-step explanation:

Answer:

Property of Symmetry

Step-by-step explanation:

The symmetric property of equality tells us that both sides of an equal sign are equal no matter which side of the equal sign they are on. Remember it states that if x = y, then y = x.

An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.

He found that before launching the new marketing plan, there were 4,800 visits.

Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Over the course of the next 5 weeks, initial visitor at x = 0, 4800

Increasing factor = 1.5

Equation of the model is given as:

f(x) = a(b)^x

From the question b = 1.5

Now the equation of model is:

f(x) = a(1.5)^x

At x = 0, f(x) = 4800

Now the equation of the model is:

4800 = a(1.5)^x

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Answer:

0

Step-by-step explanation:

I hope this helps!

Answer:

Its the same so.. 0???????

Answer:

i thank is is the number 2

a. The cost of each yoghurt to the nearest cent is 21,583 cents.

b. The cost of each yoghurt to the nearest rand is R216.

Given the following data:

a. To calculate the cost of each yoghurt to the nearest cent:

First of all, we would divide the total cost of a pack of six yoghurts by the total amount of yoghurts bought as follows:

\(A \;yoghurt = \frac{1295}{6}\)

A yoghurt = R215.833.

Conversion:

1 Rand = 100 cents.

215.833 Rand = X cents.

Cross-multiplying, we have:

X = \(215.833 \times 100\) = 21,583.3 cents.

A yoghurt ≈ 21,583 cents.

b. To calculate the cost of each yoghurt to the nearest rand:

A yoghurt = R215.833 ≈ R216.

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There are $22$ valid $3$-word sentences in gnollish.

We can count the number of valid sentences by counting the number of all possible 3-word sentences and subtracting the number of invalid sentences where "splargh'' comes directly before "glumph.''

The total number of possible 3-word sentences is 3³ = 27, as there are 3 choices for each word.

To count the number of invalid sentences where splargh'' comes before glumph,'' we can fix splargh'' in the first position and then there are only 2 choices for the second position and 2 choices for the third position (since we cannot use splargh'' or glumph'' again). Thus, there are 2 * 2 = 4 invalid sentences where splargh'' comes before ``glumph.''

Therefore, the number of valid sentences is 27 - 4 = 23. However, we must also exclude the sentence where all three words are the same (i.e., ``splargh splargh splargh''), since this sentence is not valid according to the given condition. Thus, the final answer is 23 - 1 = 22.

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Answer:

6 feet

Step-by-step explanation:

Because diameter=radiusx2

                    6 feet=3 feetx2

The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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