At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n. The weight of the i th person in the elevator Is a continuous random variable Y, with mean E(Yi)=w. The random variable N and the random variables Yi are independent. Let W be the total weight of all people in the elevator at a given time. Prove that E(w)=w. (Hint: This is very simple to prove if you use properties of conditional expectation).

The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Answer:

Given that in a walking competition, Marlinda was 15m ahead of Sandra Evliani, and Marlinda steps 1m each time Sandra Elviani's foot steps 0.8m, to determine how many steps does Sandra Elviani have to make to match Marlinda, the following calculation must be performed:

Since Sandra Elviani walks 0.8 meters for every 1 meter that Marlinda walks, and that she has an advantage of 15 meters in the competition, it is impossible that at that rate Sandra can reach her. This is so because for each step of Marlinda, Sandra will be 0.2 meters behind her, increasing the distance (1-0.8).

Answer:

46.2 degrees

Step-by-step explanation:

Use arcsin function (make sure calculator is in degree mode) and perform

\(sin^{-1} (\frac{13}{18} )\\=Angle\)

=46.2 degrees

Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2

The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201

Given that,
To complete the map diagram,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,

10th = 21
100th = 2001

For the value 17

17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,

Thus, The complete diagram map has been shown.

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She said it was a well opportunity, but I am not sure ! am ready has the comparative adverb to be incorrect.

A comparative adverb is known to be an adverb that is often used when a person want to make a comparison between one action of a verb with another.

The other part of the question are:

Conclusively, An example is: John ran fast, but Miracle came first because he ran faster than John.

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Answer:

She said it was a well opportunity, but I am not sure I am ready. Incorect

I am not feeling well today, but hopefully tomorrow I will feel more better. Incorect

The beach was more beautiful than the park. Correct

There is a good chance I will not be able to run faster than last year. Correct

Step-by-step explanation:

I took the test

Answer:

the equation 10 = x - y

Step-by-step explanation:

Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.

We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.

We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.

Therefore, the initial value of the investment was $50.

Answer:

\(\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x\)

Step-by-step explanation:

This derivative consist in the sum of three functions: \(f(x) = 81\cdot \sin^{-1} x^{9}\), \(g(x) = - x^{81}\) and \(h(x) = - x^{2}\). According to differentiation rules, the derivative of a sum of functions is the same as the sum of the derivatives of each function. That is:

\(\frac{d}{dx} [f(x)+g(x) + h(x)] = \frac{d}{dx} [f(x)]+\frac{d}{dx} [g(x)] +\frac{d}{dx} [h(x)]\)

Now, each derivative is found by applying the derivative rules when appropriate:

\(f(x) = 81\cdot \sin^{-1} x^{9}\) Given

\(f'(x) = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}}\) (Derivative of a arcsine function/Chain rule)

\(g(x) = - x^{81}\) Given

\(g'(x) = -81\cdot x^{80}\) (Derivative of a power function)

\(h(x) = - x^{2}\) Given

\(h'(x) = -2\cdot x\) (Derivative of a power function)

\(\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x\) (Derivative for a sum of functions/Result)

Answer:

a.

Step-by-step explanation:

The p-value is a measurement of the likelihood that a difference observed is due to a random chance or a sampling error. In an alternative way, the p-value of a study represents the probability or area under distribution for obtaining more radical outcomes whenever the null hypothesis is true.

Any observable change is deemed to be addressed by sampling variability if the P-value is greater than the selected alpha level. A statistical test will nearly always show a substantial difference with a suitably big sample unless there is no impact at all when the effect size is exactly zero.

As a result, simply reporting the P-value alone for a study is insufficient to fully validate the results and findings of scientific publications.

The area of the composite shape is \(21\pi\text{ sq. units}\)

The shape is made up of four semi-circular regions. (see image attached to the solution). The area can be computed as follows:

\(Area=(A-C)+(B-D)\)

where each letter represents the areas of the associated semi-circles.

The area of a semi-circle is given by

\(Area_s=\dfrac{\pi r^2}{2}\)

For region \(A\), \(r=6units\)

\(A=\dfrac{\pi\times6^2}{2}\\\\=18\pi \text{ sq.units}\)

For region \(B\), \(r=4units\)

\(B=\dfrac{\pi\times4^2}{2}\\\\=8\pi \text{ sq.units}\)

For region \(C\), \(r=3units\)

\(C=\dfrac{\pi\times3^2}{2}\\\\=4.5\pi \text{ sq.units}\)

For region \(D\), \(r=1units\)

\(D=\dfrac{\pi\times1^2}{2}\\\\=0.5\pi \text{ sq.units}\)

So, the area of the shape is

\(Area=(A-C)+(B-D)\\\\=[(18-4.5)+(8-0.5)]\pi\\\\=21\pi\text{ sq.units}\)

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Answer: (assuming the first three terms are -6, -2, 2)

(a) f(n) = 4n - 10

(b) 30

Step-by-step explanation:

(So, just as a preface, I made this answer assuming the first three terms are -6, -2, and 2 since I couldn't find a provided fourth term as the problem said)

(a) In order to create an equation for an arithmetic sequence, you need to find the common difference(d) and the 0th term. You can find the common difference by finding the difference between two consecutive terms:

2 - (-2) = 4 (or (-2) - (-6) = 4), so d = 4

Now, you need to find the 0th term. To do this, you can just subtract the d from the first term, -6:

-6 - 4 = -10.

At this point, you can write the equation:

f(n) = -10 + 4n (this is the 0th term plus the common difference, 4, times the nth term)

f(n) = 4n - 10 (reorganize by value of exponents)

(b) In order to find the 10th term, you just need to plug it into the previous equation:

where n = 10, and f(n) = 4n - 10,

f(n) = 4(10) - 10 (substitute n into the equation)

f(n) = 40 - 10 (multiply the term in the parenthesis by the constant)

f(n) = 30 (subtract)

Answer:

y=\(\frac{5}{8}x\)

Step-by-step explanation:

So in this equation you have to do this with the points to get the slope

M= \(\frac{y2-y1}{x2-x1}\)

M is the slope so using this eqaution will give you the equation.

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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Answer:

33.67

Step-by-step explanation:

BODMAS (Bracket of Division Multiplication Addition Subtraction)

bracket then divide and so on

Answer:

33.67

Step-by-step explanation:

hope this helps have a wonderful day

Answer:

Step-by-step explanation:

Given function:

The function is plotted and it is below.

The graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

Therefore graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

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Answer:

Step-by-step explanation:

-5y=20

The variation equation in the scenario is y = 25/√x

The variation statement is given as:

y varies inversely with x sqr(x)

Inverse variations are represented as:

y = k/√x

Where k represents the constant of variation/proportionality

When y = 5, x = 25

So, we have:

5 = k/√25

Evaluate the exponent

5 = k/5

Multiply by 5

k = 25

Substitute k = 25 in y = k/√x

y = 25/√x

Hence, the variation equation is y = 25/√x

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Answer:-(-1,026/3

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer: 28%

Step-by-step explanation: So, if we know that Mia's team won 18 of the 25 games they played, we need to subtract 18 from 25. We get 7. So, now we need to use this formula to solve:

Part percent / Whole number * 100

Let's plug in the numbers:

7 / 25 * 100

0.28 * 100

= 28

Therefore, they lost 28% of their games. I hope this helped!

Answer:

28%

Step-by-step explanation:

To find percentages, we need to know the number of games lost out of 25, then multiply it by 4 to get our percentage. We know that she won 18 of 25. 25 - 18 =7, so she lost 7 games. This gives us the fraction:

\(\frac{7}{25}\)

Then, we will multiply this fraction by 4 to get it out of 100:

\(\frac{28}{100}\)

This gives us 28/100, to find the percentage out of a fraction with a denominator of 100, we multiply by 100 and add a % symbol. This gives us:

\(\frac{28}{100} * 100 = 28%\)

Then, we add our percent symbol, meaning Mia's soccer team lost 28% of their games.

Hope this helped!

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Answer:

200 x 20% = 200 x 20/100 = 40.

Answer is 40.

Answer:

this is correct

Step-by-step explanation:

A dividend is a number we want to divide by another number. It's supposed to be greater than 1000.

Quotient - the integer result of division. Remainder - well, what remains.

9/4 = 2, with remainder 1.

You want to find a number greater than 1000, which, when divided by another number, results in 37, with a remainder of 4.

I would multiply 37 by an increasing number until we get a product greater than 1000. This number is the one you are dividing by. Now add 4 to the product, so that when the sum is divided by the number you found we'll get a remainder of 4.

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

31(given degree) + a(unknown degree) = 90 degrees(right angle shown is equal to 90 degrees)

31 + a = 90

-31        -31

A = 59 degrees.

Answer:

Step-by-step explanation:

1 )

\(\frac{2}{5}( \frac{5x}{4} - \frac{10}{3})-\frac{4x}{3} \\\frac{x}{2} - \frac{4}{3} - \frac{4x}{3}\\ \frac{-5x}{6}-\frac{4}{3}\)

2 )

\(\frac{17x}{8}+\frac{3x}{4}+\frac{1}{6}-\frac{7x}{12}+\frac{17}{3}\\ \frac{51x}{24}+\frac{18x}{24}-\frac{14x}{24}+\frac{35}{6}\\\frac{55x}{24}+\frac{35}{6}\)

1. The given series is

 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) =  

For n=1

L.H.S=4.6=24

R.H.S=[4×5×15]÷6

      =300÷6

      =50

So, for n=1,

L.H.S≠ R.H.S

Since the given expression is true for n=1 ,

So , the given series is untrue.

we should replace R.H.S by=4(n+1)(n+2)(4n-3)²

2.

12+42+72+.......+(3 n -2)2=

For n=1,

L.H.S=12

R.H.S=1×(6-3-1)/2

       =2/2

      =1

As L.H.S≠ R.H.S

We should Replace R.H.S by [(3 n-1)(3 n-2)]2

3.The given sequence is

2+4+6+....+2n=n(n+1)

L.H.S

P(1)=2

R.H.S

1×(1+1)

=1×2

=2

( b)  L.H.S

P(n)=2+4+6+.....2 k

This is an A.P having n terms.

tex]S_{n}=

              = n(n+ 1)

R.H.S=n(n+1)

So, P(k)=k(k+1)

(c) P(k+1)=2+4+6+.......+2(k+1)

This is an A.P having (k+1) terms.

              =(k+1)(k+2)

So, P(k+1)= (k+1)(k+2)

(Btw this is not my answer)

Answer:

10.4

Step-by-step explanation:

Trust me Sorry if wrong

Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³