if it can be assumed that the population is normal, then what is the probability that one man sampled from this population has a weight between 72kg and 88kg

If there is such a scalar function f, then

[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]

[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]

Integrate both sides with respect to y :

[tex]g(y,z)=4ye^{4z}+h(z)[/tex]

Plug this into the equation above with f , then differentiate both sides with respect to z :

[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]

Integrate both sides with respect to z :

[tex]h(z)=C[/tex]

So we end up with

[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]

Answer:

The relation ship is both are opposites

Step-by-step explanation:

so what is factorising ???

factorizing is like this example : 4x+32 = 4(x+8)

so u take the expression make it factorized or shorter or in a way that you multiply them .

what is expanding well its the opposite

suck as  4(x+8)=4x+32

Answer:

Step-by-step explanation:

y=2/5x+2

x= 5/2y-5

hopefully this works

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Answer:

(f+g)(x) = 5x + 3

Step-by-step explanation:

(f+g)(x) is the sum (term by term) of f(x) and g(x):

(f+g)(x) = 2x - 6 + 3x + 9

Combining like terms, we get

(f+g)(x) = 5x + 3

Answer:

(f+g)(x)= 5x+3

Step-by-step explanation:

The question asks us to find (f+g)(x). In other words, the sum of f(x) and g(x).

f(x) + g(x)

We know that f(x)= 2x-6 and g(x)=3x+9. Therefore, we can substitute the expressions in.

(2x-6) + (3x+9)

Now, simplify by combining like terms. Add the terms with variables, then the terms without variables.

(2x+3x) + (-6+9)

Add 2x and 3x.

5x + (-6 + 9)

Add -6 and 9.

5x + 3

If f(x)=2x-6and g(x)=3x+9, then (f+g)(x) is 5x+3

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

Answer:

40 minutes

Step-by-step explanation:

If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it  will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)

8(6) = 48

The question asks for how many more minutes it will take, so subtract 48 by 8.

48 - 8 = 40

= 40 minutes

Answer:

40 minutes

Step-by-step explanation:

We can use ratios to solve

8 minutes          x minutes

------------------- = ----------------

1/6 yard                 1 yard

Using cross products

8 * 1 = 1/6 x

Multiply each side by 6

8*6 = 1/6 * x * 6

48 = x

48 minutes total

She has already done 8 minutes

48-8 = 40 minutes

Answer:

9

Step-by-step explanation:

9 x 9 = 81

Answer:

x = ±9

Step-by-step explanation:

x^2 = 81

Take the square root of each side

sqrt(x^2 ) = ±sqrt(81)

x = ±9

Answer:

[tex]\boxed{\sf 24\ cookies}[/tex]

Step-by-step explanation:

1 cookie = 1/16 of a pound of cookie

If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16

=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]

=> [tex]\frac{3}{2} * 16[/tex]

=> 3*8

=> 24 cookies

Answer:

24 cookies

Step-by-step explanation:

3/2= 1.5 and 1/16= 0.0625

if you divide the amount of dough you have by the amount needed for each cookie you will have 24

1.5/0.0625=24

Answer:

Hey there!

[tex]\frac{75}{300}[/tex]=[tex]\frac{x}{10000}[/tex]

750000=300x

x=2500

They should make 2500 yellow shoes.

Hope this helps :)

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.

Explanation:

The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).

Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.

Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.

You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.

Answer:

Point D is located at (5, -2)

Step-by-step explanation:

The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

_____

A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

Answer:

Hey there!

Here are a few steps:

Make sure your work is properly marked, because then it will be protected under law.

Register your work.

Keep or register supporting evidence.

Let me know if this helps :)

Answer:

60 Feet =  18.288 Meters

Step-by-step explanation:

foot = 12 inch = 0.3048 m

0.3047 × 60

18.288 meters

Answer:

154.10 Feets

Step-by-step explanation:

Given the following :

Height (h) of cliff = 320 feet

Angle of depression of near side = 16.5°

Angle of depression of far side = 10.5°

Using trigonometry :

We can obtain x and y as shown in the attached picture :

Tanθ = opposite / Adjacent

Adjacent = height of cliff = 320 Feets

For the near side :

Tanθ = opposite / Adjacent

Tan (16.5°) = x / 320

0.2962134 = x / 320

x = 0.2962134 * 320

x = 94.788318 Feets

For the far side :

Tanθ = opposite / Adjacent

Tan (10.5°) = x / 320

0.1853390 = x / 320

x = 0.1853390 * 320

x = 59.308494 Feets

Length of island = (59.308494 + 94.788318) feet

= 154.10 Feets

Answer:

Solution : 6 + 6i

Step-by-step explanation:

[tex]-3\left[\cos \left(\frac{-\pi }{4})\right+i\sin \left(\frac{-\pi }{4}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi }{2}\right)\right][/tex]

This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )

( Multiply both expressions )

[tex]-6\sqrt{2}\left[\cos \left(\frac{-\pi }{4}+\frac{-\pi \:\:\:}{2}\right)+i\sin \left(\frac{-\pi \:}{4}+\frac{-\pi \:\:}{2}\right)\right][/tex]

( Simplify [tex]\left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] for both [tex]\cos \left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] and [tex]i\sin \left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] )

[tex]\left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] = [tex]\left(-\frac{3\pi }{4}\right)[/tex]

( Substitute )

[tex]-6\sqrt{2}\left(\cos \left(-\frac{3\pi }{4}\right)+i\sin \left(-\frac{3\pi }{4}\right)\right)[/tex]

Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )

sin(π / 4) = √2 / 2 = cos(π / 4)

( Substitute )

[tex]-6\sqrt{2}\left(-\sqrt{2} / 2 -i\sqrt{2} / 2 )[/tex]

= [tex]-6\sqrt{2}\left(-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] = [tex]-\frac{\left(-\sqrt{2}-\sqrt{2}i\right)\cdot \:6\sqrt{2}}{2}[/tex]

= [tex]-3\sqrt{2}\left(-\sqrt{2}-\sqrt{2}i\right)[/tex] = [tex]-3\sqrt{2}\left(-\sqrt{2}\right)-\left(-3\sqrt{2}\right)\sqrt{2}i[/tex]

= [tex]3\sqrt{2}\sqrt{2}+3\sqrt{2}\sqrt{2}i:\quad 6+6i[/tex] - Therefore our solution is option a.

Answer:

Step-by-step explanation:

I used x instead of ()

The initial function is:

● x = 1

The function after the changes is

● (1/2)x + 7

The function was shifted 15 unit to the left

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

80,023 written in scientific notation is [tex]8,0023[/tex] x [tex]10^4[/tex].

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 80,023

New Number: 8.0023

Step 2

New Number: 8 . 0 0 2 3

Decimal Count:   1 2 3 4

Now, to find b, count how many places to the right of the decimal.

There are 4 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 8.0023

b = 4

Now the whole thing:

8.0023 x 104

Step 4

Check your work:

10^4 = 10,000 x 8.0023 = 80,023

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

C. 47.5%

Step-by-step explanation:

The  summary of the given statistics include:

mean =150000

standard deviation: 1200

The  objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400

The z score formula can be use to calculate the percentage of the buyer who paid.

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

For the sample mean x = 150000

[tex]z = \dfrac{150000 - 150000}{1200}[/tex]

[tex]z = \dfrac{0}{1200}[/tex]

z = 0

For the sample mean x = 152400

[tex]z = \dfrac{152400 - 150000}{1200}[/tex]

[tex]z = \dfrac{2400 }{1200}[/tex]

z  = 2

From the standard normal distribution tables

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5% therefore option C is correct

This question is based on concept of  statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.

Given:

Mean is $150,000, and

Standard deviation is $1200.

We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

[tex]\bold{z=\dfrac{x-\mu }{\sigma}}[/tex]

As given in question sample mean i.e. X= 150,000

[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]

Now for the sample mean X = 152,400 ,

[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]

By using standard normal distribution table,

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5%

Therefore, correct option is C that is 47.5%.

For further details, please prefer this link:

https://brainly.com/question/23907081

We have

M(X) = (X + 5)/(X - 1)

N(X) = X - 3

So,

M(N(X)) =  [(X - 3) + 5]/[(X - 3) - 1]

The M(N(X)) domain will be:

D = {X / X ≠ 4}

4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be

H(X) = 1/(X - 4)

Answer:

The sine ratio is the ratio between the opposite side over hypotenuse. The cosecant ratio is the ratio between the hypotenuse over the opposite side, therefore cosecant is the reciprocal of sine.

To find a missing angle using sine, you would need to use the inverse of sine. For example,  if the sine was  [tex]\frac{30}{40}[/tex], to find the angle you would need to find sin⁻¹ of  [tex]\frac{30}{40}[/tex] which is x =  sin⁻¹ (0.75). Therefore x equals approximately 49°.  

Answer:

[tex]$\mathbf{\frac{1}{19} }[/tex]

Step-by-step explanation:

[tex]$$\bullet \Nth \ Term;\\$$$\frac{n+2}{2n^{2} +3n-2}[/tex]

[tex]$$\bullet U_{10} \ Term;\\\\$$\boxed{\frac{(10+2) }{2*10^{2} +3*10-2}= \frac{1}{19} }[/tex]

Answer:

[tex]\boxed{\displaystyle \frac{1}{19}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{n+2}{2n^2 +3n-2}[/tex]

Replace n with 10 to find the 10th term.

[tex]\displaystyle \frac{10+2}{2(10)^2 +3(10)-2}[/tex]

Evaluate.

[tex]\displaystyle \frac{12}{2(100) +30-2}[/tex]

[tex]\displaystyle \frac{12}{200 +30-2}[/tex]

[tex]\displaystyle \frac{12}{228}[/tex]

Simplify.

[tex]\displaystyle \frac{1}{19}[/tex]

Answer:

Step-by-step explanation:

Hello,

[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The correct option is  D

Step-by-step explanation:

From the question we are told that

    The standard deviation is  [tex]\sigma = 16[/tex]

     The sample size is  n =  64

The standard error of mean is mathematically evaluated as

        [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

        [tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]

        [tex]\sigma _{\= x } = 2[/tex]

Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as

              [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

Generally  [tex]\frac{ \= x - \mu }{\sigma_{\= x }} = Z (The \ standardized \ value \ of \ \= x )[/tex]

So

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]

substituting values

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]

=>     [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]

From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]

                                                          [tex]P(Z < - 1) = 0.15866[/tex]

=>  [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]

=>   [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]

Answer:

a.

y= 40x +4000

x= 100 --> y= 40(100)+4000= 4000+4000=8000

x=200 --> y= 40(200)+4000= 6000+4000= 10000

x=300 --> y= 40(300)+4000= 12000+4000= 16000

(in $)

b.

y= 40x+4000

6200= 40x+4000

6200-4000= 40x

2200= 40x

2200/40= x

55= x

(in unit)

Step-by-step explanation:

I hope this helps

if u have question let me know in comments ^_^

Answer:

Hey there!

You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.

Let  me know if this helps :)

Answer:

–3 meters per second

Step-by-step explanation:

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1