Rewrite the expression in the form y^n. y^5/4 / y^1/4

Answer:

Expected value x= 35

linear transformation is defined as a + bx

here, b=4, a=1

The transformation is [tex]z=1+4x[/tex]

now, expected value, [tex]l_z=l_z(a+bx)[/tex]

[tex]=l(a)+l(bx)[/tex]

[tex]=a+b\:l\:x[/tex]

substitute the value of a=1, b=4 and l=35

[tex]l_z=1+4\times35[/tex]

[tex]=1+140[/tex]

[tex]=141[/tex]

So, the expected value of the transformed variable is 141.

OAmalOHopeO

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

Explanation:

Let's consider a set of three values such that they're all equal to 35

{35,35,35}

This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.

If we multiply everything by 4, then we get the new set {140,140,140}

Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.

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

You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.

If we quadruple each item, then we have {34,35,36} turn into {136,140,144}

Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.

These are just two examples you could do to help see why the answer is D) 141

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

In a more general theoretical sense, we're saying the following

Y = mX+b

E[Y] = E[m*X+b]

E[Y] = E[m*X] + E[b]

E[Y] = m*E[X] + b

where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.

So,

E[Y] = m*E[X] + b

E[Y] = 4*35 + 1

E[Y] = 141

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

Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.

A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.

Step-by-step explanation:

here's the answer to your question

Answer:

x = 6 and x = 9

Step-by-step explanation:

16

MN is half the length of KL

MN = [tex]\frac{1}{2}[/tex] × 12 = 6

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

17

Δ LMN and Δ LJK are similar triangles, so the ratios of corresponding sides are equal, that is

[tex]\frac{LM}{LJ}[/tex] = [tex]\frac{MN}{JK}[/tex] , substitute values

[tex]\frac{x}{x+9}[/tex] = [tex]\frac{8.5}{17}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 9 ( subtract x from both sides )

x = 9

[tex] \sf \: \frac{5}{21 } \: rounded \: to \: 3 \: decimal \: places \: is \: \boxed{ \underline{ \bf0.238}}. \\ \longrightarrow \sf \: Just \: divide \: 5 \: by \: 21 \: upto \: 3 \: decimal \: places \\ \sf \: to \: get \: the \: answer.[/tex]

Answer:

leg = 18

hypotenuse = 18 sqrt(2)

Step-by-step explanation:

We know that sin theta = opp side / hypotenuse

sin 45 = 18 / hyp

hyp sin 45 = 18

hyp = 18 / sin 45

hyp = 18 sqrt(2)

Since this is an isosceles triangle ( the two angles are the same measure), the two legs have to be the same length

leg = 18

the lengths of the other leg and the hypotenuse

is 18 units and 18[tex]\sqrt{2}[/tex]units respectively.

Answer:

Solution given:

Let <C=<B=45°

AB=18 units

BC=?

AC=?

again

By using

By usingspecial right triangle ratios

sin C=opposite/hypotenuse=AB/AC=18/AC

Sin 45=18/AC

AC=18/sin45

AC=hypotenuse=18[tex]\sqrt{2}[/tex]units

again

Tan A=opposite/adjacent=BC/AB=BC/18

Tan45=BC/18

BC=Tan45*18

BC=length of another leg=18 units.

Answer:

263.25

Step-by-step explanation:

250 x .053 (5.3%) = 13.25 tax

250 + 13.25 = 263.25 price plus sales tax

Answer:

263.25

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

X^2 - 7 =

Since we need to evaluate the expression when X = 5, we replace X with 5.

= 5^2 - 7

Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25

= 25 - 7

Finally, we subtract.

= 18

Answer: 18

Answer:

I think this is the ans

Step-by-step explanation:

ab+c=0

(p+q)(p-q)=0

p Square-q Square =0

0=p Square-q Square

Answer:

all I know is sin square A +cos square A =1

Step-by-step explanation:

[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]

Answer:

0.75 → 0.5 → 1/3(0.33) → 1/4(0.25)

Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

Answer:

see below

Step-by-step explanation:

Part 1:

(512) ^ 1/3

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

(2197) ^ 1/3

8

-----

13

The scale factor is 8:13

Part 2

The ratios of the areas is related by scale factor squared

8^2

-----

13^2

64      

------  

169

Part 3

64       960

------  = ----------------

169     SA larger

Using cross products

64 * SA = 169 * 960

64 SA = 162240

Divide each side by 64

64 SA/ 64 = 162240 / 64

SA = 2535

2535 cm^2

Answer:

3(f - 9)(f + 4)

Step-by-step explanation:

Assuming you require to factorise the expression

3f² - 15f - 108 ← factor out 3 from each term

= 3(f² - 5f - 36) ← factor the quadratic

Consider the factors 0f the constant term (- 36) which sum to give the coefficient of the f- term (- 5)

The factors are - 9 and + 4 , since

- 9 × 4 = - 36 and - 9 + 4 = - 5 , then

f² - 5f - 36 = (f- 9)(f + 4)

Then

3f² - 15f - 108 = 3(f - 9)(f + 4)

Answer:

B

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]

Then

cosA = sinC → B

Answer:

Step-by-step explanation:

5.1, please this is just a guess from using my head to calculate

Answer:

x = 3

Step-by-step explanation:

In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.

-x,  x < -3

So, we can start by setting -x equal to -9 and solve for x:

-x = -9

x = 9

Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.

2x,   -3 ≤ x ≤ -2

We can set the value 2x equal to -9 and, again, solve for x:

2x = -9

x = -4.5

The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.

-x^2,  x > -2

One last time, we can set -x^2 equal to -9 and solve for x:

-x^2 = -9

x^2 = 9

x = 3, x = -3

We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.

In conclusion, the only solution where it fit the domain was x = 3

Answer:

x = 3

Step-by-step explanation:

x = - 3 in interval - 3 ≤ x ≤ - 2 then f(x) = 2x , so

f(- 3) = 2(- 3) = - 6 ≠ - 9

x = 9 in interval x > - 2 then f(x) = - x² , so

f(9) = - 9² = - 81 ≠ - 9

x = 3 in interval x > - 2 then f(x) = - x²

f(3) = - 3² = - 9

x = - 4.5 in the interval x < - 3 then f(x) = - x , so

f(- 4.5) = - (- 4.5) = 4.5

Thus

y = - 9 when x = 3

Answer:

firstable give c+b a polynomial value like x

so its will be x^2+11x+30

after the we have to factor it

30=6×5

and 11=6+5

so its will become

(x+6)×(x+5)=x^2+11x+30

x=c+d

(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30

have a great day

Answer:

12.56 m

Step-by-step explanation:

The circumference of a circle is given by

C  = 2 * pi *r

C = 2 * (3.14) * 2

C =12.56

Answer:

(C) 2x^3 - 3x^2 - 35x + 36

Step-by-step explanation:

First multiply 2x by x^2 + 3x - 4:

(2x)(x^2 + 3x - 4)

2x^3 + 6x^2 - 8x

Next multiply -9 by x^2 + 3x - 4:

(-9)(x^2 + 3x - 4)

-9x^2 - 27x +36

Now add the two polynomials by adding like terms:

(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)

2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36

2x^3 - 3x^2 - 35x + 36

Hope this helps (●'◡'●)

Answer:

Which subject is this . please tell

Answer:

see explanation

Step-by-step explanation:

1

(a)

Calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁  = (8, 3) and (x₂, y₂ ) = (10, 7)

m = [tex]\frac{7-3}{10-8}[/tex] = [tex]\frac{4}{2}[/tex] = 2

(b)

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

(c)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, 3) into the partial equation

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of perpendicular line

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

2

(a)

with (x₁, y₁ ) = (3, 5) and (x₂, y₂ ) = (4, 4)

m = [tex]\frac{4-5}{4-3}[/tex] = [tex]\frac{-1}{1}[/tex] = - 1

(b)

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1

(c)

y = x + c ← is the partial equation

To find c substitute (3, 5) into the partial equation

5 = 3 + c ⇒ c = 5 - 3 = 2

y = x + 2 ← equation of perpendicular line

Answer:

d) p(x)= 7x-2

Step-by-step explanation:

d) p(x) = 7x -2

Answer:

it's 'A' I guess

Step-by-step explanation:

hope it helps

Answer:

Choice A

Step-by-step explanation:

An arithmetic sequence is one which has an incremental change.

for our answer, our change is +5

Answer:

see explanation

Step-by-step explanation:

Using the identities

cotA = [tex]\frac{1}{tanA}[/tex]

cot²A = cosec²A - 1

tan²A = sec²A - 1

Consider the left side

(cotA + tanA)² ← expand using FOIL

= cot²A + 2cotAtanA + tan²A

= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1

= cosec²A - 1 + 2 + sec²A - 1

= sec²A + cosec²A - 2 + 2

= sec²A + cosec²A

= right side, thus proven

Answer:

please see the answer in the picture.

Answer:

14

Step-by-step explanation:

7*4*1/2=14

Answer:

The LCM of 100 and 120 is 600.

The LCM of 5 and 120 is 120.

LCM of 5 and 100 is 100.

Step-by-step explanation:

I think this is the answer . If it is not sorry .

Answer:

Step-by-step explanation:

The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:

                          original                 new

length

width

And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:

                           original                  new

length                       L

width                       2L

Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.

The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:

                            original                        new

length                      L                       100%L + 50%L

width                       2L

The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:

                             original                       new

length                        L                     100%L + 50%L

width                        2L                  100%(2L) - 20%(2L)

And now we'll simplify that "new" column:

                              original                         new

length                        L                         150%L = 1.5L

width                         2L               80%(2L) = 160%L = 1.6L

Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:

248 = 2(1.5L) + 2(1.6L) and

248 = 3L + 3.2L and

248 = 6.2L so

L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)