E 4) In the diagram below, the dimensions of the large rectangle are (3x-1) by (3x+7) units. The dimensions of the cut-out rectangle are x by (2x+5) units. Which choice expresses the area of the shaded region, in Square units? ​

Answer:

A buoyant girl ant

Step-by-step explanation:

Two Answers: Angle 1, Angle 4

Adjacent angles share a common segment, line, or ray. Think of two adjacent rooms sharing a common wall.

Answer:(3,-4) you just have to follow the equation.

Slope = change in y over change in x.

Slope = (-6 - -9) / (-6 - -2)

Slope = (-6 + 9) / (-6 + 2)

Slope = 3/-4

Slope = -3/4

I'm assuming

[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]

(a) f(x) is a valid probability density function if its integral over the support is 1:

[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]

Compute the integral:

[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]

So we have

k / 6 = 1   →   k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]

We have

[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

Using probability concepts, it is found that

a) The value is k = 6.

b) P(Y ≤ .4|Y ≤ .8) = 0.554.

c) The 95th percentile is x = 0.86465.

The density function is:

[tex]f(y) = ky(1 - y)[/tex]

Item a:

The condition that makes it a probability density function is:

[tex]\int_0^1 f(y) dy = 1[/tex]

Thus:

[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]

[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]

Then

[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]

[tex]k(\frac{3-2}{6}) = 1[/tex]

[tex]k = 6[/tex]

The value is k = 6.

Item b:

This probability is:

[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]

Then

[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]

[tex]p = 0.554[/tex]

Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.

Item c:

This is x for which:

[tex]\int_0^x f(y) dy = 0.95[/tex]

Thus:

[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]

[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]

Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.

A similar problem is given at https://brainly.com/question/22223588

Answer:

consistent and dependent

consistent and independent

inconsistent and independent

Step-by-step explanation:

Answer:

1

2

4

Step-by-step explanation:

has nice day

9514 1404 393

Answer:

Step-by-step explanation:

The proportion of Asian Treasure is the difference in price of the mix and Paradise tea, divided by the difference in price of Asian Treasure and Paradise tea. So the amount of Asian Treasure is ...

  (6.00 -5.00)/(7.50 -5.00)(60 ounces) = 24 ounces . . . Asian Treasure tea

The remaining 60-24 = 36 ounces will be Paradise tea.

__

Using an equation

You can get the same result if you define a variable (a) to the amount in ounces of the higher-priced contributor. Then the lower-priced contributor will be in the amount (60-a) ounces. The total cost of the mix is ...

  7.50a +5.00(60 -a) = 60(6.00)

  (7.50 -5.00)a +60(5.00) = 60(6.00) . . . rearrange the left side

  (7.50 -5.00)a = 60(6.00 - 5.00) . . . . . .  subtract 60(5.00)

  a = 60(6.00 -5.00)/(7.50 -5.00) . . . . . . divide by the coefficient of 'a'

Note that this last expression is identical to the one we used above to find the quantity of Asian Treasure tea.

Answer:

Use the number line and split the whole numbers into fractions

Step-by-step explanation:

Example: If a number line goes from -10 all the way to +10, and you are trying to find the distance between -2 1/4 and -7 3/4. You would split the number line into fourths and then locate -7 3/4. You would then count up to -2 1/4 to get 4 3/4.

Hopefully this makes sense!

Answer:

the expression is equal to 0

Answer:

96

Step-by-step explanation:

1200*92=110400/100=1104

1200-1104=96

Answer:

1152 students like rap just take the numbers n divide

Answer:

Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce

Answer:

12 ounces

Step-by-step explanation:

3.60 = .3x

divide by .3 on both sides

12 = x

Answer:

100 thousandths

Step-by-step explanation:

Answer:

below in bold

Step-by-step explanation:

f(x) = 2x - 7 - 3

~Combine like terms

f(x) = 2x - 10

When x = 2...

f(x) = 2(2) - 10

f(x) = 4 - 10

f(x) = -6

When x = 3...

f(x) = 2(3) - 10

f(x) = 6 - 10

f(x) = -4

When x = 4...

f(x) = 2(4) - 10

f(x) = 8 - 10

f(x) = -2

Best of Luck!

Answer:

Directions Unclear:

Step-by-step explanation:

I am now drowning on air.

Answer:

ok

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

The phrase is Scale by a factor of 1 /r and rotate clockwise by θ.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number.

Given:

z=r(cos θ + i sin θ)

So, to divide a complex number the best phrase to describe is Scale by a factor of 1 /r and rotate clockwise by θ.

Learn more about complex number here:

https://brainly.com/question/28007020

#SPJ2

The number of marbles Peter had when he arrived home was 43 marbles

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

The number of marbles Peter had on his way home = 171

The amount of marbles he lost on his way home = ( 3/4 ) th

Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home

The amount of marbles Peter have left = 1 - 3/4

                                                                = ( 1 / 4) th

So , The number of marbles Peter had left when he arrived home is =

Amount of marbles Peter have left x Number of marbles Peter had

The number of marbles Peter had left when he arrived home is = (1/4) x 171

= 171 / 4

= 42.75

≈ 43 marbles

Hence , the number of marbles Peter had left when he reached home is 43

To learn more about percentage click :

https://brainly.com/question/12861068

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9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

When the graph of the left side of the equation does not intersect the graph of the right side of the equation, there are no solutions.

__

Additional comment

Even if you extend the domain to complex numbers, there are no solutions. The f(x) = |x| function always returns a positive real value, even for complex numbers.

Answer:

7 pounds

Step-by-step explanation:

1 pound is $4 28/4 is 7

Answer:

7

Step-by-step explanation:

First do 3x2 to get 6, and then do 8-6, which is 2, and add that to 5 to get 7

Answer: OK, the answer is 28.

Step-by-step explanation: Also there is no remainder for this division problem, you could have the remainder if the numbers are not the same as a multiplication problem, so did you get it?

Answer:

8%

Step-by-step explanation:

Starting Principal: $  

3,000.00

Years:    

3

Annual Interest Rate:    

8

%

Results

Future Value, using...

 Simple Interest: $  

3,720.00

 Annually Compounded Interest: $  

3,779.14

Answer: 3x - 8

Hope it helps!

Answer:

9 + 6 + 4 − 2 + 1 − 1 5

9x+{\color{#c92786}{6}}+4x-2x+{\color{#c92786}{1}}{\color{#c92786}{-15}}

9x+6+4x−2x+1−15

9 − 8 + 4 − 2

Step-by-step explanation:

Answer:

c = 6+2x

Step-by-step explanation:

c = total cost, 6 = entrance fee, 2x = 2 dollars per food/drink item