Suppose U1 and U2 are i.i.d. Unif(0,1) withU1=0.1 and U2=0.8. Use the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees.
a. 0.326
b. 0.326
c. 0.663
d. 1.96

9514 1404 393

Answer:

  x = 22, y = 123

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  (2x +13)° +57° +3x° = 180°

  5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °

  5x = 110 . . . . . . . . . . . subtract 70

  x = 22 . . . . . . . . divide by 5

__

Angles in a linear pair are supplementary.

  y° + 57° = 180°

  y = 123 . . . . . . . . divide by °, subtract 57

9514 1404 393

Answer:

  x² +y² -6x -16y +48 = 0

Step-by-step explanation:

Given:

Find:

  general form equation for the circle

Solution;

The standard form equation for the circle is ...

  (x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)

  (x -3)² +(y -8)² = 5²

Subtracting 25 and expanding this will give the general form.

  x² -6x +9 +y² -16y +64 -25 = 0

  x² +y² -6x -16y +48 = 0

_____

Additional comment

"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]

Answer:

0，0

Step-by-step explanation:

n=2，

[tex] {2}^{2} - 2 - 2 = 0 [/tex]

[tex] {2}^{2} - 5 \times 2 + 6 = 0[/tex]

Answer:

The answer should be (7, 5)

Answer:

90 cause 90 times 10 is 900 and 10% times 10 is 100%

Step-by-step explanation:

Answer: 90

Step-by-step explanation: 900 × .10 = 90

Answer:

D. <S, <R, <T

Step-by-step explanation:

Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.

In ∆RST,

The longest side, SR = 22, is opposite to <T

Therefore, <T is the biggest angle.

Medium side, ST = 21, is opposite to <R, therefore,

<R is the medium angle measure

The smallest angle measure <S is opposite to the shortest side, RT.

Angels I'm order form the smallest to largest will be:

<S, <R, <T

Answer:

6

Step-by-step explanation:

We have the expression "3x is 18" and we want to find out x, so the easiest way is to isolate x. The way to do this is by dividing both 3x and 18 by 3, leaving us with 6. This means that our answer for x is 6. I hope this helped and please don't hesitate to reach out for clarification!

Answer:

6

Step-by-step explanation:

3x = 18

Divide both sides by 3

3x / 3 ( the 3s cancel out and we're left with x )

18/3 = 6

We get that x = 6

We can then plug in 6 to x in 3x = 18 to check if our answer is correct

3x = 18

Replace x with 6

3(6) = 18

3(6) = 18

18 = 18

This is true hence we can confirm that x = 6

Answer:

6, 15, 24, 33

Step-by-step explanation:

Basically, the number on top of the sigma represents the number of terms total in that sequence, and on the right you have the equation in which you can plug in whichever value that falls into what the top number says to find the output. In other words, just plug in 1 for k to find a1, 2 for k to find a2, etc.

Hope that helps!

Answer:

30 gallons of each brand

Step-by-step explanation:

1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

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

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

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

Hope this is helpful.

Answer:

x = 3

Step-by-step explanation:

A midsegment in a trapezoid is formed when one connects the midpoints of the two legs (non-parallel sides) in a trapezoid. The midsegment theorem states that the length of the midsegment is equal to the average of the two bases (that is the parallel sides).

One can apply the midsegment theorem here by stating the following;

[tex]\frac{(YZ)+(TM)}{2}=PW[/tex]

Substitute,

[tex]\frac{23+11x+2}{2}=29[/tex]

Simplify,

[tex]\frac{25+11x}{2}=29[/tex]

Inverse operations,

[tex]\frac{25+11x}{2}=29[/tex]

[tex]25+11x=58\\\\11x = 33\\\\x = 3[/tex]

Answer: just had this problem! X = 11

Answer:

B

Step-by-step explanation:

Exclude C:

[tex] |x| [/tex]

is not curved

To shift right, minus inside the

[tex] |?| [/tex]

Thus

[tex] |x - 4| [/tex]

To shift up, add outside the

[tex] |?| [/tex]

Thus:

[tex] |x +4| + 2[/tex]

B

Brainliest please~

Answer:

C

Step-by-step explanation:

The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3

Answer:

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Step-by-step explanation:

Given

[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression

Required

[tex]\cos(\theta)[/tex]

We know that:

[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]

Make [tex]\cos^2(\theta)[/tex] the subject

[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]

Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]

[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]

Evaluate all squares

[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]

Take LCM

[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]

[tex]\cos^2(\theta)= \frac{13}{29}[/tex]

Take square roots of both sides

[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]

cosine is positive in the 4th quadrant;

So:

[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]

Split

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]

Rationalize

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Answer:

))

Step-by-step explanation:

just place your decimal once to the left I think

Answer:

144

Step-by-step explanation:

We can write this as 2 shirts = 16.00 . Then, we can write this as a ratio, where

2 shirts / 16.00 = 18 shirts/ cost of 18 shirts as the cost for a pair of shirts remains the same, so the ratio will as well.

Therefore, writing the cost of 18 shirts as c, we have

2 shirts/16.00 = 18 shirts/c

multiply both sides by c to remove a denominator

2 shirts * c/16.00 = 18 shirts

multiply both sides by 16 to remove the other denominator

2 shirts * c = 18 shirts * 16

divide both sides by 2 shirts to isolate the c, as we want to figure that out

c = 18 shirts * 16/2 shirts

c=144

Answer:

Step-by-step explanation:

The solution triangle attached below :

Since we have a right angled triangle, we can make use of Pythagoras rule to obtain the vertical distance, x

Recall :

Hypotenus² = opposite² + adjacent²

Hence,

x² = 61² - 60²

x² = 3721 - 3600

x² = 121

x = √121

x = 11

Vertical distance equals 11 inches

Answer:

108801

Step-by-step explanation:

Palindrome as defined in the given question as a number which reads the same forward and backward. Examples are: 1001, 20202, 1331 etc.

Thus, to determine the smallest 6-digit palindrome divisible by 99 without a remainder, the digits should be in the form of abccba.

Therefore, the smallest 6-digit palindrome that can be divided by 99 is 108801.

So that,

108801 ÷ 99 = 1099

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.

  x ∈ {5, 7}

__

The graph is below the x-axis between these points, so that is the region where f(x) < 0

  5 < x < 7 . . . . . for f(x) < 0

In interval notation: (5, 7).

Answer:

[tex]9 + 7i[/tex]

Step-by-step explanation:

[tex]7i^5+9i^8[/tex]

[tex]i^5 = i\\ i^8 = 1[/tex]

Answer:

(-2,3,10,8)

Step-by-step explanation:

eg

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

Answer:

[tex]h(f(4))=20[/tex]

Step-by-step explanation:

We are given the functions:

[tex]f(x)=x^2,\, g(x)=5x\text{, and } h(x)=x+4[/tex]

And we want to find

[tex]h(f(4))[/tex]

Find f(4) first:

[tex]f(4)=(4)^2=16[/tex]

Thus:

[tex]h(f(4))=h(16)[/tex]

Now, evaluate h(16):

[tex]h(16)=(16)+4=20[/tex]

Hence:

[tex]h(f(4))=20[/tex]

Answer:

$23.3

Step-by-step explanation:

you can use ratios to solve this:

$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99

So, 6.99 divided by 0.3 = 23.3

so the original price is $23.3

Answer:

[tex]\displaystyle V = \frac{625 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e