There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
1. What is the probability that the first machine produces an acceptable cork?
2. What is the probability that the second machine produces an acceptable cork?
3. Which machine is more likely to produce an acceptable cork?

Answer:

There are three basic trigonometric ratios: sine , cosine , and tangent .

Step-by-step explanation:

Answer:

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1)

Step-by-step explanation:

Let a be the first term.

Let a+d be the second term where d is the common difference.

Then a+2d is the third....

And a+(n-1)d is the nth term.

Adding these terms we get:

an+(n-1)(n)/2×d

For the first term of this sum I seen we had n amount of a's and for the second term I used the well known identity sum of the first n positive integers is n(n+1)/2.

Let's simplify:

an+(n-1)(n)/2×d

Distribute:

an+(n^2d/2)-(nd/2)

Find common denominator:

(2an/2)+(n^2d/2)-(nd/2)

Combine terms into one:

(2an+n^2d-nd)/2

Reorder terms:

(n^2d+2an-nd)/2

Regroup terms:

(n^2d+(2a-d)n)/2

We want the following sum though:

4n^2+3n

This means d/2=4 (so d=8) and (2a-d)/2=3.

So plug d=8 into second equation to solve for a.

(2a-8)/2=3

2a-8=6

2a=14

a=7

The sequence has first term 7 and common difference is 8.

So the sequence is f(n)=7 + 8(n-1).

Answer:

[tex] \frac{ \sqrt{3} }{3} [/tex]

Step-by-step explanation:

[tex]\frac{1}{3} \div \sqrt{3} [/tex]

Answer:

statistics are when data analyzed in order to make decisions about the population behind the data.

The correct answer to the question is Statistics (Option D).

What is statistics?

Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.

Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.

Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.

Therefore, Statistics the correct answer.

To know more about statistics refer:https://brainly.com/question/10734660

#SPJ2

Answer:

x=3

Step-by-step explanation:

2x+1=7

2x=7-1

2x=6

x=6/2

x=3

Answer:

Solution,

2x + 1=7

or 2x = 7 - 1

or, 2x= 6

or, x = 6

2

or, x = 3

.:. x = 3

We are given the matrices A and B

[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]

Multiplying these matrices:

We multiply matrices by taking the first column of the first matrix and the first row of the second matrix

we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one

[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]

9514 1404 393

Explanation:

Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).

For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)

__

The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).

It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...

  [tex]A_{i,j}[/tex]

For matrix C = A·B, the element C(1,1) will be the sum ...

  A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)

Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.

Here the product is ...

  [tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]

Answer:

(cosB-1)(cosB+6)

Step-by-step explanation:

use u substitution . u = cosB

u^2+5u-6

factor

(u-1)(u+6)

put cosB back in for u

(cosB-1)(cosB+6)

9514 1404 393

Answer:

  100°

Step-by-step explanation:

The relevant relation for angle x is ...

  x = (AB +DE)/2

and for angle y, it is ...

  y =(AC -DE)/2

Using the second relation to write an expression for DE, we have ...

  DE = AC -2y

In the first equation, this lets us write ...

  x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2

  2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2

  (2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3

  AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values

  AC = 100°

Answer:

3rd option

[tex]A) \frac{4-2}{2-1} =2[/tex]

[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]

[tex]C)>2[/tex]

[tex]D) 1[/tex]

~OAmalOHopeO

Answer:

The third one is your answer

Answer:

13

5 - -8

When you subtract a negative number it changes to an addition so 5- -8 becomes 5 + 8 which equals 13.

Answer:

Reflection

Step-by-step explanation:

Because reflecting yourself in a mirror means pre image to image

Answer:

Step-by-step explanation:

dilation

Answer:

[tex]A)58[/tex]

Step-by-step explanation:

[tex][Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\[/tex]

[tex]Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58[/tex]

[tex]Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58[/tex]

Answer:

Step-by-step explanation:

A) 26*26*26 =17576

B)26*25*24=15600

C)26*26=676

D) 26

Answer:

i believe it'll cost 200 dollars

Answer:

55.55 and 45.55

Step-by-step explanation:

Let the car 1 speed be x km/hr and car 2 speed be x-10 km/hr.

Their relative velocity is 2x-10.

Distance covered in 9 hrs=9(2x-10).

18x-90=910, x=55.55 km/hr, x-10=45.55km/hr

Answer:

The answer is 890 . ...... :D

Answer:

-1 <x < 7

(-1,7)

Step-by-step explanation:

open circle on the left means the number is greater than

-1 <x

Open circle on the right means the number is less than

x < 7

Since both statements are true. we combine them

-1 <x < 7

open circles means parentheses, closed circles mean brackets

Answer:

14 nickels

Step-by-step explanation:

One nickel is worth 5 cents, so find the value of 14 nickels by multiplying 14 by 5:

14(5)

= 70

So, 14 nickels is equal to the 70 cents that she has in her purse.

The correct answer is 14 nickels.

Answer:

1548.3 [tex]m^{2}[/tex]

Step-by-step explanation:

Answer:

A = 1548.3 m²

Step-by-step explanation:

Answer:

A=5h(B+b)

A/5h=B+b

A/5h - b= B

Answer: y = x - 7

Slope intercept form: y = mx + b

[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+6=2x-3[/tex]

[tex]\\ \sf\longmapsto 5x-2x=-3-6[/tex]

[tex]\\ \sf\longmapsto 3x=-9[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-9}{3}[/tex]

[tex]\\ \sf\longmapsto x=-3[/tex]

Answer:

Option c.

Step-by-step explanation:

If we have a vector of N components (or variables), and we have K linear independent restrictions for these N components (such that K < N, we can't have more restrictions than components.)

The dimension of the vector will be given by N - K.

Here we know that we have a vector of 5 components, that can be written as:

[tex]v = \left[\begin{array}{ccc}v_1\\v_2\\v_3\\v_4\\v_5\end{array}\right][/tex]

And we have two restrictions, so we can expect that the dimension of the vector is:

5 - 2 = 3

But let's see it, the restrictions are:

"the first row is equal to the second row"

Then we can rewrite our vector as:

[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\v_5\end{array}\right][/tex]

Notice that now we have only 4 variables, v₁, v₃, v₄, and v₅

We also know that the sum of the rows is equal to zero, thus:

v₁ + v₂ + v₃ + v₄ + v₅ = 0

we know that v₂ = v₁, so we can replace that to get:

2*v₁ + v₃ + v₄ + v₅ = 0

Now we can isolate one of the variables, to write it in term of the others, for example, let's isolate v₅:

v₅ = -2*v₁ - v₃ - v₄

Now if we replace that in our vector, we have:

[tex]v = \left[\begin{array}{ccc}v_1\\v_1\\v_3\\v_4\\-2*v_1 - v_3 - v_4\end{array}\right][/tex]

Notice that our vector depends on only 3 variables,  v₁, v₃, and v₄, so we can define our vector in a 3-dimensional space.

Then the correct option is c, the dimension of the vector space is 3.

Answer:

15÷39

Step-by-step explanation:

I hope it will help you

cos x = adjacent÷ hypotenuse

cos x =15÷39

cos x = 5÷13

Answer:

[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

Differentiation

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]

[tex]\displaystyle V = 324 \pi[/tex]

[tex]\displaystyle x = 6[/tex]

[tex]\displaystyle y = 27[/tex]

Step 2: Differentiate

Step 3: Evaluate

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

Unit: Differentiation

Answer:

3/4

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

3/4

Check with the third and second terms

9/4 ÷3

9/4 *1/3= 3/4

The common ratio is 3/4

Answer:

55

Step-by-step explanation:

Any number that's ends with the digit 0 or 5 is divisible by 5.

Hi there!  

»»————-　★　————-««

I believe your answer is:  

D) 55

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Option A:}}\\\\108/5 = 21.6\\\\\boxed{\text{Option B:}}\\\\109/5 = 21.8\\\\\boxed{\text{Option C:}}\\\\69/5 = 13.8\\\\\boxed{\text{Option D:}}\\\\55/5 = \boxed{11}[/tex]

⸻⸻⸻⸻

55 is divisible by 5. You can also tell that it is divisible because it's last place digit is a '5'.

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

0.0009765625

Step-by-step explanation:

This is what i got its probally incorrect