A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 92.6-cm and a standard deviation of 2-cm. For shipment, 12 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 92-cm and 92.4-cm. Enter your answer as a number accurate to 4 decimal places.

Answer:

The lens is 1 inch from the mirror

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (0 , 0) and

 transverse axis parallel to the y-axis is y²/a² - x²/b² = 1

- The coordinates of the vertices are  (0 , ± a)

- The coordinates of the co-vertices are (± b , 0)  

- The coordinates of the foci are (0 , ± c) where c² = a² + b²

* Lets solve the problem

∵ The equation of the hyperbola is y²/16 - x²/9 = 1

∵ The form of the equation is y²/a² - x²/b² = 1

∴ a² = 16

∴ a = √16 = 4

∵ The coordinates of the vertices are  (0 , ± a)

∴ The coordinates of the vertices are  (0 , 4) , (0 , -4)

∴ b² = 9

∴ b = √9 = 3

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = √25 = 5

∵ The coordinates of the foci are (0 , ± c)

∴ The coordinates of the foci are (0 , 5) , (0 , -5)

∵ The camera is pointed towards the vertex of the hyperbolic mirror

   which is (0 , 4) and is positioned such that the lens is at the nearest

  focus to that vertex which is (0 , 5)

∴ The distance between the lens and the mirror equal the distance

   between the vertex and the focus

∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)

∴ The distance = 5 - 4 = 1 inch

* The lens is 1 inch from the mirror

Answer:

The probability is 14/55

Step-by-step explanation:

The word replacement contains 11 letters.

In which 4 letters are vowel = e,a,e,e

And 7 letters are not vowel = r,p,l,c,m,n,t

The probability of getting the vowel in the first try = 4/11

The probability of getting something that is not a vowel = 7/10.

The denominator is one less because the vowel card is not replaced, meaning there is one less card to choose from.

Multiply the values:

=4/11 * 7/10

=28/110

=14/55

The probability is 14/55....

Answer:

A nice way to show it is through the unit circle.

In the unit circle, the point at angle theta from the origin has a y value of sin theta.

If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).

Answer:

The verification is in the explanation.

Step-by-step explanation:

To solve this I'm going to use the difference identity for sine:

[tex]\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)[/tex].

[tex]\sin(360^\circ-\theta)=\sin(360^\circ)\cos(\theta)-\sin(\theta)\cos(360^\circ)[/tex]

We are going to apply that [tex]\sin(360^\circ)=0 \text{ while } \cos(360^\circ)=1[/tex]

[tex]\sin(360^\circ-\theta)=0 \cdot \cos(\theta)-\sin(\theta)\cdot 1[/tex]

[tex]\sin(360^\circ-\theta)=-\sin(\theta)[/tex]

Answer:

5 : 00 PM

Step-by-step explanation:

Given,

Church ring bells every 15 minutes,

School rings its bells every 20 minutes,

And, day care center rings its bells every 25 minutes,

Thus, the number of minutes after which they will ring together = LCM (15, 20, 25)

∵ 15 = 3 × 5,

20 = 2 × 2 × 5,

25 = 5 × 5,

Thus, LCM (15, 20, 25) = 300

Now, 1 minute = 1/60 hours ⇒ 300 minutes = 5 hours,

Hence, after 5 hours they will ring together,

If they rang at 12:00 PM,

Then they will ring after 5 hours that is 5:00 PM.

Answer:  [tex]\bold{a)\quad \dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]

                b) ∠H

                c) ∠E

Step-by-step explanation:

I find it easiest to do these problems if I write one polygon on top of the other.  That way I can easily see the angles and sides that match.

B C D E

F G H  I

a) BC matches to FG and FI matches to BE

   The proportion is:   [tex]\dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]

*****************************************************************************************

b) What matches with ∠D? Look at the letter below to see that it is ∠H

******************************************************************************************

c) What matches with ∠I? Look at the letter above to see that it is ∠E

Answer:

  Stretch in any direction (horizontal or vertical) means the corresponding coordinates are multiplied by the stretch factor: a horizontal stretch multiplies the x-coordinates by the stretch factor; a vertical stretch multiplies the y-coordinates by the stretch factor.

Step-by-step explanation:

If you know the coordinates, you can apply the stretch factor directly to the coordinates.

For example, consider the point (5, 25).

A horizontal stretch (only) by a factor of 3 will move this point to (15, 25).

A vertical stretch (only) by a factor of 3 will move the original point to (5, 75).

Note that only the corresponding coordinate is multiplied by 3.

___

The confusion can arise when this stretch concept is applied to the transformation of a function.

Consider the function f(x) = x^2. The point used in the example above is ...

  (5, f(5))

Vertical Stretch Function Transformation

If we want to transform the function to one that is vertically stretched by a factor of 3, we can simply multiply the function value by 3:

  g(x) = 3·f(x)

Then ...

  (5, g(5)) = (5, 75) . . . . . . the location of the vertically stretched point in the above example.

Horizontal Stretch Function Transformation

If we want to stretch the above f(x) function horizontally by a factor of 3, we want a h(x) function that will produce the point (15, h(15)) = (15, 25). We can get that using f(x), but the argument to f(x) for that y-coordinate must be 5, not 15. This means the transformation must be ...

  h(x) = f(x/3)

Dividing the function argument by the stretch factor means the argument must be larger by that factor in order to give the same function result.

  (15, 25) = (15, h(15)) = (15, f(15/3)) = (15, f(5))

_____

Summary

Vertical stretch of a coordinate by the factor "a": (x, y) ⇒ (x, ay)

Vertical stretch of a function by the factor "a": g(x) = a·f(x)

__

Horizontal stretch of a coordinate by the factor "a": (x, y) ⇒ (ax, y)

Horizontal stretch of a function by the factor "a":

  (x, y) ⇒ (ax, h(ax)), where h(x) = f(x/a), so h(ax) = f(ax/a) = f(x)

Answer:

  18 months

Step-by-step explanation:

The difference in payments is $651 -541 = $110 per month. The cost of the points is ...

  $98,000 × 0.02075 = $2033.50

So, it will take $2033.50/($110/mo) ≈ 18.48 mo to make up the cost.

It will take Todd 18 months to cover the cost of the discount points.

_____

Comment on rounding

The question asks for the answer to be rounded to the nearest whole month. Since the quotient is about 18.486, this rounds to 18. After 18 months, the cost of the points is not quite covered. $53.50 remains to be covered. It isn't until Todd's 19th payment that the cost of points has been fully covered. For "break even" problems such as this one, I prefer to round to the next higher integer, rather than the nearest integer.

Answer:

  A.  20,000 square feet

Step-by-step explanation:

The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:

  area = (200 ft)(100 ft) = 20,000 ft²

The correct option is option A.

The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.

The formula to finding the area of the rectangle is,

[tex]A=l\times b[/tex]

It is given that,

Length=100 ft

Breadth=200 ft

[tex]A=l\times b[/tex]

Now, substituting the given values into the above formula we get,

[tex]A=200 \times 100\\A=20000[/tex]

The required area is 20,000 square feet.

Learn more about the topic area of the rectangle:

https://brainly.com/question/11202023

AnswEr:

Add the two, to both sides. -2+2=0

So, the equation would like like this

x -2= 9

+2 +2

Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11

Answer:

223

Step-by-step explanation:

i honestly dont even know

Answer:b y=470+50x

Step-by-step explanation:

Answer:

1/4

23in * 19 in.

Step-by-step explanation:

The scale factor is 1/4 and the channel size is  92*1/4 * 76 * 1/4

= 23 in * 19 in screen.

Answer:

Scale factor = 1/2,  New screen 46 in by 38 in.

Step-by-step explanation:

The dimensions of screen is 92 in. by 76 in.

It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.

All four parts are equal.

Let the dimensions of new screen be x in. by y in.

[tex]2x=92[/tex] and [tex]2y=76[/tex]

Divide both sides by 2.

[tex]x=46[/tex] and [tex]y=38[/tex]

Scale factor is

[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]

[tex]\text{Scale factor}=\frac{46}{92}[/tex]

[tex]\text{Scale factor}=\frac{1}{2}[/tex]

Therefore, the scale factor is 1/2.

Answer:

d

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute parenthesis by - 1

= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms

= - x³ - 3x² + 2x + 4 → d

Answer:

Symmetric about the y-axis only

Step-by-step explanation:

Graph the function using a calculator

alternatively,

Sketch the graph via the following steps

-sketch cosθ

- reflect about the x-axis to get (- cosθ)

- multiply vertex values by 4 to get -4cosθ

- shift the graph in the positive y direction by 4 units to get 4 - 4cosθ

you will end up with the attached graph:

By observation, we can see that the graph is

1) NOT symmetric about the x-axis

2) Symmetric about the y-axis

3) Not symmetric bout the origin

to run a symmetry test on a polar, we can simply do a few ( r , θ ) replacements, if the equation resulting from the replacements, resembles the original, then it has that symmetry type, now, let's recall the symmetry trigonometry identity, cos(-θ) = cos(θ).

[tex]\bf r=4-4cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the y-axis, using }-r,-\theta ~\hfill }{(-r)=4-4cos(-\theta )\implies -r=4-4cos(\theta )}\implies r=-4+4cos(\theta )~\hfill \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{testing with respect to the x-axis, using }-\theta ~\hfill }{r=4-4cos(-\theta )\implies r=4-4cos(\theta )}~\hfill \stackrel{\textit{symmetry with respect}}{\textit{to x-axis}~\hfill }\textit{\Large\checkmark} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{testing with respect to the origin, using }-r~\hfill }{(-r)=4-4cos(\theta )\implies r=-4+4cos(\theta )}~\hfill \bigotimes[/tex]

Answer:

The function graphed is y = Ix - 5I - 4 ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve this problem

- From the graph

# The graph intersects the x-axis at x = 1 and x = 9

∴ The x-intercepts are 1 and 9

- We can find x-intercept by equate y by 0

* Lets equate the answers by zero to find the x-intercept

# y = Ix + 5I - 4

∵ Ix + 5I - 4 = 0

- Add 4 to both sides

∴ Ix + 5I = 4

- Remember in Ia + bI = c, then we have two answers :

 a + b = c  OR a + b = -c

∵ Ix + 5I = 4

∴ x + 5 = 4 ⇒ subtract 5 from both sides

∴ x = -1

- OR

∴ x + 5 = -4 ⇒ subtract 5 from both sides

∴ x = -9

∴ The x-intercepts are -1 and -9 not the same with figure

# y = Ix - 5I + 4

∵ Ix - 5I + 4 = 0

- Subtract 4 from both sides

∴ Ix - 5I = -4

- Remember in Ia + bI = c , c can't be negative because the absolute

 value is always positive

∴ We can't solve this equation

# y = Ix + 5I + 4

∵ Ix + 5I + 4 = 0

- Subtract 4 from both sides

∴ Ix + 5I = -4

- Remember in Ia + bI = c , c can't be negative because the absolute

 value is always positive

∴ We can't solve this equation

# y = Ix - 5I - 4

∵ Ix - 5I - 4 = 0

- Add 4 to both sides

∴ Ix - 5I = 4

- Remember in Ia + bI = c, then we have two answers :

 a + b = c  OR a + b = -c

∵ Ix - 5I = 4

∴ x - 5 = 4 ⇒ add 5 to both sides

∴ x = 9

- OR

∴ x - 5 = -4 ⇒ add 5 to both sides

∴ x = 1

∴ The x-intercepts are 1 and 9 the same with figure

* The function graphed is y = Ix - 5I - 4

Your answer is 3,147,200 water-filled drinking glasses.

The first thing I would do is change the value of 1,600 water-filled drinking glasses to be equivalent to the total that would result from 281 Americans.

To do this, you just want to multiply 1,600 by 281, as the value of 1,600 is from one person, and for 281 people, the 1,600 would happen 281 times.

1,600 * 281 = 449600

Next, since the value of 449,600 is for 281 Americans in one day's time, multiply by 7 to make it equal to one week's time. This is because one week = 7 days, so the 449,600 total would happen 7 times in one week.

449,600 * 7 = 3,147,200

Therefore, your answer is 3,147,200.

Hope this helps!

In a week 281 Americans will use 3,147,200 water-filled drinking glasses.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Each day one person uses 1,600 water-filled drinking glasses.

∴ In a week the person will uses (1600×7) = 11200 water-filled drinking glasses.

∴ 281 will use (11200×281) = 3,147,200 water-filled drinking glasses.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ5

Answer:

60 ADULT TICKETS

40 KIDS UNDER 12 TICKETS

Step-by-step explanation:

By playing around with numbers, you can figure out what makes this situation true. By multiplying 4.50 by 60, you get 270. Then, by multiplying 2 by 40, you get 80. Finally, add 270 and 80, which results in 350, which satisfies the problem.

Hope this helps!

By setting up a system of equations, we find that 60 adult tickets and 40 kids tickets were sold for the Saturday matinee when 100 tickets are sold for a total of $350.

Let x be the number of adult tickets sold and y be the number of kids tickets sold. We then have the following system of equations:

x + y = 100 (Total number of tickets)

$4.50x + $2.00y = $350 (Total revenue)

2x + 2y = 200

4.5x + 2y = 350

2.5x = 150

x = 60

y = 100 - 60 = 40

So, 40 kids tickets were sold.

Answer:

  d.  2/5+1/3=11/15

Step-by-step explanation:

The commutative property of addition allows you to change the order of the operands in a sum. 2/5 is the second operand in the original sum; it is the first operand in selection D.

Answer:

[tex](x^{2} +x+1)(x-1)+2[/tex]

Step-by-step explanation:

The synthetic division can be used to divide a polynomial function by a binomial of the form x-c, determining zeros in the polynomial.

step 1:  Establish the synthetic division, placing the polynomial coefficients in the first row (if any term does not appear, assign a zero coefficient) and to the extreme left the value of c.

1 |     1   0   0   1

step 2: Lower the main coefficient to the third row.

1 |     1   0   0   1

       1

Step 3: Multiply 1 by the main coefficient 1.

1 |     1   0   0   1

            1

       1

step 4: Add the elements of the second column.

1 |     1   0   0   1

            1

       1    1

step 5: Then repeat step 4 until the constant term 1 is reached.

1 |     1   0   0   1

            1    1    1

       1    1   1     2

step 6: Enter the quotient and remainder

quotient:  [tex]x^{2} + x + 1[/tex]

remainder:  2

Solution:   [tex]x^{2} + x + 1[/tex] [tex](x+1)  + 2[/tex]

Answer:

x^2+x+1+[tex]\frac{2}{x-1}[/tex]

Step-by-step explanation:

Answer:

Tasha made her mistake in step 4.

Answer:

Step 4 is the incorrect.

Step-by-step explanation:

From the table attached,

Step 1. Find a pattern in the table.

Correct

Step 2. Find the value of [tex]4^{-3}=(\frac{1}{16})(\frac{1}{4})=\frac{1}{64}[/tex]

Correct

Step 3. Find the value of [tex]4^{-4}=(\frac{1}{64})(\frac{1}{4})=\frac{1}{256}[/tex]

Correct

Step 4. Rewrite the value of [tex]4^{-4}[/tex]

[tex](\frac{1}{256})=-\frac{1}{4^{-4} }[/tex]

Incorrect.

Because it should be [tex](\frac{1}{256})(\frac{1}{4})=\frac{1}{1024}[/tex]

Answer:

  42 feet

Step-by-step explanation:

The vertex of the quadratic function described by the equation is located at ...

  t = -(40)/(2(-10)) = 2

The value of height at t=2 is ...

  h = -10(2²) +40(2) +2 = -40 +80 +2 = 42 . . . . feet

The maximum height is 42 feet.

_____

The equation gives the vertical speed at t=0 as 40 ft/sec, which is in contradiction to the number given in the problem statement as the initial velocity. We have used the given equation to answer the question. Since we don't know the throwing direction, we cannot properly adjust the equation to match the description of the scenario.

Answer:

$1,890

Step-by-step explanation:

Without including repeated instances of games (for instance, if I said that team 4 plays team 2 twice, then that would just be repeating when I already said that team 2 plays team 4 twice):

Team 1 plays:

teams 2, 3, 4, 5, 6, and 7 twice for a total of 12 games

Team 2 plays:

teams 3, 4, 5, 6, and 7 twice for a total of 10 games

Team 3 plays:

teams 4, 5, 6, and 7 twice for a total of 8 games

Team 4 plays:

teams 5, 6, and 7 twice for a total of 6 games

Team 5 plays:

teams 6 and 7 twice for a total of 4 games

Team 6 plays:

team 7 twice for a total of 2 games

--

Total it up:

[tex]12+10+8+6+4+2\\22+8+6+4+2\\30+6+4+2\\36+4+2\\40+2\\42[/tex]

Multiply by cost per game.

[tex]42*45=1890[/tex]

Answer:-28x^4y^2(-4x^3y^6)

Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.

Answer:

[tex]-28x^4y^6[/tex]

Step-by-step explanation:

The given expression is

[tex]-4x^3y^2(7xy^4)[/tex]

We need to place the indicated product in the proper location on the grid.

The given expression can be rewritten as

[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]

[tex]-28(x^3x)(y^2y^4)[/tex]

Using the product property of exponent, we get

[tex]-28\times x^{3+1}\times y^{2+4}[/tex]          [tex][\because a^ma^n=a^{m+n}][/tex]

[tex]-28\times x^{4}\times y^{6}[/tex]

[tex]-28x^{4}y^{6}[/tex]

Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].

The quick ratio is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The Golden Braid Bookstore has a quick ratio of 4.75.

The quick ratio, also known as the acid-test ratio, is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The formula for the quick ratio is:

Quick Ratio = (Cash + Accounts Receivable) / Current Liabilities

In this case, the Golden Braid Bookstore has $340,000 in cash and $40,000 in accounts receivable. Its current liabilities include $65,000 in accounts payable and $15,000 in other current liabilities. Plugging these values into the formula:

Quick Ratio = (340,000 + 40,000) / (65,000 + 15,000)

Quick Ratio = 380,000 / 80,000

Quick Ratio = 4.75

Therefore, the Golden Braid Bookstore has a quick ratio of 4.75.

Answer:

2x³  + 10x² + x + 5

Step-by-step explanation:

The coefficients of the dividend are represented by the top row, that is

2  10  1  5 → 2x³ + 10x² + x + 5

The divisor is ( x + 5) and

the quotient is represented by the first 3 numbers on the bottom row

2  0  1 → 2x² + 1

The last zero on the same row is the remainder

Since zero this indicates that (x + 5) is a factor of 2x³ + 10x² + x + 5

Answer:

b

Step-by-step explanation:

Answer:

376

Step-by-step explanation:

This is a subtraction problem.

1,213 - 837 =

   1,213

-    837

-----------

     376

Answer: 376

Answer:376

Step-by-step explanation:1213-837=376

Answer:

Step-by-step explanation:

The transformations you want are ...

Taken together, these make the transformation ...

  (x, y) ⇒ (-y+6, -x-1)

So, your points become ...

  A(0, 0) ⇒ A'(6, -1)

  B(8, 1) ⇒ B'(5, -9)

  C(5, 5) ⇒ C'(1, -6)

___

The attachment shows the original triangle in red and the progression to the final triangle in blue.

Answer:

1

Step-by-step explanation:

Please use parentheses around the coordinates of your points:

(1, 4); (0.5, 3.5), etc.

If we go from (0.5, 3.5) to (1, 4), x increases by 0.5 and y increases by 0.5.  

Thus the slope is m = rise / run = 1/1 = 1.

This is the average rate of change for the sequence shown.

The average rate of change for the sequence shown on the coordinate plane is calculated by finding the ratio of the differences in y-values to differences in x-values. For the given sequence, this average rate of change is 1.

The average rate of change in a sequence given by a series of points on a coordinate plane can be calculated by finding the difference between the y-values divided by the difference in x-values. For the given points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5, we have:

So, the average rate of change for the sequence shown is 1.

https://brainly.com/question/34745120

#SPJ3

75 percent of the art club members voted in the election.

To calculate the percentage of art club members who voted in the election, use the formula for percentage: part/whole *100. In this case, the part is the number of members who voted, and the whole is the total number of members in the art club.

Here's the step-by-step calculation:

Count the number of members who voted: 9.

Count the total number of members in the art club: 12.

Divide the number of voters by the total number of members: 9 / 12 = 0.75.

Multiply the result by 100 to get the percentage: 0.75 * 100 = 75%.

Therefore, 75 percent of the art club members voted in the election.

Final answer:

The expression for the combined total profit made by TechWiz Electronics from MP3 and DVD players last week is 17x + 2754.

Explanation:

The profit TechWiz Electronics made from selling MP3 players can be represented by the expression 35x, where x is the number of MP3 players sold.

The profit from selling DVD players can be represented by the expression 18(153-x), where 153 is the total number of players sold and x is the number of MP3 players sold.

To find the combined total profit, we can add these two expressions together:

Combined Total Profit = 35x + 18(153-x)

Using the distributive property, we can simplify as:

Combined Total Profit = 35x + 2754 - 18x

Combining like terms, we can simplify further:

Combined Total Profit = 17x + 2754

Therefore, the expression for the combined total profit TechWiz made from MP3 and DVD players last week is 17x + 2754.