Suppose that you work for a newly restructured automotive company with nearly 100,000 employees. You are in charge of purchasing engines from an overseas supplier. Company policy is that you purchase 500 engines each month to be placed into cars on the assembly line. Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test. To check out the monthly shipment of the 500 engines you randomly select and test 50 of these engines, and you find that 1 is defective. Do you think that the supplier has met the guarantee

Answer:

-1

Step-by-step explanation:

lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.

So the limit is 4-5=-1

Answer:

we need to get your brain thinking in this way. that you begin to understand how to do these things.

airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.

so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.

1. (0, -2)

2. 4

3. a geometric sequence. the common ratio is -2.0

4. the third option

5. the fourth option

Step-by-step explanation:

1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.

2. look at the line. it only starts with x>0 (it looks like x is around 1).

"input" is all the values of x the function has a defined result for (y = result values).

so, as there is no line for negative x, we can eliminate the first 2 answers.

x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).

in the answer options the only x value having an y value above or below this x value is x=4.

3. look at the difference between 2 numbers next to each other in the sequence.

2.4 to -4.8

-4.8 to 9.6

and so on.

what do we need to do to get from the left to the right ?

we need to multiply by -2.

so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :

an/an-1 = -2

4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...

but there us one thing a function can never have : multiple different y values for one x value.

in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.

in the second graph x=4 has two different y values.

in the third graph all is OK.

in the fourth graph x=-2 has two different y values.

so, only the third option is a function.

5. this function calculates the height of the thrown rock after t seconds of flight.

therefore, only the fourth answer makes sense.

Answer:

45

Step-by-step explanation:

9x5

Answer:

17.89 ft

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

8^2 +16^2 = c^2

64+ 256 = c^2

320 =c^2

Taking the square root of each side

sqrt(320) = sqrt(c^2)

sqrt(64*5) = c

sqrt(64) sqrt(5) =c

8 sqrt(5) = c

17.88854382=c

17.89 ft

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet.

so it is a right angle triangle

in a right angle triangle, According to the Pythagorean theorom,

[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]

where

The height of the ladder is [tex]\sf{8\sqrt{5} }[/tex]

Answer:    [tex]\bf 7\underline4 . 164 \approx 74[/tex]

Step-by-step explanation:

Answer:

74

Step-by-step explanation:

Keep in mind you're rounding rules!

Let S be the sum. So you have

S = 1 + 2 + 3 + … + 2004 + 2005 + 2006

as well as

S = 2006 + 2005 + 2004 + … + 3 + 2 + 1

Then

2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)

2S = 2007 + 2007 + … + 2007 + 2007

2S = 2006 × 2007

S = (2006 × 2007)/2

S = 2,013,021

which makes the last two digits 21.

Answer:

[tex]{ \tt{( - 6 {s}^{2} + 12s - 8) - (3 {s}^{2} + 8s - 6) }} \\ = { \tt{ - 9 {s}^{2} + 4s - 2 }}[/tex]

Answer:

4s - 2 - 9s²

Step-by-step explanation:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

= -6s²+ 12s - 8 - 3s²- 8s + 6

= 12s - 8s - 8 + 6 - 6s² -3s²

= 4s - 2 - 9s²

Answer:

July 4th will fall on Sunday

The date, July 4 will be Friday, the correct option is D.

Calendars represent an year of 12 months, each month has 30 or 31 days, exceptionally February has 28 days.

If today is Tuesday, May 6,

Every 7th day is going to be a Tuesday .

From May 6 to July 4, the number of days is 59

Hence we divide 59 by 7. Quotient = 8 Remainder = 3

7 x 8 = 56

56 th day is Tuesday

57 th day is Wednesday

58th day vis Thursday

59th day is Friday

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Answer:

Step-by-step explanation:

5(a-1) -15 = 3(a+2) +4, distribute multiplication over subtraction and addition

5a -5 -15 = 3a +6 + 4, isolate the variable on one side

5a -3a = 6 +4 +5 +15, combine like terms

2a = 30, divide both sides by 2

a= 15

Answer:

[tex]\mu = 47.17[/tex]

[tex]\sigma = 2.31[/tex]

Step-by-step explanation:

Solving (a): The population mean

This is calculated as:

[tex]\mu = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\mu = \frac{48.2+ 47.8 +45.6 +47.2 +49.3+51.2 +44.2 +45.4 +49.2 +43.6}{10}[/tex]

[tex]\mu = \frac{471.7}{10}[/tex]

[tex]\mu = 47.17[/tex]

Solving (b): The population standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{(48.2-47.17)^2 + (47.8-47.17)^2 +.........+(43.6-47.17)^2}{10}}[/tex]

[tex]\sigma = \sqrt{\frac{53.521}{10}}[/tex]

[tex]\sigma = \sqrt{5.3521[/tex]

[tex]\sigma = 2.31[/tex]

Answer:

All, if you're not defining the angles.

Step-by-step explanation:

The angle ACB/BCA is 55 degrees, ACE/ECA is 125 degrees, DCE/ECD is the same as ACB/BCA, and BCD/DCB is the same as ACE/ECA

Answer:

The "zero" is where it crosses the x axis which is -2 in this graph

Step-by-step explanation:

Answer:

6.045 * 10 ^40 ergs

1.8 * 10^-2 mm

Step-by-step explanation:

3.9 ⋅ 10^33 erg per second  * 1.55 * 10 ^7 seconds

3.9 * 1.55  * 10^(33+7)

6.045 * 10 ^40 ergs

Human hair is around .1 mm thick

.1  = 1 * 10 ^ -1

This is closer to 1.8 * 10^-2  

1.8 *10^2 = 180 mm which is too thick  This is approximately 18 cm

Answer:

6.045 * 10 ^40 ergs

1.8 * 10^-2 mm

Step-by-step explanation:

3.9 ⋅ 10^33 erg per second  * 1.55 * 10 ^7 seconds

3.9 * 1.55  * 10^(33+7)

6.045 * 10 ^40 ergs

Human hair is around .1 mm thick

.1  = 1 * 10 ^ -1

This is closer to 1.8 * 10^-2  

1.8 *10^2 = 180 mm which is too thick  This is approximately 18 cm

Step-by-step explanation:

Answer:

G = Fr² / Mm

Step-by-step explanation:

Given:

F = GMm / r²

Where,

F = Force of the two objects

M = mass of object 1

m = mass of object 2

G = constant

r = distance between the objects

Solve the formula for G.

F = GMm / r²

Cross product

F * r² = GMm

Fr² = GMm

Divide both sides by Mm

G = Fr² / Mm

Answer:

A.

[tex]f(x) = \frac{ \sqrt[3]{x} }{5} \: { \bf{and}} \: g(x) = 5 {x}^{3} [/tex]

Step-by-step explanation:

Consider f(x) as the original function:

[tex]{ \tt{f(x) = \frac{ \sqrt[3]{x} }{5} }}[/tex]

Let the inverse be m:

[tex]{ \tt{g(x) = f {}^{ - 1} (x) = m}} \\ { \tt{m = \frac{ \sqrt[3]{x} }{5} }} \\ { \tt{5m = \sqrt[3]{x} }} \\ { \tt{x = 5m {}^{3} }} \\ therefore : \\ { \tt{g(x) = 5 {x}^{3} }}[/tex]

Answer:

11 sqrt(2)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin 45 = x /22

22 sin 45 = x

22 ( sqrt(2)/2) =x

11 sqrt(2)

The legs are equal since the  base angles are equal

Answer:

15 pages

Step-by-step explanation:

let x be the number of pages

7x-21 = 11x-81

4x = 60

x = 15

Answer:

38

Step-by-step explanation:

Angle 6 is alternate to the angle that is given as 38 degrees because line L is parallel to line M so their measure is equal.

9514 1404 393

Answer:

  K+1 ⇒ (K+1)² = K² +2K +1

Step-by-step explanation:

Your first answers are correct. The sum of K odd numbers is K². Replacing K with K+1 in this statement gives you ...

  The sum of K+1 odd numbers is (K+1)² = K² +2K +1.

Answer:

A spurious correlation wrongly implies a cause and effect between two variables. For example, the number of astronauts dying in spacecraft is directly correlated to seatbelt use in cars: Use your seatbelt and save an astronaut life!

Interesting correlations are easy to find, but many will turn out to be spurious. Three examples are the skirt length theory, the Super Bowl indicator, and a suggested correlation between race and college completion rates.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3

Step-by-step explanation:

one line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).

and this line has the offset of y=-5 for x=0

so, the line equation is

y = -3x - 5

inverse means that we exchange x and y and then solve for y again :

x = -3y - 5

3y = -x - 5

y = -x/3 - 5/3

when we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).

and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.

for example (-2, -1)

-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1

correct.

so, the equation we got for the inverse function fits exactly with the second line in the graph.

therefore, yes, they are both inverse functions to each other.

The two given graphs are inverse functions of each other.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

One line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).and this line has the offset of y=-5 for x=0

The line equation is

y = -3x - 5

Inverse means that we exchange x and y and then solve for y again :

x = -3y - 5

3y = -x - 5

y = -x/3 - 5/3

When we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.

for example (-2, -1)

-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1

The equation we got for the inverse function fits exactly with the second line in the graph.

Therefore the two given graphs are inverse functions of each other.

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Answer:

8 units

Step-by-step explanation:

Area of a rectangle = Width multiplied by Length

Substitute in all the known numbers into this formula to get

72 = (9) × [tex](2x+4)[/tex]

Solve the equation for x, to find out the length

[tex]9(2x+4)=72[/tex]

[tex]2x+4=72/9[/tex]

[tex]2x+4=8[/tex]

[tex]2x=8-4[/tex]

[tex]2x=4[/tex]

[tex]x=4/2[/tex]

[tex]x=2[/tex]

Length of the rectangle = [tex](2x+4)[/tex]

[tex]2(2)+4[/tex]

[tex]4+4=8[/tex]

Answer:

-10 = x

Step-by-step explanation:

5=7+x/5

Subtract 7 from each side

5-7=7-7+x/5

-2 = x/5

Multiply each side by 5

-2 *5 = x/5 *5

-10 = x

Step-by-step explanation

They sold $480 of tshirts, the ratio is 480;20, simplified to 24:1.

One shirt is $20, but $4 is the amount taken from 20 for the equipment.

Multiply $24 by the $4 taken for the equipment. (Equals $96)

They make 4/20 (1/5) of the the sales as a profit for equipment.

Multiply 1/5 by 480 and you will get $96 as the club's profits.

I hope this helped ya

The chess club needs 20 T-shirts and 30 baseball caps.

Profit is a term that often refers to the financial gain that a company receives when revenue exceeds costs and expenses. A child at a lemonade stand, for example, spends one quarter to make one cup of lemonade. She then charges $2 for the drink. Her profit on a cup of lemonade is $1.75.

Given :

Total no. of items to be sold = 50

Total profit to be made = $230

Profit on each T-shirt = $4

Profit on each Baseball cap = $5

Let no. of t-shirts be x

Let no. of t-shirts be y

Forming equations according to given problem :

Eq 1 : x + y = 50

Eq 2 : 4x + 5y = 230

Multiplying Eq 1 with 4 we get : 4x + 4y = 200

Subtracting Eq 1 from Eq 2

Solving Eq1 and Eq2 we get x = 20 and y = 30.

Therefore, The chess club needs 20 T- shirts and 30 baseball caps.

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Answer:

x = 11√3

y = 11

Step-by-step explanation:

Let 60 be the reference angle

sin 60 = p/h

√3/2 = x/22

or, 22√3 = 2x

or, x = (22√3)/2

so, x = 11√3

now

[tex]h^2 = p^2 + b^2\\or, 22^2 = (11\sqrt{3} )^2+y^2\\or, 484 = 363 + y^2\\or, 484-363 = y^2\\or, 121 = y^2\\or, \sqrt{121} = y\\so, y = 11[/tex]

Answer:

a)

(i) 5.8 hours

(ii)  6.5 hours

(iii) 6 hours

(iv) 6 hours

b) 180 hours