Canine Crunchies Inc. (CCI) sells bags of dog food to warehouse clubs. CCI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 45 kilograms and a standard deviation of 1.2 kilograms.

Requried:
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?

Answer:

(c) [tex]\triangle ABC[/tex] to [tex]\triangle EDC[/tex] by AA

Step-by-step explanation:

Given

See attachment for triangles

Required

The relationship between both triangles

First, we determine the corresponding sides.

The corresponding sides will be determined based on the length of each side (i.e. bigger sides correspond while smaller sides correspond).

So, we have:

[tex]AC\ to\ EC[/tex]

[tex]BC\ to\ DC[/tex]

Next, is to name the triangle base on the corresponding sides

The names will be: [tex]\triangle ABC[/tex] and [tex]\triangle EDC[/tex]

Lastly, is to check the scale ratio (k).

For both triangles to correspond, the scale ratio must be the same

So:

[tex]k = \frac{EC}{AC} = \frac{DC}{BC}[/tex]

[tex]k = \frac{8}{6} = \frac{12}{9}[/tex]

[tex]k = \frac{4}{3} = \frac{4}{3}[/tex]

[tex]k = \frac{4}{3}[/tex]

Hence, the theorem is: [tex]\triangle ABC[/tex] to [tex]\triangle EDC[/tex] by AA

Answer:

The price per gallon of gas with a $7 car wash is $3.19

Then if you purchase x gallons of gas and also pay for the car wash, the total cost is:

C(x) = $7 + $3.19*x

In the case that you do not pay for the car wash, the cost per gallon is $3.39

Then the cost for x gallons of gas in this case is:

K(x) = $3.39*x

When is it worth it to buy the car wash?

We need to sett the equations:

C(x) = K(x)

This means that you pay exactly the same in both cases, but in one ( C(x)) you get the car wash and in the other not.

Then we need to solve:

$7 + $3.19*x = $3.39*x

$7 = ($3.39 - $3.19)*x = $0.20*x

$7/$0.20 = x = 35

Then for 35 gallons, is worth to buy the car wash.

In the case where the car wash costs $2, then the equation C(x) becomes:

C(x) = $2 + $3.19*x

Then if we solve the same equation:

C(x)  =K(x)

$2 + $3.19*x = $3.39*x

$2 = ($3.39 - $3.19)*x

$2 = $0.20*x

$2/$0.20 = x

10 = x

Then for 10 galons is whort  buy the car wash.

Step-by-step explanation:

x= 0, y = 2

have a great day

Answer:

7, 12, 13

Step-by-step explanation:

Use the Pythagorean theorem equation on all of them. The one that does not make the equation true is the  answer.

a^2 + b^2 = c^2

A.

a^2 + b^2 = 18^2 + 80^2 = 6724

c^2 = 82^2 = 6724

Right triangle.

B.

a^2 + b^2 = 7^2 + 12^2 = 193

c^2 = 13^2 = 169

Not a right triangle.

C.

a^2 + b^2 = 3^2 + 4^2 = 25

c^2 = 5^2 = 25

Right triangle.

D.

a^2 + b^2 = 45^2 + 60^2 = 5625

c^2 = 75^2 = 5625

Right triangle.

Answer: 7, 12, 13

Answer:

Step-by-step explanation:

I think it could be D

Sorry if not correct

Answer:

Step-by-step explanation:

x^2 - 17x - 60

(x - 20)(x + 3)

x^2 + 3x - 20x - 60

x^2 - 17x - 60

(x + 20) is not one of the factors

using F.O.I.L., it would have been

x^2 + 17x - 60

Answer:

314 cm^2

Step-by-step explanation:

(=^w^=)

A= 2*pi*r*h

A=2*pi*5*10

A=314.16 cm^2

Step-by-step explanation:

2×5×10=

10×10= 100 cm²

=100 cm²

Step-by-step explanation:

s=d/t

s=18/30

s=3/5km/h

Answer:

You are? so am I

Step-by-step explanation:

Answer:

1. 49, 2. 245

Step-by-step explanation:

Add 16 and 33 together to get 49 minutes. That is what Blaire listens to in one day. Multiply that by 5 and you find out what she listens to in 5 days

Ernesto bought the ceramic vase for $56 including 12% tax.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A ceramic vase was originally priced at $100 but went on sale for 50% off.

∴ The discounted price is (50/100)×100 = $50.

Now after Ernesto bought the ceramic vase he had to pay a tax of 12%.

∴ {(100 + 12)/100}×50.

= (112/100)×50.

= 56.

So he paid $56 including 12% tax.

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Answer:

12 centimenters.

Step-by-step explanation:

Answer:

6 cm

Step-by-step explanation:

We need to find the distance from R to s which is basically the radius, we know radius is r=d/2 to 12/2 (since 12 is diameter) is 6.

Step-by-step explanation:

4 smoothies = 2 1/2 banana

you need to make 2 more smoothies, So half of what you did already.

(2.5)/2= 1.25 then add them (2.5)+(1.25)

6 smoothies = 3.75 or 3 3/4, same thing.

Answer:

1/2

Step-by-step explanation:

take change in X divided by change in Y values

Answer:

0.2 I think

Step-by-step explanation:

7x6=42

35÷42=0.2

Answer:

an arithmetic sequence

Step-by-step explanation:

I think it's because it adds 5 each time and in arithmetic sequences there's a common difference, so it'd be an arithmetic sequence :)

Answer:

D- No solution

Step-by-step explanation:

Isolate x for x+2y−z=3: x=3−2y+z

then Simplify

then Isolate y for −5y+4z+6=6: y= 4z 5 −5y+4z+6=6 Subtract 6 from both sides −5y+4z+6−6=6−6 Simplify −5y+4z=0 Subtract 4z from both sides −5y+4z−4z=0−4z Simplify −5y=−4z Divide both sides by −5 −5y −5 = −4z −5 Simplify y= 4z 5

lastly simply.

Answer:   d=sqrt(41) =6.4031  

Step-by-step explanation:

We know that the distance between the two points (x  1  ,y  1  ) and (x  2  ,y  2 ) is

d= sqrt((x2-x1)^2 +(y2-y1)^2 )

as given

x1=2  ,x2=6   ,y1=3 ,y2=8

d=sqrt((6-2)^2+(8-3)^2 )

d= sqrt((4)^2+(5)^2

d=sqrt(16+25)

d=sqrt(41) =6.4031

Answer:

225 boards

Step-by-step explanation:

99 ft/0.44 ft = 225 ft

Answer:

5.24 hours

Step-by-step explanation:

I like to set these up as ratios.

279 miles/4.5 hours = 325 miles/ x hours

Then cross multiply

279x = 4.5 x 325

279x = 1462.5

divide both sides by 279

x = 5.24 hours

You can also solve 279 miles/4.5 hours to get the miles per hour driven, then divide 325 by that number:

279/4.5 = 62mph

325/62 = 5.24

Answer:

1 pair

Step-by-step explanation:

The top and bottom sides can go forever without crossing

Answer:

1

Step-by-step explanation: because the top and bottom a pair

Answer:

2/3x+8=y

Step-by-step explanation:

8x-12y=-96

8x+96=12y

8/12x+8=y

2/3x+8=y

The equation 8x – 12y = -96 of a line into slope-intercept form, simplifying all fractions, is 3y = 2x + 24.

Two expressions with variables or integers are said to be equal when they are declared to be in an equation. Since equations are essential questions, efforts to methodically find answers to these questions have been the inspiration for the development of mathematics.

Given:

The equation, E = 8x – 12y = -96,

The standard intercept form of a line,

[tex]y = mx + c[/tex]

Here m is the slope,

For this form, arrange the equation,

– 12y = -8x - 96

(Do multiplication of  -1/ 4 on both sides)

3y = 2x + 24

Therefore, the equation 8x – 12y = -96 of a line into slope-intercept form, simplifying all fractions is 3y = 2x + 24.

To know more about equation:

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Answer:

200

Step-by-step explanation:

Base of the prism is a square

So

[tex]\\ \tt {:}\longrightarrow Area\:of\:base=(side)^2[/tex]

[tex]\\ \tt {:}\longrightarrow (5)^2[/tex]

[tex]\\ \tt {:}\longrightarrow 25cm^2[/tex]

Now

[tex]\\ \tt {:}\longrightarrow Volume=Area\:of\:Base\times Height[/tex]

[tex]\\ \tt {:}\longrightarrow 25\times 8[/tex]

[tex]\\ \tt {:}\longrightarrow 200cm^3[/tex]

Answer:

Select a card from a set of cards with the letters A through D, then spin this once.

Spin this and roll an 8-sided number cube with the digits 1 to 8.

Answer:

<DEC and <IHJ

Step-by-step explanation:

Alternate exterior angles are angles on the other side of a transveral and on the exterior area.

Answer:

The figure is a parralellogram

Step-by-step explanation:

it has 4 sides and one set is parallel

Answer:

1

Step-by-step explanation:

y-intercept: the point where the line and the y-axis intersect

Answer:

y-intercept =1

Step-by-step explanation:

The y -intercept of a graph is the point where the graph crosses the y -axis.