Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.
a. If a bottle is removed from the filling line, what is the probability that it is defective?
b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?

The ratio of the length of candle A to the length of candle B at first will be 3 / 5.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

Candle A and candle B were lit at the same time. candle a could last 3 hours and candle b could last 5 hours. after 1 hour, both candles were equal in length.

Then the ratio of the length of the candle A to the length of candle B at first will be

Let the length of candle A is x and the length of candle B be y.

The common speed will be S.

Then we have

Time = length / speed

For candle A, we have

Candle A = x / S = 3 ...1

For candle B, we have

Candle B = y / S = 5 ...2

From equations 1 and 2, we have

x / 3 = y / 5

x / y = 3 / 5

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Answer:6-

Step-by-step explanation:

The total volume of this building based on the volume of its two sections is 3808 cubic feet.

In this case, it is necessary to calculate the volume of the base that has a rectangular prism shape and the volume of the top part that has a right triangular prism shape.

Note: This question is incomplete because the image is missing; here is the missing section.

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Answer:

Represent the thickness of the frame by x.

Framing the mirror will increase both its length and width by 2x. The area of the mirror with the frame is the product of the length and width which can mathematically be expressed as,

A = (3+2x)(2+2x) = 8

The equation above can be simplified into 4x^2 + 10x -2=0.

This equation can still be further simplified by dividing it by 2. However, it will give an answer which is not found on the choices. Thus, the answer is the third choice.

Answer:

The correct option would be C

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

Answer:

[tex]651*10^{-8[/tex]

Step-by-step explanation:

Sure hope this helps you

Using the z-distribution, it is found that the 99% confidence interval to estimate Q is (74.4, 96.6). The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters of the interval are given as follows:

[tex]\overline{x} = 85.5, \sigma = 19.3, n = 20[/tex].

Hence the bounds of the interval are given as follows:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 85.5 - 2.575\frac{19.3}{\sqrt{20}} = 74.4[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 85.5 + 2.575\frac{19.3}{\sqrt{20}} = 96.6[/tex]

The interpretation is that we are 99% sure that the true mean for all cars rented in the city is between these two values.

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Answer:

see the attachment!

i hope this can help you!

Answer:

1st option

Step-by-step explanation:

given 2 sides of a triangle then the third side s is in the range

difference of 2 sides < s < sum of 2 sides , that is

10 - 8 < s < 10 + 8

2 < s < 18

Answer:

If the sum is 6, the vacation destination will be London.

If the sum is 7, the vacation destination will be Alaska.

If the sum is 9, the vacation destination will be New Mexico.

If the sum is 8, 10 or 12, the vacation destination will be Puerto Rico.

Step-by-step explanation:

Create a sample space for the 2 spins (see attached).

From the sample space, the probabilities are:

Therefore, to make a fair decision:

As the sum of 6, 7 and 9 each have equal probabilities (4/16), they should each be attritbuted to one destination.

As the sum of 8, 10 and 12 combined equal the same probability as the sum of 6, 7, and 9 individually, the sum of 8, 10 and 12 should be assigned to one destination combined.

Solution

If the sum is 6, the vacation destination will be London.

If the sum is 7, the vacation destination will be Alaska.

If the sum is 9, the vacation destination will be New Mexico.

If the sum is 8, 10 or 12, the vacation destination will be Puerto Rico.

Answer:

$ 142100

Step-by-step explanation:

Profit is the difference between the revenue and the cost

        P(x) = R(x) - C(x)

                = 820x - x² - (2300 + 60x)

                = 820x - x² - 2300 - 60x

                = -x² + 820x - 60x - 2300

         P(x) = -x² + 760x - 2300

a =  -1   ; b = 760  and c = -2300

       [tex]\sf \boxed{P_{max} = c - \dfrac{b^2}{4a}}[/tex]

                  [tex]\sf = -2300 - \dfrac{760^{2}}{4*(-1)}[/tex]

                  [tex]\sf = -2300 +\dfrac{577600}{4}\\\\ = -2300 + 144400\\= 142100[/tex]

[tex]\sf \boxed{P_{max}= \$ 142100}[/tex]

Step-by-step explanation:

Asuming object is a rectangle. We know that to find the perimeter of a rectangle we must add all the sides.

Therefore the formula wound be "b + b + l + l". To simplify this equation we can goup the similar sides as "2b + 2l".

Since we know the perimeter of the rectangle lets equate this simplified formula to 400:

2b + 2l = 400

Now because we know the breath lets replace it with the b position in tge formula.

2(50) + 2l = 400

Now lets use simple algebra to solve.

100 + 2l = 400

2l = 400 - 100

2l = 300

l = 150

Therefore, the lenght is 150cm

Answer:

(5,2)

Step-by-step explanation:

if it’s (x,y) and 4 to the y to get 2

i cant give you a answer because there is no other problems

Answer:

65.28

Step-by-step explanation:

1/2 × (15.2+5.2) × 6.4 = 65.28

hope this helps ;)

Answer:

Step-by-step explanation:

So first you add them together which gives you infinity and then you divide infinity by (139+285) then keep doing it until you realise this is a scam

Answer: 30.5

Step-by-step explanation:

The density of an object is the ratio of the mass of the object to its volume. The height of the block of sugar maple is 6cm

The density of an object is the ratio of the mass of the object to its volume. Mathematically;

Density = mass/volume

Given the following

Mass of block = 82.8grams

Density = 0.69g/cm^3

volume = lwh
Volume = 20h

Substitute

0.69 = 82.8/20h
20h = 82.8/0.69
20h = 120

h = 6cm

Hence the height of the block of sugar maple is 6cm

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6cm

Step-by-step explanation i can confirm that the answer is 6 ;}

Answer:

[tex]22[/tex]

Step-by-step explanation:

Because:

[tex]a \times b = 2a - 3b + ab[/tex]

Then:

[tex]3 \times 5 + 5 \times 3[/tex]

[tex]6 - 15 + 15 + 10 - 9 + 15 \\ = 22[/tex]

Answer:

B. 22

Step-by-step explanation:

Given

3 x 5

5 x 3

⇒ 3 x 5 + 5 x 3

⇒ 6 + 16

⇒ 22 (Option B)

Answer:

D) He has a 67% chance of getting a 1, 3, 5, or 6.

At the end of one year Jasmine will have the sum of $763

The principal amount (P)= $700

The interest rate(R) = 9%

The period of investment (T) = 1 year

Therefore simple interest

= P×T×R/100

= 700×1×9/100

= 6300/100

= $63

Therefore, the total amount she will receive at the end of a year = 700 + 63

= $763

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Answer:

  114°

Step-by-step explanation:

Non-adjacent angles where two lines cross are called "vertical angles." They are congruent.

  x = 114°

#20

#21

Find LCD of 2,7x,x

So

Answer:

20.  (4)  x > 6

21.  (3)  14x

Step-by-step explanation:

Question 20

[tex]\begin{aligned}\dfrac{1}{2}x+3 & < 2x-6\\\dfrac{1}{2}x+3-3 & < 2x-6-3\\\dfrac{1}{2}x & < 2x-9\\\dfrac{1}{2}x-2x & < 2x-9-2x\\-\dfrac{3}{2}x & < -9\\-\dfrac{3}{2}x \cdot 2 & < -9 \cdot 2\\-3x & < -18\\-\dfrac{3x}{3} & < -\dfrac{18}{3}\\-x & < -6\\\dfrac{-x}{-1} & < \dfrac{-6}{-1}\\x & > 6\end{aligned}[/tex]

Rewrite all three fractions so that their denominators are the same:

[tex]\dfrac{1}{2}=\dfrac{1 \times 7x}{2 \times 7x}=\dfrac{7x}{14x}[/tex]

[tex]\dfrac{2}{7x}=\dfrac{2 \times 2}{7x \times 2}=\dfrac{4}{14x}[/tex]

[tex]\dfrac{5}{x}=\dfrac{5 \times 14}{x \times 14}=\dfrac{70}{14x}[/tex]

Therefore, the least common denominator is [tex]14x[/tex]

Answer:

Here is the ans ...hope it helps:)

Answer:

Thhe simplified form of the expression is 9

Indices are expressed as power or exponent which is raised to a number or a variable.

According to the law of indices

\begin{gathered}a^n \times a^m = a^{n+m}\\a^n \div a^m = a^{n-m}\end{gathered}

a

n

×a

m

=a

n+m

a

n

÷a

m

=a

n−m

Given the expression

3^{-6} \times (\dfrac{3^4}{3^0} )^23

−6

×(

3

0

3

4

)

2

This can also be expressed as:

\begin{gathered}=\dfrac{1}{3^6} \times (\frac{3^4}{1})^2 \ (3^0 =1)\\= \dfrac{1}{3^6} \times 3^8\\=\dfrac{3^8}{3^6}\\=3^{8-6}\\=3^2\\=9\\\end{gathered}

=

3

6

1

×(

1

3

4

)

2

(3

0

=1)

=

3

6

1

×3

8

=

3

6

3

8

=3

8−6

=3

2

=9

This shows that the simplified form of the expression is 9

Answer:

infinite number of solutions

Step-by-step explanation:

Given equations:

Rearrange the second equation to make y the subject:

⇒ -12x - 2y = -4

⇒ -12x - 2y + 2y = -4 + 2y

⇒ -12x = -4 + 2y

⇒ -12x + 4 = -4 + 2y + 4

⇒ -12x + 4 = 2y

⇒ (-12x + 4) ÷ 2 = 2y ÷ 2

⇒ y = -6x + 2

Comparing the rearranged equation with the first equation, we can see that both equations are the same.  

Therefore, as there is only one line, there are an infinite number of solutions.

Answer:

A. Makes the most sense. If you are using multiplication you'd get 18 1/16

Step-by-step explanation:

Answer:

120 failures

Step-by-step explanation:

1 out of 25    or    1/25 th of 3000

1/25 * 3000 = 120