there are 23 people attending a luncheon if a table can hold three people how many tables do they need​

Answer:

(A) The probability that a bulb burns between 778 and 834 hours is 0.51118.

(B) The probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs  is 0.00079

Step-by-step explanation:

Let X denote the life time of light bulbs.

It is provided that X follows a normal distribution with mean of 800 hours and standard deviation of 40 hours.

(A)

Compute the probability that a bulb burns between 778 and 834 hours as follows:

[tex]P(778<X<834)=P(\frac{778-800}{40}<\frac{X-\mu}{\sigma}<\frac{834-800}{40})\\\\=P(-0.55<Z<0.85)\\\\=P(Z<0.85)-P(Z<-0.55)\\\\=0.80234-0.29116\\\\=0.51118[/tex]

Thus, the probability that a bulb burns between 778 and 834 hours is 0.51118.

(B)

Compute the probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs as follows:

[tex]P(\bar X\geq 820)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}\geq \frac{820-800}{40/\sqrt{40}})\\\\=P(Z>3.16)\\\\=1-P(Z<3.16)\\\\=1-0.99921\\\\=0.00079[/tex]

Thus, the probability that the average light bulb life is at least 820 hours in a random sample of 40 bulbs  is 0.00079

Using the normal distribution and the central limit theorem, it is found that there is a:

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The probability is the p-value of Z when X = 834 subtracted by the p-value of Z when X = 778, hence:

X = 834:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{834 - 800}{40}[/tex]

[tex]Z = 0.85[/tex]

[tex]Z = 0.85[/tex] has a p-value of 0.8023.

X = 778:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{778 - 800}{40}[/tex]

[tex]Z = -0.55[/tex]

[tex]Z = -0.55[/tex] has a p-value of 0.2912.

0.8023 - 0.2912 = 0.5111

0.5111 = 51.11% probability that a bulb burns between 778 and 834 hours.

Item b:

Sample of 40, hence [tex]n = 40, s = \frac{40}{\sqrt{40}}[/tex].

The probability is 1 subtracted by the p-value of Z when X = 820, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{820 - 800}{\frac{40}{\sqrt{40}}}[/tex]

[tex]Z = 3.16[/tex]

[tex]Z = 3.16[/tex] has a p-value of 0.9992.

1 - 0.9992 = 0.0008

0.0008 = 0.08% probability that the average light bulb life is at least 820 hours.

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

Answer:

b 15/4

Step-by-step explanation:

Step-by-step explanation:

{

x

=

1

y

=

4

Explanation:

Take a look at your starting system of equations

{

5

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y

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9

10

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18

Notice that if you multiply the first equation by

(

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, and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the

x

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This will leave you with one equation with one unknown,

y

.

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(

−

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x

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Answer:

B

Step-by-step explanation:

120/60=2

2 hours

The time required in minutes to set the sterilizer is 120. The correct option is B.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that you work in a hospital, instructions for an instrument state that it should be cleaned in the sterilizer for two hours.

The time in minutes will be calculated as:-

Time = 2 hours

Time = 2 x 60 minutes

Time = 120 minutes

Therefore, the time required in minutes to set the sterilizer is 120. The correct option is B.

To know more about an expression follow

https://brainly.com/question/11096532

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Answer:

1,2,5,10

Step-by-step explanation:

Greatest common factor is 10

Answer:

B

Step-by-step explanation:

Answer:

16x^9/9+9 should be the answer

Step-by-step explanation:

Answer:

Linear Equation: A linear equation is an algebraic equation. · 2. Polynomial Equation: · 3. Quadratic Equation: · 4. Trigonometric equation: · 5. Radical Equation:

Step-by-step explanation:

Answer:

a=70 b=.16 c=350

Step-by-step explanation:

50 messages is 8 dollars

Answer:

144 grams

Step-by-step explanation:

Im assuming you want to mass of grapes, do total mass subtracted by the mass of the bowl

Answer:

y+8.1<24

Step-by-step explanation:

Sum of= addition

y+8.1

less than is <

<24

Answer:

B

Step-by-step explanation:

Y=mx=b

m= slope

b= y- intercept

x&y are variables

Answer:

6 degrees Celsius

Step-by-step explanation:

It started at 2 degrees Celsius below zero. The next day, it dropped to 12 degrees Celsius below zero. The next day, it rose to 7 degrees below zero. The next day, it increased to 6 degrees ABOVE zero. -7+13=6

Answer:

105

Step-by-step explanation:

180-(55+20)=105

105 is the missing angle because every triangle equals 180 degrees so you just subtract the angles you have already found from 180.

the person above me is correct i checked it so it is indeed 105!

Answer:

7

Step-by-step explanation:

So:a=3

b=(-2)

c=2

Substitute the numbers into each letters

so a is represented by 3,c by 2 and b -2

therefore giving us: 2

3+(-2)=9+(-2)=7

Answer: 27.00

Step-by-step explanation:

$50 - $23 = $27

Answer:

$27.00

Step-by-step explanation:

"D"

Answer:

2/5 × 3/2

I hope this helps!

Answer:

I don't have algebra but I suggest looking it up and it might show you at the very top.

Step-by-step explanation:

Hope this helps you:)

Answer:

I think it's the first one... but I'm not pretty sure.

Answer:

C

Step-by-step explanation:

edge 2020

Answer:

now using the formula (a-b) (a2+ab+b2)=a3-b3

=>x3-63

x3-216#answer

The factor of the cubic polynomial x³ + 216 will be (x + 6) and (x² – 6x + 36). Then the correct option is B.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The cubic polynomial is given below.

⇒ x³ + 216

Then the cubic polynomial is written as,

⇒ x³ + 6 × 6 × 6

⇒ x³ + 6³

We know that the formula of a³ + b³ is given as,

a³ + b³ = (a + b)(a² – ab + b²)

Compare the expression, we have a = x and b = 6. Then the expression will be

x³ + 6³ = (x + 6)(x² – 6x + 6²)

x³ + 6³ = (x + 6)(x² – 6x + 36)

The factor of the cubic polynomial x³ + 216 will be (x + 6) and (x² – 6x + 36).

Then the correct option is B.

More about the factorization link is given below.

https://brainly.com/question/6810544

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Answer:

31.4

Step-by-step explanation:

You subtract 80.00 from 48.60, and you get your answer 31.4

Answer:

128.6

Step-by-step explanation:

You have to do the inverse operation.

So you add 48.60 to each side of the equation. This cancels out the -48.60 which isolates the variable. And on the other side of the equation it leaves you with 128.6. Therefore d = 128.6

Answer:

Me too not trying to get the points but how are u suppose to solve this anyway

Step-by-step explanation:

Answer:

decimal - 0.875

percent - 87.50%

Step-by-step explanation:

Answer:

The other number is 5/9.

Step-by-step explanation:

16/3 = 48/5 * x

x = 5/9

Answer: Less than 1

Step-by-step explanation: 4.23 x 10^-5 simply translated to 0.0000423

which is less than 1.

Answer:

less than 1

Step-by-step explanation:

4.23 * 10^5 is less than 1