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Alexxandr [17]
2 years ago
5

The average diameter of sand dollars on a certain island is 5.00 centimeters with a standard deviation of 0.90 centimeters. If 1

6 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.73 centimeters. Assume that the variable is normally distributed.
Mathematics
1 answer:
Montano1993 [528]2 years ago
4 0

Answer:

the probability that the average diameter of those sand dollars is more than 4.73 centimeters is 0.5910

Step-by-step explanation:

Given information:

mean, x = 5

standard deviation, σ = 0.9

number of sample, n = 16

now we calculate the probability that the average diameter of those sand dollars is more than 4.73 centimeters.

P(x>4.73)  = P (z > (4.73 - x) / (σ \sqrt{n})

                = P (z > (4.73 - 4) / (0.9 \sqrt{16})

                = P (z > 0.203)

                = 0.5910

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A circle has diameter of 11cm
dlinn [17]

Since length of diagonal (  Diagonal= 9.9cm ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.

<u>Step-by-step explanation:</u>

Here we have , A circle has diameter of 11 cm  A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:

We know the concept that for any square to fit inside the circle without touching the edge of circle  , diagonal of square must be less than diameter of circle  . Let's find out length of diagonal by using Pythagoras Theorem :

Hypotenuse ^2 = Perpendicular^2+Base^2

For a square , Perpendicular = base = side

⇒ Diagonal^2 = 2(side)^2

⇒ Diagonal= \sqrt{2}(side)

⇒ Diagonal= \sqrt{2}(7)

⇒ Diagonal= 9.9cm

Since length of diagonal (  Diagonal= 9.9cm ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.

5 0
2 years ago
The Rockville Employment Agency just placed Howard Jacobson in a job as a junior pharmacist. The job pays $51.2k. The agency fee
yan [13]

His annual salary as a pharmacist is $51,200

There are a total of 52 weeks in an year.

(a) Weekly salary = annual salary/ number of weeks = 51,200/52 = $984.62 (rounded to the nearest cent)

Howard's weekly salary to the nearest cent = $984.62

(b) His salary in first three weeks = 984.62*3 = $2,953.85

Howard's earnings during the first three weeks  to the nearest cent  = $2,953.85

(c) He has to pay the agency 40% of his three week salary which is = 0.4*2953.85 =1,181.54

Howard must pay to  the employment agency to the nearest dollar = $1,182

6 0
2 years ago
Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon? A hexagon is shown. A triangle with a 60
damaskus [11]

Answer:

<u>The area of the hexagon is A. 96√3 cm²</u>

Step-by-step explanation:

Let's recall the formula of the area of an hexagon, this way:

Area = (3√3/2) * s²

Area = (3√3/2) * 8²

Area = (3√3/2) * 64

Area = 192√3/2

Area = 96√3 cm²

<u>The area of the hexagon is A. 96√3 cm²</u>

7 0
2 years ago
Factorise : 16x^2 +72xy + 81y^2 -12x +27y
never [62]
Hello!!

It will be the same since there is no common factor. You just need to arrange in order. 

6x^2 + 72xy - 12x + 81y^2 + 27y

Good luck :)
5 0
2 years ago
Amie works 6 hours each Saturday and 4 hours each Monday. She also makes $20 a week as a dog walker. She makes a total of $130 e
Harman [31]
I feel like the answer is 

10h = 110 

although it's so simple that I'm not even sure it would be considered an equation. 

I got the answer because she works, in total, 10 hours a week. She makes $130 a week, but since $20 comes from the dog walking, you have to do 130 minus 20 which is 110. That's what I did anyway. 
6 0
2 years ago
Read 2 more answers
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