MATHEMATICS COLLEGE

PhD’s in Engineering. The National Science Foundation reports that 70% of the U.S. graduate students who earn PhD degrees in engineering are foreign nationals. Consider the number Y of foreign students in a random sample of 25 engineering students who recently earned their PhD.a) Find the probability that there are exactly 10 foreign students in your sample – use equation for thisb) Find the probability that there are less than or equal to 5 foreign students in your sample andc) Find the mean and standard deviation for Y

Answers

Answer 1

Answer:

Answer:

a) P(Y=10)=0.0013

b) P(Y≤5)=0.00000035

c) Mean = 17.5

S.D. = 2.29

Step-by-step explanation:

We can model this as a binomial random variable with n=25 and p=0.7.

The probability that k students from the sample are foreign students can be calculated as:

$P(y=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(y=k) = \dbinom{25}{k} 0.7^(k) 0.3^(25-k)\n\n\n$

a) Then, for Y=10, the probability is:

$P(y=10) = \dbinom{25}{10} p^(10)(1-p)^(15)=3268760*0.0282475249*0.0000000143\n\n\nP(y=10)=0.0013\n\n\n$

b) We have to calculate the probability P(Y≤5)

$P(y\leq5)=P(Y=0)+P(Y=1)+...+P(Y=5)\n\n\nP(x=0) = \dbinom{25}{0} p^(0)(1-p)^(25)=1*1*0=0\n\n\nP(y=1) = \dbinom{25}{1} p^(1)(1-p)^(24)=25*0.7*0=0\n\n\nP(y=2) = \dbinom{25}{2} p^(2)(1-p)^(23)=300*0.49*0=0.0000000001\n\n\nP(y=3) = \dbinom{25}{3} p^(3)(1-p)^(22)=2300*0.343*0=0.0000000025\n\n\nP(y=4) = \dbinom{25}{4} p^(4)(1-p)^(21)=12650*0.2401*0=0.0000000318\n\n\nP(y=5) = \dbinom{25}{5} p^(5)(1-p)^(20)=53130*0.16807*0=0.0000003114\n\n\n\n$

$P(y\leq5)=0+0+0.0000000001+0.0000000025+0.0000000318+0.00000031\n\nP(y\leq5)= 0.00000035$

c) The mean and standard deviation for this binomial distribution can be calculated as:

$\mu=np=25\cdot 0.7=17.5\n\n\sigma=√(np(1-p))=√(25\cdot0.7\cdot0.3)=√(5.25)=2.29$

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Which of the following expressions has the greatest value when x=5? show how you arrived at your choice.2x^2+7

x^3-5/3

10x -2/ x-3

Answers

Answer:

2x^2+7

Step-by-step explanation:

Let x=5

2x^2+7

2 ( 5)^2 +7 = 2*25 +7 = 50+7 = 57

(x^3-5)/3

(5^3 -5)/3 = (125-5)/3 = 120/3 = 40

(10x -2)/ (x-3)

(10*5-2)/(5-3) = (50-2)/(2) = 48/2 = 24

ABCD is a trapezoid.
What is the area of trapezoid?

Answers

Let h represent the height of the trapezoid, the perpendicular distance between AB and DC. Then the area of the trapezoid is
Area = (1/2)(AB + DC)·h
We are given a relationship between AB and DC, so we can write
Area = (1/2)(AB + AB/4)·h = (5/8)AB·h

The given dimensions let us determine the area of ∆BCE to be
Area ∆BCE = (1/2)(5 cm)(12 cm) = 30 cm²

The total area of the trapezoid is also the sum of the areas ...
Area = Area ∆BCE + Area ∆ABE + Area ∆DCE
Since AE = 1/3(AD), the perpendicular distance from E to AB will be h/3. The areas of the two smaller triangles can be computed as
Area ∆ABE = (1/2)(AB)·h/3 = (1/6)AB·h
Area ∆DCE = (1/2)(DC)·(2/3)h = (1/2)(AB/4)·(2/3)h = (1/12)AB·h

Putting all of the above into the equation for the total area of the trapezoid, we have
Area = (5/8)AB·h = 30 cm² + (1/6)AB·h + (1/12)AB·h
(5/8 -1/6 -1/12)AB·h = 30 cm²
AB·h = (30 cm²)/(3/8) = 80 cm²

Then the area of the trapezoid is
Area = (5/8)AB·h = (5/8)·80 cm² = 50 cm²

A rectangular prism has a base 3 cm by 4 cm and is 5 cm in height.What is the surface area of the rectangular prism?
A. 94 cm2
C. 60 cm
B. 70 cm2
D. 47 cm

Answers

Answer:

94 cm2

Step-by-step explanation:

Base x Width x height

4 x 5 x 3

Answer:

A: 94 cm2

Step-by-step explanation:

the surface area is 94 cm2

4. The net of a square pyramid is shownbelow What is the surface area of the
pyramid?
8 cm
8 cm
A 100 cm
B 138 cm
C 172 cm?
D 192 cm?

Answers

Answer:

It’s c or a

Step-by-step explanation:

Please help now I need to find the missing perimeter please show the work

Answers

Answer:

30 cm

Step-by-step explanation:

The first one it says 4cm. That means all sides equal to 4 cm.

The second one it says 5 cm. That means all sides equal to 5 cm.

Lets do the second shape.

Since you see 6 sides with 5cm.

You do 6 times 5. Which equals to 30.

You add the label, so 30cm.

You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?

Answers

Answer:

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Step-by-step explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.

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