Ten students begin college at the same time. The probability of graduating in four years is 63%. Which expanded expression shows the first and last terms of the expression used to find the probability that at least six will graduate in four years?

Answers

Answer 1

Answer:

The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term: $C(10, 6) * (0.63)^6 * (1 - 0.63)^4$

Last term: $C(10, 10) * (0.63)^(10) * (1 - 0.63)^0$

To find the probability that at least six students will graduate in four years, we can use the binomial probability formula.

The first and last terms of the expanded expression for this probability can be determined using the binomial coefficients.

The binomial probability formula is given by:

$P(X \geq k) = C(n, k) * p^k * (1 - p)^{(n - k)$

Where:

P(X ≥ k) is the probability that X is greater than or equal to k,

n is the number of trials (students in this case),

k is the desired number of successes (six or more students graduating),

p is the probability of success in a single trial (probability of graduating in four years).

In this case, the number of trials (n) is 10, and the probability of success (p) is 0.63.

To find the first term, we substitute k = 6 into the formula:

$P(X \geq 6) = C(10, 6) * (0.63)^6 * (1 - 0.63)^{(10 - 6)$

C(10, 6) represents the binomial coefficient, which can be calculated as:

C(10, 6) = 10! / (6! * (10 - 6)!)

To find the last term, we substitute k = 10 into the formula:

$P(X \geq 10) = C(10, 10) * (0.63)^(10) * (1 - 0.63)^{(10 - 10)$

C(10, 10) = 10! / (10! * (10 - 10)!)

Hence, The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term: $C(10, 6) * (0.63)^6 * (1 - 0.63)^4$

Last term: $C(10, 10) * (0.63)^(10) * (1 - 0.63)^0$

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Answer 2

Answer: Since this is dealing with binomial you do something like this

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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a is a random variable that is uniformly distributed between $10,000 and $15,000.a. Suppose you bid $12,000. What is the probability that your bid will be accepted? (please show calculations)
b. Suppose you bid $14,000. What is the probability that your bid will be accepted? (please show calculations)
c. What amount should you bid to maximize the probability that you get the property? (please show calculations)d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

Answers

Answer:

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

$10,000 and $15,000

The interval of the accepted bidding is $[ {\rm{\$ 10,000 , \$ 15,000}]$ , where b = $15000 and a = $10000.

The interval of the provided bidding is [$10,000,$12,000]. The probability is calculated as,

$\begin{array}{c}\nP\left( {X{\rm{ < 12,000}}} \right){\rm{ = }}1 - P\left( {X > 12000} \right)\n\n = 1 - \int\limits_(12000)^(15000) {\frac{1}{{15000 - 10000}}} dx\n\n = 1 - \int\limits_(12000)^(15000) {\frac{1}{{5000}}} dx\n\n = 1 - \frac{1}{{5000}}\left[ x \right]_(12000)^(15000)\n\end{array}$

$=1- ([15000-12000])/(5000)\n\n=1-0.6\n\n=0.4$

(b) The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

$\begin{array}{c}\nP\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\n\n = 1 - \int\limits_(14000)^(15000) {\frac{1}{{15000 - 10000}}} dx\n\n = 1 - \int\limits_(14000)^(15000) {\frac{1}{{5000}}} dx\n\n = 1 - \frac{1}{{5000}}\left[ x \right]_(14000)^(15000)\n\end{array} P(X<14,000)=1-P(X>14000)$

$=1- ([15000-14000])/(5000)\n\n=1-0.2\n\n=0.8$

(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

$\begin{array}{c}\nf\left( {X = {\rm{15,000}}} \right){\rm{ = }}\frac{{{\rm{15000}} - {\rm{10000}}}}{{{\rm{15000}} - {\rm{10000}}}}\n\n{\rm{ = }}\frac{{{\rm{5000}}}}{{{\rm{5000}}}}\n\n{\rm{ = 1}}\n\end{array}$

(d) The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.

A theorem in geometry states that the measure of an inscribed angle is half the measure of its intercepted arc. In the figure, angle C intercepts arc AB and line AB is the diameter of the circle. Which equation is a step in showing that the measure of angle C=90 degrees?

Answers

Answer:The fourth option

Step-by-step explanation:

Answer:

The Fourth Answer

Step-by-step explanation:

A kite flier wondered how high her kite was flying. She used a protractor to measure an angle of 33° from level ground to the kite string. If she used a full 90 yard spool of string, how high, in feet, was the kite? Round your answer to 3 decimal places. (Disregard the string sag and the height of the string reel above the ground.)

Answers

Answer: height of kite is 147.042 feets

Step-by-step explanation:

The diagram of the kite is shown in the attached photo

Triangle ABC is formed and it is a right angle triangle.

The kite string made an angle of 33 degrees with the ground. The string used was 90 yards We will convert the 90 yards to feets.

I yard = 3 feets

90 yards would become

90×3 = 270 feets

This 270 feets form the hypotenuse of the triangle.

To determine the height of the kite h, we will use trigonometric ratio

Sin# = opposite / hypotenuse

Where

# = 33 degrees

Hypotenuse = 270 feets

Opposite = h feets

Sin 33 = h/270

h = 270sin33

h = 270 × 0.5446 = 147.042 feets

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Answers

Step-by-step explanation:

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Mean of second batch:

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= 6055/8

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Z-alpha/2 = 1.64

= (750.2-756.875)-1.64*√20²/15 + 20²/8

= -21.0348

(750.2-756.875)+1.64*√20²/15 + 20²/8

= 7.68

2. The upper limit of the interval is less than 10 so in conclusion the difference in mean batch viscosity is about 10 or less than 10

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Answers

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Answers

Answer:

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Step-by-step explanation:

5/4 = 1.25

Therefore 6 rational numbers between - 4 and 5/4:

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