At a local community college, 57% of students who enter the college as freshmen go on to graduate. Five freshmen are randomly selected.
a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations Round your final answer to 4 decimal places Probability
b. What is the probability that at most four will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)
c. What is the expected number that will graduate? (Round your final answer to 2 decimal places)

Answers

Answer 1

Answer:

a) 0.0147 = 1.47% probability that none of them graduates from the local community college.

b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.

c) The expected number that will graduate is 2.85.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

57% of students who enter the college as freshmen go on to graduate.

This means that [tex]p = 0.57[/tex]

Five freshmen are randomly selected.

This means that [tex]n = 5[/tex]

a. What is the probability that none of them graduates from the local community college?

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]

0.0147 = 1.47% probability that none of them graduates from the local community college.

b. What is the probability that at most four will graduate from the local community college?

This is:

[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]

So

[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]

0.9398 = 93.98% probability that at most four will graduate from the local community college.

c. What is the expected number that will graduate?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 5*0.57 = 2.85[/tex]

The expected number that will graduate is 2.85.


Related Questions

pls help! I need the answer fast!

Answers

Answer:

B is the answer

Step-by-step explanation:

hope it helps

3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}

A.657
B.2433
C. -843

Answers

Answer:

657

Step-by-step explanation:

pemdas

The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

Hence option A is correct.

Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,

Let's break down the expression step by step:

First, let's simplify the expression inside the innermost parentheses:

8 - 2 x 3 = 8 - 6 = 2

Next, let's simplify the expression inside the brackets:

3 x 23 - 2 = 69 - 2 = 67

Now, let's substitute the simplified expression inside the brackets back into the original expression:

(300 - 70 ÷ 5) - 67

Next, let's simplify the expression inside the remaining parentheses:

70 ÷ 5 = 14

Now, let's substitute the simplified expression inside the parentheses back into the expression:

(300 - 14) - 67

Next, let's simplify the expression inside the remaining parentheses:

300 - 14 = 286

Now, let's substitute the simplified expression inside the parentheses back into the expression:

286 - 67

Finally, let's perform the subtraction:

286 - 67 = 219

Now, let's multiply the result by 3:

3 x 219 = 657

Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

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Help Please
2(-1+-4)-d^2

Answers

−d^2 + 7
Hope this helps !

The black graph is the graph of
y = f(x). Choose the equation for the
red graph.

a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)

Answers

9514 1404 393

Answer:

  b. y = f(x -3)

Step-by-step explanation:

The translation right h and up k units is ...

  y -k = f(x -h)

Here, the red graph is translated right 3 and up 0, so the translated function is ...

  y = f(x -3)

_____

Additional comment

You can check this if you like by listing a couple of corresponding points:

  y = f(x)

  1 = f(-3) . . . . left-most point on black graph.

The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...

  1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)

Which expression is equivalent to 3√x10

Answers

Answer: 3x^5

Explanation

sqrt(x^10) is x^5 since the power of x is 10 and the square root is of degree 2, so 10/2 = 5 and x^5 will be the new power of x after the square root. Hence, 3x^5.

Hope this helps :)

Answer:

Hes correct ^

Step-by-step explanation:

A 13-ounce can of coffee costs $2.73. What is the unit price per pound (1 pound=16 ounces)?

Answers

($2.73/13ounces) (16 ounces/1 pound) = PRICE PER PROUND
= $3.36 per pound
Hope that helps :)

Use Taylor series to evaluate
limx→0(tan x − x)/x^3

Answers

Recall that

tan(x) = sin(x)/cos(x)

and

sin(x) = x - x ³/6 + x ⁵/120 - x ⁷/5040 + …

cos(x) = 1 - x ²/2 + x ⁴/24 - x ⁶/720 + …

Truncate the series to three terms. Then

[tex]\displaystyle \lim_{x\to0}\frac{\tan(x)-x}{x^3} = \lim_{x\to0}\frac{\frac{x-x^3/6+x^5/120}{1-x^2/2+x^4/24}-x}{x^3} \\\\ = \lim_{x\to0}\left(\frac{x-x^3/6+x^5/120}{x^3-x^5/2+x^7/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2-x^4/2+x^6/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac{1-x^2/2+x^4/24}{x^2\left(1-x^2/2+x^4/24\right)}\right) \\\\ = \lim_{x\to0}\frac{x^2/3-x^4/30}{x^2\left(1-x^2/2+x^4/24\right)} \\\\ = \lim_{x\to0}\frac{1/3-x^2/30}{1-x^2/2+x^4/24} = \boxed{\frac13}[/tex]

find the product of 8×53×(-125) by using suitable property​

Answers

Answer:

-53,000

Step-by-step explanation:

Now to find this answer you use the PEMDAS rule now that stands for:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction  

Now the first thing that you do is look for the parenthesis now there is but there is no equation in that so we go to the next one exponents and there are no exponents. So we go to the multiplication and we multiply everything and that is how you get that answer.

Hope it helped!

Help me
Thank you

(Make you the brainliest☺️)

Answers

Answer:

55°

Step-by-step explanation:

sin(x°) = [tex]\frac{opposite}{hypotenuse}[/tex]

x° = [tex]sin^-1(\frac{9}{11} )=54.90319877[/tex]

Rounded to the nearest degree, the answer is 55°

Find the coordinates of the vertices of the figure after the given transformation: T<0,7>

A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)

Answers

Answer: B

Step-by-step explanation:

Why did historians choose to study this topic?

Someone help please

Answers

9514 1404 393

Answer:

  B.

Step-by-step explanation:

The relation between a function f(x) and its inverse g(x) is ...

  f(g(x)) = g(f(x)) = x

On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.

__

If we call the two given functions f and g, then we have ...

  A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses

__

  B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses

     f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses

__

  C. f(0) = -2, g(-2) = 0 . . . . possible inverses

     f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses

__

  D. f(0) = 5, g(5) = 27 . . . . not inverses

_____

Additional comment

Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.

the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)

Answers

9514 1404 393

Answer:

  all real numbers

Step-by-step explanation:

The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.

The domain of g(x) = f(-x) is all real numbers.

The Barnes store manager prefers that customers use the Barnes preferred
customer credit card for most purchases. In which case, would the manager prefer
customers use their MCVS credit card?
A. When the purchase is less than $100.00
B. When the purchase is less than $150.00
C. When the purchase is greater than $300.00
D. When the purchase is greater than $350.00

Answers

Answer:

D. When the purchase is greater than $350.

Step-by-step explanation:

Stores prefer to use credit card for customer whose purchase are worth high. The Barnes store manager prefer that customers use credit card for most purchases. When customers buy more than worth of $350, the store manager will prefer to use credit card.

Answer:

B

Step-by-step explanation:

Which comparison is correct?

Answers

Answer:

C is correct

Step-by-step explanation:

10/12=0.83...

2/3=0.66...

2/3<10/12

Answer:

C

Step-by-step explanation:

Why the others are incorrect:

A: [tex]\frac{2}{10} > \frac{3*2}{5*2}[/tex] → [tex]\frac{2}{10} > \frac{ 6}{10}[/tex] This statement/comparison is false

B : [tex]\frac{2*2}{4*2} > \frac{4}{8}[/tex] → [tex]\frac{4}{8} > \frac{4}{8}[/tex] This statement/comparison is false

D:[tex]\frac{9}{12} < \frac{3*2}{6*2}[/tex] → [tex]\frac{9}{12} < \frac{6}{12}[/tex] This statement/comparison is false

Why answer C is Correct

C: [tex]\frac{2*4}{3*4} < \frac{10}{12}[/tex] → [tex]\frac{8}{12} < \frac{10}{12}[/tex] This statement/comparison is true

Help me out with this question linked below.

Answers

Answer:

B) 21.6

Step-by-step explanation:

Area = 34.4/360⁰ * 22/7 r² = 139.6

0.30031/0.30031 r² = 139.6/0.30031

r² =√ 464.8

r = 21.560180 or 21.6

Algebra II Part 1
Choose the expression or equation that correctly represents this information
Rose works eight hours a day for five days a week. How many hours will she work in sa
weeks?
hours = 40 = 6
hours = 40.6
hours = 6 = 40

Answers

Answer:

240 i.e 40*6

Step-by-step explanation:

if rose works 8hrs per day then she works 40 hrs per week (5 days) therefore 40 hrs per 6 weeks =40*6=240

Answer:

40

Step-by-step explanation:

urgent !!!!!!!!!!!!!!! 10 points

Answers

Answer:

136 cm²

Step-by-step explanation:

Surface area = 2(lw+wh+hl)

l = 7

w = 2

h = 6

so,

2(7×2+2×6+7×6)

= 136 cm²

Answer:

136 cm^2

Step-by-step explanation:

L 7cm

W 6cm

D 2cm

7 x 6 + 6 x 2 + 2 x 7 (x 2) = 68 x 2 = 136cm^2

Help me please --------------------

Answers

9514 1404 393

Answer:

  139.39 in

Step-by-step explanation:

The length of a semicircle of diameter D is ...

  C = (1/2)πD

For the given diameter of 27 inches, the length of the curved edge of the figure is ...

  C = 1/2(3.14)(27 in) = 42.39 in

__

The perimeter of the figure is the sum of the side lengths. Clockwise from left, that sum is ...

  P = 27 + 35 + 42.39 + 35 = 139.39 . . . inches

The perimeter of the figure is 139.39 inches.


Compose an expression to find the 20th term of any arithmetic sequence in terms of just a and d. Look at the pattern in
part A with the first three terms to help you.
20th term:

Answers

Answer:

Hello,

Step-by-step explanation:

u(i) is the ith term of the a.s

a is the first term and d the common difference

for n in {1,2,3...}: u(n)=a+(n-1)*d

u(1)=a+0*d=a

u(2)=u(1)+d=a+d=a+1*d

u(3)=u(2)+d=a+1*d+d=a+2*d

...

u(20)=a+19*d

Answer:

a+19d

Step-by-step explanation:

edmentum

please help me solve this question​

Answers

Y = 196 hope it helps!

identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)

Answers

Answer:

d. y+8=2(x-4)

Step-by-step explanation:

There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.

Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].

Explain why the equation x=x+1 is a contradiction

Answers

Answer:

It results in no solution.

Step-by-step explanation:

If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.

Aidan has four cards with +, -, x, ÷ printed on them.

He inserts them between the five numbers 5, 4, 3, 2 and 1 to form the expression 5 + 4 x 3 -2 , which the value 15.

Emma says:

"Aidan put the operation in the order +, -, x, ÷.
If I place the operation cards in a different order between the number 5, 4, 3, 2, 1. I can make the value equal to 19."

Which operation would Emma do first?

Answers

9514 1404 393

Answer:

  multiply (×)

Step-by-step explanation:

5 ×4 - 3 +2 ÷1 = 19

Emma would place the multiply (×) operation first.

The length of a rectangle is shown below:

On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. Point A is on ordered pair negative 4, 5, and the point B is on ordered pair 5, 5.

If the area of the rectangle to be drawn is 90 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?

C(4, −5), D(−3, −5)
C(5, −4), D(−4, −4)
C(5, −5), D(−4, −5)
C(−5, 5), D(−5, −4)

Answers

Answer:

C(5, −5), D(−4, −5)

Step-by-step explanation:

                  9 across

A(-4, 5) ————————— B(5, 5)

     |                                            |

     |          90 square units        |   10 down

     |                                            |

D(-4, -5) ————————— C(5, -5)

–20 ÷ 5 =

I need help

Answers

The answer is -4
-20 divided by 5 ^

find the derivative of y=(x³-5)⁴(x⁴+3)⁵ ​

Answers

Answer:

[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]

Step-by-step explanation:

Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)

Answers

Answer:              It would be the first equation because:

Step-by-step explanation:        

In order to be an exponential function, the X

variable has to be in the exponent, that eliminates

the second and fourth answers

       f(X) = 4(3)X

using the point (2,36)

  f(2) = 4 (3)2

         = 4 (9 )

         = 36

The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the point on the graph be P ( 2 , 36 )

So , when x = 2 , the value of y = 36

f ( x ) = 4 ( 3 )ˣ   be equation (1)

when x = 2

f ( 2 ) = 4 ( 3 )²

f ( 2 ) = 4 x 9

f ( 2 ) = 36

Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ

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A random variable X is generated as follows. We flip a coin. With probability p , the result is Heads, and then X is generated according to a PDF f X|H which is uniform on [0,1] . With probability 1−p the result is Tails, and then X is generated according to a PDF f X|T of the form
f X|T (x)=2x,if x∈[0,1]. (The PDF is zero everywhere else.)
1. What is the (unconditional) PDF f X (x) of X ? For 0≤x≤1 : f X (x)=
2. Calculate E[X] .

Answers

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For point a:

[tex]fx|H(x) = 1;0< x<1\\\\fX|T(x) = 2x; 0\leq x \leq 1\\\\fx(x) = P(H \bigcap X = x) +P(T \bigcap X=x)\\\\[/tex]

[tex]=P(H)fX|H(x)+P(T)fX|T(x)\\\\= p(1) + (1-p)2x\\\\= p(1 -2x)+2x\\\\[/tex]

Using the PDF of the X value

[tex]fX(x) =2x +p(1 - 2x); \ 0\leq x\leq 1[/tex]

0 ; otherwise

For point b:

[tex]E(X)=\int^{1}_{0} \ x fX (x)\ dx=\int^{1}_{0} \ x(2x+p(1-2x))\ dx\\\\=\int^{1}_{0} \ (2x^2+(x-2x^2)p) dx\\\\[/tex]

[tex]= 2(\frac{x^3}{3}) + (\frac{x^2}{2}-2(\frac{x^3}{3}) \begin{vmatrix} x=1\\ x=0\end{vmatrix} \\\\[/tex]

[tex]= \frac{2}{3} + (\frac{1}{2} - \frac{2}{3})p\\\\= \frac{2}{3} -\frac{p}{6}\\\\= \frac{(4 - p)}{6}[/tex]

someone help me pls i need to pass summer school

Answers

16 to the 0 power 16 to the 0 power 16 to the 0 power 16 to the 0 power 16 to the 0 power

Answer:

A

Step-by-step explanation:

The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain

14 → 4

12 →5

10 →6

8 →7

what is the value of k

Answers

Answer:

(A)

Step-by-step explanation:

M=-2

therefore

x¹=3, y¹=-12, x²=6 y²=k

M=(y²-y¹)/(x²-x¹)

-2=(k+12)/(6-3)

-2×3=k+12

-6=k+12

k=-18

Answer:

A. -18

Step-by-step explanation:

The end points of a line segment AB are A (3, -12) & B (6, k)

What is the value of k if the slope of line segment AB is -2?
•••••••••••••••••••••••••••••••••••••••••••••••••
Answer + explanation:

Basically they’re asking us to find out the y2 of the second point of the line segment.

To find out k, use Slope-Formula

m = slope

m = (y2 - y1)/(x2 - x1)

where the first point describes (x1, y1) & the second point describes (x2, y2)

Points: (3, -12) & (6, k)

m = (k - -12)/(6 - 3)

Place the slope at the end of the formula to solve for k

(k - -12)/(6 - 3) = -2

Subtract 6 - 3

(k - -12)/(3) = -2

K is a negative number since we have a negative slope

Substitute k for the possible value

((-18) - (-12))/3 = -2

Two negative signs make addition

-6/3 = -2

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