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.
3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}
A.657
B.2433
C. -843
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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Someone help please
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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.
Help me out with this question linked below.
Answer:
B) 21.6Step-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
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)
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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.
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)
Answer: B
Step-by-step explanation:
Why did historians choose to study this topic?
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
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:
Help me please --------------------
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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.
someone help me pls i need to pass summer school
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
pls help! I need the answer fast!
Answer:
B is the answer
Step-by-step explanation:
hope it 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)
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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 comparison is correct?
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 CorrectC: [tex]\frac{2*4}{3*4} < \frac{10}{12}[/tex] → [tex]\frac{8}{12} < \frac{10}{12}[/tex] This statement/comparison is true
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)
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].
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
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:
find the product of 8×53×(-125) by using suitable property
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!
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:
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
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?
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Answer:
multiply (×)
Step-by-step explanation:
5 ×4 - 3 +2 ÷1 = 19
Emma would place the multiply (×) operation first.
–20 ÷ 5 =
I need help
what is the value of k
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
Help Please
2(-1+-4)-d^2
Use Taylor series to evaluate
limx→0(tan x − x)/x^3
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]
Help me
Thank you
(Make you the brainliest☺️)
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°
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)
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)
A 13-ounce can of coffee costs $2.73. What is the unit price per pound (1 pound=16 ounces)?
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
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:
please help me solve this question
urgent !!!!!!!!!!!!!!! 10 points
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
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)
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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Which expression is equivalent to 3√x10
Answer:
Hes correct ^
Step-by-step explanation:
Explain why the equation x=x+1 is a contradiction
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.
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] .
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]
