Answer:
a) 0.7696 = 76.96% probability that at least 11 of them graduated.
b) 0.0474 = 4.74% probability that exactly 9 of them graduated.
c) Since 9 is less than 2.5 standard deviations from the mean, it would not be unusual.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they graduated, or they did not. Each student is independent of each other. So we use the binomial probability distribution 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.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Unusual outcome:
An outcome in the binomial distribution is unusual if it is more than 2.5 standard deviations from the mean.
92.4% for the medical students admitted through special programs.
This means that [tex]p = 0.924[/tex]
a. If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated.
This is [tex]P(X \geq 11)[/tex] when [tex]n = 12[/tex]. So
[tex]P(X \geq 11) = P(X = 11) + P(X = 12)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 11) = C_{12,11}.(0.924)^{11}.(0.076)^{1} = 0.3823[/tex]
[tex]P(X = 12) = C_{12,12}.(0.924)^{12}.(0.076)^{0} = 0.3873[/tex]
[tex]P(X \geq 11) = P(X = 11) + P(X = 12) = 0.3823 + 0.3873 = 0.7696[/tex]
0.7696 = 76.96% probability that at least 11 of them graduated.
b. If 12 of the students from the special programs are randomly selected, find the probability that exactly 9 of them graduated.
This is P(X = 9). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{12,9}.(0.924)^{9}.(0.076)^{3} = 0.0474[/tex]
0.0474 = 4.74% probability that exactly 9 of them graduated.
c. Would it be unusual to randomly select 12 students from the special programs and get exactly 9 that graduate?
The mean number of students expected to graduate is:
[tex]E(X) = np = 12*0.924 = 11.09[/tex]
The standard deviation is
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{12*0.924*0.076} = 0.92[/tex]
11.09 - 2.5*0.92 = 8.79
This means that anything below 8.79 is unusual, so, since 9 is less than 2.5 standard deviations from the mean, it would not be unusual.
If a watch costs $40 and you must pay 6.5 % sales tax, how much will the tax be?
Please give me the correct answer this is for a test and im on a time limit :(
Answer:
$2.60
Step-by-step explanation:
40 x 0.065 = $2.60
Answer:
the tax would be 2.60$
Step-by-step explanation:
6.5% of 40 is 2.6
(6.5 x .40=2.6)
Find the length of side x in simplest radical form with a rational denominator
Answer:
[tex] x = \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \tan 30 \degree = \frac{x}{ \sqrt{6} } \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{ \sqrt{6} } \\ \\ x = \frac{ \sqrt{6} }{ \sqrt{3} } \\ \\ x = \frac{ \: \sqrt{3} \times \sqrt{2} }{ \sqrt{3} } \\ \\ x = \sqrt{2} [/tex]
the graph of y=f(x) is shown on the grid
Answer:
Equation for M → g(x) = [tex]\frac{5}{4}x^{2} + 2[/tex]
Equation for N → h(x) = [tex]\frac{5}{4}(x+4)^2-1[/tex]
Step-by-step explanation:
Vertex of the graph of y = f(x) is (2, -1)
Therefore, equation of the function will be,
y = a(x - 2)² - 1
Since this graph passes through a point (0, 4),
4 = a(0 - 2)² - 1
4 = 4a - 1
a = [tex]\frac{5}{4}[/tex]
Hence, we get the equation of the function 'f' as,
f(x) = [tex]\frac{5}{4}x^{2} -1[/tex]
Now this graph has been shifted 3 unit up to get the new graph M
Equation for M will be,
g(x) = f(x) + 3
g(x) = [tex]\frac{5}{4}x^{2} - 1 + 3[/tex]
g(x) = [tex]\frac{5}{4}x^{2} + 2[/tex]
Further graph of function 'f' is shifted 4 units to the left then equation of the new function (N) will be,
h(x) = f(x + 4)
h(x) = [tex]\frac{5}{4}(x+4)^2-1[/tex]
♂️♂️♂️help me plz I dont no 1+1
Answer:
The answer is 2
Step-by-step explanation:
Since the number 1 plus 1 is 2
5x-11=24
????????????
Answer:
x= 7
Step-by-step explanation:
5x-11=24
+11 +11
5x = 35 35/5 = 7 x=7
5(7) - 11 = 24
35 - 11 = 24
Answer:
x=7
Step-by-step explanation:
5x7= 35
35-11=24
5x7-11=24
hope this helps!!!
Formula for parallelogram law of addition
Answer:
answers?
Step-by-step explanation:
13,406,109 pennis into dollars
Answer:
$134,061.09
Step-by-step explanation:
hope this helps
Answer:
134,061.09
Step-by-step explanation:
Divide 13,409,109 by 100
$134,061.09This can also be expressed as 134, 061 dollars, and 9 pennies.
An object that weighs 18 pounds on Mercury weighs approximately 60 pounds on Earth. A rock weighs 120 pounds on Mercury. What is the approximate weight of the rock, in pounds, on Earth
Answer: 400
Step-by-step explanation:
I'm not sure 400
The equation that Passes through the points (-4,2) and (5,-3)
Answer:
m= -5/9
Step-by-step explanation:
m= y2-y1/ x2-x1
m= -3-2/ 5-(-4)
m= -3-2/ 5+4
m= -5/9
y= mx + b
(-4,2)
2= -5/9(-4) + b
2= 2.2+ b
-2.2 +2= b
-0.2= b
Find the slope of the line that passes through(9,36) (93,-10)?
Answer:
[tex]m = -\frac{23}{42}[/tex]
Step-by-step explanation:
here is the equation for slope (m):
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
where:
y₂ = y-coordinate of 2nd point = -10
y₁ = y-coordinate of 1st point = 36
x₂ = x-coordinate of 2nd point = 93
x₁ = x-coordinate of 1st point = 9
plug values into equation:
[tex]m =\frac{-10-36}{93-9} \\\\m = \frac{-46}{84} \\[/tex]
reduce the fraction:
[tex]m = -\frac{23}{42}[/tex]
The membership fee at a sports club was $600 per year. Each year, the membership fee increased by 7%.
Which equation models the cost of the membership fee, y, after 2 years?
Answer:
600(1.07)^2=y
Step-by-step explanation:
Find the midpoint of A and B where A has coordinates (8,5)
and B has coordinates (3, 7).
Answer:
Step-by-step explanation:
Average of x-coordinates = (8+3)/2 = 5.5
Average of y-coordinates = (5+7)/2 = 6
Midpoint at (5.5,6)
Can someone help me find the distance between the points (-5,3) and (-4,2)
Answer: 1.4142
Step-by-step explanation:
Input Data :Point 1 (xA,yA) = (-5, 3) Point 2(xb,yB) = (-4, 2)
Objective : Find the distance between two given points on a line?
Formula :Distance between two points = √(xB-xA)^2+(yB−yA)^2
Solution :
Distance between two points = √(−4−−5)2+(2−3)2= √12+(−1)2= √1+1= √2 = 1.4142
Distance between points (-5, 3) and (-4, 2) is 1.4142
May I please have brainlest I'm trying to achieve a new rank
What is the product?
213 × 314
Answer:
66882
Step-by-step explanation:
Answer:
product
Step-by-step explanation:
213×314=66,882
find the value of n the equation 1/2(n+4)=6
Answer:
n = 8
Step-by-step explanation:
1/2(n + 4) = 6
1/2 of n + 2 = 6
6 - 2 = 4
4 × 2 = 8
1/2 of 8 + 2 = 6
4 + 2 = 6
n = 8
f (x) = 5x -3 what is f (5) =
Answer:
22is answer
f (x) = 5x -3
f (5) =5×5-3=25-3=22
Answer:
5
Step-by-step explanation:
f(x)=5x−3
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n−1 .
5x^1−1
Subtract 1 from 1.
5x^0
For any term t except 0, t^0 =1.
5×1
For any term t, t×1=t and 1t=t.
5
Find the area of the figure
Answer:
Step-by-step explanation:
Just add it
How many 1/3 are in 2 3/4?
Answer: For example, in order to explain why 1/3 + 1/4 = 7/12, we considered the task of dividing 7 apples between 12 boys under the restriction that an apple ... How many halves are in the whole? ... 1 = 3 × 1/3, 2 = 6 × 1/3, 3 = 9 × 1/3, 4 = 12 × 1/3.
Step-by-step explanation:
boom your nice wanna be my friend
Which expression is equivalent to 2(3 - x) - 12 + 4x
1. 3x - 6
2. 3x - 7
3. 2x - 6
4. 2x - 7
PLEASE HELP GEOMETRY
Answer:
Step-by-step explanation:
Find the volume of the cylinder and cone, then add them together.
★ Volume of cylinder :-
V = πr²hHere,
r is radius h is heightWe have :
r = 2cm h = 7cmSubstituting the values :
> V = π (2 × 2) × 7
> V = 4π × 7
> V = 28π
★ Volume of cone :-
V = ⅓ π²hWe have :
r = 2cm h = 6 cmSubstituting the values :
> V = ⅓ × π × (2 × 2) × 6
> V = ⅓ × π × 4 × 6
> V = ⅓ × π × 24
> V = 8π
★ According to the question :-
Adding them together,
> Total Volume = 8π + 28π
> Total Volume = 36π
[tex]Total \: \: \: Volume = (88+176) {cm}^{2} \\ \\ = 264 {cm}^{2} .[/tex]
Which line has a slope of -1/2?
A large rectangular movie screen in an IMAX theater has an area of 7,875 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide.
Answer:
Width=75
length=105
Step-by-step explanation:
Width=x
length=30+x
= 7875=x*30+x
x^2+30x-7875=0
x^2+105x-75x-7875=0
x(x+105)-75(x+105)=0
There are 15 students on the chess team. Seven of the students are in the fourth grade.
Which shows the fraction of the team that is in the fourth grade?
A.
4
5
B.
7
15
O
C
8
15
OD. 15
7
Answer:
7/15 (B)
Step-by-step explanation:
7 fourth graders out of 15 total = 7/15
E=mc squared m=3 c=6
Answer:
E = 108
Step-by-step explanation:
E = 3 * [tex]6^{2}[/tex]
= 108
Answer:
e=mc^2 if m=3 and c=6
e=3([tex]6^2[/tex])
e=3[tex](36)[/tex]
e=108
Step-by-step explanation:
hope this helps have a good rest of your day/afternoon :) ❤
The scatter plot shows which type of correlation?
A. No correlation
B. Cant be determined
C. Negative correlation
D. Positive correlation
Answer:
negative correlation
Step-by-step explanation:
because it starts from the y axis
I need help with this
50 points
Shanna received a small box from the mailman. What is a reasonable weight for the small box? A. 6 grams B. 6 pounds C. 16 millimeters D. 60 inches
Answer:
b is the answer brainliest please i need 1 more
Step-by-step explanation:
jayfeather friend me
Answer:
6 pounds
Step-by-step explanation:
6 grams is the weight of 2 paperclips, and 16 millimeters and 60 inches are used to measure volume, not weight.
hope it helps! :3
What is the perimeter of a rectangle with two lentghs of 5
Answer:
20
Step-by-step explanation:
in perimeter you have to add all the sides but rectabgless all have the same size so 5 x 4 since rectangle has 4 sides equls 20 so 20 is the answer
Leon’s older brother is 4 3/4 feet tall Leon is a 1/3 foot shorter than his brother how. tall is Leon?
Answer:
Leon is 4 5/12
Step-by-step explanation:
4 3/4 - 1/3 change 4 4/12 - 4/12 = 4 5/12