Step 1: 360÷30(exterior angle)= 12 sides
Step 2: (12-2)×180= 1800 (sum of the interior angles of the polygon)
Test: 1800÷ 12 sides= 150 ( 1 interior angle)
Solve the equation for x: 3x + 4 = 9x − 1 by using a common base.
A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 92.4% for the medical students admitted through special programs. Be sure to enter at least 4 digits of accuracy for this problem!
If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated.
prob =
At least 4 digits!
If 12 of the students from the special programs are randomly selected, find the probability that exactly 9 of them graduated.
prob =
At least 4 digits!
Would it be unusual to randomly select 12 students from the special programs and get exactly 9 that graduate?
no, it is not unusual
yes, it is unusual
If 12 of the students from the special programs are randomly selected, find the probability that at most 9 of them graduated.
prob =
At least 4 digits!
Would it be unusual to randomly select 12 students from the special programs and get at most 9 that graduate?
yes, it is unusual
no, it is not unusual
Would it be unusual to randomly select 12 students from the special programs and get only 9 that graduate?
no, it is not unusual
yes, it is unusual
Answer:
A) 0.7696
B) 0.0474
C) Yes it's unusual
D) 0.05746
E) No, it is not unusual
F) No, it is not unusual
Step-by-step explanation:
This is a binomial probability distribution question.
We are told that 92.4% of those admitted graduated.
Thus; p = 92.4% = 0.924
From binomial probability distribution, q = 1 - p
Thus;
q = 1 - 0.924
q = 0.076
Formula for binomial probability distribution is;
P(x) = nCx × p^(x) × q^(n - x)
A) At least 11 graduated out of 12.
P(x ≥ 11) = P(11) + P(12)
P(11) = 12C11 × 0.924^(11) × 0.076^(12 - 11)
P(11) = 0.3823
P(12) = 12C12 × 0.924^(12) × 0.076^(12 - 12)
P(12) = 0.3873
P(x ≥ 11) = 0.3823 + 0.3873
P(x ≥ 11) = 0.7696
B) that exactly 9 of them graduated out of 12. This is;
P(9) = 12C9 × 0.924^(9) × 0.076^(12 - 9)
P(9) = 0.0474
C) We are not given significance level here but generally when not given we adopt a significance level of α = 0.05.
Now, exactly 9 out of 12 that graduated which is P(9) = 0.0474.
We see that 0.0474 is less than the significance level of 0.05. Thus, we can say that it is unusual to randomly select 12 students from the special programs and get exactly 9 that graduate
D) that at most 9 of them out of 12 graduated.
P(x ≤ 9) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)
This is going to be very long so I will make use of an online probability calculator to get the values of P(0) to P(8) since I already have P(9) as 0.0474.
Thus, we have;
P(0) = 0
P(1) = 0
P(2) = 0
P(3) = 0.00000001468
P(4) = 0.00000040161
P(5) = 0.00000781232
P(6) = 0.00011081163
P(7) = 0.00115477385
P(8) = 0.00877476184
Thus;
P(x ≤ 9) = 0 + 0 + 0 + 0.00000001468 + 0.00000040161 + 0.00000781232 + 0.00011081163 + 0.00115477385 + 0.00877476184 + 0.04741450256
P(x ≤ 9) = 0.05746
E) P(x ≤ 9) = 0.05746 is more than the significance level of 0.05, thus we will say it is not unusual.
F) from online binomial probability calculator, probability of getting only 9 out of 12 is more than the significance value of 0.05. Thus, we will say it is not unusual
what is the answer
help
Answer: With that assumption, we have a square, whose area is given by the formula Asquare=a2, and two semicircles. The distance D is simply the square's diagonal. The area of each semicircle is given by the formula Asemicircle=π*r2/2. then you will get your answer!
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
a. What’s the probability density function?
b. What’s the probability that X will take on a value between 21 and 25?
c. What’s the probability that X will take on a value of at least 26?
Answer:
a) The probability distribution is [tex]f(x) = \frac{1}{8}[/tex]
b) 0.5 = 50% probability that X will take on a value between 21 and 25.
c) 0.25 = 25% probability that X will take on a value of at least 26.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{a - x}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniform distribution over the interval from 20 to 28.
This means that [tex]a = 20, b = 28[/tex]
a. What’s the probability density function?
The probability density function of the uniform distribution is:
[tex]f(x) = \frac{1}{b - a}[/tex]
In this question:
[tex]f(x) = \frac{1}{28 - 20} = \frac{1}{8}[/tex]
b. What’s the probability that X will take on a value between 21 and 25?
[tex]P(21 \leq X \leq 25) = \frac{25 - 21}{28 - 20} = \frac{4}{8} = 0.5[/tex]
0.5 = 50% probability that X will take on a value between 21 and 25.
c. What’s the probability that X will take on a value of at least 26?
[tex]P(X > 26) = \frac{28 - 26}{28 - 20} = \frac{2}{8} = 0.25[/tex]
0.25 = 25% probability that X will take on a value of at least 26.
The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3
Write a general formula to describe each variation.
The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3
Answer:T² = [tex]\frac{18a^3}{d^2}[/tex]
Step-by-step explanation:Few things to note:
i. direct variation: When a variable x varies directly with another variable y, we write it in this form;
x ∝ y.
This can then be written as;
x = ky
Where;
k = constant of proportionality variation.
ii. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;
x ∝ [tex]\frac{1}{y}[/tex]
This can then be written as;
x = k([tex]\frac{1}{y}[/tex])
Where;
k = constant of proportionality or variation
iii. combined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;
x ∝ ([tex]\frac{y}{z}[/tex])
This can then be written as;
x = k ([tex]\frac{y}{z}[/tex])
Where;
k = constant of proportionality or variation
From the question;
The square of T varies directly with the cube of a and inversely with the square of d.
Note that
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝ [tex]\frac{a^3}{d^2}[/tex]
=> T² = k ([tex]\frac{a^3}{d^2}[/tex]) -------------------(i)
Since;
T = 4 when a = 2 and d = 3
We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;
(4)² = k ([tex]\frac{2^3}{3^2}[/tex])
16 = k ([tex]\frac{8}{9}[/tex])
8k = 16 x 9
8k = 144
k = [tex]\frac{144}{8}[/tex]
k = 18
Now substitute the value of k back into equation (i);
T² = 18 ([tex]\frac{a^3}{d^2}[/tex])
T² = [tex]\frac{18a^3}{d^2}[/tex]
Therefore, the general formula that describes the variation is;
T² = [tex]\frac{18a^3}{d^2}[/tex]
Watch help video
In the diagram below of triangle MNO, P is the midpoint of MO and Q is the
midpoint of NO.If PQ = 49 – 8x, and MN = 41 + 3x, what is the measure of
MN?
O
N
P
M M
Answer:
MN = 50
Step-by-step explanation:
Given:
PQ = 49 – 8x
MN = 41 + 3x
Required:
Measure of MN
Solution:
PQ = ½(MN) => Mid-segment theorem of a triangle
Substitute
49 - 8x = ½(41 + 3x)
Multiply both sides by 2
2(49 - 8x) = 41 + 3x
98 - 16x = 41 + 3x
Collect like terms
98 - 41 = 16x + 3x
57 = 19x
57/19 = 19x/19
3 = x
x = 3
Find MN:
MN = 41 + 3x
Plug in the value of x
MN = 41 + 3(3) = 41 + 9
MN = 50
Please help!!! It wants the x and y coordinates
Answer:
the y-coordinate will be at (0, 2.4)
the x-coordinate will be at (6, 0)
Step-by-step explanation:
y coordinate of the graph is the point where the curve cuts the y axis
According to the graph, the curve cuts the y axis at y = 2.4. Hence the y-coordinate will be at (0, 2.4)
Similarly, the x-coordinate of the graph is the point where the curve cuts the x-axis
According to the graph, the curve cuts the x-axis at x = 6. Hence the x-coordinate will be at (6, 0)
Which system of inequalities has the solution set shown in the graph?
25 < (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 < (x – 1)2 + y2 and 16 < x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 < x2 + (y + 4)2
lmoa what
Answer:
A. 25 < (x – 1)² + y² and 16 > x² + (y + 4)²
Step-by-step explanation:
the solutions are in the outside of the bigger circle, but inside of the smaller circle
The inequality is 25 < (x – 1)² + y² and 16 > x² + (y + 4)². Option A is correct.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than.
The solutions are on the outside of the bigger circle, but inside of the smaller circle.
The radius of the bigger circle is 5 and the radius of the smaller circle is 4. The graph of the inequality is attached with the answer below.
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ5
Is -5/250 a rational number
Answer:
Hello There!!
Step-by-step explanation:
The answer is that=>Yes It is a rational number.
hope this helps,have a great day!!
~Pinky~
Answer:
Yes.
Step-by-step explanation:
A rational number is any number that can be written as a fraction. These include whole numbers, fractions, decimals that end, and decimals that repeat. Positive and negative do not affect rationality.
Please answer this your award will be 20 points for the first answer and brainliest
Step-by-step explanation:
pool = 1600 sq.cm
1600 sq.sm = 50cm × 32cm
AB = 50cm
the area of the park of A'B' :
50cm×4=200 sq.cm
which number is 3/8closet to
Answer:
616
Step-by-step explanation:
A fraction that is equivalent to 38 is 616
Marking brainliest(for correct answers)
Factor completley:
9(x-1)-(x-1)^2
What is the answer?
2x2-1/3x2+7/3x2 plzzzzzzzzzzzz fast
Answer:
8
Step-by-step explanation:
8 is the correct answer
Answer:
12 2/3
Step-by-step explanation:
A ramp is in the shape of a triangle
Answer:
Step-by-step explanation:
The table shows the completion times of four Horses in a race.
Horses
Time (Seconds)
Horse-3
1512
Horse-4
15.4
Horse-2
154
Horse-1
15.8
Which list shows the Horses in order by their completion times from fastest to slowest?
A. Horse-1, Horse-3, Horse-2, Horse-4
B.
Horse-4, Horse-3, Horse-2, Horse-1
C. Horse-4, Horse-2, Horse-3, Horse-1
D. Horse-1, Horse-2, Horse-3, Horse-4
Answer:
I think the answer is option B
Answer:
I think it is (b
Step-by-step explanation:
Five cards are drawn randomly from a standard deck of 52 cards.
Determine the probability that exactly 3 of these cards are Aces. Write your answer in decimal form, rounded to 5 decimal
places
Answer:
=========================================================
Explanation:
There are 4 ways to select 3 aces where order doesn't matter. It's basically the same as saying there are 4 ways to leave out one ace.
Then we have 2 slots left to fill. There are (48*47)/2 = 1128 ways to do this where order doesn't matter. The 48 is from the fact there are 52-4 = 48 cards that aren't aces. We step down to 47 after picking the first non-ace card. The 2 in the denominator is to correct for double counting.
We found there were 4 ways to pick the three aces, and 1128 ways to pick the other two non-ace cards. Overall, there are 4*1128 = 4512 ways to pick all five cards where we have exactly 3 aces.
This is out of 52C5 = 2,598,960 ways to select any five cards from a 52 card deck. I'm using the nCr formula which is
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
Use n = 52 and r = 5 to get the value mentioned. The exclamation marks indicate factorial.
------------------------------------
To recap, there are
4512 ways to pick exactly three aces2,598,960 ways to pick five cards without any restrictionsDividing the two values gets us the final answer
4512/(2,598,960) = 0.001736079047
This value rounds to 0.00174
The probability that exactly 3 of these cards are Aces is 0.004%.
Given that five cards are drawn randomly from a standard deck of 52 cards, to determine the probability that exactly 3 of these cards are Aces the following calculation must be performed:
Each particular probability must be multiplied by each other, and its result by one hundred, to obtain the probability percentage. (3/52 x 2/51 x 1/50) x 100 = X 0.004 = X
Therefore, the probability that exactly 3 of these cards are Aces is 0.004%.
Learn more in https://brainly.com/question/821892
cho p(A)=0,5 ; p(B) = 0,3 ;p(A∩B)=0,2. Tính p(B∪A) ?
Answer:
.6
Step-by-step explanation:
BUA= A+B-A∩B
.5+.3-.2= .6
Which fraction is represented by point A on the number line?
0
А
-0 -1
о
IT
os
O 1
Which multiplication problem is represented by the model?
Divide. Write your answer in simplest form.
1/5 ÷ 4
tell this !!!!............
Answer:
D
Step-by-step explanation:
Answer:
D....................
coz 100 has 0 so the number should at least have 0 in it
triangle ABC has angle measures as shown.
A) what is the value of x? show your work.
B) what is the measure of angle C? show your work.
Answer:
12°
Step-by-step explanation:
Sum of interior angles of the triangle is 180°:
m∠A + m∠B + m∠C = 180°
3x + 28° + 5x + 52° + 2x - 10° = 180°
10x + 70° = 180°
10x = 110°
x = 11°
Find the measure of angle C:
m∠C = 2x - 10° = 2(11°) - 10° = 22° - 10° = 12°
Answer:
Step-by-step explanation:
(2x - 10)° + (5x + 52)° + (3x + 28)° = 180°
10x + 70 = 180
x = 11
m∠C = [ 2(11) - 10 ]° = 12°
a cone has a volume of 374 cubic inches and a height of 4 inches
Answer:
1496 cubic inches
Step-by-step explanation:
Use the following image to determine the measure of arc GH.
Answer:
Arc GH = 78°
Step-by-step explanation:
Inscribed angle = m<GIH = 39°
Measure of arc related to inscribed angle = arc GH = ?
Thus:
m<GIH = ½(arc GH) => Inscribed angles theorem
Substitute
39° = ½(arc GH)
Multiply both sides by 2
2*39° = arc GH
78° = arc GH
Arc GH = 78°
a train moving at the rate of 50 km per hour in struck by a stone moving with a velocity of 40 km above are making an angle of 60 degree with the direction of the train find the velocity with which the stone appears to an observed in the train to strike
the train
Answer:
Step-by-step explanation:
the pidgeon is flying east
The missing number in the arithmetic sequence: 20,
36, 44 is:
None of these choices are correct
26
27
28
29
Answer:
28
Step-by-step explanation:
it is missing where ?
based on the answer options I guess it is missing between 20 and 36.
if that is true, then the answer is 28.
the difference between 36 and 44 is 8.
the difference between 20 and 36 is 16.
the right answer should cut the interval of 16 into 2 parts (first logical approach to cut it in 2 halves of 8) and be related to the next interval between 36 and 44 (8).
the solution covering both considerations is the middle of the large interval = 20 + 8 = 28.
PLEASE HELP GEOMETRY!!!!
Solve for x in the diagram shown.
A) 3.2
B) 6.6
C) 8
D) 20
9514 1404 393
Answer:
A) 3.2
Step-by-step explanation:
In this geometry, all of the right triangles are similar. This means side lengths are proportional:
short side/hypotenuse = x/8 = 8/20
x = 8×8/20 = 64/20
x = 3.2
Plss help Give brainiest if right!
One pipe can fill the pool in 6 hours. The second pipe can drain
the pool in 18 hours. How long will it take to fill the pool if the
two pipes are both working?
Answer:
Will take 8hrs.
Step-by-step explanation:
if pipe 1 takes 6 hrs then the 2nd pipe drains it 3x slower
Which means pipe 1 will take 1 hr slower every 3 hrs taken
and will be at ratio 3:2 for when pipe 2 is used
6 + 2 = 8 (hrs)
Will take 8hrs.
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 7 if there were 5887 no votes what was the total number of votes
Determine the value of x
Answer:
B is the answer.
Step-by-step explanation: