The mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .
To find the mean, variance, and standard deviation of a binomial distribution with given values of [tex]\( n \)[/tex] and [tex]\( p \)[/tex], we use the following formulas:
Mean [tex](\( \mu \)) = \( n \times p \)[/tex]
Variance [tex](\( \sigma^2 \)) = \( n \times p \times (1 - p) \)[/tex]
Standard Deviation [tex](\( \sigma \)) = \( \sqrt{\text{Variance}} \)[/tex]
Given:
[tex]\( n = 123 \)[/tex]
[tex]\( p = 0.85 \)[/tex]
Let's calculate each of these:
Mean [tex](\( \mu \))[/tex]:
[tex]\( \mu = n \times p \)[/tex]
[tex]\( \mu = 123 \times 0.85 \)[/tex]
[tex]\( \mu = 104.55 \)[/tex]
Variance [tex](\( \sigma^2 \))[/tex]:
[tex]\( \sigma^2 = n \times p \times (1 - p) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times (1 - 0.85) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 104.55 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 15.6825 \)[/tex]
Standard Deviation [tex](\( \sigma \))[/tex]:
[tex]\( \sigma = \sqrt{\sigma^2} \)[/tex]
[tex]\( \sigma = \sqrt{15.6825} \)[/tex]
[tex]\( \sigma \approx 3.9599 \)[/tex]
Therefore, the mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .
You cut a 90 cm long rope into two pieces. the longer piece is 2 times as long as the shorter piece. what is length of the longer piece and the shorter piece respectively?
Each marble bag sold by leila's marble company contains 5 yellow marbles for every 8 green marbles. if a bag has 35 yellow marbles, how many green marbles does it contain?
A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?
Answer: 21 seconds
Step-by-step explanation:
We know that a parabola with equation [tex]y=ax^2+bx+c[/tex] attains its maximum height at :-
[tex]x=\dfrac{-b}{2a}[/tex]
The given function: [tex]h=-16t^2 +672t[/tex]
It will attain its maximum height at :
[tex]t=\dfrac{-672}{2(-16)}=21[/tex]
Hence , after 21 seconds the projectile will reach its maximum height .
Geometry please help !!
Given the points A (3,2) and B (-21,0) determine:
a. the slope of line AB
b. the length of AB
c. the midpoint of AB
d. an equation of AB
There is a traffic light at the intersection of Walnut Street and Lawrence Avenue. The traffic light on Walnut Street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds. As you travel along Walnut and approach the intersection, what is the probability that the first color you see is red?
1/5
1/3
3/5
1/2
If 1/3 of an office staff is on vacation and 1/4 of those not on vacation are out sick, what fraction of the staff is in the office
The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and the common ratio.
Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root 3
The area of a regular hexagon is mathematically given as
A=665.1 sq units
What is the area of a regular hexagon whose side length is 16 in.?Question Parameter(s):
a regular hexagon whose side length is 16 in.
and the apothem is 8 square root 3
Generally, the equation for the area is mathematically given as
A=(3√3)/2 *a^2
Therefore
A = 6*(0.5*16*8√3)
A= 384√3 sq units
A=665.1 sq units
In conclusion, the area of a regular hexagon
A=665.1 sq units
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If you apply the changes below to the absolute value parent function, F(x)=|x|, what is the equation of the new function? Shift 8 units left, shift 3 units down.
A. G(x)=|x-3|-8
B. G(x)=|x-3|+8
C. G(x)=|x-8|-3
G(x)=|x+8|-3
a rectangle has a perimeter of 182 in and length of 52 in. What is the width?
Julio is playing a trivia game .on his first turn ,he lost 100 points on his second turn ,he lost 75 points . On his third, he lost 85 points. Write a sum of three nagative integer that models the change to julio score after his first three turns
Is 70 thousand written in standard form or word form explain.
Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)
19779 - 57(11) = 19779 - 627 = 19152
m = 19152*2/(56*57)
m = 12
she saved $12 more every month
A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
The slope of the line passing through the points (6, -1) and (7, -2) is
A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x = 1/12y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.
The digital monitoring system attached at 6 inch from telescope.
What is Parabola?A curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a stationary point is equal to its distance from a fixed line.
Here, we have a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.
So, the equation that in this situation is
x = y² / 12
12x = y²
y= √12x
So, at x= 3 the y will be
y = √12(3)
y = √36
y = 6
Thus, the digital monitoring system attached at 6 inch from telescope.
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Need help please!!!!
I can't see the question...maybe I would be better at helping if I knew what to assist with.
;)
Which of the following shows the graph of a line through (-2,2) and (2,4)
Answer:
Attachment for graph.
Step-by-step explanation:
Given: (-2,2) and (2,4)
Two points are given and to find the equation of line passing through the points.
First we find the slope of the line.
[tex]\text{Slope }=\dfrac{4-2}{2+2}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Point: (2,4)
using point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=\dfrac{1}{2}(x-2)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
Now, we draw the graph using two given points. Plot the points on graph and join them.
Please find the attachment for graph.
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6. Applying Newton's cooling model, the temperature of the tea after 2 hours will be ºF
Answer:
T = 109 degrees f
Step-by-step explanation:
The dot plot shows the number of words students spelled correctly on a pre-test. Which statement best describes the shape of the graph?
A.) The graph is skewed right.
B.) The graph is nearly symmetrical.
C.) The graph is skewed left.
D.) The graph is perfectly symmetrical.
Let's think of this problem easily by looking at it instead of going through rigorous mathematics.
When a graph is skewed right, most of the values are to the left side.
When a graph is skewed left, most of the values are to the right side.
Perfectly symmetrical is that both sides, with respect to the median, are same. Here mean and median is equal.
Nearly symmetrical would really close to perfect symmetry, only varying a bit on both sides. Mean would be approximately equal to median.
Now counting the dots as well as looking closely, we can rule out skewed right and skewed left. Now, is the graph perfectly symmetrical? No! So the correct answer is "nearly symmetrical". Correct choice is B.
ANSWER: B
Answer:
The answer is neary symmetrical or answer B
Step-by-step explanation:
If you cut the graph in half exactly, both side would almost line up perfectly.
A bacteria culture starts with 120 and after 3 hours the population consists of 200 bacteria. What is the rate of the increase to the nearest percent?
The rate of the increase would be 18.56% to the nearest percent.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Seema obtained a score of 57% on her exam, that corresponds to 67 out of 100.
We have been given 120 bacteria to start, which increases to 200 bacteria in 3 hours.
The population-increasing formula is given by
⇒ P(n) = P₀(1+ r)ⁿ
Here P(n) = 200, P₀ = 120, and n = 3
Substitute the values in the above equation,
⇒ 200 = 120(1+ r)³
⇒ 200 / 120 = (1+ r)³
⇒ 5/3 = (1+ r)³
⇒ ∛5/3 = 1+ r
⇒ ∛5/3 - 1 = r
⇒ r = 0.18563
⇒ % r = 18.56%
Therefore, the rate of the increase would be 18.56% to the nearest percent.
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The rate of increase for a bacteria culture that starts with 120 bacteria and grows to 200 after 3 hours is calculated by dividing the increase in population (80) by the initial population (120) and then multiplying by 100 to get the percentage. The rate of increase is 66.67%, which rounds to 67% to the nearest percent.
To find the rate of increase to the nearest percent for a bacteria culture that starts with 120 bacteria and grows to 200 bacteria after 3 hours, we must calculate the percentage growth over the time period given.
First, we need to find the absolute increase in the number of bacteria:
Final population - Initial population = Increase in population
200 - 120 = 80
Next, we calculate the rate of increase based on the initial population:
(Increase in population / Initial population)
(80 / 120)
Multiplying by 100 to get the percentage: (80 / 120) ×100
Rate of increase = 66.67%
Rounded to the nearest percent, the rate of increase is 67%
After John worked at a job for 10 years, his salary doubled. If he started at $ x , his salary after 10 years is _____.
$ x
$ x + 2
$ x - 2
$2 x
The sum of the page numbers on the facing pages of a book is 81. what are the page? numbers?
True or false the opposite angles of a quadrilateral in a circumscribed circle are always complementary
Answer: This statement is false.
Step-by-step explanation:
False, the opposite angles of a quadrilateral in a circumscribed circle is not complementary.
As we know that the sum of opposite angles of a cyclic quadrilateral ( quadrilateral circumscribed circle ) is always supplementary.
So, Sum of opposite angles is 180° .
Hence, this statement is false.
Answer:
False
Step-by-step explanation:
We are given that
Opposite angles of a quadrilateral in a circumscribed circle are always complementary.
We have to find that this statement is true or not.
We know that
When a quadrilateral in a circumscribed circle is called cyclic quadrilateral.
We know that
Sum of opposite angles of cyclic quadrilateral is always 180 degrees.
When sum of two angle is equal to 180 degrees then , the angles are called supplementary.
Hence, the sum of opposite angles of cyclic quadrilateral is always supplementary.
Therefore, the given statement is false.
Find an equation of the vertical line that passes through (x, y) = (5, 11).
ASAP!!
Shortly before a 1992 mayoral election, a local radio station conducted a Internet survey of voters. Based on the results of the survey, the magazine predicted that the Democratic candidate would beat the Republican candidate by a landslide. In fact, exactly the opposite happened. The trouble with the survey was that the radio station was a largely liberal station and few Republicans visited its Web site. This is a classic example of an error in which phase of inferential statistics?
A.Data gathering
B.Data analysis
C.Probability-based inference
D.Data organization
This is a classic example of an error in data gathering phase of inferential statistics.
What is data gathering?Data gathering is the process of collection and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes.
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Solve for x: 8x + 10 - 5x = 15.
8x+10-5x = 15
3x+10 = 15
3x = 5
x = 5/3
Solve the system of equations by substitution. x + y = x + 7y = 8
Answer:
1 and 1
Step-by-step explanation:
Please help me answer this math question.
all 3 angles in a triangle need to equal 180 degrees
62 +73 = 135 degrees are known
180-135 = 45
so angle B = 45 degrees