Answer:
[tex]X \sim Binom(n=10, p=0.96)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
For this case the expected value is given by:
[tex] E(X) = np = 10 *0.96 = 9.6[/tex]
Part b
For this case the standard deviation is given by:
[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
Let X the random variable of interest "number of workers in the sample who are union members", on this case we now that:
[tex]X \sim Binom(n=10, p=0.96)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part a
For this case the expected value is given by:
[tex] E(X) = np = 10 *0.96 = 9.6[/tex]
Part b
For this case the standard deviation is given by:
[tex] \sigma = \sqrt{np(1-p)}= \sqrt{10 *0.96*(1-0.96)}= 0.620[/tex]
A. The mean number of union members in a sample of 10 workers is 9.6. B. The standard deviation is approximately 0.620.
A) Mean (Expectation) Calculation
The number of union members in the sample can be modeled using a binomial distribution since each worker either is or isn't a union member.
For a binomial distribution, the expectation (mean) is given by:
Mean (μ) = n * p
where n is the number of trials (in this case, the number of workers in the sample), and p is the probability of success in a single trial (the probability that a worker is a union member).
Here, n = 10 and p = 0.96, so:
Mean (μ) = 10 * 0.96 = 9.6
B) Standard Deviation Calculation
For the same binomial distribution, the standard deviation (σ) is given by:
σ = √(n * p * (1 - p))
Substituting the given values:
σ = √(10 * 0.96 * (1 - 0.96))
= √(10 * 0.96 * 0.04)
= √0.384
= 0.620
Thus, the standard deviation of the distribution is approximately 0.620
Consider the graphs of f(x)= sin x and g(x) = cos x. Which of the following features are the same for both graphs? Select all that apply.
Answer:
Step-by-step explanation:
All but the x- and y-intercepts are the same.
We can conclude the following similarities between the sin(x) and cos(x) -
Their amplitudes are same i.e. 1They have same domain.They have same range.They have same period of 2π.What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given are the graphs of the function -
f(x) = sin(x)
g(x) = cos(x)
For the functions sin(x) and cos(x) -
Their amplitudes is same i.e. 1They have same domain.They have same range.They have same period of 2π.Therefore, we can conclude the following similarities between the sin(x) and cos(x) -
Their amplitudes are same i.e. 1They have same domain.They have same range.They have same period of 2π.To solve more questions on functions, visit the link below-
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The mean age of five children is 8 years
4 months. When Amina joins the children,
their mean age becomes 8 years 5 months.
How old is Amina?
Answer:
9
Step-by-step explanation:
Answer:
its 8
Step-by-step explanation:
what’s the answer? i really need help ???
Answer:
C, 288 square yards
Step-by-step explanation:
The first step is to find the area of the triangular base. [tex]\frac{6\cdot 8}{2}=24[/tex]. Now you can multiply by the length of the prism, 12, to find the volume. 12*24=288, or option C. Hope this helps!
To rent a boat it costs 11$ plus an additional 10$ per hour if you have 71$ write and solve an equation to solve an equation to determine how many hours you can rent the boat
One letter was selected at random from the words San Antonio. What is the probability that the selected letter was either an a or an n
The required probability of the selected letter was either an a or an n is 0.5.
Given that,
One letter was selected at random from the words San Antonio. The probability that the selected letter was either an a or an n is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total letters = 10
Total a and n = 2 and 3
The probability is given as = 2 / 10 + 3 / 10
= 5/10 = 1/2 = 0.5
Thus, the required probability of the selected letter was either an a or an n is 0.5.
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Factor x2 – 2x – 80.
A. (x – 3)(x + 10)
B. (x + 6)(x - 1)
C. (X + 8)(x - 10)
D. (+3)(x+6)
Answer:
(x-10) (x+8)
Step-by-step explanation:
x^2 – 2x – 80.
What two numbers multiply to -80 and add to -2
-10*8 = -80
-10+8 = -2
(x-10) (x+8)
=====================================================
Explanation:
The last term is -80 and the middle coefficient is -2
Find two numbers that
Multiply to -80, and,add to -2Those two numbers are 8 and -10
8 times -10 = -808 plus -10 = -2which is why the original expression factors to (x+8)(x-10)
We can use the FOIL rule to expand out (x+8)(x-10) to end up with x^2-10x+8x-80 = x^2-2x-80, which confirms we have the correct factorization. You can use the box method as an alternative.
Supriya is decorating her bedroom. She plans to hang strings of twinkle lights all the way around her walls. She measures the walls and finds she will need 36 meters of lights. Which measurement did Supriya find?
Answer:
Perimeter
Step-by-step explanation:
Perimeter is the distance all round a particular shape. Since we are not given the shape of her bedroom, we may not have a particular formula that was uses to find the perimeter. Despite all that, the only way that she could arrive to conclusion that 36 meters of light are needed, then Supriya it is by finding the perimeter.
geometry please help
Answer:
b. 46°
Step-by-step explanation:
In a circle, measure of minor arc is equal to the measure of its corresponding central angle.
[tex] \therefore m\overset{\frown} {BD} = m\angle BAD = 148°\\
\because m\overset{\frown} {BD}= m\overset{\frown} {BC}+ m\overset{\frown} {CD}\\
\therefore 148° = 102° + m\overset{\frown} {CD}\\
\therefore m\overset{\frown} {CD}= 148° - 102°\\
\huge\purple {\boxed {\therefore m\overset{\frown} {CD}= 46°}} \\ [/tex]
Un automóvil sale de una estación y recorre en linea recta 400 metros a la derecha , luego se devuelve 500 metros se detiene y vuelve a correr 100 metros a la derecha . De acuerdo con este recorrido el automóvil esta : A. 200 metros ala izquierda de la estación B. 100 metros a la derecha de la estación C. 50 metros a la derecha de la estación D. En la estación
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. Suppose water is pumped out of the pool at a rate of 216ft3 per hour. If the pool starts completely full, how many hours does it take to empty the pool?
Answer: it will take 9 hours to empty the pool.
Step-by-step explanation:
The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is
30 × 18 × 4 = 2160 ft³
If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + d(n - 1)
Where
a represents the first term of the sequence(initial amount of water in the pool when completely full).
d represents the common difference(rate at which it is being pumped out)
n represents the number of terms(hours) in the sequence.
From the information given,
a = 2160 degrees
d = - 216 ft3
Tn = 0(the final volume would be zero)
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
0 = 2160 - 216 (n - 1)
2160 = 216(n - 1) = 216n + 216
216n = 2160 - 216
216n = 1944
n = 1944/216
n = 9
Step-by-step explanation:
Answer: it will take 9 hours to empty the pool. Step-by-step explanation: The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is 30 x 18 x 4 = 2160 ft3 If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as Tn = a + d(n - 1) Where a represents the first term of the sequence(initial amount of water in the pool when completely full). d represents the common difference(rate at which it is being pumped out) n represents the number of terms(hours) in the sequence. From the information given, a = 2160 degrees 216 ft3 d = Tn = 0(the final volume would be zero) We want to determine the number of terms(hours) for which Tn would be zero.
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
O = 2160 - 216 (n - 1) 2160 = 216(n - 1) = 216n + 216 216n = 2160 - 216 216n = 1944 %3D n = 1944/216 n = 9
Please help my grade is really low in this class
Answer:
A
Step-by-step explanation:
When completing the square, the first thing you want to do is get all of the numbers on one side, and all the x terms on the other.
Answer:
A
Step-by-step explanation:
the first thing you should do while completing the square should be moving your 'c' value to the other side of the equation!
do so by subtracting 8 on both sides,
your new equation should now look like x^2 -6x = -8
that is the first step of completing the square!
i hope this helps!!
you can totally bring your grade in math up!!
i believe in you!
stay safe!
:)
Matrix question is so confusing
(These values are the same as in the given matrix)
The bottom row's answer boxes are: 0, 1, -9/13=======================================================
Explanation:
Row echelon form will have us turn the "3" into a 0. To do this, we multiply everything in row 1 by the value -3
Row 1 is initially: 1, -4, 3
Multiply that row by -3 to get: -3, 12, -9
Then add these values to the values in row 2 and we get:
-3+3 = 0
12+1 = 13
-9+0 = -9
These three sums replace what you see in row 2
This is the new matrix we have now
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 13 & -9\end{array}\right][/tex]
Again the first row has not changed. Only the second row has been altered.
The next and last step is to turn that 13 into a 1. Recall we want the pivot positions to be 1. Divide everything in row 2 by 13 to get this accomplished.
0---> 0/13 = 0
13 ----> 13/13 = 1
-9 ---> -9/13
we now have
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 1 & \frac{-9}{13}\end{array}\right][/tex]
We stop here since we don't need to get the matrix into reduced row echelon form (RREF) and instead only need to get it into row echelon form (REF). Throughout this whole process, row 1 has not changed.
the ratio of wins to loses is 5.4 for a basketball team. if the bball team played 90 games, how many games did they win ?? show work!
Answer:
40
Step-by-step explanation:
UESTION 3 Researchers discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with a mean of 55.7 centimeters and a standard deviation of 12 cm. The minimum and maximum size limits for captured sea turtles in the legal marine turtle fishery are 40cm and 60cm, respectively. How likely are you to capture a green sea turtle that is considered illegal?
Final answer:
The probability of capturing a green sea turtle considered illegal due to its size is about 45.52%. This is calculated using Z-scores and probabilities from the normal distribution, given the mean turtle size and standard deviation.
Explanation:
In the scenario provided, the probability of capturing a green sea turtle that is considered illegal (outside the 40cm to 60cm size limits) can be determined using normal distribution calculations. Given that the curved carapace length of these turtles is approximately normally distributed with a mean of 55.7 centimeters and a standard deviation of 12 cm, we will calculate the Z-scores for both size limits and then find the corresponding probabilities.
The Z-score formula is: Z = (X - μ)/σ, where X is the value in question, μ is the mean, and σ is the standard deviation. For the minimum size limit (40cm), Z = (40 - 55.7)/12 = -1.308. For the maximum size limit (60cm), Z = (60 - 55.7)/12 = 0.358.
Using standard normal distribution tables or a calculator, we find the probability corresponding to the Z-score of -1.308 and 0.358. The area to the left of Z = -1.308 is approximately 0.0951, and to the left of Z = 0.358 is approximately 0.6399. The probability of catching an illegal turtle is the sum of the probabilities of catching one smaller than 40cm and one larger than 60cm, which is P(X < 40) + P(X > 60) = 0.0951 + (1 - 0.6399) = 0.0951 + 0.3601 = 0.4552, or 45.52%.
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
Answer:
y = 1/4x -8
Step-by-step explanation:
First find the slope of the line
x-4y =3
Subtract x from each side
x-4y -x = -x+3
-4y = -x+3
Divide each side by -4
-4y/-4 = -x/-4 +3/-4
y = 1/4 x -3/4
This is in the form y= mx+b where the slope is m and the y intercept is b
The slope is 1/4
We want the same slope
y = 1/4x +b
we know the y intercept is -8
y = 1/4x -8
A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible. a. What is the largest number of groups that could be formed? groups b. If that many groups are formed, how many students of each grade level would be in each group? sixth-grade students and seventh-grade students
Answer:
a) 15 is the largest number of groups that can be made.
b) There would 6 sixth grade students and 5 seventh grade students in each group.
Step-by-step explanation:
Number of sixth-grade students = 90
Number of seventh-grade students = 75
a) What is the largest number of groups that could be formed?
Since the music director wants to make groups with the same combination of sixth and seventh grade students in each group,
The greatest common factor (GCF) of the number of sixth and seventh grade students would give us the required combination.
Factor of 90 = 2*45 = 2*3*15 = 2*3*3*5
Factor of 75 = 3*25 = 3*5*5
The greatest common factors are 3 and 5
GCF = 3*5 = 15
Therefore, 15 is the largest number of groups that can be made.
b. If that many groups are formed, how many students of each grade level would be in each group?
Sixth grade = 90/15 = 6
Seventh grade = 75/15 = 5
Therefore, there would 6 sixth grade students and 5 seventh grade students in each group.
1. 15 groups. The greatest common factor of 75 and 90 is 15. 2. 6 sixth-grade students and 5 seventh-grade students
2. 6 sixth-grade students and 5 seventh-grade students ( 6 ⋅ 15 = 90 and
5 ⋅ 15 = 75 )
Simplify the following expression.
7(2y + 5z) - 35z
A.
9y
B.
14y - 40z
C.
9y - 70z
D.
14y
Answer: 14y
Step-by-step explanation:
7 times 2 = 14
7 times 5 = 35
14y + 35z - 35z
35 - 35 = 0
You are left with 14y
The results of a color spinner experiment are shown in the table. Consider the experimental probability of the spinner landing
on green. If the experiment is repeated with 50 spins, what is the prediction for the number of spins that will land on green?
Frequency
Result
Blue
Red
Green
Yellow
colos
Save and Exit
Next
Submit
Mark this and return
If the experiment is repeated with 50 spins, the prediction for the number of spins that will land on green is 5
From the question, we have the following parameters that can be used in our computation:
The table of values
Calculate the total number of spins
So, we have
Total spins = 5 + 3 + 1 + 1
Total spins = 10
We have that
The frequency of landing on green is 1
The experimental probability of landing on green is then represented as
[tex]\[ \text{Probability of green} = \frac{1}{10} \][/tex]
Using the experimental probability to predict the number of spins that will land on green in 50 spins, we have
Predicted number of green spins = [tex]\frac{1}{10} \times 50 = 5[/tex]
So, if the experiment is repeated with 50 spins, the prediction for the number of spins that will land on green is 5
Question
The results of a color spinner experiment are shown in the table. Consider the experimental probability of the spinner landing
on green. If the experiment is repeated with 50 spins, what is the prediction for the number of spins that will land on green?
Result Frequency
Blue 5
Red 3
Green 1
Yellow 1
A drawer contains 5 black socks(B), 7 grey socks(G) and 13 white socks(W). Matthew selects two socks from the drawer at random. What is the probability that they are the same color? Give your answer as a decimal correct to three significant figures.
Answer:
0.363
Step-by-step explanation:
Number of Black(B) Socks =5
Number of Grey(G) Socks =7
Number of White(W) Socks =13
Total Number of Socks=5+7+13=25
If the two socks are picked one after the other, the total number reduces and the number of that particular color of socks picked also reduces.
To pick the same color, they could either be both black, grey of white.
Therefore:
P(they are of the same color)=P(BB)+P(GG)+P(WW)
[tex]=(\frac{5}{25}X\frac{4}{24})+(\frac{7}{25}X\frac{6}{24})+(\frac{13}{25}X\frac{12}{24})\\=0.363[/tex]
The probability that they are of the same color is 0.363 correct to 3 significant figures.
solve the system of equations
-5x+2y=9
y=7x
Answer:
x=1, y=7
Step-by-step explanation:
-5x+2y=9
y=7x
Since you know what y is relative to x, you can plug it into the formula to find your answer.
-5x+2(7x)=9
14x-5x=9
x=1
y=7
Hope this helps!
HURRRY PLEASE N HELP
Coach McGee uses the
table to show her team's current basketball shot average compared to previous years,
2010
2008
-5.8
2009
4.4
10
-
2012
2013
2011
3.6
Which comparison is true? Use the number line to help you.
-6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
0 -5.8>-53
Answer:
b
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation
hope it helps!
The expression 62.4d-21062.4d−21062, point, 4, d, minus, 210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange
Answer:601.2
Step-by-step explanation:
Todd earned some money doing chores. He spent one-fourth of his money see a movie. Then he spent $6.00 on popcorn and drinks. When he went home, he had $24.00 left. How much did Todd earn mowing the neighbor's lawn?
Answer: Todd earned $40 mowing the neighbor's lawn.
Step-by-step explanation:
Let x represent the amount of money that Todd earned, mowing his neighbor's lawn.
He spent one-fourth of his money see a movie. It means that the amount spent in seeing a movie is x/4
Then he spent $6.00 on popcorn and drinks. It means that the total amount spent is
x/4 + 6
The amount left would be
x - (x/4 + 6) = x - x/4 - 6
When he went home, he had $24.00 left. It means that
x - x/4 - 6 = 24
x - x/4 = 24 + 6
x - x/4 = 30
Cross multiplying by 4, it becomes
4x - x = 120
3x = 120
x = 120/3
x = $40
Answer: 40$ got it right on edge :)
Step-by-step explanation:
The recipe has 10 tomatoes, 6 cucumbers, and 3 peppers. What is the ratio of tomatoes to peppers?
Group of answer choices
10/3
6/3
3/6
3/10
Answer:
10/3
Step-by-step explanation:
Answer:
no of tomatoes: no of pepper
10:3
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 555 every 222222 days, and can be modeled by a function, LLL, which depends on the amount of time, ttt (in days). Before the first day of spring, there were 760076007600 locusts in the population. Write a function that models the locust population ttt days since the first day of spring.
Answer: L(t)= 7600 times 5^t/22
Step-by-step explanation:
kahn answer
To model the locust population, we can use an exponential growth function. The initial population is given as 7600, and it increases by a factor of 555 every 222222 days. The function is L(t) = 7600 * 555^(t/222222).
Explanation:To model the locust population, we can use an exponential growth function. The initial population is given as 7600. The population increases by a factor of 555 every 222222 days. Let's denote the time since the first day of spring as t. The function can be written as:
L(t) = 7600 * 555^(t/222222)
For example, if we want to find the locust population after 1 year (365 days), we can substitute t = 365 into the function:
L(365) = 7600 * 555^(365/222222)
By evaluating this expression, we can determine the locust population at any given time since the first day of spring.
A rectangle has a height of 333 and a width of 3x^2+4x3x 2 +4x3, x, squared, plus, 4, x. Express the area of the entire rectangle. Expression should be expanded.
Answer:
[tex]9x^2+12x[/tex]
Step-by-step explanation:
Height of the Rectangle =3
Width of the Rectangle =[tex]3x^2+4x[/tex]
Area of a Rectangle = Height X Width
[tex]=3(3x^2+4x)\\=9x^2+12x[/tex]
The area of the rectangle is therefore given by:
[tex]9x^2+12x[/tex]
To find the area of the rectangle, multiply its height by its width. In this case, expand the expression for the width by distributing the terms. Simplify and combine like terms to get the expanded expression for the area: 999x^4 + 36x^3 + 16x.
Explanation:To find the area of a rectangle, we multiply its length (height) by its width. In this case, the height is given as 333 and the width is given as 3x^2 + 4x3x^2 + 4x3x, x^2 + 4, x. To expand this expression and find the area, we can distribute the numbers/variables inside the parentheses.
We have (3x^2 + 4x3x^2 + 4x3x) * (x^2 + 4x). Distributing the terms inside, we get 3x^2 * x^2 + 3x^2 * 4x + 4x3x^2 * x^2 + 4x3x^2 * 4x + 4x3x * x^2 + 4x3x * 4x. Simplifying further, we have 3x^4 + 12x^3 + 4x^4 + 16x^3 + 4x^3 + 16x.
The area of the rectangle is the product of the height and width, so the expanded expression for the area is (333) * (3x^4 + 12x^3 + 4x^4 + 16x^3 + 4x^3 + 16x). Combining like terms, we have 999x^4 + 36x^3 + 16x. This is the expanded expression for the area of the rectangle.
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A line intersects the points (-1, 3) and
(-4, 9). What is the slope-intercept
equation for this line?
Answer:
I was able to get: y = -(6/3)x + 1
Jiffy Mix in Chelsea, Michigan has a machine that fills the Jiffy Corn Muffin Mix boxes with Mix. It dispenses corn muffin mix with a normal distribution and has a mean of 10.0 and a standard deviation of 0.1 ounces
Question:
A. The middle 95% of Jiffy Corn Muffin Mix boxes contain between _____ and ________ounces of cereal
Answer:
Therefore the middle 95% of Jiffy Corn Muffin Mix boxes contain between _9.994____ and _10.0062_______ounces of cereal
Step-by-step explanation:
The question requires us to construct the 95% confidence interval of the normal distribution as follows;
The mean, μ = 10
The sample standard deviation, σ = 0.1
Assumption
Number of boxes, n = 1000
The formula for confidence interval is as follows;
[tex]CI= \mu \pm z\frac{\sigma}{\sqrt{n}}[/tex]
Where, z at 95% confidence level is given as ±1.96
Plugging in the values, we have;
[tex]CI=10 \pm 1.96 \times \frac{0.1}{\sqrt{1000}}[/tex]
Therefore the middle 95% of Jiffy Corn Muffin Mix boxes contain between _9.994____ and _10.0062_______ounces of cereal.
Jenny invests $1,599 in a retirement account with a fixed annual interest rate of 9% compounded continuously. How long will it take for the account balance to
reach $3.002.30?
o
А буеаrѕ
0
B. 7 years
0
c. 9 years
0
D. 8 years
Answer:
Step-by-step explanation:
Between x=2 and x=3 which function has a greater average rate of change than y=1/3^-x
A)y=2^x
B)y=5^x-2
C)y=1/4^-x
D)y=2/3^-x
Answer:
C) y = (1/4)^(-x)
Step-by-step explanation:
The average rate of change on an interval [a, b] is found using the formula ...
arc = (f(b) -f(a))/(b -a)
For an exponential function with base b on interval [2, 3], the rate of change is ...
arc = (b^3 -b^2)/(3 -2) = b^2(b -1)
This expression assumes a positive sign on the exponent.
We can compute the arc for each answer choice as ...
(reference) 1/3^-x = 3^x ⇒ arc = 3²(3 -1) = 18
A) 2^x ⇒ arc = 2²(2 -1) = 4
B) 5^(x-2) = (1/25)5^x ⇒ arc = (1/25)(5²)(5 -1) = 4
C) 1/4^-x = 4^x ⇒ arc = 4²(4 -1) = 48
D) (2/3)^-x = (3/2)^x ⇒ arc = (3/2)²(3/2 -1) = 9/8
An average rate of change greater than 18 is demonstrated by (1/4)^-x.