combing like terms? 4(1.75y-3.5)+1.25y
Answer:
8.25y-14
Step-by-step explanation:
The given expression is [tex]4(1.75y-3.5)+1.25y[/tex]
Distribute 4 over the parenthesis
[tex]4\cdot1.75y+4\cdot(-3.5)+1.25y\\\\=7y-14+1.25y[/tex]
Now. group the like terms
[tex](7y+1.25y)-14[/tex]
Finally combine the like terms
[tex]8.25y-14[/tex]
Therefore, the simplified expression is 8.25y-14
The national vaccine information center estimates that 90% of americans have had chickenpox by the time they reach adulthood.50 (a) is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled american adults had chickenpox during childhood. (b) calculate the probability that exactly 97 out of 100 randomly sampled american adults had chickenpox during childhood. (c) what is the probability that exactly 3 out of a new sample of 100 american adults have not had chickenpox in their childhood? (d) what is the probability that at least 1 out of 10 randomly sampled american adults have had chickenpox? (e) what is the probability that at most 3 out of 10 randomly sampled american adults have not had chickenpox?
The correct answers are:
A) yes; B) 0.0059; C) 0.0059; D) 1; E) 0.9872.
Explanation:
A) A binomial experiment is one in which the experiment consists of identical trials; each trial results in one of two outcomes, called success and failure; the probability of success remains the same from trial to trial; and the trials are independent.
All of these criteria fit this experiment.
B) The formula for the probability of a binomial experiment is:
[tex] _nC_r\times(p^r)(1-p)^{n-r} [/tex]
where n is the number of trials, r is the number of successes, and p is the probability of success.
In this problem, p = 0.9.
For part B, n = 100 and r = 97:
[tex] _{100}C_{97}(0.9)^{97}(1-0.9)^3
\\=\frac{100!}{97!3!}\times (0.9)^{97}(0.1)^3
\\
\\=161700(0.9)^{0.97}(0.1)^3=0.00589\approx 0.0059 [/tex]
C) We are changing the probability of success this time. Since 90% of people have had chicken pox, then 100%-90% = 1-0.9 = 0.1 have not had chicken pox. For part C, n = 100, r = 3, and p = 0.1:
[tex] _{100}C_3(0.1)^3(1-0.1)^{100-3}
\\
\\=_{100}C_3(0.1)^3(0.9)^{97}
\\=\frac{100!}{97!3!}\times (0.1)^3(0.9)^{97}
\\
\\=161700(0.1)^3(0.9)^{97}=0.00589\approx 0.0059 [/tex]
D) For this part, we want to know the probability that at least 1 person has contracted chicken pox. For this part, p = 0.9, n = 10 and r = 0. We will then subtract this from 1; this will first give us the probability that none of the 10 contracted chicken pox, then subtracting from 1 means that 1 or more people did:
[tex] 1-(_{10}C_0(0.9)^0(1-0.9)^{10-0})
\\
\\=1-(\frac{10!}{0!10!}\times (0.9)^0(0.1)^{10})
\\
\\=1-(1\times 1\times (0.1)^{10})= 1-0 = 1 [/tex]
E) For this part, we find the probability that 3 people, 2 people, 1 person and 0 people have not had chicken pox. The probability p = 0.1; n = 10; and r = 3, 2, 1 and 0, respectively:
[tex] _{10}C_3(0.1)^3(1-0.1)^{10-3}+_{10}C_2(0.1)^2(1-0.1)^{10-2}+
_{10}C_1(0.1)^1(1-0.1)^{10-1}+_{10}C_0(0.1)^0(1-0.1)^{10-0}
\\
\\=_{10}C_3(0.1)^3(0.9)^7+_{10}C_2(0.1)^2(0.9)^8+_{10}C_1(0.1)^1(0.9)^9+
_{10}C_0(0.1)^1(0.9)^{10}
\\
\\120(0.1)^3(0.9)^7+45(0.1)^2(0.9)^8+10(0.1)^1(0.9)^9+1(0.1)^0(0.9)^{10}
\\
\\0.057395628+0.1937102445+0.387420489+0.3486784401
\\
\\=0.9872 [/tex]
The binomial distribution is appropriate for calculating the probability of having a specific number of American adults who had chickenpox during childhood. The probability of exactly 97 out of 100 adults having chickenpox can be calculated using the binomial probability formula. The probability that at least 1 out of 10 adults have had chickenpox and at most 3 out of 10 adults have not had chickenpox can also be calculated using the binomial probability formula.
Explanation:(a) To determine if the use of the binomial distribution is appropriate, we need to check if the conditions for using it are satisfied: (1) There are only two possible outcomes - having or not having chickenpox. (2) Each trial is independent - one person's chickenpox status does not affect another person's. (3) The probability of having chickenpox is the same for each person. The given information satisfies these conditions, so the binomial distribution is appropriate.
(b) The probability of exactly 97 out of 100 randomly sampled American adults having chickenpox during childhood can be calculated using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes (97 in this case)
C(n, k) is the number of ways to choose k successes out of n trials (100 in this case)
p is the probability of success (probability of having chickenpox = 0.90)
n is the total number of trials (100 in this case)
Using these values, we can calculate:
P(X = 97) = C(100, 97) * 0.90^97 * 0.10^3
= 100 * (0.90)^97 * (0.10)^3
≈ 0.0975
So, the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood is approximately 0.0975 or 9.75%.
(c) The probability that exactly 3 out of a new sample of 100 American adults have not had chickenpox in their childhood can be calculated using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes (3 in this case)
C(n, k) is the number of ways to choose k successes out of n trials (100 in this case)
p is the probability of success (probability of not having chickenpox = 0.10)
n is the total number of trials (100 in this case)
Using these values, we can calculate:
P(X = 3) = C(100, 3) * 0.10^3 * 0.90^97
= 161,700 * (0.10)^3 * (0.90)^97
≈ 0.0315
So, the probability that exactly 3 out of a new sample of 100 American adults have not had chickenpox in their childhood is approximately 0.0315 or 3.15%.
(d) To calculate the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox, we can use the complement rule: P(at least 1) = 1 - P(none)
Where P(none) is the probability of none of the 10 sampled adults having chickenpox.
Using the binomial formula:
P(X = 0) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = 0) is the probability of getting exactly 0 successes
C(n, k) is the number of ways to choose 0 successes out of n trials (10 in this case)
p is the probability of success (probability of having chickenpox = 0.90)
n is the total number of trials (10 in this case)
Using these values, we can calculate:
P(X = 0) = C(10, 0) * 0.90^0 * 0.10^10
= 1 * (0.90)^0 * (0.10)^10
≈ 0.3487
So, P(none) ≈ 0.3487
Therefore, P(at least 1) = 1 - P(none) = 1 - 0.3487 = 0.6513
So, the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox is approximately 0.6513 or 65.13%.
(e) To calculate the probability that at most 3 out of 10 randomly sampled American adults have not had chickenpox, we can add up the probabilities of getting 0, 1, 2, and 3 successes:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
We can use the binomial probability formula to calculate each individual probability:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes (0, 1, 2, or 3 in this case)
C(n, k) is the number of ways to choose k successes out of n trials (10 in this case)
p is the probability of success (probability of not having chickenpox = 0.10)
n is the total number of trials (10 in this case)
Using these values, we can calculate each individual probability:
P(X = 0) = C(10, 0) * 0.10^0 * 0.90^10
P(X = 1) = C(10, 1) * 0.10^1 * 0.90^9
P(X = 2) = C(10, 2) * 0.10^2 * 0.90^8
P(X = 3) = C(10, 3) * 0.10^3 * 0.90^7
Adding up these probabilities, we get:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
≈ 0.9873
So, the probability that at most 3 out of 10 randomly sampled American adults have not had chickenpox is approximately 0.9873 or 98.73%.
Write the expression that shows 3 time the sixth power of 10
If a straight line passes through the point x = 8 and y = 4 and also through the point x = 12 and y = 6, the slope of this line is
The slope of the line that passes through (4, 8) and (6, 12) will be 1/2.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
If a straight line passes through the point x = 8 and y = 4 and also through the point x = 12 and y = 6. Then the slope is given as,
m = (6 - 4) / (12 - 8)
m = 2 / 4
m = 1 / 2
The slope of the line that passes through (4, 8) and (6, 12) will be 1/2.
More about the linear equation link is given below.
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how do you equally divide 12 cookies with 8 people. what fraction of cookies would each person receive?
Final answer:
To equally divide 12 cookies among 8 people, each person would receive 1 1/2 or 1.5 cookies, which is a fraction of 3/2 per person when simplified.
Explanation:
To divide 12 cookies equally among 8 people, we need to perform a simple division operation where 12 (total number of cookies) is divided by 8 (number of people). Mathematically, this can be represented as 12/8 which simplifies to 1 1/2 or 1.5 cookies per person. This means that each person would receive one and a half cookies.
If the problem requires the answer as a fraction, we can simplify 12/8 by dividing both numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, we get 12/8 = (12÷4) / (8÷4) = 3/2. Therefore, each person gets 3/2 or one and a half cookies.
A red string of holiday lights blinks once every 3 seconds while a string of blue lgihts blink once every 4 seconds. how many times with both sets of lights blink at the same time in 1 minute
a jet descended 0.44 mile in 0.8 minute. What was the plane's average change of altitude per minute?
The pie below is cut into 6 equal slices. Show shade 2/3 of this pie.
For each function f(n) and time t in the table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds
The question involves estimating the largest problem size a one-teraflop computer can solve in a given time, by equating the time complexity function of the problem to the number of operations the computer can perform per second, and solving for n.
The task is to estimate the largest problem size n that can be solved by a one-teraflop machine within a given time t. A teraflop machine is capable of performing 1012 operations per second. To determine n, we must consider the time complexity function f(n) that describes how the number of operations grows with the size of the problem. Given that the machine can perform 1012 instructions per second, and t is measured in microseconds, we first convert t to seconds.
For example, if the function f(n) follows a linear time complexity, such as f(n) = n, and the computation time t is 1 second, the largest problem size that can be solved is 1012, since the machine can perform 1012 operations in one second.
If the computational complexity is higher, say quadratic as f(n) = n2, we would solve for n in the equation n2 = 1012 to find the largest n that can be solved within 1 second.
Similarly, for more complex functions, we would find the value of n that satisfies the equation f(n) = 1012 * t in seconds, ensuring the result is within the operational constraints of the machine.
Differentiate
y=(6x)/(1-cot(x))
Tom jogged 3/5 mile on Monday and 2/6 mile on Tuesday how much farther did Tom joy on Monday then on Tuesday
Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 32 miles per hour faster than his driving. Assume that the train travels the same distance as the car.
The distance Fritz travels to work is 24 miles if Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
Let the distance Fritz travels to work is x.
As we know,
1 hour = 60 minutes
36/60 = 0.6 hrs
20/60 = 0.33 hrs
Speed = distance/time
Train speed - drive speed = 32
x/0.33 - x/0.6 = 32
After simplification:
9d - 5x = 96
4x = 96
x = 96/4
d = 24 miles
Thus, the distance Fritz travels to work is 24 miles if Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
Learn more about the distance here:
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An airlines records show that its flights between two cities arrive on the average 5.4 minutes late with a standard deviation of 1.4 minutes. at least what percentage of its flights between the two cities arrive anywhere between
The next train will arrive in 32 minutes and 30 seconds. In how many seconds will the next train arrive
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2, and a vertical shift up 3 units.
y =
(I don't have the option to use the characters "/" or "[tex] \pi [/tex]" so they must not be in the answer.
Answer:
y = sin 4x + 3
Step-by-step explanation:
A sine function is represented as y = a sin(bx + c) + d
Given values in the question are a = amplitude = 1
period = π/2 = 2π/b
Vertical shift d = 3 units up.
Horizontal shift c = 0
Since 2π/b = π/2
[tex]b=\frac{2\pi }{\frac{\pi }{2}} =\frac{4\pi }{\pi }=4[/tex]
Now the sinusoidal function will be
y = 1. sin( 4x ) + 3
y = sin 4x + 3
The cost of a ticket to a soccer game is $6. There are y number of people in a group that want to go to a game. Which of the following expressions describes the total amount of money the group will need to go to the soccer game?
the equation would look something like
total = 6y
since you don't show the choices look for something similar.
Find a ·
b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.
To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
Explanation:To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.
Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.
What is 51,908 rounded to the nearest hundred dollar?
15/16 is 1 sixteenth groups of what size
For rhombus LMNO, m∠LON = 102° and NP = 5 units. Use the diagram of rhombus LMNO to find the missing measures. The measure of ∠LPM is °. The measure of ∠PMN is °. The length of LN is units.
Answer:
1. 90
2. 50
3. 10
Step-by-step explanation:
Go has 3 orange pick for every 2 green if ther are 25 picks in all how many picks are orange
Answer:
15
Step-by-step explanation:
It has been given that Go has 3 orange pick for every 2 green.
Hence, the ratio of Go to Green is 3:2
Total number of picks = 25.
Number of picks of orange in 25 picks is given by
[tex]\frac{3}{3+2}\times25[/tex]
Simplifying, we get
[tex]=\frac{3}{5}\times25[/tex]
Multiply the numerator, we get
[tex]=\frac{75}{5}[/tex]
Dividing, we get
[tex]=15[/tex]
Hence, the number of picks of orange are 15.
What is 160,656 rounded to the nearest ten thousandth?
at 7 p.m. last night, the temputure was 10 degrees. At 7 a.m. the next morning, the temputure was -2 degrees. By how much did the temputure change From 7 p.m. to 7 a.m.
10 to 0 =10
0 to -2 = 2
10+2 =12
it changed by 12 degrees
if the flour to sugar ratio is 5 liters flour to 1 liter sugar, then how much sugar is needed if only 2 liters of flour are used ?
Answer:
0.4 liters of sugar.
Step-by-step explanation:
Hello, I think I can help you with this
you can easily solve this by using a rule of three
Step 1
if
5 liters flour⇒ 1 liter sugar
2 liters flour⇒ x?liter sugar
do the relation
[tex]\frac{5\ liters\ flour}{1\ liter\ sugar}=\frac{2\ liters\ flour}{x}\\\\solve\ for\ x\\\\\\\frac{x*5\ liters\ flour}{1\ liter\ sugar}=2\ liters\ flour\\x=\frac{2\ liters\ flour*1\ liter\ sugar}{5\ liters\ flour} \\x=\frac{2}{5}liter\ sugar\\x=0.4\ liters\ of\ sugar\\[/tex]
0.4 liters of sugar
I hope it helps, Have a great day-
Write y = 2x + 3 using function notation
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.
In January, Emma was 62.25 in tall. In December, she was 65.5 inches tall. How much did Emma grow between January and December?
she "grew" negative 3.25 inches
it is negative because she was taller in December than she was in January
Determine tan(t) if cos(t)= -3/5 and sin(t) >0
Joan and Jane are sisters. Jean is Joan's daughter and 12 years younger than her aunt. Joan is twice as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?
Jean is 12 years old. Joan is 24 years old, and Jane is 20 years old. Four years ago, Joan was 20 and Jane was 16.
Let's denote:
- Joan's current age as J
- Jane's current age as N
- Jean's current age as I
Given:
1. Jean is 12 years younger than Joan: I = J - 12
2. Joan is twice as old as Jean: J = 2I
3. Four years ago, Joan was the same age as Jane is now: J - 4 = N
4. Jane was twice as old as her niece four years ago: N - 4 = 2(I - 4)
Using equation (1) and (2):
J = 2(J - 12)
J = 2J - 24
J = 24
Now substituting J = 24 into equation (1):
I = 24 - 12
I = 12
So, Jean is currently 12 years old.
Find the standard equation of the circle having the given center (6,-2) and radius 1/5.