70.5% of all eligible California residents are fully vaccinated.
Suppose you take a random sample of 250 eligible California residents and ask them if they are fully vaccinated to find the sample proportion of residents fully vaccinated. Let sample proportion be X. By Central Limit theorem the distribution of X follows Normal distribution.
Answers
The distribution of X can be approximated by a normal distribution with mean 0.705 and standard deviation 0.033.
What is probability?\
Probability theory, a subfield of mathematics, quantifies the likelihood that an event will take place or that a statement is true. The probability for an event happening is a number between 0 and 1, where around 0 indicates how likely the occurrence is to occur and 1 indicates certainty. A value of probability is a mathematical representation of the likelihood that a certain event will occur. The range of percentages that can be used to indicate probabilities is 0% to 100% along with 0 to 1. the probability of occurrences in a whole collection of identically probable possibilities that results in a certain occurrence divided by the number of outcomes.
given,
That's correct. By the central limit theorem, the sample proportion X, which represents the proportion of fully vaccinated residents in the sample, will follow an approximately normal distribution with mean equal to the population proportion (p) and standard deviation equal to the square root of [(p)(1-p)/n], where n is the sample size.
In this case, p = 0.705 (70.5% expressed as a decimal), and n = 250. Therefore, the mean of the sample proportion distribution is:
μ = p = 0.705
And the standard deviation is:
σ = √[(p)(1-p)/n] = √[(0.705)(0.295)/250] = 0.033
So the distribution of X can be approximated by a normal distribution with mean 0.705 and standard deviation 0.033.
We can use this distribution to calculate probabilities or confidence intervals for the sample proportion of fully vaccinated residents in different scenarios.
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Related Questions
There are two independent file servers in a web site. Either file server works with a probability of 0.6. And this web site is up if either file server is working. The probability that the web site is up is _____.
Answers
Answer:
The probability that the web site is up is 0.84 = 84%.
Step-by-step explanation:
For each web server, there are only two possible outcomes. Either it is working, or it is not. The probability of a web server being working is independent of any other web server, which meas that the binomial probability distribution is used 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.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
Either file server works with a probability of 0.6.
This means that \(p = 0.6\)
Two servers.
This means that \(n = 2\)
The probability that the web site is up is
At least one server working, which is:
\(P(X \geq 1) = 1 - P(X = 0)\)
In which
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16\)
Then
\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84\)
The probability that the web site is up is 0.84 = 84%.
1 of 9
Express the ratio below in its simplest
form.
12 : 6
Answers
2:1 is the simplified ratio
The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8.
Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget
of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of
new-release and classic movies bought?
Answers
Answer:
16 new releases and 22 classic movies.
PLEASE ANDWER FAST
Sora is also making a salad. Her salad dressing recipe uses 6 teaspoons of vinegar for every 15
teaspoons of olive oil.
2.1 How much vinegar does Sora need for 5 teaspoons of olive oil?
2.2 How much olive oil does Sora need for 8 teaspoons of vinegar?
2.3 If Sora makes 42 teaspoons of salad dressing, how much of each ingredient is in it?
2.4 If Sora makes 14 teaspoons of salad dressing, how much of each ingredient is in it?
Answers
The following answers are given as:
2.1)
2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.
2.2)
8 teaspoons of vinegar are needed for 20 teaspoons of olive oil.
2.3)
There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.
2.4)
There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
6 teaspoons of vinegar = 15 teaspoons of olive oil.
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 2 on both sides.
2 teaspoons of vinegar = 5 teaspoons of olive oil.
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 8 on both sides.
8 teaspoons of vinegar = 20 teaspoons of olive oil.
Now,
Total number of teaspoons = 42
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 12 on both sides.
12 teaspoons of vinegar = 30 teaspoons of olive oil.
12 + 30 = 42 teaspoons
Now,
1 teaspoon of vinegar = 5/2 teaspoons of olive oil.
Multiply 4 on both sides.
4 teaspoons of vinegar = 10 teaspoons of olive oil.
4 + 10 = 14 teaspoons
Thus,
2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.
8 teaspoons of vinegar are needed for 20 teaspoons of olive oil.
There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.
There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.
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In ΔFGH, h = 840 inches, � m∠F=93° and � m∠G=49°. Find the length of g, to the nearest 10th of an inch.
Answers
Let's use the formula:
g / sin(G) = h / sin(H)
Substituting the given values:
g / sin(49°) = 840 / sin(93°)
Now, we can solve for g. Rearranging the equation, we have:
g = (sin(49°) * 840) / sin(93°)
Using a calculator, we can evaluate this expression to find the approximate length of g.
g ≈ (0.7502 * 840) / 0.9998
g ≈ 630.168 / 0.9998
g ≈ 630.227
Therefore, the length of side g, rounded to the nearest tenth of an inch, is approximately 630.2 inches.
Which graph is defined by f(x) = x²-x-2|?
O A.
О в.
OC.
O D.
graph A
graph B
graph C
graph D
Answers
A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
Answers
The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.
How to calculate the value?Length of the small plant = 2 1/2 = 5/2 inches
Rate of growth = 3/4 inches
Increase in length in 3 weeks will be:
= 3 × 3/4 = 4
Total length = 5/2 + 9/4
= 19/4 inches.
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4 - 1/(8w) < 16if y'all could answer this with work that would be great thank you :D
Answers
Consider the given inequality,
\(4-\frac{1}{8w}<16\)Add -4 on both sides,
\(4-\frac{1}{8w}-4<16-4\Rightarrow\frac{-1}{8w}<12\)Multiply both sides by -8, (the inequality sign will get changed),
\(\frac{1}{w}>-96\)Take reciprocals of both the sides,
\(w<-\frac{1}{96}\)Thus, the solution region contains all the points strictly less than negative 1/96.
The corresponding number line representation is given below,
elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).
Answers
Please explain your answer to the question in the picture with steps
Answers
Answer:
x = 31.2
Step-by-step explanation:
You want the solution to the proportion 12/x = 5/13.
Rational equationYou can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...
\(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)
Now, the value of x is found by dividing both sides by its coefficient.
\(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)
__
Additional comment
The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.
Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.
You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.
Any proportion can be written 4 ways:
\(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)
These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.
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Can someone answer my question I need lots of help!!!!
Answers
Answer:
yes
Step-by-step explanation:
you didn't provide a question
Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Answers
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
The height of a building, measured in feet, is an example of:_______.
a. qualitative data
b. either qualitative or quantitative data
c. feet data
d. quantitative data
Answers
Answer:
Option d (quantitative data) is the correct choice.
Step-by-step explanation:
Quantitative data seems to be a collection or kind of data which is concerned regarding quantitative information or methods. That indicates its value, as well as the condition, could be represented arithmetically. All evidence that can be quantified, checked, and suitable for statistical analysis categorizes as quantitative methods.The remaining three options do not apply to the specified scenario. Therefore the description made will serve as an example of quantitative data.
total area of 3 figures
Answers
Given dimensions:
x=31 feet, y= 24 feet and z= 95 feet
We can split the shape above into 3 components: A, B, and C
To find the total area, we will find the sum of the areas of each component
For A
The shape of A is that of a semi-circle.
The area of a semi-circle is given to be
\(\text{Area}=\text{ }\frac{1}{2}\text{ x }\pi r^2\)The radius will be the diameter divided by 2
y= diameter
r= radius = y/2
r=24/2 =12 feet
pi=3.14
\(\begin{gathered} \text{Area}=\frac{1}{2}\text{ x 3.14 x 12 x 12} \\ \text{Area}=226.08\text{ ft}^2 \end{gathered}\)For B
The shape is a rectangle
The area of a rectangle is given by
A = l x b
where l = 31 and b = 24
Area = 31 x 24
Area = 744 square feet
For C
The shape is a triangle
The area of the triangle is given by
\(A=\frac{1}{2}\text{ x base x height}\)base = 64 feet, height = 24 feet
\(\text{Area}=\frac{1}{2}\text{ x }64\text{ x 24 =768 ft}^2\)The total area is
22
One radius of a circle is the same length as any other radius of the same
circle.
A. True
B. False
Answers
A. True
In a circle, all radii have the same length. The radius is the distance from the center of the circle to any point on its circumference. Since the center is equidistant from all points on the circumference, all radii will have the same length. Therefore, the statement is true.
what is the third term of an arithmetic sequence whose second term is 7 and whose sixth term is 23
Answers
Answer: 11
Step-by-step explanation:
Given
The second term of an AP is 7
The sixth term of an AP is 23
Suppose a and d be the first term and common difference of the sequence
\(\Rightarrow 7=a+d\quad \ldots(i)\\\Rightarrow 23=a+5d\quad \ldots(ii)\)
Subtract the above equations
\(\Rightarrow 23-7=5d-d\\\Rightarrow 16=4d\\\Rightarrow d=4\)
Put d in equation (i)
\(\Rightarrow 7=a+4\\\Rightarrow a=3\)
So, the third term of the AP is \(a+2d\)
\(\Rightarrow 3+2\times 4=11\)
If csc(x) = 2, for 90° < x < 180°, then
sin(x/2)=
cos(x/2)=
tan(x/2)=
Answers
csc(x) = 2 = 1/sin(x)
Solving for sin(x), we get:
sin(x) = 1/2
Next, we can use the half-angle formulas to find the values of sin(x/2), cos(x/2), and tan(x/2):
sin(x/2) = ±√[(1 - cos(x))/2] = ±√[(1 - √(1 - sin^2(x)))/2] = ±√[(1 - √(1 - (1/2)^2))/2] = ±√[(1 - √3/2)/2] = ±√[(2 - √3)/4]
cos(x/2) = ±√[(1 + cos(x))/2] = ±√[(1 + √(1 - sin^2(x)))/2] = ±√[(1 + √(1 - (1/2)^2))/2] = ±√[(1 + √3/2)/2] = ±√[(2 + √3)/4]
tan(x/2) = sin(x/2)/cos(x/2) = [±√(2 - √3)]/[±√(2 + √3)] = (2 - √3)/(2 + √3) = (√3 - 1)/(√3 + 1)
Note that the plus or minus signs in the formulas for sin(x/2) and cos(x/2) depend on the quadrant in which x lies. Since we know that 90° < x < 180°, we can conclude that sin(x/2) and cos(x/2) are both negative. Therefore:
sin(x/2) = -√[(2 - √3)/4]
cos(x/2) = -√[(2 + √3)/4]
tan(x/2) = (√3 - 1)/(1 + √3)
A pound of rice has a mixture of two types of rice, each costing $10 and $30, if the average cost per is $24, what is the ratio of the different types of rice?
Answers
Answer:
3:7
Step-by-step explanation:
Let x = pounds of the $10 rice in the mixture
Let y = pounds of the $30 rice in the mixture
Total cost of the $10 rice = 10x
Total cost of the $30 rice = 30y
(10x + 30y) / (x + y) = 24
Solve this equation for y/x:
10x + 30y = 24(x + y)
10x + 30y = 24x + 24y
30y - 24y = 24x - 10x
6y = 14x
y/x = 6/14 simplify the fraction
y/x = 3/7
So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.
2. Name the numerator and the denominator in each fraction.
a.
11/12
b. 7512
C.
12/0
d. ²8
Answers
Answer:
Step-by-step explanation:
a.11/12 =11 is numerator and 12 is denominator
b.7/512 =75 is numerator and 512 is denominator
c.12/10 = 12 is numerator and 10 is denominator
d0/78 = 0 is numerator and 78 is denominator
point to remember : In fraction,upper part is always numerator and down part is denominator.
PLEASE HELP!! will mark brainliest
Answers
Step-by-step explanation:
3,13 Because when graphed you can see
ezekiel has $250 in his bank account
Answers
A school supervisor wants to determine the percentage of students that bring their lunch to school. What method would assure random selection of a sample population?
Answers
To assure the random selection of a sample population for determining the percentage of students who bring their lunch to school, a method known as simple random sampling can be employed.
Simple random sampling is a technique that provides each member of the population an equal chance of being selected for the sample. Here's an explanation of how simple random sampling can be implemented in this scenario:
Define the population: The school supervisor needs to clearly define the population of interest, which would be all the students in the school.Assign a unique identifier: Each student should have a unique identifier, such as a student ID number, to differentiate them from one another.Generate a sampling frame: A sampling frame is a list of all the unique identifiers of the students. This could be obtained from the school's records or databases.Determine the sample size: The school supervisor needs to decide on the desired sample size, ensuring it is representative of the population while being practical to manage.Use a random selection method: Employ a random selection method, such as using a random number generator or a random number table, to select the required number of unique identifiers from the sampling frame.Contact selected students: Once the sample has been selected, the chosen students can be contacted to participate in the survey or data collection regarding whether they bring their lunch to school.know more about percentage here:
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The Simple interest on $160
for 6 month's at 5% per
annum
Answers
Answer:4$
Step-by-step explanation:
R
135
Р
S
Given isosceles trapezoid PQRS.
what are the measures of angles P. Q, S?
Answers
Answer:
huushshsusjvevshshd
Step-by-step explanation:
q=135 s and p= 45
Enter an inequality that represents the phrase "the sum of 7 and y is less than 9."
whats the inequality?
Answers
Answer:
Inequality Form:
y<2
Interval Notation:
(−∞,2)
The answer your looking for is: y<2
Ryan buys lunch for $16.83. If sales tax is 8.4%, How much money does Ryan need total for lunch
Answers
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)
PLEASE ANSWER - PLEASE ANSWER
The diagram shows triangle ABC. ABC and BED are straight lines. AB = 12.2cm, CD = 5.8cm, BE:ED = 3:1, Angle ADB = 90°, Angle ABD = 38°.
Work out the size of angle DCE, correct to 1 decimal place. SHOW ALL WORKING IN TEXT FORM, NO IMAGES.
Answers
The measure of angle DCE in this problem is given as follows:
m < DCE = 22.5º.
How to obtain the measure of angle DCE?The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:
cos(38º) = DB/12.2
DB = 12.2 x cosine of 38 degrees
DB = 9.6 cm.
BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:
DE = 1/4 x 9.6
DE = 2.4 cm.
Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:
tan(x) = 2.4/5.8
x = arctan(2.4/5.8)
x = 22.5º
m < DCE = 22.5º.
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Answer:
x = 22.5°
Step-by-step explanation:
BD = cos(38)*12.2 = 9.61DE = 9.61*¼ = 2.4∠DCE = tan(2.4/5.8) = 22.5°Will give 100 points to anyone who can find the arc measure and show work! thanks!
Answers
Answer:
2π/3 radians----------------------
Given:
Arc length (s) = 8π/3 Radius (r) = 4 kmTo find the arc measure (θ) in radians, we can use the formula:
s = rθNow, plug in the given values:
8π/3 = 4θTo solve for θ, divide both sides by 4:
(8π/3) / 4 = θSimplify the expression:
2π/3 = θSo, the arc measure (θ) is 2π/3 radians
Rewriting 3x^2=6x and solving with rewritten
Answers
Answer:
x = 0 , x = 2
Step-by-step explanation:
3x² = 6x ( subtract 6x from both sides )
3x² - 6x = 0 ← factor out 3x from each term
3x(x - 2) = 0
equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 2 = 0 ( add 2 to both sides )
x = 2
solutions are x = 0 , x = 2
11 family members are going on a trip together. They have cars that only fit 4 people how many cars will they need to take?