To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.
How is probability determined from a continuous distribution?Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.
For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.
Why is this easy for the uniform distribution and not so easy for the normal distribution?The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.
Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.
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Dentify the solution to the following system of equations
Identify the solution to the following system of equations
No solution
(0. 29, 2. 73)
(0. 78, 0. 05) and (-4. 32, 12. 80)
( -1, 4. 5)
If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.
To do this, we can set the coefficients of x and y in the two equations equal to each other:
6 - 4m = 2k(2m - 1)
2n - 7 = 3k
Simplifying these equations, we get:
8m - 6 = 4km
2n - 7 = 3k
We can solve the first equation for k:
k = (8m - 6)/(4m)
Substituting this into the second equation and solving for n, we get:
n = (16m - 29)/(8m - 12)
Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.
We find that the expressions for k and n are the same for m = 3/2.
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Complete Question:
Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m−1)x+3y−5=0
3x+(n−1)y−2=0
Your teacher prepares a large container full of colored
beads. She claims that 1/8 of the beads are red, 1/4 are
blue, and the remainder are yellow. Your class will take a
simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you
can take so that the conditions for performing inference
are met is.
15
16
30
40
90
The smallest number of beads we can take so that the conditions for performing inference are met is 40.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.
According to the Question:
Given in the question,
Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.
Quadrant Frequency
1 18
2 22
3 39
4 21
The proportions are 1/8 , 1/4 and 5/8
Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.
Now,
The expected frequencies are calculated as:
E = np₁ = 15 (1/8) = 1.875
E = np₂ = 16(1/8) = 2
E = np₃ = 30(1/8) = 3.75
E = np₄ = 40(1/8) = 5
E = np₅ = 80(1/8) = 10
Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.
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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answer: 576
Step-by-step explanation:
134+254+188= 576
help me please i have to finish this soon and im stuck on this problem
Answer:
hjjjbcujnkknvcczynmcs
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
The correct answer is the triangle
Triangle : 239 yards
Square : 224 yards
The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:
The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].
What is Hypothesis test?Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.
Using the appropriate notation, the hypotheses can be expressed as:
$H_0: p = 0.08$
$H_a: p < 0.08$
Therefore, the appropriate set of hypotheses for the mayor's significance test are:
[tex]$$H_0: p = 0.08$$[/tex]
[tex]$$H_a: p < 0.08$$[/tex]
Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate
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if l is parallel to m find the values of x and y (10x-17) (6y+29) (8x+1)
X = 22
Y = 15
youre welcome! Brainliest would be appreciated :)
All of the following are assumptions of the error terms in the simple linear regression model except a. Errors are normally distributed b. Error terms are dependent on each other c. Error terms have a mean of zero d. Error terms have a constant variance e. Error terms are independent of the Explanatory variable
Assumptions of the error terms in the simple linear regression model except (D) Error terms have a constant variance.
Linear Regression Model:
A linear regression model states that the relationship between a dependent variable y and one or more independent variables X. The dependent variable is also known as a response variable. Independent variables are also called explanatory variable. In statistics, linear regression is a linear method of modeling the relationship between a scalar response and one or more explanatory variables (also called dependent and independent variables). The case of one explanatory variable is called simple linear regression for more than one, the procedure is called multiple linear regression.
The term differs from multiple linear regression, which predicts multiple correlated dependent variables rather than a single scalar variable.
Error Term:
The error term represents the margin of error in a statistical model; it is the sum of the deviations inside the regression line and it provides an explanation of the difference between the theoretical value of the model and the actual observations.
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Please help I’m very confused!!
Answer:
x=-2.5
Step-by-step explanation:
3 4(2.5-5) = (1/27) 2(-2.5+10)
I hohonestly don't know how to explain it
67% of teenagers, ages fifteen to seventeen, are concerned about their credit scores. Suppose we randomly select fifteen- to seventeen-year-old teenagers until we find one who is concerned about his/her credit score. Let X be the number of teenagers we select who are not concerned about their credit scores before we find the first teenager who is concerned . Let Y be the number of teenagers we select who are not concerned about their credit scores before the second teenager who is concerned is found.
a. What is the probability that none of the first three people are concerned about their credit scores?
b. What is the expected value of X?
c. What is the variance of X?
d. What is the probability that X = 0?
e. What is the probability that X ≤ 4?
f. What is the probability that Y = 6?
g. What is the probability that Y = 0?
The probability of the following parts is: a. 0.33 b. 1.925 c. 0.176 d. 0.67 e. 0.99955416 f. 0.018318006 g. 0.4489
a. To find out the probability that none of the first three people is concerned about their credit scores, we need to find: P(none of the first three is concerned about their credit scores)we have been given the probability that a teenager is concerned about his/her credit score is 0.67. So the probability that a teenager is not concerned about his/her credit score is 0.33. Now we can say that this is a binomial distribution since we are repeating a procedure until success is achieved. So we can use the binomial distribution to find the above probability: P(none of the first three are concerned about their credit scores) = (0.33)^3 = 0.0359375
b. The expected value of X is given by: E(X) = 1/p = 1/0.67 = 1.4925
c. Variance of X is given by: Var(X) = (1-p)/p^2 = (0.33)/(0.67)^2 = 0.176
d. Since X is the number of teenagers we select who are not concerned about their credit scores before we find the first teenager who is concerned. The probability that X = 0 is the probability that the first teenager we select is concerned about his/her credit score, which is given by: P(X = 0) = p = 0.67
e. To find out the probability that X ≤ 4, we can use the complement rule: P(X ≤ 4) = 1 - P(X > 4) = 1 - [P(X = 5) + P(X = 6) + ....... to ∞] = 1 - (1 - p)^5 = 1 - (0.33)^5 = 0.99955416
f. To find out the probability that Y = 6, we need to find: P(Y = 6)We know that for Y = 6, we need to select 7 teenagers such that the first and the second teenager we select are not concerned about their credit scores, and the third to the seventh teenager we select are concerned about their credit scores. The probability that the first and the second teenager we select are not concerned about their credit scores is given by: P(selecting 2 teenagers not concerned about their credit scores) = (0.33)^2 = 0.1089 And the probability that the third to the seventh teenager we select are concerned about their credit scores is:
P(selecting 5 teenagers concerned about their credit scores) = (0.67)^5 = 0.16806957Therefore, P(Y = 6) = P(selecting 2 teenagers not concerned about their credit scores) * P(selecting 5 teenagers concerned about their credit scores) = 0.018318006
g. To find out the probability that Y = 0, we need to select the first two teenagers who are concerned about their credit scores. P(Y = 0) = P(selecting the first two teenagers who are concerned about their credit scores) = (0.67)^2 = 0.4489.
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What is the slope of the line that passes through the points (4,7) and (8,12)
*Your answer should be numerical value only, it may be in the form of
a/b, if applicable. Remember to simplify your answer.
NEED HELP ASAP
Answer:
The slope is 5/4 or 1.25
Step-by-step explanation:
You can find the slope by using the equation (y2-y1)/(x2-x1)=Slope
This time it would be (12-7)/(8-4)
Simplified it would be 5/4 or 1.25
Find 184.1% of 93. Round to the nearest tenth.
Answer:
171.21
Step-by-step explanation:
statistical literacy (a) if we have a distribution of x values that is more or less mound-shaped and somewhat symmetric, what is the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal? (b) if the original distribution of x values is known to be normal, do we need to make any restriction about sample size in order to claim that the distribution of sample means x taken from random samples of a given size is normal
It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.
then the sample size needs to be larger, possibly 50 or 30the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal depends on the shape of the original distribution of x values. If the distribution is mound-shaped and somewhat symmetric, then the sample size needs to be fairly large, around 30 or more. However, if the original distribution of x values is strongly skewed or has outliers statisticl literacyif the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.
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some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)
Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt
Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C
a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt
Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.
Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,
we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:
S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)
dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change
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mr warren the physical education teacher has 7 boxes of helmets each box has h helmets write an expression to represent the total number of helmets
Answer:
t = 7h
Step-by-step explanation:
lets have the total amount of helmets as t and helmets per box as h. Then it is t = 7h
At the end of the reaction, Marco finds that the mass of the contents of the
beaker is 247 g. He repeats the experiment and gets the same result.
a Has he made a mistake?
Suggest why Marco got this result. how the
b
Answer: To determine if Marco has made a mistake, we would need to know the expected mass of the contents of the beaker before the reaction took place. If the expected mass was 247 g or close to it, then Marco may not have made a mistake.
However, if the expected mass was significantly different from 247 g, then it is possible that Marco made a mistake in his experiment. It could be a measurement error, a calculation error, or a procedural error.
There are several reasons why Marco may have obtained a mass of 247 g at the end of the reaction. One possibility is that the reaction produced a product that was relatively volatile, and some of it was lost during the experiment. Another possibility is that Marco did not completely dry the product before weighing it, which could result in a higher measured mass due to the presence of residual moisture.
To determine the exact reason why Marco obtained a mass of 247 g, further investigation and experimentation would be needed.
Step-by-step explanation:
A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much do the barista's secret-formula beans cost per pound?
Answer: $22.50
Step-by-step explanation:
Let x be the cost per pound of the secret-formula coffee beans.
The total cost of the secret-formula beans is 12x dollars.
The total cost of the other beans is 15 × 18 = 270 dollars.
The total cost of the mix is (12 + 15) × 20 = 540 dollars.
Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.
We can set up an equation based on the total cost of the mix:
12x + 270 = 540
Subtracting 270 from both sides:
12x = 270
Dividing both sides by 12:
x = 22.5
Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.
Rotate the arrowhead 90 degrees anticlockwise around (0,0)
The new position of arrowhead graph ABCD is A'B'C'D' as shown in the below graph.
Define the term graph rotation?Graph rotation refers to the process of rotating a graph, which involves changing the orientation of the edges or nodes in the graph while preserving the relationships between them.
From the given arrowhead graph as below; the points labelled are
A (-2, 2), B (0, 5), C (2, 2) and D (0, 3)
On rotating the graph through 90° anticlockwise around the origin (0, 0), the new positions of the points are:
A (-2, 2) ⇒ A' (-2, -2)
B (0, 5) ⇒ B' (-5, 0)
C (2, 2) ⇒ C' (-2, 2)
D (0, 3) ⇒ D' (-3, 0)
Therefore, the new position of arrowhead graph ABCD is A'B'C'D' as shown in the below graph.
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What are the answers to this I’m confused?
Answer:
Step-by-step explanation:
5,9.8,0,4
Use context to determine the meaning of the word unabated as it is used in Narrative of the Life of Frederick Douglass, An American Slave. Write your definition of unabated here and tell how you found it.
The wοrd "unabated" is used in Narrative οf the Life οf Frederick Dοuglass, An American Slave.
The wοrd "unabated" in this cοntext can be interpreted tο mean "cοntinuing withοut any reductiοn in intensity οr strength." "That cheerful eye, under the influence οf slavery, swοre red with rage; that vice, made all οf sweet accοutrement, changed tο a οne οf harsh and hοrrid discοrd; and that angelic face gave way tο that οf a demοn."
The authοr is describing hοw the slavehοlder's pοwer οver the slaves cοrrupts the wοman's character, turning her previοusly kind demeanοur intο οne οf rage and discοntent. The wοrd "unabated" emphasises hοw persistent and unyielding this transfοrmatiοn is and hοw unlikely it is that it will diminish.
By examining the surrοunding text and cοmmοn usage, I was able tο determine the definitiοn οf the wοrd "unabated." In this sentence, the authοr's descriptiοn οf the slavehοlder's transfοrmatiοn is well-suited tο the wοrd "unabated," which is generally used tο describe sοmething that cοntinues withοut any lοss οf intensity οr strength.
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a company purchased a new computer system for $28,000. one year later, the resale value of the system was $15,700. assume that the value of the computer system declines according to an exponential model. At what rate was the value of the computer system changing 4 years after it was purchased?
A. Declining at the rate of $2,767.74 per year.
B. Declining at the rate of $1,601.26 per year.
C. Declining at the rate of $3,6214.88 per year.
D. Declining at the rate of $8,803.21 per year.
E. Declining at the rate of $2,546.52 per year.
F. None of the above.
The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.
We can use the exponential decay formula [tex]V(t) = V0 * e^{-kt}[/tex], where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.
We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:
[tex]$15,700 = $28,000 * e^{-k*1}[/tex]
[tex]e^{-k} = 0.5607[/tex]
-k = ln(0.5607) ≈ -0.5797
k ≈ 0.5797
Therefore, the decay rate is approximately 0.5797 per year.
To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:
dV/dt = -k * V0 * [tex]e^{-kt}[/tex]
Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:
dV/dt = -0.5797 * $28,000 * [tex]e^{-0.5797*4}[/tex] ≈ -$8,803.21 per year
Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.
The correct answer is (D) Declining at the rate of $8,803.21 per year.
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I need help!! I need to show the steps on how I found the answer but I don’t know the answer! Please help!
Answer:
A
Step-by-step explanation:
The axis are counting by 2's.
If you start at (0,0) and to one unit to the right and one unit down. You will be at the point (2,-2). That point is on the line and in the table. If you, again, start at (0,0) and go one unit to the lefts and 2 units down, you will be at the point (-2,-4). Again you are on line line. This is the only graph that shows those two points on the line.
Helping in the name of Jesus.
a patient visits a dentist. the dentist knows that 1 in 10 patients has a toothache. one patient in 23 patients has cavity. 71% of patients with cavity has a toothache. what is the probability that the patients with a toothache has a cavity?
The probability that the patients with a toothache has a cavity is 0.3073.
Probability is the extent to which an event is likely to occur.
The probability that the patient has a toothache given that they have a cavity is equal to the percentage of patients with cavities that have toothaches. So, it can be calculated as:
P(toothache | cavity) = 71% = 0.71
Also, the probability that a patient has a cavity is equal to the ratio of patients with cavities to total patients, which is given to be 1 in 23. So,
P(cavity) = 1/23 = 0.04347
The probability that the patient has a toothache can be determined from the fact that 1 in 10 patients have a toothache. So,
P(toothache) = 1/10 = 0.1
The probability that a patient has a toothache and a cavity is calculated as:
P(toothache and cavity) = P(toothache | cavity) * P(cavity) = 0.71 * 0.04347 = 0.0308
The probability that the patient has a toothache given that they have a cavity can be calculated using Bayes' theorem:
P(cavity | toothache) = P(toothache | cavity) * P(cavity) / P(toothache)= 0.71 * 0.04347 / 0.1 = 0.3073
Therefore, the probability that patients with a toothache have a cavity is 0.3073 or about 30.73%.
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a ladder leans against the side of a house. the top of the ladder 8ft is from the ground. the bottom of the ladder is from the side of the house. find the length of the ladder. if necessary, round your answer to the nearest tenth.
The length of the ladder is c = √(x^2 + 64) ft.
The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.
The Pythagorean Theorem states that a^2 + b^2 = c^2.
Therefore, x^2 + 8^2 = c^2
Solving for c: x^2 + 64 = c^2
Taking the square root of both sides: √(x^2 + 64) = c
Therefore, the length of the ladder is c = √(x^2 + 64).
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Please some help me
Answer:
x=4/7
Step-by-step explanation:
To start, use the distributive property and multiply 2 by what is in the parenthesis. Do 2x3x as well as 2x-1. This will get you 6x-2 on the left side. On the right side, since there is a minus sign, change the x to -x and 3 to -3. You will ultimately get 6x-2=5-x-3. To solve this, you must isolate the variable by using inverse operations. The final answer is 4/7.
1. Arya is taking an exit poll from a polling booth. As voters leave, she asked them if they voted for candidate Frey. The probability that a person voted for Frey is 40%. Let be the number of people that Arya polls until finding the fifth person that voted for candidate Frey. You may assume that people leaving the poll are independent of each other. a. (3 points) What is the distribution of the random variable Z. Make sure to include the appropriate support b. (3 points) What are the mean and standard deviation of Z? c. (2 points) What is the probability that 15 people must be asked for Arya to find 5 people who voted for Frey?
The probability that 15 people must be asked for Arya to find 5 people who voted for Frey is 0.0610.
a. The distribution of the random variable Z is Negative Binomial distribution. It has the support {5, 6, 7, ... } which represents the total number of trials until the fifth success. b. Let p = probability of success = 0.4 and q = probability of failure = 0.6Then, mean of Z, μ = 5/p = 5/0.4 = 12.5and variance of Z, σ² = (1-p)/p² = (0.6)/(0.4²) = 3.75So, standard deviation of Z, σ = √3.75 = 1.9365 (approx)
Therefore, the mean and standard deviation of Z are 12.5 and 1.9365 respectively.c. The probability that 15 people must be asked for Arya to find 5 people who voted for Frey is P(Z = 15).Using the Negative Binomial probability formula,P(Z = k) = (k-1)C(r-1) p^r q^(k-r)where k is the number of trials, r is the number of successes required,
p is the probability of success and q is the probability of failure.P(Z = 15) = (15-1)C(5-1) (0.4)^5 (0.6)^(15-5)= 14C4 (0.4)^5 (0.6)^10= (14!/4!10!) (0.4)^5 (0.6)^10= 1001 (0.01024) (0.00060466176)≈ 0.0610
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Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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there are 2 coins in a bin. when one of them is flipped it lands on heads with probability 0.6 and when the other is flipped it lands on heads with probability 0.3. one of these coins is to be randomly chosen and then flipped. without knowing which coin is chosen, you can bet any amount up to 10 dollars and you then either win that amount if the coin comes up heads or lose if it comes up tails. suppose, however, that an insider is willing to sell you, for an amount c, the information as to which coin was selected. what is your expected payoff if you buy this information? note that if you buy it and then bet x, then you will end up either winning x - c or -x - c (that is, losing x c in the latter case). also, for what values of c does it pay to purchase the information? reference: https://www.physicsforums/threads/expected-payoff-given-info.200076/
It pays to purchase the information for any value of c less than $13.25 then we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
To calculate it Let C1 be the event that the first coin is selected and C2 be the event that the second coin is selected. Then, we have:
P(C1) = P(C2) = 1/2 (since one of the two coins is randomly chosen)
P(H|C1) = 0.6 (probability of getting heads when the first coin is flipped)
P(H|C2) = 0.3 (probability of getting heads when the second coin is flipped)
Let's consider the case when we do not buy the insider's information. Then, our expected payoff can be calculated as follows:
E(X) = P(C1) * P(H|C1) * (10) + P(C1) * P(T|C1) * (-10) + P(C2) * P(H|C2) * (10) + P(C2) * P(T|C2) * (-10)
= (1/2) * (0.610 - 0.410 + 0.310 - 0.710)
= -1
Therefore, if we do not buy the insider's information, our expected payoff is a loss of $1.
Now, let's consider the case when we buy the insider's information for an amount c.
If we buy the information, we will know which coin was selected and we can bet accordingly to maximize our expected payoff.
If we know that the first coin was selected, we should bet on heads since it has a higher probability of occurring. If we know that the second coin was selected, we should bet on tails since it has a higher probability of occurring.
Therefore, if we buy the insider's information, our expected payoff can be calculated as follows:
E(X|buying information) = P(C1) * P(H|C1) * (10-c) + P(C1) * P(T|C1) * (-c) + P(C2) * P(H|C2) * (-c) + P(C2) * P(T|C2) * (10-c)
= (1/2) * (0.6*(10-c) - 0.4c + 0.3(-c) - 0.7*(10-c))
= -0.2c + 1.5
To find the values of c for which it pays to purchase the information, we need to solve the inequality:
E(X|buying information) > E(X)
-0.2c + 1.5 > -1
Solving for c, we get:
c < 13.25
Therefore, it pays to purchase the information for any value of c less than $13.25. If we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.
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Chang each expression into radical form and then give the value. no calculators should be necessary.
The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.
What is expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².
Here,
a. [tex]125^{2/3}[/tex]
radical form:
[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]
[tex]125^{1/2}[/tex] = √125
= 5√5
Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]
= [tex](5^3)x^{2/3}[/tex]
= [tex]5x^{3*2/3}[/tex]
= 5²
= 25
b. √16
In radical form:
√16 = 4
Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]
= 4
c. [tex]16^{1/2}[/tex]
In radical form:
1/√16 = 1/4
Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]
= 1/4
d.[tex]\sqrt[4]{81}[/tex]
In radical form:
[tex]\sqrt[4]{81}[/tex] = √(√81)
= √9
= 3
Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]
= 1/3
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select the p-value(s) at which you would reject the null hypothesis for a two-sided test at the 90% confidence level. select all that apply.a. 0.9500b. 0.9000c. 0.8900d. 0.1100e. 0.0900f. 0.0500
The p values that would reject the null hypothesis are (f) 0.0500 and (e) 0.0900
Identifying the p values that would reject the null hypothesisTo reject the null hypothesis for a two-sided test at the 90% confidence level, we would compare the p-value to the significance level (alpha), which is equal to 1 - confidence level.
In this case, the confidence level is 90%, so alpha is 1 - 0.9 = 0.1.
Any p-value that is less than or equal to the significance level of 0.1 would lead to rejection of the null hypothesis.
So the p-values at which we would reject the null hypothesis are: 0.0500 and 0.0900
Therefore, the correct answers are options, (e), and (f).
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