Answers
The experimental probability of winning the contest based on the data of all 3 games is 0.432.
What is experimental probability ?
Experimental probability is a measure of the likelihood of an event occurring based on the results of an experiment or observation. It is determined by dividing the number of times the event occurred by the total number of trials or observations. The more trials or observations conducted, the more accurate the experimental probability will be. Experimental probability is often used in situations where the probability of an event cannot be determined theoretically or where the theoretical probability is difficult to calculate. It is also commonly used in scientific experiments, market research, and other fields where the results of an experiment or observation can be used to make predictions or inform decisions.
Finding the experimental probability of winning the contest :
In this case, the event is winning the contest by choosing a marble from a bag, and the trials are the three games played by Hal.
Total number of players in all three games = 123 + 155 + 172 = 450
Total number of winners in all three games = 52 + 63 + 65 = 180
Experimental probability of winning the contest = Number of winners / Total number of players = 180/450 = 0.432
Therefore, the experimental probability of winning the contest based on the data of all 3 games is 0.432.
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Related Questions
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.59°C and 0.88°C.
Answers
The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.
What is mean?The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.
In this question, using the formula,
z-score = (x – μ) / σ
where:
x: individual data value
μ: population mean
σ: population standard deviation
for x=0.59
μ= 0
σ= 1
z-score= 0.59
Probability=0.7224
for x=0.88
z-score= 0.88
Probability=0.8106
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OBFW Publishers
Joy Milne of Perth, UK, smelled a "subtle musky odor" on her husband Les that she had never smelled before. At first, Joy
thought maybe the smell was from Les's sweat after long hours of work. But when Les was diagnosed with Parkinson's 6 years
later, Joy suspected the odor might be a result of the disease. Scientists were intrigued by Joy's claim and designed an
experiment to test her ability to "smell Parkinson's." Joy was presented with 12 shirts, each worn by a different person, some of
whom had Parkinson's and some of whom did not. The shirts were given to Joy in random order, and she had to decide whether
each shirt was worn by a Parkinson's patient or not. Joy identified 11 of the 12 shirts correctly. If we assume that Joy was just
guessing, she would have probability 1/2 of correctly identifying each shirt.
(a) Find the probability that Joy would identify at least 11 shirts correctly by random guessing.
Round your answer to 4 decimal places.
Leave your answer in decimal form.
about us
careers
Answers
the probability of indentifying at least 11 shirts correctly by random guessing is 0.0002
What is Probability?The ratio of favaourable outcomes to all possible outcomes of an event is known as the probability. The total number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
Total no.of event=12
the probability that Joy will identify at least 11 shirts correctly by random guessing=
P(X≥11)=P(X=11)+P(X=12)
=¹²C₁₁(½)¹(½)¹¹+¹²C₁₂×(½)¹²(½)⁰
=12×½×(1/2)¹¹+(½)¹²
=0.00024414062≈0.0002
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given natural numbers a and b not both equal to 0, we know that there exist integers k and l with ak bl
Answers
The equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l).
The equation ak + bl = 0 is a linear equation in two variables and is solved using the method of elimination. The equation can be written in the form ax + by = c, where a, b, c are constants. To solve this equation, both sides of the equation should be divided by the coefficient of one of the variables (a or b). This will result in a equation of the form x + qy = r, where q and r are constants. Then, the equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l). The two variables can then be calculated using the point of intersection by substituting the x and y values into the two equations. In this way, the two variables k and l can be found such that ak + bl = 0.
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What are the integers k and l such that ak + bl = 0?
Let f be the function given by f(x) = e-2x2.
a) Find the first four nonzero terms and the general termof the power series for f(x) about x = 0.
b) Find the interval of convergence of the power series forf(x) about x = 0. Show the analysis that leads to yourconclusion.
c) Let g be the function given by the sum of the first fournonzero terms of the power series for f(x) about x = 0. Show thatabsolute value(f(x) - g(x)) < 0.02 for -0.6<= x <=0.6.
Answers
a) The first four nonzero terms of the power series for f(x) about x=0 are
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is (-2)^n (2x)^(2n) / (2n)!
b) The interval of convergence of the power series is (-∞, ∞).
c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula
f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ
where fⁿ(0) denotes the nth derivative of f evaluated at x=0.
In this case, we have
f(x) = e^6(-2x^2)
fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)
So, we can write the power series as
f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)
= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)
To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula
f(0) = e^6
f'(0) = 0
f''(0) = 24
f'''(0) = 0
So, the first four nonzero terms of the power series are:
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is
(-2)^n (2x)^(2n) / (2n)!
b) To find the interval of convergence of the power series, we can use the ratio test
lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|
= lim [n→∞] |-4x^2/(2n+1)(2n+2)|
= lim [n→∞] 4x^2/(2n+1)(2n+2)
Since this limit depends on the value of x, we need to consider two cases
i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.
ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value
|4x^2/(2n+1)(2n+2)| < 1
This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).
c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].
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in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
Answers
The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)
where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.
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Complete question:
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'
B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---
C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°
D. ΔY = f(x₁ +Xq, X2, Xk).
On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
Answers
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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when comparing the distribution of the population of individual scores to the distribution of means, the distribution of means will always have
Answers
The population distribution of scores has a similar average as the distribution of means.
In a sample distribution of means, the distribution will roughly resemble a normal distribution, the sampling distribution's mean will be equal to the population's mean, and the sampling distribution's standard deviation is based on the Central Limit Theorem.
The central limit theorem (CLT) of probability theory states that the distribution of a sample variable tends towards a normal distribution (i.e., a "bell curve") as the sample size increases, under the premise that all samples are of equal size and regardless of the population's actual distribution shape.
In other terms, the central limit theorem (CLT) is a statistical presumption that the mean of all sampled variables from the same population will be substantially equal to the mean of the entire population, given a large enough sample size from a population with little volatility. These samples likewise resemble a normal distribution in accordance with the law of large numbers, with their variances nearly matching the variance of the population as the sample size rises.
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the actual question is :
When comparing the size of the standard error of the mean with the size of the standard deviation of the underlying distribution of individual scores:
a. the standard error of the mean is always larger
b. the standard error of the mean is always smaller
c. the standard error of the mean is sometimes larger and sometimes smaller, depending on the sample size
d. none of these
which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
Answers
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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7. Complete the comparison: 17>?
O A. 18
O B. 17
O C. 39
O D. 1
O Mark for review will be highligh
Answers
Answer: 39
39 is the only answer option greater than 17
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble??
A) 11
B) 33
C) 32
D) 22
Answers
The number οf times that Greg chοοses a yellοw pebble is 22 times.
Thus, option D is correct.
Finding the number οf chοices:Tο find the number οf pοssible chοices, calculate the number οf chances in the tοtal number οf οutcοmes.
Since we need tο find the number οf chοices that are expecting a yellοw pebble, find the tοtal number οf yellοw pebbles in the number οf pebbles in bοth Claire and Laura's cases and find the tοtal number οf yellοw pebbles.
Here we have
A table belοw shοws the number οf painted pebbles by Claire and Laura
Frοm the table,
Number οf pebbles that Laura painted = 8 yellοw, 7 green, 10 blue
Number οf pebbles that Claire painted = 14 yellοw, 5 green, 6 blue
Tοtal number οf yellοw pebbles = 8 + 14 = 22
Given that
Greg chοοses a pebble at randοm frοm the bοx 75 times, and each time replaces the pebble
Hence, the number οf time that Greg get yellοw pebble = number οf yellοw pebbles
Therefοre, The number οf times that Greg chοοses a yellοw pebble is 22 times.
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write a quadratic function in standard form that passes through the points (-8,0) ,(-5, -3) , and (-2,0) .
F(x)=
Answers
A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].
What are some examples of quadratic functions?f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
How do you determine whether an equation is quadratic?In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.
[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]
is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],
[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]
[tex]= > 64a - 8b + c = 0 -------(2)[/tex]
Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]
[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]
[tex]= > 25a - 5b + c = -3 --(3)[/tex]
Continue for third point [tex](-2,0)[/tex]
[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]
[tex]= > 4a -2b + c = 0 --(4)[/tex]
So, we have three equations and three values to determine.
Subtract equation [tex](4)[/tex] from [tex](2)[/tex]
[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]
[tex]= > 60a - 6b = 0[/tex]
[tex]= > 10a - b = 0 --(5)[/tex]
subtract equation [tex](4)[/tex] from [tex](3)[/tex]
[tex]= > 21a - 3b = -3 --(6)[/tex]
from equation (4) and (5),
[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]
[tex]= > 30a - 3b - 21a + 3b = 3[/tex]
[tex]= > 9a = 3[/tex]
[tex]= > a = 1/3[/tex]
from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]
from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]
So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]
Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].
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Answer:
f(x) = (1/3)x² + (10/3)x + 16/3-------------------------------------
Given 3 points of a quadratic function and two of them lie on the x-axis:
(-8, 0) and (-2, 0)These two points are representing the roots of the function. With known roots we can show the function in the factor form:
f(x) = a(x - x₁)(x - x₂), where a - coefficient, x₁ and x₂ are rootsSubstitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:
-3 = a(- 5 + 8)((-5 + 2)- 3 = a(3)(-3)3a = 1a = 1/3This gives us the function in the factor form:
f(x) = (1/3)(x + 8)(x + 2)Convert this into standard form of f(x) = ax² + bx + c:
f(x) = (1/3)(x + 8)(x + 2)f(x) = (1/3)(x² + 10x + 16)f(x) = (1/3)x² + (10/3)x + 16/3Find the Z-score for each of the following IQ scores
90 160(Einstein's IQ)
Answers
Answer:
z=3.75
Step-by-step explanation:
Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Answers
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.
Answers
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:
y[n] = x[n] * h[n]
y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])
y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])
y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
Thus, the impulse response of the system is:
h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.
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d. Two judges in a beauty contest rank the ten competitors in the following order.
Do d. Two judges in a beauty contest rank the ten competitors in the following order.
Do the two judges appear to agree in their standard? the two judges appear to agree in their standard?
Answers
The correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.
What is correlation and causation in statistics?Nevertheless, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other.
There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
For the given ranks for two judges the difference between their ranks is:
d: 0.0 4.0 -2.0 1.0 -0.5 1.5 -1.0 -1.0 0.5 2.0
Squaring the given distance we have:
d²: 0.0 16.0 4.0 1.0 0.25 2.25 1.0 1.0 0.25 4.0
Σd² = 29.75
The Spearman's rank correlation coefficient is given as:
ρ = 1 - (6Σd²)/(n(n²-1))
ρ = 1 - (629.75)/(10(10²-1))
ρ ≈ 0.03
Since the correlation coefficient is close to zero, we can conclude that the two judges do not appear to agree in their standards.
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The complete question is:
Find an equation of the plane that passes through the given point and contains the specified line. (-1, 0, 1); x = 5t, y=1+t, z= -t
Answers
The equation of the plane passing through the point (-1,0,1) and containing the lines x = 5t, y=1+t, z= -t is y + z = 1 .
We substitute , t=0 in the given line equations ,
we get; x=0 , y = 1 and z = 0 ;
So, the plane contain the line , Thus plane will also pass through (0,1,0);
Now, we have that plane passes through (-1,0,1) and (0,1,0), direction ratios of line joining these 2 points are ;
⇒ DR₁ = (-1-0 , 0-1 , 1-0) = (-1,-1,1);
So , the line can be written as x/5 = (y-1)/1 = z/-1 = t;
So, the direction ratio of this line will be :
⇒ DR₂ = (5 , 1 , -1);
The Direction Ratio of normal to the plane is = DR₁ × DR₂;
= (-1,-1,1) × (5,1,-1);
= [tex]\left|\begin{array}{ccc}i&j&k\\-1&-1&1\\5&1&-1\end{array}\right|[/tex]
On solving ,
We get;
= 4j + 4k = (0,4,4) ;
We know that for a normal with direction ratios (a,b,c), equation of plane is written as ax + by + cz = d;
We got direction ratio for plane normal = (0,4,4);
So, equation of plane is 0x+ 4y + 4z = d;
the plane passes through the point (-1,0,1) ;
⇒ 4(0) + 4(1) = d ⇒ d = 4;
we get the equation of plane is 4y + 4z = 4;
⇒ y + z = 1.
Therefore, the equation of the required plane is y + z = 1.
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59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer
Answers
The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).
The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].
We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].
This is a infinite geometric series with first term a = -5x and common ration r = -5x.
It is convergent when
|r| < 1
|-5x| < 1
|-5| |x| < 1
5|x| < 1
Divide by 5 on both side, we get
|x| < 1/5
The series is convergent when x ∈ (-1/5, 1/5).
Sum of the series is
Sₙ = a/1 - n
Sₙ = (-5x)/{1 - (-5x)}
Sₙ = (-5x)/(1 + 5x)
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The complete question is:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]
School administrators asked a group of students and teachers which of two
school logo ideas, logo A or logo B, they prefer. This table shows the results.
Students
Teachers
Total
Logo A
14
14
28
Logo B
86
11
97
Total
100
25
125
Are being a student and preferring logo B independent events? Why or why
not?
A. Yes, they are independent, because P(student) = 0.8 and
P(student logo B) = 0.89.
B. No, they are not independent, because P(student) = 0.8 and
P(student logo B) 0.78.
C. No, they are not independent, because P(student) = 0.8 and
P(student logo B) * 0.89.
D. Yes, they are independent, because P(student) = 0.8 and
P(student logo B) 0.78...
Answers
B, No, they are not independent events because the probability of a student preferring logo B (0.78) is different from the overall probability of preferring logo B (0.89), which includes both students and teachers.
How to find independent events?To determine whether being a student and preferring logo B are independent events, we need to compare the probability of a student preferring logo B (P(student logo B)) with the overall probability of preferring logo B (P(logo B)).
P(student logo B) = 0.78 (from the table)
P(logo B) = (86 + 11) / 125 = 0.89
If the two probabilities are equal, then the events are independent. However, in this case, P(student logo B) is not equal to P(logo B), indicating that being a student and preferring logo B are dependent events. Therefore, being a student and preferring logo B are dependent events.
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THERE ARE 2 PARTS PLEASE ANSWER BOTH RIGHT TY HELPP!! There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.
Part A. What is the theoretical probability of drawing a purple card from the hat?
Part B.
In a trial, a card is drawn from the hat and then replaced 1,080 times. A purple card is drawn 324 times. How much greater is the experimental probability than the theoretical probability?
Enter the correct answers in the boxes.
A. The theoretical probability of drawing a purple card from the hat is ______.
B. The experimental probability of drawing a purple card is ____%
greater than the theoretical probability.
Answers
Part A. The probability pf drawing a purple card out of the hat is 28%.
Part B. The experimental probability is 2% greater than the theoretical probability.
Define probability?The probability that a specific event will occur is known as probability. The ratio of favourable outcomes to all other possible outcomes serves as a stand-in for the likelihood that an event will occur.
In numerous disciplines, including mathematics, statistics, physics, economics, and computer science, uncertain events are described and understood using probability theory. It is used to analyse risks, make decisions, and forecast events.
Now in the given question,
Total cards in the hat = 12 + 17 + 14 + 7 = 50 cards
Total purple cards in the hat = 14
Probability of getting a purple card from the hat = 14/50
= 0.28
= 28%
Now similarly for the experiment,
Probability = 324/1080
= 0.3
= 30%
Therefore, the experimental probability is 30% - 28% = 2% greater than the theoretical probability.
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Asaad invests $6800 in two different accounts. The first account paid 14 %, the second account paid 11 % in interest. At the end of the first year he had earned $856 in interest. How much was in each account?
Answers
Answer:
Step-by-step explanation:
Let x be the amount invested in the first account, which pays 14% interest. Then the amount invested in the second account, which pays 11% interest, is 6800 - x.
The interest earned on the first account is 0.14x, and the interest earned on the second account is 0.11(6800 - x). The total interest earned is the sum of these two amounts, so we have:
0.14x + 0.11(6800 - x) = 856
Simplifying and solving for x, we get:
0.14x + 748 - 0.11x = 856
0.03x = 108
x = 3600
Therefore, Asaad invested $3600 in the first account and $3200 (6800 - 3600) in the second account.
can anyone help with this triangle question
Answers
The triangle's other leg, side B, measures 12 cm in length.
Are there 180 right triangles in all?When one of the interior angles is 90 degrees, or a right angle, the triangle is said to be a right triangle. The three internal angles of a triangle add up to 180 degrees in a right triangle because one angle must always be 90 degrees and the other two must always total to 90 degrees (they are complementary).
We can observe that the given triangle is a right triangle because angle A's measure is 90 degrees. The hypotenuse, which is represented by the letter "c," is the side that is opposite the right angle. The legs are the other two sides, and they are indicated by "a" and "b".
We are told that the hypotenuse (side c) is 13 cm long and that one leg (side a) is 5 cm long. The length of the other leg must be determined (side b).
The Pythagorean theorem, which asserts that in a right triangle, can be used.
a² + b² = c²
Inputting the values provided yields:
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12
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In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
Answers
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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Write the equation for a parabola with a focus at (2,2) and a directrix at x=8
Answers
Answer:
(y - 2)² = -12(x - 5)
Step-by-step explanation:
A parabola is a locus of points, which are equidistant from the focus and directrix;
Generic cartesian equation of a parabola:
y² = 4ax, where the:
Focus, S, is: (a, 0)
Directrix, d, is: x = -a
a > 0
Put simply, a is the horinzontal difference between the directrix and the vertex or between the vertex and focus;
Always a good idea to do a quick drawing of the graph;
We are the told the focus, F, is: (2, 2) and directrix, d, is: x = 8;
First thing to note, the vertex, or turning point will be in line with the focus vertically, i.e. they will share the same y-coordinate;
Horizonatally, it will be halfway between the focus and the directrix, i.e. halfway between 8 and 2;
Therefore, the vertex will be will be (5, 2);
We can also work out a:
a = 8 - 5 = 5 - 2
a = 3
Substituting this value of a into the generic cartesian equation:
y² = 4(3)x
y² = 12x
The focus and directrix will be:
S: (3, 0)
d: x = -3
Next thing to note, a parabola curves away from the directrix;
In this case, the directrix is x = 8, so the vertex will be the right-most point on the parabola, it will curve off to the left and the focus will also be to the left;
What we want to do is compare with y² = 12x;
This parabola, has a vertex (0, 0), which is the left-most point that curves off to the right and a focus also to the right;
Since we know the formula of this parabola, if we figure out how to transform it into the one in the question, we can find out it's equation;
What we should recognise first is that the parabola in the question is reflected in the y-axis, compared to y² = 12x;
So we apply the transformation that corresponds to this, i.e. use the f(-x) rule:
y² = 12(-x)
y² = -12x
Now the two graphs will have the same shape and orientation;
The focus and directrix will also be affected:
S: (-3, 0)
d: x = 3
Now, the only remaining difference would be the coordinates of the focus and directrix of the two graphs;
The focus of the graph in the question is 5 units to the right and 2 units upwards compared to the focus of y² = -12x;
The directrix is 5 units to the right of that of y² = -12x;
So we apply a translation transformation of 5 units right and 2 units up, like so:
(y - 2)² = -12(x - 5)
Replace y with (y - 2) to translate up 2 units;
Replace x with (x - 5) to translate 5 units right.
We know have a parabola with focus, (2, 2), directrix, x = 8 and vertex, (5, 2), i.e. the parabola in the question;
Hence, the equation of the parabola in the question is:
(y - 2)² = -12(x - 5)
It might seem a bit long and complicated to begin with, but can be done very quickly if you can get used to it.
4^(-x)=1/256
I believe it is x=4, but I need how to work it out pls thxxx
Answers
Answer:
x = 4
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]4^{-x}[/tex] = [tex]\frac{1}{4^{x} }[/tex]
and 256 = [tex]4^{4}[/tex]
then
[tex]\frac{1}{4^{x} }[/tex] = [tex]\frac{1}{4^{4} }[/tex]
so
[tex]4^{x}[/tex] = [tex]4^{4}[/tex]
since bases on both sides are equal, bot 4 then equate exponents
x = 4
The following joint probability density function for the random variables Y1 and Y2, which represent the proportions of two components in a somaple from a mixture of insecticide.
f(y1,y2) = { 2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1+y2 <=1
{ 0, elsewhere
For the chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).
Answers
The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.
To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:
E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2
= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex](y1 + y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (2y1 + 1) (1-y1)² dy1
= 5/12
To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².
First, we need to find E[(Y1+Y2)^2]:
E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2
= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex] (y1² + y2² + 2y1y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (1/3)y1³ + (1/2)y1² + (1/2)y1
(1/3)y1 + (1/4) dy1
= 7/12
Next, we need to find [E(Y1+Y2)]²:
[E(Y1+Y2)]² = (5/12)² = 25/144
Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.
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I'm not sure where I'm going wrong here and need a detailed explanation with a full answer please.
Answers
Answer:
g(x) = 1/2|x - 1| + 2
Step-by-step explanation:
You were almost there, you just got the slope wrong.
original vertex (h, k): (0, 0)
transformed vertex (h', k'): (1, 2)
original slope: 1
transformed slope: m = (3-2)/(3-1) = 1/2 pick any 2 points to find the slope
equation for the transformed function shown in the graph:
g(x) = 1/2|x - h'| + k'
g(x) = 1/2|x - 1| + 2
Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Total
89
101
190
Male
Female
Total
Meat-eater
35
37
72
12
23
35
24
14
38
Vegan
18
27
45
What is the probability that a randomly selected person is a meat-eater? Round your
answer to the hundredths place.
Answers
Answer:
To find the probability that a randomly selected person is a meat-eater, we need to add up the number of meat-eaters and divide by the total number of individuals surveyed. From the given table, we can see that there are 72 meat-eaters out of a total of 190 individuals surveyed:
Total meat-eater = 72
Total surveyed = 190
So the probability of selecting a meat-eater is:
P(meat-eater) = Total meat-eater / Total surveyed
P(meat-eater) = 72 / 190
P(meat-eater) = 0.38 (rounded to the hundredths place)
Therefore, the probability that a randomly selected person is a meat-eater is 0.38 or 38%.
Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answers
Answer: numbers 1,3 and 4
Step-by-step explanation:
Y=3x-4 4x+3y=1 what does X and y equal?
Answers
Answer:
{y,x}={-1,1}
to leave and take
Mr. and Mrs. Davenport have 3 kids, ages 3, 6, and 13. Their financial matters for 2019 are as follows:Adjusted Gross Income: $65,000Un-reimbursed Medical Expenses: $5,250How much would the Davenports' medical expenses contribute to their total itemized deductions?
Answers
The Davenports' medical expenses contribute to their total itemized deductions are $375 (7.5% for 2019).
The costs you incurred for state and local income or sales taxes, real estate taxes, personal property taxes, mortgage interest, and disaster losses are all included in itemised deductions. You can also count charitable donations and a portion of your out-of-pocket medical and dental costs.
Currently for the 2019 (due 2020), you can deduct medical expenses that exceed 7.5% of your AGI, but back then in 2019, the threshold was 7.5%, not 10%.
So the Davenports can only deduct
$5,250 - ($65,000 x 7.5%) = $375
if they decided to itemize their deductions.
The threshold will increase back to 10% starting 2020 (due 2021) tax returns.
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