Answer:
P(hh) = 0.2209
P(ht) = 0.2491
P(th) = 0.2491
P(tt) = 0.2809
John von Neumann suggested that if both tosses results in same outcome then discard the result and start again. If each result is different then accept the first one
Step-by-step explanation:
We are given that a coin is unfair and the probabilities of getting a head and tail are
P(h) = 0.47
P(t) = 0.53
John von Neumann suggested a way to make perfectly fair decisions, even with a possibly biased coin.
He suggested to toss the coin twice, so the possible outcomes are
Sample space = {hh, ht, th, tt}
The probabilities of these outcomes are
P(hh) = P(h)*P(h)
P(hh) = 0.47*0.47
P(hh) = 0.2209
P(ht) = P(h)*P(t)
P(ht) = 0.47*0.53
P(ht) = 0.2491
P(th) = P(t)*P(h)
P(th) = 0.53*0.47
P(th) = 0.2491
P(tt) = P(t)*P(t)
P(tt) = 0.53*0.53
P(tt) = 0.2809
He suggested that if both tosses results in same outcome then discard the result and start again.
If each result is different then accept the first one, for example,
if you get heads on the first toss and tails on the second toss then result is heads.
if you get tails on the first toss and heads on the second toss then result is tails.
If you notice the probability of P(ht) and P(th) are same therefore, this strategy allows to make fair decision even when the coin is biased.
What is the equation of the line, in point slope form, that passes through the points (4,8) and (2,-2)
Answer:
Step-by-step explanation:
1) point slope form is:
y-y1=m(x-x1)
y1=8
x1=4
m=(slope)
to find m: y2-y1/x2-x1
hence
-2-8/2-4=-10/-2=5
m=5:
y-8=5(x+4)
The function s(t) describes the motion of a particle along a line. s(t) = 14t − t2 (a) Find the velocity function v(t) of the particle at any time t ≥ 0. v(t) = 14−2t (b) Identify the time interval on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (7,[infinity]) (d) Identify the time at which the particle changes direction.
a. The velocity function is v(t) = 14 - 2t. b. The particle is moving in a positive direction on the interval (0, 7). c. The particle is moving in a negative direction on the interval (7, infinity). d. The particle changes direction at t = 7.
Explanation:a. The velocity function can be found by taking the derivative of the position function, s(t). The derivative of s(t) with respect to t is v(t) = 14 - 2t.
b. To determine the time interval on which the particle is moving in a positive direction, we need to find the values of t that make v(t) > 0. Solving the inequality 14 - 2t > 0, we get t < 7. Therefore, the particle is moving in a positive direction on the interval (0, 7).
c. Similarly, to determine the time interval on which the particle is moving in a negative direction, we need to find the values of t that make v(t) < 0. Solving the inequality 14 - 2t < 0, we get t > 7. Therefore, the particle is moving in a negative direction on the interval (7, infinity).
d. The particle changes direction at the time t = 7. This can be determined from the fact that v(t) changes sign at this time.
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Find the volume of a right circular cone that has a height of 12.5 m and a base with a radius of 2.2 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
The volume of the cone is 63.3m³
Step-by-step explanation:
First of all to solve this problem we need to know the formula to calculate the volume of a cone
v = volume
r = radius = 2.2m
h = height = 12.5m
π = 3.14
v = 1/3 * π * r² * h
we replace with the known values
v = 1/3 * 3.14 * (2.2m)² * 12.5m
v = 1/3 * 3.14 * 4.84m² * 12.5m
v = 63.32m³
rount to the neares tenth
v = 63.32m³ = 63.3m³
The volume of the cone is 63.3m³
Answer: 63.4
Step-by-step explanation:
You round to the tenths giving you 63.4
Does anybody know these two questions?!
Answer:
Both are true statements
Step-by-step explanation:
By definition of an angle, an angle is a union of two rays at a common endpoint and lines can contain rays.
A full circle measures 360 degrees.
Answer:
Question7:true
Question8:true
Step-by-step explanation:
Question 7: an angle is made when two lines or rays come together
Question 8:an angle that has 360° is a circle
Raul is y years old. Kayla is 6 years older than raul and isaac is 4 years younger than raul what is kayla's age?
Answer:
9
Step-by-step explanation:
It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.
Answer:
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 55, \pi = \frac{24}{55} = 0.4364[/tex]
93% confidence level
So [tex]\alpha = 0.07[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.07}{2} = 0.965[/tex], so [tex]Z = 1.81[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 - 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.3154[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4364 + 1.81\sqrt{\frac{0.4364*0.5636}{55}} = 0.5574[/tex]
The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).
Given the graph of a system of equations, which
statements are true about the solution? Check all that
apply.
V
The x-value is an integer.
2
The x-value is between 3 and 4.
-4
2.
2
The y-value is between-2 and -1.
The x-value is positive.
The x- and y-values have the same sign.
-2
-4
Answer:
B. The x-value is between 3 and 4.
C. The y-value is between –2 and –1.
D. The x-value is positive.
Step-by-step explanation:
I did the Assignment on Edg.
The true options are: The x-value is between 3 and 4, the y-value is between –2 and –1 and the x-value is positive.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the graph, we have the following highlights
The point of intersection of the two lines is in the fourth quadrant.
The value of x is between 3 and 4.
The value of y is between -1 and -2.
x is positive, and y is negative.
x is not an integer.
x is between 3 and 4, while y is between -1 and -2
Hence, the true options are: The x-value is between 3 and 4.
the y-value is between –2 and –1 and the x-value is positive.
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Use properties of power series, substitution, and factoring of constants to find the first four nonzero terms of the Taylor series centered at 0 for the function given below. Use the Taylor series (1 plus x )Superscript negative 2 Baseline equals 1 minus 2 x plus 3 x squared minus 4 x cubed plus times times times, for negative 1 less than x less than 1. (1 plus 9 x )Superscript negative 2 The first term is nothing. The second term is nothing. The third term is nothing. The fourth term is nothing.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Question 1
State the value of the discriminant for y = x2 – 8x + 10.
a) 10.2
b) 4.9
c) 104
d) 24
Answer:
D = 24
Step-by-step explanation:
The given quadratic equation is [tex]y=x^2-8x+10[/tex].
It is required to find the value of the discriminant. The value of discriminant of any quadratic equation is given by :
[tex]D=b^2-4ac[/tex]
Here, a = 1, b = -8 and c = 10
On plugging all the values, we get :
[tex]D=(-8)^2-4\times 1\times 10\\\\D=24[/tex]
So, the value of discriminant for y is 24.
Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Select two options
The vertex form of the function is f(x) = (x - 2)2 + 2.
The vertex of the function is (-3, -13).
The axis of symmetry for the function is x = 3.
The graph increases over the interval (-3,
).
The function does not cross the x-axis.
Answer:
2 and 4
Step-by-step explanation:
A function assigns the values. The statements that are true about the given function are B and D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
To know the correct statements about the graph of the function f(x)=6x-4+x², we need to plot the graph, as shown below.
A.) The vertex form of the function is f(x)=(x-2)²+2.
To know if the vertex form of the function is f(x)=(x-2)²+2, solve the equation and check if it is of the form f(x)=6x-4+x².
[tex]f(x)=(x-2)^2+2\\\\ f(x)=x^2+4-4x+2\\\\f(x) = x^2-4x+6[/tex]
Since the two functions are not equal this is not the vertex form of the function is f(x)=6x-4+x².
B.) The vertex of the function is (-3, -13).
As can be seen in the image below, the vertex of the function lies at (-3,-13.) Therefore, the statement is true.
C.) The axis of symmetry for the function is x = 3.
As the vertex is at -3, therefore, the function symmetry will be about x=-3.
Hence, the given statement is false.
D.) The graph increases over the interval (-3).
The given statement is true since the graph will be showing a positive slope in the interval (-3, +∞).
E.) The function does not cross the x-axis.
It can be observed that the function intersects the x-axis exactly at two points, therefore, the given statement is false.
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A guy wire is needed to support a tower. The wire is attached from the top of the tower to a place on the ground 5m from the base of the tower. How long is the wire if the tower is 10m tall?
Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________.
Answer:
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
Therefore, for the case above;
Let u1 represent the mean age of audience for American idol and
u2 represent the mean age of audience for 60 minutes.
The null hypothesis is H0; u1 - u2 = 0
The mean age of each audience is the same.
g Which of the following is true about a p-value? Group of answer choices It measures the probability that the null hypothesis is true. It measures the probability of observing your test statistic, assuming the null hypothesis is true. It measures the probability of observing your test statistic, assuming the alternative hypothesis is true. It measures the probability that the alternative hypothesis is true.
Answer:
It measures the probability of observing your test statistic, assuming the null hypothesis is true.
Step-by-step explanation:
The p-value, also known as the probability value measures the probability of observing your test statistic, assuming the null hypothesis is true.
A low p-value means a higher chance of the null hypothesis to be true.
It lies between 0 and 1. A small p-value indicates fewer chances of the null hypothesis to be true.
y2 – 3y + 2 = 0 solve buy factoring
Answer:
y²-3y+2=0
=> y²-(2+1)y +2=0
=> y²-2y-y+2=0
=> y(y-2)-1(y-2)=0
=> (y-2)(y-1)=0
=> y = 2 or y= 1
f(t) = t - 6
f(u + 6) =
Answer:
f(u +6) = u
Step-by-step explanation:
Put (u+6) in place of t and simplify:
f(u+6) = (u+6) -6
f(u+6) = u
To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume the mean height of chimneys in these factories is 10D meters (an EPA-acceptable height) with a standard deviation 12 meters. A random sample of 40 chimney heights is obtained. What is the probability that the sample mean height for the 40 chimneys is greater than 102 meters?
Answer:
The probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
Step-by-step explanation:
Let the random variable X be defined as the height of chimneys in factories.
The mean height is, μ = 100 meters.
The standard deviation of heights is, σ = 12 meters.
It is provided that a random sample of n = 40 chimney heights is obtained.
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Since the sample selected is quite large, i.e. n = 40 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean heights of chimneys.
[tex]\bar X\sim N(\mu_{\bar x},\ \sigma^{2}_{\bar x})[/tex]
Compute the probability hat the sample mean height for the 40 chimneys is greater than 102 meters as follows:
[tex]P(\bar X>102)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}})>\frac{102-100}{12/\sqrt{40}})[/tex]
[tex]=P(Z>1.05)\\=1-P(Z<1.05)\\=1-0.85314\\=0.14686\\\approx 0.1469[/tex]
*Use a z-table fr the probability.
Thus, the probability hat the sample mean height for the 40 chimneys is greater than 102 meters is 0.1469.
A University wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no". The point estimate for this problem is __________.
Answer:
The point estimate for this problem is 0.48.
Step-by-step explanation:
We are given that a University wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students.
A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no".
Let [tex]\hat p[/tex] = proportion of students who felt comfortable reporting cheating by their fellow students
Now, point estimate ([tex]\hat p[/tex]) is calculated as;
[tex]\hat p=\frac{X}{n}[/tex]
where, X = number of students who answered yes = 1,344
n = number of students surveyed = 2,800
So, Point estimate ([tex]\hat p[/tex]) = [tex]\frac{1,344}{2,800}[/tex]
= 0.48 or 48%
Final answer:
The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students is 48%.
Explanation:
The point estimate for the percentage of students who felt comfortable reporting cheating by their fellow students can be calculated by dividing the number of students who answered 'Yes' by the total number of students surveyed, and then multiplying by 100%. In this case, the point estimate is:
Point estimate = (Number of 'Yes' responses / Total number of students surveyed) * 100% = (1344 / 2800) * 100% = 48%
Consider the system of linear equations. 7 x + 16 y = negative 2. 9 x minus 4 y = 22. To use the linear combination method and addition to eliminate the y-terms, by which number should the second equation be multiplied? –4 Negative one-fourth One-fourth 4
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population means? 4.90 hrless than
This question is incomplete. I got the complete part (the boldened part) of it from google as:
The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:
4.90 hrs < μ1 - μ2 < 17.50 hrs.
Answer:
A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population means?
The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.
Step-by-step explanation:
The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.
Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.
PLEASE IM BEING TIMED
Answer:
A
Step-by-step explanation:
First you use the equation [tex]2(\pi r^{2})[/tex] to find the area of the circles combined and you find the radius by diving the height by 2(getting 5)
Then you find the area of the squares with the circles(10 x 20= 200)
Finally you subtract the area of both circles and the total area. (200-157=43)
Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she will have 7 times as many dollars as Timmy. How many dollars does Timmy have?
Answer:
$5
Step-by-step explanation:
Using algebra to solve this problem.
Let 'x' be Timmy’s amount.
->Mara has 3 times as many dollars as her brother i.e 3x dollars
->If Mara is given $20 by their mother, then expression would be
3x + 20
Since Mara’s new amount is supposed to be seven times Timmy’s
current amount, this forms an equation
3x + 20 = 7x
Solving for 'x'
7x -3x=20
4x = 20
x=20/4
x=5
Timmy has an amount of $5
Final answer:
By setting up two equations based on the given information and solving for T, we find that Timmy has $5.
Explanation:
Let's denote the amount of dollars Timmy has as T. According to the question, Mara has 3 times as many dollars as Timmy, so we can write this as M = 3T, where M is the amount Mara has. Now, we are told that if Mara is given an additional $20, she will have 7 times the amount Timmy has. We can express this as M + 20 = 7T. Using the two equations, we can solve for the value of T.
First, substitute the value of M from the first equation into the second equation:
3T + 20 = 7T
20 = 7T - 3T
20 = 4T
T = 20 / 4
T = $5
Therefore, Timmy has $5.
Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
Answer:
a) The company should expect to replace 11.51% of its batteries.
b) 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 43.8, \sigma = 6.5[/tex]
(a) If Quick Start guarantees a full refund on any battery that fails within the 36-month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 43.8}{6.5}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151.
The company should expect to replace 11.51% of its batteries.
(b) If quick Start does not want to make refunds for more than 10% of its batteries under the full refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
The warranty should be the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 43.8}{6.5}[/tex]
[tex]X - 43.8 = -1.28*6.5[/tex]
[tex]X = 35.48[/tex]
To the nearest month, 35 months.
Final answer:
To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36.
Explanation:
In this question, we are given information about the average life of a Quick Start car battery, which follows a normal distribution with a mean of 43.8 months and a standard deviation of 6.5 months.
(a) To calculate the percentage of batteries that will be expected to be replaced within the 36-month period, we need to find the area under the normal distribution curve from 0 to 36. We can use the z-score formula to standardize the value of 36 and then use a standard normal distribution table to find the corresponding area. The percentage of batteries that will be expected to be replaced is the same as the percentage of batteries that fall within the range of 0 to 36 months.
Subtract the mean from 36: 36 - 43.8 = -7.8Divide the result by the standard deviation: -7.8 / 6.5 = -1.2Using the z-score -1.2, find the corresponding area under the standard normal distribution curve using a standard normal distribution table or a calculator with standard normal distribution capabilities.How long is it until 20000 mosquitoes are in the colony?
Answer :The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1400 after 1​ day
Step-by-step explanation:
Answer:
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1600 after 1 day, what is the size of the colony after 4 days
Step-by-step explanation:
Torres was planning a trip to china. Before going, he did some research and learned that the exchange rate is one Yuan for $0.15. How many Yuan would he get if he exchanged $300?
Answer:
The answer is 2000 yuan.
Step-by-step explanation:
Devise a proportion for this, and then cross-multiply. I believe that is the easiest way.
[tex] \frac{1}{0.15} = \frac{x}{300} \\ 0.15x = 300 \\ x = \frac{300}{0.15} \\ x = \frac{30000}{15} \\ x = \frac{10000}{5} \\ x = 2000[/tex]
Using the given exchange rate of $0.15 for 1 Yuan, Torres will receive 2000 yuan when he exchanges his $300.
Explanation:Torres plans to go to China and wants to exchange his money into the Chinese currency, known as the Yuan. The exchange rate he finds is $0.15 for 1 Yuan. This means for every 1 yuan, he needs to supply $0.15. Because he wants to exchange $300, the number of Yuan he will receive can be calculated by the formula Amount_in_dollars / Exchange_rate.
Here, the Amount_in_dollars is $300 and the Exchange_rate is $0.15. So, the calculation will be $300 / $0.15 = 2000 yuan. Therefore, Torres will receive 2000 yuan when he exchanges his $300.
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Suppose seven pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why?Since there are 7 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . It follows that if a minimum of Incorrect: Your answer is incorrect. boots are chosen, at least two must be from the same pair.
Answer:
We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.
Step-by-step explanation:
From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.
Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;
Number of single boots = 7 x 2 = 14
Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.
Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.
To ensure getting a matched pair from a pile of 7 pairs of boots, you would need to pick eight individual boots. This is based on the counting principle in mathematics where in the worst-case scenario, each boot you pick could be from a different pair.
Explanation:The question is about probability and counting principles in mathematics, specifically about how to identify a matched pair of boots from a pile of similar looking pairs. In the pile, there are seven pairs of boots, which means there are 14 individual boots from seven different pairs.
Now, if you randomly pick one boot, it could be from any pair. If you pick a second boot, it could also be from any pair, including the same pair as the first one. But to be sure that you get a matched pair, you will have to pick up eight boots. This is because, in the worst-case scenario, you might pick seven different boots each from a different pair. Once you pick the eighth boot, it is guaranteed to match one of the earlier seven because there are only seven pairs.
The minimum number of individual boots that you must pick to be sure of getting a matched pair is eight.
Learn more about Counting Principle here:https://brainly.com/question/29594564
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Theme park spending In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard deviation of $15. Construct and interpret a 99% confidence interval for the mean amount spent daily per person at the theme park.
Answer:
The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.
This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.
Step-by-step explanation:
We have the sample standard deviation, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 40 - 1 = 39
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.7079
The margin of error is:
M = T*s = 2.7079*15 = 40.62
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 93.43 - 40.62 = $52.81.
The upper end of the interval is the sample mean added to M. So it is 93.43 + 40.62 = $134.05
The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.
This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.
Teddy has 6 lollipops and 9 cookies. Annie say for every 3 lollipops there are 2 cookies. Teddy says I don’t agree. What mistake has Annie made
Answer:
She switched her say
Step-by-step explanation:
Answer:
Annie made the mistake of either swapping the numbers or the items in her comparison.
Step-by-step explanation:
The ratio of lollipops to cookies is:
6/9
This can be simplified to:
2/3
That means that for every two lollipops, there are three cookies. Therefore Annie made the mistake of either swapping the numbers or the items in her comparison.
Consider a drug testing company that provides a test for marijuana usage. Among 317 tested subjects, results from 25 subjects were wrong (either a false positive or a falsenegative). Use a 0.05 significance level to test the claim that less than 10 percent of the test results are wrong. Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pless than<0.10.1 B. Upper H 0H0: pless than<0.10.1 Upper H 1H1: pequals=0.10.1 C. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pgreater than>0.10.1 D. Upper H 0H0: pequals=0.10.1 Upper H 1H1: pnot equals≠0.10.1 Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is nothing. (Round to two decimal places as needed.) Identify theP-value for this hypothesis test. The P-value for this hypothesis test is nothing. (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fail to rejectFail to reject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. B. RejectReject Upper H 0H0. There is notis not sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. C. RejectReject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. D. Fail to rejectFail to reject Upper H 0H0. There isis sufficient evidence to warrant support of the claim that less than 1010 percent of the test results are wrong. Click to select your answer(s).
Answer:
The null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]
The test statistic for this hypothesis test is z=-1.15.
The P-value for this hypothesis test is P-value=0.124.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that less than 10 percent of the test results are wrong.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.1\\\\H_a:\pi<0.1[/tex]
The significance level is 0.05.
The sample has a size n=317.
The sample proportion is p=0.079.
[tex]p=X/n=25/317=0.079[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{317}}\\\\\\ \sigma_p=\sqrt{0.000284}=0.017[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.079-0.1+0.5/317}{0.017}=\dfrac{-0.019}{0.017}=-1.153[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.153)=0.124[/tex]
As the P-value (0.124) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that less than 10 percent of the test results are wrong.
Suppose the ages of multiple birth mothers (4 or more births) are normally distributed with a mean age of 35.5 years and a standard deviation of 7. 5 years What percent of these mothers are between the ages of 32 to 40?................................ What percent of these mothers are less than 30 years old?......................................... What percent of these mothers are more than 38 years old?
Answer:
40.65% of these mothers are between the ages of 32 to 40
23.27% of these mothers are less than 30 years old
37.07% of these mothers are more than 38 years old
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 35.5, \sigma = 7.5[/tex]
What percent of these mothers are between the ages of 32 to 40?
This is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 32.
X = 40
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40 - 35.5}{7.5}[/tex]
[tex]Z = 0.6[/tex]
[tex]Z = 0.6[/tex] has a pvalue of 0.7257
X = 32
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32 - 35.5}{7.5}[/tex]
[tex]Z = -0.47[/tex]
[tex]Z = -0.47[/tex] has a pvalue of 0.3192
0.7257 - 0.3192 = 0.4065
40.65% of these mothers are between the ages of 32 to 40
What percent of these mothers are less than 30 years old?
This is the pvalue of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 35.5}{7.5}[/tex]
[tex]Z = -0.73[/tex]
[tex]Z = -0.73[/tex] has a pvalue of 0.2327
23.27% of these mothers are less than 30 years old
What percent of these mothers are more than 38 years old?
This is 1 subtracted by the pvalue of Z when X = 38.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35.5}{7.5}[/tex]
[tex]Z = 0.33[/tex]
[tex]Z = 0.33[/tex] has a pvalue of 0.6293
1 - 0.6293 = 0.3707
37.07% of these mothers are more than 38 years old
Como podríamos saber cuantos camellos le corresponden a cada hermano en realidad
Answer:
Eldest brother = 18 camels
2nd brother = 12 camels
Youngest brother = 4 camels
Step-by-step explanation:
Question posted:
How could we know how many camels actually correspond to each brother?
It is from "the man who calculated":
The question is incomplete without the background information.
Based on the question, It has to do with sharing an inheritance of 35 camels among 3 brothers.
"The man who calculated", by Malba Tahan.
Since the complete question isn't available, we are going to look at the following question to understand how to do the calculation.
Question:
How can an inheritance of 35 camels be divided among three brothers in such a way that the eldest brother gets half of them, the second one gets 1/3 of the total and the youngest brother gets 1/9 of the total camels?
Solution:
Total number of camels= 35
Eldest brother gets half: 1/2 of 35 gives a fraction and not an whole number
2nd brother = 1/3 of 35 (gives a fraction)
3rd brother = 1/9 of 35 (gives a fraction)
Since we can't have a camel in fraction except in whole number, we would look for the closest number to 35 that would be divided by 2, 3 and 9 respectively without giving a fraction.
Number 36 is the closest number to 35 that satisfies this condition.
1st brother = 1/2 × 36 = 18 camels
2nd brother = 1/3 × 36 = 12 camels
3rd brother = 1/9 × 36 = 4 camels
Now let's add the camels the 3 brother got together = 18 + 12 + 4 = 34 camels
Total camels - amount shared = 35 -34 = 1
Meaning one camel is remaining. The distributor would keep the remaining one as that's the way such distributions could be achieved.