Answer:
7) d)
standard error of the mean of one sample of 'n' observation = 0.20
8) a)
The margin of Error = 0.392
9) d
The 95% of confidence intervals are (8.61 , 9.39)
Step-by-step explanation:
7)
solution:-
The Given data sample size 'n' = 81
Given Population standard deviation 'σ' = 1.8 hours
The standard error of the mean of one sample of 'n' observation is
Standard error (SE)
= [tex]\frac{S.D}{\sqrt{n} }[/tex]
= σ / √n
= [tex]\frac{1.8}{\sqrt{81} } =0.2[/tex]
standard error of the mean of one sample of 'n' observation = 0.20
8)
Solution:-
The Given data sample size 'n' = 81
Given Population standard deviation 'σ' = 1.8 hours
Given the probability is 0.95
The z- score = 1.96 at 0.05 level of significance.
The margin of Error = [tex]\frac{z_{0.95} S.D}{\sqrt{n} }[/tex]
= [tex]\frac{1.96 (S.D)}{\sqrt{n} }[/tex]
= [tex]\frac{1.96 (1.8)}{\sqrt{81} }[/tex]
= 0.392
The margin of Error = 0.392
9)
Solution:-
The 95% of confidence intervals are
[tex](x^{-} - 1.96\frac{S.D}{\sqrt{n} } , x^{-} + 1.96\frac{S.D}{\sqrt{n} } )[/tex]
[tex](9 - 1.96\frac{1.8}{\sqrt{81} } , 9+ 1.96\frac{1.8}{\sqrt{81} } )[/tex]
(9 - 0.392 , (9 + 0.392)
(8.609 , 9.392)
The 95% of confidence intervals are (8.61 , 9.39)
Kirk goes to the gym every 3 days. Deshawn goes to the
gym every 4 days. If they join the gym on the same day,
when is the first day that they'll be at the gym together?
The day when they would meet first time after joining the gym together will be 12.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Kirk goes to the gym every 3 days.
Deshawn goes to the gym every 4 days.
If they join the gym on the same day.
Then the day when they would meet first time after joining the gym together will be
LCM of 4, 3 will be 12.
Then the day will be 12.
More about the Algebra link is given below.
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Final answer:
Kirk and Deshawn will be at the gym together on the 12th day since they joined.
Explanation:
Gym memberships for Kirk and Deshawn occur every 3 days and 4 days respectively. To find the first day they'll be at the gym together, we need to find the lowest common multiple of 3 and 4.
LCM(3, 4) = 12. Therefore, Kirk and Deshawn will be at the gym together on the 12th day since they joined the gym.
Find BC if BC=x+2, AB=2x-6, and AC=17.
Answer:
BC = 9
Step-by-step explanation:
Assuming this is a straight line
AB + BC = AC
2x-6 + x+2 = 17
Combine like terms
3x -4 = 17
Add 4 to each side
3x-4+4 = 17+4
3x = 21
Divide each side by 3
3x/3 =21/3
x =7
We want to find BC
BC =x+2
=7+2
=9
What is the place value of 4 in 4.09
Consider the polynomial p(s) = s2 + bs + c where b and c are real numbers. Show that all the roots of p(s) are both contained in the open left half plane {s : s < 0} if and only if b > 0 and c > 0. Hint: use the quadratic formula.
Answer:
It is shown in the explanation
Step-by-step explanation:
p(s) = s² + bs + c
a = 1
b = b
c = c
We get Δ as follows
Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0 ⇒ b² > 4c ⇔ c > 0
s = (-b + √(b² - 4c))/2(1)
⇒ s₁ = (-b + √(b² - 4c))/2
s₂ = (-b - √(b² - 4c))/2(1)
⇒ s₂ = (-b - √(b² - 4c))/2
We have that -b < 0 ⇔ b > 0
then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0
Answer:
For roots to lie on the left half plane, b ⊃ 0 and c ⊃0
Step-by-step explanation:
From quadratic formula, we have;
x = -b±√(b²-4ac)/2a
From the given expression p(s) = s² + bs + c,
x = s
a = 1
b = b
c = c
The quadratic formula can then be written as;
s = -b±√(b²-4*1*c)/2*1
= -b±√(b²-4c)/2
s₁ = -b+√(b²-4c)/2
s₂ = -b±√(b²-4c)/2
From the equation above,
Sum of root = -b
Product of root = c
If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0
Also, the product root will be positive, c ⊃ 0
Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0
The following gambling game has been proposed, which a player must pay to play. First, a value U is chosen uniformly from the set [0, 10]. Next, a number is chosen according to a Poisson random variable with a parameter U. Letting X be the number chosen, the player receives $X. Find E[X], which is the amount a player should pay to make this a fair game HINT: Use the Law of Total Probability for Expectations, E[X]
Answer:
The player should be required to pay $5 to make this a fair game.
Step-by-step explanation:
U ~ Uniform(0, 10)
E[U] = (0 + 10)/2
= 5
X | U ~ Poisson(U)
E[X | U] = U
By law of total probability for expectations,
E[X] = E[E[X|U]] = E[U] = $5
Therefore the player should be required to pay $5 to make this a fair game.
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
Answer:
Approximately 20,579 units.
When telephone subscribers call from the National Magazine Subscription Company, 18% of the people who answer stay on the line for more than one minute. If 800 people are called in a day, find the probability that a. at least 150 stay on the line for more than one minute. (Use normal approximation to binomial). b. more than 200 stay on the line. (Use Normal approximation to Binomial).
Answer:
a) 30.50% probability that at least 150 stay on the line for more than one minute.
b) 0% probability that more than 200 stay on the line for more than one minute.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 800, p = 0.18[/tex]
So
[tex]\mu = E(X) = np = 800*0.18 = 144[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.18*0.82} = 10.87[/tex]
a. at least 150 stay on the line for more than one minute.
Using continuity correction, [tex]P(X \geq 150 - 0.5) = P(X \geq 149.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 149.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{149.4 - 144}{10.87}[/tex]
[tex]Z = 0.51[/tex]
[tex]Z = 0.51[/tex] has a pvalue of 0.6950
1 - 0.6950 = 0.3050
30.50% probability that at least 150 stay on the line for more than one minute.
b. more than 200 stay on the line.
Using continuity correction, [tex]P(X \geq 200 + 0.5) = P(X \geq 200.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 200.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200.5 - 144}{10.87}[/tex]
[tex]Z = 5.2[/tex]
[tex]Z = 5.2[/tex] has a pvalue of 1
1 - 1 = 0
0% probability that more than 200 stay on the line for more than one minute.
a box of cookies contain 12 chocolate chip cookies, 6 peanut butter cookies, and 6 sugar cookies, what is the probability of randomly selecting a chocolate chip cookie, eating it, and then randomly selecting a sugar cookie?
The probability of first selecting a chocolate chip cookie and then selecting a sugar cookie from a box containing 24 cookies in total is 6/46 or approximately 0.1304.
The question refers to calculating the probability of selecting cookies of different flavors one after the other without replacement from a box. To begin with, we must find the probability of selecting a chocolate chip cookie followed by the probability of selecting a sugar cookie after one chocolate chip cookie has been removed.
Firstly, the total count of cookies is 12 chocolate chip + 6 peanut butter + 6 sugar cookies = 24 cookies. The probability (P) of selecting a chocolate chip cookie first is P(chocolate chip) = 12/24 = 1/2. After eating the chocolate chip cookie, there are 23 cookies left and the probability of then selecting a sugar cookie is P(sugar) = 6/23 since there are 6 sugar cookies left out of the remaining 23 cookies.
Since these events are sequential without replacement, we can find the combined probability of both events by multiplying the probabilities of each event. Thus, the combined probability is P(chocolate chip then sugar) = P(chocolate chip) *P(sugar) = (1/2) * (6/23) = 6/46.
The combined probability of first selecting a chocolate chip cookie and then selecting a sugar cookie is therefore 6/46 or about 0.1304.
What is your favorite color? A larger survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of n = 75 college students were surveyed and x = 19 of them said that blue is their favorite color. Does this information imply that the proportion of college students who prefer blue differs from that of the general population? Use ???? = 0.05.
Answer:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
X=19 represent the students said that blue is their favorite color
[tex]\hat p=\frac{19}{75}=0.253[/tex] estimated proportion of students said that blue is their favorite color
[tex]p_o=0.24[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is different from 0.24.:
Null hypothesis:[tex]p=0.24[/tex]
Alternative hypothesis:[tex]p \neq 0.24[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Answer:
0.792
Step-by-step explanation:
i need this answered asap
It's a parallelogram, opposite sides congruent.
6x - 7 = 2x + 9
4x = 16
x = 4
12 = y + 3
9 = y
Answer: x=4, y=9
Answer:
x = 4 and y = 9
Step-by-step explanation:
This is a parallelogram, which we can tell because of the arrows. Basically, opposite sides are parallel. By definition, then, opposite sides of this polygon are equal: LM = ON and LO = MN. That means we can set the various expressions equal to each other:
LM = ON ⇒ 6x - 7 = 2x + 9 ⇒ 4x = 16 ⇒ x = 4
LO = MN ⇒ 12 = y + 3 ⇒ y = 9
Thus, x = 4 and y = 9.
Hope this helps!
A simple random sample of size nequals10 is obtained from a population with muequals63 and sigmaequals18. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x overbar.
Answer:
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem
The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.
If it is:
[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]
The sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.
please help????
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In a bag of candy, there are 2 cinnamon, 1 butterscotch, and 2 peppermints. What is the probability of randomly selecting a peppermint?
Answer:
2/5
Step-by-step explanation:
The total number of candies are 2+1+2 = 5 candies
P (peppermint) = number of peppermints/total
=2/5
Answer:
2/5
Step-by-step explanation:
The probability is 2/5.There are five in all and two peppermint.Put it as a fraction and you get 2/5.
Find the absolute value.
|-89= 0
please help thank you
the answer is 89
Step-by-step explanation:
it does not matter if the number is negative the absolute value is the number inside the lines
Answer:
The absolute value of this one is 89. Because for example: |-3|=3 because any number is in that sign || the number will turn to positive. For example, If it is |-3| it will turn to 3
5(y+4)=6y need help in this math is for my son
Answer:
y =20
Step-by-step explanation:
5(y+4)=6y
Distribute
5y +20 = 6y
Subtract 5y from each side
5y-5y+20=6y-5y
20 =y
Answer:
solution
5y+20=6y
5y-6y=20
-y=20
Housing prices in Athens have been researched extensively by faculty at UGA. The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
(a) What proportion of housing prices in Athens are less than $234,000? (3 decimal places)
(b) A realtor takes a random sample of 134 houses in Athens. Determine the probability the average selling price is greater than $239,000? (3 decimal places)
(c) A realtor in Asheville, NC wants to estimate the mean housing price of houses in Asheville. The realtor believes the distribution of housing prices in Asheville is similar to those in Athens.
If this realtor takes a random sample of 134 homes in Asheville, what is the standard error of the estimate? (3 decimal places)
How many homes in Asheville should the realtor sample to be 98% confident the estimate is within $500 of the true mean price? Use the critical value to exactly 3 decimal places.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes.
Step-by-step explanation:
The current thinking is that housing prices follow an approximately normal model with mean $238,000 and standard deviation $5,041.
a) We need to know the proportion of housing prices in Athens that are less than $234,000. We can calculate this from the z-score for the population distribution.
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{234,000-238,000}{5,041}=\dfrac{-4,000}{5.041}=-0.793\\\\\\ P(x<234,000)=P(z<-0.793)=0.214[/tex]
The proportion of housing prices in Athens that are less than $234,000 is 0.214.
b) Now, a sample is taken. The size of the sample is n=134.
We have to calculate the probability that the average selling price is greater than $239,000.
In this case, we have to use the standard error of the sampling distribution to calculate the z-score:
[tex]z=\dfrac{\bar x-\mu}{\sigma/\sqrt{n}}=\dfrac{239,000-238,000}{5,041/\sqrt{134}}=\dfrac{1,000}{435.476}= 2.296 \\\\\\P(\bar x>239,000)=P(z>2.296)=0.011[/tex]
The probability that the average selling price is greater than $239,000 is 0.011.
c) We have another sample taken from a distribution with the same parameters.
We have to calculate the sample size so that the margin of error for a 98% confidence interval is $500.
The expression for the margin of error of the confidence interval is:
[tex]E=z\cdot \sigma/\sqrt{n}[/tex]
We can isolate n from the margin of error equation as:
[tex]E=z\cdot \sigma/\sqrt{n}\\\\\sqrt{n}=\dfrac{z\cdot \sigma}{E}\\\\n=(\dfrac{z\cdot \sigma}{E})^2[/tex]
We have to look for the critical value of z for a 98% CI. This value is z=2.327.
Now we can calculate the minimum value for n to achieve the desired precision for the interval:
[tex]n=(\dfrac{z\cdot \sigma}{E})^2\\\\\\n=(\dfrac{2.327*5,041}{500})^2= 23.461 ^2=550.410\approx551[/tex]
The realtor should sample at least 551 homes.
Answer:
a) 0.214 or 21.4%
b) P=0.011
c) The realtor should sample at least 551 homes
Step-by-step explanation:
Three forces act on a hook. Determine the magnitude of the resultant of the force.
Use Hooke's law... (just kidding)
Break down each force vector into horizontal and vertical components.
[tex]\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y[/tex]
The resultant force is the sum of these vectors,
[tex]\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y[/tex]
and has magnitude
[tex]|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N[/tex]
The closest answer is D.
To determine the magnitude of the resultant force acting on a hook when three forces are applied, you can use vector addition. If you have the information of the forces and the angles between them, you can calculate the resultant force using trigonometric functions.
Explanation:To determine the magnitude of the resultant force when three forces act on a hook, you must realize that forces are vector quantities. This means that they have both a magnitude (how much force is being applied) and a direction (the direction the force is being applied in).
If the forces are concurrent (i.e., they act at the same point), one usually uses the parallelogram law or the triangle rule to find the resultant force. You can add two forces to create a resultant, then add the third force to that resultant to find the total resultant. If the forces and the angles between them are known, you can use trigonometric functions to calculate the resultant force.
For instance, if the three forces are F1, F2, and F3, and the angles between them are θ1, θ2, and θ3, the resultant force R can be found using the following equation:
R = √[ (F1 + F2cosθ2 + F3cosθ3)^2 + (F2sinθ2 + F3sinθ3)^2 ]
This equation will give the magnitude of the resultant force. Please note that to use this equation, you must have enough information about the forces and the angles between them.
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does this answer and help me with all subjects?
Two similar cylinders have surface areas of 24 cm2 and 54 cm2. The volume of the smaller cylinder is 16 cm2.
What is the volume of the larger cylinder?
Given:
Given that two similar cylinder have surface areas 24π cm² and 54π cm².
The volume of the smaller cylinder is 16π cm³
We need to determine the volume of the larger cylinder.
Volume of the larger cylinder:
The ratio of the two similar cylinders having surface area of 24π cm² and 54π cm², we have;
[tex]\frac{24 \pi}{54 \ pi}=\frac{4}{9}[/tex]
[tex]=\frac{2^2}{3^2}[/tex]
Thus, the ratio of the surface area of the two cylinders is [tex]\frac{2^2}{3^2}[/tex]
The volume of the larger cylinder is given by
[tex]\frac{2^2}{3^2}\times \frac{2}{3}=\frac{16 \pi }{x}[/tex]
where x represents the volume of the larger cylinder.
Simplifying, we get;
[tex]\frac{2^3}{3^3}=\frac{16 \pi }{x}[/tex]
[tex]\frac{8}{27}=\frac{16 \pi }{x}[/tex]
Cross multiplying, we get;
[tex]8x=16 \pi \times 27[/tex]
[tex]8x=432 \pi[/tex]
[tex]x=54 \pi \ cm^3[/tex]
Thus, the volume of the larger cylinder is 54π cm³
Answer:
54π cm³
Step-by-step explanation:
Toby skated from his house to the beach at a constant speed of 8 88 kilometers per hour, and then skated from the beach to the park at a constant speed of 7 77 kilometers per hour. The total distance Toby skated was 20 2020 kilometers, and it took him twice as long to get to the park.
Answer:
8b+7p=20
p=2b
Step-by-step explanation:
You're welcome. Thou shall complete thou work without any trouble.
A circle is centered on point B. Points A, C and D lie on it's circumference. If ADC measures 20 degrees, what does ABC measure
The Answer is : ABC = 40
Find the product of 0.032 and -1.9
Answer:
i think it's -0.0608
Step-by-step explanation:
"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 19 of the participants. (a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.) ( .138 Incorrect: Your answer is incorrect. , .503 Incorrect: Your answer is incorrect. )
Answer:
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
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 = 51, \pi = \frac{19}{51} = 0.373[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 - 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.24[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 + 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.506[/tex]
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
What is the relationship between x and y
Given:
Given that the table with values of x and y.
We need to determine the relationship between x and y.
Slope:
The slope of the relation can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (2,11) and (4,9), we get;
[tex]m=\frac{9-11}{4-2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Thus, the slope of the relation is m = -1.
y - intercept:
The y - intercept of the relation is the value of y when x = 0.
Hence, from the table, it is obvious that when x = 0, the value of y is 13.
Thus, the y - intercept of the relation is b = 13.
Relationship between x and y:
The relationship between x and y can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting m = -1 and y =13, we get;
[tex]y=-x+13[/tex]
Thus, the relationship between x and y is [tex]y=-x+13[/tex]
78.3 + -17 evaluate the expression
Answer:
it is 61.3
Step-by-step explanation:
Help me plz
Solve for X
20 points*
Answer:
x = 4
Step-by-step explanation:
14x - 15 + 139 = 180
(Alternate & Supplementary angles)
14x = 56
x = 4
After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favored firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To do this they test the hypotheses H0: p = 0.50 versus Ha: p > 0.50.
(A) What is the P-value for this hypothesis test?
The P-value for this hypothesis test is 0.0228.
Explanation:To find the P-value for this hypothesis test, we need to calculate the proportion of alumni who favored firing the coach in the sample. Out of 100 alumni, 64 were in favor. So, the sample proportion is 64/100 = 0.64.
Now, we need to calculate the test statistic, which follows a normal distribution. The formula for the test statistic is: z = (p' - p) / sqrt(p * (1-p) / n), where p' is the sample proportion, p is the claimed proportion under the null hypothesis, and n is the sample size.
Plugging in the values, we get: z = (0.64 - 0.50) / sqrt(0.50 * (1-0.50) / 100) = 2.00
The P-value is the probability of observing a test statistic as extreme as 2.00, assuming the null hypothesis is true. We can look up this probability in a standard normal distribution table or use a statistical software. In this case, the P-value is 0.0228.
A rectangular box is to have a square base and a volume of 72 ft3. If the material for the base costs $0.62/ft2, the material for the sides costs $0.15/ft2, and the material for the top costs $0.18/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
a. length
b. width
c. height
Answer:
a. length = 0.7211 ft
b. width = 0.7211 ft
c. height = 140.3846 ft
Step-by-step explanation:
This is an optimiztion with restriction problem.
We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.
As the cost for the sides is constant, we know that length and width are equal.
Then, we can express the volume as:
[tex]V=x\cdot y\cdot z=x^2z=73[/tex]
being x: length and z: height
We can express the height in function of the length as:
[tex]x^2z=73\\\\z=73x^{-2}[/tex]
Then, the cost of the box can be expressed as:
[tex]C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}[/tex]
To optimize C, we derive and equal to zero
[tex]\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211[/tex]
The height z is then
[tex]z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846[/tex]
12x+7<-11 and 5x-8>= 40
Answer:
no solution
Step-by-step explanation:
First inequality:
12x < -18 . . . . subtract 7
x < -18/12 . . . divide by 12
x < -1.5 . . . . . . write as decimal
__
Second inequality:
5x -8 ≥ 40
5x ≥ 48 . . . . . . add 8
x ≥ 9.6 . . . . . . . divide by 5
__
There are no solutions to this pair of inequalities. No value of x can be both less than -1.5 and greater than 9.6.
how much water does it take to completely fill a pool that is 50m long 25m wide and 2.5m deep
Answer:
[tex]3,125[/tex]
Step-by-step explanation:
If you want to fill a pool, you will use the formula for finding the volume:
[tex]v=l*w*h[/tex]
In this case, height being depth:
[tex]v=l*w*d[/tex]
Insert values
[tex]v=50*25*2.5[/tex]
Simplify
[tex]v=1,250*2.5\\v=3,125[/tex]
You would need a lot of water.
Answer:
3125000 liter
Step-by-step explanation:
hope i helped
if i can be brainliest that would be great