Answer:
A 90% confidence interval of the true mean is [$119.86, $123.34].
Step-by-step explanation:
We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.
Also, the standard deviation of the population was $6.36.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean amount of money spent on textbooks = $121.60
[tex]\sigma[/tex] = population standard deviation = $6.36
n = sample of students = 36
[tex]\mu[/tex] = population mean
Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] , [tex]121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }[/tex] ]
= [$119.86, $123.34]
Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. 0.989 0.978 0.927 0.167 0.530
Answer:
0.989
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they find a job in their chosen field within a year after graduation, or they do not. The probability of a graduate finding a job is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A study conducted at a certain college shows that "53%" of the school's graduates find a job in their chosen field within a year after graduation.
This means that [tex]p = 0.53[/tex]
6 randomly selected graduates
This means that [tex]n = 6[/tex]
Probability that at least one finds a job in his or her chosen field within a year of graduating:
Either none find a job, or at least one does. The sum of the probabilities of these outcomes is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.53)^{0}.(0.47)^{6} = 0.011[/tex]
So
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.011 = 0.989[/tex]
UTGENT! I really need help, can anyone help me?
Answer:
x = 3.6
Step-by-step explanation:
By the Postulate of intersecting chords inside a circle.
[tex]x \times 5 = 3 \times 6 \\ 5x = 18 \\ x = \frac{18}{5} \\ x = 3.6 \\ [/tex]
Timmy writes the equation f(x) - *x-1. He then doubles both of the terms on the right side to create the equation g(x) =
2x - 2. How does the graph of g(x) compare to the graph of f(x)?
The line of g(x) is steeper and has a higher y-intercept.
The line of g(x) is less steep and has a lower y-intercept.
The line of g(x) is steeper and has a lower y-intercept.
The line of g(x) is less steep and has a higher y-intercept.
Answer:
The line of g(x) is steeper and has a lower y-intercept.
Step-by-step explanation:
Doubling the function expands it vertically by a factor of 2. Everything is twice as far from the x-axis as it was. The line becomes steeper, and the y-intercept moves twice as far away. It was at -1, now is lower, at -2.
The line of g(x) is steeper and has a lower y-intercept.
What is the total surface area of the square pyramid 8in 5in
Answer:
A≈166.45 in^2
Step-by-step explanation:
A=a^2+2a√(a2/4+h^2)
a = base = 8 in
h = height = 5 in
A = 8^2+16√(8^2/4+5^2) = 166.449... in^2
224
Step-by-step explanation:
because my teacher said it was right
Write the Algebraic expression for each of the following.
1. Sum of 35 and 65
2. Take away 14 from y
3. Subtract 3 from the product of 6 and s
4. 10 times the sum of x and 8 5. Take away p from 6
Step-by-step explanation:
1. 35 + 65
2. y - 14
3. (6 x s) - 3
4. 10(x+8.5).. 6-p
plz help me divide and simplify
Answer:
Step-by-step explanation:
If you were having a party and you expect each guest to eat 0.25 pounds of meat, how many pounds of meat should you buy if you expect 30 guest?
Answer:
7.5 pounds
Step-by-step explanation:
30/4=7.5 :)
In march 2011, the pew research center conducted a survey of us adults to determine whether higher education provides students with a good value compared to the cost. pollsters randomly selected 2,142 adults ages 18 and older living in the continental us. a total of 1,052 interviews were completed with respondents contacted by landline telephone and 1,090 with those contacted on their cellular phone. which feature of the sampling plan makes the sample representative of the population?
Answer:
The feature that makes the sample representative of the population is the choice of the contact mode (telephone landline or cellular phone line) with proportions representative of the ages of the subjects to be represented.
Step-by-step explanation:
The feature that makes the sample representative of the population is the choice of the contact mode (telephone landline or cellular phone line) with proportions representative of the ages of the subjects to be represented.
Older people tend to manage with landline phones, while younger people tend to have no landline phones but cell phone. Both groups must be proportionally represented to be representative of an adult population (18 years or older).
Homer and other Greek writers used a literary technique called in medias res. Choose the item below that best
describes what that Latin phrase means and how it works out in a piece of literature.
It means to intercede between two entities, and Homer uses it in the section where Jove and Neptune are talking about what to do
about the Phaeacians having helped Ulysses.
It means in the middle of a race, and Homer's use of it is obvious when Ulysses and his crew are rowing hard to get away from
Polyphemus.
It means in the center of a kingdom, and it's the technique Homer uses when Ulysses has to travel into the city looking for King
Alcinous's palace.
It means in the middle of things, and Homer uses it in the Odyssey at the beginning of the epic because the story starts after the
Trojan War but before Ulysses gets back home.
Answer:
It means in the middle of things, and Homer uses it in the Odyssey at the beginning of the epic because the story starts after the Trojan War but before Ulysses gets back home.
Explanation:
Media res is a Latin phrase that means a situation where the narration starts in the middle of the story. In simple words, it means when a speaker talks about a story, starting with the middle of the plot but before the ending.
Likewise, Homer used this technique in his epic narrative story The Odyssey when he starts the story after the Trojan War and in the middle of the journey bur before the culmination of the story. Media res allows the middle of the plot to be the starting point and then gradually go back and forth in the narration between the past and the current/ situation.
Thus, the correct answer is the last or fourth option.
if cos theta < 0 and cot theta > 0, then the terminal point determined by theta is in:
A. Quadrant 1
B. Quadrant 3
C. Quadrant 4
D. Quadrant 2
please help me !
Answer:
If cosine theta < 0 and cotangent theta > 0, then the terminal point determined by theta is in: quadrant 3.
Step-by-step explanation:
hope this helps you :) my answer is the Step-by-step explanation: and the answer :)
Considering the signals of the sine and the cosine of the trigonometric function, it is found that it's quadrant is given by:
B. Quadrant 3
What are the signals of the sine and the cosine in each quadrant?Q1: cos > 0, sin > 0.Q2: cos < 0, sin > 0.Q3: cos < 0, sin <0.Q4: cos > 0, sin < 0.In this problem, we have that the cosine is negative, and the cotangent is positive. Cotangent is cosine divided by sine, hence if it is positive, both cosine and sine have the same signal, since cos < 0, sine is negative, they are in third quadrant and option B is correct.
More can be learned about the quadrants of trigonometric functions at https://brainly.com/question/24551149
#SPJ2
hey guys please help
Answer:
[tex]7.98 \:m[/tex]
Step-by-step explanation:
Area of a triangle is base times height divided by 2.
[tex]A= \frac{bh}{2}[/tex]
[tex]69.6= \frac{b \times 17.45}{2}[/tex]
[tex]69.6 \times 2= b \times 17.45[/tex]
[tex]139.2=b \times 17.45[/tex]
[tex]\frac{17.45b}{17.45}=\frac{139.2}{17.45}[/tex]
[tex]b=\frac{2784}{349}[/tex]
[tex]b=7.97707[/tex]
The appropriate unit is meters.
Answer:
7.98 m
Step-by-step explanation:
Please answer this correctly
Answer:
There are 8 sections and 5 of them are less than 7 so the answer is 5/8 = 62.50%.
Answer:
62.5 percent
Step-by-step explanation:
there are a total of 8 options (2,3,4,5,6,7,8,9) the spinner could land on. 5 of these options are less than 7 (6,5,4,3,2)
5/8 is also 62.5 percent
A man wants to set up a 529 college savings account for his granddaughter. How much would he need to deposit each year into the account in order to have $50,000 saved up for when she goes to college in 17 years, assuming the account earns a 5% return?
Answer:
1937.98
Step-by-step explanation:
In the given question, to find the value to be added per year we will use the formula
P= A. r/n/ (1 +r/n)ⁿ - 1
Here A = 50,000
r (rate of interest) = 5 % or 0.05.
n = 1
t = 17
P = value deposit per year
therefore, P = (50,000 X 0.05)/ (1 +0.05)¹⁷ - 1
P = 2500 / 2.29- 1
= 1937.98 $.
therefore, person has to deposit 1937.98 $ per month.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
C =81.64 cm
Step-by-step explanation:
The circumference is given by
C = 2* pi *r
The radius is 13
C = 2 * 3.14 * 13
C =81.64 cm
Answer:
[tex]= 81.64cm \\ [/tex]
Step-by-step explanation:
[tex]c = 2\pi \: r \\ = 2 \times 3.14 \times 13 \\ = 81.64cm[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Translate the words into math symbols. The difference of nine and a number is three. What steps would you take to translate the statement? Check all that apply
Answer:
9-x=3
x=9-3=6
x=6
9-6=3
Answer:
B,C,D,F
Step-by-step explanation:
i took the test and i got it right!!!!
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer: a) base = 1 ft b) height = 4 ft
Step-by-step explanation:
Set this up as a right triangle where base = x, height = 2x + 2, and hypotenuse (length of the ladder) = 13
Use Pythagorean Theorem to create a quadratic equation, factor, then apply the Zero Product Property to solve for x.
(x)² + (2x + 2)² = 13²
x² + 4x² + 8x + 4 = 169
5x² + 8x - 165 = 0
(5x + 13) (x - 1) = 0
x = -13/5 x = 1
We know that distance cannot be negative so disregard x = -13/5.
The only valid answer is x = 1
base = x --> x = 1
height = 2x + 2 --> 2(1) + 2 = 4
Find f(x) - g(x) when f(x) = 2x^2 - 4x g(x) = x^2 + 6x
3x^2
x^2 + 2x
x^2 - 10x
3x^2 + 2x
Answer:
x^2 - 10x
Step-by-step explanation:
2x^2 - 4x - x^2 +6x
You subtract x^2 from 2x^2 and you get x^2
Then you add 6x and 4x together and get 10x
So then you have x^2 - 10x
(plus I took the test and this was the correct answer.)
Two con terminal angles 3pi/4 negative and positive answer in radians
Answer:
Negative Coterminal: -5π/4
Positive Coterminal: 11π/4
Step-by-step explanation:
The easiest way to find specific (not infinite) coterminal values is to ±2π. When you subtract 2π, you will get a negative coterminal. When you add 2π, you will get a positive coterminal. Keep in mind though that a tan∅ or cot∅ only needs ±π, not ±2π.
Given that TU=8x+11 and UV=12x−1, what are x, TU, UV, and TV?
Answer:
x = 3TU = UV = 35TV = 70Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached.
From the diagram, it can be seen that point U is the midpoint of T and V. This means that TU = UV
Given TU=8x+11 and UV=12x−1
8x+11 = 12x -1
8x-12x = -1-11
-4x = -12
x = 3
Since TU = 8x+11
TU = 8(3)+11
TU = 24+11
TU = 35
Also UV = 12x-1
UV = 12(3)-1
UV = 36- 1
UV = 35
TV = TU+UV
TV = 35+35
TV = 70
Which of the following is the graph of y = negative StartRoot x EndRoot + 1?
Answer:
see below
Step-by-step explanation:
y = -sqrt(x) +1
We know that the domain is from 0 to infinity
The range is from 1 to negative infinity
Answer:
b
Step-by-step explanation:
e2020
Help plssss
Stephn says that the numbers 38 and 40 are relatively prime. explain why he is incorrect in making this statement.
Answer:
When you say that two numbers are relatively prime, it means that both numbers do not have a common factor except 1. Stephen is incorrect because 38 and 40 are both multiples of 2.
Answer:
Prime numbers are number that has its factors to be 1 and itself
38 and 40 are not prime because they have more than one factor
38 = { 1 , 2 , 19 , 38} and
40 = { 1 , 2 , 4 , 5 , 8 , 10 , 20 , 40 }
This make his statement incorrect.
Hope this helps.
f(x)
9 - 4x
8x - 1
INVERSE??
Answer:
(x+9)/(8x+4)
Step-by-step explanation:
What are the domain and range of f(x) = 2|x – 4|?
Answer:
Domain: All real numbers or (negative infinity, positive infinity)
Range: [0, positive infinity)
Step-by-step explanation:
Domain; Since all values of x would work for this equation, simply any number could be plugged in. That means the domain would stretch to infinity because there are an infinite amount of inputs and outputs
Range; Even though we have an infinite amount of domain, when we plug in a negative x, anything inside the absolute value will turn positive. Therefore, no output (y) value will ever go below zero, and we have [0, positive infinity).
People were surveyed worldwide, being asked the question "How important is acquiring wealth to you?" of 1500 respondents in country A, 1185 said that it was of more than average importance. In country B, of 1302 respondents, 613 said it was of more than average importance.
1) (Round to three decimal places as needed):
a. The sample proportions for country A are: ___
b. The sample proportions for country B are: ___
2) What is the confidence interval for country A? Select the correct choice below and, if necessary, fill in the answer boxes within your choice.
a. The 90% confidence interval for country A is (__%, ___%) [Round to one decimal place as needed.]
b. The conditions for constructing a confidence interval are not satisfied.
3) Compare to the confidence interval for country B. Choose the correct answer below.
a. It is not possible to make a comparaison because the conditions for creating a confidence interval are not satisfied.
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
c. It appears that the proportion of adults who feel this way in country A is about the same as those in country B.
d. it appears that the proportion of adults who feel this way in country B is more than those in country A.
Answer:
1) A = 0.79
B = 0.4708
2) CI = (0.7728, 0.8072)
3) CI = (0.4481, 0.4935)
b. It appears that the proportion of adults who feel this way in country A is more than those in country B.
Step-by-step explanation:
1) Sample proportions for both Population A and B
For country A:
Sample size,n = 1500
Sample proportion = [tex] \frac{1185}{1500} = 0.79 [/tex]
For Country B:
Sample size,n = 1302
Sample proportion = [tex] \frac{613}{1302} = 0.4708 [/tex]
2) Confidence interval for country A:
Given:
Mean,x = 1185
Sample size = 1500
Sample proportion, p = 0.79
q = 1 - 0.79 = 0.21
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.79 - 1.64}{\sqrt{(0.79 * 0.21)/1500}}, \frac{0.79 + 1.64}{\sqrt{(0.79 * 0.21)/1500}} [/tex]
[tex] CI = (0.7728, 0.8072) [/tex]
3) Confidence interval for country A:
Given:
Mean,x = 613
Sample size = 1302
Sample proportion, p = 0.4708
q = 1 - 0.4708 = 0.5292
Using z table,
90% confidence interval, [tex] Z _\alpha /2 = 1.64 [/tex]
Confidence interval, CI:
[tex] \frac{p +/- Z_\alpha_/2}{\sqrt{(p * q)/n}} [/tex]
[tex] = \frac{0.4708 - 1.64}{\sqrt{(0.4708 * 0.5292)/1302}}, \frac{0.4708 + 1.64}{\sqrt{(0.4708 * 0.5295)/1302}} [/tex]
[tex] CI = (0.4481, 0.4935) [/tex]
From both confidence interval, we could see that that the proportion of adults who feel this way in country A is more than those in country B.
Option B is correct.
Sally makes 23,200 per year how much do Sally make per week.
Answer:
446.153846154 per week
Step-by-step explanation:
What is the rule for the geometric sequence ?
Answer:
Option 3 or 4 is correct depending on the first term and common ratio
aₙ= a₁rⁿ⁻¹
Option 3 in case the first term is 1/2 and common ratio is 972
Option 4 in case the first term is 972 and common ratio is 1/2
Answer:
its D & the next is 7.594
Step-by-step explanation:
just got it on edge2020
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly se
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?
Answer:
P( X' ∩ Y' ) = 0.205
Step-by-step explanation:
Let X is the event that the customer insures more than one car.
Let X' is the event that the customer insures exactly one car.
Let Y is the event that customer insures a sport car.
Let Y' is the event that customer insures not a sport car.
From the given information we have
70% of customers insure more than one car.
P(X) = 0.70
20% of customers insure a sports car.
P(Y) = 0.20
Of those customers who insure more than one car, 15% insure a sports car.
P(Y | X) = 0.15
We want to find out the probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
P( X' ∩ Y' ) = ?
Which can be found by
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
From the rules of probability we know that,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y ) (Additive Law)
First, we have to find out P( X ∩ Y )
From the rules of probability we know that,
P( X ∩ Y ) = P(Y | X) × P(X) (Multiplicative law)
P( X ∩ Y ) = 0.15 × 0.70
P( X ∩ Y ) = 0.105
So,
P( X ∪ Y ) = P(X) + P(Y) - P( X ∩ Y )
P( X ∪ Y ) = 0.70 + 0.20 - 0.105
P( X ∪ Y ) = 0.795
Finally,
P( X' ∩ Y' ) = 1 - P( X ∪ Y )
P( X' ∩ Y' ) = 1 - 0.795
P( X' ∩ Y' ) = 0.205
Therefore, there is 0.205 probability that a randomly selected customer insures exactly one car, and that car is not a sports car.
A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.070.07. If 492492 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.030.03?
Answer:
The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:
[tex]\mu_{\hat p}=p=0.07\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.07(1-0.07)}{492}}=0.012[/tex]
Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:
[tex]P(|\hat p-p|>0.03)=P(|\frac{\hat p-p}{\sigma_{\hat p}}|>\frac{0.03}{0.012})[/tex]
[tex]=P(|Z|>2.61)\\\\=1-P(|Z|\leq 2.61)\\\\=1-P(-2.61\leq Z\leq 2.61)\\\\=1-[P(Z\leq 2.61)-P(Z\leq -2.61)]\\\\=1-0.9955+0.0045\\\\=0.0090[/tex]
Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
A ladder leans against the side of a house. The angle of elevation of the ladder is 66 degrees, and the top of the ladder is 15 ft above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answer:
x ≈ 6.7 ft
Step-by-step explanation:
We are going to use tan∅ to find our answer:
tan66° = 15/x
xtan66° = 15
x = 15/tan66°
x = 6.67843 ft
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
38 units
Step-by-step explanation:
We can find the perimeter of the shaded figure be finding out the number of unit lengths we have along the boundary of the given figure.
Thus, see attachment below for the number of units of each length of the figure that we have counted.
The perimeter of the figure = sum of all the lengths = 7 + 7 + 10 + 2 + 2 + 6 + 2 + 2 = 38
Perimeter of the shaded figure = 38 units