Answer:
The 95% confidence interval for the population proportion is (0.778, 0.884).
Step-by-step explanation:
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.831.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.831*0.169}{195}}\\\\\\ \sigma_p=\sqrt{0.00072}=0.027[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.027=0.053[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sisgma_p = 0.831-0.053=0.778\\\\UL=p+z \cdot \sisgma_p = 0.831+0.053=0.884[/tex]
The 95% confidence interval for the population proportion is (0.778, 0.884).
10 = - 9 - x
Show me all the steps
Step-by-step explanation:
10= - 9 - X
- x - 9 = 10
-× = 10 + 19
-× =19
× = -19
Anthony is informed that there is a 10% chance that he will be hired by the prestigious Acme corporation. He believes that, given his outstanding skill as a golfer, once he is hired there is an 80% chance that he will earn a spot on the celebrated Acme Corporation golf team. Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
Answer:
8% probability that Anthony will soon be playing on the Acme golf team
Step-by-step explanation:
We have these following probabilities:
10% probability that he is hired by the corporation.
If he is hired by the corporation, an 80% probability that he will earn a spot on the golf team.
Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
80% of 10%
So
P = 0.8*0.1 = 0.08
8% probability that Anthony will soon be playing on the Acme golf team
A college official conducted a survey to estimate the proportion of students currently living in dormitories about their preference for single rooms, double rooms, or multiple (more than two people) rooms in the dormitories on campus. Which of the following does not a ect the college official's ability to generalize the survey results to all dormitory students?(a) Five thousand students live in dormitories on campus. A simple randomsample of only 500 were sent the survey.(b) The survey was sent only to first year students.(c) Of the 500 students who were sent the survey, only 160 responded.(d) All of the above present a problem for generalizing the results.
Answer:
b
Step-by-step explanation:
all the options reflect the college's official's ability ot generalize the survey results except b. Option b represents a particular group of the total population.
The ability to generalize survey results is compromised when the survey is biased, the sample size is inadequate relative to the population, or the response rate is low. Each of the listed issues affects the generalizability of the survey outcome, with specific concerns in terms of sample representativeness and potential biases.
Explanation:The question concerns the ability to generalize survey results to a larger population of dormitory students. Options a, b, and c each presents issues related to sample representativeness and survey methodology, which can affect the college official's ability to generalize findings.
Option a suggests that the sample may be too small relative to the total population. However, a random sample of 500 can theoretically represent 5,000 students well if selected appropriately. Option b indicates a selection bias because only first-year students were surveyed, which does not reflect the entirety of dormitory residents.
Option c points to a low response rate, which can result in nonresponse bias if the 160 respondents have different preferences than those who did not respond.
John took all his money from his savings account. He spent $52 on a radio and 1/2 of what was left on presents for his friends, Of the money remaining, John put 4/13 into checking account and the last remaining $180 was left to charity. How much money did John originally have in his savings account?
Answer:
John had $572 in his savings account.
Step-by-step explanation:
Let the total amount John took from his savings account be T.
He spent $52. That means he has $(T - 52) left.
He then spent 1/2 of what was left on presents for his friends. That is:
[tex]\frac{1}{2} * (T - 52) = \frac{T - 52}{2}[/tex]
Which means he is left with another half of what was left, that is, [tex]\frac{T - 52}{2}[/tex]
Of the money remaining, John put 4/13 into checking account.
This means that he is left with 9/13 of [tex]\frac{T - 52}{2}[/tex].
We are told that this is equivalent to the last remaining $180 that John left to charity.
=> [tex]\frac{9}{13} * \frac{T - 52}{2} = 108[/tex]
Hence:
[tex]\frac{9(T - 52)}{13 * 2} = 180\\\\9(T - 52) = 180 * 13 * 2\\\\9(T - 52) = 4680\\\\T - 52 = \frac{4680}{9} = 520\\\\[/tex]
=> T = 520 + 52 = $572
Hence, John took $572 from his savings account. Since this is all he had in his savings account, John had $572 in his savings account.
Working backward, we determined that John originally had $572 in his savings account before spending on the radio, presents, putting money into his checking account, and giving to charity.
Explanation:To solve this mathematics problem, we need to work backward from the information provided. John spent $52 on a radio and then spent half of the remaining amount on presents. After that, he put 4/13 of the remaining money into his checking account and then gave $180 to charity. Let's represent the original amount of money John had as x.
After buying the radio, John had x - $52 left. He then spent half on presents, so he had (x - $52)/2 remaining. After putting 4/13 of what was left into his checking, the equation becomes ((x - $52)/2) * (9/13) since 9/13 is the complement of 4/13, which goes into the checking account. This amount equaled the last remaining $180.
The equation to find the original amount x is:
(((x - $52) / 2) * (9/13)) = $180
Now solve for x:
Multiply both sides by 13/9 to get (x - $52) / 2 = $260.Multiply both sides by 2 to get x - $52 = $520.Finally, add $52 to both sides to get x = $572.So, the original amount of money John had was $572.
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The two-way table below describes the practice habits of members of the school band and choir.
Practice Habits of School Musicians
Less than
30 Minutes per Day
38
At Least
30 Minutes per Da
26
12
Band Students
Choir Students
Which statement best describes the relationship between the two variables?
O
O
There is an association because the relative frequencies by row are different.
There is an association because the relative frequencies by row are similar.
There is no association because the relative frequencies by row are different.
There is no association because the relative frequencies by row are similar.
O
Mark this and return
Save and Exit
Next
Answer:
D.
Step-by-step explanation:
i took the quiz
What value of y makes the equation true. y+2.9=11
Answer:
y = 8.1
Step-by-step explanation:
y+2.9=11
Subtract 2.9 from each side
y+2.9-2.9 = 11-2.9
y =8.1
From a point on the ground 47ft from the base of a tree, the angle
of elevation to the top of the tree is 35 degrees. Find the height
of the tree to the nearest foot.
Answer:
33 ft
Step-by-step explanation:
In a diagram of the geometry, you see that the angle of elevation is opposite the triangle leg representing the tree height, and is adjacent to the triangle leg representing distance from the tree.
The tangent ratio relates these lengths to the angle:
Tan = Opposite/Adjacent
Opposite = Adjacent×Tan
tree height = (47 ft)tan(35°) ≈ 33 ft
The height of the tree is about 33 feet.
What is the circumference of a circle with a radius of 56 feet?
feet
(Use 3.14 for Pi.)
Answer:
351.68
Step-by-step explanation:
c = 2πr
c = 2(3.14)(56)
c = 6.28(56)
c = 351.68
Answer:
Step-by-step explanation:
The volume of a CONE-shaped hole is 75pi ft cubed. If the hole is 9 feet deep, what is the radius of the hole?
(1 Point)
Answer:
The radius of hole is 5 feet
Step-by-step explanation:
Depth of conical hole = 9 feet
Let the radius of hole be r
Volume of conical hole =[tex]\frac{1}{3} \pi r^2 h[/tex]
So, Volume of conical hole =[tex]\frac{1}{3} \pi \times r^2 \times 9[/tex]
We are given that volume of a CONE-shaped hole is 75pi ft cubed.
So,[tex]\frac{1}{3} \pi \times r^2 \times 9=75 \pi[/tex]
[tex]\frac{1}{3} \times r^2 \times 9=75[/tex]
[tex]r^2=\frac{75 \times 3}{9}[/tex]
[tex]r=\sqrt{\frac{75 \times 3}{9}}[/tex]
r=5
Hence The radius of hole is 5 feet
According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage or less. A state politician wants to verify this statement for his state. He uses a sample of 500 female workers and finds 42 are paid at the minimum wage or less. Use a 5% significance level to test to test whether that state differs from the nation.
State clearly the null and the alternative hypothesis, the test statistic, the decision rule and the conclusion.
Answer:
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Decision rule
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
Conclusion
The information is not enough to back the claim that state differs from the nation
Step-by-step explanation:
From the question we are told that
The percentage of US female workers paid at the minimum wage or less is [tex]k_o =[/tex] 7% = 0.07
The sample size is [tex]n = 500[/tex]
The number paid minimum wage or less is x = 42
The significance level is [tex]\alpha =[/tex]5% = 0.05
Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as
[tex]\= k = \frac{x}{n}[/tex]
substituting value
[tex]\= k = \frac{42}{500}[/tex]
[tex]\= k = 0.084[/tex]
The Null Hypothesis is [tex]H_o:k_o = 0.07[/tex]
The alternative hypothesis is [tex]H_a :k_o \ne 0.07[/tex]
Generally the test statistics is mathematically evaluated as
[tex]z = \frac{\= k - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }[/tex]
substituting value
[tex]z = \frac{0.084 - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }[/tex]
[tex]z = 1.23[/tex]
Now the Decision rule is stated as
If the test staistics is greater than the critical value of significance level then [tex]H_o[/tex] is accepted else [tex]H_o[/tex] is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
[tex]t_{0.05} = 1.645[/tex]
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
So the conclusion will be
The information is not enough to back the claim that state differs from the nation
-4.0 -y=24
Complete the missing value in the solution to the equation.
8)
Answer:
y=-28
Step-by-step explanation:
add 4 to both sides which gets you -y =28. Then you have to move the negative sign to the other side because y can't end with a negative
Which function's graph has axis of symmetry x = 2?
y = 3x² + 12x+6
y = 3x2 - 6x+12
y=-3x2 - 12x+6
y=-3x2 + 12x+6
Answer:
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one has axis of symmetry x = 2
Step-by-step explanation:
y = 3x² + 12x+6 : x = -12/6 = -2
y = 3x2 - 6x+12 , x = -(-6)/2*3 = -1
y=-3x2 - 12x+6 , x = -(-12)/2*3 = 2 this one
y=-3x2 + 12x+6 , x = -12/2*3 = -2
Recall that the primes fall into three categories: Let Pi be the set of
primes congruent to 1 (mod 4) and P3 be the set of primes congruent to
3 (mod 4). We know that
{primes} = {2} UP, UP3.
We have previously proved that P3 is infinite. This problem completes
the story and proves that P1 is infinite. You can do this by following these
steps:
A) Fix n > 1 and define N = (n!)2 + 1. Let p be the smallest prime divisor
of N. Show p>n.
B) If p is as in part (a), show that p ⌘ 1 (mod 4). (To get started, note
that (n!)2 ⌘ 1(mod p), raise both sides to the power p1 2 and go from
there. You will need Fermat’s Theorem)
C) Produce an infinite increasing sequence of primes in P1, showing P1
is infinite.
Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
I don’t know this..I need help
Answer:
26
Step-by-step explanation:
To find the area of a triangle, you simply need to multiply the base by the height and divide by 2. In this case, 13*4/2=26 square centimeters. Hope this helps!
Gary used 8 gallons of gas to travel 176 miles. How many miles can Gary travel on 1 gallon of gas
Answer: Gary can travel 22 miles on 1 gallon gas.
Step-by-step explanation:
176/8 = 22
Which would be the most appropriate subject line for
the e-mail with this claim?
Claim: Cell phones should be allowed in schools
because banning them is no longer universally
accepted as the best policy.
YOUR POLICY IS TERRIBLE
Cell phones as an educational tool
Help! Students are at a disadvantage!
You should know that.
Answer:
B ✔️
Step-by-step explanation:
"Cell phones as an educational tool"
Find the circumference of circle L. Write your answer as a decimal, rounded to the nearest hundredth.
please show work
find the leght of the arch for one degree by doing
2.25 ÷ 114°
u will get
0.0197368421 ft every 1°
and since a full circumference is equal to 360°, just do this:
0.0197368421 ft × 360° = 7.10526315789 ft
ROUND IT OFFFFFF
u get 7.105 ft
VOILA
If liam ate 4 apples out of a tree of 100 apples how many does he have left?
Answer:
96 apples
Step-by-step explanation:
100-4=96
Answer:
96
Step-by-step explanation:
Bruh just subtract 4 from 100 like seriously XD
Find the area and perimeter of the given rectangle.
Answer:
Area: 48 sq. units
Perim: 28 units
Step-by-step explanation:
The distance between (-4, 3) and (-4,-3) is 6. The distance between (-4,-3) and (4,-3) is 8. So, 6 x 8 is 48, and that is the area.
6, 6, 8, and 8 are the lengths, so add those up to find the perimeter and you get 28.
A roller coaster travels 80 ft of track from the loading zone before reaching its peak. The horizontal distance between the loading zone and the base of the peak is 50 ft. At what angle, to the nearest degree, is the roller coaster rising?
Answer:
the answer is answer b, or 30.83ft
Step-by-step explanation:
A flock of broiler chickens has a mean weight gain of 700 g between ages 5 and 9 weeks, and the narrow-sense heritability of weight gain in this flock is 0.80. Selection for increased weight gain is carried out for 5 consecutive generations, and in each generation the average of the parents is 50 g greater than the average of the population from which the parents were chosen.
Assuming that the heritability remains constant at 0.80, what is the expected mean weight gain after the 5 generations of selection?
The expected mean weight gain of the broiler chickens after 5 generations of selection is 900 grams.
Explanation:The expected mean weight gain of the broiler chickens can be calculated using the equation:
Σ = µ + (h^2 * S * t)
where µ is the initial population mean, h^2 is the heritability, S is the selection differential, and t is the number of generations.
From the question:
µ = 700gh^2 = 0.80S = 50gt = 5 generationsSubstituting these values into the equation gives:
Σ = 700g + (0.80 * 50g * 5) = 700g + 200g = 900g
So, the expected mean weight gain after 5 generations of selection is 900 grams.
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After 5 generations of selection with a heritability of 0.80 and a selection differential of 50 g, the expected mean weight gain for the flock is 900 g.
To determine the expected mean weight gain after 5 generations, we use the breeder's equation, which is R = h²S, where R is the response to selection, h² is the narrow-sense heritability, and S is the selection differential.
The narrow-sense heritability h² is given as 0.80 and the selection differential S is 50 g. Therefore, the response to selection for one generation is:⇒ R = h² x S
⇒ 0.80 x 50 g = 40 g
After 5 generations, the total expected gain can be calculated by multiplying the response by the number of generations:⇒ Total gain = R x 5
⇒ 40g/generations x 5 generations = 200 g
Starting with the initial mean weight gain of 700 g, we add the total gain:⇒ Expected mean weight gain after 5 generations = 700 g + 200 g
= 900 g
Thus, the expected mean weight gain after 5 generations of selection is 900 g.
Find the length of the arc. Round to the nearest tenth.
Answer:28.8 m
Step-by-step explanation:
length of arc=theta/360 x 2 x π x radius
Length of arc=150/360 x 2 x3.14x11
length of arc=(150x2x3.14x11) ➗ 360
Length of arc =10362 ➗ 360
Length of arc =28.8
Suppose you are taking a 15 question True/False quiz which you are not prepared for. You find yourself simply guessing at every answer. What is the probability that you get less than 3 answers correct?
Answer:
[tex]P(X=0)=(15C0)(0.5)^0 (1-0.5)^{15-0}=0.0000305[/tex]
[tex]P(X=1)=(15C1)(0.5)^1 (1-0.5)^{15-1}=0.000457[/tex]
[tex]P(X=2)=(15C1)(0.5)^2 (1-0.5)^{15-2}=0.00320[/tex]
And adding the results we got:
[tex] P(X<3) =P(X \leq 2) = 0.0036875[/tex]
Step-by-step explanation:
We can define the variable of interest s X representing the number of correct questions for the exam. and we can model this random variable with a binomial distribution. The probability of select the correct answer would be [tex]p =\frac{1}{2}[/tex] since is a true/false question.
[tex] X \sim Binom (n =15, p=0.5[/tex]
And we want to find this probability:
[tex]P(X <3)= P(X\leq 2)=P(X=0) +P(X=1) +P(X=2)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex]P(X \leq 2)=P(X=0)+P(X=1)+P(X=2)[/tex]
We can find the individual probabilities and we got:
[tex]P(X=0)=(15C0)(0.5)^0 (1-0.5)^{15-0}=0.0000305[/tex]
[tex]P(X=1)=(15C1)(0.5)^1 (1-0.5)^{15-1}=0.000457[/tex]
[tex]P(X=2)=(15C1)(0.5)^2 (1-0.5)^{15-2}=0.00320[/tex]
And adding the results we got:
[tex] P(X<3) =P(X \leq 2) = 0.0036875[/tex]
A sociologist is studying the social media habits of high school students in a school district. The sociologist wants to estimate the average total number of minutes spent on social media per day in the population. A random sample of 50 high school students was selected, and they were asked, “How many minutes per day, on average, do you spend visiting social media sites?"
Which of the following is the most appropriate inference procedure for the sociologist to use?
A one-sample z-interval for a population proportion
A
A one-sample t-interval for a population mean
B
A matched-pairs t -interval for a mean difference
C
A two-sample z-interval for a difference between proportions
D
A two-sample t-interval for a difference between means
Answer:
A one-sample t-interval for a population mean
Step-by-step explanation:
As the question is "How many minutes per day, on average, do you spend visiting social media sites?", the answer will be in a numerical form (number of hours, positive integer or real number).
As this is not a proportion, the option "A one-sample t-interval for a population mean" is discarded.
As the study does not defined another variable to compare in pairs, it is not a matched-pairs test. Option "A matched-pairs t -interval for a mean difference" discarded.
There are not two means in the study, so there is no "difference between means" variable. Options "A two-sample z-interval for a difference between proportions" and "A two-sample t-interval for a difference between means".
This should be a one-sample t-interval for a population mean, as there is only one sample, one population mean and the population standard deviation is not known.
The required correct statement 'A one-sample t-interval for a population mean'.
We have to determine, Which of the following is the most appropriate inference procedure for the sociologist to use?
According to the question,
The sociologist wants to estimate the average total number of minutes spent on social media per day in the population.,
A random sample of 50 high school students was selected,
And they were asked, “How many minutes per day, on average, do you spend visiting social media sites.
The answer will be in a numerical form (number of hours, positive integer or real number).
The time spent on social media keeps increasing. it can deduce as at now that trending social media platforms take much of the time spent on social media.
On average, spend 240 minutes per day on social media sites. As New social media handles keep coming,
As the given condition is not a proportion, the option "A one-sample t-interval for a population mean" is discarded.
The study does not defined another variable n difference" discarded.
There are not two means in the study, so there is no "difference between means" variable.
"A two-sample z-interval for a difference between proportions" and "A two-sample t-interval for a difference between means".
This should be a one-sample t-interval for a population mean, as there is only one sample, one population mean and the population standard deviation is not known.
Hence, The required correct statement 'A one-sample t-interval for a population mean'.
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what is the circumference of a circle with a diameter of 5?
Answer:
C≈15.71cm
Step-by-step explanation:
C=2πr
d=2r
C=πd=π·5≈15.70796cm
F(x)=4x-1 and G(x) =x2+7 what is G(F(x)
Answer:
The answer is 16x^2-8x+8
The answer is c
Step-by-step explanation:
On a certain portion of an experiment, a statistical test result yielded a p-value of 0.21. What can you conclude? 2(0.21) = 0.42 < 0.5; the test is not statistically significant. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant. 0.21 > 0.05; the test is statistically significant. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time, so the test is not statistically significant. p = 1 - 0.21 = 0.79 > 0.05; the test is statistically significant.
Answer: correct: B. If the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant.
Step-by-step explanation:
the test of the statistical p helps us to find the probability that a statistical value occurs in the null hypothesis, in the exercise we obtain a value of p of 0.21, we assume that for it to have statistical significance the value must be less than 0.05 which is constant, if this result is higher it indicates that there is no statistically significant evidence
Subtract the following military times 2330 - 0540
The final result is 17 hours and 50 minutes, or in military time format, 1750.
To subtract the military times 2330 and 0540, we can approach it as a regular subtraction problem, but we need to borrow from the hour when the minutes in the subtrahend (0540) are larger than the minutes in the minuend (2330). Since military time is on a 24-hour clock, we treat 2330 as 23 hours and 30 minutes, and 0540 as 5 hours and 40 minutes.
Step 1: Since we cannot subtract 40 minutes from 30 minutes, we need to borrow 1 hour from the 23 hours, converting it to 22 hours and 90 minutes.
Step 2: Now we subtract the minutes: 90 minutes - 40 minutes = 50 minutes.
Step 3: Then we subtract the hours: 22 hours - 5 hours = 17 hours.
So, the final result is 17 hours and 50 minutes, or in military time format, 1750.
What is the perimeter, in feet, of a square whose area is 9 square feet
Answer:
12 feet.
Step-by-step explanation:
Note that by definition of a square, all side measurements are the same (as all sides are congruent).
You can solve the area of square by using the following equation:
A (square) = s²
A (square) = side x side.
Plug in 9 for A in the equation:
9 = s²
Isolate the variable, s. Root both sides:
√9 = √s²
s = √9 = √(3 * 3) = 3
One side of the square is 3 feet.
Next, solve for the perimeter. A square has 4 congruent sides, so multiply 3 with 4:
3 x 4 = 12 feet
12 feet is your answer.
~
which word describes the four angels formed by the intersection of two perpendicular lines
The word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" because they each measure 90 degrees and create an L-shaped corner.
The four angles formed by the intersection of two perpendicular lines are often described as "right angles." A right angle measures exactly 90 degrees, and it is the angle at which two lines meet and form a perfect L shape.
Right angles are a fundamental concept in geometry and have many practical applications in everyday life. They are essential in fields such as architecture, engineering, and mathematics. Right angles are known for their symmetry and balance, making them a crucial element in various geometric shapes and constructions.
In summary, the word that describes the four angles formed by the intersection of two perpendicular lines is "right angles" due to their characteristic 90-degree measurement and significance in geometry.
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Complete question below :
What word describes the four angles formed by the intersection of two perpendicular lines?