Answer:
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A hotel manager believes that 23% of the hotel rooms are booked.
This means that [tex]p = 0.23[/tex]
Sample of 610 rooms
This means that [tex]n = 610[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.23[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]
What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?
p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So
X = 0.26
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]
[tex]Z = 1.76[/tex]
[tex]Z = 1.76[/tex] has a p-value of 0.9608
X = 0.2
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]
[tex]Z = -1.76[/tex]
[tex]Z = -1.76[/tex] has a p-value of 0.0392
0.9608 - 0.0392 = 0.9216
0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%
Using the following image, solve for x.
Answer:
please provide an image.
Not sure how to do this.
Answer:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
Step-by-step explanation:
A function shows the relationship between two or more variables. A function is said to be constant over an interval if its output value is same for every input value within that interval.
As seen in the question, the x variable is the input while the y variable is the output. The function is constant from x = -4 to x = -2. Also, the function is constant within the interval from x = 4 to x = 7. Hence, the interval is:
-4 ≤ x ≤ -2, 4 ≤ x ≤ 7
2(-x-4)+3=-7x+5+5x
Pls help!!!!!!!!
Please help bbbsbsshhdbdvdvdvsvxggddvvdgddvd
(B)
Step-by-step explanation:
The graph has zeros at x = -5 and x = 3 and passes through (4, 9). We can write the equation for the graph as
[tex]y = (x + 5)(x - 3) + c[/tex]
Since the graph passes through (4, 9), we can solve for c, which gives us c = 0. Therefore, the equation for the graph is
[tex]y = (x + 5)(x - 3) = x^2 + 2x - 15[/tex]
Answer:
Step-by-step explanation:
The answer is B) y= x^2+2x-15
What transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = – } (x + 5) + 7?
A. Reflected over the x-axis
B. Vertically compressed by a factor of 2
O c. Shifted right 5 units
D. Shifted up 7 units
Answer:
C.
Step-by-step explanation:
The function shifted left five units instead of right five units.
There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.
calculate limits x>-infinity
-2x^5-3x+1
Given:
The limit problem is:
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]
In the function [tex]-2x^5-3x+1[/tex], the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.
So, the function approaches to positive infinity as x approaches to negative infinity.
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex]
Therefore, [tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex].
what is answer if 2xyx5
Answer:
Answer is 3bu2(DeEZ)=1
Step-by-step explanation:
alvin is 5 years older than elga. the sum of their age is 85. what is elga age
Answer:
40 years old.
Step-by-step explanation:
We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.
[tex]x+5=y[/tex]
We also know that the sum of their ages is 85.
[tex]x+y=85[/tex]
We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:
[tex]x+(x+5)=85[/tex]
We can combine like terms to get
[tex]2x+5=85[/tex]
Subtracting 5 from both sides results in
[tex]2x=80[/tex]
After that, we can divide both sides by 2 to get
[tex]x=40[/tex]
Thus, Elga is 40 years old.
Answer:
e = 40
a=45
Step-by-step explanation:
a + e = 85
a = e+5
e + 5 + e = 85
2e = 80
e = 40
a=45
Find the least positive integer, written only by numbers 0, 1 and 2, which is divisible by 225.
9514 1404 393
Answer:
1,222,200
Step-by-step explanation:
A search using a computer program found ...
5432 × 225 = 1,222,200
__
1000 mod 225 = 100
4 × 225 = 900
This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.
SECTION B
Answer ALL questions. Write your answers in the spaces provided.
1 Data set A has a median value of 3.1
Here is data set B.
14
-9
28
-38
-13
-2
(a) Write a statement to compare the median values of the two sets of data.
(2)
Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
Step-by-step explanation:
Order the dataset from least to greatest:
-38 → -13 → -9 → -2 → 14 → 28
Then find the values that lies in the middle:
-38 → -13 → -9 → -2 → 14 → 28
Since there are 2 values, find the average of those 2 values:
[tex]\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5[/tex]
The median value = -5.5.
The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
Which proportion resulted in the equation 3a = 7b?
Hello!
3a = 7b =>
=> 3 × a = 7 × b =>
=> a/b = 7/3
Good luck! :)
Please help with this question!?
Answer:
7
Step-by-step explanation:
Substitute 2 for x.
[tex] {2}^{2} + 3 = 7[/tex]
solve the quadratic equation x²+x-2
Step-by-step explanation:
ii hope this will help you
please mark me as brinalist friend
Answer:
x = 1
x = -2
Step-by-step explanation:
Hello!
We can solve the quadratic by factoring the equation.
Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Given our equation: [tex]x^2 + x - 2 = 0[/tex]
a = 1b = 1c = -2Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.
Factor by Grouping[tex]x^2 + x - 2 = 0[/tex][tex]x^2 + 2x - x - 2 = 0[/tex][tex]x(x + 2) -1(x + 2) = 0[/tex][tex](x - 1)(x + 2) = 0[/tex]Set each factor to 0 and solve for x:
[tex]x - 1 = 0\\x = 1[/tex][tex]x + 2 = 0\\x = -2[/tex]The solutions for x are 1 and -2.
PLEASE HELP WILL MARK BRAINLIEST!
9514 1404 393
Answer:
7.5
Step-by-step explanation:
Corresponding sides are proportional, so ...
UV/VW = LM/MN
x/6 = 15/12
x = 6(15/12) = 15/2
x = 7.5
HELP ASAP?
the two answers not showing on screen are
C:y<6x-3
D:y<6-3
Answer:
A is that answer
A) y<2x-3
Mark gathered data about the number of pink and red flowers that bloomed on several of his flowering shrubs. The scatter plot shows the data he gathered and the line of best fit.
The scatter plot showing data gathered and line of best fit is attached below :
Answer:
69
Step-by-step explanation:
Given the regression model :
y = 1.73x + 0.0924
Where,
y = number of pink flowers
x = Red flowers
Slope = 1.73
Intercept = 0.0924
The number of pink flower that are predicted to bloom on a shrub of 40 red flowers :
Put x = 40 and calculate the value of y
y = 1.73(40) + 0.0924
y = 69.2 + 0.0924
y = 69.2924
Number of pink flowers = 69
hlo all here is your question in this question the chooses are below
Answer:
1. centimeter
2. kilogram
3. gram
4. milligram
5. centimeter
6. meter
7. kilometer
8. liter
9. kiloliter
10. millimeter
Step-by-step explanation:
you really cannot answer that yourself ?
you don't understand yet the difference between length or distance, area, volume, weight, ... ?
I how this helps then
1. is length, and it is rather short. so, we use a rather small unit to express it.
2. is weight. and a big one. so, we use a bigger unit.
3. is weight. but a small one.
4. is weight. and a really tiny one.
5. is length. similar dimension of size as the finger.
6. is length. and a bigger one.
7. is length. and a truly big one.
8. is volume. liquid volume at that. but rather small.
9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...
10. is length. and a very tiny one.
Find functions f(x) and g(x) so the given function can be expressed as
h(x) = f(g(x)).
(Use non-identity functions for
f(x) and g(x).)
h(x) = 5/x-4
Answer:
[tex]f(x) = \frac{5}{x}[/tex]
[tex]g(x) = x - 4[/tex]
Step-by-step explanation:
Composite function:
[tex]h(x) = f(g(x)) = (f \circ g)(x)[/tex]
h(x) = 5/x-4
We have x on the denominator and not the numerator, so the outer function is given by:
[tex]f(x) = \frac{5}{x}[/tex]
The denominator is x - 4, so this is the inner function, so:
[tex]g(x) = x - 4[/tex]
How can one estimate a car annual fuel expense
Answer:
determine the number of miles the car drives in a year.
divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.
Step-by-step explanation:
Work out the area of the shape,show working out
help me and I think I did the sides wrong
Which expression can be used to determine 50% of 42?
42-2 ,42÷2,42÷10,42-10
Answer:
42÷2
Step-by-step explanation:
Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating.
(A) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?
a) μ < 16.4.
b) μ > 16.4.
c) μ = 16.4.
d) μ ≠ 16.4.
(B) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?
a) μ < 16.4.
b) μ = 16.4.
c) μ ≠ 16.4.
d) μ > 16.4.
(C) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?
a) μ < 16.4.
b) μ ≠ 16.4.
c) μ > 16.4.
d) μ = 16.4.
(D) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?
a) μ > 16.4.
b) μ = 16.4.
c) μ ≠ 16.4.
d) μ < 16.4.
(E) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?
a) left; right; both.
b) left; both; right.
c) both; left; right.
d) right; left; both.
Answer:
a) c) μ = 16.4.
b) d) μ > 16.4.
c) a) μ < 16.4.
d) c) μ ≠ 16.4.
e) d) right; left; both.
Step-by-step explanation:
Question a:
Test if it is getting worse, so at the alternative hypothesis we test if the mean is of greater than 16.4 inches, but at the null hypothesis we test if it is still of 16.4 options, so option C.
Question b:
At the alternative hypothesis we test if the mean is of greater than 16.4 inches, as said above, so the answer is given by option d.
Question c:
Dying down, so if the mean is lower than 16.4 inches, so option a.
Question d:
Don't know, so just test if it is different, which includes both lower or greater, so the correct answer is given by option c.
Question e:
Test if more -> right, so on question b) is a right tailed test.
Test if less -> left, so on question c) is a left tailed test.
Different -> both sides, so on question d) it is a two-tailed test.
Thus the correct answer is given by option d.
A bag contains 7 red marbles, 11 blue marbles, and 7 yellow marbles.
Two marbles are selected, one at a time, without replacement.
Find the probability that the first marble is blue and the second marble is red.
Express your answer as a decimal, rounded to the nearest hundredth.
1 pts
Ounction 3
Answer:
the total of marbles = 7 red + 11 blue + 7 Yellow
= 25 marbles
P ( b n r) = 11/25 + 7/24
=0.732
Step-by-step explanation:
1. find the total marbles
2. find the probability of each without replacement means the demoinator will reduce
3.add the two probability
GET 95 POINTS Let f(x) = 1/x and g(x)=x² + 6x. What
two numbers are not in the domain of fᵒg?
Separate your answers with a comma.
Answer:
hey there hope this answer helps you out
Step-by-step explanation:
we have two functions f(x) and g(x) such that
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} + 6x[/tex]
solving for f ° g, we'll substitute the x in f(x) by the value of g(x)
[tex]fog = \frac{1}{g(x)} [/tex]
[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]
taking x common in denominator
[tex]fog = \frac{1}{x(x + 6)} [/tex]
for a function to exist it should not have 0 in its denominator
checking the values of x for which the denominator of f ° g becomes 0 :-
x = 0 and x = -6so the function doesn't exist at values x = 0, -6
So, 0, -6 cannot be in the domain of f°g
Can you tell me the procedure of these
x-7 = -2
x-1 = 7
9-x = -10
If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)
Answer:
a) The bullet hits the ground after 64 seconds.
b) The bullet hits the ground 113,511.7 feet away.
c) The maximum height attained by the bullet is of 16,384 feet.
Step-by-step explanation:
Equations of motion:
The equations of motion for the bullet are:
[tex]x(t) = (v_0\cos{\alpha})t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]
In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.
Initial speed of 2048 ft/s at an angle of 30o to the horizontal.
This means that [tex]v_0 = 2048, \alpha = 30[/tex].
So
[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]
(a) After how many seconds will the bullet hit the ground?
It hits the ground when [tex]y(t) = 0[/tex]. So
[tex]1024t - 16t^2 = 0[/tex]
[tex]16t^2 - 1024t = 0[/tex]
[tex]16t(t - 64) = 0[/tex]
16t = 0 -> t = 0 or t - 64 = 0 -> t = 64
The bullet hits the ground after 64 seconds.
(b) How far from the gun will the bullet hit the ground?
This is the horizontal distance, that is, the x value, x(64).
[tex]x(64) = 1773.62(64) = 113511.7[/tex]
The bullet hits the ground 113,511.7 feet away.
(c) What is the maximum height attained by the bullet?
This is the value of y when it's derivative is 0.
We have that:
[tex]y^{\prime}(t) = 1024 - 32t[/tex]
[tex]1024 - 32t = 0[/tex]
[tex]32t = 1024[/tex]
[tex]t = \frac{1024}{32} = 32[/tex]
At this instant, the height is:
[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]
The maximum height attained by the bullet is of 16,384 feet.
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
A person participates in a weekly office pool in which he has one chance in ten of winning the prize. If he participates for 5 weeks in succession, what is the probability of winning at least one prize.
The probability of winning at least one prize is 0.40951.
What is probability?Probability is the likelihood that an event will occur.
The following information can be deduced:
P = probability of winning = 1/10
q = probability of not winning = 1- (1/10) = 9/10
x = no. of winning
then, p (x ≥ 1) = 1 - p (x < 1)
= 1 - p (x=0)
= 1 - ⁵C₀ (1/10)^⁰ (9/10)^(5-0)
= 1 - (1) (1) (9/10)^5
= 1 - (9/10)^5
= 1 - 0.59049
= 0.40951
Therefore, the probability is 0.40951.
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
How to find B?
what type of angle is it?
Answer:
Obtuse angle; 57°
Step-by-step explanation:
b and 43° form a right angle. A right angle is 90°. Solution: 90°-43°=57°
43° is acute, so angle b must be obtuse.
Please answer i will give you brainlest please help me
have attached the solution, couldn't solve 13 and 17 tho, if it helps, then do mark me the brainliest...
Btw, which class r u in?
Step-by-step explanation: