Answer:
(a)
[tex]S = \{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}[/tex]
(b)
[tex]P(A) = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
The above sample space
A = Event of an occurrence of 3 or 4 then a head
(a): List out the sample space:
The rolls of the dice come first, followed by the toss of the coin.
So, the sample space are:
[tex]S = \{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}[/tex]
The number of the sample space is:
[tex]n(S) = 12[/tex]
(b): Find P(A)
First, we list out the outcomes of event A
[tex]A = \{(3,H),(4,H)\}[/tex]
The number of outcome is:
[tex]n(A) = 2[/tex]
The probability of A is then calculated as:
[tex]P(A) = \frac{n(A)}{n(S)}[/tex]
[tex]P(A) = \frac{2}{12}[/tex]
Simplify fraction
[tex]P(A) = \frac{1}{6}[/tex]
Tourism is extremely important to the economy of Florida. Hotel occupancy is an often-reported measure of visitor volume and visitor activity (Orlando Sentinel). Hotel occupancy data for February in two consecutive years are as follows.
Current Year Previous Year
Occupied Rooms 1,470 1,440
Total Rooms 1,750 1,800
Required:
a. Formulate the hypothesis test that can be used to determine if there has been an increase in the proportion of rooms occupied over the one-year period. (Let p1 = population proportion of rooms occupied for current year and p2 = population proportion of rooms occupied for previous year.)
b. What is the estimated proportion of hotel rooms occupied each year?
c. Calculate the test statistic.
Answer:
Step-by-step explanation:
The null hypothesis and alternative hypothesis can be formulated as:
[tex]\mathbf{H_o: P_1 - P_2 \le 0}[/tex]
[tex]\mathbf{H_1 : P_1 -P_2> 0}[/tex]
From the information given:
The sample proportion of rooms occupied for the current year.
[tex]P_1 = \dfrac{1470}{1750}[/tex]
[tex]P_1 = 0.84[/tex]
Sample size [tex]n_1[/tex] = 1750 (total number of rooms for the current year)
The sample proportion of rooms occupied for the previous year.
[tex]P_2 = \dfrac{1440}{1800}[/tex]
[tex]P_2 =0.8[/tex]
Sample size [tex]n_2[/tex] = 1800 (total number of rooms for the previous year)
Thus, the estimated proportion of the hotel rooms occupied each year are:
Current Previous
0.84 0.80
Since this is a one-sided right-tailed test;
The pooled proportion can be computed as:
[tex]\hat p= \dfrac{p_1 \times n_1 + p_2 \times n_2}{n_1 + n_2}[/tex]
[tex]\hat p= \dfrac{0.84 \times 1750 + 0.80 \times1800}{1750 +1800}[/tex]
[tex]\hat p=0.8197[/tex]
The standard error SE = [tex]\sqrt{\hat p ( 1- \hat p) ( \dfrac{1}{n_1} + \dfrac{1}{n_2} )}[/tex]
[tex]= \sqrt{0.8197 ( 1-0.8197) ( \dfrac{1}{1750} + \dfrac{1}{1800} )}[/tex]
[tex]= \sqrt{0.8197 ( 0.1803) (0.00112698 )}[/tex]
[tex]=0.0129[/tex]
Finally, the test statistics is calculated as:
[tex]Z_{calc} = \dfrac{(0.84 - 0.8)}{0.0129}[/tex]
[tex]Z_{calc} = 3.101[/tex]
Subtract -13xy from -5xy so
-5xy -(-13xy)=?
Answer:
8xy
Step-by-step explanation:
Subtract -13xy from -5xy
-5xy - (-13xy) =
-5xy + 13xy =
8xy
good luck, i hope this helps:)
If I add a -5 to both sides of an inequality, then the inequality symbol will change direction. True or False
Answer:
true
Step-by-step explanation:
The original price of a stove is $570.00. If it has a 25% discount, find the selling price. please
Answer:
$547.20
Step-by-step explanation:
Answer:
EFLKWFFELWKMFEWLMWEFL
Step-by-step explanation:
Determine which would make this solution true s < 0.43
A.1.75
B.0
C.0.43
D.0.42
HELP DUE TODAY!!!!!!!!
Answer:
B and D it ez
Step-by-step explanation:
Find the least common
multiple of 12 and 48.
144
48
32
96
Help
Answer:
Step-by-step explanation:
48
Phil needs to run at least 30 miles this week for his training. If he has already run 18 miles this week, then how many miles should he run on each of the remaining 3 days?
Answer:
4 miles
Step-by-step explanation:
30-18=12
12÷3=4
hope this helped :)
Which triangle side lengths form a right triangle? Choose all that apply.
5,6,7
6, 8, 14
8,15, 17
10,12,15
15, 20, 25
16, 18, 20
Answer:
8.,15,17
Step-by-step explanation:
use pythagoras theorem formula
Are 5x²y and 5y^2x LIKE TERMS or NOT LIKE TERMS?
A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in mg/dL, were measured before and after treatment for each individual, with the following results: Subject Before After 1 283 215 2 299 206 3 274 185 4 284 212 5 255 178 6 275 212 7 293 192 8 277 196 Can you conclude that the mean cholesterol level after treatment is less than the mean before treatment
It can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.
Let the hypothesis be:
H₀: The difference in the mean is less than or equal to 0.
H₁: The difference in the mean is greater than 0.
Here, the sample size, n = 8.
Assume, α = 0.05.
First, find the mean of the differences.
[tex]\bar{d}=\frac{(283-215)+(299-206)+...+(277-196)}{8}[/tex]
[tex]=79.375[/tex]
Now, the standard deviation of the difference is:
[tex]s_d=\sqrt{\frac{(68-79.375)^2+...+(81-79.375)^2}{8-1}}[/tex]
[tex]=13.3838[/tex]
The t value is:
[tex]t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}[/tex]
[tex]=16.7745[/tex]
Now, the degree of freedom is 8 - 1 = 7.
The p-value corresponding to this is 0.0005, which is less than the value of 0.05.
So, reject H₀.
Hence, it can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.
Learn more about t-value here :
https://brainly.com/question/31475463
#SPJ12
Whats your zodiac sign?
Answer:
cancer the worst
Step-by-step explanation:
Where can you find the hypotenuse of a right triangle
Answer:
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.
Step-by-step explanation:
Answer:
Opposite to the 90 degree angle.
Step-by-step explanation:
the hypotenuse is always the longest side with right triangles its always opposite of the right angle
when multiplying or dividing by a negative coefficient, you must flip the sign.
•True
or
•False
Answer:
I think the answer is True!
Step-by-step explanation:
Hope this helps
Answer:
true
Step-by-step explanation:
a negative times a negative is a positive same with dividing a negative by a negative
a positive times a negative is also negative
6) Which expression is equivalent to 512 in exponential form.
A
B
C
D
Look at the picture.
Answer:
C
Step-by-step explanation:
they need the answer in exponential form i.e should have an index or power
I need help fast find the answer
Answer:
22
Step-by-step explanation:
72/120 simplified help help help
Answer:
3/5
you get this by dividing 24 to both sides of 72/120
PLSSS HELP AND SHOW WORK PLEASE!
*Ms.Wilson ate 1/4 of a pizza in 12 minutes.*
1. If the pizza has 8 slices, how many slices will she eat in 18 minutes?
2. What fraction of the pizza will she eat in 30 minutes?
Problem 1
Answer: 3 slices-------------------------------------
Explanation:
1/4 = 0.25
She eats 25% of a pizza in 12 minutes
We can form the ratio 0.25/12
This ratio is then set equal to x/18. The value of x represents what proportion of the pizza is eaten after 18 minutes.
Solve for x
0.25/12 = x/18
0.25*18 = 12x ..... cross multiply
4.5 = 12x
12x = 4.5
x = 4.5/12
x = 0.375
x = 375/1000
x = (125*3)/(125*8)
x = 3/8
She ate 3/8 of the whole pizza in 18 minutes.
There are 8 slices in a full pizza, so (3/8)*8 = 3 means that she ate 3 slices.
Or you could say "eating 3 slices out of 8 total means she ate 3/8 of the full pizza".
===================================================
Problem 2
Answer: 5/8-------------------------------------
Explanation:
We'll use the same idea as before. Though now we're setting 0.25/12 equal to x/30
Solving for x leads to...
0.25/12 = x/30
0.25*30 = 12x
7.5 = 12x
12x = 7.5
x = 7.5/12
x = 0.625
x = 625/1000
x = (125*5)/(125*8)
x = 5/8
She will eat 5/8 of the pizza in 30 minutes.
Lin’s family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?
Multiple choice question.
A)
24.5 miles
B)
50 miles
C)
59.5 miles
D)
200 miles
Answer:
It is 50 miles to Republic City so they must have started in the western earth kingdom
Step-by-step explanation:
only nerds will get this but the answer is B
What is the answer to
-5 +2y = 9
y = 7x ?
Answer:
x = 1
y = 7
Step-by-step explanation:
Two equations, two unknowns. We know that y = 7x so we can substitute that into the first equation to get:
[tex]-5+2\left(7x\right)=9[/tex]
[tex]-5+14x=9[/tex]
[tex]14x=14[/tex]
This gives us x = 1.
Now plug this bag into either equation to find y, I will use the second since it's easier:
y = 7(1) = 7
5. Which of the following is a pair of alternate exterior angles?
Angles 1 and 4
Angles 2 and 8
Angles 1 and 7
Angles 4 and 7
Answer: angle 1 and 7
Step-by-step explanation: you just do it
Which expression is equivalent to -8 + 7.25 – 6 + 0.5?
A. 7.25 +0.5 - (8 - 6)
B. -(8 + 6) + (7.25 +0.5)
C.-13 + 7.75
D. -14 - 7.25
What is the weight of the y, in grams?
y 1
1 1
1 1
1 1
1
1
answers=
-1/3
-1
-4
-3
Answer:
-1
Step-by-step explanation:
what is the solution to the equation x^2=64
Answer: Positive and negative 8
Step-by-step explanation:
Take the square root on both sides
[tex]\sqrt{x^2} =\sqrt{64}[/tex]
x = ±8
Answer:
x = - 8, x = 8
Step-by-step explanation:
[tex] {x}^{2} = 64 \\ \\ x = \pm \sqrt{64} \\ \\ x = \pm8 \\ \\ x = - 8, \: \: x = 8[/tex]
What is the ansar to 2+2 please I’m 3 and I hove preK hamewark
Answer:
4
Step-by-step explanation:
2+2=4
Find the length of the third side of a triangle, given the legs are 12in. and 36 in
Answer:
37.94
Step-by-step explanation:
not sure if this is what you need but if you use Pythagoras therom you should get there
a^2 + b^2= c^2
12^2+36^2=c^2
12^2+36^2= 1440
the square root of 1440 is 37.9433192
A sample of 25 PCC studentsspent an average of $75 with a standard deviation of $17.50. Another sample of 20 ELAC studentsshowed that they spent an average of $89 with a standard deviation of $14.40. Assume that the amounts by all PCCand all ELAC students are normally distributed with equal but unknown population standard deviations.
Required:
Using 5% significance level and a formal hypothesis test can you conclude that the mean amount spent by all PCC students is less than the mean spent by all ELAC students?
Answer:
Step-by-step explanation:
Given that:
For PCC
The sample size [tex]n_1[/tex] = 25
sample mean [tex]\overline x_1[/tex] = 75
standard deviation [tex]s_1[/tex] = 17.50
For ELAC
The sample size [tex]n_2[/tex] = 20
Sample mean [tex]\overline x_2 = 89[/tex]
Standard deviation [tex]s_2[/tex] = 14.40
Significance level = 0.05
The null hypothesis:
[tex]H_o : \mu_1 =\mu_2[/tex]
The alternative hypothesis;
[tex]H_1 : \mu_1< \mu_2[/tex]
Since the population standard deviation are synonymous pooled standard deviation; Then:
[tex]sp = \sqrt {\dfrac {(n_1-1)s_1^2)+(n_2-1)s_2^2 }{n_1+n_2-2}[/tex]
[tex]sp = \sqrt {\dfrac {(25-1)17.50^2)+(20-1)14.40^2 }{25+20-2}[/tex]
[tex]sp = 16.20[/tex]
The test statistics can be computed as:
[tex]t = \dfrac{\overline x_1 -\overline x_2}{sp \times \sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2} }}[/tex]
[tex]t = \dfrac{75-89}{16.20 \times \sqrt{\dfrac{1}{25} + \dfrac{1}{20} }}[/tex]
[tex]t = -2.88[/tex]
The p-value [tex]= P(t_{n_1+n_2-1} <t)[/tex]
[tex]= P(t_{43} <-2.88)[/tex]
= 0.0031
Decision Rule: To reject the null hypothesis if the p-value is less than the significance level
Conclusion: There is sufficient evidence to conclude that the mean amount spent by all PCC students is less than the mean amount spent by all ELAC students.
mr.twain asked the students in his class to sea the figure below using a scaled factor of 3. then, he asked students to tell him one of the new side lengths of the figure. Some students responses are below
select all that answers mr.twain’s question correctly.
Answer:
We cannot see the questions on top
The point G(6,4) is rotated 180° clockwise around the origin. What
are the coordinates of the resulting point, G'?
Answer:
Step-by-step explanation:
when (x,y) is rotated through 180 then new coordinates are (-x',-y')
G(6,4)→G'(-6,-4)
2 5/8 divided by 3/7
Answer:
Answer is 6.125
Step-by-step explanation:
I hope it's helpful!
can anyone help me with this please
Answer:
n+6
Step-by-step explanation:
Chang is 6 inches taller then Nancy so you must add 6 inches to Nancy's height to figure out Chang's height.
Answer:
it's n+6
Step-by-step explanation:
nancys height is unknown so n is the variable and Chang is 6 inches taller so you add Nancy's height plus 6