Answer:
Step-by-step explanation:
The question is incomplete. The missing data is:
30, 155, 205, 235, 180, 235, 70, 250, 135, 145, 225, 230, 30
Solution:
Mean = (30 + 155 + 205 + 235 + 180 + 235 + 70 + 250 + 135 + 145 + 225 + 230 + 30)/13 = 163.5
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (30 - 163.5)^2 + (155 - 163.5)^2 + (205 - 163.5)^2+ (235 - 163.5)^2 + (180 - 163.5)^2 + (235 - 163.5)^2 + (70 - 163.5)^2 + (250 - 163.5)^2 + (135 - 163.5)^2 + (145 - 163.5)^2 + (225 - 163.5)^2 + (230 - 163.5)^2 + (30 - 163.5)^2 = 73519.25
Standard deviation = √(73519.25/13) = 75.2
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 150
For the alternative hypothesis,
µ > 150
It is a right tailed test.
a) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 13,
Degrees of freedom, df = n - 1 = 13 - 1 = 12
t = (x - µ)/(s/√n)
Where
x = sample mean = 163.5
µ = population mean = 150
s = samples standard deviation = 75.2
t = (163.5 - 150)/(75.2/√13) = 0.65
The lower the test statistic value, the higher the p value and the higher the possibility of accepting the null hypothesis.
b) We would determine the p value using the t test calculator. It becomes
p = 0.26
Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data does not show significant evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150.
c)
1.The test statistic value is the difference between the sample mean and the null hypothesis value.
Evaluate each expression. 16 5/4 x 16 1/4 / (16 1/2)/2=
Answer: the answer is 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4 on edgunity 2020
A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is this distance?
Answer:
150
Step-by-step explanation:
If you draw a diagram, this will be a rectangle and the line across cuts it into a right triangle, with a base of 120 and a height of 90. The need to know the length of the hypotenuse of the triangle, so we can use the pythagorean theorem.
90^2 + 120^2 = c^2
c=150
Last weekend, Lena worked 7.5 hours on Friday, 9.75 hours on Saturday, and 6.25 hours on Sunday.
She earns £8.60 per hour. How much did she earn in total?
Answer:202.1
Step-by-step explanation:
7.5hrs +9.75hrs+6.25hrs=23.5
8.60 X 23.5 =202.1 pounds
Solve for X 10(x-1) = 8x-2
Answer:
X = 4 x
over 5 ( x − 1 ) − 1 5 ( x − 1 )
Answer:
x = 4
Step-by-step explanation:
10(x-1) = 8x-2
Distribute
10x-10 = 8x-2
Subtract 8 from each side
10x-10-8x = 8x-2-8x
2x-10 = -2
Add 10 to each side
2x-10+10 = -2+10
2x = 8
Divide each side by 2
2x/2 = 8/2
x = 4
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.18 and the probability that the flight will be delayed is 0.14. The probability that it
will not rain and the flight will leave on time is 0.74. What is the probability that the
flight would leave on time when it is not raining? Round your answer to the thousand
Answer:
0.902 = 90.2% probability that the flight would leave on time when it is not raining
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Not raining
Event B: Flight leaving on time.
The probability that it will rain is 0.18.
This means that there is a 1 - 0.18 = 0.82 probability of not raining. So [tex]P(A) = 0.82[/tex]
The probability that it will not rain and the flight will leave on time is 0.74.
This means that [tex]P(A \cap B) = 0.74[/tex]
What is the probability that the flight would leave on time when it is not raining?
[tex]P(B|A) = \frac{0.74}{0.82} = 0.902[/tex]
0.902 = 90.2% probability that the flight would leave on time when it is not raining
g A cannonball is shot with an initial speed of 62 meters per second at a launch angle of 25 degrees toward a castle wall that is 260 meters away. If the wall is 20 meters tall, how high off the ground will the cannonball hit
Answer:
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Step-by-step explanation:
Given;
Initial speed v = 62m/s
Angle ∅ = 25°
Horizontal distance d = 260 m
Height of wall y = 20
Resolving the initial speed to vertical and horizontal components;
Horizontal vx = vcos∅ = 62cos25°
Vertical vy = vsin∅ = 62cos25°
The time taken for the cannon ball to reach the wall is;
Time t = horizontal distance/horizontal speed
t = d/vx (since horizontal speed is constant)
t = 260/(62cos25°)
t = 4.627 seconds.
Applying the equation of motion;
The height of the cannonball at time t is;
h = (vy)t - 0.5gt^2
Acceleration due to gravity g = 9.81 m/s
Substituting the given values;
h = 62sin25×4.627 - 0.5×9.81×4.627^2
h = 16.2264134736
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Which of the lists of letters all have line symmetry? A, B, C, D W, X, Y, Z L, M, N, O S, T, U, V
Answer:
A, W, X, Y, M, O, T, U, V, C, D
Step-by-step explanation:
If you put a line through the middle, then the left and the right side will look the same
Solve x-6y = 11 for y
Answer:
2
Step-by-step explanation:
Answer: y = 11 - x / -6
Step-by-step explanation:
X - 6y = 11
Since we are solving for y, we need to isolate the variable.
Move x to the other side of the equation.
- 6y = 11 - x
Now divide bith sides by -6 to cancel out -6y and get the variable y
-6y/ -6 = 11 - x/ -6
y = 11 - x / -6
Im not sure if it was solving for y, or if it was solve for x if y = 11
Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year's mean arrival rate with 98 percent confidence and an error of ± 0.5?
Answer:
25
Step-by-step explanation:
use a Poisson process to model the arrival.
the mean rate of arrivals is λ=4.5
The standard deviation is calculated as:
σ==√λ =2.1213
The z-value for a 98% CI is z=2.3262.
If the 98% CI has to be within a error of 0.5 then:
Ul-Ll=2z*σ/√n=2*0.5=1
√n=z*σ=2.3262*2.1213=4.9346
√n=4.9346 and n = 4.9346^2=24.35 rounded to 25
The sample size needed is n=25.
At a local college, 138 of the male students are smokers and are non-smokers. Of the female students, are smokers and are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Answer:
The probability that both the male and female student are non-smokers is 0.72.
Step-by-step explanation:
The complete question is:
At a local college,178 of the male students are smokers and 712 are non-smokers. Of the female students,80 are smokers and 720 are nonsmokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
Solution:
Let, X denote the number of non-smoker male students and Y denote the number of non-smoker female students.
It is provided that:
X' = 178
X = 712
Tx = 890
Y' = 80
Y = 720
Ty = 800
Compute the probability of selecting a non-smoker male student as follows:
[tex]P (\text{Non-smoker Male student})=\frac{712}{890}=0.80[/tex]
Compute the probability of selecting a non-smoker female student as follows:
[tex]P (\text{Non-smoker Female student})=\frac{720}{800}=0.90[/tex]
Compute the probability that both the male and female student are non-smokers as follows:[tex]P(\text{Non-smoker Male and Female})=P(\text{Non-smoker Male})\times P(\text{Non-smoker Female})[/tex]The event of any female student being a non-smoker is independent of the male students.
[tex]P(\text{Non-smoker Male and Female})=0.80\times 0.90[/tex]
[tex]=0.72[/tex]
Thus, the probability that both the male and female student are non-smokers is 0.72.
In the arcade game Skee Ball, players roll a ball up a ramp and receive 10 to 50 points based on where the ball lands. Players will attempt to aim the ball to receive higher scores, which are more difficult to achieve based on size and location. However, if a ball is rolled randomly up the ramp, the probabilities of the ball landing in different scoring areas are not equal. Assume the following probabilities for each possible score:
Score 10 Points 20 Points 30 Points 40 Points 50 Points
Probability 0.50 0.25 0.15 0.07 0.03
Assume that a player rolls three balls at random.
Required:
a. What is the probability of a total score of at least 100 points?
b. If the first ball scores 30 points, what is the probability of a total score of at least 100 points?
c. Are the events "the first ball scores 30" and the "total score is at least 100" independent? Why or why not??
d. What is the expected total score? What is the variance of the score on one roll?
Answer:
Step-by-step explanation:
a) sum of 100 can be achieved from following set of score
10,40,50. This score can be achieved in 3! ways
20,30,50. This score can be achieved in 3! ways
20,40,40. This score can be achieved in 4 ways
30,30,40. This score can be achieved in 4 ways
So,
P(score of 100)=
Question 14
For the following system of equations, determine how many solutions there are.
6x + y = -1 and -6x - 4y = 4
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
[tex]6x+y=-1\\y=-6x-1[/tex]
second equation:
[tex]-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1[/tex]
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Graph the image of the figure given the translation. 1. (x, y) → (x +4, y - 1)
Answer:
Y=(-1,0)
G=(0,1)
F=(-1,3)
Step-by-step explanation:
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
3. The difference between two numbers is 5
Answer:
The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s
Step-by-step explanation:
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)
Solve -3(2x - 9) = -3.
Answer:
X=4
Step-by-step explanation:
1. Distribute 3 to 2x and -9
2. You will get "6x-27 = -3"
3. Next, add 27 to -27 and -3
4. You will get "6x = 24"
5. Then, you will divide 6x and 24 by 6
6. You will get "6x/6 = 24/6"
7. The 6 will cancel the 6 in 6x.
8. Then, you will divide 24 and 6. which will give you the answer of 4
9. Add the "X=..." and...
10. You will get the answer of "X=4"
We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person
Answer:
The correct answer to the following question will be "No". The further explanation is given below.
Step-by-step explanation:
Probability (Keeping the disease out of 1 contact)
= [tex]0.5[/tex]
Probability (not keeping the disease out of 1 contact)
= [tex]1-0.5[/tex]
= [tex]0.5[/tex]
Now,
Probability (not keeping the disease out of 2 contact)
= Keeping the disease out of 1 contact × not keeping the disease out of 1 contact
On putting the estimated values, we get
= [tex]0.5\times 0.5[/tex]
= [tex]0.25[/tex]
So that,
Probability (Keeping the disease out of 2 contact)
= [tex]1-0.25[/tex]
= [tex]0.75 \ i.e., 75 \ percent[/tex]
∴ Not 100%
What is the value of X?
Answer:
x = 41 ft
Step-by-step explanation:
35(35+23) = 29(29+x)
2030 = 29(29+x)
70 = 29 + x
x = 41 ft
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h
Answer:
d = 48 h
Step-by-step explanation:
Lamar's distance traveled is directly proportional to the number of hours be drove.
So distance (d) ∝ hours (h)
Lamar traveled 288 miles in 6 hours
Since d ∝ h
then d = kh [ where k is the proportionality constant ]
if 288 = k × 6
k = =288/48
Therefore, equation will be d = 48 h will be the equation
Chen spent 7 hours at school on Friday he spent 30 minutes at lunch 50 minutes at a school assembly and the rest in class how much time did Chen spend in class
Answer:
5 hours and 40 minutes would be class
Step-by-step explanation:
We know that the total time is 7 hours, which in minutes would be:
7 * 60 = 420
420 minutes would be class, now, we subtract the other times that are not to be in class and it would be:
420 - 30 - 50 = 340
So we could say that in class it takes 340 minutes, and if we spend hours it would be:
340/60 = 5.67 hours or also 5 hours and 40 minutes would be class.
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. What is the sample space for the chance experiment of selecting two students at random
Answer:
Step-by-step explanation:
The following is the information provided
number of students is 5
The number of math major = 3
The number of statistic major = 2
Label math students as A, B, C
And statistic students as D, E
The total number of ways to select two students from 5 students is 10
The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}
Yes , in the sample space the events are equally alike
What is the probability that both selected students are statistics majors
The selected students of statistic major are DE
the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]
= 1/10
What is the probability that both students are math majors
The selected students of statistic major are AC,AB,BC
the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]
= 3/10
What is the probability that at least one of the students selected is a statistics major
Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}
the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]
7/10
What is the probability that the selected students have different majors
Number of ways to select students with different major is {AD,AE,BD,BE,CD,CE,}
the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]
6/10
Find and of the function = − −( − ).
Answer:
Thats not possible
Step-by-step explanation:
There is no:
numbersvariablesonly negative signsCan anyone help???????
Answer:
80
Step-by-step explanation:
For every additional 10 hrs, you get 200 more dollars.
write (2n^2)^3 without exponents
Answer:
8n x n x n x n x n x n x n
Step-by-step explanation:
(2n^2)^3 = 8n^ 6
Now just write "n" 6 times and there you go
The given expression without exponents can be written as 8×n×n×n×n×n×n.
The given expression is (2n²)³.
We need to write the given expression without exponents.
What is an exponent?The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times.
Now, the given expression can be simplified as follows:
(2n²)³=2³×(n²)³
=2×2×2×[tex]n^{6}[/tex] (∵[tex](a^{m}) ^{n}=a^{m\times n}[/tex])
=8×n×n×n×n×n×n
Therefore, the given expression without exponents can be written as 8×n×n×n×n×n×n.
To learn more about exponents visit:
https://brainly.com/question/219134.
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After a series of major corporations admitted to large accounting irregularities, a public policy research institute conducts a survey to determine whether the public favors increased governmental regulation and oversight of corporations. Which of the following questions will deliver an unbiased response?
a. In light of the recent wave of shocking corporate accounting fraud, should government increase its regulation and oversight of corporations?
b. Should privately-owned companies be subjected to intrusive governmental regulation and oversight?
c. ls the government doing enough to protect American shareholders from corporate greed?
d. None of the above
Answer:
I think option B
Step-by-step explanation:
Should privately-owned companies be subjected to intrusive governmental regulation and oversight?
This question will produce an unbiased answer either a yes or a no. The question is simple and not too loaded and it is direct without including an inclination to bend to a particular direction. It will produce unbiased responses in that no comment was made about the admittance to large accounting irregularities.
The following simple linear regression analyzes the relationship between the number of classes students are taking (the independent variable, labeled in the following output as X[,2]) and the number of books they have in their backpack (the response) at randomly chosen times. Assume all relevant assumptions are met. Which of the following are correct interpretations of the slope?
a. Each additional class a student takes is associated with about a 58.7% increase in the number of books in their backpack on average.
b. Each additional class a student takes is associated with about an additional 0.587 books in their backpack on average.
c. Taking an additional class causes students to carry 0.587 extra books with them on average.
d. The population average number of books in a studentâs backpack is 0.587.
Answer:
The answer is B.
Step-by-step explanation:
Why do we say that the answer is B?
For each additional class there is a significant increase that represents a minimum value over a total of books, that is, 100% that will always remain, therefore the increase will be an additional average over the other "books" that are already in backpack.
A pair of shoes usually sells for $70. If the shoes are 30% off, and sales tax is 5%, what is the total price of the shoes, including tax?
Answer:
The total price of the shoes including tax is 51.45
Step-by-step explanation:
You could go about this 2 ways.
One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.
The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.
A card is drawn at random from a standard 52-card deck. Find the following probabilities: (2 points) a. The probability the card is a diamond or a face card. (2 points) b. The probability that the card is neither an ace nor a heart. (2 points) c. The probability that the card is a face card or a 3
Answer:
(a)[tex]\dfrac{11}{26}[/tex]
(b)[tex]\dfrac{9}{13}[/tex]
(c)[tex]\dfrac{4}{13}[/tex]
Step-by-step explanation:
Number of cards in a Standard Deck=52
(a)
Number of Diamonds (D)=13
Number of Face Cards(F) = 12
Number of Diamonds that are face cards = 3
[tex]Pr($that the card is a diamond or a face card)=P(D)+P(F)-P(D \cap F)\\=\dfrac{13}{52} +\dfrac{12}{52} -\dfrac{3}{52} \\=\dfrac{22}{52} \\=\dfrac{11}{26}[/tex]
(b)The probability that the card is neither an ace nor a heart.
Number of Aces (A)=4
Number of Hearts(H) = 13
Number of Hearts that are Aces = 1
[tex]Pr($that the card is a Ace or a Heart), P(A \cup H)=P(A)+P(H)-P(A \cap H)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\$Therefore, probability that the card is neither an ace nor a heart.\\=1-P(A \cup H)\\=1-\dfrac{16}{52}\\=\dfrac{36}{52}\\=\dfrac{9}{13}[/tex]
(c)The probability that the card is a face card or a 3
Number of 3 cards(T)=4
Number of Face Cards(F) = 12
[tex]Pr($that the card is a three or a face card)=P(T)+P(F)\\=\dfrac{4}{52} +\dfrac{12}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]
You have also been asked to set up the basket ball court what is the circumference of the circle
Answer: circumference of the circle is 11.31 meters
C=\pi d\\C=\pi (2r)\\C=2\pi r
Where radius (r) is half of diameter (d)
Since radius of the circle shown in 1.8m, we plug it in the formula and get:
C=2\pi r\\C=2\pi (1.8)\\C=11.31
So C = 11.31 meters