Answer:
51/4
Step-by-step explanation:
To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.
X~ Uniform(0,100)
Then the probability mass function is given as follows.
[tex]f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}[/tex]
Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located 70 meters away from city A then the mid point between 20 and 70 is (70+20)/2 = 45 then we can represent D as follows
[tex]D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.[/tex]
Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable [tex]Y = D(X)[/tex], [tex]Y[/tex] is a random variable as well, remember that there is a theorem that says that
[tex]E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx[/tex]
Where [tex]f(x)[/tex] is the probability mass function of X. Using the information of our problem
[tex]E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75[/tex]
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
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
10 = - 9 - x
Show me all the steps
Step-by-step explanation:
10= - 9 - X
- x - 9 = 10
-× = 10 + 19
-× =19
× = -19
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.
Learn more about Broiler Chickens Weight Gain here:https://brainly.com/question/10458236
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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.
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"
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!
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
-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
14. Find the height of a cylinder if the surface area is 408.41 square inches and the radius is 5
inches.
Final answer:
To find the height of a cylinder with a given surface area and radius, use the formula for the surface area of a cylinder. In this case, the height is approximately 4 inches.
Explanation:
Surface Area of a Cylinder Formula: S = 2πrh + 2πr²
Given: surface area = 408.41 sq in, radius = 5 in
Plug in the values: 408.41 = 2π(5)h + 2π(5)²
Solve for height: h = (408.41 - 50π) / 10π ≈ 4 in
Therefore, the height of the cylinder is approximately 4 inches.
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 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
x 2 + 13x + 40 = 0
solving quadratic
Answer: x=-5 or x=-8
Step-by-step explanation:
x^2+13x+40=0
x^2 + 8x + 5x +40=0
x(x+8)+5(x+8)=0
(x+5)(x+8)=0
x+5=0 or x+8=0
x=-5 or x=-8
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:
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 new alloy is made by mixing 72 grams of iron with 9 grams of zinc. How many grams of iron are required to make the alloy when combined with 144 grams of zinc?
A) 992 grams
B) 1,152 grams
C) 1,226 grams
D) 1,445 grams
Answer:
B) 1,152 grams
Step-by-step explanation:
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
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:
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
suppose the null hypothesis is rejected. state the conclusion based on the results of the test. six years%E2%80%8B ago, 11.4% of registered births were to teenage mothers. a sociologist believes that the percentage has increased since then. which of the following is the correct%E2%80%8B conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Answer: the correct option is B
Step-by-step explanation:
The question is incorrect. The correct one is:
Suppose the null hypothesis is rejected. State the conclusion based on the results of the test. Six years ago, 11.4% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. which of the following is the correct conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Solution:
This is a test of two population proportions. We would set up the hypothesis. The given proportion is 11.4/100 = 0.114
For the null hypothesis,
p = 0.114
For the alternative hypothesis,
p < 0.114
Since the null hypothesis is rejected, it means that there was sufficient evidence to reject it and the alternative hypothesis is accepted. the correct conclusion would be
b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Final answer:
When the null hypothesis is rejected, it indicates there is enough evidence to support the alternative hypothesis. In this case, the result would suggest an increase in the percentage of teenage mothers from six years ago.
Explanation:
If the null hypothesis is rejected, the correct conclusion would be that there is sufficient evidence to support the alternative hypothesis. In this scenario, the sociologist believes that the percentage of teenage mothers has increased since six years ago. Therefore, if we reject the null hypothesis, our conclusion would be option (a) - there is sufficient evidence to conclude that the percentage of teenage mothers has increased.
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:
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.
~
Haala buys 13 identical shirts and 22 identical ties for £363.01
The cost of a shirt is £15.35
Find the cost of a tie.
Answer:
£7.43
Step-by-step explanation:
The total cost is ...
13s +22t = 363.01
13(15.35) +22t = 363.01 . . . . fill in the cost of a shirt
22t = 163.46 . . . . . . . . . . . . . subtract 199.55
t = 7.43 . . . . . . . . . . . divide by 22
The cost of a tie is £7.43.
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
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
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.
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
solve for x x/25 > 5
Answer:
x > 125
Step-by-step explanation:
x/25 > 5
Multiply both sides by 25
x/25 × 25 > 5 × 25
x > 125
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
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
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