Answer:
B. The interval will be narrower if the researchers increase the sample size of droplets.
Step-by-step explanation:
Margin of error of a confidence interval:
The higher the margin of error, the wider an interval is.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level(the higher the confidence level, the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
From this, we conclude that:
If we increase the confidence level, the interval will be wider.
If we increase the sample size, the interval will be narrower.
Which of the following statements about a 95 percent confidence interval for the mean width is correct?
Increasing the sample size leads to a narrower interval, so the correct answer is given by option B.
What is the measure of
Answer:
Just Plus the 2 Given and Minus in the 360 Because 360 It has a Fourside The Answer is 168degrees
Mateo is training for a race. On Monday Mateo ran 7/10 mile. On Tuesday Mateo ran 9/10 mile. how much farther did Mateon run on Tuesday than on Monday
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{9}{10} -\frac{7}{10} =\frac{2}{10} =\frac{1}{5}[/tex]
Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct, Since Richard has not attended a class recently, he doesn't know any of the answers, Assuming that Richard guesses on all 10 questions. Find the indicated probabilities.
A) What is the probability that he will answer all questions correctly?
B) What is the probability that he will answer all questions incorrectly?
C) What is the probability that he will answer at least one of the questions correctly?
Then use the fact that P(r1) = 1 P(r = 0).
D) What is the probability that Richard will answer at least half the questions correctly?
Answer:
a) 0.0000001024 probability that he will answer all questions correctly.
b) 0.1074 = 10.74% probability that he will answer all questions incorrectly
c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Each question has five answers, of which only one is correct
This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]
10 questions.
This means that [tex]n = 10[/tex]
A) What is the probability that he will answer all questions correctly?
This is [tex]P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]
0.0000001024 probability that he will answer all questions correctly.
B) What is the probability that he will answer all questions incorrectly?
None correctly, so [tex]P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
0.1074 = 10.74% probability that he will answer all questions incorrectly
C) What is the probability that he will answer at least one of the questions correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
Since [tex]P(X = 0) = 0.1074[/tex], from item b.
[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]
0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
D) What is the probability that Richard will answer at least half the questions correctly?
This is
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]
[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]
[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]
[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]
So
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]
0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Write a real-world scenario for the equation 10x + 2 = 8x + 8. Solve the equation.
Answer:
3
Step-by-step explanation:
Frank wants to find a number that is multiplied by 10 is 2 less than 8 times the number plus 8.
Hope that helps :)
In ΔVWX, x = 9.1 inches, w = 5.4 inches and ∠W=161°. Find all possible values of ∠X, to the nearest 10th of a degree
Answer:
NO POSSIBLE TRIANGLES
Step-by-step explanation:
Answer:
no possible triangles
Step-by-step explanation:
A stack of cards are numbered from 1 through 100. If a student selects a card, what is the
probability that the student will select a card that has both the same number in the ones place
and the tens place?
Answer:
10 out of 100
Step-by-step explanation:
Because
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Can y’all help me on question 27?!
Answer:
B and D
Step-by-step explanation:
A would be:
57 + 2j
C would be:
13-t
I’ll give points and brainalist for answer / explanation
Answer:
A. 91 ft
Step-by-step explanation:
The path is 2ft wide and the pool's radius is 12.5ft (radius is half diameter, diameter is 25ft). This means that the radius of the circle created by the path is 14.5ft (2+12.5).
Knowing the radius, we can find the circumference.
Circumference = 2πr
Circumference = 2π(14.5) = 91.10618695ft ≈ 91ft
Amath class has a total of 45 students. The number of males is 13 more than the number of females. How many males and
how many females are in the class
Number of males:
Number of females
Answer:
Males: 29
Females: 16
Step-by-step explanation:
2x+ 13 = 45
2x = 45 - 13
2x = 32
x = 16
16 + 13 = 29
29 +16 = 45
(8x + 11x) + (-7 - 18)
Answer:
19x - 25
steps:
(8x + 11x) + (-7 - 18)
19x + (-25)
positive x negative = negative
19x - 25
Answer:
19x - 25
Step-by-step explanation:
(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...
19x + (-7 - 18) <--------------- subtract the bold ones...
(19x) - 25 <-------------------- eliminate parenthases
19x - 25 <--------------------- solution...
Help please!!!!!! I don't have a lot of time
Answer:
Its 5,...................
Answer:
5
Step-by-step explanation:
simplify the exponent
35/8-1
simplify
35/7
simplify
5
Arthur spends his salary of k3550 for food, clothing, recreation and savings, which are in the ratio of 48:20:15:37, respectively.How much does he spend for each category?
What is the sum of the two polynomials?
Given:
The two models for the two polynomials.
To find:
The sum of the given polynomials.
Solution:
From the given figure, it clear that
[tex]\text{First polynomial}=a^2+a+2[/tex]
[tex]\text{Second polynomial}=-a-1[/tex]
Adding both polynomials, we get
[tex]Sum=a^2+a+2+(-a-1)[/tex]
[tex]Sum=a^2+a+2-a-1[/tex]
[tex]Sum=a^2+1[/tex]
Therefore, the correct option is A.
please help
what is the slope of the line ?
Answer:
Slope would be -3/1
Answer:
-3/1 is the slope since you are going down 3 and going to the right one time.
PLEASE HELP ILL MARK BRAINIEST
Answer:
Length of pendulum = 72 feet
Step-by-step explanation:
Given:
Time period (T) = 9.42
pi = 3.14
According to question,
T = 2 x pi x root(L/32)
9.42 = 2 x 3.14 x root(L/32)
9.42 = 6.28 × root (L/32)
9.42/6.28 = root(L/32)
1.5 = root(L/32)
Squaring both sides,
2.25 = L/32
L = 2.25 x 32
L = 72
Answer:
L=72
Step-by-step explanation:
T=2pi[tex]\sqrt{L/32\\}[/tex]
9.42 = (2 x 3.14)[tex]\sqrt{L/32}[/tex]
1.5=[tex]\sqrt{L/32}[/tex]
2.25 = L/32 (I squared both sides)
L=72
Hope this Helps
A 13-foot ladder leaning against a building meets the side of the building exactly 12 feet above the ground. How far from the building is the base of the ladder rounded to the nearest hundredth foot?
Answer:
At the moment in question, we have a 5-12-13 right triangle.
x^2 + y^2 = 13^2
2x dx/dt + 2y dy/dt = 0
2(5)(2/3) + 2(12) dy/dt = 0
dy/dt = -5/18 ft/s
the area is 1/2 xy, so
da/dt = 1/2 y dx/dt + 1/2 x dy/dt
= (1/2)((12)(2/3) + (5)(-5/18))
= 119/36
Step-by-step explanation:
can somebody help me solve for x.
Answer:
8/3
Step-by-step explanation:
x : 4 = 4 : 6
x = 16/ 6
x = 8/3
Help me ASAP. Need help please
Question 12!!
Answer:
x = -1 and -4.Explanation is given in the above photo.
Find the perimeter of the figure. due today
Answer:
62
Step-by-step explanation:
Since you are simply finding the perimeter, I assume they just want you to add all the sides. 13 + 15 + 10 + 10 + 14 = 62
A single die is rolled. Find the odds in favor of rolling a number greater than 1.
Answer:
5/6
Step-by-step explanation:
x > 1
x = 2,3,4,5,6
( quantity of 2,3,4,5,6)/(total)
5/6
Which property is shown by the equation 23 + 0 = 23
Answer:
The identity property of addition
Step-by-step explanation:
It is the identity property of addition.
The graphs below have the same shape. What is the equation of the graph of g(x)? A. g(x) = x^2 + 4
B. g(x) = x^2- 4
C. g(x) = (x - 4)^2
D. g(x) = (x + 4)^2
The given graph of g(x) is translated 4 units to left, so the function is g(x)=(x+4)². Therefore, option D is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
From the graph, f(x)=x².
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0,0)
Focus: (0,1/4)
Axis of Symmetry: x=0
Directrix: y= -1/4
In the graph we can graph of g(x) is translated 4 units to left, so the function is g(x)=(x+4)²
Therefore, option D is the correct answer.
To learn more about the parabola visit:
https://brainly.com/question/21685473.
#SPJ1
In a certain tropical forest, litter (mainly dead vegetation such as leaves and vines) forms on the ground at the rate of 10 grams per square centimeter per year. At the same time, however, the litter is decomposing at the rate of 80% per year. Let f(t) be the amount of litter (in grams per square centimeter) present at time t. Find a differential equation satisfied by f(t).
Answer:
df(t)/dt = 10 - 0.8f(t)
Step-by-step explanation:
The net rate of change, df(t)/dt = rate in - rate out
The rate in = rate litter forms on ground = 10 g/cm²/yr
Since f(t) is the amount of litter present at time, t, in g/cm² the rate out = rate of decomposition = the percentage rate × f(t) = 80% per year × f(t) = 0.8f(t) g/cm²/yr
Since df(t)/dt = rate in - rate out
df(t)/dt = 10 - 0.8f(t)
So the desired differential equation is
df(t)/dt = 10 - 0.8f(t)
231+X=? HELLLLLLLLLLLLLLLLLLLL!!!!!!!!
Answer:
231+X = 231+X
Step-by-step explanation:
Hope it helps!!!!!!!!
Which transformation should be applied to show similarity?
Nancy and Evan are each writing a 6-page essay. Nancy completed 4/6 of her essay in the morning and 2/6 of her essay in the afternoon. Evan completed 3/6 of his essay before school and 2/6 of his essay after school. Nancy says that she completed more of her essay than Evan. Evan says that he completed more of his essay than Nancy. Who is correct?
Answer:Nancy completed more of the essay.
Step-by-step explanation:4/6 + 2/6 = 6/6 = Nancy
3/6 + 2/6 = 5/6 = Evan
Therefore Nancy did more of the essay.
What is the value of x in the figure below?
The distance around the outside of an apartment is 0.3 mile. Keira ran 0.1 of the distance during her lunch. How far did she run?
Answer:
0.1
Step-by-step explanation:
g The average midterm score of students in a certain course is 70 points. From the past experience it is known that the midterm scores in this course are Normally distributed. If 29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points, find the probability that the average midterm score of these students is at most 75 points. (Round your final answer to 3 places after the decimal point).
Answer:
0.98 = 98% probability that the average midterm score of these students is at most 75 points.
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 estabilishes 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.
The average midterm score of students in a certain course is 70 points.
This means that [tex]\mu = 70[/tex]
29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.
This means that [tex]\sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44[/tex]
Find the probability that the average midterm score of these students is at most 75 points.
This is the pvalue of Z when X = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{75 - 70}{2.44}[/tex]
[tex]Z = 2.05[/tex]
[tex]Z = 2.05[/tex] has a pvalue of 0.98.
0.98 = 98% probability that the average midterm score of these students is at most 75 points.