Researchers studying the sticky droplets found on spider webs will measure the widths of a random sample of droplets. From the sample, the researchers will construct a 95 percent confidence interval to estimate the mean width of all such droplets. Which of the following statements about a 95 percent confidence interval for the mean width is correct?
A. The interval will be narrower if the researchers increase the level of confidence to 99 percent.
B. The interval will be narrower if the researchers increase the sample size of droplets.
C. The interval will be wider if the researchers decrease the level of confidence to 90 percent.
D. The interval will be wider if the researchers increase the sample size of droplets.
E. The width of the interval will not be affected if the researchers increase or decrease the number of droplets in the sample.

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:

Answer:

0.1

Step-by-step explanation:

Answer:

8/3

Step-by-step explanation:

x : 4 = 4 :  6

x = 16/ 6

x = 8/3

Answer:

Its 5,...................

Answer:

5

Step-by-step explanation:

simplify the exponent

35/8-1

simplify

35/7

simplify

5

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

Answer:

Explanation is given in the above photo.

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.

Answer:

Just Plus the 2 Given and Minus in the 360 Because 360 It has a Fourside The Answer is 168degrees

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

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10} -\frac{7}{10} =\frac{2}{10} =\frac{1}{5}[/tex]

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...

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.

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

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

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.

Answer:

B and D

Step-by-step explanation:

A would be:

57 + 2j

C would be:

13-t

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

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.

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

Answer:

10 out of 100

Step-by-step explanation:

Because

Answer:

NO POSSIBLE TRIANGLES

Step-by-step explanation:

Answer:

no possible triangles

Step-by-step explanation:

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.

Answer:

The identity property of addition

Step-by-step explanation:

It is the identity property of addition.

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.

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)

Answer:

231+X = 231+X

Step-by-step explanation:

Hope it helps!!!!!!!!

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

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 :)