1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
garri49 [273]
3 years ago
10

A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it punctures the b

ike’s tire. After the bike has moved forward another 56π inches, how high above the ground is the screw? Round to the nearest tenth of an inch. 4 inches 8 inches 12 inches 16 inches
Mathematics
1 answer:
Julli [10]3 years ago
3 0

Answer:

The correct option is;

16 inches

Step-by-step explanation:

The parameters of the motion given are;

The diameter, D of the bicycle = 16 inches;

The distance the bike moves (forward) after the screw punctures the tire = 56·π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16·π inches

Therefore;

56·π inches/(16·π inches) = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A×cos(Bx - C) + D

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2·π/B

B·x = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The midline = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

After the bike moves forward another 56·π inches the height of the screw = 16 inches.

You might be interested in
Simplify the following expression 8x+9-6x-7
mamaluj [8]
8x + -6x = 2x 2 + 2x
4 0
2 years ago
Read 2 more answers
25 POINTS!!!!
seropon [69]

Answer:

1,080,000

Step-by-step explanation:

==> First divide 78 by 26

==> answer = 3

==> 135,000×2 = 270,000

==> 270,000 × 2 = 540,000

==> 540,000 × 2 = 1,080,000

==> 1,080,000

3 0
2 years ago
Read 2 more answers
The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by WorldOne Research, included the question, "Ho
vitfil [10]

Answer:

Therefore, the sampling distribution of \bar{x} is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

The 95% interval estimate of the population mean \mu is

LCL = 7.431 hours to UCL = 10.569 hours

Step-by-step explanation:

Let X be the number of hours a legal professional works on a typical workday. Imagine that X is normally distributed with a known standard deviation of 12.6.

The population standard deviation is  

\sigma = 12.6 \: hours

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

The sample size is

n = 250

The sample mean is  

\bar{x} = 9 \: hours  

Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.

The population mean would be the same as the sample mean that is

 \mu = \bar{x} = 9 \: hours

The sample standard deviation would be  

$ s = {\frac{\sigma}{\sqrt{n} }  $

Where   is the population standard deviation and n is the sample size.

$ s = {\frac{12.6}{\sqrt{250} }  $

s = 0.7969 \: hours

Therefore, the sampling distribution of \bar{x} is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

The population mean confidence interval is given by

\text {confidence interval} = \mu \pm MoE\\\\

Where the margin of error is given by

$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\

Where n is the sampling size, s is the sample standard deviation and  is the t-score corresponding to a 95% confidence level.

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 250 - 1 = 249

From the t-table at α = 0.025 and DoF = 249

t-score = 1.9695

MoE = t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\\\MoE = 1.9695\cdot \frac{12.6}{\sqrt{250} } \\\\MoE = 1.9695\cdot 0.7969\\\\MoE = 1.569\\\\

So the required 95% confidence interval is

\text {confidence interval} = \mu \pm MoE\\\\\text {confidence interval} = 9 \pm 1.569\\\\\text {LCI } = 9 - 1.569 = 7.431\\\\\text {UCI } = 9 + 1.569 = 10.569

The 95% interval estimate of the population mean \mu is

LCL = 7.431 hours to UCL = 10.569 hours

8 0
3 years ago
Isaac keeps track of the amount of money in his savings certificate each month. He has accumulated the following data:
Dafna1 [17]

Answer:

d. The common ratio is 1.1

Step-by-step explanation:

To see if the data has a common ratio or common difference, we have to see if the division between them is equal(common ratio), or if the difference between them is equal(common difference).

In this case, since 60.5 - 55 \neq 55 - 50, it has a common ratio.

To find it, we divide consecutive terms. For example:

\frac{55}{50} = 1.1

So the correct answer is:

d. The common ratio is 1.1

3 0
2 years ago
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.Refer to
Dafna11 [192]

Given that

the weight of football players is distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

And we need to find What is the minimum weight of the middle 95% of the players?

Explanation -

Using the Empirical Rule, 95% of the distribution will fall within 2 times of the standard deviation from the mean.

Two standard deviations = 2 x 25 pounds = 50 pounds

So the minimum weight = 200 pounds - 50 pounds = 150 pounds

Hence the final answer is 150 pounds.

3 0
1 year ago
Other questions:
  • In the equation  Ax+By=C , if A is positive, and B and C are negative, which of the following are true? Select all that apply.
    12·1 answer
  • I don't get # 2 please help and fast
    10·1 answer
  • (Don't look at the bottom part)
    9·2 answers
  • 2. Exercise 18, 19 Page 188. Determine if the following statements are true. If a statement is true, give a proof from the defin
    15·2 answers
  • If you roll a dice 600 times, on how many occasions would you expect to land on a 6
    12·2 answers
  • Graph<br><br> y−5=43(x−5) <br><br> help quick
    10·2 answers
  • A square has a perimeter of 36 ft. What is the length of each side?
    15·1 answer
  • En la tiendita de la escuela venden frapés de los siguientes sabores: fresa,
    12·1 answer
  • 4 3/8+ 2 7/12 <br> Alguém sabe a resposta
    9·1 answer
  • Find the inequality represented by the graph pleasseee help me​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!