Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.
Answers
Answer:
a) The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
We are 95% confident that the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is within 9,009 and 10,585 steps.
b) No, we can not use the confidence interval to estimate the probability of individual values. It can onlybe used to make inference about the population mean.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=9,797.
Ths sample standard deviation is s=2,313.
The sample size is N=61.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2313}{\sqrt{61}}=\dfrac{2313}{7.81}=296.15\)
The degrees of freedom for this sample size are:
\(df=n-1=61-1=60\)
The t-value for a 99% confidence interval and 61 degrees of freedom is t=2.66.
The margin of error (MOE) can be calculated as:
\(MOE=t\cdot s_M=2.66 \cdot 296.15=787.84\)
Then, the lower and upper bounds of the confidence interval are:
\(LL=M-t \cdot s_M = 9797-787.84=9009\\\\UL=M+t \cdot s_M = 9797+787.84=10585\)
The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
b) The value of 8,500 steps is outside the confidence interval, but this means that it is an unusual value for the mean number of steps for all people in New York City who wear an activity tracker.
We can not use the confidence interval to estimate the probability of individual values.
The activity tracking devices.
The activity tracker re those devices such as watches and a bands that tells you about your physical activity such as skipping, running, and walking. They simply count the steps and tell you about the daily goals and targets. They are quite effective for monitoring blood pressure and more.
Thus answer is 9,009, 10,585 workers, 9,009, and 10,585 steps and population mean.
As per the question, the smart trackers are used by the new york people on a daily basis and they measure the footsteps of the people. A sample of random 61 people was taken and selected on the basis of the tracers. It was found that with these statistical tests a 99% confidence interval was taken for the mean on a typical workday for all people working in City that is 9,009, 10,585. The 95% confidence that the mean number of steps taken by workers of the City was within 9,009 and 10,585 steps.The confidence interval can be used to estimate the probability of the individual values. It can be used for drawing inferences for the population mean.Learn more about the trackers are electronic.
brainly.com/question/17434350.
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Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x
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On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )
What is quadratic equation?A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.
public static double solve(double a, double b, double c, boolean flag)
{ double d = Math.sqrt(b*b - 4*a*c); if(flag)
{ return (-b + d) / (2*a); }
else { return (-b - d) / (2*a); } }
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volume of a sphere = ³, where ris 3 ㅠ the radius. Titanium has a density of 4.506 g/cm³. How many kilograms would a sphere of titanium with a radius of 11 cm weigh? Give your answer to 1 d.p.
Answers
After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).
what is radius?In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.
The formula for the volume of a sphere of radius "r" is:
V = (4/3)πr³
Substituting the specified radius value (r = 11 cm), we get:
V = (4/3)π(11)³ \sV = 5575.279 cm³
Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:
Density = Volume Weight
Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3
When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:
The weight is 25.121811974 kg.
As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).
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can someone help me on number 4
Answers
Answer:
\(P = 48 in\),\(A= 120in^2\)
Step-by-step explanation:
Again we can use Pythagorean theorem to find the missing side
x^2 + 15^2 = 17^2
x^2 + 225 = 289
Subtract 225 from both sides
x^2 = 64
Find the square root of both sides
√x^2 = √64
x = 8
So
l = 15in, w = 8in
P=2(15) + 2(8)
P = 30 + 18
P = 48 in
A= 15(8)
A= 120in^2
2x+8=15 help fast please and show work!
Answers
Answer:
\(x=\frac{7}{2}=3.5\)
Step-by-step explanation:
So we have the equation:
\(2x+8=15\)
To solve for x, we need to isolate it. Let's subtract 8 from both sides:
\((2x+8)-8=(15)-8\)
The left cancels. Subtract on the right:
\(2x=7\)
Now, let's divide both sides by 2:
\(\frac{2x}{2}=\frac{7}{2}\)
The left cancels. So:
\(x=\frac{7}{2}=3.5\)
So, our answer is 7/2 or 3.5.
And we're done!
Answer:
x=7/2
Step-by-step explanation:
First bring the 8 to the other side of the equation
2x=15-8
Then solve for x
2x=7
x=7/2
A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate (in km/h) is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
Answers
The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).
To solve this problem, we can use the concepts of trigonometry and related rates.
Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.
Given:
The plane is flying with a constant speed of 360 km/h.
The plane passes over the radar station at an altitude of 1 km.
The plane is climbing at an angle of 30°.
We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.
We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:
sin(30°) = 1/D.
To find dD/dt, we can differentiate both sides of this equation with respect to time:
cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.
Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:
cos(30°) * 0 = -1/D^2 * dD/dt.
We can substitute the known values:
cos(30°) = √3/2,
D = 1 km.
Therefore, we have:
√3/2 * 0 = -1/(1^2) * dD/dt.
Simplifying further:
0 = -1 * dD/dt.
This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.
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Determine which is the appropriate approach for conducting a hypothesis test. Claim: The mean RDA of sodium is 2400mg. Sample data: n150, 3400, s550. The sample data appear to come from a normally distributed population.
Answers
Answer:
Use the student t distribution
Step-by-step explanation:
Here is the formula
t = (x - u) ÷(s/√N)
From the information we have in the question:
n = 150
s = 550
x = 3400
u = mean = 2400
= 3400 - 2400÷ 500/√150
= 1000/44.9
= 22.27
At 0.05 significance level, df = 149 so t tabulated will be 1.65.
We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.The selling prices on
distributed with a mean of $221,000 and a standard deviation of $30,000.
Answers
(Irrational Numbers MC)
Approximate -10 + √30 to the nearest tenth. HELP PLS
Answers
-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5
Answer:
-4.5
Step-by-step explanation:
\(\sqrt{30}\) is approximately 5.47722557505. You can find this number with a calculator.
-10 + 5.47722557505 = -4.52277442495
To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value. Absolute value just means thinking of both numbers as positive numbers.
Helping in the name of Jesus.
HELP!! URGENT!!
Find the perimeter of the triangle. Simplify your answer.
Answers
The expression that represent the perimeter of the triangle is 3d² - 4d + 1.
What is the perimeter of the given triangle?The perimeter of any two-dimensional figure is simply the distance around the figure.
Hence, the perimeter of the triangle is the sum of all its 3 side lengths.
From the diagram:
Side length 1 = ( d² + 3 )
Side length 2 = ( 4d² + 3d - 2 )
Side length 3 = ( -2d² - 7d )
Hence, the perimeter of the triangle will be:
Perimeter = side length 1 + side length 2 + side length 3
Plug in the expressions
Perimeter = ( d² + 3 ) + ( 4d² + 3d - 2 ) + ( -2d² - 7d )
Collect and add like terms:
Perimeter = d² + 3 + 4d² + 3d - 2 + -2d² - 7d
Perimeter = d² + 4d² - 2d² + 3d - 7d + 3 - 2
Perimeter = 3d² - 4d + 1
Therefore, the perimeter is 3d² - 4d + 1.
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question is in the image below
Answers
The perimeter of Sam's string is 178 inches.
Given information:
Sam has a rectangular shaped window.
Length = 65 inches.
Width = 24 inches.
To find the perimeter:
you can use the formula:
Perimeter = 2 x (Length + Width)
Substituting the values into the formula, we have:
Perimeter = 2 x (65 + 24)
Perimeter = 2 x 89
Perimeter = 178 inches
Therefore, the perimeter of the rectangular window is 178 inches.
So, the perimeter of the rectangular window is 178 inches. This means that if you were to walk along the outline of the window, you would cover a total distance of 178 inches. It's important to note that the perimeter represents the total length of all the sides combined, and it is measured in the same unit (in this case, inches) as the length and width of the window.
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Explain how adding and subtracting decimals is similar to adding and subtracting whole
numbers. Explain how they are different.
Answers
Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit
How to illustrate tye decimal?One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.
Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.
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The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
O The function is increasing for all real values of x
where
x < 0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1
O The function is decreasing for all real values of x
where
x < 1.5.
Answers
The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.
Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).
The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.
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What are the big corporations doing with their wealth? One way to answer this question is to examine profits as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information.
Profit as percentage of assets 8.6-12.5 12.6-16.5 16.6-20.5 20.6-24.5 24.6-28.5
Number of companies 13 18 7 5 7
Estimate the sample mean, sample variance, and sample standard deviation for profit as percentage of assets. (Round your answers to three decimal places.)
x
s2
s
Answers
The estimated sample mean for profit as a percentage of assets is approximately 17.970, the estimated sample variance is approximately 24.437, and the estimated sample standard deviation is approximately 4.943.
To estimate the sample mean, sample variance, and sample standard deviation for profit as a percentage of assets based on the given information, we can calculate the respective measures using the midpoint of each interval and the number of companies in each interval.
First, let's calculate the midpoint for each interval:
Midpoint of 8.6-12.5:= 10.55
Midpoint of 12.6-16.5: = 14.55
Midpoint of 16.6-20.5: = 18.55
Midpoint of 20.6-24.5: = 22.55
Midpoint of 24.6-28.5: = 26.55
Next, let's calculate the estimated sample mean:
Sample Mean = (Midpoint1 * Frequency1 + Midpoint2 * Frequency2 + Midpoint3 * Frequency3 + Midpoint4 * Frequency4 + Midpoint5 * Frequency5) / (Total Frequency)
Sample Mean = (10.55 * 13 + 14.55 * 18 + 18.55 * 7 + 22.55 * 5 + 26.55 * 7) / 50
Sample Mean ≈ 17.970
To estimate the sample variance, we'll use the formula:
where X is the midpoint, X is the sample mean, and n is the total frequency.
Using this formula, we can calculate the estimated sample variance:
\(\frac{ [(13 * (10.55 - 17.970)^2 + 18 * (14.55 - 17.970)^2 + 7 * (18.55 - 17.970)^2 + 5 * (22.55 - 17.970)^2 + 7 * (26.55 - 17.970)^2)}{ (50 - 1)}\)
Sample Variance ≈ 24.437
Finally, we can estimate the sample standard deviation by taking the square root of the sample variance:
Sample Standard Deviation = √Sample Variance
Sample Standard Deviation ≈ √24.437 ≈ 4.943
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Given the polynomial 3x3 − 4x2 + 9x − 12, rewrite the polynomial as a product of binomials.
(x2 + 3)(3x + 4)
(x2 + 3)(3x − 4)
(x2 − 3)(3x + 4)
(x2 − 3)(3x − 4)
Answers
Answer:
(x^2+3)(3x-4)
Step-by-step explanation:
To answer this question we can employ a technique called factor by grouping. This strategy has us factor out values from the first two numbers and last two numbers to simplify the expression.
3x^3-4x^2+9x-12
x^2(3x-4)+3(3x-4)
(x^2+3)(3x-4)
Therefore, the answer is the second option.
. You are a contractor specializing in small commercial projects. You have been contracted to refinish the restrooms in an office building. In order to lay out a tile pattern for the floor, you need to know how many tiles you will use in each row. The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side. Assuming there is no spacing allotment needed, how many tiles will you use for each row across the room?
Answers
The number of tiles is 96
From the question, we have
The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.
16 feet = 192 inches
Number of tiles = (192*8)/(4*4)
= 96 tiles
The number of tiles is 96.
Multiplication:
The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.
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HELPP
ASAP I will mark brainist
Answers
Answer:
its C.7
Step-by-step explanation:
3^2 + 6^2 = 45
square root 45 and u get 6.7 round up and u get 7
Please see the attached.
Answers
Answer:
min: 56
lower quartile: 70
median: 74
upper quartile: 80
max: 86
PLEASE HELP THESE ROBOTS ARE SPAMMING ME
What led to the formation of the 2 political parties?
A. The Revolutionary War
B. Hamilton's financial plan
C. the Whiskey Rebellion
D. A loss in rock, paper, scissors
Answers
Step-by-step explanation:
The answer is the Revolutionary War
2. The probability that a car will come to a complete stop at a particular stop sign is 0.4. Assume that the next four cars
arrive at the stop sign are independent of one another. Find each of the following probabilities:
a) None of the four cars come to a complete stop?
Answers
Answer:
\(P(X = 0) = 0.1296 \)
Step-by-step explanation:
This can be solved using the binomial distribution because the cars arriving at the stop are independent of each other. This means we will use:
\(P(X = x) = \binom{n}{x} p^{x} q^{n - x}\)
Where p is the probability of success, q = 1 - p is the probability of failure and n is the number of cars sampled.
p = 0.4
q = 0.6
n = 4
Therefore,
\(P(X = 0) = \binom{4}{0} 0.4^{0} 0.6^{4}\)
This is equal to
\(P(X = 0) = 1 \times 1 \times 0.1296 \)
\(P(X = 0) = 0.1296 \)
show your work” below and solve the given equation for x showing all your steps.
3.5(6 – x) + 14 = 7 – 1.5(5x + 16)
please make the steps as clear as you can for brainliest!
Answers
Answer:
x=-13
Step-by-step explanation:
21-3.5x+14=7-7.5x-24
21+14-3.5x=7-24-7.5x
35-3.5x=-17-7.5x
35+17=3.5x-7.5x
52=-4x
-4. -4
x=-13
HELPPPPPPP MEEEEEEEEEEEE
Answers
Answer:
your answer is b 32/4=8
Step-by-step explanation:
if you take the groups of 4 and count them up it is 32 and then you divide them in to equal groups and it is 8 groups of 4
hope this helped
:)
whats the area of a parallelograms with a base of 8m height of 4m and width of 5 m
Answers
Answer:
Step-by-step explanation:
in a parallelogram
base(b) = 8 m
height(h) = 4 m
AREA
= b * h
= 8 * 4
= 32 m²
Answer:
I think this is the answer!
Step-by-step explanation:
A=b×h
A=6×7
A=42m²
plz can you give me brainliest?
Find the slope of the line that passes through these two points: (-2,-2) and (1,2).
Answers
Answer:
Step-by-step explanation:
(2 + 2)/(1 + 2)= 4/3
3. Determine the midpoint betweeh the points (1, 4) and (5,-4).
A. (3, 1)
B. (-1,0)
C. (4, -8)
OD. (3, 0)
E. (6, 0)
Answers
Answer:
D.
Step-by-step explanation:
(x1+x2/2,y1+y2/2)
(1+5/2,4+-4/2) add
(6/2,0/2) divide
(3,0)
what is the range of ordered pairs shown in the graph?
I WILL MARK BRAINLIEST
Answers
The set that represents the range of the function given is -
{-2, 0, 3, 5}
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y), after we have substituted the domain.
Given is a graph as shown in the image.
For the given graph, the set of {y} coordinates represent the range of the function. So, the set that represents the range of the function given is -
{-2, 0, 3, 5}
Therefore, the set that represents the range of the function given is -
{-2, 0, 3, 5}
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PLS PLSSS HELP PLSSS ASAP
Answers
Hope this helps!
Answer:
k<5
Step-by-step explanation:
All you have to do is divide 2 on each side.
2k < 10
/2 /2
k < 5
I hope this helps, and have a great day! :)
If a pair of tyres cost $75, how much would it cost to supply these tyres to twelve cyclists on the tour?
Answers
Answer:1800
Step-by-step explanation:
Answer:
$900
Step-by-step explanation:
You want to know the cost of supplying tyres to twelve cyclists if the cost per pair is $75.
PairsEach cyclist requires one pair of tyres, so 12 cyclists will need 12 pairs. At $75 per pair, the total cost is ...
($75/pair) × (12 pairs) = $900
It would cost $900 to supply these tyres to 12 cyclists.
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How can you represent a proportional relationship with an equation? PLS help me with an explanation.
Answers
Answer:
A proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.
Step-by-step explanation:
hope this explains well, good luck !
pls help me solve this
Answers
The results of operations between vectors are, respectively:
Case A: u + w = <- 3, - 1>
Case B: - 6 · v = <6, 6>
Case C: 3 · v - 6 · w = <- 21, - 15>
Case D: 4 · w + 3 · v - 5 · u = <39, 4>
Case E: |w - v| = √(4² + 3²) = 5
How to determine the operations between vectors
In this problem we must determine the operations between vectors, this can be done by following definitions:
Vector addition
v + u = (x, y) + (x', y') = (x + x', y + y')
Scalar multiplication
α · v = α · (x, y) = (α · x, α · y)
Norm of a vector
|u| = √(x² + y²)
Now we proceed to determine the result of each operation:
Case A:
u + w = <- 6, - 3> + <3, 2>
u + w = <- 3, - 1>
Case B:
- 6 · v = - 6 · <- 1, - 1>
- 6 · v = <6, 6>
Case C:
3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>
3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>
3 · v - 6 · w = <- 21, - 15>
Case D:
4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>
4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>
4 · w + 3 · v - 5 · u = <39, 4>
Case E:
|w - v| = |<3, 2> - <- 1, - 1>|
|w - v| = |<4, 3>|
|w - v| = √(4² + 3²) = 5
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A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 3ft and a diameter of 8ft. The tank will be made from metal (including its top and bottom). If the metal costs $29 for each square foot, how much will the metal cost in total?
Answers
The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.
What is the total cost?In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.
The total surface area of a closed cylinder can be determined by adding the area of all its faces.
Total surface area of the closed cylinder = 2πr(r + h)
Where:
r = radius = diameter / 2 = 8/2 = 4ft
h = height
π = pi = 3.14
(2 x 3.14 x 4)(4 + 3)
25.12 x 7 = 175.84 ft²
Total cost of the metal = $29 x 175.84 = $5,099.36
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