The expected value E(Y) = 5.6, Var(Y) = 326.64 and σ ≈ 18.07.
(a) To compute the expected value E(Y), we need to multiply each value of y with its corresponding probability and sum them up. Here's the calculation:
E(Y) = (2 * 0.10) + (4 * 0.40) + (7 * 0.20) + (8 * 0.30) = 0.2 + 1.6 + 1.4 + 2.4 = 5.6
(b) To compute the variance Var(Y) and standard deviation σ, we first need to find E(Y^2) and then use the formula Var(Y) = E(Y^2) - (E(Y))^2.
E(Y^2) = (2^2 * 0.10) + (4^2 * 0.40) + (7^2 * 0.20) + (8^2 * 0.30) = 4 + 64 + 98 + 192 = 358
Now, we can compute Var(Y):
Var(Y) = E(Y^2) - (E(Y))^2 = 358 - (5.6)^2 = 358 - 31.36 = 326.64
Finally, we can compute the standard deviation σ:
σ = sqrt(Var(Y)) = sqrt(326.64) ≈ 18.07
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Luis is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $0.50 per mile driven. Company B charges an initial fee of $10 for the rental plus $1 per mile driven. Let A A represent the amount Company A would charge if Luis drives x x miles, and let B B represent the amount Company B would charge if Luis drives x x miles. Graph each function and determine the interval of miles driven, x , x, for which Company A is cheaper than Company B.
Which type of relationship is indicated by the residual plot?
Onon-linear relationship
linear relationship
exponential relationship
quadratic relationship
cannot be determined
The non-linear relationship is the type of relationship that is indicated by the residual plot.
What is the non-linear relationship?A non-linear relationship denotes a kind of connection between two variables whereby one variable does not consequentially result in a proportional transformation for the other.
To elaborate, instead of delineating a direct line, such an association is generally expressed as a curve, exponential formula, or other convoluted mathematical equations.
Notwithstanding, the rate of difference in these variables isn't fixed and may shift in tandem with changes to either one of their numerical values.
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f the series is convergent, use the alternating series estimation theorem to determine the minimum number of terms we need to add in order to find the sum with an error less than 0.00005. (if the quantity diverges, enter diverges.)
To use the alternating series estimation theorem, we need to check that the series alternates in sign and that the absolute value of the terms decreases monotonically.
Assuming these conditions are met, the alternating series estimation theorem tells us that the error in approximating the sum of the series by the sum of the first n terms is bounded by the absolute value of the (n+1)th term.
To determine the minimum number of terms we need to add in order to find the sum with an error less than 0.00005, we can set the absolute value of the (n+1)th term to be less than or equal to 0.00005 and solve for n. If such an n exists, then we know that adding n terms will give us an approximation with the desired level of accuracy. If no such n exists, then the series diverges and we cannot find an approximation with the desired level of accuracy.
Note that the alternating series estimation theorem only applies to alternating series, so if the given series is not alternating, then we cannot use this theorem to determine the minimum number of terms needed for a desired level of accuracy.
The Alternating Series Estimation Theorem states that for a convergent alternating series with decreasing positive terms, the error in the partial sum is less than the first omitted term.
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An angle measures 4° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of the angle is 92 degrees, and its supplementary angle measures 88 degrees.
Given information:
An angle measures 4° more than the measure of its supplementary angle.
Let x be the measure of the angle in degrees.
Then, its supplementary angle measures 180° - x degrees.
According to the problem, we have:
x = (180 - x) + 4
Simplifying and solving for x, we get:
2x = 184
x = 92
Therefore, the measure of the angle is 92 degrees, and its supplementary angle measures 180 - 92 = 88 degrees.
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a sailfish can travel as fast as 68 miles per hour. at that rate, how far would a sailfish travel in 45 minutes
Therefore, a sailfish would travel 51 miles in 45 minutes if it maintained a speed of 68 miles per hour in the equation.
To calculate the distance traveled in a given time, we can use the formula distance = rate x time, where rate refers to the speed of travel and time refers to the duration of travel. In this scenario, we are given a rate of 68 miles per hour and a time of 45 minutes.
To use the formula, we first need to convert the time to hours since the rate is given in miles per hour. We do this by dividing the time by 60, since there are 60 minutes in an hour. In this case, 45 minutes divided by 60 minutes per hour gives us 0.75 hours.
Now, we can plug in the values for rate and time into the formula and solve for distance. Multiplying 68 miles per hour by 0.75 hours gives us a distance of 51 miles.
45 minutes / 60 minutes per hour = 0.75 hours
Then, we can use the formula: distance = rate x time
distance = 68 miles per hour x 0.75 hours
distance = 51 miles
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Please help i’m in 10th grade and i don’t understand this-
Answer:
negative linear association
the statistical power of a test is the probability that the test will correctly reject a false null hypothesis. that is, if a null hypothesis is false at the population level, the statistical power of a test is the probability that a researcher rejects the null hypothesis in his or her sample too. group of answer choices true false
The statement provided in the question is true. The statistical power of a test is the probability of correctly rejecting a false null hypothesis. It is the ability of a statistical test to detect a true effect, given that one exists. In other words, it is the likelihood that a study will be able to detect a difference or relationship between variables if such a difference or relationship truly exists in the population being studied.
The statistical power of a test depends on several factors, including the sample size, the effect size, and the level of significance chosen for the test. A larger sample size, a larger effect size, and a smaller level of significance all increase the power of a test. A low statistical power may indicate that the sample size is too small or that the test is not sensitive enough to detect the true effect.
Therefore, it is important to consider statistical power when designing and interpreting studies.
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
Part A
How many dots will the line plot have in all?
A.
2
B.
6
C.
7
D.
10
Part B
The students will make the line plot using one fractional unit. What fractional unit should the students use so that all of the data can be plotted above a label?
A.
tenths
B.
eighths
C.
fourths
D.
halves
HELP MEEEE
Answer: I don't know, sorry!
Step-by-step explanation:
15 The line plot shows the weights of ten eggs laid by one hen. EGGS LAID BY ONE HEN
THE PICTURE
what is the total weight, in onces, of the four heaviest eggs?
A 4
B 7
C 8 1/2
D 8 3/4
Pls tell me the answer again!
Answer:
I believe its 8 3/4
Step-by-step explanation:
Describe any patterns or trends you noticed when finding the products in part C.
Generalize the patterns you noticed in part D to create a rule or identity to describe those patterns. For example, if you notice that every time you multiply a negative number by another negative number the result is positive, we can
generalize this by saying (-a)(-b) = c, where a, b, and c are all positive real numbers.
Edmentum
This equation generalizes the patterns seen in part D, where a and b represent real numbers:
(a + bi)(a − bi) = a2 + b2.
What is an Equation?An equation expresses the equivalence of two mathematical expressions utilizing an equal sign to separate its two sides. Each side, comprising one or more terms, is a distinct entity conveying a specific value, variable or operator.
Equations represent essential components used to express linear relationships between variables as well as for problem-solving purposes in various domains including science and math. The resolution of equations involves discovering values of variables that establish both aspects of the equation to be held equal by equating them with solutions deemed valid.
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Help me find the volume! PLEASE ITS IMPORTANT!!!!
The volume of the given pyramid is approximately 780.975 cubic kilometers.
Given information:
The provided shape is a pyramid with a triangular base.
And the width of the base is 11.7 kilometers and the length of the base is 26.7 kilometers.
And the height of the pyramid is 15 kilometers.
To find the volume of a pyramid with a triangular base, we use the formula:
V = (1/3)Bh
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, we are given that the base of the pyramid is a triangle with a width of 11.7 kilometers and a length of 26.7 kilometers.
To find the area of this triangle, we use the formula for the area of a triangle:
B = (1/2)bh
where b is the width and h is the length of the base of the triangle.
Substituting the given values, we get:
B = (1/2)(11.7)(26.7)
B = 156.195 km²
Now, we substitute the values of B and h into the formula for the volume of a pyramid:
V = (1/3)(156.195)(15)
V = 780.975 km³.
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can Someone please help me answer this? i really don't know what to do for this one and it due tmr and I got a bunch of questions lefttt ty for whoever helps :D
Health Club B costs $8 less in monthly membership fees than Health Club A.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.For Club A, the monthly cost is given as follows:
$60.
For Club B, we have that each 4 months, the cost increases by $208, hence the monthly cost is given as follows:
208/4 = $52.
Which is $8 less than Club A.
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Points A and B are 80km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 8 hours, but if they travel in opposite directions, they meet in 1 hour 20 mins. What are their speeds in km/hr?
The speeds of the car are 35 km/hr and 25 km/hr, if a car starts from A and another car starts from B at the same time. If both cars travel in the same direction, they cross in 8 hours, but if these cars travel in opposite directions, they meet each other in 1 hour 20 mins. A and B have a distance of 80 km.
Let the speed of the car at A be [tex]v_1[/tex]
the speed of the car at B be [tex]v_2[/tex]
In the first case, they travel in the same direction, the relative velocity is given by [tex]v_1-v_2[/tex]
[tex]v_1-v_2[/tex] = [tex]\frac{80}{8}[/tex]
[tex]v_1-v_2[/tex] = 10 -----(i)
In the second case, they travel in the opposite direction, the relative velocity is given by [tex]v_1+v_2[/tex]
[tex]v_1+v_2[/tex] = [tex]\frac{80}{1\frac{1}{3} }[/tex]
[tex]v_1+v_2[/tex] = [tex]\frac{80*3}{4}[/tex]
[tex]v_1+v_2[/tex] = 60 ------(ii)
Add equations (i) and (ii)
[tex]2v_1[/tex] = 70
[tex]v_1[/tex] = 35 km/hr
From equation (i)
[tex]v_2[/tex] = 25 km/hr
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Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 33.7 mpg and 4.4 mpg, respectively. What is the probability that a randomly selected passenger car gets more than 35 mpg?
P(X > 35) ≈ 0.384
To find the probability that a randomly selected passenger car gets more than 35 mpg given that the miles-per-gallon (mpg) ratings are normally distributed with a mean of 33.7 mpg and a standard deviation of 4.4 mpg, follow these steps:
1. First, calculate the z-score, which represents how many standard deviations away from the mean our target value (35 mpg) is:
z = (X - μ) / σ
z = (35 - 33.7) / 4.4
z ≈ 0.295
2. Next, use a standard normal distribution (z) table or an online calculator to find the probability that corresponds to the z-score of 0.295. This gives you the probability of a car having 35 mpg or less.
3. Since we want to find the probability of a car getting more than 35 mpg, subtract the probability obtained in step 2 from 1:
P(X > 35) = 1 - P(X ≤ 35)
Using a z-table or an online calculator, the probability for a z-score of 0.295 is approximately 0.616. Thus,
P(X > 35) = 1 - 0.616
P(X > 35) ≈ 0.384
So, the probability that a randomly selected passenger car gets more than 35 mpg is approximately 38.4%.
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325 degrees to radians in terms of pi
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180 & \pi \\ 325& r \end{array} \implies \cfrac{180}{325}~~=~~\cfrac{\pi }{r} \\\\\\ \cfrac{ 36 }{ 65 } ~~=~~ \cfrac{ \pi }{ r }\implies 36r=65\pi \implies r=\cfrac{65\pi }{36}[/tex]
Answer:
[tex]\dfrac{65\pi}{36}[/tex]
Step-by-step explanation:
To convert 325° to radians in terms of π, we can use the conversion ratio:
[tex]\dfrac{2\pi}{360\°}[/tex]
Multiplying 325° by the conversion ratio:
[tex]325\° \cdot \dfrac{2\pi}{360\°}[/tex]
↓ multiplying the numerators
[tex]\dfrac{650\pi\°}{360\°}[/tex]
↓ canceling degree signs
[tex]\dfrac{650\pi}{360}[/tex]
↓ simplifying the fraction
[tex]\boxed{\dfrac{65\pi}{36}}[/tex]
on the next test one of the students in mr arthur's class scores 100 but the other 4 score 50 what is the average
Answer
The average for the next test would be 60
Step-by-step explanation:
50+50+50+50+100= 300
then divide by 5 students
300/5 = 60
Company's Complaints
Number
of Complaints
225
205
187
169
147
130
Week
1
23
3
45
6
Based on the line of best fit, how many complaints should the company expect at the end of week 8?
A 110
B 96
C 91
D 75
The company ought to anticipate 96 complaints at the conclusion of week 8 based on the line of best. (Option B).
How to Solve the Problem?To anticipate the number of complaints at the conclusion of week 8, we got to utilize the line of best fit condition, which speaks to the relationship between the weeks and the number of complaints.
Expecting that we have as of now calculated the line of best fit and determined that it may be a straight relationship, we are able utilize the slope-intercept frame of a line:
y = mx + b
where:
y = the anticipated number of complaints at the conclusion of week 8
m = the slant of the line of best fit
x = 8 (since we need to predict the number of complaints at the conclusion of week 8)
b = the y-intercept of the line of best fit
We will calculate the slant and y-intercept utilizing the given information:
Incline (m): To discover the slant of the line of best fit, we got to utilize the equation:
m = (n∑xy - ∑x∑y) / (n∑x^2 - (∑x)^2)
where:
n = the number of information focuses (in this case, 6 weeks)
∑xy = the entirety of the items of the x and y values
∑x = the whole of the x values
∑y = the whole of the y values
∑x^2 = the entirety of the squared x values
Utilizing the information given within the table, ready to calculate:
∑xy = (1225) + (2205) + (3187) + (4169) + (5147) + (6130) = 2859
∑x = 1 + 2 + 3 + 4 + 5 + 6 = 21
∑y = 225 + 205 + 187 + 169 + 147 + 130 = 1063
∑x^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 91
Utilizing these values, ready to calculate the incline:
m = ((62859) - (211063)) / ((6*91) - (21^2)) = -17.5
Y-intercept (b): To discover the y-intercept of the line of best fit, we will utilize the equation:
b = y - mx
where:
y = the cruel of the y values
m = the slant of the line of best fit
x = the cruel of the x values
Utilizing the information given within the table, able to calculate:
y = (225 + 205 + 187 + 169 + 147 + 130) / 6 = 177.17
x = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5
Utilizing these values, ready to calculate the y-intercept:
b = 177.17 - (-17.5 * 3.5) = 235.92
Presently that we have the incline and y-intercept, we are able to utilize the condition for a line to anticipate the number of complaints at the conclusion of week 8:
y = -17.5x + 235.92
where x = 8 (since we need to anticipate the number of complaints at the conclusion of week 8)
y = -17.5(8) + 235.92
y = 96.42
Adjusting to the closest entirety number, the answer is (B) 96 complaints. Therefore, the company ought to anticipate 96 complaints at the conclusion of week 8 based on the line of best
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need help on number 15 and 16 pleasee
Answer:
15) Let n = 1 be the first term of each sequence.
[tex] - 65536 \times - 4 = 262144[/tex]
[tex]a(n) = 262144( - { \frac{1}{4}) }^{n} [/tex]
[tex]a(9) = ( {4}^{9} ) {( - \frac{1}{4} )}^{9} = {( - 1)}^{9} = - 1[/tex]
16)
[tex] 6 \div (- 3 )= - 2[/tex]
[tex]a(n )= ( - 2) ({( - 3)}^{n} )[/tex]
[tex]a(9) = - 2(( { - 3)}^{9} ) [/tex]
[tex]a(9) = - 2 \times - 19683 = 39366[/tex]
Use the given information to find the minimum sample sizerequired to estimate an unknown population mean mu.Margin of error: $130, confidence level: 99%, sigma = $544
The minimum sample size required to estimate the unknown population mean mu with the given margin of error and confidence level is 117.
To find the minimum sample size required to estimate an unknown population mean with a margin of error of $130 and a confidence level of 99% while assuming a known population standard deviation (sigma) of $544, we can use the following formula:
n = (Z^2 * sigma^2) / E^2
Where:
n = sample size
Z = z-score for the given confidence level (99%) = 2.576
sigma = population standard deviation ($544)
E = margin of error ($130)
Substituting the given values, we get:
n = (2.576^2 * $544^2) / $130^2
n = 208.10
Rounding up to the nearest whole number, the minimum sample size required is 209. Therefore, we would need to sample at least 209 individuals from the population to estimate the population mean with a margin of error of $130 and a confidence level of 99%, assuming a known population standard deviation of $544.
To find the minimum sample size required to estimate an unknown population mean mu, we need to use the formula for margin of error (E) in a normal distribution:
E = Z * (sigma / sqrt(n))
Here, E is the margin of error, Z is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, and n is the sample size. We are given E = $130, confidence level = 99%, and sigma = $544.
First, find the z-score corresponding to the 99% confidence level. Since we want 99% of the area under the curve, we need to find the z-score that leaves 1% (100% - 99%) in the tails. We split the 1% into two tails, which gives 0.5% in each tail. From the z-table, we find the z-score that corresponds to 99.5% (since we want 0.5% in the right tail) is approximately 2.576.
Now, we can plug in the values into the formula:
130 = 2.576 * (544 / sqrt(n))
To solve for n, we need to follow these steps:
1. Divide both sides by 2.576:
130 / 2.576 = (544 / sqrt(n))
50.465 = 544 / sqrt(n)
2. Rearrange the equation to isolate the square root of n:
sqrt(n) = 544 / 50.465
sqrt(n) ≈ 10.78
3. Square both sides to find n:
n ≈ (10.78)^2
n ≈ 116.20
Since we cannot have a fraction of a person in the sample, we round up to the nearest whole number. Therefore, the minimum sample size required to estimate the unknown population mean mu with the given margin of error and confidence level is 117.
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Solve x^2-4x+4=0 by graphing. Select all solutions that apply.
Answer:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
Step-by-step explanation:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
You have 7 different video games. How many different ways can you arrange the games side by side on a shult? You can arrange the 7 different video games in different ways
There are 5,040 different ways to arrange the 7 video games side by side on a shult.
To calculate the number of different ways you can arrange the 7 different video games on a shult, you can use the formula for permutations, which is n!/(n-r)!. In this case, n is the total number of games (7) and r is the number of games being arranged at once (also 7, since you are arranging all of them).
So the calculation would be:
7! / (7-7)! = 7! / 0! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
Therefore, there are 5,040 different ways you can arrange the 7 different video games side by side on a shult.
To arrange the 7 different video games side by side on a shult, you can use the concept of permutations. In this case, there are 7 video games, and you want to arrange all of them. So, the number of ways to arrange the video games can be calculated using the formula:
Number of arrangements = 7! (7 factorial)
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Therefore, there are 5,040 different ways to arrange the 7 video games side by side on a shult.
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find the value of y. round to the nearest tenth, if necessary
Answer:
8.9
Step-by-step explanation:
according to the Pythagorean theorem:
c^2=a^2+b^2
Where c is the longest side, the hypotenuse, and a and b are the sides.
Substitute the numbers in:
12^2=8^2+y^2
144=64+y^2
144-64=y^2
80=y^2
Y= square root of 80
Y= 8.944
After rounding to the nearest tenth, that would be 8.9
use the differential to find a decimal approximation of the radical expression. round to four decimal places. (60)^1/2
The decimal approximation of √60, rounded to four decimal places, is 7.7450. Approximate the square root of 60 using the differential method. To do this, we will use linear approximation and the derivative of the square root function.
Let f(x) = x^(1/2), and we want to find f(60). Choose a nearby value of x that is easy to work with, such as x = 64, because f(64) = 8. Now, we will find the derivative of f(x) to determine the rate of change at x = 64.
f'(x) = (1/2)x^(-1/2)
Now, we'll find f'(64):
f'(64) = (1/2)(64)^(-1/2) = 1/16
Using the linear approximation formula, we have:
f(60) ≈ f(64) + f'(64)(60-64)
f(60) ≈ 8 + (1/16)(-4)
f(60) ≈ 8 - (1/4)
f(60) ≈ 7.75
So, the decimal approximation of √60, rounded to four decimal places, is 7.7450.
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pls help ASAPP v(if u dont know the answer then dont GUESS the answer. and no links please)
the answer is b or the second one
Answer:
Step-by-step explanation:
first do Pemdas and thats it
Evaluate the equation. 2 + n=8 1/3
Answer: n= 6 1/3
Step-by-step explanation:
2+n=8 1/3
-2 -2
n=6 1/3
you just subtract 2 from both sides
32% of drivers have driven drowsy in the past month. law enforcement officials are planning a survey or 1,000 drivers to determine what proportion are driving drowsy. what is the mean of the sampling distribution?
The mean of the sampling distribution can be estimated using the formula for the mean of a binomial distribution, which is μ = np, where n is the sample size and p is the probability of success (in this case, the proportion of drivers who have driven drowsy in the past month).
Given that 32% of drivers have driven drowsy in the past month, we can convert this proportion to a decimal by dividing 32 by 100, which gives us p = 0.32.
The sample size in this case is 1,000 drivers, which we can represent as n = 1,000.
Therefore, the mean of the sampling distribution would be:
μ = np
μ = 1,000 x 0.32
μ = 320
So the mean of the sampling distribution would be 320 drivers who have driven drowsy in the past month, assuming that the sample of 1,000 drivers is representative of the larger population of drivers.
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if each complete revolution of the pedals moves the bike 5.20 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. neglect work done by friction and other losses. the pedals turn in a circle of diameter 34.4 cm.
Average force ≈ 0.208 times the total force exerted in a revolution.
To calculate the average force exerted on the pedals tangent to their circular path, we need to first find the circumference of the pedal circle and then determine the force exerted per revolution.
1. Calculate the circumference of the pedal circle:
Circumference = π * diameter
Circumference = π * 0.344 m (converted 34.4 cm to meters)
Circumference ≈ 1.081 m
2. Calculate the force exerted per revolution:
We are given that each complete revolution moves the bike 5.20 m along its path. The force exerted per revolution is directly proportional to the work done.
Work done = Force * distance
Force = Work done / distance
Force = Work done / (5.20 m / 1.081 m)
Since the work done by friction and other losses is neglected, we only need to know the ratio of distances to determine the average force exerted on the pedals tangent to their circular path. Therefore,
Average force = 1.081 m / 5.20 m
Average force ≈ 0.208 times the total force exerted in a revolution.
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find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest.
The three consecutive integers are 10, 11, and 12.
To find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest, follow these steps:
1. Let the smallest integer be x. Then, the other two consecutive integers are x + 1 and x + 2.
2. The sum of their squares is x^2 + (x + 1)^2 + (x + 2)^2.
3. The given condition is that this sum is 65 more than three times the square of the smallest integer: x^2 + (x + 1)^2 + (x + 2)^2 = 3x^2 + 65.
4. Simplify the equation:
x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 3x^2 + 65
5. Combine like terms:
3x^2 + 6x + 5 = 3x^2 + 65
6. Subtract 3x^2 from both sides to eliminate the x^2 terms:
6x + 5 = 65
7. Subtract 5 from both sides:
6x = 60
8. Divide by 6:
x = 10
So, the three consecutive integers are 10, 11, and 12.
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a random sample of 85 supervisors revealed that they worked an average of 7.9 years before being promoted. the population standard deviation was 3.1 years. using the 0.95 level of confidence, what is the confidence interval for the population mean?
the confidence interval for the population mean is (7.245, 8.555) at a 0.95 level of confidence.
To find the confidence interval for the population mean, we can use the formula:
Confidence interval = sample mean +/- margin of error
where the margin of error is calculated as:
Margin of error = z* (population standard deviation / sqrt(sample size))
z* is the z-score corresponding to the confidence level of 0.95, which can be found using a standard normal distribution table or calculator. For a 0.95 confidence level, the z* value is 1.96.
Plugging in the given values, we have:
Sample mean = 7.9 years
Population standard deviation = 3.1 years
Sample size (n) = 85
z* = 1.96
Margin of error[tex]= 1.96 * (3.1 / \sqrt(85)) = 0.655[/tex]
Confidence interval = 7.9 +/- 0.655
Therefore, the confidence interval for the population mean is (7.245, 8.555) at a 0.95 level of confidence.
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Someone please help me with this question.
The value of the angle x of the regular octagon is: x = 112.5°
How to find the interior angle of a polygon?The formula for the Interior angle of a Polygon is:
θ = 180(n - 2)/n
We are given that the polygon has 8 sides. Thus:
θ = 180(8 - 2)/8
θ = 135°
Sum of angles in a triangle is 180° and as such, the base angles of the Isosceles triangle formed is:
base angle = (180 - 135)/2
= 22.5°
Thus:
x = 135 - 22.5
x = 112.5°
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