The mean amount of time people spend working out each day is 37 minutes with a standard deviation of 17 minutes. If 40 people are randomly selected, what is the probability that the mean amount of time they spend working out is more than 32 minutes?
Mean :
Standard Deviation :
Probability :
Answers
Consequently, the likelihood that their average workout session lasts more than 32 minutes is 0.9699, or around 97%.
what is mean absolute deviation ?The mean (also known as the average) is a statistic that expresses the degree of central tendency of a set of numerical data. It is calculated by dividing the total number of values by the sum of all the values in the data set. The mean is a measure of the average or centre value of the data set. The standard deviation is a gauge of how far apart from the mean a data set's values are from one another. It is calculated as the square root of variance, which is the sum of the squared departures from the mean of each value in the data set. Common descriptive statistics for summarising and analysing numerical data include the mean and standard deviation.
given
SE = σ/√n
SE = 17/√40 = 2.68
We must standardise the sample mean using the following method in order to determine the likelihood that the average amount of time they spend exercising is greater than 32 minutes:
z = (x - μ) / SE
where SE is the standard error of the mean, x is the sample mean, and is the population mean.
z = (32 - 37) / 2.68 = -1.87
The likelihood of receiving a z-score less than -1.87 is found to be 0.0301 using a standard normal distribution table or calculator.
As we are interested in the likelihood of receiving a sample mean bigger than 32 minutes, we need to subtract this probability from 1:
P(X > 32) = 1 - P(X < 32) = 1 - 0.0301 = 0.9699
Consequently, the likelihood that their average workout session lasts more than 32 minutes is 0.9699, or around 97%.
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Related Questions
Given that triangle triangle RST cong triangle XYZ and RS = 11x - 1 , XY = 9x + 5 and XZ = 7x + 5 find XZ
Answers
The value of XZ is given by 26.
Given that the triangles RST and XYZ are congruent to each other.
So, RS = XY, since corresponding parts of Congruent triangles are equal.
Given also that,
RS = 11x-1
XY = 9x+5
XZ = 7x+5
So, RS = XY gives
11x-1 = 9x+5
11x-9x = 5+1
2x = 6
x = 6/2
x = 3
Substituting the value of x in the value of XZ is given by,
XZ = 7x+5 = 7*3+5 = 21+5 = 26
Hence the value of XZ is 26.
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find the value of xand y : x=2y and x+y=6
Answers
Answer:
y=2 x=4
Step-by-step explanation:
Substitute x with 2y so the second equation is 2y+y=6
Then simplify your new equation:
3y=6
y=2
If y=2 and x=2( 2) then x=4
Helppppllp plsssssssss
Answers
ok oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo oooooooooooooooooo
Select True or False for each statement.TrueFalseA straight line on a coordinate plane always represents a function.The equation y = 2x + 1 represents a function.1
Answers
1. In a function, every input value is related to only one output value. In consequence, a straight line on a coordinate plane where the line is perpendicular to the x-axis is not a function because the only input value would be related to infinitely many outputs.
A straight line on a coordinate plane always represents a function. False
2. Every line on a coordinate plane that is not perpendicular to the x-axis represents a function. This kind of line has the form: x = constant. The equation y = 2x + 1, has not this form, therefore it is not perpendicular to the x-axis. In consequence, The equation y = 2x + 1 represents a function is True
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Among the given options, 90 degrees (option A) is not a solution to the equation sin(2θ) = 1. The equation sin(2θ) = 1 represents the values of θ for which the sine of twice the angle is equal to 1. To determine which option is not a solution, we need to evaluate each choice.
A) 90 degrees: If we substitute θ = 90 degrees into the equation sin(2θ) = 1, we get sin(180 degrees) = 1. However, sin(180 degrees) is actually 0, not 1. Therefore, 90 degrees is not a solution to the equation sin(2θ) = 1.
B) 45 degrees: Substituting θ = 45 degrees gives sin(90 degrees) = 1, which is true. Therefore, 45 degrees is a solution to the equation sin(2θ) = 1.
C) 225 degrees: When we substitute θ = 225 degrees, we get sin(450 degrees) = 1. However, sin(450 degrees) is also 0, not 1. Thus, 225 degrees is not a solution to sin(2θ) = 1.
D) -135 degrees: Similarly, substituting θ = -135 degrees gives sin(-270 degrees) = 1. However, sin(-270 degrees) is 0, not 1. Hence, -135 degrees is not a solution to the equation sin(2θ) = 1.
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find the area of the figure below, composed of a rectangle with two semicircles removed.
Answers
This is a composite shape composed of a rectangle with two semicircles removed. The area will be calculated by subtracting the area of the two semicircles from the area of the rectangle
The area of a rectangle is given by:
\(\begin{gathered} Area(rectangle)=length\cdot width \\ length=12 \\ width=6 \\ Area(rectangle)=12\cdot6=72 \\ Area(rectangle)=72 \end{gathered}\)The area of the two semicircles is given by:
\(\begin{gathered} Area(2semicircles)=2(\frac{1}{2}\pi r^2) \\ Area(2semicircles)=\pi r^2 \\ r=\frac{diameter}{2}=\frac{6}{2}=3 \\ Area\mleft(2semicircles\mright)=\pi\cdot3^2=3.14\cdot9=28.26 \\ Area\mleft(2semicircles\mright)=28.26 \end{gathered}\)Therefore, the area of the figure is:
\(\begin{gathered} Area(figure)=Area(rectangle)-Area(2semicircles) \\ Area(figure)=72-28.26 \\ Area(figure)=43.74\approx43.7 \\ Area(figure)=43.7 \end{gathered}\)Question 5 of 10
The expression (tanx + cotx)2 is the same as
A. sec2x+ csc2x
B. cos2x+ sin2x
C. tan2x + cotax
D. sec2x + cos2x
Answers
Answer: option A - sec2x + csc2x
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A
P
E
X
Hello! I need help in answering question number 3 which I will attach. Geometry 3 D shapes. It reads To make one order you need to fill the cone with ice cream first, and then add the scoop on top. How many total cubic inches of ice cream are in one order?
Answers
The ice-cream is made up of of a sugar cone and a scoop in the shape of half a sphere
Hence, the formula for the volume V of the total cubic inches of ice cream is:
\(\begin{gathered} V\text{ = Volume of cone + half a volume of a sphere} \\ V\text{ = }\frac{1}{3}\pi r^2h\text{ + }\frac{2}{3}\pi r^3 \end{gathered}\)Given:
height of cone = 4.6 inches
radius of cone = 1.7 inches
radius of sphere = 1.7 inches
Substituting the given values:
\(\begin{gathered} V\text{ = }\frac{1}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^2\text{ }\times\text{ 4.6 + }\frac{2}{3}\text{ }\times\text{ }\pi\times\text{ 1.7}^3 \\ =\text{ 24.211 in}^3 \\ \approx\text{ 24.21 in}^3 \end{gathered}\)Answer:
24.21 cubic inches
present ages of two children are 2 and 5 years the rspectively. After how long will the sum of their square ages be 45.
Answers
Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.
Calculating the duration to get the sum to 45Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.
Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;
let x represent the number of years from now when the sum of square of their respective age will be
45.(x + 2)² + (x + 5)² = 45
Expanding the brackets;
x² + 4x + 4 + x² + 10x + 25 = 45
2x² + 14x + 29 = 45
2x² + 14x + 29 - 45 = 0
2x² + 14x - 16 = 0
Solving the quadratic equation for x;
x = 1, x = -8
Taking the positive value, the value of x is 1
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Emilio spent $21 at the state
fair. He paid $3 for admission and bought
12 tickets for rides. Solve the equation
12t +3= 21 to find the cost of each
ticket
Answers
Answer:
t = $1.5Steps:
12t+3 = 21
12t = 21-3
12t = 18
t = 18/12
t = 3/2
t = $1.5A group of adult males has foot lengths with a mean of 28.02 cm and a standard deviation of 1.35 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 31.1 cm significantly low or significantly high? Explain.
Answers
The bounds of non-unusual measures are given as follows:
Lower bound: 25.32 cm.Upper bound: 30.72 cm.Hence an adult male foot length of 31.1 cm is significantly high, as it is greater than the upper bound.
What is the range rule of thumb?The range rule of thumb states that measures that are more than two standard deviations from the mean in a data-set are considered unusual.
Considering the mean and the standard deviation for this problem, the bounds are given as follows:
Lower bound: 28.02 - 2 x 1.35 = 25.32 cm.Upper bound: 28.02 + 2 x 1.35 = 30.72 cm.More can be learned about the range rule of thumb at https://brainly.com/question/15825971
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quadratic regression for (1,-8) (2,-4) (3,6)
Answers
The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7
What is quadratic equatiοn?
A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.
Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.
We can start by using the three given pοints tο set up a system οf three equatiοns:
\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)
SimpIifying each equatiοn, we get:
a + b + c = -8 (equatiοn 1)
4a + 2b + c = -4 (equatiοn 2)
9a + 3b + c = 6 (equatiοn 3)
AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.
SοIving the system using technοIοgy, we get:
a = 5
b = -20
c = 7
Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:
y = 5x² - 20x + 7
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Given f(x)=x^2+6x and g(x)=4 x^2, find fg. fg(x)=
Answers
The composite function f·g(x) is 4x⁴+24x³.
The given functions are f(x)=x²+6x and g(x)=4x².
We need to find f·g(x).
We know that, f·g(x)=f(x)×g(x)
Here, f·g(x)=(x²+6x)×4x²
= x²×4x²+6x×4x²
= 4x⁴+24x³
Therefore, the composite function f·g(x) is 4x⁴+24x³.
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Monica drinks 0.125 liters of milk during breakfast and 0.20 liters of milk after dinner everyday. Find the total amount of milk she drinks in a day, using significant digits.
A. 0.325 L
B. 0.33 L
C. 1 L
D. 3.25 L
Answers
The total number of milk drank in a day since the significant figure is not specified is 0.325 L.
What are significant figures?Significant figures are a way of approximation of large numbers to the required approximation such as two significant figures, three significant figures, or more, as the case may be.
From the given information:
Monica drinks 0.125 liters of milk during breakfast, and0.20 liters of milk after dinner every dayThe total number of milk drank in Liters in a day is:
= (0.125 + 0.20) L
= 0.325 L
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Answer:
the correct answer is B. 0.33 L
Explanation:
I just took this quiz and this was the correct answer.
An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. The accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column). The class is composed of 100 students. Y 10 15 6 2 10 15 20 10 10 1 15 14 1 Compute the correlation between the scores of students from the two parts of the quiz.
Answers
As per the concept of covariance, the correlation between the scores of students from the two parts of the quiz is 9.6
What is meant by covariance and correlation?
In math, the covariance is a measure of the linear relationship between two random variables where as the correlation is used to measure the linear relationship between two random variables if it is zero then variables are said to be uncorrelated and if one then perfectly correlated.
Here we have given that, instructor has given a short quiz consisting of two parts and the accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column).
And we need to find the the correlation between the scores of students from the two parts of the quiz.
Let us consider X refers the number of points earned on the first part and Y refers the number of points earned on the second part.
=> E(max(a, x)) = ∑ₐ∑ₓ y max(x, y)p(x, y)
And then when we apply the values on it, then we get,
=> max(0, 0)p(0, 0)+max(0, 5)p(0, 5)+· · ·+max(10, 10)p(10, 10)+max(10, 15)p(10, 15)
When we simplify this one, then we get,
=> 0 ∗ 0.02 + 5 ∗ 0.06 + · · · + 10 ∗ 0.14 + 15 ∗ 0.01 = 9.6.
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Recall that lim f(x) = L means: For all € > 0 there is a 6 > 0 such that for all x satisfying 0 < Ix ~ cl < & we have that |f(x) - Ll < € What if the limit does not equal L? Think about what the means in €, 6 language. Consider the following phrases: 1.€ > 0 2.6 > 0 3.0 < Ix - cl < 6 4. Wf(x) - Ll > e 5. but 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form rigorous assertion that lim flx) + L and enter their reference numbers in the appropriate sequence in these boxes:
Answers
As per the given limit, the rigorous assertion of the function is a − δ < x < a + δ
In math term function is called as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
Here we have given that the distance between two points a and b on a number line is given by |a−b|.
And we need to find the rigorous assertion of the function.
Then the statement is written as
=> |f(x)−L|<ε
And it can be be interpreted as the distance between f(x) and L is less than ε.
Here we have another statement that is written as
=> 0<|x−a|<δ
And it ma be interpreted as the value of x≠a and the distance between x and a is less than δ.
Here we have also important to look at the following equivalences for absolute value that the statement |f(x)−L|<ε is equivalent to the statement L−ε<f(x)<L+ε.
And the statement 0<|x−a|<δ is also equivalent to the statement a−δ<x<a+δ here we know that x≠a.
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Recall that with base-ten blocks: 1 long 10 units, 1 flat 10 longs, and 1 block 10 flats. What is the fewest number of multibase blocks that can be used to represent the corresponding numeral in the given base?
a. 20 longs in base seven
b. 10 longs in base three
Answers
a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.
In base seven, we have the following conversions:
1 long = 1 unit
1 flat = 10 units
1 block = 10 flats
To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.
So, the fewest number of multibase blocks required would be 2 flats.
Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.
b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.
In base three, we have the following conversions:
1 long = 1 unit
1 flat = 3 units
1 block = 3 flats
To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.
So, the fewest number of multibase blocks required would be 3 flats and 1 unit.
Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.
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Help will give Brainly points
Answers
is the right answer
Jemma wants to solve the following system using the elimination method:
y = x − 6
y = 6x − 19
What number should the equation y = x − 6 be multiplied by to eliminate x?
1
2
4
−6
Answers
Answer:
Your answer is -6
Step-by-step explanation:
Hey I was doing a math assignment and i need your help
Answers
Answer
\(6\frac{1}{3}\text{ }\)Explanation
The given scale factor of Abraham Lincoln is:
\(1\text{ inch }=\frac{4}{9}\text{ f}eet\)The height of Lincoln on the poster is:
\(14\frac{1}{4}\text{ inches}\)What to find:
Lincoln's actual height in feet.
Let Lincoln's actual height in feet be represented as x:
\(\begin{gathered} \text{Since 1 inch }=\frac{4}{9}\text{ f}eet \\ \text{then }14\frac{1}{4}\text{ inches }=x\text{ f}eet \end{gathered}\)To get the value of x, cross multiply:
\(\begin{gathered} x\times1=14\frac{1}{4}\times\frac{4}{9} \\ x=\frac{57}{4}\times\frac{4}{9} \\ x=\frac{57}{9} \\ x=\frac{19}{3} \\ x=6\frac{1}{3}\text{ fe}et \end{gathered}\)find the values of x where the graph of the function has a point of inflection given f(x)=x^4-x^3
a) x=0
b) x=1/2
c) x=0, x=3/4
d) x=0, x=1/2
Answers
Option C. The function has points of inflection at x = 0 and x = 3/4.
To find the points of inflection, we need to find the second derivative of the function f(x), and then solve for x where the second derivative equals zero or does not exist.
\(f(x) = x^4 - x^3\)
\(f(x) = x^4 - x^3\)
\(f''(x) = 12x^2 - 6x\)
Setting the second derivative equal to zero and solving for x, we get:
\(12x^2 - 6x = 0\)
6x(2x - 1) = 0
So, the critical points of the second derivative are x = 0 and x = 1/2.
Now, we need to determine the nature of the points of inflection by examining the signs of the second derivative on either side of each critical point.
When x < 0, f''(x) > 0, so the graph is concave up.
When 0 < x < 1/2, f''(x) < 0, so the graph is concave down.
When x > 1/2, f''(x) > 0, so the graph is concave up.
Therefore, the function has a point of inflection at x = 1/2.
When x < 0, f''(x) > 0, so the graph is concave up.
When 0 < x < 3/4, f''(x) > 0, so the graph is concave up.
When x > 3/4, f''(x) < 0, so the graph is concave down.
Therefore, the function has points of inflection at x = 0 and x = 3/4.
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HURRYYYYT A researcher compared the heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data,
where x is the shoe size and y is the height, in inches.
y = 1.6r +48
Based on the equation, what is the approximate shoe size for a man having a height of 60 inches?
O A 71 / 갈
B. 104
C. 12
Ο Ο
OD. 14
Answers
Answer:
7.5
Step-by-step explanation:
60=1.6r+48
60-48=12
12/1.6=7 1/2
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
Question 2
b. What does the coefficient of the expression in part (a) represent?
Responses
the total cost (in dollars) of adopting one dog
the total cost (in dollars) of adopting one dog
the total amount (in dollars) the veterinarian is paid when one dog is adopted
the total amount, (in dollars), the veterinarian is paid when one dog is adopted
the total cost (in dollars) of adopting x dogs
the total cost (i, n dollars), of adopting x dogs
the total amount (in dollars) the animal shelter earns when x dogs are adopted
the total amount (, in dollars) the animal shelter earns when , x, dogs are adopted
please and thank you!
Answers
Answer:$190
Step-by-step explanation:
for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.
solve it and show full calculus.
thank you!
Answers
Answer:
Hi
Please mark brainliest ❣️
Thanks
Step-by-step explanation:
The answer is NO
Reason
x= 2 y= 1
Now input in the first inequality
y≤ -x + 4
1 ≤ -2 +4
1≤ 2 i.e 1 is less than two
Next inequality
y≤ x +1
1 ≤ 2 + 1
1≤ 3 i.e 1 is less than 3
But 1 is not equal to 3 and also not equal to 2
Hence our answer is NO
4. You are given 20 boxes. 19 of the boxes each have 20 balls weighing 30kg per ball. However, one box has 20 balls weighing 29kg each. All the balls and boxes are identical in appearance. You are asked to determine which box contains the 29kg balls. You have a suitable scale, but may only take a single measurement. No other measurements may be taken (like trying to determine by hand). You may remove balls from the boxes but may still only take one measurement. How can you determine the box with 29kg balls.
Answers
To find out the box number the boxes, extract the same number of balls as the number of the box, calculate the total weight.
What are the steps to find the box with the 29 kg balls?Considering you can only weigh the balls extracted once and you need to find the box with balls that are 1-kilo lighter; here are the steps you can follow:
Number the boxes from 1 to 19.Extract the same number of balls as the number given to the box. For example, from box 9 extract 9 balls.Weight all the balls together.Find out the box with the 29 kg balls. Here is an example:The total weight using this method would be 6,300 kg which is the result of adding 30 kg (first box) + 60 kg (second box)... However, since there is a box with lighter balls the total weight will be less.
Let's imagine the weight is 6,290, this means there are 10 fewer kilos and therefore the box with the lighter balls is box 10 since this is the box number from which 10 balls were extracted.
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I made this IMPOSSIBLE Question to see who can answer it correctly
(GIVING BRAINLIEST)
Answers
Answer:
im assuming c
Step-by-step explanation:
ut i think im wrong. the false statement goes with a though
Answer:
b i think
Step-by-step explanation:
(IMPOSSIBLE Question)
Find the equation of a line that contains points (5,-3) and (-2,-4) in standard form
Answers
To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.
Determine the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
For the given points (5, -3) and (-2, -4), we have:
m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7
Use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (5, -3), we have:
y - (-3) = (1/7)(x - 5)
Simplifying:
y + 3 = (1/7)(x - 5)
Convert the equation to standard form:
Multiply both sides of the equation by 7 to eliminate the fraction:
7y + 21 = x - 5
Rearrange the equation to have the x and y terms on the same side:
x - 7y = 26
The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.
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Multiply -5/3 and -9/1
Answers
Multiplying two negatives gives a positive:
5/3 x 9/1
Reduce the numbers using the greatest common factor (3):
5 x 3/1
5 x 3
15
Final answer is: 15
In fractional form: 15/1
f(0) = 2 and f(2) = 4
Answers
Answer:
Use the slope formula and slope-intercept form
y
=
m
x
+
b
to find the equation.
f
(
x
)
=
3
x
−
1
Step-by-step explanation:
Answer:
Since we get '2' as an output when we input '0'
So, the function must be increasing the value of x by 2
We see that happen in the second case as well, as our input is incremented by 2
Hence, we can say that
f(x) = x + 2
Kindly Mark Brainly, Thanks
What is the range of the graph of the equation y= k/x?
Answers
Answer:
all real number except 0
Step-by-step explanation: