If the variance in the thickness of 20 textbooks is 0.0665 , then the random error in the mean value is ±0.1207 inches and the confidence interval is (1.013 ± 0.1207) inches .
The number of textbooks (number of observations) , n = 20 ;
So , v = n - 1 = 20 - 1 = 19 ;
For v = 19 and 95% confidence interval , we have t = 2.093 ;
The variance (σ²) is = 0.0665 ;
So , σ = √0.665 = 0.258 inches ;
We know that , Random Error (Δ) = tσ/√n = (2.093 × 0.258)/√20
= 0.1207 ;
The mean of the thickness of textbooks is ( [tex]\bar x[/tex] ) = 1.013 inches ;
So , the Random Error in the mean is = ±Δ = ±0.1207 inches ;
and the 95% confidence interval is = [tex]\bar x[/tex] ± Δ
⇒ (1.013 ± 0.1207) inches ;
Therefore , the Random Error is ±0.1207 inches , and the interval is (1.013 ± 0.1207) inches .
Learn more about Confidence Interval here
https://brainly.com/question/24131141
#SPJ4
if a, b, and c are boolean variables, then the value of !(a & !(b & !c)) is the same as which of these expressions: !a || (!b || c) !a || (b & !c) (!a || b) & !c
The value of the expression is the same as the second option: !a || (b & !c).
What are boolean variables?Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.
The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:
!(a & !(b & !c)) = !a || (b & !c)
Therefore, the value of the expression is the same as the second option: !a || (b & !c).
Learn more on boolean variables here https://brainly.com/question/13527907
#SPJ1
eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. find the work required to stretch the spring an additional 3 inches.
The work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
We can use Hooke's law to find the force required to stretch the spring 4 inches from its natural length:
[tex]F = kx[/tex]
where F is the force in pounds, x is the displacement in inches, and k is the spring constant in pounds per inch (which we want to find).
Since 18 foot-pounds of work is required to stretch the spring 4 inches, we know that the work done is equal to the potential energy stored in the spring:
[tex]W = (1/2) k x^2[/tex]
Solving for k, we get:
[tex]k = (2W) / x^2[/tex]
Plugging in the values for W and x, we get:
[tex]k = (2 * 18) / (4^2) = 2.25[/tex]
So the spring constant is 2.25 pounds per inch.
Now we can use Hooke's law again to find the force required to stretch the spring an additional 3 inches:
[tex]F = kx[/tex]
= [tex]2.25 * 3[/tex]
= 6.75 pounds
Finally, we can find the work required to stretch the spring an additional 3 inches:
[tex]W = (1/2) k x^2[/tex]
= [tex](1/2) * 2.25 * 3^2[/tex]
= 10.125 foot-pounds
Therefore, the work required to stretch the spring an additional 3 inches is 10.125 foot-pounds.
Learn more about Hooke's law here:
https://brainly.com/question/4404276
#SPJ4
question 7
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
16.5 cm²
Step-by-step explanation:
the measure of an exterior angle (32°) is found by dividing the difference between the measures of the intercepted arcs (54° and arc abject BF) by two.
32 = (BF - 54)/2
64 = BF - 54
arc angle BF = 64 + 54 = 118°
the area of that sector is
pi×r² × 118/360 = pi×4² × 118/360 = pi×16 × 118/360 =
= pi×2 × 118/45 =
= 16.47590814... ≈ 16.5 cm²
NEED THIS DONE ASAP Please
The expression which represents the perimeter of the rectangle is 2x + 14
Area of the rectangle = 4x + 12Area of the rectangle if x = 7 is 40 square unitsThe following expressions represent the descriptions respectively;
6x
(x - 5)
(x + 2.99)
The total cost of membership of each gym is represented by;
Gym A total cost = 80 + 25m
Gym B total cost = 40m
What is the expression to represent the perimeter of a rectangle?Length= x + 3
Width = 4
Perimeter of a rectangle= 2(length + width)
= 2{(x + 3) + 4}
= 2(x + 3 + 4)
= 2(x + 7)
Perimeter of the rectangle = 2x + 14
Area of the rectangle= length × width
= (x + 3) × 4
Area of the rectangle = 4x + 12
If x = 7
Area of the rectangle = 4x + 12
= 4(7) + 12
= 28 + 12
= 40 square units
If x is the cost of each apple, the total cost of 6 apples = 6x
Adam is x years old. John is 5 years younger.
So, John's age = (x - 5) years
Ben spent x dollars on a book and $2.99 on a pack of pencil.
Ben spent a total of x + 2.99
Gym A total cost:
80 + 25m
Gym B total cost:
40m
Where,
number of months= m
If m = 6 months
Gym A total cost:
80 + 25m
= 80 + 25(6)
= 80 + 150
= $230
Gym B total cost:
40m
= 40(6)
= $240
Therefore, the gym which is the best deal for 6 months is gym A
Read more on algebraic expression:
https://brainly.com/question/4344214
#SPJ1
Determine a relationship between the x- and y-values. Write an equation.
x 1:2,3,4
y -4,-3,-2,-1
Oy=x-8
O y = -5x+1
O y=-x-5
O y=x-5
The linear equation that shows the relationship between y and x is y = x - 5
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The slope intercept form of an equation is:
y = mx + b
where m is the rate of change and b is the y intercept.
From the values given, using (1, -4) and (2, -3):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-4)=\frac{-3-(-4)}{2-1} (x-1)\\\\y=x - 1-4\\\\y=x-5[/tex]
The linear equation is y = x - 5
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
someone help me asap
Given one point and a slope:
(-3, - 4) and m = - 5To graph the line plot the given point first.
Then find the second point, consider the slope by adding 1 to the x-coordinate and -5 to the y-coordinate, this gives us:
x = - 3 + 1 = - 2y = - 4 - 5 = - 9Next, plot the second point (-2, - 9).
Now connect the two pints and extend either side. This is the line you need.
Ms. Morris charges $5.00 to print 20 photos for Science Fair. At this rate , what is the cost to print 50 photos?
The cost to print 50 photos is $12.50
What is proportion?
The proportion formula is used to determine whether or not two ratios or fractions are equal.
We can use a proportion to find the cost to print 50 photos based on the cost to print 20 photos. Since Ms. Morris charges $5.00 to print 20 photos, we can set up the proportion:
[tex]\frac{cost \ of \ 20\ photos}{number \ of\ photos } =\frac{cost \ of \ 50 \ photos}{number\ of \ photos}[/tex]
Plugging in the given values, we get:
$5.00 / 20 photos = x / 50 photos
Simplifying, we can cross-multiply to get:
20 photos * x = $5.00 * 50 photos
Multiplying and simplifying further, we get:
20x = $250.00
Dividing both sides by 20, we get:
x = $12.50
Therefore, the cost to print 50 photos is $12.50.
To know more about proportion visit,
https://brainly.com/question/19994681
#SPJ1
the sun is shining and a spherical snowball of volume 260 ft3 is melting at a rate of 11 cubic feet per hour. as it melts, it remains spherical. at what rate is the radius changing after 6.5 hours?
If the spherical snowball is melting , then the rate at which the radius changing after 6.5 hours is 0.208 ft/h .
A spherical snowball has volume = 260 ft³ that is melting at a rate of 11 cubic feet per hour, while remaining spherical.
We have to find the rate at which the radius is changing after 6.5 hours.
So , let "V" = volume of snowball, "r" = radius of snowball, and "t" = time.
Volume Of Sphere is V = (4/3)πr³ and dV/dt = -11 ft³/h ;
So, dr/dt when t = 6.5 hours. is dV/dt = (dV/dr)×(dr/dt) ;
derivative of volume formula with respect to "r", we get:
⇒ dV/dr = 4πr² ;
Substituting the given values in chain rule equation, we get:
⇒ -11 = (4/3)πr² × dr/dt ;
⇒ dr/dt = -11/((4/3)πr²)
For rate of change of the radius when t = 6.5 hours, we find the radius at that time.
The initial volume of the snowball = 260 ft³.
After 6.5 hours of melting at a rate of 11 ft³/h, the remaining volume will be: V = 260 - (11 × 6.5) = 188.5 ft³ ;
So , V = (4/3)πr³
⇒ 188.5 = (4/3)πr³
⇒ r³ = (188.5 × 3 / (4π)) ;
≈ 3.55ft
Now we substitute r = 3.55 feet
⇒ dr/dt = -11/[(4/3)π(3.55)²] ;
⇒ dr/dt ≈ -0.208 ft/h ;
Therefore , the rate at which radius is changing after 6.5 hours is approximately 0.208 feet per hour and negative sign represents that radius is decreasing .
Learn more about Rate Of Change here
https://brainly.com/question/28891125
#SPJ4
20% of what number is 5
Answer: 25
Step-by-step explanation: 5x5 =25
Answer: 25
20% is one-fifth of a whole. This means we must multiply our known number times five.
5 x 5 is 25.
To make sure that our answer is correct, we can figure out the 20% of 25, which is 5.
This means that 25 is our correct answer.
I hope this helps & good luck <3 !!!
Lisa's average score on 4 tests is 82. What does she need to score on her fifth test to have an average final score of 85?
Answer:
Lisa would need to score 97 on her 5th test.
Step-by-step explanation:
If Lisa has an average score of 82 on 4 tests, then the total sum of her scores would be 82 multiplied by 4, which is equal to 328.
If she wants an average final score of 85 over 5 tests, then the total sum of her scores needs to be 425 (i.e. 85 multiplied by 5).
To determine what she needs to get on her 5th test we need to subtract 328 from 425.
425 - 328 = 97
a car depreciated 1000 each year it was owed and driven. what type of depreciation is this?
Answer:
Straight line Depreciation
What is A ‘ C please help
Answer: 11.7 in.
Step-by-step explanation:
I don't really know this stuff myself since I'm in 8th grade, but I can say that AA is 12in. long. I measured the length of A'C, and it was a little shorter than AA. So therefore, I think the answer is 11.7 in. I just wanted to help you out.
does a parallelogram have 2 pairs of parallel sides
Answer:
A parallelogram is a quadrilateral with 2 pairs of parallel sides
A board 50 inches long is to be cut into two parts so that one part will be 6 inches longer than the other. How long should each part be?
The board should be 28 inches long.
What is an expression?
An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed in accordance with context-dependent principles.
Let's call the length of the first part "x". Then, the length of the second part would be x + 6 inches. The total length of both parts is 50 inches, so we can set up an equation to solve for x:
x + (x + 6) = 50
Expanding and solving for x:
2x + 6 = 50
2x = 44
x = 22
So, the first part should be 22 inches long, and the second part should be 22 + 6 = 28 inches long.
The board should be 28 inches long
Given below is a sample of expression please refer the following
https://brainly.com/question/25968875
#SPJ1
The altitude y in feet of a hawk that is descending can be represented by the equation y=−20x+350, where x represents the time in minutes. The equation y=−10x+400 represents the altitude y in feet of an eagle after descending x minutes.
plsss help
By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.
Which bird is closer to the ground after 8 minutes?We know that the height of the hawk is modeled by:
y=−20x+350
And the height of the eagle is modeled by:
y=−10x+400
Now we need to evaluate both equations in x = 8.
hawk:
y = -20*8 + 350 = 190
For the Eagle:
y = -10*8 + 400 = 320
We can see that the hawk is closer to the ground.
Learn more about evaluating equations at:
https://brainly.com/question/4344214
#SPJ1
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $8,000, annual interest: 7%, interest periods: 4, number of years: 10
Please help
Can someone explain and help me through this?
a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.
b. Let t = 10 and solve for the distance the cheetah covered in 10 minutes.
Information from the Warm Up:
According to the Travel Almanac, the world’s fastest land animal is the cheetah. It can travel at up to 70 mph. Think of this scenario: A cheetah sitting under a tree sprints toward its prey at 70 mph. It runs back to its initial spot by the tree at a modest 40 mph. The cheetah has embarked on a round-trip. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.
Can we say that this cheetah’s average rate was 55 mph?
That’s one of the things you’ll determine as you work to complete this task. Make a conjecture. What do you think the answer will be?
well, let's get the info first.
so going forth the Cheetah goes 70mph and going back it modestly does 40mph.
can we say that on average it did 55mph?
well, what's that? on average means, that in total if we sum all units up and divide them evenly by relevant intervals, that's our average value.
well, let's see both intervals, on is forth and another is back 2 intervals, and the speed values are 70 and 40, so the average will really be (70 + 40) ÷ 2 = 55, that is an average of 55mph, so yes, we can say that.
A)
since an hour is 60 minutes, the Cheetah is really doing 70 miles per 60 minutes, or we can say
[tex]70\cdot \cfrac{miles}{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} hour \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{60~minutes}\implies \cfrac{70}{60}\cdot \cfrac{miles}{minutes} \implies 1.1\overline{66}\frac{miles}{minutes}[/tex]
[tex]{\Large \begin{array}{llll} \stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t \end{array}}[/tex]
B)
[tex]\stackrel{\textit{miles covered}}{m(t)}~~ = ~~1.1\overline{66}t\implies \stackrel{t=10}{m(10)=1.1\overline{66}(10)}\implies \stackrel{\textit{miles in 10 minutes}}{m(10)=11.\overline{66}}[/tex]
Pls help thank you will mark the Brainliest
The exponential equation is given by the function y = 30.5(0.7)ˣ
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The standard form of an exponential equation is:
y = abˣ
where b is the rate of change and a is the initial value.
Let y represent the number of games sold x years since 2015.
From the graph, at point (0, 30.5):
30.5 = ab⁰
a = 30.5
Also, at point (1, 21.35):
21.35 = ab¹; but a = 30.5, hence:
21.35 = 30.5b
b = 0.7
The equation is y = 30.5(0.7)ˣ
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Why is the standard deviation used more frequently than the variance?
The standard deviation is used more frequently then the variance because standard deviation is more stable and less sensitive to outliers.
The Standard Deviation and Variance are defined as two closely related measures of the spread or dispersion of a set of data.
The Variance is defined as average of squared differences from mean, while Standard Deviation is square root of variance.
The reason why the standard deviation is used more frequently than variance is because the standard deviation is expressed in same units as the original data, whereas the variance is expressed in squared units.
For Example, if we measure heights of a group of people in inches, the standard deviation will be expressed in inches, whereas variance will be expressed in square inches.
Learn more about Variance here
https://brainly.com/question/29758680
#SPJ4
10 cm
8 cm
12 cm
5 cm
6.4 cm
The perimeter of the rectangle is 36 cm.
What is a rectangle?A rectangle is a two-dimensional figure with length and width.
The area of a rectangle is Length x width.
We have,
Length = 10 cm
Width = 8 cm
Now,
The perimeter of the rectangle.
= 2 (length + width)
= 2 (10 + 8)
= 2 x 18
= 36 cm
Thus,
The perimeter of the rectangle is 36 cm.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ9
The complete question.
The length ad width of a rectangle is 10 cm and 8 cm.
Find the perimeter of the rectangle.
a) 28
b) 12
c) 6.4
d) 36
Write tan theta in terms of a and b.
Answer:ab
Step-by-step explanation:
because..........
Kile is choosing between two international phone plans for his upcoming business trip. Plan A costs $40 for unlimited calls and texts plus $10 per day for data. Plan B costs $28 for unlimited calls and texts plus $12 per day for data. a. Let x represent the number of days Kile will be on the trip and y represent the total cost of the plan. Write a system of equations to represent the problem situation.
The system of two equations can be represented as y = 10x + 40 and
y = 12x + 28.
What are the three types of solutions for a system of linear equations?The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution if a system of equations only has two linear equations with two variables.
Because there are only three possible methods to graph two straight lines in the plane, there are only three matching forms of solution for a given system of equations.
Let, 'x' represent the number of days and 'y' represent the total cost.
Plan A can be represented as y = 10x + 40.
And, PlanB be can be represented as y = 12x + 28.
learn more about the system of linear equations here :
https://brainly.com/question/90105
#SPJ9
one reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a popu- lation mean is that (a) z can be used only for large samples. (b) z requires that you know the population standard deviation s. (c) z requires that you can regard your data as an srs from the population. (d) z requires that the sample size is at most 10% of the population size. (e) a z critical value will lead to
One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.
The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.
To learn more about standard normal curve here:
https://brainly.com/question/28971164
#SPJ4
What the least common denominator of the 2, 3/7, 3,4 ?
The least common denominator of the number 2, 3, 4, 7 is found to be 42.
Here, the least common denominator of the following numbers is asked,
2, 3, 4, 7
Now, first understand the meaning of least common denominator, it is basically meant that what is that least common value that will divide all of the four above mentioned numbers. So, it is actually ased about the least common multiple (LCM).
We can find the value which will be a multiple of all those numbers,
4 is multiple of 2 but 3 and 7 are not.
6 is a multiple of 2 and 3 but 7 is not.
42 is the number that is multiple of 6 as well as 7 and it also the smallest number doing so.
So, the least common denominator of 2, 3, 4, 7 is 42.
To know more about LCM, visit,
https://brainly.com/question/233244#:~:text=Expert%2DVerified%20Answer&text=The%20LCM%20is%20multiple%20which,the%202%20and%204%20LCM.
#SPJ4
Complete question - What is the least common denominator of 2, 3, 7, 4.
A newspaper randomly chooses 100 names from it's subscriber database and then survey's those subscribers to find if they read the restaurant review is this biased or non biased
Answer:
Non biased (kind of)
Step-by-step explanation:
It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs
Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State the sampling method Charlie used.
Charlie could have used quota sampling instead of non-random sampling.
What are sampling methods?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 studentsGiven is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.
Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.
Therefore, Charlie could have used quota sampling instead of non-random sampling.
To solve more questions on sampling, visit the link -
brainly.com/question/30098550
#SPJ1
{COMPLETE QUESTION IS -
Charlie is studying the time it takes members of his company to travel to the office.
He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.
State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}
How are the ordered pairs (,) and (,−) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
Answer: no exact answer
Step-by-step explanation:
which of the following continuous improvement tools is often used to initiate a root cause analysis effort? group of answer choices scatter plot. cause-and-effect (fishbone) diagram. pareto chart. swim lane process map.
Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.
The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis
Find out more about cause-and-effect (fishbone) diagram.
brainly.com/question/14273901
#SPJ4
Rolando is making buttons that are shaped like circles. Each button has an area of 36 square centimeters. Which measurement shows
the circumference of each of the buttons in centimeters?
Answer
A 113.1 cm
B 18.8 cm
C56.5 cm
D 37.7 cm
A measurement that shows the circumference of each of the buttons in centimeters is: D. 37.7 cm.
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circle = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of a circle = πr²
36π = π × r²
Radius, r = √36
Radius, r = 6 centimeters.
Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
Circumference of a circle = 2πr
Circumference of a circle = 2 × 3.14 × 6
Circumference of a circle = 37.7 cm.
Read more on a circle here: brainly.com/question/6615211
#SPJ1
Complete Question:
Rolando is making buttons that are shaped like circles. Each button has an area of 36π square centimeters. Which measurement shows the circumference of each of the buttons in centimeters?
Answer
A 113.1 cm
B 18.8 cm
C56.5 cm
D 37.7 cm
W X
Y
Z
List the sample space for the experiment.
Os = {X, Y, Z}
Os = {W, Z, Z}
Os = {W.Y.Y. Z}
Os = {W, X, Y, Z}
Answer:
Os = {W, X, Y, Z}
Step-by-step explanation:
The sample space for the experiment is the set of all possible outcomes, in this case, W, X, Y, and Z. It represents all the outcomes that can occur in a single trial of an experiment. The sample space is usually denoted as a set, and the elements in the set are the individual outcomes. In this case, the sample space is the set {W, X, Y, Z}.
Answer:
the answer is the last one
Step-by-step explanation:
os= {w, x, y, z}
