Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence. Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
Answer:
The sample size necessary is of 168.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
This means that [tex]\sigma = 39.6[/tex]
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence.
This is n for which M = 6. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{39.6}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 1.96*39.6[/tex]
[tex]\sqrt{n} = \frac{1.96*39.6}{6}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*39.6}{6})^2[/tex]
[tex]n = 167.34[/tex]
Rounding up:
The sample size necessary is of 168.
Which of the following have both 2 and -5 as solutions?
X2+3x-10-0
X2-3x-10=0
X2+7x+10=0
X2-7x+10=0
Answer:
X^2 + 3x - 10=0
If three times a number added to 8 is divided by the number plus 7, the result is four thirds. Find the number.
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Answer:
4/5
Step-by-step explanation:
The wording is ambiguous, as it often is when math expressions are described in English. We assume you intend ...
[tex]\dfrac{3n+8}{n+7}=\dfrac{4}{3}\\\\3(3n+8)=4(n+7)\qquad\text{multiply by $3(n+7)$}\\\\9n+24=4n+28\qquad\text{eliminate parentheses}\\\\5n=4\qquad\text{subtract $4n+24$}\\\\\boxed{n=\dfrac{4}{5}}\qquad\text{divide by 5}[/tex]
The number is 4/5.
A business rents in-line skates and bicycles to tourists on vacation. A pair of skates rents for $5 per day. A bicycle rents for $20 per day.
On a certain day, the owner of the business has 25 rentals and takes in $425.
Write a system of equation to represent this situation, then solve to find the number of each item rented.
Show both the equations and the solution.
Answer:
5x+20y=425
Step-by-step explanation:
Its 5 bucks for x pairs of skates
Its 20 dollars for y bikes
x+y rentals have to equal 25
all of this is equal to 425. All that is left to do is test with number until the statement is true.
try :
5(5)+(20)(20)=425
x + y do equal 25, and the total is equal to 425.
What is the simplified expression for the
expression below? 4(x+8)+5(x-3)
A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 95% confidence interval with an error of no more than 0.08. A consultant has informed them that a previous study found the mean to be 3.1 soft drinks per week and found the variance to be 0.49. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
The minimum sample size required to create the specified confidence interval is 295.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance of 0.49:
This means that [tex]\sigma = \sqrt{0.49} = 0.7[/tex]
They want to construct a 95% confidence interval with an error of no more than 0.08. What is the minimum sample size required to create the specified confidence interval?
The minimum sample size is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 1.96\frac{0.7}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96*0.7[/tex]
[tex]\sqrt{n} = \frac{1.96*0.7}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.7}{0.08})^2[/tex]
[tex]n = 294.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is 295.
The regression analysis can be summarized as follows: Multiple Choice No significant relationship exists between the variables. A significant negative relationship exists between the variables. For every unit increase in x, y decreases by 12.8094. A significant positive relationship exists between the variables
Answer:
A significant negative relationship exists between the variables
Step-by-step explanation:
Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.
Let f(x) = 5 + 12x − x^3. Find (a) the x- coordinate of all inflection points, (b)
the open intervals on which f is concave up, (c) the open intervals on which
f is concave down.
Answer:
A) x = 0.
B) f is concave up for (-∞, 0).
C) f is concave down for (0, ∞).
Step-by-step explanation:
We are given the function:
[tex]f(x)=5+12x-x^3[/tex]
A)
We want to find the x-coordinates of all inflection points.
Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:
[tex]f'(x) = 12-3x^2[/tex]
And the second:
[tex]f''(x) = -6x[/tex]
Set the second derivative equal to zero:
[tex]0=-6x[/tex]
And solve for x. Hence:
[tex]x=0[/tex]
We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:
[tex]f''(-1) = 6>0[/tex]
And testing x = 1:
[tex]f''(1) = -6<0[/tex]
Since the signs change for x = 0, x = 0 is indeed an inflection point.
B)
Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.
From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:
[tex](-\infty, 0)[/tex]
C)
From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:
[tex](0, \infty)[/tex]
In factons you divide the numerator and the whole number .. then denominator
Correct?
Answer:
Step-by-step explanation:
yes
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015
Answer:
The projected world population in 2015 was 8,705,121,030 people.
Step-by-step explanation:
Given that the population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year, assuming that the world population follows an exponential growth model, to find the projected world population in 2015 the following calculation must be performed :
5,000,000,000 x 1.02 ^ (2015-1987) = X
5,000,000,000 x 1.02 ^ 28 = X
5,000,000,000 x 1.741024 = X
8,705,121,030 = X
Therefore, the projected world population in 2015 was 8,705,121,030 people.
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
I need some help! thank you!
Answer:
The 1st,Thrid, Fifth Option
Step-by-step explanation:
The first option is true. We can move the orginal square root function to get g(x).
The second option is false. Function g(x) which equals
[tex] \sqrt{x - 3} - 1[/tex]
Domain is all real numbers greater than or equal to 3.
The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is
[tex]0 - 1 = - 1[/tex]
We can take the sqr root of 0 so
So all real numbers that are greater than or equal to -1 is true.
The fourth option is false, we need to add 3 instead of subtract 3.
The fifth option is true, we can do that to get back to our original function
identify the angles relationship
If he is correct, what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months
Complete Question
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad
Answer:
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Step-by-step explanation:
From the question we are told that:
Population mean \mu=91
Sample Mean \=x =2.08
Standard Deviation \sigma=10
Sample size n=68
Generally the Probability that The sample mean would differ from the population mean
P(|\=x-\mu|<2.08)
From Table
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
T Test
[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]
[tex]Z=1.72[/tex]
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
[tex]P(-1.72<Z<1.72)[/tex]
Therefore From Table
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Evaluate − x 2 −5 y 3 when x = 4 and y =−1
Answer:
-11
Step-by-step explanation:
I am going to assume that it is -x^2-5y^3.
-(4^2)-5(-1^3)
-16-5(-1)
-16+5
-11
Answer:
- 11
Step-by-step explanation:
If x = 4, y = -1
then,
- x^2 - 5y^3 = - (4)^2 - 5(-1)^3
= - 16 + 5
= - 11
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h = 7+23t-16t^2
Find all values of 1 for which the ball's height is 15 feet.
Answer:
Step-by-step explanation:
If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:
[tex]15=-16t^2+23t+7[/tex] and
[tex]0=-16t^2+23t-8[/tex]
Factor this however you factor a quadratic in class to get
t = .59 seconds and t = .85 seconds.
This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.
Lisa reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
A graph titled Lisas Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 350 at increments of 50. A straight line joins the ordered pairs 0, 250 and 1, 200 and 2, 150 and 3, 100 and 4, 50 and 5, 0.
Which equation best models the relationship between x and y?
y = −50x + 250
y = −5x + 50
y = −50x + 350
y = −5x + 250
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Answer:
(a) y = −50x + 250
Step-by-step explanation:
In case you don't realize that the graph starts at 250 and decreases by 50 for each increase of 1 in x, you can see if any of the equations match the given points. The only one that does is the first one:
y = -50x +250
Answer:
(a) y = −50x + 250
Step-by-step explanation:
Use the functions below to complete Parts 1 and 2.
f(x)= |x| g(x)= |x+2| - 3
Part 1: Graph f(x) and g(x) on the grid below. Label each graph.
HINT: Making a table of values for each function may help you to graph them.
Part 2: describe how the graph of g(x) relates to the graph of its parent function, f(x).
HINT: Think about how f(x) was shifted to get g(x).
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Answer:
1. see below
2. g(x) is f(x) translated left 2 and down 3
Step-by-step explanation:
1. The graphs are attached. F(x) is in red; g(x) is in blue.
__
2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.
Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?
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Answer:
see attached
Step-by-step explanation:
The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).
The graph of g(x) is attached.
People's movements between places is called
Answer:
The three answers I can think of are migration, immigration, and emigration.
Step-by-step explanation:
Hope this helps!
What is the solution to this equation?
6
O A. x = 18
O B. x= -2
O c. x= -18
O D. X= 21
Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answer:
[tex]Cold = \frac{1}{6}\ mins[/tex]
Step-by-step explanation:
The correct given parameters are:
[tex]Both = \frac{1}{4}\ mins[/tex]
[tex]Hot = \frac{1}{12}\ mins[/tex]
Required
Time taken by the cold water faucet
We have:
[tex]Cold + Hot = Both[/tex]
Make Cold the subject
[tex]Cold = Both -Hot[/tex]
So, we have:
[tex]Cold = \frac{1}{4}-\frac{1}{12}[/tex]
Take LCM
[tex]Cold = \frac{3-1}{12}[/tex]
[tex]Cold = \frac{2}{12}[/tex]
Divide by 2
[tex]Cold = \frac{1}{6}[/tex]
The number 0 is a critical point of the autonomous differential equation dx/dt = 7xn, where n is a positive integer. For what values of n is 0 asymptotically stable? Semi-stable? Unstable?
Answer:
a) 0 is stable when n = odd
b) 0 is semi-stable when n = even
c) 0 is unstable when n is odd
Step-by-step explanation:
Th differential equation for this question
dx/dt = x^n
n = positive integer
a) value of n where 0 is stable
0 is stable when x^n is replaced with -x^n
because considering n to be an odd number
-x^n > 0 when x < 0 while -x^n < 0 when x > 0
∴ In this scenerio we can conclude that 0 is stable when n = odd number
b) Value of n where 0 is Semi-stable
assuming n is an even number
x^n > 0 for all the values of x
c) Value of n where 0 is unstable
lets assume n is odd
when n < 0, xⁿ < 0
when n > 0, xⁿ > 0
i.e. 0 is asymptotically unstable when n is an odd number
There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.
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Answer:
b = 80 -6n . . . . boys who wear spectacles
Step-by-step explanation:
We know the ratio of boys who wear spectacles to those who don't is ...
(4/5) : (1 -4/5) = 4 : 1
If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.
Let's define a few groups:
boys who wear spectacles: bboys who do not wear spectacles: b/4girls who wear spectacles: (2/3)(40 -5b/4)girls who do not wear spectacles (1/3)(40 -5b/4)Then the total of children who do not wear spectacles is ...
n = b/4 +(1/3)(40 -5b/4)
12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12
2b = 160 -12n . . . . . . . . . . . . . add 2b-12n
b = 80 -6n . . . . the desired relation, b = boys who wear spectacles
_____
Additional comment
The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.
−3 1/2 ÷ 1 1/4
khan academy
answer in simplified proper fraction
or
simplified improper fraction
Answer:
Step-by-step explanation:
Change the mixed numbers to improper fractions.
Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)
Bcoz I really need this rn :(
DUEEEE AFTERRR LUNCHH! :(:(:(:(
If your answer is NONSENSE it will be deleted as soon as possible!
But if your answer is CORRECT, HELPFUL, HAS AN EXPLANATION, I'll chose your answer as the BRAINLIEST ANSWER!
Answer:
The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.
The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2
Explanation:
Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.
The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.
I hope this helps!
Answer:
In LDR
Exterior = d Interior = a, bIn PDR
Exterior = 4Interior = 1, 2Exterior angle of a triangle is formed when one side of the triangle is extended .
Interior remote angles the angles in the triangle that do not lie on the extended side.
Simplify 3/4 + 5/8 over 3/4 - 1/2
Answer:
11/2
Step-by-step explanation:
[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]
= 3/4 + 5/8 = 11/8 (take LCM)
3/4 - 1/2 = 1/4 (take LCM)
11/8 ÷ 1 /4
= 11/8 x 4
= 11/2
Answered by Gauthmath
I need help finding the answer to this question on edge.
Answer:
6
Step-by-step explanation:
We need to evaluate :-
[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]
Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,
[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]
Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,
[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]
Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,
[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]
Hence the required answer is 6.
find c.round to the nearest tenth
Answer:
we need a picture...
Step-by-step explanation:
. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]
Answer:
j * .07 +j
Step-by-step explanation:
The tax on the jewelry is J* .07
Add the tax to the cost of the jewelry to get the total cost
j * .07 +j
