Answer:
The responses to these question can be defined as follows:
Step-by-step explanation:
[tex]x=3 \\\\n=50\\\\\hat{p}=\frac{x}{n}=0.06\\\\\hat{q}=1-\hat{p}=0.94[/tex]
In point a:
[tex]98\%[/tex] confidence interval for population proportion (p):
[tex]c=98\%=0.98\\\\\alpha=1-c=0.02\\\\\frac{\alpha}{2}=\frac{0.02}{2}=0.01\\\\z_{\frac{\alpha}{2}}=2.326\\\\[/tex]
For point b:
[tex]98\% \ confidence\ interval =\hat{p} \pm z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\[/tex]
[tex]=0.06 \pm 2.326 \sqrt{\frac{0.06\times 0.94}{50}}\\\\ =0.06 \pm 2.326 (0.0336)\\\\=0.06 \pm 0.078\\\\98\% \ CI =(-0.018, 0.138)[/tex]
For point c:
[tex]The\ difference\ between \ 98\% \ CI\ is \ -0.018\ to\ 0.138[/tex]
Write the augmented matrix for the following system of equations.
x - 2 = 0
2y = 4 - 2
9514 1404 393
Answer:
[tex]\left[\begin{array}{cc|c}1&0&2\\0&2&2\end{array}\right][/tex]
Step-by-step explanation:
The system of equations can be written in standard form as ...
x + 0y = 2
0x +2y = 2
The augmented matrix representation of these is ...
[tex]\left[\begin{array}{cc|c}1&0&2\\0&2&2\end{array}\right][/tex]
4/5mm what are the perimeter and the area of the square
length+ breadth and 2×side
Step-by-step explanation:
4÷2 =2
5×2=10
10+2=12
12 ans
25x to the 2nd power minus 49
Answer:
(5x+7) (5x-7)
Step-by-step explanation:
you can look up the answer on symbolab if needed
2.
A bag contains 8 red pens, 7 blue pens, and 14 black pens. Denato will pull a pen from the bag.
When Denato pulls a pen from the bag, how many outcomes are possible?
14
29
8
7
Answer:
Your answer is 29
Step-by-step explanation:
Answer:
The answer is - 29!!!!
Step-by-step explanation:
: D 100% correct
Which of the following is a solution to the equation sin (x) + 2 = 1
Answer:
-1
Step-by-step explanation:
Tell the error and leave if you disagree or agree.
Answer:
Step-by-step explanation:
9. disagree;
error: he should have divided 60 by 4, not subtracted. So the correct answer is x = 15.
10. disagree;
error: it should be 3x + 2 = 127 (opposite angles)
so x = 125/3
Match each equation on the left with the number and type of its solutions on the right.
Answer:
Step-by-step explanation:
1). Given equation is,
2x² - 3x = 6
2x² - 3x - 6 = 0
To find the solutions of the equation we will use quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a, b and c in the formula,
a = 2, b = -3 and c = -6
x = [tex]\frac{3\pm\sqrt{(-3)^2-4(2)(-6)}}{2(2)}[/tex]
x = [tex]\frac{3\pm\sqrt{9+48}}{4}[/tex]
x = [tex]\frac{3\pm\sqrt{57}}{4}[/tex]
x = [tex]\frac{3+\sqrt{57}}{4},\frac{3-\sqrt{57}}{4}[/tex]
Therefore, there are two real solutions.
2). Given equation is,
x² + 1 = 2x
x² - 2x + 1 = 0
(x - 1)² = 0
x = 1
Therefore, there is one real solution of the equation.
3). 2x² + 3x + 2 = 0
By applying quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
x = [tex]\frac{-3\pm\sqrt{3^2-4(2)(2)}}{2(2)}[/tex]
x = [tex]\frac{-3\pm\sqrt{9-16}}{4}[/tex]
x = [tex]\frac{-3\pm i\sqrt{7}}{4}[/tex]
x = [tex]\frac{-3+ i\sqrt{7}}{4},\frac{-3- i\sqrt{7}}{4}[/tex]
Therefore, there are two complex (non real) solutions.
Please help me solve this!
Answer:
The functions are:
f(x) = $14.75*x + $2
s(x) = $12.25*x + $17
Both iSpice and Spice Magic charge $90.50 for 6 pounds of paprika.
Step-by-step explanation:
A linear equation has the general shape:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the function passes through the points: (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Ok, knowing this, let's look at the first table, we need to work with only two points, so let's use the first one (1, $16.75) and the second one (2, $31.50)
Then the slope of the equation is:
a = ($31.50 - $16.75)/(2 - 1) = $14.75
Then the equation is something like:
y = f(x) = $14.75*x + b
To find the value of b, we can use one of the two points. For example, the point (1, $16.75) means that when x = 1, we must have y = $16.75
Replacing these values in the equation we get:
$16.75 = f(1) = $14.75*1 + b
$16.75 - $14.75 = b = $2
Then the function f(x) is:
f(x) = $14.75*x + $2
Now let's go to the other function, again we can choose two points, let's use the first one (1, $29.25) and the third one (3, $53,75).
Then the slope is:
a = ($53.75 - $29.25)/(3 - 1) = $12.25
Then the equation is something like:
y = s(x) = $12.25*x + b
To find the value of b we do the same as before, if we use the first point (1, $29.25) we get:
$29.25 = s(1) = $12.25*1 + b
$29.25 - $12.25 = b = $17
Then this equation is:
y = s(x) = $12.25*x + $17
The two equations are:
f(x) = $14.75*x + $2
s(x) = $12.25*x + $17
b) now we want to find the value x such that the price is the same in both cases, then we need to solve:
f(x) = g(x)
$14.75*x + $2 = $12.25*x + $17
$14.75*x - $12.25*x = $17 - $2
$2.5*x = $15
x = $15/$2.5 = 6
This means that for 6 pounds of paprika the price is the same on both companies, and the price is:
f(6) = g(6) = $14.75*6 + $2 = $90.50
Find the area of the figure 2m 3m 6m 3m
Estimate the sum of 1,256, 379 and 305,986 by first rounding each number to the nearest ten thousand.
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Answer:
1,570,000
Step-by-step explanation:
The sum is approximately ...
1,260,000 +310,000 = 1,570,000
_____
Additional comment
It is a good idea to estimate the error associated with an estimate. Here, both numbers are rounded up by about 4000 each, so the estimate is around 8000 high.
What is the y-intercept for f(x) = x2 - 4x +6 ?
Answer:
6
Step-by-step explanation:
the constant is the y-intercept
An article in The Engineer (Redesign for Suspect Wiring," June 1990) reported the results of an investigation into wiring errors on commercial transport aircraft that may produce faulty information to the flight crew. Such a wiring error may have been responsible for the crash Of a British Midland Airways aircraft in January 1989 by causing the pilot to shut down the wrong engine. Of 1600 randomly selected aircraft, eight were found to have wiring errors that could display incorrect information to the flight crew.
Required:
a. Find a 99% confidence interval on the proportion of aircraft that have such wiring errors. Round your answers to 4 decimal places.
b. Suppose we use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate of p that we are 99% confident differs from the true value by at most 0.009?
c. Suppose we did not have a preliminary estimate of p. How large a sample would be required if we wanted to be at least 99% confident that the sample proportion differs from the true proportion by at most 0.009 regardless of the true value of p?
Answer:
a) The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).
b) A sample of 408 is required.
c) A sample of 20465 is required.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Of 1600 randomly selected aircraft, eight were found to have wiring errors that could display incorrect information to the flight crew.
This means that [tex]n = 1600, \pi = \frac{8}{1600} = 0.005[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 - 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0005[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 + 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0095[/tex]
The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).
b. Suppose we use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate of p that we are 99% confident differs from the true value by at most 0.009?
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A sample of n is required, and n is found for M = 0.009. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.009 = 2.575\sqrt{\frac{0.005*0.995}{n}}[/tex]
[tex]0.009\sqrt{n} = 2.575\sqrt{0.005*0.995}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.005*0.995}}{0.009}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575\sqrt{0.005*0.995}}{0.009})^2[/tex]
[tex]n = 407.3[/tex]
Rounding up:
A sample of 408 is required.
c. Suppose we did not have a preliminary estimate of p. How large a sample would be required if we wanted to be at least 99% confident that the sample proportion differs from the true proportion by at most 0.009 regardless of the true value of p?
Since we have no estimate, we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.009\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.009}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2[/tex]
[tex]n = 20464.9[/tex]
Rounding up:
A sample of 20465 is required.
Question #3 show steps or how you know
Answer: Choice D)
(-1.5, -1) and (0, 1)
=============================================================
Explanation:
Exponents can be a bit clunky if you have too many of them, and if they're nested like this. Writing something like e^(x^2) may seem confusing if you aren't careful. I'm going to use a different notation approach. I'll use "exp" notation instead.
So instead of writing something like e^(x^2), I'll write exp(x^2).
The given derivative is
f ' (x) = exp(x^4-2x^2+1) - 2
and this only applies when -1.5 < x < 1.5
Apply the derivative to both sides and we'll find the second derivative
f ' (x) = exp(x^4-2x^2+1) - 2
f '' (x) = d/dx[ exp(x^4-2x^2+1) - 2 ]
f '' (x) = exp(x^4-2x^2+1)*d/dx[ x^4-2x^2+1 ]
f '' (x) = exp(x^4-2x^2+1)*(4x^3-4x)
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
From here, we need to find the roots of f '' (x).
Set f '' (x) equal to zero and solve to get...
f '' (x) = 0
(4x^3-4x)*exp(x^4-2x^2+1) = 0
4x^3-4x = 0 ..... or .... exp(x^4-2x^2+1) = 0
4x(x^2-1) = 0
4x(x+1)(x-1) = 0
4x = 0 or x+1 = 0 or x-1 = 0
x = 0 or x = -1 or x = 1
Those are the three roots. We ignore the equation exp(x^4-2x^2+1) = 0 because it doesn't have any real number solutions.
---------------------
The three roots of x = 0 or x = -1 or x = 1 represent possible locations of points of inflection (POI). Recall that a POI is where the function changes concavity. To determine if we have a POI or not, we'll need to a sign test.
Draw out a number line. Plot -1, 0, and 1 in that order on it. Pick something to the left of -1 but larger than -1.5, lets say we pick x = -1.2. Plugging this into the second derivative function leads to...
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
f '' (-1.2) = (4(-1.2)^3-4(-1.2))*exp((-1.2)^4-2(-1.2)^2+1)
f '' (-1.2) = -2.563
That value is approximate. The actual value itself doesn't matter. What does matter is the sign of the result. The negative second derivative value tells us we have a concave down region. So we just found that f(x) is concave down for the interval -1.5 < x < -1, which converts to the interval notation (-1.5, -1)
Repeat the process for something between x = -1 and x = 0. I'll pick x = -0.5 and it leads to f '' (-0.5) = 2.63 approximately. The positive result tells us that we have a concave up region. Therefore, -1 < x < 0 is not part of the answer we're after.
Repeat for something between x = 0 and x = 1. I'll pick x = 0.5 and it produces f '' (0.5) = -2.63 approximately. So the region 0 < x < 1 is also concave down. Meaning that the interval notation (0,1) is also part of the answer.
So far we have the interval notation of (-1.5, -1) and (0,1) as part of our solution set.
Lastly, we need to check something to the right of x = 1, but smaller than 1.5; let's go for x = 1.2
You should find that f '' (1.2) = 2.563 which allows us to rule out the region on the interval 1 < x < 1.5
Overall, the final answer is (-1.5, -1) and (0, 1)
A rental car company charges $33 per day to rent a car and $0.12 for every
mile driven. Zachary wants to rent a car, knowing that:
• He plans to drive 400 miles.
• He has at most $180 to spend.
Use the drop-down menu below to write an inequality representing d, the
total number of days Zachary can rent the car while staying within his budget.
d
Answer:
2 days
Step-by-step explanation:
0.12x 400=48.00+33.00=81×2=162.00 for 2 days
Solve for all values of x by factoring.'
x2 + 10x + 21 = 0
Answer:
Step-by-step explanation:
2x+10x=12x
12x=-21
x=-1.75
Answer:
x=-7,-3
Step-by-step explanation:
x2+10x+21
(x+7)(x+3)
x=-7,-3
A true-false examination was constructed with the answers running in the following sequence: T F F T F T F T T F T F F T F T F T T F Does this sequence indicate a departure from randomness in the arrangement of T and F answers?
Answer:
yes
Step-by-step explanation:
lets use a significance level of = 0.1
Determine if the sequence indicates randomness
First step :
H0 : pattern is random
H1 : pattern not random
n1 ( number of true answers ) = 10
n2 ( number of false answers ) = 10
also number of runs for T = 5
number of runs for F = 5
Total number of runs = 5+ 5 = 10
Given that critical value at 0.05 = 23
we will reject the null hypothesis ( i.e the sequence departs from randomness )
How much wrapping paper is needed to cover the gift box shown below?
SA = 2Lw + 2Lh + 2wh
Answer:
528 square inches
Step-by-step explanation:
SA = 2(10·16) + 2(10·4) +2(4·16)
= 2(160)+2(40)+2(64)
= 320 + 80 + 128
= 528 square inches
solve x/2 + 2x/5v= 9
please I need it ASAP
Answer:
x/2+2xv/5=9
Step-by-step explanation:
12. If one line passes through the points
(-3,8) & (1,9), and a perpendicular line passes
through the point (-2,4), what is another point
that would lie on the 2nd line. Select all that apply.
A. (-1,0)
B. (2,5)
C. (5,2)
D. (-6,3)
E. (8,-3)
F. (-3,8)
9514 1404 393
Answer:
A, F
Step-by-step explanation:
Points A(-1, 0) and F(-3, 8) lie on the 2nd line. (Its equation is 4x+y=-4.)
A 24 ft ladder is positioned next to a house for window cleaning. The manufacturer recommends the ladder rest at an angle of 76° with respect to the ground for safe operation. How far away from the house should the ladder be positioned to ensure the recommended angle of 76°? Round your answer to the nearest foot.
A 76 degree angle of elevation is drawn. The line from the horizontal axis to the vertical axis measures 24 units.
Enter your answer in the box.
Answer:
6 feet
Step-by-step explanation:
cos = adj/hyp
cos76 = adj/24
multiply both sides by 24
24 * cos76 = adj
5.806125494392025 = adj
Rounded
6 feet
The table of values represents a function f(x).
How much greater is the average rate of change over the interval [7, 9] than the interval [4, 6]?
Enter your answer in the box.
Answer:
It is 603 units greater
Step-by-step explanation:
Given
See attachment for table
Average rate of change over (a,b) is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]
For interval [7,9], we have:
[tex][a,b] = [7,9][/tex]
So, we have:
[tex]Rate = \frac{f(9) - f(7)}{9-7}[/tex]
[tex]Rate = \frac{f(9) - f(7)}{2}[/tex]
From the table:
[tex]f(9) = 3878[/tex]
[tex]f(7) = 1852[/tex]
So:
[tex]Rate = \frac{f(9) - f(7)}{2}[/tex]
[tex]Rate = \frac{3878 - 1852}{2}[/tex]
[tex]Rate = \frac{2026}{2}[/tex]
[tex]Rate = 1013\\[/tex]
For interval [4,6], we have:
[tex][a,b] = [4,6][/tex]
So, we have:
[tex]Rate = \frac{f(6) - f(4)}{6-4}[/tex]
[tex]Rate = \frac{f(6) - f(4)}{2}[/tex]
From the table:
[tex]f(6) = 1178[/tex]
[tex]f(4) = 358[/tex]
So:
[tex]Rate = \frac{f(6) - f(4)}{2}[/tex]
[tex]Rate = \frac{1178 - 358}{2}[/tex]
[tex]Rate = \frac{820}{2}[/tex]
[tex]Rate = 410[/tex]
Calculate the difference (d) to get how much greater their rate of change is:
[tex]d = 1013 - 410[/tex]
[tex]d = 603[/tex]
Answer:
603
Step-by-step explanation:
i took it
HELPPPPP PLEASEEEE I BEG YOUUUUUU
Answer:
D 5 This the answerStep-by-step explanation:
HOPE it HELPS
your ans. is D.........
ANSWER QUICK
1. Give the value of y.
3y = 51
2. Give the value of w.
w ÷ 5 = 4
Answer:
1) y = 17
2) w = 20
Step-by-step explanation:
Answer:
y= 17
w= 20
Step-by-step explanation:
Can someone please help with both I will mark u brilliant
Answer:
75%
Step-by-step explanation:
To get the average first you would add up all of the scores, 48+93+78+89+32+92+93. Which equals 525. Then you would divide by the amount of tests (7) so 525/7. Which is 75
Answer:
Hello! answer: the mode for question 1 is 23
answer: the mean for question 2 is
75 The teacher might want you to round though cause that's a lot of numbers
A survey was initiated and intended to capture the prevalence of specific learning disorder (SLD) among school-aged children with autism spectrum disorder (ASD). Out of a sample of 1,483 participants, a total of 241 were found to have SLD. Calculate 95% confidence interval for the proportion of participants who have SLD among the children with ASD.
Answer:
The 95% confidence interval for the proportion of participants who have SLD among the children with ASD is (0.1437, 0.1813).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Out of a sample of 1,483 participants, a total of 241 were found to have SLD.
This means that [tex]n = 1483, \pi = \frac{241}{1483} = 0.1625[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1625 - 1.96\sqrt{\frac{0.1625*0.8375}{1483}} = 0.1437[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1625 + 1.96\sqrt{\frac{0.1625*0.8375}{1483}} = 0.1813[/tex]
The 95% confidence interval for the proportion of participants who have SLD among the children with ASD is (0.1437, 0.1813).
Examine the graph of the logarithmic function f(x).
The function f(x) has a vertical asymptote at x= Blank.
Answer:
The function f(x) has a vertical asymptote at x = 3
Step-by-step explanation:
We can define an asymptote as an infinite aproximation to given value, such that the value is never actually reached.
For example, in the case of the natural logarithm, it is not defined for x = 0.
Then Ln(x) has an asymptote at x = 0 that tends to negative infinity, (but never reaches it, as again, Ln(x) is not defined for x = 0)
So a vertical asymptote will be a vertical tendency at a given x-value.
In the graph is quite easy to see it, it occurs at x = 3 (the graph goes down infinitely, never actually reaching the value x = 3)
Then:
The function f(x) has a vertical asymptote at x = 3
Find the missing value of: -1 = 7 - ?
Answer:
-1 = 7 - 8
Step-by-step explanation:
A rectangle has a length of 8ft
and a width of 4ft, what is the
area of the rectangle in square
feet?
Answer:
32
Step-by-step explanation:
A=wl=4·8=32
Which of the following numbers makes the statement true? 3/8 > < 3/6
Answer:
2/5
Step-by-step explanation:
3/8 = 375/1000
1/2 = 500/1000
2/5 = 400/1000
Anybody know the answer to this it would be very helpful
Answer:
The cost for 4 snacks is 18 dollars.
Cost for x snacks: 4.5x
Step-by-step explanation:
4 x 4.5 = 18
Answers:
Cost for 4 snacks = 70 dollarsCost for x snacks = 4.50x+52 dollarsThe algebraic expression shown above is the same as writing 52+4.50x
You may not need to type in "dollars" or a dollar sign, as your teacher may just want the numbers and algebraic symbols.
=====================================================
Explanation:
There are four people going to the movies, and each ticket costs $13 a piece, so that means the total so far is 4*13 = 52 dollars.
If we want to include snacks, then it costs $4.50 per snack. Buying 4 packages will cost an additional 4.50*4 = 18 dollars. In total, if Kiran wants to buy four snacks, then he'll need 52+18 = 70 dollars.
---------------------
Instead of computing 4.50*4 to get 18, we can leave the "4.50*4" like it is. Adding it onto the 52 found earlier leads to the expression 52+4.50*4
Now imagine that instead of "4", we just had a generic placeholder x take over. The x is standing in for any positive real number, or it could stand in for 0 if Kiran decides to not buy any snacks at all.
If we replace that "4" with x, then the expression
52+4.50*4
is the same as
52+4.50*x
Often times, you'll see the multiplication symbol omitted and the expression could look like 52+4.50x
Because we can add two numbers in any order, that expression above is the same as 4.50x+52
-------------------
Extra info (optional section):
The useful thing about something like 4.50x+52 is that we can graph y = 4.50x+52 and/or set up a table to be able to quickly determine how much money it will cost for buying any amount of snacks.
For example, let's say he wants to buy 10 snacks. That means we replace x with 10 and evaluate like so
4.50x+52 = 4.50*10+52 = 45+52 = 97
Buying 10 snacks, on top of the 4 movie tickets, cost $97 in total.