9514 1404 393
Answer:
29
Step-by-step explanation:
We can use ...
(a +b +c)² = a² +b² +c² +2(ab +bc +ca)
9² = a² +b² +c² +2(26)
a² +b² +c² = 81 -52 = 29
Step-by-step explanation:
We know the formula:
(a+b+c)² = a² + b² + c² + 2(ab+bc+ca)
Given:
a+b+c = 9 & ab+bc+ca = 26
Now putting the values in the above formula,
We get,
(9)² = a² + b² + c² + 2×26
81 = (a² +b² +c²) + 52
(a² +b²+c²) = 81-52
(a² + b² + c²) = 29 (Answer)
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
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 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).
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
Find the area of the figure 2m 3m 6m 3m
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
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
PLS HELP 50 POINTS
A rectangular prism has a surface area of 8 square feet. A similar rectangular prism has a surface area of 200 square feet. How many times larger is the surface area of the larger prism?
25
625
10
5
Answer:
25
Step-by-step explanation:
20x8+5x8=200
20+5=25 the answer would be 25
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
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
In a certain year, 88% of all Caucasians in the U.S., 73% of all African-Americans, 73% of all Hispanics, and 75% of residents not classified into one of these groups used the Internet for e-mail. At that time, the U.S. population was 64% Caucasian, 11% African-American, and 13% Hispanic. What percentage of U.S. residents who used the Internet for e-mail were Hispanic
Answer:
The total percentage of U.S. residents who used the Internet for e-mail were Hispanic was 9.5%
Step-by-step explanation:
Given
In a certain year the % share of American population that was Hispanic was 13%
Out of these 13%, 73% Hispanic used the internet for emails.
Now the total percentage of U.S. residents who used the Internet for e-mail were Hispanic was 0.13 * 0.73 = 0.095 = 9.5%
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:
Which of the following is the solution to the quadratic equation x2 + 6x + 8 = 0?
A)x = 4,-2
B)x= -4,2
C)X = 4,2
D)X=-4, -2
Step-by-step explanation:
D)X=-4, -2is the answer
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
What is the y-intercept for f(x) = x2 - 4x +6 ?
Answer:
6
Step-by-step explanation:
the constant is the y-intercept
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
solve x/2 + 2x/5v= 9
please I need it ASAP
Answer:
x/2+2xv/5=9
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
Help 100 points to answer the page
Answer:
Use trigonometry
sine = opposite leg / hypotenusecosine = adjacent leg / hypotenusetangent = opposite leg / adjacent leg#123/x = sin 68x = 23 / sin 68x = 24.8Choice A
#221/x = tan 26x = 21/ tan 26x = 43.1Choice D
Note. All numbers below are rounded to the nearest tenth#312/x = sin 53x = 12 / sin 53x = 15.0#48/x = tan 34x = 8/tan 34x = 11.9#5x/ 12 = cos 26x = 12 cos 26 x = 10.8#6x / 13 = sin 34x = 13 sin 34x = 7.3#7x / 18 = sin 53x = 18 sin 53 x = 14.4#8x / 10 = tan 30x = 10 tan 30 x = 5.8#9cos X = 21/35 = 3/5#10tan X = 32/24 = 4/3Answer:
the person above me is correct i said that because i did the math and solved it
Step-by-step explanation:
If the standard deviation of a data set were originally 4, and if each value in
the data set were multiplied by 1.75, what would be the standard deviation of
the resulting data?
A. 3
B. 4
c. 7
D. 1
Please help
Answer:
it's a.
Step-by-step explanation:
you have to find the mean
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
Which of the following is a solution to the equation sin (x) + 2 = 1
Answer:
-1
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 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 )
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]
Estimate the sum of 1,256, 379 and 305,986 by first rounding each number to the nearest ten thousand.
9514 1404 393
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.
f(z) = (z - 5)(2x + 7) (73 = 3) has zeros at x = -3.5, x=3/7 , x=5 What is the sign of f on the interval 3/7 < x <5?
======================================================
Explanation:
3/7 = 0.42857 approximately
Pick a number between that value and 5, not including either endpoint. Let's say we pick x = 2
Plug x = 2 into the f(x) function
f(x) = (x - 5)(2x + 7)(7x-3)
f(2) = (2 - 5)(2*2 + 7)(7*2-3)
f(2) = (2 - 5)(4 + 7)(14-3)
f(2) = (-3)(11)(11)
f(2) = -363
The actual result doesn't matter. All we're after is whether the result is positive or negative. We see the result is negative. This means f(x) is negative when 3/7 < x < 5. The f(x) curve is below the x axis on this interval.
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.
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.