The condition number for the problem of evaluating the function f(x) = 1/cos(x) near the point x = 1.5708 is approximately 10 raised to power 16
This means that a small change in the input x can cause a large change in the output f(x).
The condition number of a function is a measure of how sensitive the function is to changes in its input. The larger the condition number, the more sensitive the function is to changes in its input. The condition number for the function f(x) = 1/cos(x) can be estimated as follows:
K = |f'(x)| / |f(x)|
where f'(x) is the derivative of f(x) and f(x) is the value of f(x) at the point x. At the point x = 1.5708, f'(x) = -1 and f(x) = 0.017453292519943295. Therefore, the condition number is approximately:
K = |-1| / |0.017453292519943295| = 10 raised to power 16
This means that a small change in the input x can cause a large change in the output f(x). For example, if the input x is changed by 1e raised to power of -16, the output f(x) will change by approximately 10 raised to power of 16.
This large condition number is due to the fact that the function f(x) = 1/cos(x) is very sensitive to changes in the input x near the point x = 1.5708. This is because the cosine function is very close to zero at this point.
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ANSWERRRRRR :puppy eyes emoji:
Answer:
A rhombus is a special type of parallelogram
Step-by-step explanation:
Similarities in a rhombus and parallelogram:
Both pairs of opposite sides are equal and parallel.Diagonals bisect each other and are unequal.Opposite angles are equal.None of the angles is 90 degrees.A rhombus is a special type of parallelogram in that
All its sides are equal.The diagonals bisect each other at right angles.Each diagonal bisects the angle at the vertices.Open Ended Questions
Show all work to receive full credit
16. Use the model for vertical motion given by the equation h = -16t^2 + vt +s, where h is the
height in feet, t is the time in seconds, v is the initial upward velocity, and s is the initial height
in feet.
A. Rick tossed a baseball in the air from a height of 15 feet with an initial upward velocity of 8
feet per second. How long was the ball in the air before it hit the ground?
B. How high was the ball after 1 second?
Answer:
Step-by-step explanation:
We've established that heights of 10-year-old boys vary
according to a Normal distribution with mu = 138cm and sigma = 7cm
What proportion is between 152 and 124 cm ?
The proportion of values between 152 and 124 cm is 0.8996 or 89.96%.
Proportion between 152 and 124 cm according to a normal distribution with mu = 138cm and sigma = 7cm is 0.8996.
According to the given question, we know that the mean is μ = 138 cm, standard deviation is σ = 7 cm.
We have to find the proportion that is between 152 and 124 cm.
To solve the problem, first we have to find the z-scores for 152 and 124 cm.
We can calculate the z-scores as follows:Z-score for 152 cm is given by:z152=(152−138)7=2z_{152}=\frac{(152-138)}{7}=2z152=(152−138)7=2Z-score for 124 cm is given by:z124=(124−138)7=−2z_{124}=\frac{(124-138)}{7}=-2z124=(124−138)7=−2
We can use a z-table or calculator to find the proportion of values between these two z-scores.
The area under the standard normal curve between z = -2 and z = 2 is approximately 0.8996.
Therefore, the proportion of values between 152 and 124 cm is 0.8996 or 89.96%.
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The blue segments below is a diameter of oo. What is the length of the radius of the circle?
Answer:
C. 5.1 unitsStep-by-step explanation:
Given Information :
Diameter : 10.2 units
Radius (r) = ?
[tex]r = \frac{d}{2} [/tex]
Input the values
[tex]r = \frac{10.2}{2} \\ \\ r = 5.1[/tex]
the other one i need help with asap!!
Answer:
(3x-2)(2x-3)
Step-by-step explanation:
Good luck!
What is the equation of the axis of symmetry?
Can someone please help me answer this question asap thank you
Answer:
250
Step-by-step explanation:
i did cross multiplication 40/100 = 100/x
100*100 and divide by 40
I can't figure it out
Answer:
V = 17,371.8
Step-by-step explanation:
V = π r^2 h
V = π (12)^2 (38.4)
V = 17,371.75073729
V = 17,371.8
You have to calculate the area of the base of the cylinder (the circle) by using the formula π r^2, r = the radius of the circle. You are squaring the r because r^2 = diameter. The formula to get the area of a circle is π r ^2. To get the volume you need to multiply the area of the circle by the height of the cylinder. All together the total formula to get the volume of a cylinder is π r^2 h
Will help you with something if u help me plsss
Steph Curry went crazy buying houses and carsafter the Warriors won the first round of the playoffs. Now he doesn’t have enough money to make his mortgage payment. Alyssa and Step are good friends, so Alyssa decided to lend Steph $7,500. Alyssa is going to charge Step 8% interest, which will compound monthly. How much will Steph owe Alyssa if he pays her back in 2 years?
Answer:
21900
Step-by-step explanation:
Find 8% of 7500 (600) and multiply it by 24 (amount of months) then add that to 7500
(1 point) suppose that the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32. find the eigenvalues of a. the eigenvalues of a are . (enter your answers as a comma separated list.)
If the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32, the eigenvalues of matrix a are 4 and 8.
To find the eigenvalues of a 2×2 matrix, we can use the following formula:
λ² - tr(a) * λ + det(a) = 0,
where λ represents the eigenvalues, tr(a) is the trace of the matrix, and det(a) is the determinant.
In this case, we are given that tr(a) = 12 and det(a) = 32. Substituting these values into the formula, we have:
λ^2 - 12λ + 32 = 0.
To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring the equation, we get:
(λ - 4)(λ - 8) = 0.
Setting each factor equal to zero, we find two solutions:
λ - 4 = 0 => λ = 4,
λ - 8 = 0 => λ = 8.
The trace and determinant of a matrix provide valuable information about its eigenvalues. In this case, by substituting the given trace and determinant into the eigenvalue formula, we were able to find the eigenvalues of the 2×2 matrix a.
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A marketing class of 50 students evaluated the instructor using the following scale superior, good, average, poor or inferior. The descriptive summary showed the following survey results: 2% superior, 8% good, 45% average, 45% poor, and 0% inferior Multiple Choice The instructor's performance was great! The instructor's performance was inferior Most students rated the instructor as poor or average What type of variable is "pounds of popcorn" served at a movie theater? Multiple Choice Ratio Discrete Continuous
The variable "pounds of popcorn" served at a movie theater is a continuous variable that can take any value within a certain range. It is not restricted to specific discrete values or categories.
A continuous variable is one that can take any value within a certain range. In the case of "pounds of popcorn" served at a movie theater, it can have fractional values and can vary continuously from very small amounts to large amounts.
It is not restricted to specific discrete values or categories. In contrast, discrete variables can only take on specific values, while ratio variables have a meaningful zero point and allow for comparisons of ratios. Since the amount of popcorn served can be measured with any level of precision, it falls under the category of a continuous variable.
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A random sample {X_1, X_2} of size 2 is drawn from a population with mean µ and variance δ^2. (So X_1 & X_2 are i.i.d.) Let we have two unbiased estimator of the population mean µ
V_1 =1/2(X_1+X_2) and V2 =1/2(X_1+2X_2)
Which estimator would you use?
The estimator V₁ = 1/2(X₁ + X₂) is preferred over V₂ = 1/2(X₁ + 2X₂) because it is unbiased and has a smaller variance.
What is the correct estimator to use?To determine which estimator to use, consider the properties of unbiased estimators and compare the variances of V₁ and V₂.
Unbiasedness:
For V₁:
E(V₁) = E(1/2(X₁ + X₂)) = 1/2(E(X₁) + E(X₂)) = 1/2(µ + µ) = µ
For V₂:
E(V₂) = E(1/2(X₁ + 2X₂)) = 1/2(E(X₁) + 2E(X₂)) = 1/2(µ + 2µ) = 3/2µ
From the calculations, we can see that V₁ is an unbiased estimator of the population mean µ, while V₂ is biased since E(V₂) ≠ µ
Therefore, V₁ is preferred in terms of unbiasedness.
Variance:
Var(V₁) = Var(1/2(X₁ + X₂)) = 1/4(Var(X₁) + Var(X₂) + 2Cov(X₁, X₂))
Var(V₁) = 1/4(δ² + δ² + 2*0) = 1/2δ²
Var(V₂) = Var(1/2(X₁ + 2X₂)) = 1/4(Var(X₁) + 4Var(X₂) + 2Cov(X₁, 2X₂))
Var(V₂) = 1/4(δ² + 4δ² + 2*0) = 5/4δ²
Comparing the variances, we can see that Var(V₁) = 1/2δ², while Var(V₂) = 5/4δ².
Since Var(V₁) is smaller than Var(V₂), V₁ is preferred in terms of variance as well.
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help PLz will mark brain list
Answer:
10.10 15.15
Step-by-step explanation:
25.30 15.12 25.13
There are 96 children in a room.
40 of them are girls.
Find the fraction of the children that are boys.
Write your answer in its simplest form.
I will need it by this midnight
Answer:
7/12
Step-by-step explanation:
Basically to find the boys fraction I subtracted 40 from 96 and got 56. Your answer for the number of boys would be 56/96. I divided 4 from each and got 14/24. lastly I divide by 2 and got 7/12.
assume x and y are functions of t. evaluate for the following. y³=2x²+14; dx/dt =3,x=5, y=4
dy/dt = __ (Round to two decimal places as needed.)
To evaluate dy/dt given the equation y³ = 2x² + 14, along with dx/dt = 3, x = 5, and y = 4, we can use implicit differentiation and substitute the given values.
dy/dt is approximately equal to 0.51 (rounded to two decimal places).
To explain the solution, let's start by differentiating both sides of the equation implicitly with respect to t:
3y²(dy/dt) = 4x(dx/dt)
Now, we substitute the given values x = 5, y = 4, and dx/dt = 3 into the equation:
3(4)²(dy/dt) = 4(5)(3)
Simplifying this expression, we have:
48(dy/dt) = 60
Dividing both sides by 48, we find:
dy/dt = 60/48 = 1.25
Therefore, dy/dt is approximately equal to 1.25. Rounded to two decimal places, the value is 0.51.
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Find the volume of the square pyramid. The work has been started for you.
V = 1
3
Bh
B = 6.5(6.5) = 42.25 m2
Complete question
A square pyramid. The square base has side lengths of 6.5 meters and the height of 6 meters.
What is the volume of the pyramid?
Answer:
84.5m³
Step-by-step explanation:
The volume of a square. Pyramid is given as :
V = 1/3 * base * height
Base = l² ; l = side length
Base = 6.5² = 42.25 m²
V = 1/3 * 42.25 * 6
V = 42.25 * 2
V = 84.5
The volume of square pyramid = 84.5m³
help quick which ones greater 7.133 is _______ 7.1437
Answer:
7.1437 is greater
Step-by-step explanation:
Answer:
7.133 < 7.1437
Step-by-step explanation:
Line up the numbers till you find one that is greater
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS-
Answer:
4. 50,000 square miles
5. The office would round to $800,000 instead of $700,000 because they would lose that needed $35,495. If they rounded down, their budget would be cut short, and they won’t have enough money for the office.
6. Five numbers that could also be the population: 577,777; 575,555; 578,999: 578,787; 581,545.
7. 600,000
8.584,000
9. 260,000
Step-by-step explanation:
4. In this question, we’re rounding the number, “54,555” go the nearest ten thousand. When rounding numbers you look at the number next to the digit your rounding. In this case, since the second number is not 5 or higher, we round it to 50,000 as that’s closer than 60,000.
5. Like I stated above: if they round to the lowest amount, they won’t have enough money to but what they need. Therefore, even if according to rounding it needs to be lower, it will not be beneficial to the company.
6. This are all possible numbers cause they can all by round to 580,000 AND 600,000
7. Since the number next to six is not five or higher, we round it to the closest number which is 600,000.
8. Since the number next to 3 is 5, we round it to the higher number. So it’s 584,000
9. Since the number next to the underlined nunber is 6, we round it to the closest number which is 260,000
If you have any more questions, you can ask me :)
Can some help me with this please and ty.
Answer:
4 centimetres per hour.
Step-by-step explanation:
Find the area of the given triangles.
154 yd ²
the formula is (b • h) / 2 = A
so plug it in (14 • 22) / 2 = 154
PLEASE HELP!!!! WILL MARK BRAINLIEST IF CORRECT!!!!!!
The picture shows the question, tables, and multiple-choice answers.
Love you, tysm, happy tuesday <3
The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet
Complete question :
The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.
Answer:
17
Step-by-step explanation:
From Pythagoras :
Hypotenus = sqrt(opposite² + adjacent²)
From the diagram
l = sqrt((l-9)² + 15²)
l² = (l² - 18x + 81 + 225)
Square both sides
l² = l² - 18x + 306
l² - l² = 306 - 18x
18l = 306
l = 306/18
l = 17
In a survey, music club members select their preference between Song A or Song B. Song A is selected by 30 teens and 10 adults. Of 20 members who select Song B, five are teens.
Make a two-way frequency table to organize the data.
Is it reasonable to say that more people surveyed prefer Song A? Explain.
Is it reasonable to say that more adults than teens participated in the survey? Explain.
Answer: 40 people like song A whereas 20 people like song B. Thus, it is reasonable to say that more people liked Song A .
Step-by-step explanation:
The solution set of IR - 31 = 10 is?
{7, 13)
(-7, 13)
(-13, 13)
Answer:
{7, 13)
Step-by-step explanation:
IR - 31 = 10
IR = 41
7*13 = 41
(-7)*13 = -41
(-13)*13 = -169
How many different 3-digit odd number can be formed with the digit 0,1,2 up to 9 if the repitition of digits is not allowed
Answer:
The answer is "320".
Step-by-step explanation:
They have to be 1, 3, 5, 7, and 9 as your final digit. Your middle digit may be anything other than the first digit, and only the last digit or 0, is anything.
Now let us take a look at strange digits ending in 1.
This can start from any digit other than 0, so there are 8 options during the first digit.
Its middle digit could only be 1 digit and 1 digit. Even so, it can also be 0, since it has 8 options.
So, [tex]8\times 8 = 64[/tex] strange number ending in 1.
For other strange amounts, the very same logic is working.
And thus there are 64 possible odd numbers for just about any number ending in any of the five odd digits: 1, 3, 5, 7, or 9.
The answer is [tex]5 \times 64 = 320[/tex].
A group of students was asked about the number of e-mails they each sent
that day. The results are:
0,0,0,0,1,2,2,3,5,5, 8, 9, 10, 10, 10
Which histogram correctly shows the data set?
Answer:
C
Step-by-step explanation:
It was right on the quiz
Answer:
It’s B
explanation:
How do you find the value of x while working with adjacent and vertical angles? The angle is adjacent btw if that helps... I am in 7th grade and need help with this topic
Answer:
The angles are adjacent because they have a common side and vertex. Basically, they are both right next to each other.
x = 28
Step-by-step explanation:
When (x + 6)° and 56° are added together, they need to equal 90° since they are both parts of a right angle.
(x + 6) + 56 = 90
x + 62 = 90
x = 28
Find the marginal distribution of military status in percentages. Round to the nearest whole percent.
The question is incomplete. Here is the complete question.
Mavis is interested whether military status is related to gender in American Samoa. The data she collected about the population of American Samoa in 2010 is below.
Find the marginal distribution of military status in percentages. Round to the nearest whole percentages.
In Armed Forces:
Military-dependent:
Civilian:
Answer: In Armed Forces: 0%
Military-dependent: 3%
Civilian: 97%
Step-by-step explanation: Marginal Distribution is defined as the probability distribution of variables contained in a subset.
For the American Samoa's military status, marginal distribution is
1) In Armed Forces:
[tex]p_{1}=\frac{87}{55,519}*100[/tex]
[tex]p_{1}=0.15[/tex]
2) Military-dependent:
[tex]p_{2}=\frac{1709}{55,519}*100[/tex]
[tex]p_{2}=3.08[/tex]
3) Civilian:
[tex]p_{3}=\frac{53,723}{55,519}*100[/tex]
[tex]p_{3}=96.77[/tex]
Now round each percentage to the nearest whole percentage:
Armed forces: 0%
Military: 3%
Civilian: 97%
The marginal distributions of military status are, in nearest whole percentage:
Armed forces: 0%
Military: 3%
Civilian: 97%
A data point far from the mean of both the x's and y's is always:
a) an influential point and an outlier
b) a leverage point and an influential point
c) an outlier and a leverage point
d) None of the above
The correct answer is c) an outlier and a leverage point.A data point far from the mean of both the x's and y's is both an outlier and a leverage point.
A data point that is far from the mean of both the x-values and y-values can be considered an outlier and a leverage point. An outlier is a data point that significantly deviates from the overall pattern of the data. It lies far away from the majority of the data points and can have a significant impact on statistical analysis.
On the other hand, a leverage point is a data point that has an extreme value in terms of its x-value. It has the potential to influence the regression line and can greatly affect the regression model's fit. Therefore, a data point far from the mean of both x's and y's can be considered both an outlier and a leverage point.
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If x=(y+2)^2 and y= -7 then what is x
Answer:
X=25
Step-by-step explanation:
y+2=-7+2=5
[tex]5^{2} =25[/tex]