in july of 2013, australians were asked if they thought unemployment would increase, and 47% thought that it would increase. in november of 2013, they were asked again. at that time 338 out of 800 said that they thought unemployment would increase. at the 8% level, is there enough evidence to show that the proportion of australians in november 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in july 2013?

Regardless of whether f is positive or negative on I, we have shown that the function f keeps a constant sign throughout the interval I.

To show that the function f keeps a constant sign on an interval I, we can use the intermediate value theorem.

First, let's assume that f is positive on I. We want to show that f remains positive throughout the interval I.

Since f is continuous on I and does not vanish (i.e., f(x) ≠ 0 for all x in I), we can apply the intermediate value theorem.

Suppose there are two points, a and b, in I such that a < b. Since f is positive on I, we have f(a) > 0 and f(b) > 0.

Now, consider any point c between a and b (a < c < b). Since f is continuous on I, it must also be continuous on the closed interval [a, c] and [c, b].

By the intermediate value theorem, since f(a) > 0 and f(c) is a value between f(a) and f(b), we have f(c) > 0 for the interval [a, c]. Similarly, for the interval [c, b], we have f(c) > 0.

Thus, we have shown that for any point c in the interval I, f(c) > 0. Therefore, f keeps a constant sign (positive) on the interval I.

Similarly, if we assume that f is negative on I, we can apply the same argument to show that f keeps a constant sign (negative) on the interval I.

To know more about interval refer to-

https://brainly.com/question/11051767

#SPJ11

The amount that each of the 20 students paid is $4.685

We know that there are 20 students, and they paid:

15*$2.4 in the sodas, this is: 15*$2.4 = $31.5

8*$4.8 in the snacks, this is 8*$4.8 = $38.4

And $23.8 in other things for decorating.

Then the total amount they spent is:

T = $31.5 + $38.4 + $23.8 = $93.70

We can divide that evenly by the number of students, then the amount that each of the students paid is:

p = $93.70/20 = $4.685

Learn more about divisions at:

https://brainly.com/question/28768606

#SPJ1

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
To learn more about : equity

https://brainly.com/question/27821130

#SPJ8

The volume of the cone in the image is  405.04 cm ³

The volume of a cone of radius R and height H is given by the formula:

V = (1/3)*pi*H*R²

Where pi = 3.14

Here we can see that the dimensions are:

R = 6.1 cm

H = 10.4 cm

Replacing that we will get:

V = (1/3)*3.14*10.4cm*(6.1 cm)²

V = 405.04 cm ³

That is the volume of the cone.

Learn more about volumes at:

https://brainly.com/question/1972490

#SPJ1

Answer:

B

Step-by-step explanation:

I think it's B because it's looks equal

Answer:

A

Step-by-step explanation:

9x-5x=4x

3-(-7)=10

4x+10

The numbers of different ways that they can be seated is 144.

The First thing to do is that we need to fix the spot for where the teachers need to go.

Then, we can also put in the points where the students also need to go. Note that there is found to be 4 spaces for the students to sit.

Hence, there is 4! ways to be able to seat the students. In response to the above also, there are found to 4! ways to be able to order the teachers.

Hence, there is 24 x 24 ways to be able to order them. But, the question states that you need to order them in a circular table, and this implies that you must divide by 4 to be able to tell the number of rotations and reflections that is therein.

Therefore,  24 x 24/4  = 144.

Learn more about circular table from

https://brainly.com/question/24104335

#SPJ1

start by graphing the function

After having the graph we can see that the function is decreasiong over the interval

and increasing over the interval

The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.

First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.

In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.

Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.

Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.

Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.

Learn more about probability here:

brainly.com/question/27342429

#SPJ11

The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

Learn more about the Lagrange Multipliers at

https://brainly.com/question/15019779

#SPJ1

Answer:

144

Step-by-step explanation:

An angle of a regular pentagon is of 180(5-2)/5=108°

and that all the sides are equal so angle MNL=108/3=36

then MNK=180-MNL=180-36=144

I don't know if you understand this but it's hard to work without more points :)

Answer:

why is there a korean letter in there im  so lost lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of Rectangular Prism: V = lwh.

Surface Area of Rectangular Prism: S = 2(lw + lh + wh)

Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)

천만에요

너 도넛

Answer:

C

Step-by-step explanation:

5 - 1 = 4

5 - 5 = 0

5 - -1 = 6

I hope this helps but the answer most likely is C

Answer:

I think it's letter C ..........

Answer:

d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

π is an irrational number, meaning that it cannot be written as the ratio of two integers.

The speed of the train is 1 m/s.

A train travelled along a track for 70 s at a constant speed. What was its speed in metres per second (m/s)?The speed of the train in metres per second is the distance covered by the train in one second. Therefore, to determine the speed of the train, we must first determine the distance it covered during 70 seconds along the track.

The speed of the train can be calculated by dividing the distance covered by the train in meters by the time taken in seconds.  Therefore,Speed = Distance/TimeThe formula for distance is;Distance = Speed x TimeThe time taken by the train is 70s.The distance travelled by the train is not given, but we can calculate it using the speed of the train and time taken.

Therefore;Distance = Speed x Time Substituting the values;Distance = Speed x 70To find the speed of the train, we rearrange the formula as shown below;Speed = Distance/TimeNow we can substitute the value of distance to get the speed;Speed = (Speed x 70)/70Simplifying the expression,Speed = Speed

for more search question speed

https://brainly.com/question/26046491

#SPJ8

Answer:

23.3 and 11.05

Step-by-step explanation:

hope it helped!

By using the associative property of addition, we can break down the addition problem 997 + 543 into smaller, more manageable calculations.

The associative property of addition states that the grouping of numbers being added does not affect the result. In other words, (a + b) + c is equal to a + (b + c).

To make the mental calculation easier for 997 + 543, we can break down the numbers into smaller parts. Let's split 543 into 500 and 43:

997 + (500 + 43)

Now, we can calculate the addition in two steps:

Step 1: Add 500 and 43:

(997 + 500) + 43

Step 2: Add the results together:

1497 + 43

Calculating this mentally:

1497 + 43 = 1540

By utilizing the associative property of addition, we broke down the numbers into smaller parts and performed the addition in multiple steps. The sum of 997 + 543 is equal to 1540. This approach simplifies the mental calculation by breaking it down into manageable chunks.

To know more about Associative Property , visit:

https://brainly.com/question/13181

#SPJ11

Answer:

number 4 is right

The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.

Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.

Know more about the SAS theorem here:

https://brainly.com/question/22472034

#SPJ4

Answer:

8.24243226

Step-by-step explanation:

Same as the previous one I answered.

Tan = Opposite/ Adjacent

Adjacent = Opposite / Tan(20)

Answer:

y = − 5 x − 21

Step-by-step explanation:

Use the point slope formula y − y 1 = m ( x − x 1 )   to find the parallel line.

Answer:

1

Step-by-step explanation:

Slope is rise

              run

identify 2 points on the graph that the line passes through. start at the leftmost point and determine how many points up the next point is (this is the rise part). then determine how far the points are from each other (this is the run part)

In this case you end up with 1/1, 2/2, 3/3, etc. All of which are equal to one

have a nice day :)

Two thirds = fraction = 2/3

A number = x

one half = also a fraction = 1/2

equation:

2/3x=1/2

Solve:

multiply both sides by 3/2

3/2 (2/3x) = 1/2 (3/2)

x = 3/4

Answer: 10 times 8 and 8 times 10

Step-by-step explanation:

those are the first in the multiplication table that have the same digits

The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

Learn more about Pythagorean identity here:

https://brainly.com/question/24220091

#SPJ11

The general solution for the given differential equations is ln(|x - 3y|) = 3 * ln(|x|) + 3C

Rearrange the equation in standard form:

2x+y³ + 3xy²- dx = 0.

Identify the integrating factor (IF):

The integrating factor is given by \(IF = e^{\int\limits2 dx},\) where ∫2 dx is the integral of the coefficient of y with respect to x.

In this case, ∫2 dx = 2x.

So, the integrating factor \(IF = e^{2x}\).

Multiply the entire equation by the integrating factor as

\(e^{2x}* dy/dx + 2e^{2x} * y = 17e^{2x}\)

the product rule on the left-hand side (LHS) to simplify the equation:

\(d/dx (e^{2x} * y) = 17e^{2x}\)

Integrate both sides with respect to x:

\(\int\limits d/dx (e^{2x} * y) dx \int\limits 17e^{2x} dx\)

\(e^{2x} * y = ∫17e^{2x}) dxe^{2x} * y = (17/2) * e^{2x} + C\)

Step 6: Solve for y:

\(y = (17/2) + Ce^{-2x}\)

So, \(y = (17/2) + Ce^{-2x}\), where C is the constant of integration.

x * dy/dx + 3xy - x² = 0

Step 1: Rearrange the equation:

x * dy/dx = x² - 3xy

Step 2: Separate the variables:

dy/(x² - 3xy) = dx/x

Step 3: Integrate both sides:

∫dy/(x² - 3xy) = ∫dx/x

This integration can be a bit involved.

x²- 3xy = x(x - 3y)

∫dy/(x(x - 3y)) = ∫dx/x

Using partial fractions we can write:

∫(A/x + B/(x - 3y)) dy = ∫dx/x

A = 1/3 and B = -1/3.

So, the integral becomes:

∫(1/3) * (1/x - 1/(x - 3y)) dy = ∫d

To Solve for y:

(1/3) * ln(|x - 3y|) = ln(|x|) + C

ln(|x - 3y|) = 3 * ln(|x|) + 3C

Learn more about differential equation here: brainly.com/question/2273154

#SPJ4

Answer:

Step-by-step explanation:

We can solve this problem by using a system of linear equations. Let's call a and b the two numbers we are looking for. We know that a times b equals 10000 and that a plus b equals some other number x. We can write these two equations as follows:

a * b = 10000

a + b = x

We can solve for a in terms of b by rearranging the first equation:

a = 10000 / b

Substituting this expression for a into the second equation gives:

10000 / b + b = x

Multiplying both sides by b gives:

10000 + b^2 = bx

Rearranging this equation gives:

b^2 - xb + 10000 = 0

This is a quadratic equation in terms of b. We can solve for b using the quadratic formula:

b = (x ± sqrt(x^2 - 4 * 10000)) / 2

Since neither a nor b are divisible by 10, we know that both a and b must be multiples of 5. Therefore, we can assume that x is also divisible by 5.

Let's try an example where x equals 5005:

b = (5005 ± sqrt(5005^2 - 4 * 10000)) / 2

b ≈ (5005 ± sqrt(25000025 - 40000)) / 2

b ≈ (5005 ± sqrt(24960025)) / 2

b ≈ (5005 ± 4996) / 2

So we have two possible values for b:

b ≈ (5005 + 4996) / 2 = 5000.5

b ≈ (5005 - 4996) / 2 = 4.5

Since neither a nor b are divisible by 10, we know that the correct value for b is:

b ≈ (5005 - 4996) / 2 = 4.5

Substituting this value for b into the first equation gives:

a ≈ 2222.22

Therefore, a plus b equals approximately 2226.72.

Source: https://www.hackmath.net/en/calculator/solving-system-of-linear-equations?input=a%2Bb%3D10000%0D%0Aa+%3D+4b&submit=1

Answer:

54a6b2+9ab2 factored is

9ab2(6a⁵+ 1)

The significant difference between the observed and expected proportions of rabbits with long fur is tested using chi square goodness of fit.

To test whether 25% of rabbits have long fur and our alternative hypothesis is that 25% of rabbits don't have long fur, you can use a Chi-Square goodness-of-fit test. Here's a step-by-step explanation:

1. Define the null hypothesis (H0): 25% of rabbits have long fur.
2. Define the alternative hypothesis (H1): 25% of rabbits don't have long fur.
3. Collect a random sample of rabbits and record their fur lengths (long, medium, or short).
4. Calculate the expected frequencies for each fur length category, assuming the null hypothesis is true (25% long fur, and 75% for medium and short fur combined).
5. Calculate the observed frequencies for each fur length category from your sample data.
6. Calculate the Chi-Square test statistic, χ², using the formula: χ² = Σ[(observed - expected)² / expected]
7. Determine the degrees of freedom (df) for the test, which in this case is 1 (since there are two categories: long fur and not long fur).
8. Compare the calculated χ² test statistic to the critical value from the Chi-Square distribution table, given your chosen significance level (e.g., 0.05) and the calculated degrees of freedom.
9. If the test statistic is greater than the critical value, reject the null hypothesis in favor of the alternative hypothesis. Otherwise, fail to reject the null hypothesis.

By following these steps, you can determine if there is a significant difference between the observed and expected proportions of rabbits with long fur.

To learn more about expected proportions, refer here:

https://brainly.com/question/11935883#

#SPJ11

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer: 2 5/6 I think.

Wait no. I just did the math and it would be 2 1/2