Your generous wealthy aunt wants to ensure you have enough money to cover rent and food while you go to college so you don’t need to work while you’re in classes. Together you decide $18,000 per year is sufficient to cover your basic needs. How much does your aunt need to invest in a bond mutual fund that yields 3.0% in order for it to provide $18,000 a year for you?

Answer:

-5.44

Step-by-step explanation:

Y/3.4+4.1 =2.5

Y+(3. 4)(4.1)/(3.4)=2.5

Y+13.94/3.4 =2.5 cross multiply (3.4)(2.5)to get

Y+13.94=8.5

Y=8.5-13.94

= (-5.44)

Step-by-step explanation:

45 minutes is 3/4 of an hour.

how often does 3/4 fit into 3 ?

3 / 3/4 = 3/1 / 3/4 = (3×4)/(1×3) = 4

so, it will be rung 4 times.

Answer: 4 times.

Step-by-step explanation:

We can divide 3 hours by 45 minutes, to get the number of times the bell will ring in 3 hours:

3 hours ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

We can also think of it like this: 3 hours is 180 minutes, and the bell rings every 45 minutes.

So, we can divide 180 by 45 to get the number of times the bell will ring:

180 minutes ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

a) The mean number of paintings owned by these five people is 40. b) No, the mean is not a good average to use to describe the number of paintings that these people own

a) To find the mean number of paintings owned, we add up all the values and divide by the total number of people:

Mean = (1+0+2+196+1)/5 = 40

Therefore, the mean number of paintings owned by these five people is 40.

b) No, The mean is not necessarily a good average to use to describe the number of paintings that these people own.

This is because the data is skewed by the one outlier value of 196, which is much larger than the other values.

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Answer:

The distribution for the number of weeks pregnancy lasts for a mother is typically a unimodal distribution, with a single peak. The majority of pregnancies last around 38-42 weeks, with fewer pregnancies lasting shorter or longer than this period. This creates a bell-shaped curve, with the peak at the most common duration and a gradual decrease in frequency as the duration becomes shorter or longer than the mode.

However, it's worth noting that there can be some variations in this distribution based on different factors, such as the age of the mother, health status, and other demographic characteristics. For example, teenage pregnancies and pregnancies in older women may have slightly different distributions with different peaks due to biological and social factors. Nonetheless, a unimodal distribution is the most commonly observed distribution for the number of weeks pregnancy lasts for a mother.

The equation (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

Given that:

(x - 3)²+(y - 7)² = 36

Expanding the square in the given equation, we get:

(x - 3)² + (y - 7)² = 36

(x - 3)(x - 3) + (y - 7)(y - 7) = 36

x² - 6x + 9 + y² - 14y + 49 = 36

x² + y² - 6x - 14y + 22 = 0

Therefore, the equation of the circle (x - 3)² + (y - 7)² = 36 in general form will be x² + y² - 6x - 14y + 22 = 0

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We can use Newton's law of cooling to solve this problem:

T(t) = T_a + (T_0 - T_a) * e^(-kt)

where T(t) is the temperature of the object at time t, T_a is the ambient temperature, T_0 is the initial temperature of the object, and k is a constant. We can solve for k by using the information that the object cools from 200 degrees to 131 degrees in 5 minutes:

131 = 20 + (200 - 20) * e^(-5k)

Simplifying this equation, we get:

e^(-5k) = 0.625

Taking the natural logarithm of both sides, we get:

-5k = ln(0.625)

k = -ln(0.625) / 5

k ≈ 0.1078

Now we can use this value of k to find the temperature of the object after 9 minutes:

T(9) = 20 + (200 - 20) * e^(-0.1078 * 9)

T(9) ≈ 94.9 degrees Celsius

Therefore, the temperature of the object at the end of 9 minutes will be approximately 94.9 degrees Celsius.

Answer:

The final price of the stapler is 11.97 dollars and they would get 4.49 dollars in revenue.

Answer:

x=-7

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

For all the questions the correct option is 3 units² because nor the translation not the reflection change the size.

Remember that for any shape, the transformations that change the area of the shape are dilations and contractions.

Here we start with a triangle of base B = 3 and height H = 2, then its area is:

A = 3*2/2 = 3 square units.

Now, any translation will result in a triangle of the same area.

Any reflection will result in a triangle of the same area.

Then for all the given questions, the correct option is 3 units²

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Because the angles add up to 180°, we conclude that the shelves are parallel.

Two adjacent angles always should add up to 180°. The top shelve and middle shelve will be parallel only if:

∠1 = ∠5

∠2 = ∠6

And we know that:

∠1 + ∠2 = 180°

Then we could rewrite this as:

∠5 + ∠2 = 180°

Replacing the measures we will get:

60° + 120° = 180°

180° = 180°

That equation is true, this, the shelves are parallel.

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After 200 years, there will be 47.43 pounds left of the material.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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The year in which the population of the town was 12,354 include the following: B. 1970.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

Based on the information provided about the population of this small town, a linear function that models the population as a function of time, t, in years past 1940 is given by;

P(t) = 1,854 + 350t

12,354 = 1,854 + 350t

12,354 - 1,854 = 350t

t = 10,500/350

t = 30

Since the years is past 1940, we have:

Year = 1940 + 30 = 1970.

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Complete Question:

The population of a small town, P, as a function of time, t, in years past 1940 is given below. P = 1,854 + 350t. For which of the following years was the population of the town 12,354?

A.1967

B. 1970

C. 1974

D. 1964

The step to solve the system of equations using is

Step 1 : A-Since the second equation is solved for x, substitute 6y + 1 for x in the first equation.

Step 2: C-Solve the resulting equation for y

Step 3: B-Substitute the value for y into either equation to find x.

Step 4: D- Write the solution as an ordered pair, and check the solution.

From the question, we are to match each step to show how to solve the system of equations.

The given system of equations is

7x - 2y = -1

x = 6y + 1

Step 1: Since the second equation is solved for x, substitute 6y + 1 for x in the first equation

7(6y + 1) - 2y = -1

Step 2: Solve the resulting equation for y

7(6y + 1) - 2y = -1

42y + 7 - 2y = -1

42y - 2y = -1 - 7

40y = -8

Divide both sides by 40

y = -8/40

y = -1/5

Step 3: Substitute the value for y into either equation to find x

x = 6y + 1

x = 6(-1/5) + 1

x = -6/5 + 1

x = -1/5

Step 4: Write the solution as an ordered pair, and check the solution

7x - 2y = -1

7(-1/5) - 2(-1/5) = -1

-7/5 + 2/5 = -1

-1 = -1

True

x = 6y + 1

-1/5 = 6(-1/5) + 1

-1/5 = -6/5 + 1

-1/5 = -1/5

True

Hence, the steps to solve the system of equations using is

Step 1: A

Step 2: C

Step 3: B

Step 4: D

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The amount is $4,000 invested in the 3% account.

Let x be the amount invested in the 3% account. Then, the amount invested in the 5% account is $6,000 - x.

The interest earned from the 3% account is 0.03x, and the interest earned from the 5% account is 0.05($6,000 - x) = $300 - 0.05x.

The total interest earned is given as $220, so we can write the equation:

0.03x + 300 - 0.05x = 220

Simplifying the equation, we get:

-0.02x + 300 = 220

-0.02x = -80

x = 4,000

Therefore, $4,000 was invested in the 3% account.

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Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

84 adult tickets were consequently sold on that day.

Let's fix this issue using a set of equations. Let x represent how many adult tickets were sold, and y represent how many kid tickets were sold.

We learn the following from the issue:

Total number of tickets sold = x + y

Total sales equal 9.9x + 5.5y = 1216.6.

To find y, we can utilize the first equation:

y = 146 - x

We obtain the following by substituting this into the second equation: 9.9x + 5.5(146 - x) = 1216.6

The result of simplifying and finding x is: 4.4x = 369.6 x = 84

Therefore, 84 adult tickets were consequently sold on that day.

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The surface area of the triangular prisms is calculated to be equal to 132 square meters.

The figure can be observed to be two identical triangular prisms with square base, and the surface area can be calculated as follows:

the slant height of a triangle face is derived using Pythagoras;

√(2² + 8²) = √68 m

area of one triangle face = 1/2 × 4 m × √68 m

area of one triangle face = 16.4924 m²

surface area of the figure = 8 × 16.4924 m²

surface area of the figure = 131.9392.

Therefore, the surface area of the triangular prisms is calculated to be equal to 132 square meters.

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The probability that her Internet service is not broken for five days in a row is given by P ( A ) = 0.0102

Given data ,

Let the probability that the internet connection is lost = 60 %

Now , We may utilize the probability of independent occurrences occurring sequentially to determine the likelihood that her Internet service won't be down for five days in a row. We may add the probability for five days as the occurrences of her Internet service being down or up on each day are independent.

The likelihood of her Internet service remaining operational for one day is 0.40.

Her chances of having uninterrupted Internet access for five days are equal to (0.40)⁵

P ( A ) =  (0.40)⁶ is about equivalent to 0.0102

Hence , the probability of Ashley's Internet service remaining up for five consecutive days is around 0.0102 or 1.02%

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If you invest $2,000 at the end of each year for the next 30 years and earn an annual rate of return of 13%, you would have a total of approximately $75,994.18 saved for retirement.

To calculate the future value of the investment, we can use the formula for the future value of an annuity:

[tex]FV = PMT \times \dfrac{((1 + r)^{n - 1})} { r}[/tex]

where PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

In this case, we have PMT = $2,000, r = 0.13 (since the stock market has earned 13% per year), and n = 30 (since we are investing for 30 years).

Plugging in the values, we get:

FV = $2,000 x ((1 + 0.13)³⁰ - 1) / 0.13

= $2,000 x (4,919.04) / 0.13

= $75,994.18

Therefore, a total of about $75,994.18 would be saved for retirement if you invested $2,000 at the end of each year for the next 30 years and saw a 13% annual return.

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After 8 years, Savings Account B will have more money because it is modeled by the equation A = 975 * (1 + 52.65 * t), where the investment grows at a much faster rate

Account A shows an end balance of approximately $1,622.40 after eight years based on a model of continual compounding with an annual percentage rate of 5.4%.

In contrast, account B's future balance prediction is roughly $411,641.00 at the end of an eight-year period, which utilizes a simple interest model and grows at breakneck speeds due to a growth percentage of 5265%.

After 8 years, Savings Account B will have more money because it is modeled by the equation A = 975 * (1 + 52.65 * t), where the investment grows at a much faster rate

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Each of two savings accounts begins with $975 as an initial deposit and 5.4% annual interest rate; however, the interest is accrued distinctly for each account. As demonstrated below in Table I:

- Savings Account A: A = 975 * (1 + 0.054 / 12) ^ (12 * t);

- Savings Account B: A = 975 * (1 + 52.65 * t).

Thus, after eight years, which account will yield a higher balance and why remains to be determined?

A price-setter company will use more: cost-plus pricing methods

A company endowed with the capability to set their own market prices is likely to resort to various pricing approaches, such as cost-plus, target costing, and target pricing methods.

However, targeting pricing proves to be the most preferable scheme of these since it involves establishing the desired selling price based on estimated market value before factoring in acceptable expenses to procure an adequate profit margin.

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A price-setter company, which has considerable market power, is more likely to use cost-plus pricing methods. This method ascertains the price of a product by determining the cost of production and then adding a certain amount for profit. Hence, this strategy ensures that the company covers all costs and makes a profit on each sale.

A price-setter company, which has significant market power, is likely to use more cost-plus pricing methods. In a cost-plus pricing method, the company sets the price of a product by determining the cost of production and then adding a specific amount or percentage as profit. This pricing strategy is straightforward and ensures that all costs are covered and a profit is made on each sale. It offers stability and predictability, which is desirable for a price-setter company with substantial control over the market.

On the other hand, target costing and target pricing methods involve setting a price first and then figuring out how to meet that price with production. These methodologies are typically used in more competitive industries, where companies don't have as much power to set their own prices.

However, a price-setter company, assuming it's not in a perfectly competitive market, has the power to set the price without having to intensely consider competitors' prices or customers' price sensitivity, therefore, it may use cost-plus pricing methods more.

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The probability that at least 50 of these 200 callers are male is approximately 0.0266 and the probability that more than half of these 200 callers are female is 0.

Let X be the number of male callers among 200 callers.

X follows a binomial distribution with n=200 and p=0.2. We need to find P(X ≥ 50).

μ = np = 200 × 0.2 = 40

σ = √np(1-p)) = √200 × 0.2 × 0.8)

= 5.65

P(X ≥ 50) = P(Z ≥ (50-0.5-40)/5.65)

= P(Z ≥ 1.94)

=0.0266

Therefore, the probability that at least 50 of these 200 callers are male is approximately 0.0266.

b) Let Y be the number of female callers among 200 callers.

Y follows a binomial distribution with n=200 and p=0.8

We need to find P(Y > 100).

P(Y > 100) = P(Z > (100+0.5-40)/5.65)

= P(Z > 11.23) =0

Therefore, the probability that more than half of these 200 callers are female is  0.

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Center-to-center spacing between the beams is 11.375in

If there are 19 beams then there will be 18 spaces between them.

Let's call the center-to-center spacing "x". Then we can set up the following equation:

18x = 204.75

To solve for x, we can divide both sides by 18:

x = 204.75 / 18

x = 11.375 (to 3 decimal places)

Briefly, a beam is a structural element that is designed to resist loads applied transverse to its longitudinal axis.

Beams are often made of materials like:

Beam comes in various sizes and shape depend on the specific application and the loads that they are designed to support.

Beams are an important component of many types of structures, from buildings and bridges to vehicles and machinery.

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The measure of angle θ is 45 degrees.

The measure of angle θ is calculated by applying trigonometry ratio as follows;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height and the adjacent side is given, so the value of θ is calculated as follows;

tan θ = (206 - 7 ) / (199)

tan θ = 1

θ = arc tan (1)

θ = 45⁰

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The 99.5% confidence interval for the mean reduction in cholesterol is 0.922 < μ < 0.978.

To construct a 99.5% confidence interval for the mean reduction in total cholesterol, we can use the formula CI = x ± Z*(σ/√n).

Substituting the given values, we get:

CI = 0.95 ± 2.807*(0.18/√318)

CI = 0.95 ± 2.807*0.01009389877

CI = 0.95 ± 0.02833357384

CI = 0.95 + 0.0283 or 0.95-  0.0283

CI = 0.9783 or 0.9217

This means we are 99.5% confident that the true population mean reduction in total cholesterol lies within this interval.

Full question "A sample of 318 patients between the ages of 38 and 82 were given a combination of drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.95 millimole per liter. Assume the population standard deviation is = 0.18. Construct a 99.5% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drug"

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If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.

One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.

Another factor that can decrease the money supply is the sale of treasury bonds to banks.

Raising the interest rates also decreases the money supply.

Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.

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In the initial value problem the value of f(π/5) ≅ -5.26

Given the initial value problem f"(x) = -25sin(5x) and f'(0) = 3 and f(0) = -2, we desire to find f(π/5). We proceed as follows

f"(x) = -25sin(5x)

Integrating both sides of the equation, we have that

∫f"(x) = ∫-25sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25∫sin(5x)

f'(x) = -25(-cos(5x))/5 + C

f'(x) = 5cos(5x) + C

Given that f'(0) = 3, substituting the values of the variables into the equation, we have that

f'(x) = 5cos(5x) + C

f'(0) = 5cos(5(0)) + C

3 = 5cos(0) + C

3 = 5(1) + C

3 = 5 + C

C = 3 - 5

C = -2

So, we have that f'(x) = 5cos(5x) - 2

To find f(x), we integrate f'(x). So, we have that

f'(x) = 5cos(5x) - 2

∫f'(x) = ∫(5cos(5x) - 2)dx

f(x) = ∫5cos(5x)dx - ∫2dx

= 5sin(5x)/5 - 2x + C'

f(x) = sin(5x) - 2x + C'

Since f(0) = -2, we have that

f(0) = sin(5(0)) - 2(0) + C'

-2 = sin0 - 0 + C'

- 2 = 0 - 0 + C'

- 2 = 0 + C'

C' = -2

So, substituting C' into the equation, we have that

f(x) = sin(5x) - 2x + C'

f(x) = sin(5x) - 2x - 2

So, to find f(π/5), substituting this into the equation, we have that

f(π/5) = sin(5π/5) - 2(π/5) - 2

f(π/5) = sin(π) - 2π/5 - 2

f(π/5) = 0 - 2π/5 - 2

f(π/5) = - 2π/5 - 2

f(π/5) = (- 2π - 10)/10

f(π/5) = - 2(π + 10)/10

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(π + 10)/5

f(π/5) = - 2(3.142 + 10)/5

f(π/5) = - 2(13.142)/5

f(π/5) = - 26.284/5

f(π/5) = -5.2568

f(π/5) ≅ -5.26

So, f(π/5) ≅ -5.26

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There are 190 pennies and 110 nickels.

Let's begin by giving the unknown quantities variables. y is the quantity, in cents.

Let x represent the quantity of nickels and y represent the quantity of pennies.

The issue reveals that the combined worth of the coins is $7.40. The following equation can be written since a nickel is worth $0.05 and a penny is worth $0.01:

0.05x + 0.01y = 7.40.

The fact that there are 80 more pennies than nickels is also known. You can write this as

y = x + 80.

Now we can use substitution to solve for x:

0.05x + 0.01(x + 80) = 7.40

0.05x + 0.01x + 0.80 = 7.40

0.06x = 6.60

x = 110

There are 110 nickels in total. The second equation can be used to calculate the amount of pennies:

y = x + 80 = 110 + 80 = 190

Therefore, there are 190 pennies and 110 nickels.

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The x-intercepts of the function are (-0.25, 0) and (4, 0).

The line of symmetry is 1.875.

The vertex of the parabola is 72.25.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the given quadratic equation f(t) = -16t² + 60t + 16, we have:

[tex]x = \frac{-(60)\; \pm \;\sqrt{(60)^2 - 4(-16)(16)}}{2(-16)}\\\\x = \frac{-60\; \pm \;\sqrt{3600 + 1024}}{-32}\\\\x = \frac{-60\; \pm \;\sqrt{3600 + 1024}}{-32}[/tex]

x = -0.25 or x = 4.

Line of symmetry, Xmax = -b/2a

Line of symmetry, Xmax = -60/2(-16)

Line of symmetry, Xmax = 60/32

Line of symmetry, Xmax = 1.875

Vertex, f(1.875) = -16(1.875)² + 60(1.875) + 16

Vertex, f(1.875) = 72.25.

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The statements about the attached daily temperature data that are true include the following:

A. the average temperature was below 90°F on less than 75% of the days.

C. the average temperature was below 75°F on less than 25% of the days.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot for the daily temperature data, the five-number summary for the given data set include the following:

Minimum (Min) = 65.

First quartile (Q₁) = 70.

Median (Med) = 75.

Third quartile (Q₃) = 85.

Maximum (Max) = 90.

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