Ame, Devon, Micah, and Shawna ran in a long distance race. The graph shows their progress during the race.
Distance (meters)
B. Devon
Legend
Time (minutes)
Which runner started out fast, then ran the rest of the race at a slower rate of speed?
OA Ame
Oc. Micah
OD. Shawna
Ame
Devon
Micah
Shawna

Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.

Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:

n1 - n2

To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.

Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:

- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.

- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.

- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.

Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:

The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.

The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.

Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:

n1 - n2 = 0.16T - 0.025T = 0.135T

Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.

Step-by-step explanation:

The answer is $359.25, which is closest to option A: $363.75.

Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.

The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:

$75 × $4.79 = $359.25

Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.

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The area of the room is 144 sq. ft. The volume of the room is 1,440 cu. ft. The rate of change in air is 150 ACs per hour. The room differential pressure with respect to the adjacent hallway, be negative.

HVAC stands for Heating, Ventilation, and Air Conditioning. It is a system designed to provide thermal comfort and acceptable indoor air quality in residential, commercial, and industrial buildings. The HVAC system works by controlling the temperature, humidity, and air quality within a building. It does this by using a combination of heating, cooling, ventilation, and air filtration. The heating component of the system can be achieved through furnaces, boilers, or heat pumps, while the cooling component can be achieved through air conditioning units or heat pumps. Ventilation is provided through the use of ductwork and fans that circulate fresh air throughout the building, and air filtration is achieved through the use of filters that remove contaminants from the air. Overall, the HVAC system is a vital component of modern buildings, as it ensures that indoor spaces are comfortable, healthy, and safe for occupants.

• We need to convert inches to feet, so divide it by 12. Therefore, the area of the room in square feet is:

Area = (144/12) x (144/12) = 12 x 12 = 144 sq. ft.

• To find the volume of the room in cubic feet, we need to multiply the area of the floor by the height of the room:

Volume = Area x Height = 144 sq. ft. x (120/12) ft. = 1,440 cu. ft.

• The total CFM of the HEPA filters is 6 x 600 = 3,600 CFM.

The rate of change in air can be calculated as:

N = 60Q/Vol = 60 x 3,600/1,440 = 150 ACs per hour

• If the door to the room were opened, the room differential pressure with respect to the adjacent hallway would most likely become negative because the air would flow out of the room into the hallway due to the pressure gradient.

Therefore, the answer is Negative.

Note: The final pressure differential direction will depend on several factors, such as the number of air changes per hour, the size of the door, and the location of the HVAC system. It is always best to consult with an HVAC professional for specific cases.

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The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).

A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.

The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².

The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.

The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).

Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).

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To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So 3/10 divided by 5/8 is equal to (3/10) * (8/5) which simplifies to 24/50 or 12/25 in its simplest form12. Therefore, 3/10 divided by 5/8 is equal to 0.48 when rounded to four decimal points

Hope this helps fellow friend!

The required answer is (3/10) ÷ (5/8) equals 12/25. in other words, the quotient fraction obtained is 12/25

To divide fractions, we can use the reciprocal (or multiplicative inverse) of the second fraction and then multiply the two fractions together. Let's solve the division problem (3/10) ÷ (5/8) step by step:

Step 1: Take the reciprocal of the second fraction. The reciprocal of 5/8 is 8/5.

Step 2: Multiply the first fraction by the reciprocal of the second fraction:

(3/10) * (8/5)

Step 3: Multiply the numerators together:

3 x 8 = 24

Step 4: Multiply the denominators together:

10 x 5 = 50

Step 5: Write the result as a fraction:

24/50

Step 6: Simplify the fraction, if possible:

Both the numerator and the denominator have a common factor of 2:

24 ÷ 2 = 12

50 ÷ 2 = 25

The simplified fraction is 12/25.

Therefore, (3/10) ÷ (5/8) equals 12/25.

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If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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Answer:

if question is a fraction then -0.001429, if not then 624.0235948

Answer:

x = 2.16228,  -4.16228

Step-by-step explanation:

(2x² - 2x) - 5 = (x - 2)²

2x² - 2x - 5 = x² - 4x + 4

x² + 2x - 9 = 0

Use quadradic equation to find the roots of x:  a=1 , b=2, c=-9

x = 1 ± √10

x = 2.16228,  -4.16228

Answer:

Step-by-step explanation:

Answer:  The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.

To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).

Using these rules, we can find the derivative of g(x) as follows:

g(x) = 3x² + 7x - 1

g'(x) = (3x²)' + (7x)' - (1)'

g'(x) = 6x + 7 - 0

g'(x) = 6x + 7

Therefore, the derivative of g(x) is g'(x) = 6x + 7.

Step-by-step explanation:

The difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

Assume that the data is n-sized as follows:

x1, x2, x3 .....xn

Let the mean of this data be: x'

The mean of the absolute differences between the observations and the mean of the data to which they belong, then, is the mean absolute deviation of such a data.

It is determined by:

M.A.D = ∑ |xi - x'| / n  (i = 1 ....n)

Hence, mean absolute deviation is the average deviation of the data values, regardless of whether it is above or below the mean.

Due to the fact that:

The mean absolute deviation of the monthly temperatures in New Orleans is 43.5°F, which implies that on average, the temperature deviates 43.5°F from the average monthly temperature.

where mean displays New Orleans, Louisiana's typical monthly temperature.

Thus, the difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

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Answer:

8

Step-by-step explanation:

Let's use algebra to solve the problem.

Let x be the number we're looking for.

The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:

x + 2 = 2x - 6

To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:

x + 2 - x = 2x - 6 - x

Simplifying:

2 = x - 6

Now we can isolate x by adding 6 to both sides:

2 + 6 = x - 6 + 6

Simplifying:

8 = x

Therefore, the number we're looking for is 8.

Answer:

8

Step-by-step explanation:

In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.

So, the camel can drink 7.5 gallons of water in 5 minutes.

The unitary method is a mathematical technique used to solve problems related to proportionality.

It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.

The unitary method is useful in solving problems that involve direct proportion or inverse proportion.

To find out how much water the camel can drink in 5 minutes, we can use the unitary method.

We know that the camel can drink 15 gallons of water in 10 minutes.

So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.

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The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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The area to the right of  [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex]  .

The region where [tex]z > 1.42[/tex]  in the standard normal distribution corresponds to the area under the curve to the right of [tex]1.42[/tex] on the z-axis.

To find this area, we can use a standard normal distribution table or a calculator with a cumulative distribution function (CDF) for the standard normal distribution.

Using a calculator with a CDF for the standard normal distribution, we can input 1.42 and calculate the area to the left of 1.42. Then, we subtract this area from 1 to get the area to the right of 1.42. Here's the calculation:

[tex]P(Z > 1.42) = 1 - P(Z < 1.42)[/tex]

Using a standard normal distribution table or a calculator, we find that  [tex]P(Z < 1.42)[/tex] is approximately 0.9207. Subtracting this value from 1, we get:

[tex]P(Z > 1.42) \approx 1 - 0.9207 \approx 0.0793[/tex]

Therefore, the area to the right of  [tex]1.42[/tex] in the standard normal distribution is approximately   [tex]0.0793[/tex].

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The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.

To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.

For the tax year 2021, the federal income tax brackets and rates for single filers are:

10% on taxable income from $0 to $9,950

12% on taxable income from $9,951 to $40,525

22% on taxable income from $40,526 to $86,375

24% on taxable income from $86,376 to $164,925

32% on taxable income from $164,926 to $209,425

35% on taxable income from $209,426 to $523,600

37% on taxable income over $523,600

To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.

Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.

Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.

Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.

Adding these three amounts together, we get the total tax owed:

$995 + $3,384.48 + $2,312.72 = $6,692.20

Therefore, the closest answer choice is B) $6,919.00.

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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).

An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.

Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.

=$51100* 22/100

=$11242

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To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

Answer:

2

Step-by-step explanation:

add them and make them equal to 90 because its a right angle

5m+80=90

subtract 80 to isolate m

5m=10

divide 5 to isolate m even more

m=2!

The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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The indicators which would cause you to reject normality for a sample of data are:

A histogram of the data shows bar heights decreasing from left to right.

A histogram of the data shows bar heights decreasing from right to left.

In statistics, a sample refers to a group of individuals, objects, or observations selected from a larger population. The sample is chosen to represent the population and to provide information about the characteristics, behavior, or preferences of the population. Sampling is a common method used in statistical analysis to estimate population parameters, such as the mean or standard deviation. By analyzing the sample data, researchers can draw inferences about the population from which the sample was drawn.

Here,

Both of these indicators suggest that the data is not symmetric and may have a skewed distribution. The following indicators suggest that the data is likely normally distributed:

A normal probability plot of the data follows a linear pattern.

A histogram of the data shows that all bars have similar heights.

A normal probability plot is a graphical tool used to assess the normality of a data set. If the plot follows a straight line, it suggests that the data is normally distributed. Similarly, a histogram with bars of similar heights suggests that the data is symmetric and may be normally distributed.

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2x + 3/x + 5 is the value of expression .

What is an expression in mathematics?

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

                                     The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.  

g(x) = -5+2x/1+x

g(x+4) = -5+2(x + 4)/1+(x + 4 )

          = -5 + 2X + 8/1 + X + 4

          = 2x + 3/x + 5

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Answer:

7.96 cm .

Step-by-step explanation:

7.96 cm .

1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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The perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

To find the perimeter of the regular octagon inscribed in a circle with radius 14 inches, we need to use the formula:

Perimeter of octagon = 8 x length of one side

Since the octagon is regular, all sides are congruent. Let s be the length of one side of the octagon.

The radius of the circle is 14 inches, which is also the distance from the center of the circle to any vertex of the octagon. We can divide the octagon into eight congruent isosceles triangles, each with base s and legs of length 14 inches. We can then use the Pythagorean theorem to find the length of the base s:

s² = 14² - (s/2)²

s² = 196 - s²/4

5s²/4 = 196

s² = 156.8

s ≈ 12.52

Therefore, the perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches (rounded to 2 decimal places).

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Answer:

We can use the Law of Cosines to find the distance between points a and b.

Using the angles given, we can find the angle between points a and b:

Angle C = 180 - (76 + 32) = 72 degrees

Next, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the distance between points a and b, a is the distance between point c and point a (210 ft), b is the distance between point c and point b (150 ft), and C is the angle between points a and b (72 degrees).

Plugging in the values:

c^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

c^2 ≈ 21069.27

Therefore, the distance between points a and b is approximately:

c ≈ 145.2 ft