Flying against the wind, an airplane travels 4340 kilometers in 7 hours. Flying with the wind, the same plane travels 3120 kilometers in 3 hours. What is the
rate of the plane in still air and what is the rate of the wind?

The relation that is defined by a set of ordered pairs that is a function is: A. {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}.

A function can be described as a type of relation whereby every x-value has an exact y-value it corresponds to.

In a relation that is defined by a set of ordered pairs, if every x-value has only one y-value it corresponds to, then the relation represents a function.

In the relation, {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}, no x-value has two different y-values, therefore the relation is defined by a set of ordered pairs that is a function.

{(–2, 6), (3, –6), (–4, 5), (6, –6), (6, –7)} is not a function because x-value 6 has two different y-values, -6 and -7.

{(2, 6), (3, 6), (4, 5), (6, 6), (6, 7)} is also not a function because x-value 6 has two y-values 6 and 7.

The relation {(6, 2), (6, 3), (5, 4), (6, 6), (7, 6)} has an x-value 6, that corresponds to more than one y-value, therefore, it is not a function.

In conclusion, the relation that is defined by a set of ordered pairs that is a function is: A. {(2, 6), (3, 6), (4, 5), (6, 6), (7, 6)}.

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So the balloon payment six years from now will be approximately $24,612.09.

(P, R, and T) / 100 is the SI unit.

In this case, SI stands for Straightforward Interest. P is the initial investment or loan amount, and R is the interest rate.

To find the amount of the balloon payment six years from now, we can use the formula for the present value of a series of payments:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

where PV is the present value of the payments, PMT is the monthly payment, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years for the loan.

In this case, we have:

PMT = $1,300 (paid for 5 years)

r = 0.05 (5% APR)

n = 12 (monthly compounding)

t = 6 (total loan term, including the first year with no payments)

To calculate the present value of the payments, we first need to find the present value of the $93,500 loan, one year from now, when the payments begin. This is equivalent to finding the future value of the loan now, and then discounting it back one year using the interest rate.

The future value of the loan after one year is:

FV = $93,500 x (1 + r)¹ = $98,175.00

The present value of this future amount, discounted back one year at an interest rate of 5%, is:

PV = $98,175.00 / (1 + r)¹ = $93,500.

So the present value of the loan one year from now, when the payments begin, is approximately $93,500.

Using this present value as the principal amount for the remaining 5 years of payments, we can calculate the balloon payment using the present value formula above:

PV = PMT x (1 - (1 + r/n)^(-nt)) / (r/n)

PV = $1,300 x (1 - (1 + 0.05/12)⁻⁶⁰) / (0.05/12)

PV = $68,887.91

Therefore, the balloon payment six years from now will be the remaining principal on the loan after five years of payments, which is:

Balloon payment = $93,500 - $68,887.91 = $24,612.09.

So the balloon payment six years from now will be approximately $24,612.09.

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The equation of variation by the given data is y= 6.

We are given that;

y = 4, x = 8 and z = 14.

The equation of variation is y = kx/z, where k is a constant of proportionality. To find k, we can use the given values of x, y and z:

y = kx/z 4 = k(8)/14 k = 7

So the equation of variation is y = 7x/z.

To find z when x = 36 and y = 6, we can plug in these values and solve for z:

y = 7x/z 6 = 7(36)/z z = 42

Therefore, by the equation z will be 42 when x is 36 and y will be 6.

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

i did it on edge

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

The value of f⁻¹(3) is 6.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

The inverse function of f(x) is denoted by f⁻¹(x). It is a function that reverses the action of f(x). That is:

if f(x) = y, then f⁻¹(y) = x.

In this case, we know that f(6) = 3. This means that if we input 6 into f(x), we will get 3 as the output.

Therefore, the inverse function of f(x) must take 3 as input and give 6 as output. This means that f⁻¹(3) = 6.

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The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Since the distance was measured to the nearest metre, the upper bound for the distance is 101 metres.

1. To calculate the lower bound for Kelly's average speed, we need to divide the lower bound distance by the upper bound time. Since the distance was measured to the nearest metre, the lower bound for the distance is   \(99\) Metres.

Since the time was measured to the nearest hundredth of a second, the upper bound for the time is  \(10.53\) seconds. Therefore, the lower bound for Kelly's average speed is:

\(99/10.53 = 9.411\)  metres per second (to three decimal places)

2. To calculate the upper bound for the perimeter of the regular hexagon, we need to multiply the upper bound length of a side by 6.

Since the length was measured to the nearest millimetre, the upper bound for the length is \(3.601 cm\)  (since 3.6005 cm would round up to 3.601 cm). Therefore, the upper bound for the perimeter is:

\(6 x\times3.601 = 21.606 cm\)   (to three decimal places)

3. To calculate the upper bound for the area of the rectangle, we need to multiply the upper bounds for the length and width. Since the length is correct to the nearest cm, the upper bound for the length is 35.5 cm (since 34.5 cm would round up to 35 cm).

Since the width is correct to the nearest cm, the upper bound for the width is 26.5 cm (since 25.5 cm would round up to 26 cm). Therefore, the upper bound for the area is:

 \(35.5 \times 26.5 = 942.25 cm^2\) (to two decimal places)

4. To calculate the lower bound for Kelly's average speed, we need to divide the upper bound distance by the lower bound time.

Since the time was measured to the nearest hundredth of a second, the lower bound for the time is 10.51 seconds. Therefore, the lower bound

(d) To calculate the lower bound for Kelly's average speed, we need to divide the lower bound of distance by the upper bound of time.

The lower bound of distance is 99.5m (since the measurement was rounded down to the nearest metre).

The upper bound of time is 10.525s (since the measurement was rounded up to the nearest hundredth of a second).

So, the lower bound for Kelly's average speed is:

speed = distance / time \(= 99.5 / 10.525 = 9.45260637\) ...

We need to round this to two decimal places to match the precision of the time measurement, giving us:

speed = \(9.45 m/s\)

Therefore, the figures on the calculator display are: 99.5 ÷ 10.525 = 9.45260637... ≈ 9.45.

The length of the rectangle is measured as 645 mm correct to the nearest 5 mm. This means that the actual length could be anywhere between 642.5 mm and 647.5 mm (since rounding up or down depends on the decimal value being greater or less than 0.5 respectively).

Similarly, the width of the rectangle is measured as 400 mm correct to the nearest 5 mm. This means that the actual width could be anywhere between 397.5 mm and 402.5 mm.

5. To calculate the lower bound for the area of the rectangle, we need to find the product of the smallest possible length and width.

Smallest possible length \(= 642.5 mm\)

Smallest possible width  \(= 397.5 mm\)

Area = length x width

Lower bound for area = \(642.5 mm x 397.5 mm = 255542.5 mm²\)

Rounding this off to 3 significant figures, we get the final answer as 2.56 x 10^5 mm².

Therefore, the lower bound for the area of the rectangle is \(2.56 x 10^5\)  mm².

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Answer:

Step-by-step explanation:

Using confidence interval concepts, it is found that:

a)

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

The interpretation is:

iii. We are 99% confident that this interval contains the true population mean.

b)

A sample size of 664 would be required.

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.

\(\pi \pm M\)

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).

The interpretation of a x% confidence interval between a and b is that we are x% confidence that the true population mean lies in this interval, thus, option iii is correct.

In this problem:

Then:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(M = 2.575\sqrt{\frac{0.27(0.73)}{2005}}\)

\(M = 0.026\)

The interval is:

\(M - \pi = 0.27 - 0.026 = 0.244\)

\(M + \pi = 0.27 + 0.026 = 0.296\)

The 99% confidence interval for the proportion of all adult Americans who believe in astrology is (0.244, 0.296).

Item b:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.05 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.05\sqrt{n} = 2.575(0.5)\)

Dividing both sides by 0.05.

\(\sqrt{n} = 2.575(10)\)

\((\sqrt{n})^2 = [2.575(10)]^2\)

\(n = 663.1\)

Rounding up:

A sample size of 664 would be required.

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The probability of getting a blue and then not getting an orange is 5/23.

The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of getting a blue lollipop first is 6/24 = 1/4.

Once a blue lollipop has been selected, there are 23 lollipops left in the bag and 3 of those are orange. So, the probability of not getting an orange on the second pull is 20/23.

Multiplying the probabilities of the two independent events gives us the probability of getting a blue and then not getting an orange:

1/4 x 20/23 = 5/23

So, the answer is 5/23.

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Answer: The answer is D, II and III only.

The statements that are correct include:

Alzheimer's disease is a form of dementia which lead to memory loss and can lead to a mental disorder.

Based on the information given, this is an observational study as a certain population was looked at. It also shows that taking the B12 vitamin daily contributes to protecting against Alzheimer's disease.

Therefore, the correct option is D.

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Answer:

The greatest common factor of 15 and 31 is 1.

Step-by-step explanation:

What are the factors of 15?

1, 15 and 3, 5

What are the factors of 31?

31 and 1

We can see that 31 and 15 only share on common factor, which is 1.

1 is the greatest and the only factor!

Answer:

GCF - 1

Step-by-step explanation:

15 - 1, 3, 15

31 - 1, 31

31 is a prime number so the only factors of it are 1 and itself. Therefore, the answer has to be 1.

GCF = 1

Hope this helps! :)

Answer:

Step-by-step explanation:

26/7

Answer:

89  sq meters

Step-by-step explanation:

The whole rectangle  13x8 = 104

Now subtract the white triangle

(6x5)/2 = 15

104-15 = 89

Answer:

i wish i could help but its kind of over a minute but the answer is C

The inequality y≤ 1/2 x -4 which is shown by red shaded region gives the solution (0, -4) and (8, 0).

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have the Inequality y≤ 1/2 x -4.

Now, we plot the inequality on the Graph as shown by the red region.

As, the inequality intersect the axis at (0, -4) and (8, 0).

Thus, the solution is (0, -4) and (8, 0).

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Answer:

y-intercept=2

Step-by-step explanation:

2y=-3x+4

divide both sides by 2

y=-1.5x+2

y=mx+c

'c' is the y-intercept so '2' is the answer.

Answer:

= -3/2

Step-by-step explanation:

The equation of the line = 2y = -3x + 4

2y = -3x + 4

2y = -3x + 4

2 2 2

y intercept of the line = -3/2.

Answer:

skewed  to the right

Step-by-step explanation:

look at the graph

divide it in half

if both the sides are not equal then it is skewed

then to find out which way it is skewed look which side has more.

Step-by-step explanation:

yx = k, where k is a real constant.

When y = 30, x = 3.

=> k = (30)(3) = 90.

Hence when y = 6, x = k/y = (90)/(6) = 15.

The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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The volume of the described solid is V = 16r³/3

Given,

A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)

Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^b_a {A(x)} \, dx\)

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = ₋\(\int\limits^r_r {A(x)} \, dx\)

Substitute A(x) from (1)

V = ₋\(\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx\)

⇒V = 4[r²x - x³/3 ]

⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

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let length be x

ATQ

\(\\ \sf\longmapsto \dfrac{2}{8}\times x=28\)

\(\\ \sf\longmapsto \dfrac{2x}{8}=28\)

\(\\ \sf\longmapsto \dfrac{x}{4}=28\)

\(\\ \sf\longmapsto x=4(28)\)

\(\\ \sf\longmapsto x=112\)

Step-by-step explanation:

there is something wrong with your problem description.

the offered answer options do not fit to the solution as it is described.

2/8th of a rope is 28 meters long. how long is the whole rope ?

as the other answer said : 2/8 = 1/4

and 1/4th of the rope x = 28 m

1/4 × x = 28

x (the length of the whole rope) = 4×28 = 112 meters

but - maybe the original problem said that 7/8th (and not 2/8th) of a rope is 28 m.

7/8 × x = 28

1/8 × x = 4

x = 32 m

then A (32) would be the right answer !