It took a skydiver 12 seconds to drop 450 feet. What is the rate (in feet per/second) of the skydiver's drop?

Answer:

I

Step-by-step explanation:

I don't know love you tho

The total area of the figure 3,978 m², So correct option is D.

Composite figures, in geometry, refer to a figure that is made up of two or more simple shapes. These simple shapes can be basic figures such as triangles, circles, rectangles, and squares. The process of finding the area or perimeter of composite figures involves breaking them down into their individual simple shapes and finding the area or perimeter of each of those shapes, then adding them together. Composite figures can be classified as geometric shapes that are made up of more than one basic shape, such as a rectangle with a triangle on top or a figure made up of multiple circles or rectangles.

The figure you described is a three-dimensional shape, with two parallel bases and a height that connects them. It is likely that the figure is a triangular prism.

To find the total area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular lateral faces.

Let's consider the triangular base with the shorter side of 43m as the base of the triangle.

The area of the triangular base can be found by using the formula for the area of a triangle:

A = (b×h)/2 = (43 ×34)/2 = 738 square meters

The area of the second triangular base is similar, using the height of 34m and the other side of 18m as the base of the triangle

A = (b×h)/2 = (18 × 34)/2 = 306 square meters

The three lateral faces are rectangles, with the length of the rectangle being the height of the prism (34m), and the width being the distance between the two vertices (22m).

Area = lw = 3422 = 748 square meters

The total area of the composite figure is the sum of the area of both triangular bases and the three lateral faces.

Area = 738 + 306 + (3×748) = 738 + 306 + 2244 = 3,278 square meters

So the total area of the composite figure is 3,278 square meters, which is closest to option D) 3,978 m²

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Answer:

- 1

Step-by-step explanation:

Multiplying a negative quantity by a negative quantity results in a positive.

Also multiplying by 1 leaves the other value as is, then

- 1 × - \(\frac{7}{11}\) = \(\frac{7}{11}\)

The probability that the radar set will correctly detect exactly three aircraft before it fails to detect one is approximately 0.0883 (rounded to four decimal places).

To solve this problem, we can use the concept of a geometric distribution. The geometric distribution models the number of trials required until the first success occurs in a sequence of independent Bernoulli trials.

In this case, the probability of success (correctly detecting an aircraft) for each radar set is 0.97 (1 - 0.03). We want to find the probability that the radar set detects exactly three aircraft before it fails to detect one.

The probability of detecting three aircraft before the first failure can be calculated as follows:

P(3 successes before the first failure) = P(success) * P(success) * P(success) * P(failure)

P(success) = 0.97 (probability of detecting an aircraft)

P(failure) = 0.03 (probability of failing to detect an aircraft)

P(3 successes before the first failure) = 0.97 * 0.97 * 0.97 * 0.03

P(3 successes before the first failure) ≈ 0.0883

Therefore, the probability that the radar set will correctly detect exactly three aircraft before it fails to detect one is approximately 0.0883 (rounded to four decimal places).

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Answer:

The answer is B.

Step-by-step explanation:

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution.

Formula of the standard error of the means is standard deviation divided by square root of the sample size.

SE = δ/√n

This formula also gives the standard deviation of the sample means.

The answer is standard deviation of the sample (B).

For example, "The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean)."

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer: X=-4

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Answer:

(3x-2)^2

Step-by-step explanation:

3^2x^2-2*3x*2+3^2

(3x)^2 -2*3x*2+2^2

And youll get (3x-2)^2

Answer:

y = 1/4x + 4

Step-by-step explanation:

y = mx + b

Since the lines are parallel, the slope is the same. m = 1/4

y = 1/4x + b

Substitute (4,5)

5 = 1/4(4) + b

5 = 1 + b

4 = b

The y-intercept is (0, 4).

y = 1/4x + 4

The transformations required for y = x² to become y = (-x + 3)² - 5 are: A horizontal shift of 3 units to the right.A vertical shift of 5 units down.A reflection over the x-axis.

The original function, y = x², is a parabola that opens upwards. The vertex of the parabola is at the origin (0, 0). The new function, y = (-x + 3)² - 5, is also a parabola that opens upwards

. However, the vertex of the new parabola is at (3, -5). This means that the new parabola has been shifted 3 units to the right and 5 units down. The new parabola has also been reflected over the x-axis. This is because the coefficient of x in the new parabola is negative.

To visualize the transformations, we can graph the original function and the new function. The following graph shows the original function in blue and the new function in red:

graph of y = x² in blue and y = (-x + 3)² - 5 in reopens in a new window graph of y = x² in blue and y = (-x + 3)² - 5 in red.As we can see, the new parabola has been shifted 3 units to the right and 5 units down. The new parabola has also been reflected over the x-axis.

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Answer:

y=-0.5x+4

Step-by-step explanation:

x intercept=-0.5/1

y intercept=4

Step-by-step explanation:

again option D x = 10, y= 3

is the correct answer of this question.

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Answer:

x = 10

y = 7

Step-by-step explanation:

4x-2 = x+28

4x-x = 28+2

3x = 30

x = 30÷3

x = 10

4y-7 = y+14

4y-y = 14+7

3y = 21

y = 21÷3

y = 7

Answer:

x = 23

y = 119

Step-by-step explanation:

Line m is parallel to line n and the angle given as 61 and the angle that is represented with 4x - 31 are alternate angles and have equal measurement.

We can write the following equation based on this information:

4x - 31 = 61 add 31 to both sides

4x = 92 divide both sides by 4

x = 23

now onto y,

the angle represented with y and the angle that is represented with 4x - 31 are supplementary and their measures add up to 180:

4x - 31 + y = 180 replace x with 23

4*23 - 31 + y = 180

92 - 31 + y = 180 subtract like terms

61 + y = 180 subtract 61 from both sides

y = 119

Step-by-step explanation:

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The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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Answer:

663.

Step-by-step explanation:

Answer with Step-by-step explanation:

2 ( 2x -1 ) + 3 ( x + 1 )

First, let us find the value of the above expression.

2 ( 2x -1 ) + 3 ( x + 1 )

4x - 2 + 3x + 3

Combine like terms

4x + 3x - 2 + 3

7x + 1

Therefore, it is clear that the given expression is equal to 7x + 1.

∴ 7x + 1 = 2 ( 2x -1 ) + 3 ( x + 1 )

(a) The mean of the number of different species of plants in some gardens is 4.5 .

(b) The standard deviation of the number of different species of plants in some gardens is 2.12 (Approximately)

It is given in the question that the number of different species recorded are:-

1 2 3 4 4 5 5 6 7 8

We have to find the mean and standard deviation of the given data of the number of plants of different species.

(a) We know that, the formula for mean is :-

Sum of all the observations/ Total number of observations

Hence,

Mean = \(\frac{1+2+3+4+4+5+5+6+7+8}{10} =\frac{45}{10}=4.5\)

(b) Standard deviation = \(\sqrt{\frac{Sum(X-m)^{2} }{N} }\)

Where,

X = each value

m = mean

N = number of values

Hence,

\(Sum(X-m)^{2} =(1-4.5)^{2}+(2-4.5)^{2}+ (3-4.5)^{2}+ (4-4.5)^{2}+ (4-4.5)^{2}+ (5-5.5)^{2}+ (5-5.5)^{2}+ (6-5.5)^{2}+ (7-5.5)^{2}+ (8-5.5)^{2}\\ \\ Sum(X-m)^{2}=(-3.5)^{2} +(-2.5)^{2}+ (-1.5)^{2}+ (-0.5)^{2}+ (-0.5)^{2}+ (0.5)^{2}+ (0.5)^{2}+ (1.5)^{2}+ (2.5)^{2}+ (3.5)^{2} \\\\\)

\(Sum(X-m)^2=12.25+6.25+2.25+0.25+0.25+0.25+0.25+2.25+6.25+12.25\\\\=42.5\)

Standard deviation = \({\sqrt{\frac{{42.25}}{10} }} =\frac{6.7}{\sqrt{10} }=\frac{6.7}{3.16}=2.12\)  (approximately).

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The minimum value of the product xy is achieved when x = 0, resulting in y = -3. This occurs at the vertex (0, -3) of the parabola y = 4x^2 - 3. Therefore, the minimum value of the product xy is 0.

To find the minimum value of the product xy, we need to determine the coordinates of the vertex of the parabola. The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(x) represents the value of y. In this case, the equation is y = 4x^2 - 3, which can be rewritten as y = 4x^2 + 0x - 3.

Comparing this equation with the standard form y = ax^2 + bx + c, we have a = 4, b = 0, and c = -3. Using the vertex formula, we can calculate the x-coordinate of the vertex: x = -b/2a = -0/(2*4) = 0. Substituting x = 0 into the equation y = 4x^2 - 3, we find the y-coordinate of the vertex: y = 4(0)^2 - 3 = -3.

Therefore, the coordinates of the vertex are (0, -3). The product xy at the vertex is given by xy = 0*(-3) = 0. Hence, the minimum value of the product xy is 0.

The minimum value of the product xy is 0, which occurs at the vertex (0, -3) of the parabola represented by the equation y = 4x^2 - 3.

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We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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Equation of the line  that passes through the midpoint and is perpendicular to PQ is 2x - y +1 = 0.

One way to describe a perpendicular bisector is as a line segment that cuts through another line segment at a 90 degree angle. Simply said, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle. Measuring a line segment that needs to be bisected will help you discover a perpendicular bisector.

The midway of the measured length can then be determined by dividing it by two. From this center, extend a line at a 90-degree angle. All you need to do to determine the perpendicular bisector of two points is to discover their midpoint and negative reciprocal, then enter these results into the slope-intercept form of the equation for a line.

Here points are P( -4 ,3 ) and Q ( 4,-1)

Mid -point of PQ :

\(=(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )\\\\=(\frac{-4+4}{2} ,\frac{3-1}{2} )\\\\=(0,1)\\\)

Slope of PQ:

\(m = \frac{y_{2}{-y_{1} } }{x_{2}{-x_{1} }} \\\\m =\frac{-1-3}{4+4}\\\\ m= \frac{-4}{8} \\\\m = \frac{-1}{2}\)

The slope of the line is Perpendicular to PQ

so, slope 2= -1/m

slope 2 = -1/(-1/2)

slope 2 = 2

Equation of the line  that passes through the midpoint and is perpendicular to PQ

\(y-y_{1} =m(x-x_{1}) \\y-1 =2(x-0}) \\\\y-1=2x\\\)

2x - y +1 = 0.

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Correct Question:

Find the midpoint of PQ with endpoints P (-4, 3) and Q (4,-1) . Then write an equation of the line that passes through the midpoint and is perpendicular to PQ. This line is called the perpendicular bisector.

Answer:

D

Step-by-step explanation:

Answer:D

Step-by-step explanation: got it right

Answer:

3.15

Step-by-step explanation:

This graph is proportional. divide the y by x (k=y/x) (constant of proportionality. 6.3/3=3.15 18.9/6=3.15 28.35/9=3.15 15.75/6=3.15 3.15/1=3.15

The ATI Capstone Comprehensive Assessment evaluation normally comprises of multiple-choice questions, with 90 to 130 possible answers. Certain versions may also include extra alternative questions kinds, such as fill-in-the-blank or select-all-that-apply

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Answer:

answer: 1/8

Step-by-step explanation:

because the probability of getting a nickel is 2/4 and the probability of getting a quarter is 1/4 now when I multiply them together 2/4 × 1/4 = 1/8 Hope that helps!

The vector computation has been done and is shown in the attached image below.

In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.

Vector computations involve operations such as addition, subtraction, scalar multiplication, dot product, and cross product on vectors. To perform these operations, first, make sure that the vectors have the same dimensionality.

Then, for addition and subtraction, simply add or subtract corresponding components of the vectors.

For scalar multiplication, multiply each component of the vector by the scalar.

For dot product, multiply the corresponding components of the vectors and add the results.

For cross-product, use a formula that involves the components of the vectors.

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