A parachutists speed during a free fall reaches 153 miles per hour. What is this speed in feet per second? at this speed, how many feet will the parachutist fall during 15 seconds of free fall? in your computations, use the fact that 1 mile is equal to 5280 feet. do not round your answer

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0

Completing the square for x and y, we get:

\((x-1)^{2}\)  + \((y-1)^{2}\)  = \(6^{2}\)

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

6

Step-by-step explanation:

The slope of a line indicates how steep it is calculated mathematically as "rise overrun". It calculates the rate where the variable y changes when the relevant variable changes, and the further calculation can be defined as follows:

Given Points:

\((-4,-2) , (-2,-10)\)

To find:

slope (m)=?

Solution:

\((-4,-2),(-2,-10)\\x_{1} =-4\\y_{1} =-2\\x_{2}= -2\\y_{2}=-10\\\)

Using formula:

\(slope(m)=\frac{y_{2-} y_{1} }{x_{2-} x_{1} } \\=\frac{-10-(-2)}{-2-(-4)} \\\\=\frac{-10+2}{-2+4}\\=\frac{-8}{2} \\=-4\)

Therefore,  the slope is "- 4".

Answer:

an= -3+5(n-1)

Step-by-step explanation:

Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.

Answer:

A.) an = -3 + 5(n - 1)

Explanation:

Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)

Arithmetic Series: a + (n - 1)d

['a' is first term, 'n' determines term position, 'd' is common difference]

Determine the following:

Putting into equation:

The value of f( -10 ) in the piecewise function is 150.

A piecewise function is simply a function which has different definitions of values for different intervals.

Given the piecewise function;

         t² - 5t; t ≤ -10

f(t) = { t + 19; -10 < t < -2

         t³/( t + 9 ); t ≥ -2

To solve for f( -10 ), we check the interval where -10 falls into.

Since -10 is less than or equal to -10, it falls in the interval of t ≤ -10.

Hence;

f(t) =  t² - 5t

Replace t with -10 and simplify.

f( -10 ) =  ( -10 )² - 5( -10 )

f( -10 ) =  100 + 50

f( -10 ) =  150

Therefore, the value of f( -10 ) is 150.

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The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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The derivative is: xdy + ydx

Given the function xy, the derivative is obtained by product rule.

Hold x constant and differentiate y, plus hold y constant and differentiate x

Answer:

\( \sqrt{170} \)

Answer:

The cost price of each mango was $3

Step-by-step explanation:

The man bought 500 mangoes, but 1/4 of them were rotten. There were 1/4*500 = 125 rotten mangoes, thus the number of mangoes he sold is

500 - 125 = 375 mangoes

Selling them at $3.36 each, he had revenue of

375*3.36=$1,260

That amount includes the 12% profit, that is, it's 112% of the cost price, thus the cost price of all mangoes is

1,260 / 112 * 100 = $1,125

The price of each mango was $1,125 / 375 = $3

The cost price of each mango was $3

Answer:

5/3

Step-by-step explanation:

3=9x-12

9x-12=3

9x-12+12=3+12

9x=15

9x/9=15/9

x=5/3

Answer:

(2,6)

x = 2, y = 6

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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Considering the expression of a line, the price of the guitar in 2011 is $354.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

Being:

the slope can be calculated as:

m= (300 - 246)÷ (2008 - 2005)

m= 54÷ 3

m= 18

Considering point 2 and the slope m, you obtain:

300= 18×2008 + b

300= 36,144 + b

300- 36,144 = b

-35,844 = b

Finally, the equation of the line is Price= 18×Year - 35,844

Now, you want to know the price of the guitar in 2011. Replacing in the linear equation, you get:

Price= 18×2011 - 35,844

Solving:

Price= 36,198- 35,844

Price= 354

In summary, the price of the guitar by 2011 is $354.

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To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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Answer:

Step-by-step explanation:

Interpreting as: 6000

Input:

6000

Number line:

Number line

Number name:

six thousand

Roman numerals:

\!\(\("V"\)\&_\)M

Binary form:

1011101110000_2

Prime factorization:

2^4×3×5^3

Residues modulo small integers:

m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

6000 mod m | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 6

Properties:

6000 is an even number.

6000 is a number that cannot be written as a sum of 3 squares.

6000 has the representation 6000 = 3^5 5^2 - 75.

6000 divides 49^10 - 1.

Character code 6000:

| Tagbanwa letter sa

Unicode: U+1770 (decimal: 6000)

Mathematica: \:1770

(Tagbanwa)

The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

From the question, we have the following parameters that can be used in our computation:

5y+4= (x+3)²+12

Swap x and y in the equation

So, we have

5x + 4= (y + 3)² + 12

When we make the vairiable y the subject, we have

y = -3 ± √(5x - 8)

Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)

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The constant of proportionality is A. 9.

The constant of proportionality is simply used to show that the numbers given have a constant value.

From the information, the Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 18 jars. The constant will be:

= Number of jars / Number of hours

= 18/2

= 9

In 6 hours, it bottles 54 jars of honey. The constant will be:

= 54 / 6

= 9

Therefore, the constant is 9.

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Answer:

it can be 100 because percentages are out of 100

Solution :

If \(S_n\) is the total spending generated after n transactions, then \(a_n\) is the spending generated during the n-th transaction. Since the government spends D dollars, then \(a_1\) = D.

Then the second person will receive D dollars and spend \(D_c\) dollars. Therefore, \(a_2=D_c\). The next person will receive \(D_c\) dollars, which means they are spending \(a_3 = (D_c)c = Dc^2\) dollars. Therefore,

\(a_1 = D\)

\(a_2=D_c\)

\(a_3 = Dc^2\)

\(a_4 = (Dc^2)c= Dc^3\)

....

\(a_n=Dc^{n-1}\)

∴ \(S_n=a_1+a_2+a_3+....+a_n\)

  \(S_n = D+Dc+Dc^2+Dc^3+...+Dc^{n-1}\)

  \(S_n= D(1+c+c^2+...+c^{n-1})\)

  \(S-n=D . \frac{1-c^n}{1-c}\)

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The input that would give an output value of -1/3 is 19

A linear equation is an equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The table of values that completes the question is added as an attachment

A system of linear equations is a collection of at least two linear equations.

In this case, the linear equation is given as

y = -1/3x + 7

From the complete question, the output value is given as:

y = 2/3

Substitute y = 2/3 in y = -1/3x + 7

2/3 = -1/3 * x + 7

Subtract 7 from both sides of the equation

-1/3 * x = 2/3 - 7

Take the LCM

-1/3 * x = (2 - 7 * 3)/3

Evaluate the product

-1/3 * x = (2 - 21)/3

Evaluate the difference

-1/3 * x = -19/3

Multiply both sides by -3

x = 19

Hence, the input that would give an output value of -1/3 is 19

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Answer:

answer is 19

Step-by-step explanation:

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Translation is the movement of a point up, down, left or right.

Transformation is the movement of a point from its initial location to a new location.

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Therefore the coordinates remains same as previous figure.

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Answer: -20

Step-by-step explanation: I got negative twenty because if f(x) equals negative thirteen the we add negative seven because we need to flip the sign since it is negative and when you add you get negative twenty

To check, simply solve the eqation the way it first was, for example, f(x)=-20+7 which would be correct, equaling -13

Hopefully this helped, I' sorry if i am wrong

Answer:

12 pints

Step-by-step explanation:

\(\frac{1}{8}\) = \(\frac{8}{96}\)

8 ounces is equal to 1 pint.  8 x 12 = 96, so 1 x 12 is 12

Answer:

1. 55.5

2. 54.5

Step-by-step explanation:

Use division to convert the fraction to a decimal:

1/4 = 1 ÷ 4 = 0.25

Multiply by 100 to get percent value:

0.25 × 100 = 25%

Answer:

1. 0.56

percentage: 56%

2. 0.55

percentage: 55%

Step-by-step explanation:

5/9 to decimal= 0.56

to percentage multiply by 100

same for the second one

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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