Find the total number of different permutations of the set {a, b, c, d, e, f, g}.

The five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.

In statistics, the five-number summary is a set of descriptive statistics that provide a summary of the distribution of a dataset. The five-number summary consists of the minimum value, the first quartile (Q1), the median (M), the third quartile (Q3), and the maximum value.

To find the five-number summary for the given data on the number of calories in a hot dog for each of 17 brands of meat hot dogs, we need to order the data from smallest to largest.

107 135 136 138 139 146 147 153 172 173 175 179 182 190 191 195

The minimum value is the smallest value in the dataset, which is 107.

The first quartile (Q1) is the value that is greater than or equal to 25% of the data and less than or equal to 75% of the data. To find Q1, we take the median of the lower half of the data:

Q1 = median(107, 135, 136, 138, 139, 146, 147, 153) = 138

The median (M) is the value that is in the middle of the dataset when the data is ordered from smallest to largest. For the given data, there are 17 values, so the median is the 9th value:

M = median(107, 135, 136, 138, 139, 146, 147, 153, 172, 173, 175, 179, 182, 190, 191, 195) = 175

The third quartile (Q3) is the value that is greater than or equal to 75% of the data and less than or equal to 25% of the data. To find Q3, we take the median of the upper half of the data:

Q3 = median(172, 173, 175, 179, 182, 190, 191, 195) = 190

The maximum value is the largest value in the dataset, which is 195.

Therefore, the five-number summary for the given data is Min = 107, Q1 = 138, M = 175, Q3 = 190, and Max = 195.

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Answer:

tan 33° = 0.6494

C = 65°

Step-by-step explanation:

Use a calculator.

tan 33° = 0.6494

cos C = 0.4226

Use the inverse cosine function on a calculator.

C = 65°

The exact value of the volume of the volleyball with radius 6 inches is 904.32 cubic inches

A volleyball has the shape of a sphere.

Volume of a sphere = 4/3πr³

Radius, r = 6 inches

π = 3.14

So,

Volume of a sphere = 4/3πr³

= 4/3 × 3.14 × 6³

= 4/3 × 3.14 × 216

= 2,712.96 / 3

= 904.32 cubic inches

Therefore, the volleyball has a volume of 904.32 cubic inches

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Answer:

Option C

Step-by-step explanation:

Given inequality is,

-3(2x - 4) ≤ 7(3 - x)

Solve the given inequality further,

-6x + 12 ≤ 21 - 7x

(-6x + 12) + 7x ≤ (21 - 7x) + 7x

x + 12 ≤ 21

(x + 12) - 12 ≤ 21 - 12

x ≤ 9 Or {x real | x ≤ 9}

Therefore, Option C will be the correct option.

Answer:

this is your answer look it once

The multiplied form of the Algebraic expression is 10x -0.8\(x^{2}\)

An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.

These expressions may be linear, quadratic or polynomials and the numbers in front of each term is called coefficient while the symbols or letters are called variable

2x( 5 - 0.4x)

we multiply each term in the bracket by 2x

2x  x 5  - 2x x 0.4x = 10x - 0.8\(x^{2}\)

In conclusion, 2x(5 - 0.4x) reduces to 10x - 0.8\(x^{2}\)

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Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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The best-predicted value of Modifying Above y with caret given that the twin born first has an IQ of 104​ is 106.2.

The dependent variable's predicted value in basic linear regression is given by the equation = b0 + b1x.

In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).

Use regression equation

ŷ=14.68+0.88x​

plug in IQ, which is x

y = 14.68 + 0.88(104)

 = 106.2

Hence, the answer is 106.2

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Answer:

28°

Step-by-step explanation:

sin ? = 19/41

? = arcsin (19/41)

? = 28° (rounded to the nearest degree)

Answered by GAUTHMATH

Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

2/8

÷2

1/4

1/4=0.25

1/8=0.25

In summary, we are given a second-order linear homogeneous differential equation, 2y" + 5y' - 3y = 0, along with initial conditions y(0) = 3 and y'(0) = 19. We need to find the solution to this initial-value problem.

To solve this initial-value problem, we can use the method of undetermined coefficients or the characteristic equation. Since the equation is linear and homogeneous, we can use the characteristic equation approach. We assume a solution of the form y(t) = e^(rt), where r is a constant to be determined. By substituting this form into the differential equation, we obtain the characteristic equation 2r^2 + 5r - 3 = 0.

Solving the characteristic equation, we find two distinct roots: r = 1/2 and r = -3/2. Therefore, the general solution to the differential equation is y(t) = c₁e^(1/2t) + c₂e^(-3/2t), where c₁ and c₂ are constants determined by the initial conditions. Plugging in the initial conditions y(0) = 3 and y'(0) = 19, we can set up a system of equations to solve for the constants. Finally, substituting the values of c₁ and c₂ back into the general solution, we obtain the specific solution to the initial-value problem.

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The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

To convert the given differential equation y + 5y + 3y'' + 4u + lu into a state-space representation with zero initial conditions, follow these steps:

1. Rewrite the differential equation: y'' + 5y' + 3y = -4u - lu.
2. Define state variables: Let x1 = y and x2 = y'. Then, x1' = y' = x2 and x2' = y''.
3. Rewrite the differential equation in terms of state variables: x2' + 5x2 + 3x1 = -4u - lu.
4. Solve for x2': x2' = -5x2 - 3x1 + 4u + lu.
5. Write the state-space equations:

  x1' = x2
  x2' = -5x2 - 3x1 + 4u + lu

With the initial conditions being zero, we have x1(0) = 0 and x2(0) = 0. This gives us the state-space representation of the given differential equation.

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Answer:

The number of blocks that will be needed to build the wall is 2500

Step-by-step explanation:

The number of blocks that will be needed to build the wall is;

\(n = \frac{volume of wall}{volume of block} \\volume = l *b*h\\\)

given the dimensions of the block and wall as;

block = 22cm by 11cm by 7cm

wall = 5 1/2m long, 22cm thick and 3 1/2m high. = 550cm by 22cm by 350cm

substituting into the equation, we have;

\(n = \frac{volume of wall}{volume of block} \\volume = l *b*h\\\\n = \frac{550*22*350}{22*11*7} \\n = 2500\)

The number of blocks that will be needed to build the wall is 2500

Shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

To find the shortest distance between a point and a plane, we can use the formula:

distance = |ax + by + cz + d| / √(a² + b² + c²)

where a, b, and c are the coefficients of the plane's equation, d is the constant term, and (x, y, z) is the coordinates of the point.

In this case, the plane is x + y + z = 1, so a = 1, b = 1, c = 1, and d = -1. The point is (2, 0, -3), so x = 2, y = 0, and z = -3. Plugging in these values, we get:

distance = |1(2) + 1(0) + 1(-3) - 1| / √(1² + 1² + 1²)

= 3 / √3

= √3

Therefore, the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1 is √3 units.

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Answer:

a. y = -x

b. Area = xy

c. x = -y

Step-by-step explanation:

a. The perimeter of the garden is the distance all the way around, in this would be x+y+x+y, or 2x + 2y. To solve for y, we’re trying to isolate it on one side. We need to subtract 2x to get 2y = -2x. Divide by 2 to get y = -x.

b. Area is length times width, so x • y, or xy.

c. To express in terms of x, we can take the equation y = -x and multiply it by -1 to get x = -y

To create a square with 50px sides, we need to draw four lines that are each 50px long and perpendicular to one another.

A square is a quadrilateral (a four-sided shape) with four equal sides and four equal angles of 90 degrees each. To create a square with 50px sides, we need to follow a few steps.

Step 1: Draw a line that is 50px long using a ruler or any other measuring tool.

Step 2: At the end of the line, draw a second line that is also 50px long and perpendicular to the first line. This will form the first side of the square.

Step 3: From the end of the second line, draw a third line that is also 50px long and perpendicular to the second line. This will form the second side of the square.

Step 4: Finally, draw a fourth line that is 50px long and perpendicular to the third line, connecting back to the starting point of the first line. This will form the remaining two sides of the square.

By following these steps, you have successfully created a square with 50px sides.

In summary, a square is a four-sided shape with four equal sides and angles of 90 degrees each. The resulting shape will be a square with 50px sides.

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Answer:

10

Step-by-step explanation:

If the sides of the rectangle is 6cm and 8cm, then we mean that, the length and breadth are 6cm and 8cm

The diagonal which cross at AX will be the hypotenus of the triangle formed by drawing the diagonal.

Hence,

Hypotenus = sqrt (opposite² + adjacent²)

AX = sqrt[(8²) + (6²)]

AX = sqrt(64 + 36)

AX = sqrt(100)

AX = 10

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Knowing whether the mean is more than or less than the median can give us information about the skewness of a distribution because the mean and median represent different aspects of the distribution's central tendency.

In a positively skewed distribution, the tail of the distribution extends towards higher values, meaning there are some extreme high values that pull the mean towards the right. In this case, the mean is greater than the median because it is influenced by those high values, shifting the central tendency towards the right.

On the other hand, in a negatively skewed distribution, the tail of the distribution extends towards lower values, indicating the presence of extreme low values that pull the mean towards the left. As a result, the mean is lower than the median because the central tendency is shifted towards the left by those low values.

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Answer:

3 1/2

Step-by-step explanation:

You turn negative ten fourths into -2 1/2 and then take that out of 6

Answer:

(-1 ; 3)

Step-by-step explanation:

when they say find the ordered pair they simply mean find the corresponding y value when x = -1

* where you see x substitute-1 *

f(-1) = 3(-1) + 6

=3

EXPLANATION

We can affirm that the length of the adjacent leg is 5 units and the length of the hypotenuse is 8 units.

As given, the length of the third side is 6.245 units.

Now, computing sin A give us the following expression:

The solution is 1249/1600

Answer:

7/40

Step-by-step explanation:

Since 1 ounce is 1/20 of 20 ounces, she needs to use 1/20 of 3 1/2 cups.

1/20 * 3 1/2 = 1/20 * 7/2 = 7/40

Answer:

7/40

Step-by-step explanation:

Given:

3 1/2 cups of sugar to make 20 ounces of Lemonade

To Find:

How many cups of sugar would be used to make 1 ounce of Lemonade?

Solution:

To find how many cups of sugar would be used to make 1 ounce of lemonade. First we have to divided 3 1/2 by 20.

And which it will give us 7/40 equal 0.175 as a decimal.

Hence, Octavia need 7/40 cups of sugar to make 1 ounce of Lemonade

Given:

Machine A covers 5/8 square feet in 1/2 hour.

Machine B covers 2/3 square feet in 1/3 hour.

Solution:

The unit rate of the machine A will be as

The unit rate of the machine B will be as

Answer:

Hence, the unit rate of the machine B is greater.

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer:

Uhhh the previous campers?

Step-by-step explanation:

No idea if this is some sort of trick question but I'm just going to go ahead and say the campers.

Answer:

a

Step-by-step explanation: