There are a total of 5500 people in the stadium consisting of men, women, and children altogether in a swimming pool. There are twice as many women as men and four times as many children as women. How many men, women, and children are at the swimming pool?

Answer:

Step-by-step explanation:

f: 1 * 1 = 1

o: 1 * - 2i

i: 2i * 1

l: 2i * - 2i = - 4i^2 = -4 * i^2 = -4 * -1 = 4

Answer

1 - 2i + 2i + 4

5

(1+2i) · (1-2i) - Start with the given expression.

(1) · (1) · (1) · (-2i) + (2i) · (1) + (2i) · (-2i) - FOIL.

1 - 2i + 2i - 4i² - Multiply.

1 - 2i + 2i - 4 · (-1) - Replace i²  with -1. - Note: i² = -1

1 - 2i + 2i + 4 - Multiply.

5 + 0i - Combine like terms.

5 - Simplify

So (1 + 2i) · (1-2i) = 5.

The expression is now in standard form  a + bi where  a =5 and b = 0

The equation of line perpendicular to the line y = -2x-7 passing through (4,3) is : 2y = x+2

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

Here, the equation of line given is y = -2x-7 first calculating its slope (\(m_{1}\)) by comparing it with slope- intercept form of line i.e. y = mx+c

Therefore, the slope of the given line \(m_{1}\) is -2.

Now the slope (\(m_{2}\)) of the line perpendicular to the given line is calculated using relation :

\(\begin{aligned}m_{1}m_{2}&=-1\\m_{2}&=\frac{-1}{-2}\\&=\frac{1}{2}\end{aligned}\)

Now the equation of the line passing through (4,3) and slope 1/2 will satisfy the equation y = mx +c

\(\begin{aligned}y&= mx +c \\3&=\frac{1}{2}\cdot 4+c\\c&=1\end{aligned}\)

Therefore the equation of line perpendicular to the line y = -2x-7 passing through (4,3) is : 2y = x+2

\(\begin{aligned}y&= mx +c \\y&=\frac{1}{2}x+1\\2y&=x+2\end{aligned}\)

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

-2

Step-by-step explanation:

h(-5) represents the y value when x is -5.

Answer:

10.6 hours

Step-by-step explanation:

To find the curvature of the curve defined by the vector function r(t) = < t^2, ln(t), t ln(t) > at a given point, we need to calculate the curvature using the formula:

κ = |dT/ds| / ||dT/ds||,

where dT/ds is the unit tangent vector and ||dT/ds|| is its magnitude.

Let's proceed with the calculations:

Step 1: Find the first derivative of r(t) to get the tangent vector T(t):

r'(t) = < 2t, 1/t, ln(t) + t/t > = < 2t, 1/t, ln(t) + 1 >.

Step 2: Calculate the magnitude of the tangent vector:

||r'(t)|| = sqrt((2t)^2 + (1/t)^2 + (ln(t) + 1)^2)

         = sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1).

Step 3: Differentiate r'(t) to find the second derivative:

r''(t) = < 2, -1/t^2, 1/t + 2/t > = < 2, -1/t^2, (t + 2)/t >.

Step 4: Calculate the magnitude of the second derivative:

||r''(t)|| = sqrt(2^2 + (-1/t^2)^2 + ((t + 2)/t)^2)

          = sqrt(4 + 1/t^4 + (t^2 + 4t + 4)/t^2)

          = sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2).

Step 5: Calculate the curvature:

κ = |dT/ds| / ||dT/ds||

  = (||r'(t)|| / ||r''(t)||^3)

  = ((sqrt(4t^2 + 1/t^2 + ln(t)^2 + 2ln(t) + 1)) / (sqrt((t^6 + 4t^5 + 4t^4) + (t^2 + 4t + 4) + 4t^2))^3).

To find the curvature at a specific point, substitute the value of t into the expression for κ.

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Answer:

x = 1

Step-by-step explanation:

1/2(8x-6) = -1/3(9x-12)   distribute

4x-3 = -3x+4                 add 3x to both sides

7x-3 = 4                        add 3 to both sides

7x = 7                            divide by 7 on both sides

x = 1

Given:

The quadratic function is:

\(f(x)=x^2+3x-4\)

To find:

The zeros of the given quadratic function.

Solution:

We have,

\(f(x)=x^2+3x-4\)

Splitting the middle term, we get

\(f(x)=x^2+4x-x-4\)

\(f(x)=x(x+4)-1(x+4)\)

\(f(x)=(x+4)(x-1)\)

For zeros, \(f(x)=0\).

\((x+4)(x-1)=0\)

\(x=-4,1\)

Therefore, the correct option is (b).

The possible coordinates for point B could be (12, 4) if each coordinate increment is 1.

To find the coordinates of point B given that there are 10 equally spaced points between point A and point B, we need to determine the distance between the two points and divide it by 10 to find the increment for each coordinate.

Let's assume the coordinates of point B are (x, y).

The x-coordinate increment would be the difference between the x-coordinates of point B and A divided by 10:

Δx = (xB - xA) / 10

The y-coordinate increment would be the difference between the y-coordinates of point B and A divided by 10:

Δy = (yB - yA) / 10

Substituting the known values:

Δx = (xB - 2) / 10

Δy = (yB - (-3)) / 10

Since we have 10 equally spaced points between A and B, we can calculate the coordinates of point B by multiplying the increments by the number of points from A:

xB = 2 + 10 * Δx

yB = -3 + 10 * Δy

Now we can calculate the possible coordinates for point B using these formulas.

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Answer:

I got $0.42

Step-by-step explanation:

Answer:

she would need to work at least 13 hours lifeguarding to get to the 290 her with the of working an extra 3 hours  

Step-by-step explanation:

subtract the 30 dollars from babysitting from the 290 needed you 260 then divide it by 20

The minimum number of whole hours lifeguarding that she must work to meet her requirements will be 14 hours.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Annabelle is working two summer jobs, making $10 per hour babysitting and making $20 per hour lifeguarding.

In a given week, she can work no more than 19 total hours and must earn no less than $290.

Now,

Let x represents the number of hour for babysitting, and 'y' represents the number of hours for lifeguarding.

Since, In a given week, she can work no more than 19 total hours and must earn no less than $290.

Hence, We can formulate;

⇒ x + y < 19

And, 10x + 20y > 290

So, For Annabelle worked 3 hours babysitting, the minimum number of whole hours lifeguarding is,

⇒ 3 + y < 19

⇒ y < 16

And, 10x + 20y > 290

⇒ 30 + 20y > 290

⇒20y > 290 - 30

⇒ 20y > 260

⇒ y > 13

Thus, The possible value of y = 14, 15

So, The minimum number of whole hours lifeguarding that she must work to meet her requirements will be 14 hours.

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Step-by-step explanation:

4.25 x 5 = 21.25 cm

Hope this helped!

Answer:

It should also equal to 28° because bisect means to divide into 2 equal parts.

To find the volume of the solid obtained by rotating the region enclosed by the curve y = -2x + 8 in the first quadrant about the line x = 7, we can use the method of cylindrical shells.

The equation y = -2x + 8 represents a straight line with a y-intercept of 8 and a slope of -2. The region enclosed by this line in the first quadrant lies between x = 0 and the x-coordinate where the line intersects the x-axis. To find this x-coordinate, we set y = 0 and solve for x:

0 = -2x + 8

2x = 8

x = 4

So, the region is bounded by x = 0 and x = 4.

Now, let's consider a thin vertical strip within this region, with a width Δx and height y = -2x + 8. When we rotate this strip about the line x = 7, it forms a cylindrical shell with radius (7 - x) and height (y).

The volume of each cylindrical shell is given by:

dV = 2πrhΔx

where r is the radius and h is the height.

In this case, the radius is (7 - x) and the height is (y = -2x + 8). Therefore, the volume of each cylindrical shell is:

dV = 2π(7 - x)(-2x + 8)Δx

To find the total volume, we need to integrate this expression over the interval [0, 4]:

V = ∫[0,4] 2π(7 - x)(-2x + 8) dx

Now, we can calculate the integral:

V = ∫[0,4] 2π(-14x + 56 + 2x² - 8x) dx

= ∫[0,4] 2π(-14x - 8x + 2x² + 56) dx

= ∫[0,4] 2π(2x² - 22x + 56) dx

Expanding and integrating:

V = 2π ∫[0,4] (2x² - 22x + 56) dx

= 2π [ (2/3)x³ - 11x² + 56x ] | [0,4]

= 2π [ (2/3)(4³) - 11(4²) + 56(4) ] - 2π [ (2/3)(0³) - 11(0²) + 56(0) ]

= 2π [ (2/3)(64) - 11(16) + 224 ]

= 2π [ (128/3) - 176 + 224 ]

= 2π [ (128/3) + 48 ]

= 2π [ (128 + 144)/3 ]

= 2π [ 272/3 ]

= (544π)/3

Therefore, the volume of the solid obtained by rotating the region about the line x = 7 is (544π)/3 cubic units.

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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The equation of each line given the y-intercept and x-intercept

5 and -4 is 4y- 20 = 5x.

The line has an x-intercept at x = -4 and y intercept at y = 5 this means that the line passes through the points(,0) and(,5).

Now we find the pitch m of the line passing through the points(,0) and(,5)(x-intercept).

The pitch of the line is

m = y2- y1/ x2- x1

= 5- 0/ 0-(- 4)

= 5/ 4

Point- pitch Formula y = m(x-x1)

where m is the pitch and( x, y) is the given point.

Now substituting the values

y- 0 = (5/4)( x-(- 4))

y = (5/4)( x 4)

4y- 20 = 5x

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The complete question :

Find the equation of the line that has an y intercept and x-intercept at

5 and -4.

​

The name given to this type of design is a factorial design. A factorial design is a design in which researchers investigate the effects of two or more independent variables on a dependent variable.

In this study, two independent variables were used: room color (yellow, blue) and room temperature (20, 24, 28 degrees Celsius), while the dependent variable was happiness.

Each level of each independent variable was tested in conjunction with each level of the other independent variable. There are a total of six experimental conditions (two colors × three temperatures = six conditions), and twenty students were randomly assigned to each of the six conditions.

The researcher then examined how each independent variable and how the interaction of the two independent variables affected the dependent variable (happiness). Therefore, this study is an example of a 2 x 3 factorial design.

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1. The slope of the water table between the two wells can be calculated by determining the difference in water table levels and dividing it by the distance between the wells. 2. The slope of Deer Creek can be determined by calculating the difference in elevation between its source and the valley floor and dividing it by the length of the creek. 3. To determine the ground measurements corresponding to 3.5 inches on the map, we need to use the map's scale. The scale of 1:24000 means that 1 inch on the map represents 24000 inches on the ground.

1. To calculate the slope of the water table between the wells, we subtract the water table level at one well (100 feet) from the level at the other well (300 feet), resulting in a difference of 200 feet. Since the wells are half a mile apart (2640 feet), we divide the difference in water table levels by the distance between the wells, giving us a slope of approximately 0.076 ft/mi.

2. The slope of Deer Creek can be determined by subtracting the elevation of its source (2700 meters) from the elevation at the valley floor (1290 meters), resulting in a difference of 1410 meters. Since the creek flows for 8 kilometers, we divide the elevation difference by the length of the creek, giving us a slope of approximately 176.25 m/km or 0.176 m/m.

3. To determine the ground measurements corresponding to 3.5 inches on the map, we use the scale of 1:24000. Since 1 inch on the map represents 24000 inches on the ground, 3.5 inches on the map would represent 84000 inches on the ground, which is approximately 7000 feet or 1.32 miles.

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Answer: horizontally shrink by a factor of 2.

The graph of g(x) will be compressed in the y-direction by a factor of 1/2 as compared to f(x).

Dilation is a type of transformation in which the object either compresses or enlarges.

Rewrite the function g(x) in terms of f(x).

g(x)= (1/2) f(x)

Compare the obtained equation by g(x)=cf(x) and determine the value of c.

c=1/2

Since 0<c<1, the dilated function will be compressed in the y-direction by a factor of c=1/2.

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

Answer:

3.9

Step-by-step explanation:

Let me know if I'm wrong, if I am I'm sorry

A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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Calculating this value will give us the approximate number of revolutions made by each tire during the six-mile trip.

To determine the number of revolutions made by each tire during a six-mile trip, we need to calculate the distance traveled by one revolution of the tire and then divide the total distance by this value.

The circumference of a tire can be found using the formula: circumference = π * diameter.

Given that the diameter of each tire is feet, we can calculate the circumference as follows:

circumference = π * diameter = 3.14 * feet.

Now, to find the number of revolutions, we divide the total distance of six miles by the distance traveled in one revolution:

number of revolutions = (6 miles) / (circumference).

Substituting the value of the circumference, we have:

number of revolutions = (6 miles) / (3.14 * feet).

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Answer:

The value of N = 5 Step-by-step

Write a Python program that accepts an integer (n) and computes the value of n+nn+nnn.

Sample value of n is 5

Python int(x, base=10):

The function returns an integer object constructed from a number or string x, or return 0 if no arguments are given. If x is a number, return x.__int__(). For floating point numbers, this truncates towards zero.

Answer:

Yes, Eleri is correct

Step-by-step explanation:

In June, there was abput 48 mm on rainfall, in May, there was about 96. 48*2=96

Answer:

Step-by-step explanation:

Idk

Step-by-step explanation:

mark me as brilliant plzzz

Answer:

4/3 = tan A

4/5 = sin A

3/5 = cos A

Step-by-step explanation:

Define the adjacent, hypotenuse, and opposite lengths in the triangle.

Hypotenuse: 20

Opposite: 18

Adjacent: 12

Tan, sin, and cos formulas:

I think it should be pretty easy to do the rest by simplifying the fractions and then getting the answer!

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

2,6x +5 = y

Step-by-step explanation:

Don’t know if you wanted the equation, but this is how it’s written

Answer: Im not giving answer to that but i will do this one

A water tank holds 256 gallons but is leaking at the rate of 3 gallons per week. A second water tank holds 384 gallons and is leaking at a rate of 5 gallons per week.After how many weeks will the amount of water in the two tanks be the same.

Step-by-step explanation:

you have: one is leaking 3 gallons per week and holds 256 gallons; whereas, the other one is leaking 5 gallons per week and holds 384 gallons.

Set up both the equations....

In y=mx+b form--->>>

y=-3x+256

y=-5x+384

To figure out when they will be equal..set the equations equal to each other....(remember to isolate the variable)

-3x+256=-5x+384

-3x+256=-5x+384

     -256        -256

-3x=-5x+128

-3x=-5x+128

+5x+5x

2x=128

x=64

After 64 weeks the amount of water in both tanks will be the same.

Thus, your answer.