An architect needs to design a new light house. an average-man (6 ft tall) can see 1 mile


into the horizon with binoculars. if the company building the light house would like for


their guests to be able to see 20 miles out from the top of the light house with binoculars,


then how tall does the building need to be?

Answer: \(14w+28y-7\)

Step-by-step explanation:

multiply everything by -7

Answer:

Step-by-step explanation:

14w+28y-7

3/5 = 6/x

3x = 30

x = 10

PLEASE pay attention in class, you basically asked every question on what seems to be homework

10 is the answer to this problem.

The middle 50% of jumpers in skydiving freefall for a time range of approximately 19 to 21 seconds.

The given information states that the time spent in freefall during skydiving follows a normal distribution with a mean of 20 seconds and a standard deviation of 2 seconds. In a normal distribution, the middle 50% of the data lies within one standard deviation from the mean. Since the standard deviation is 2 seconds, we can calculate the range by subtracting and adding 1 standard deviation from the mean.

To find the lower end of the range, we subtract 1 standard deviation (2 seconds) from the mean: 20 - 2 = 18 seconds. This means that approximately 25% of the jumpers freefall for less than 18 seconds.

To find the upper end of the range, we add 1 standard deviation (2 seconds) to the mean: 20 + 2 = 22 seconds. This means that approximately 25% of the jumpers freefall for more than 22 seconds.

Therefore, the middle 50% of jumpers freefall for a time range of approximately 18 to 22 seconds. However, since the problem specifically asks for the middle 50%, we can conclude that the middle 50% of jumpers freefall for a time range of approximately 19 to 21 seconds.

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The rate of change is (-1)

To solve this, we need to look at graphic to know the values of the function f(x) when x is equal to 1 and 3.

Then we have two points of the graph: (1,6) and (3,4).

The rate of change between two points is:

In this case,

Note that its the same whatever coordinate put first:

But when you do the difference between the coordinates, make sure to respect the order: if you use the y coordinate of the point P minus the y coordinate of point Q, you must to do the same for the x coodinate; Px-Qx

Step-by-step explanation:

99+111+arc QR=360°

arc QR=360-210 =150°

again,

RPQ=150/2{inscribed angle is half of it's arc}

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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Answer:

Below.

Step-by-step explanation:

1) 245.

2) Approximate slope =  -(245-200)/15 = -3.

The y intercept is 250 and the slope is -10/3.

The equation of a line is linear in two variables, usually x and y, that is satisfied by points of the line.

We have the following ordered pairs in the line given:

(0, 250) and (30, 150)

Calculating the slope:

m = 150 - 250/ 30 - 0

m = -100/30

m = -10/3

Therefore, the slope is -10/3

Finding the y-intercept:

The equation of a line has the form:

y = mx + b, where m is the slope

Replacing by the values we know:

150 = -10/3 * 30 + b

b = 150 + 100

b = 250

Therefore, the y intercept is 250.

Hence the y intercept is 250 and the slope is -10/3.

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Answer: 450 is divisible by 2, 3, 5, 6, and 9

Step-by-step explanation: 450 is divisible by 2 because the last digit (0) is an even number.

Divisible by three because the sum of all the digits in 450 is a multiple of three: 4+5+0 = 9 which is 3*3.

Divisible by 5 because it ends with a 0 (could also end in 5)

Divisible by 6 because it is divisible by both 2 and 3 (2*3=6)

Divisible by 9 because 45 is divisible by 9.

The total cost for Bob's ride is C = x + m and no. of minutes of the ride is

m = C - x.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given,  A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.

Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.

Therefore, The total bill(C) for Bob's ride is,

C = x + m.

The no. of minutes Bob ride the scooter is simply,

m = C - x.

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Answer:

i need to get the full question, then i can help u. goodluck :)

Step-by-step explanation:

Based on the image below, if ∠8 = ∠4, then AD is parallel to BC using the concept of alternate interior angles.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

The converse is also true. If a pair of angles formed on inner side of two lines, but on opposite side of transversal are equal, then the two lines are said to be parallel.

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Answer:

D. 48

Step-by-step explanation:

f(x) = 5x^2 + 2 and g(x) = x^2 - 1; find g(f(-1))

First, we have to find f(-1). You will take the f(x) equation and substituute-1 for x

f(x) = 5x^2 + 2

f(-1) = 5(-1)^2 + 2

f(-1) = 5(1) + 2

f(-1) = 5 + 2

f(-1) = 7

Now we know f(-1) is equal to 7, which means g(f(-1)) is the same thing as g(7). We will be using the g(x) equation now and substitute 7 for x.

g(x) = x^2 - 1

g(7) = 7^2 - 1

g(7) = 49 - 1

g(7) = 48

The correct is 48 (D).

Answer:

D

Step-by-step explanation:

The Negative solution is -4 or Negative number is -4

The difference of the square of a number and 36 is equal to 5 times that number.

To find the negative solution.

Now, According to the question:

Let the unknown number be = x

Given that:
\(x^{2} -36 = 5x\\\\x^{2} -5x-36=0\\\)

Factories the above Equation:

\(x^{2} -9x+4x-36=0\\\\\)

x (x - 9) + 4 (x - 9) = 0

(x + 4) (x - 9 ) = 0

x + 4 = 0 and x - 9 = 0

x = -4 and x = 9

Hence, The Negative solution is -4

What is Factories Method?

Factorization is the process of reducing the bracket of a quadratic equation, instead of expanding the bracket and converting the equation to a product of factors which cannot be reduced further.

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Answer: cylinder

Step-by-step explanation:

Which property is demonstrated below?

a(b + c) = (a*b) + (a*c)

O Inverse property

O Distributive property

O Communitive property

O Identity property

Answer:

3/8

Step-by-step explanation:

if cameron ate 1/4 of a full pie, there would be 3/4 of it left. amy ate half of what is left so to figure this out, we should make the 3 into an even number, and the lowest fraction of this would be 6/8, and half of this is 3/8, so after amy had her share, there was 3/8 of the pie left.

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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If out of people who were chosen 3 out of 8 were chosen-again, then the ratio of people who were chosen twice is 3:10.

The "Ratio" is defined as a way of expressing the quantitative relationship between two or more quantities.

We know that, 40 people were selected and out of those 40 selected, 4 out of 5 were chosen, and

Out of the chosen people, 3 out of 8 were chosen again,

Now, we calculate the total-number of people who were chosen,

⇒ 40 selected × (4/5 chosen) = 32 people were chosen in the first round,

⇒ 32 chosen × (3/8 chosen again) = 12 people were chosen again in the second round.

So, the total number of people who were chosen twice is 12,

Now, we find ratio of people who were "chosen-twice" to "total-number-of-people" who were selected,

⇒ Ratio of people chosen twice to total people selected = 12/40,

On simplifying the ratio "12/40",

We get,

⇒ 12/40 = 3/10,

Therefore, the required ratio is 3:10.

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Answer:

Step-by-step explanation:

3n² + 9n - 6 = 3(n² + 3n - 2)

a) Median will be an appropriate measure for the distribution. b) Mean will be an approprate measure for the distribution.

Here we already have the data available to us. From the data, we can clearly see that

Mode < Mean < Median

Hence this is a negatively skewed distribution.

Therefore the appropriate measure of central tendency for this distribution will be the median. The median will tell us the point at which the frequency is divided by 50%.

Hence we can say that the median will a more appropriate measure.

Now if the data has another aspect of sex included, then the frequency column would be divided into separate columns with each gender identity taking up its own column.

Since now this will become multivariate data, the best measure of central tendency will be Mean.

The difference in the measure of central tendency will depend upon how skewed the data for every sex will be. For example, if in a country, men preferred to be educated over women, then the mean for men will be a lot higher than that of women. On the other hand, the EDUC for women will be a lot lower.

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Answer: A. The wrong region is shaded

Step-by-step explanation:

Let's solve for y in the first equation.

3x−2y<−5

Step 1: Add -3x to both sides.

3x−2y+−3x<−5+−3x

−2y<−3x−5

Step 2: Divide both sides by -2.

\(\frac{-2y}{-2}\)< \(\frac{-3x-5}{-2}\)

y > \(\frac{3}{2}x+\frac{5}{2}\)

graph the equation using the slope \(\frac{3}{2}\) and the y-intercept \(\frac{5}{2}\)

The line is dotted because it is > (not ≥)

shade in the left side by plugging in (0,0) into x and y and finding

0 is not > than \(\frac{5}{2}\). This means you shade in the side not include the origin.

Do this same thing for the next equation.

Let's solve for y in the second equation.

x+4y>8

Step 1: Add -x to both sides.

x+4y+−x>8+−x

4y>−x+8

Step 2: Divide both sides by 4.

\(\frac{4y}{4}\) > \(\frac{-x+8}{4}\)

y > \(\frac{-1}{4}x+2\)

graph the equation using the slope \(-\frac{1}{4}\) and the y-intercept 2

(Dotted line), (plug in 0,0 and find 0 is not > than 2. So shade the region not including the origin (0,0).

Hope this helps.

Answer:

# of sides \({}\)  Interior               One Interior Angle  Exterior           One

           \({}\)        Angle Sum                                          Angle Sum     Exterior Angle

14   \({}\)              2,160°                 154.3°                            360°           25.714°    

24    \({}\)            3,960°                165°                                360°            15°

8    \({}\)               1,080                 135°                                360°            45°

30    \({}\)            5,040                 168°                                360°            12°

12    \({}\)             1,800                  150°                                360°            30°

Step-by-step explanation:

Please find attached the table of values calculated with Microsoft Excel

From the given table, we have the formula for the following parameters;

Number of sides = n

Interior Angle Sum = 180×(n - 2)

Measure of ONE Interior = 180×(n - 2)/n        

Angle (regular polygon)  

Exterior Angle Sum = 360°

Measure of ONE Exterior = 360°/n

Angle (regular polygon)

1) When n = 14, we have;

The interior Angle Sum = 180×(14 - 2) = 2,160°

The measure of one Interior angle (regular polygon) ;  180×(14 - 2)/14 ≈ 154.3°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/14 ≈ 25.714°

2) When n = 24, we have;

The interior Angle Sum = 180×(24 - 2) = 3,960°

The measure of one interior angle (regular polygon);  180×(24 - 2)/24 = 165°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/24 = 15°

3) When the interior angle sum = 180×(n - 2) = 1,080°, we have;

n = 1,080°/180° + 2 = 8

n = 8

The measure of one interior angle (regular polygon);  180×(8 - 2)/8 = 135°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/8 = 45°

4) When the interior angle sum = 180×(n - 2) = 5,040°

n = 5,040°/180° + 2 = 30

n = 30

The measure of one interior angle (regular polygon);  180×(30 - 2)/30 = 168°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/30 = 12°

5) When the measure of one interior angle (regular polygon), 180×(n - 2)/n = 150°, we have;

180°·n - 2×180° - 150°·n = 0

30°·n = 360°

n = 360°/30° = 12

n = 12

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/12 = 30°

1) The first iteration, n, turns out to be (x1, y1) = ( , ).

2) If the second iteration, n, is (x2, y2) = ( , ).

To find the values of (x1, y1) and (x2, y2), we need additional information or the specific steps of the gradient method applied in MATLAB. The gradient method is an optimization algorithm that iteratively updates the variables based on the gradient of the function. Each iteration involves calculating the gradient, multiplying it by the learning rate (λ), and updating the variables by subtracting the result.

3) After s many iterations (and perhaps changing the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt, yopt) = ( , ).

To determine the values of (xopt, yopt), the number of iterations (s) and the specific algorithm steps or convergence criteria need to be provided. The gradient method aims to reach the minimum of the function by iteratively updating the variables until convergence is achieved.

4) The value of the minimum, once the convergence is reached, will be determined by evaluating the function at the point (xopt, yopt). The specific value of the minimum is missing and needs to be provided.

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the complete question is:

Matlab The Gradient Method Was Used To Find The Minimum Value Of The Function North F(X,Y)=(X^2+Y^2−12x−10y+71)^2 Iterations Start At The Point (X0,Y0)=(2,2.6) And Λ=0.002 Is Used. (The Number Λ Is Also Known As The Size Or Step Or Learning Rate.) 1)The First Iteration N Turns Out To Be (X1,Y1)=( , ) 2)If The Second Iteration N Is (X2,Y2)=( ,

Matlab

The gradient method was used to find the minimum value of the function north

f(x,y)=(x^2+y^2−12x−10y+71)^2 Iterations start at the point (x0,y0)=(2,2.6) and λ=0.002 is used. (The number λ is also known as the size or step or learning rate.)

1)The first iteration n turns out to be (x1,y1)=( , )

2)If the second iteration n is (x2,y2)=( , )

3)After s of many iterations (and perhaps change the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt,yopt)=( , );

4)Being this minimum=

Number of cups of water consumed per hour = 1 2/3 cups = 5/3 cups .

Number of hours spent in exercise = 14 hours

Number of cups consumed in the given month = ( Number of cups consumed per hour )(Total number of hours)

Therefore,

Thus the number of cups of water consumed is ,

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

Step-by-step explanation:

Consecutive exterior angles lie outside on the same side of a transversal.

So it should be 3,45 and 6