Solve the systems by graphing.

Y=1/4 x-5
y=-X+4

By using the Pythagorean theorem we conclude that the rope net is about 40.31 feet long.

The Pythagorean Theorem is a fundamental theorem in mathematics that describes the relationship between the sides of a right triangle.

We can use the Pythagorean theorem to solve this problem.

Let's consider the rope net as the hypotenuse of a right triangle, and the horizontal distance from the base of the platform to the starting point of the rope net as one leg of the triangle.

The other leg of the triangle is the vertical height of the platform.

Using the Pythagorean theorem, we have:

length of rope net = √(horizontal distance² + vertical height²)

Substituting the given values, we get:

length of rope net = √(35² + 20²)

= √(1225 + 400)

= √1625

= 40.31 feet (rounded to two decimal places)

Therefore, the rope net starts 35 feet from the platform base, and the platform is 20 feet high and the rope net is about 40.31 feet long.

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Answer:

AA Similarity

i hope this helps :)

Since trapezoid ABCD is inscribed in circle O, we know that angles A and D are right angles. We also know that the measure of angle ABD is equal to half the measure of arc AC. Since DC is a diameter of the circle, arc AC is a semicircle and thus has a measure of 180 degrees. Therefore, angle ABD has a measure of 90 degrees.

We also know that the sum of the measures of the angles in a trapezoid is equal to 360 degrees. Therefore, we can set up the following equation:

mAB + mBC + mCD + mDA = 360

Substituting the given values, we get:

80 + mBC + 90 + 90 = 360

Simplifying, we get:

mBC = 100

Therefore, mBC is equal to 100 degrees.

1. Statistic, 2. Data, 3. Pοpulatiοn, 4. Variable, 5. Parameter, 6. Sample

Statistic:  

A statistic is a numerical value that describes a characteristic οf a sample.

Parameter: A parameter is a numerical value that describes a characteristic οf a pοpulatiοn.

Data: Data refers tο the infοrmatiοn cοllected in a study οr experiment. This can include numbers, text, οr οther fοrms οf infοrmatiοn that can be analyzed.

Variable: A variable is any characteristic οr attribute that can take οn different values in a study οr experiment.

Sample: A sample is a grοup οf individuals οr οbjects selected frοm a larger pοpulatiοn fοr the purpοse οf cοnducting a study οr experiment. The characteristics οf the sample are used tο make inferences abοut the larger pοpulatiοn.

Pοpulatiοn: A pοpulatiοn is the entire grοup οf individuals οr οbjects that a study οr experiment is cοncerned with. The characteristics οf the pοpulatiοn are οften οf interest, but it is usually nοt feasible tο cοllect data frοm every member οf the pοpulatiοn, sο a sample is used instead.

Here we have

A rancher is interested in the average age that a cοw begins prοducing milk.

The fοllοwing vοcabulary can be matched as fοllοws

1. The average age fοr the 62 milk cοws as they first prοduced milk - Statistic

2. The list οf the 62 ages - Data

3. All milk cοws - Pοpulatiοn

4. The age when a milk cοw first prοduced milk - Variable

5. The average age that all milk cοws are when they first prοduce milk - Parameter

6. The 62 milk cοws that were οbserved by the rancher: Sample

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So the equation in the form y=kx is: y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equal sign, with the expression to the left of the equal sign indicating the left-hand side of the equation, and the expression to the right of the equal sign indicating the right-hand side of the equation. Equations can be used to describe relationships between variables, to solve problems, and to model real-world phenomena.

Here,

a. Yes, the cost of the commercials is proportional to the length of time the commercial aired.

b. To find the cost of a commercial in dollars per second, we need to divide the cost by the length of the commercial in seconds. Using the given values, we get:

For a 15-second commercial: $2,700,000 ÷ 15 = $180,000 per second

For a 60-second commercial: $10,800,000 ÷ 60 = $180,000 per second

For a 90-second commercial: $16,200,000 ÷ 90 = $180,000 per second

For a 120-second commercial: $21,600,000 ÷ 120 = $180,000 per second

We can see that the cost per second is constant at $180,000. So the equation in the form y=kx is:

y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

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The empirical probability that the student studied in E, B, and F is approximately 0.635.

The total number of students who studied abroad in the 2008-2009 school year is not given, so we cannot calculate the empirical probability directly. However, we can assume that the sample size is very large, and therefore the empirical probability of selecting a student who studied in each of the destinations listed is approximately equal to the relative frequency of students who studied in each of the destinations.

The total number of students who studied abroad in these 10 destinations is:

14,012 + 27,731 + 11,011 + 10,722 + 10,650 + 8,311 + 6,407 + 6,222 + 5,779 + 5,274 = 106,939

Therefore, the empirical probability of selecting a student who studied in E, B, and F is approximately:

≈ (14,012 + 27,731 + 11,011) / 106,939 ≈ 0.635

So, the empirical probability that the student studied in E, B, and F is approximately 0.635.

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Answer:

360

Step-by-step explanation:

.05n = 18

n = 360 campers

The value of x for the given rectangle in which the perimeter of both the rectangle are equal is x = 15.

What about rectangle?

A rectangle is a four-sided plane figure with four right angles (90-degree angles) and opposite sides that are parallel and equal in length. In other words, it is a parallelogram with all angles being right angles. The two pairs of parallel sides of a rectangle are called the length and width (or height) respectively. The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding up the lengths of all four sides. Rectangles are commonly used in mathematics, geometry, engineering, and architecture, among other fields.

Define perimeter of rectangle:

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is the sum of the lengths of all four sides of the rectangle. If the length of the rectangle is denoted by "l" and the width (or height) is denoted by "w", then the formula for the perimeter of a rectangle is:

⇒ Perimeter = 2(l + w)

According to the given information:

As, we know that the perimeter of the rectangle is sum of all side of the rectangle in which,

The perimeter of first rectangle is =   [tex]2(1.4x + 5x + 5.25)[/tex]

The perimeter of second rectangle is = [tex]2(4.25x + 3x - 7.5)[/tex]

It is given that perimeter of both the rectangle are equal so,

2(1.4x + 5x + 5.25) = 2(4.25x + 3x - 7.5)

2.8x + 10x + 10.5  = 8.5x + 6x - 15

2.8x + 10x - 8.5x -6x = -15 - 10.5

-1.7x = -25.5

x = 15.

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The absοlute fοrm οf the given inequality is |x+1|>6.

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

Given inequality is

x<−7 οr x>5

The distance between -7 and 5 is

5- (-7) = 5+7= 12

Dividing that by 2 we get,

12/2 =6

It is the c value

We use the greater than since we have an οr

|x−b|>6 ----------------- (1)

Substituting  a value  x=5 in equatiοn (1) with an equals sign tο determine b we get

5-b =6

b= -1

The absοlute fοrm οf the given inequality is |x+1|>6

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Answer: A

Step-by-step explanation:

In linear equation, $-0.0143 is the rate of change of the quantity demanded when the price increases .

What in mathematics is a linear equation?

An mathematical equation with only a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

the demand function:

x² + p² = 2450

Differentiating both sides of the demand function with respect to time t using the chain rule, we get:

  2x * dx/dt + 2p * dp/dt = 0

We also know that at the point where the price is $7, p = 7 and x satisfies:

   x² + p² = 2450

Substituting p = 7 into the demand function, we get:

  x² + 7²  = 2450

     x² = 2450 - 49x²

       x = 49

substitute x = 49, p = 7, and dp/dt = $0.10 into the differentiated demand function and solve for dx/dp

     2x * dx/dp + 2p * dp/dx = 0

  2(49) * dx/dp + 2(7) * 0.10 = 0

   98 dx/dp + 1.40 = 0

  dx/dp = $-0.0143

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Step-by-step explanation:

50 tries experimentalprobabilities:

open :  2/50 = 1/25

closed  6/50 = 3/25

side :   42/50 = 21/25

Answer:

Open Side Up: 2/50 = 1/25 = 4%

Closed Side Up: 6/50 = 3/25 = 12%

Landing on Side: 42/50 = 21/25 = 84%

The value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90% is 1.812.

To find the value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90%, we can use a t-table.

Using a t-table, we can find the t-value that corresponds to a 5% area in the upper tail of the distribution, since the area between -t and t is 90% (leaving 10% in the tails).

For a t-distribution with 10 degrees of freedom, the critical value for a 5% area in the upper tail is 1.812. Check the attached image.

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The answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how probable it is.

We can use Bayes' theorem to find P(W|S), the probability that a day fell on a weekend given that it is sunny:

P(W|S) = P(S|W) * P(W) / P(S)

We are given that 15 days were sunny out of a 30-day month, so P(S) = 15/30 = 1/2.

Out of the 30 days, 8 fell on a weekend, so P(W) = 8/30 = 4/15.

We are also given that 5 of the sunny days fell on a weekend, so P(S|W) = 5/8.

Substituting these values, we get:

P(W|S) = (5/8) * (4/15) / (1/2) = 5/12

Therefore, the answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".

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The true statement is that the mode of the set of scores is 96. The solution has been obtained by using measures of central tendency.

What are measures of central tendency?

A summary measure called a measure of central tendency, also known as a measure of centre or a measure of central placement, aims to characterise the entirety of a set of data with a single number that corresponds to the centre or centre of its distribution.

We are given scores as 96, 77, 82, 96, and 89.

So, from this we get

⇒ Mean = (96 + 77 + 82 + 96 + 89) ÷ 5

⇒ Mean = 440 ÷ 5

⇒ Mean = 88

Similarly,

Arranging the numbers, we get 77, 82, 89, 96, 96.

So, the median is 89.

Mode is 96 as it is appearing two times.

Hence, the third statement is the true statement.

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Answer:

Min: 85

Q1: 95

Median: 110

Q3: 120

Max: 125

The list that shows the side lengths, in inches, of the triangle Riley drew is: 59/5, 57/5, 3/2

What is Triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is commonly used in various fields such as engineering, physics, and architecture. The sum of the angles of a triangle always adds up to 180 degrees.

To find the side lengths of the triangle Riley drew, we need to multiply each of Jim's side lengths by the scale factor of ‡, which means multiplying by 3.

The side lengths of Jim's triangle, when written with common denominators, are:

3¼ = 13/4

4.9 = 38/10

5/10 = 1/2

Multiplying each of these by 3 gives:

13/4 * 3 = 39/4

38/10 * 3 = 114/10 = 57/5

1/2 * 3 = 3/2

So, the side lengths of the triangle Riley drew are:

39/4, 57/5, 3/2

We can simplify these fractions by finding a common denominator:

39/4 = 236/20

57/5 = 228/20

3/2 = 30/20

So, the side lengths of the triangle Riley drew, in inches, are:

236/20, 228/20, 30/20

Simplifying further by dividing each numerator by 4, we get:

59/5, 57/5, 15/10

Therefore, the list that shows the side lengths, in inches, of the triangle Riley drew is:

59/5, 57/5, 3/2

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The index form is solved to give 1/z^13/12

Index forms are described as mathematical forms used to represent numbers too large or small in more proper ways.

Other names for index forms are scientific notations and standard forms.

They are represented as numbers raised to a variable or an exponent.

The rules of index forms are;

From the information given, we have;

z^-1/4/ z1/2 z1/3

Add the exponents

z^-1/4 / z  5/6

Subtract the exponents

z^ -6 - 20 /24

z^-26/24

1/z^13/12

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Step-by-step explanation:

The volume of a cube is similar to that of a rectangular prism, the volume equals the length times width times height, however because it’s a cube all the measurements are the same, in this case 7 inches. So volume equals 7^3, thus equaling 343 inches cubed. Hope this helps!

Answer:

Slope curve is the gradiient

Step-by-step explanation:

Gradient equation is m = change in y over change in x

Therefore the first answer is correct

Answer:

  a) 7 m

  b) 22 cm

Step-by-step explanation:

Given plans at a scale of 1 : 50, you want (a) the actual length corresponding to a plan length of 14 cm, and (b) the plan length corresponding to an actual length of 11 m.

The actual lengths are wanted in meters, so we can rewrite the scale to translate between plan cm and actual m.

  plan : actual = 1 cm : 50 cm

  = 1 cm : 0.5 m

  = 2 cm : 1 m

Multiplying the scale by 7, we have ...

  2 cm : 1 m = 14 cm : 7 m

The actual length is 7 meters.

Multiplying the scale by 11, we have ...

  2 cm : 1 m = 22 cm : 11 m

The plan length is 22 cm.

Answer: Two other positive angles of rotation that take A to B are:

- 13π/6 radians counterclockwise

- 25π/6 radians clockwise

Step-by-step explanation:

Answer:

We do not know if the triangles are congruent because we have no information about congruent sides.

The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.

A graph of y = f⁻¹(x) is shown below.

An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:

0 < a

Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:

[tex]a^x > a^{x+1}[/tex]

1 > a

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Answer:

The student made a mistake when squaring -4.

-4 * -4 = 16.  Had the expressions said -x^2, then the answer would indeed be -16 since -1 *(-4*-4) = -16

Furthermore, since the answer is 16, you'd do (16 - 7) ^3, which equals (9)^3, which is 729 and not -12,167

Answer: This type of sample is called a stratified random sample. The population (city) is divided into various zones, and then a random sample of households (5 from each zone) is taken from each stratum (zone). This helps ensure that the sample is representative of the population as a whole and includes a proportional number of households from each zone.

Step-by-step explanation:

stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

How to study sample?

This sampling method is an example of stratified random sampling, where the population is divided into different subgroups or strata, and a random sample is drawn from each stratum. In this case, the strata are the various zones of the city, and the researcher randomly selects five households from each zone.

Stratified random sampling is a commonly used sampling method in research because it can increase the representativeness of the sample and reduce sampling error. By dividing the population into different strata based on relevant characteristics, such as geographic location, age, gender, or income level, the researcher can ensure that each stratum is adequately represented in the sample.

In this example, the researcher is interested in studying public transportation usage in different zones of the city. By stratifying the population by zone and selecting a random sample of households from each zone, the researcher can obtain a representative sample of the population and draw conclusions about public transportation usage in each zone.

Overall, stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

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Your complete question is :-A city collects data about public transportation. The researcher divides the city into various zones, and randomly chooses 5 households from each zone to survey. Which type of sample does this represent?

Answer:

y > 3x - 1

set y = 0

0 > 3x - 1

x > 1/3

points are [ 1/3,0]

set x = 0

y > 3(0) - 1

y > - 1

points are [0,-1]

second question

x + y ≤ - 2

set x = 0

y ≤ - 2

points are [0,-2]

set y = 0

x ≤ - 2

points are [-2,0]

So therefore A should be shaded.

Answer:

1.5 * 7 that is the answer of the question

Using the slope of curve,

1. If x=0.5, then the slope is: 0.3333.

2. If x=0.9, then the slope is: 0.2632

3. If x=0.99, then the slope is: 0.2513

4. If x=0.999, then the slope is: 0.2501

5. If x=1.5, then the slope is: 0.2

6. If x=1.1, then the slope is: 0.2381

7. If x=1.01, then the slope is: 0.2488

8. If x=1.001, then the slope is: 0.2499

Define a curve?

Three easy procedures can be used to compute the area under the curve. The curve's equation (y = f(x)), the boundaries within which the area is to be determined, and the axis encompassing the area must first be known.

The curve is given as:

y = x/1+x

Point, P = (1, 1/2) lies on the curve.

Point, Q = (x, x/1+x) is an arbitrary point on the curve.

The slope of the secant line PQ is:

y2-y1/x2-x1

= x-1/2(x+1) × 1/(x-1)

=1/2(x+1)

1. If x=0.5, then the slope is:

1/2(0.5+1)

= 1/3

= 0.3333

2. If x=0.9, then the slope is:

1/2(0.9+1)

= 1/3.8

= 0.2632

3. If x=0.99, then the slope is:

1/2(0.99+1)

= 1/3.98

= 0.2513

4. If x=0.999, then the slope is:

1/2(0.999+1)

= 1/3.998

= 0.2501

5. If x=1.5, then the slope is:

1/2(1.5+1)

= 1/5

= 0.2

6. If x=1.1, then the slope is:

1/2(1.1+1)

= 1/4.2

= 0.2381

7. If x=1.01, then the slope is:

1/2(1.01+1)

= 1/4.02

= 0.2488

8. If x=1.001, then the slope is:

1/2(1.001+1)

= 1/4.002

= 0.2499

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Answer:

value of ∅ = 67.5°

Step-by-step explanation:

cos135° = [tex]-\frac{1}{\sqrt{2} }[/tex]

so 2Ф = 135

Ф = [tex]\frac{135}{2} = 67.5[/tex]°