How do you apply the slope criteria for parallel and perpendicular lines to solve geometric problems?

Two different age brackets (18-21 and 22-29) were surveyed and the number of people who responded and refused to respond was recorded.

We can use the formula for probability:

Probability = Number of favorable outcomes by Total number of outcomes, P(A) = f / N

First, let's find the number of people in the 22-29 age bracket who agreed to respond:

238 out of 268 people in this age bracket agreed to respond.

Next, let's find the number of people in the 18-21 age bracket who agreed to respond:

70 out of 83 people in this age bracket agreed to respond.

So, the total number of people who agreed to respond is 238 + 70 = 308 out of 351 people.

Therefore, the probability of getting someone in the 22-29 age bracket or someone who agreed to respond is 308/351.

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The graph of function f is shown. If g(x) = -2f(x), which graph is the graph of function g is show on the attachment

Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x).  That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).

See the attached image.  The table shows how the values of y change for each value of x used in the respective function.  Plot those new values to produce the graph.

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Answer:

150000

Step-by-step explanation:

Slope=0.500/2.000=0.250

-6/1 = 6.00000

6/4 = 3/2 = 150000

The length of b from the given triangle ABC is 4.1 inches.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔABC, a = 6 inches, m∠A=121° and m∠B=36°.

Here, sin 121°/6=sin 36°/b

0.8571/6=0.5877/b

0.8571b=0.5877×6

0.8571b=3.5262

b=3.5262/0.8571

b=4.1 inches

Therefore, the length of b from the given triangle ABC is 4.1 inches.

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The equation to illustrate this will be 600 + 28m m.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this situation, the owners of a recreation area are filling a small pond with water and they are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start.

The equation to illustrate this will be:

= 600 + (28 × m)

= 600 + 28m

m = number of minutes.

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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 28 liters per minute. There are 600 liters in the pond to start. Write the equation to illustrate this.

Answer:

half a rotaoin

Step-by-step explanation:

think there is a crycle and you divide half and eat it and the secand half is 180 degree

Our point A(x,y) becomes A' when a point is rotated 180 degrees counterclockwise about the origin. All we actually do is turn both x and y negative.

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When rotated about it’s center, a regular heptagon has 5 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 7 lines of reflectional symmetry.

The number of times an object is precisely the same as the original object during a full 360° revolution is known as rotational symmetry, a sort of symmetry. It can be found in various geometrical objects as rhombuses, squares,

A sort of symmetry that pertains to reflections is called reflection symmetry. Line symmetry and mirror symmetry are other names for reflection symmetry. If a figure has at least one line dividing it into two halves, one half is said to be the mirror image of the other half.

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With a significance level of 0.05 (i.e., a confidence level of 95%), the confidence interval is calculated using the T function.

As a result, the range between 190,078.9152 and 209,921.0852 is represented by the confidence interval of 200,000 9921.0848.

Find the 0.025 critical value t* for 129 degrees of freedom in order to determine a 95% confidence interval for the mean based on the sample mean of 98.249 and sample standard deviation of 0.733. The critical value for 100 degrees of freedom is roughly 1.962.

Depending on the degree of confidence you want to have, choose the significance level. The two-tailed t table's =.05 corresponds to the most typical confidence level of 95%.

In the two-tailed t table, determine the critical value of t.

Add s/n to the crucial value of t.

Calculate the top limit of the confidence interval by adding this value to the mean, and the lower limit by deducting this value from the mean.

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As y varies directly as (x−2)² and y = 5/3 when x = 4, then the equation for y in terms of x is y = (5/12)(x - 2)²

If the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.

For y = 5/3 when = 4, we can solve for the constant k as follows:

5/3 = k(4 - 2)² {we simplify the expression in the bracket}

5/3 = k2²

5/3 = k4

k = 5/(3 × 4) {cross multiplication}

k = 5/12

Therefore, as y varies directly as (x−2)² and y = 5/3 when x = 4, the equation for y in terms of x is y = (5/12)(x - 2)²

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Answer:

r = ±4.

Step-by-step explanation:

The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To write the equation 2r^2 - 32 in this form, you can subtract 32 from both sides to get 2r^2 - 32 = -32, and then divide both sides by 2 to get r^2 - 16 = -16. Finally, you can add 16 to both sides to get r^2 = 0, which is the standard form of a quadratic equation.

So, the equation 2r^2 - 32 = 0 can be written as the quadratic equation r^2 = 16, which has two real roots, r = ±4.

At the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Given that the function is:

f(x) = 5x + 7

To evaluate the function at the specified values substitute the value in x:

a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33

b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10

c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52

Hence, at the specified values of the independent variables the function is a. f(-8) = 5(-8) + 7 = - 40 + 7 = -33 b. f(0.6) = 5 (0.6) + 7 = 3 + 7 = 10 c. f (x + 9) = 5 (x + 9) + 7 = 5x + 45 + 7 = 5x + 52.

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The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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The number of tiles that will fit along the edge of the square mosaic is 28 tiles.

The concept used here is finding the square root of an area to determine the length of a side of a square and then using simple division to determine the number of tiles that will fit along the edge of the square. This involves using the formulas for finding the area of a square and the perimeter of a square.

To determine the number of 2 in x 2 in tiles that will fit along the edge of a square mosaic, you need to determine the length of one side of the square mosaic. You can do this by finding the square root of the total area:

sqrt(196) = 14

So one side of the square mosaic is 14 inches. The perimeter of the square is 4 * 14 = 56 inches.

Since each tile is 2 inches wide, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

Thus, the number of tiles that will fit along the edge of the square mosaic is 56 / 2 = 28 tiles.

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the boundary condition at a perfectly insulated surface is expressed mathematically as (0) -k = 0 depending on the physical characteristics of the surface.

A boundary condition is a mathematical expression that describes the behavior of a physical system at its boundaries, such as a surface.

Mathematically, a perfectly insulated surface is represented as an isothermal surface, meaning that the temperature is constant across the surface.

This is described by the equation (0) = 0, where эт represents the rate of heat transfer at the surface.

In other words, a perfectly insulated surface does not allow heat to flow through it.

This equation shows that the heat transfer is in the opposite direction of the temperature gradient at the surface.

Finally, the boundary condition at a perfectly insulated surface can also be expressed as эт (0,) -k = 0, which means that the heat transfer at the surface is equal to zero and there is no net heat transfer at the surface.

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The Surface area are shown below.

The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.

Given:

1. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

2. The measure of sides are

A = 12

B = 10

C= 5

D= 13

So, the Lateral Surface Area

= ( 12 + 13 + 5) x 10

= 30 x 10

= 300 cm²

and, the total surface Area

= Area of two triangles + Area of rectangle

= 2 x 1/2 x 5 x 12 + 300

= 60+ 300

= 360 cm²

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f (2) = 2^2 = 2 * 2 = 4

f (3) = 3^2 = 3 * 3 = 9

f(2) + f(3) = 4 + 9 = 13

f (5) = 5^2 = 5 * 5 = 25

13 does not equal 25

a. 4

b. 9

c. f(2) + f(3) ‡ f(5) can be stated as 13 does not equal 25

Given that, the function s(t) describes the motion of a particle along a line. s(t) = t³ − 13t² + 35t − 220

We need to find the time intervals in which the particle moves in the positive direction and the negative direction.

The given equation is s(t) = t³ − 13t² + 35t − 220

Taking the derivative,

v(t) = s'(t) = 3t² -26t + 35 = velocity at time t

s'(t) = 3t² -26t + 35 = 0

(3t -5)(t-7) = 0

t = 5/3 and 7 seconds

Therefore, the velocity > 0 when s'(t) > 0, when t>7 or t < 5/3 seconds

velocity <0 when 5/3 < t < 7 seconds

When moving in a positive direction, the intervals :-

(-∞, 5/3) ∪ (7, ∞)

When moving in a negative direction, the interval :-

(5/3, 7)

Hence, the time intervals are; positive direction (-∞, 5/3) ∪ (7, ∞) and negative direction (5/3, 7)

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The question was incomplete, so I solved for the question;

The function s(t) describes the motion of a particle along a line.

s(t) = t³ − 13t² + 35t − 220

(a) Find the velocity function v(t) of the particle at any time t ≥ 0.

(b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.)

(c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.)

The standard deviation of the sample mean decreases as the sample size increases. This is because the larger the sample size, the more accurately it reflects the population mean.

The standard deviation of the sample mean is a measure of how close the sample mean is to the population mean. The sample mean is an estimate of the population mean, and the standard deviation of the sample mean is a measure of how accurate that estimate is. When the sample size is increased, the sample mean becomes a more accurate estimate of the population mean, thus the standard deviation of the sample mean decreases. This is because the larger the sample size, the more accurately it reflects the population mean, and the closer the sample mean is to the population mean, the lower the standard deviation of the sample mean. The decrease in the standard deviation of the sample mean as the sample size increases is called the law of large numbers.

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The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As the figure is rotated by 90 degree and translated by moving from 2nd and 3rd quadrant to 1st and end quadrant.

Hence,

           The ΔDEF is mapped onto ΔD'E'F' by translation and rotation rules of triangle.

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The graph of the model is illustrated below and  the resistance when x = 85 is 1.12

The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).

The resistance of the wire can be approximated using the mathematical model:

=> y = 10,770/x² - 0.375,

where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.

To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,

=> y = 10,770/(10²) - 0.375 = 106.975 ohms.

The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.

Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.

In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.

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Answer:

-7.925

Step-by-step explanation:

Answer:

Solution

or, 11°=90° {being complementary angle}

or,90°-11°

79°

Answer is 79°

The statement Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2) is correct.

The probability that an event will occur is equal to the ratio of positive outcomes to all outcomes, according to the probability formula. The proportion of positive outcomes to overall outcomes, or P(E), determines the likelihood that an event will occur.

Given three softball players discussed their batting averages after a game.

Probability

Player 1 is seven elevenths = 7/11

P(Player 1) = 0.636

Player 2 is six ninths = 6/9

P(Player 2) = 0.666

Player 3 is = five sevenths = 5/7

P(Player 3) = 0.714

so the probability of P(Player 3) > P(Player 2) > P(Player 1).

so Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).

Hence option D is correct.

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Answer: 0.8  miles

Step-by-step explanation:

A segment that connects the vertex of a triangle with the opposite side so it makes a 90-degree angle is called Altitude.

In geometry, Altitude is used to describe the height of a polygon, triangle, or other two-dimensional shapes. The altitude of a figure is a line segment perpendicular to the base and passes through the vertex of the constitution. It is used to calculate the area of the figure and to determine the lengths of the sides and angles.

In three-dimensional figures, the altitude can also refer to the distance between the highest and lowest points of the constitution. The concept of altitude is widely used in mathematics, particularly in geometry, trigonometry, and related fields.

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Complete Question:

A line that connects the vertex of a triangle with the opposite side so it makes a 90 degree angle_____.

The expression that represents the volume of the rectangular prism is given as follows:

8 x 3 x 2 units ³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

Hence the volume is given by the multiplication of these dimensions as follows:

8 x 3 x 2 units ³.

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The number of solutions to the system of linear equations shown on the graph is given as follows:

D. One solution at (2, −3).

The number of solutions of the system of equations is given by the number of times which the two functions intersect.

From the image given at the end of the answer, the two functions intersect once, at x = 2 and y = -3, hence the correct option is given by option D.

The graph is given by the image presented at the end of the answer.

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The probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

What is probability?

Calculating probability is a method of determining how likely something is to occur. The probability scale runs from 0 to 1, where 0 denotes impossible and 1 denotes certainty.

We are given that a single die is rolled 100 times.

So, the outcomes can be {1,2,3,4,5,6}

Now,

P(odd) = Probability of odd numbers

Odd numbers are 1, 3 and 5

So, P(odd) = 3/6 = 1/2

P(>4) = Probability of numbers greater than 4

Numbers greater than 4 are 5 and 6

So, P(>4) = 2/6 = 1/3

P(prime) = Probability of prime numbers

Prime numbers are 1, 2, 3 and 5

So, P(prime) = 4/6 = 2/3

P(8) = Probability of number 8

In a dice, the maximum number is 6

So, P(8) = 0

Hence, the probabilities from least to greatest are P(8), P(>4), P(odd) and P(prime).

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The final value of z = xy will be 1.05 times the original value.

The formula for calculating the growth rate of z = xy is z’/z = (x’/x)+(y’/y). The prime symbol (‘) denotes the rate of growth. In this case we can substitute the given rates of growth of x and y: x’/x = 2% and y’/y = 3%. By substituting these values into the formula we can calculate the rate of growth of z. z’/z = (2% + 3%) = 5%.

Therefore z = xy will grow approximately by 5%. To calculate the exact change in z, we can use the formula for compound growth: z’ = z (1 + r/100)^t, where r is the rate of growth and t is the number of time periods. In this case, r = 5% and t = 1 (as the growth rate is per period). Therefore, z’ = z (1 + 5/100)^1 = z (1.05) = z * 1.05. This means that the final value of z = xy will be 1.05 times the original value.

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