The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points?

The probability that a student surveyed was either a boy or had a bicycle is 0.62.

What is probability?

The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.

We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.

So, Total number of boys = 490

Total number of girls with bicycle = 130

Total number of students that was either a boy or had a bicycle is

490 + 130 = 620

The probability is

620 / 1000 = 0.62

Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.

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The value of y that satisfies the equation is y = -11.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two sides, separated by an equals sign (=), with each side containing one or more terms that may include variables, constants, and mathematical operators.

We can start by setting up the equation:

(y+1)/(y-5) + 10/(y+5) = (y+1)/(y-5) × 10/(y+5)

To solve for y, we need to simplify and manipulate the equation:

Multiply both sides by (y-5) × (y+5) to eliminate the denominators:

(y+1)(y+5) + 10(y-5) = 10 × (y+1)

Expand and simplify:

y² + 6y - 15 + 10y - 50 = 10y + 10

Combine like terms:

y² + 16y - 55 = 0

Factor the quadratic:

(y + 11)(y - 5) = 0

Solve for y:

y = -11 or y = 5

However, we need to check if either solution makes the denominators of the original equation equal to zero, since division by zero is undefined:

For y = -11, the denominators are -16 and -6, respectively, which are both nonzero. Therefore, y = -11 is a valid solution.

For y = 5, the denominator of the first fraction is 0, which is not allowed. Therefore, y = 5 is an extraneous solution and should be discarded.

Therefore, the value of y that satisfies the equation is y = -11.

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Answer:

Exact form: 121π

Decimal form: 380.1327111...

Step-by-step explanation:

The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.

Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.

We can then put this into the formula to find the area of the circle:

A = πr²

A = π * 11²

A = 121π

Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.

The distance between Point A and Point B is 840 meters.

Let's start by using the formula:

distance = speed x time

Since Coco swam at a constant speed of 1.2 m/s, we can find his distance using:

distance(Coco) = speed(Coco) x time

where time is the same for both Coco and Azlinda. Let's call this common time "t".

distance(Coco) =[tex]1.2 m/s \times t[/tex]

Now, let's consider Azlinda's situation. After 5 minutes (or 5/60 = 1/12 hours), she had swum a distance of 420 m and was 37 m away from Coco. Let's call the distance between Point A and Point B "d".

Since Azlinda was swimming towards Point A, she must have covered a distance of (d - 37) m by the time she had swum 420 m. We can use the formula above to find her speed:

speed(Azlinda) = distance(Azlinda) / time

speed(Azlinda) = (d - 37) m / (1/12) h

speed(Azlinda) = 12(d - 37) m/h

Now, we know that Azlinda and Coco were swimming towards each other for a total of 5 minutes (or 1/12 hours), so their total distance apart at that time was:

distance apart = distance(Coco) + distance(Azlinda)

distance apart = [tex]1.2 m/s \times t + 12(d - 37) m/h \times (1/12) h[/tex]

distance apart =[tex]1.2t + d - 37[/tex]

We also know that when they were 37 m apart, Azlinda had swum a distance of 420 m, so we can write:

420 = d - 37 - distance(Coco)

Substituting the expression for distance(Coco) from above, we get:

420 = d - 37 - 1.2t

Now we have two equations with two unknowns (d and t). We can substitute into the other equation and solve for one variable in terms of the other. For example, we can solve the second equation for t:

[tex]1.2t = d - 37 - 420\\1.2t = d - 457\\t = (d - 457) / 1.2[/tex]

When we enter this into the initial equation, we obtain:

distance apart = [tex]1.2t + d - 37[/tex]

distance apart = [tex]1.2((d - 457) / 1.2) + d - 37[/tex]

distance apart = [tex]d - 380.6[/tex]

Now we can substitute this expression for distance apart into the second equation:

[tex]420 = d - 37 - 1.2t\\420 = d - 37 - 1.2(d - 457) / 1.2\\420 = d - 37 - (d - 457)\\420 = -d + 420\\d = 840[/tex]

Therefore, the distance between Point A and Point B is 840 meters.

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The simplified ratio of factored polynomials is 18/(6(x-8)).

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial is x^2 + 5x + 6.

The question is asking to simplify the ratio of factored polynomials (18(3x-4))/(6(x-8)(3x-4)). To simplify this ratio, we can divide the numerator and denominator by the common factors.

The numerator and denominator both have the factor of 3x-4, so we can divide both the numerator and denominator by this common factor.


The numerator then becomes 18/(6(x-8)) and the denominator becomes 1.

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Step-by-step explanation:

a) To form a committee of 8 with 3 prefects, we need to choose 3 prefects from the 5 available prefects, and 5 non-prefects from the remaining 7 boys. We can do this by using the combination formula:

Number of ways = (Number of ways to choose 3 prefects) × (Number of ways to choose 5 non-prefects)

Number of ways to choose 3 prefects from 5 = C(5, 3) = 10

Number of ways to choose 5 non-prefects from 7 = C(7, 5) = 21

Therefore, the total number of committees of 8 with 3 prefects that can be formed is:

Number of ways = 10 × 21 = 210

b) To form a committee of 8 with at least 3 prefects, we need to consider two cases: one where we choose exactly 3 prefects, and one where we choose all 5 prefects. We can calculate the number of ways for each case using the combination formula:

Number of ways to choose exactly 3 prefects and 5 non-prefects = C(5, 3) × C(7, 5) = 210

Number of ways to choose all 5 prefects and 3 non-prefects = C(5, 5) × C(7, 3) = 35

Therefore, the total number of committees of 8 with at least 3 prefects that can be formed is:

Number of ways = (Number of ways to choose exactly 3 prefects and 5 non-prefects) + (Number of ways to choose all 5 prefects and 3 non-prefects)

Number of ways = 210 + 35 = 245

The final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

To determine the indicated angle, we can use the Law of Cosines, which states that: \[ c^2 = a^2 + b^2 - 2ab\cos(C) \]We can rearrange this equation to solve for the cosine of the indicated angle: \[ \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \]Plugging in the given values for a, b, and c, we get: \[ \cos(C) = \frac{69.01^2 + 39.28^2 - 42.65^2}{2(69.01)(39.28)} \]Simplifying the expression, we get: \[ \cos(C) = 0.7664 \]Now, we can use the inverse cosine function to find the indicated angle: \[ C = \cos^{-1}(0.7664) \]This gives us an angle of 40.32 degrees. However, the question asks us to round our answer to two decimal places, so the final answer is: \[ C = 40.32^{\circ} \]Therefore, the indicated angle is 40.32 degrees.

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According to the Census Bureau, of the people 21 to 64 years old, 12.3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. The words that look like different answers to one question are "not high school graduates," "graduated high school," "some college," "bachelor's degree," and "advanced degree."

These words all describe different levels of education and could be potential answers to a question about a person's education level. The paragraph describes the educational attainment of people between the ages of 21 and 64. The different percentages represent the proportion of individuals in each education category.

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The converse of Theorem 6.6 states that if a group G is such that every proper subgroup is cyclic, then G is cyclic. This statement is false, as shown by the following counterexample:

Let G = {e, a, b, ab}, where e is the identity element, and a and b are two distinct elements such that ab = ba.

This group is not cyclic because it does not contain an element of order 4, and thus cannot be generated by a single element. However, every proper subgroup is cyclic. For example, the subgroup {e, a} is cyclic, and the subgroup {e, b} is cyclic.

Therefore, this example provides a counterexample to the converse of Theorem 6.6.

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The measurement of the angle F in the given circle is 41°

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle, with secants FX and FB, we need to find the measurement of the angle F in the given circle

Using the property of circle,

∠ F = 1/2(arc XB - arc VW)

∠ F = 1/2(126°-44°)

∠ F = 1/2 x 82

∠ F = 41°

Hence, the measurement of the angle F in the given circle is 41°

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angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

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Using long division . The quotient of  (4x^3-6x^2-4x+8) divided by (2x-1) is: 2x^2 - 2x - 2 with a remainder of 7.

Let use long division to determine the quotient of (4x^3-6x^2-4x+8) divided by (2x-1).

Long division:

   2x^2  - 2x  - 2

    --------------------

2x - 1 | 4x^3  - 6x^2  - 4x  + 8

       - (4x^3  - 2x^2)

       --------------

            -4x^2  - 4x

            +  (4x^2  - 2x)

            --------------

                      -2x  + 8

                      -(-2x  + 1)

                      --------

                               7

Therefore, the quotient of (4x^3 - 6x^2 - 4x + 8) divided by (2x - 1) is:

2x^2 - 2x - 2 with a remainder of 7.

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According to the question the resulting table would have 109 rows.

Table is a piece of furniture with a flat top and one or more legs, used as a surface for working at, eating from or on which to place things. Tables come in a variety of materials, shapes, and sizes and are used in many different settings, including homes, offices, and commercial establishments.

This is because all 90 players who played for 1 day would be joined, plus the 10 players who played across 2 days. Of the 90 players who played for 1 day, 82 would have 1 row each from the join, 7 would have 2 rows from the join, and 1 would have 0 rows from the join (since it was not in Table B). Of the 10 players who played across 2 days, 9 would have 1 row each from the join, and 1 would have 2 rows from the join. This adds up to a total of 109 rows.

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The second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

What is factorization?

A number or other mathematical object is factorization or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort.

To find the smallest number that has 1, 2, 3, 4, and 5 as factors, we can simply multiply these numbers together, since they are all factors of their product:

1 × 2 × 3 × 4 × 5 = 120

Now we need to find the second smallest number with these factors. One way to approach this is to list out the multiples of 120 until we find a number that also has the factors 1, 2, 3, 4, and 5, and is larger than 120.

Multiplying 120 by 2, 3, 4, 5, and 6 gives us the multiples:

240, 360, 480, 600, 720

Checking each of these multiples, we see that only 360 has all the factors 1, 2, 3, 4, and 5. Therefore, the second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

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Answer:

Step-by-step explanation:

its is 192 ft2

The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.

However, they have different coefficients and constant terms, which means that they will have different shapes and positions.

Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.

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The measure m∠UTS is approximately 90 degrees.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angle VUR=(10x-23)degree

Angle TUV=(3x+19)degree

Now,

Since RSTU is a rhombus, its diagonals are perpendicular bisectors of each other, which means that angle VUT is a right angle. Therefore, we have:

m∠VUR + m∠TUV + m∠VUT = 180°

Substituting the given values, we get:

(10x - 23) + (3x + 19) + 90 = 180

13x + 86 = 180

13x = 94

x = 7.23 (rounded to two decimal places)

Now, we can find m∠UTS as follows:

m∠UTS = m∠VUR + m∠TUV

Substituting the value of x, we get:

m∠UTS = (10x - 23) + (3x + 19)

m∠UTS = (10 × 7.23 - 23) + (3 × 7.23 + 19)

m∠UTS = 72.3 - 23 + 21.69 + 19

m∠UTS = 89.99

Therefore, the answer of the given rhombus will be 90 degrees.

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Therefore, the original price of the shirts was $18.75 each.

An equality on both sides of the equal to sign signifies a mathematical equation, which is a relationship between two expressions. Here is an example of an equation: 3y = 16.

If the selling price of the shirts was 80% of their regular price, then we can use the following equation to find the original price:

Original price * 0.8 = Selling price

Let's substitute the given values into the equation:

Original price * 0.8 = 15

To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.8:

Original price = 15 ÷ 0.8

Original price = 18.75

Therefore, the original price of the shirts was $18.75 each.

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Answer:

Gina has 47 nickels

Step-by-step explanation:

Let's call the number of nickels that Gina has "n" and the number of dimes she has "d". We know that she has a total of 70 nickels and dimes, so:

n + d = 70 (equation 1)

We also know that the value of her nickels and dimes is $4.65, which is equal to 465 cents. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value of n nickels is 5n cents and the value of d dimes is 10d cents. Therefore, we can write another equation based on the value of the coins:

5n + 10d = 465 (equation 2)

We can simplify equation 2 by dividing both sides by 5:

n + 2d = 93 (equation 3)

Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable. For example, we can solve equation 1 for d:

d = 70 - n

Substituting this expression for d into equation 3, we get:

n + 2(70 - n) = 93

Simplifying this equation, we get:

n + 140 - 2n = 93

-n + 140 = 93

-n = -47

n = 47

Therefore, Gina has 47 nickels and 23 dimes (since n + d = 70), and the total value of her coins is $4.65.

Answer:

47 nickels

Step-by-step explanation:

47 nickels

The sum of two consecutive integers 42 and 43  is 85.

The sum of two consecutive integers is 85. This means that we need to find two integers that are next to each other on the number line and add up to 85. We can write this as an equation:
x + (x + 1) = 85

Simplifying the equation gives us:
2x + 1 = 85

Subtracting 1 from both sides gives us:
2x = 84

Dividing both sides by 2 gives us:
x = 42

This means that the first integer is 42. Since the two integers are consecutive, the second integer is 42 + 1 = 43. Therefore, the two integers are 42 and 43.

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Answer: $30

Step-by-step explanation:

Let x be the cost of one pen
Then x + 1 will be the cost of one book

From the problem, we know that:

5x + 4(x + 1) = 31 (Lester paid $31 for 5 pens and 4 books. A book costs $1.00 more than a pen)

Simplifying the equation:

5x + 4x + 4 = 31

9x = 27

x = 3

So one pen costs $3 and one book costs $4.

Now we can find the cost for Stephan:

6 pens cost 6 x $3 = $18

3 books cost 3 x $4 = $12

So Stephan will pay $18 + $12 = $30.

Answer:

5/33

Step-by-step explanation:

5/6 divided by 11/2

Invert the divider

5/6 x 2/ 11

10/66

Reduce to smallest fraction

5/33

Answer:

5/33

Step-by-step explanation:

Apply the fraction rule: a/b ÷ c/d = (a × d) ÷ (b × c) for 5/6 ÷ 11/2

a = 5

b = 6

c = 11

d = 2

(5 × 2) ÷ (6 × 11)

For "(6 × 11)", break 6 down into "2 × 3", so that you can cancel out the common factor, because there is also a 2 in "5 × 2".

= (5 × 2) ÷ (2 × 3 × 11)         -- cancel out the 2's

= 5 ÷ (3 × 11)     *****3 × 11 = 33*****

= 5/33

The unknown side 'x' is found using pythagorean theorem as: x = 12.69.

The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.

Pythagorean Theorem is also known as:

a²+ b² = c²

Given sides are:

13, 3 and x.

Then,

3²+ x² = 13²

x² = 13² - 3²

x² = 169 - 9

x² = 160

x = √160

x = 12.69

Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.

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The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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After the transformation from f to g, g(x) = eˣ/3.

Vertical shrink refers to a transformation of a function that causes it to be compressed vertically. To perform a vertical shrink, you must multiply the output (y) values of the function by a constant value between 0 and 1.

The transformation of f(x) to g(x) involves a vertical shrink by a factor of 1/3. This means that the value of g(x) will be one third of the value of f(x). We can write this transformation as: g(x) = 1/3 · f(x).

Since f(x) = eˣ, we can substitute this into the equation for g(x) to find the final expression for g(x):

g(x) = (1/3)eˣ

Therefore, the function g(x) after the vertical shrink by a factor of 1/3 is g(x) = (1/3)eˣ or g(x) = eˣ/3.

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if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]

The diameter of the circle is 28 inches.

The formula for the area of a circle is:

[tex]A = \pi r^2[/tex]

Where A is the area and r is the radius.

Any straight line segment that travels through the centre of a circle and has endpoints that are on the circle is said to have a diameter.

To find the diameter of the circle, we first need to find the radius. We can rearrange the formula for the area to solve for the radius:

[tex]r = \sqrt{ (A/\pi )}[/tex]

Plugging in the given values:

[tex]r = \sqrt{(615.44/3.14)} = 14[/tex]

So the radius of the circle is 14 inches. The diameter is twice the radius, so:

d = 2r = 2(14) = 28

Therefore, the diameter of the circle is 28 inches.

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Answer:

A. This shape is a rectangular prism — a rectangle with a third dimension of depth. In technical terms, it is "a polyhedron with two congruent and parallel bases." - BYJU's Maths

B. We could find the area of its net, since the surface area of a shape is the sum of the areas of its sides.

Answer: $170

Step-by-step explanation:

6x + 18(6) = 1128.

6x + 108 = 1128

6x = 1020

x = 170

The price of one ticket is 170

The zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.

To find the zeros of a quadratic function, we can either factor the equation or use the quadratic formula. In this case, we can easily factor the equation to find the zeros.

First, we need to find two numbers that multiply to give us 12 and add to give us 7. These numbers are 3 and 4.

Next, we can rewrite the equation using these numbers:

[tex]f(t) = t^(2) + 7t + 12 = (t + 3)(t + 4)[/tex]

Now, we can set each factor equal to zero and solve for t:

[tex]t + 3 = 0  ->  t = -3[/tex]

[tex]t + 4 = 0  ->  t = -4[/tex]

So, the zeros of the function are -3 and -4.

In conclusion, the zeros of the function [tex]f(t) = t^(2) + 7t + 12[/tex] are -3 and -4.

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