250 people travelled to a conference either by bus or by train
95 of the people travelled by bus
102 of the 126 people who arrived late travelled by train
use this information ro complete the frequency tree

The inclination of the line represented by the equation y = x + 3 is 1, and the inclination of the line represented by the equation 3x - 2y = 6 is 3/2.

To determine the inclination (or slope) of a straight line, we can examine the coefficients of the variables x and y in the equation of the line.

The inclination represents the ratio of how much y changes with respect to x.

Equation: y = x + 3

In this equation, the coefficient of x is 1, which means that for every increase of 1 in x, y also increases by 1.

This indicates that the inclination of the line is positive, meaning it slopes upwards as x increases.

Since the coefficient of x is 1, the inclination can be expressed as 1/1 or simply 1.

Equation: 3x - 2y = 6

To determine the inclination, we need to rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope.

First, isolate y:

-2y = -3x + 6

Divide the entire equation by -2 to solve for y:

y = (3/2)x - 3

Now we can observe that the coefficient of x is 3/2.

This indicates that for every increase of 1 in x, y increases by 3/2. Therefore, the inclination of this line is positive, indicating an upward slope.

The inclination can be expressed as 3/2.

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(a). The distance QR is equal to 45.3 using the cosine rule.

(b) Bearing of Q from P is 315°

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

(a). Let ∆PQR be the triangle formed with bearings so that:

angle P = 45° + 40° {alternate angles from Q and R respectively to P}

angle P = 85°

PQ = 25km

PR = 40km

The distance QR is calculated using the cosine rule as follows:

QR² = 25² + 40² - 2(25)(40)cos85° {cosine rule}

QR² = 2225 - 174.3115

QR = √2050.6885 {take square root of both sides}

QR = 45.2845

(b) Bearing of point Q from P is the angle measured from the north of P to the straight line distance between Q and P

Bearing of Q from P = 45° + 270° = 315°

Therefore, the distance QR is equal to 45.3 using the cosine rule. Bearing of Q from P is 315°

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Holly's expression is equal to 864, and Jim's expression is equal to 36. So, Jim's expression is 828 less than the other expression.

Holly's notebook:

6 × (24 ÷ 2)²

= 6 × (12)²

= 6 × 144

= 864

Jim's notebook:

6 × 24 ÷ 2²

= 6 × 24 ÷ 4

using PEMDAS

P = parenthesis

E = exponents

M = multiplication

D = Division

A = Addition

S = Subtraction

6 × 24 ÷ 4

= 144 ÷ 4

= 36

Therefore, Jim's expression is less than Holly's expression.

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The area of a triangle is:

12x² -18x - 12

The area of a triangle can be calculated using the formula:

A = 1/2 * b * h

where b is the base and h is the height of the triangle

We have:

b = -6x + 3

h =  4(x - 2) = 4x - 8

substituting into the formula:

A = 1/2 * (6x + 3) * (4x - 8)

A = 1/2 * (24x² -48x + 12x - 24)

A = 1/2 * (24x² -36x - 24)

A = 12x² -18x - 12

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There exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2.

To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use the concept of the longest path in a tree and the properties of odd integers.

First, let's consider the longest path in the tree T.

Since the tree has n vertices, the longest path can have at most n-1 edges.

Let's denote this longest path as P.

Since n is an odd integer, we have n = 2k + 1, where k is a non-negative integer.

This implies that n-1 = 2k, which is an even number.

Now, consider the middle vertex x of the longest path P.

If P has an odd number of vertices, then x is unique.

If P has an even number of vertices, then there are two possible middle vertices, but we can choose any one of them.

Next, let's consider the distance between v and x along the longest path P. Since x is the middle vertex, this distance can be at most (n-1)/2.

This is because the longest path P divides the tree into two parts, each containing (n-1)/2 vertices at most.

Now, let's consider the subtree rooted at x, which consists of all vertices that can be reached from x.

Since the distance between v and x is at most (n-1)/2, it implies that v is within this subtree.

Therefore, we have found a vertex u (in this case, x) in the subtree rooted at x such that the distance between u and v is at most (n-1)/2.

By proving the existence of such a vertex u, we have shown that for any vertex v in the tree T, there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Step-by-step explanation:

volume of any type of pyramid :

1/3 × base area × height

FYI (not needed to solve the problem) :

base area is a pentagon.

the area of a pentagon is

1/2 × p × a

p is the perimeter (5 × side length) of the pentagon.

a is the apothem (the direct - right-angled- distance from the center of the pentagon to the center of a side).

volume of any type of regular prism :

base area × height

since the sides of the pentagon are the same, also their base areas are the same.

the height is the same.

so, when we compare both formulas, we see that the only difference is the factor 1/3.

the volume of the pyramid is 1/3 the volume of the prism.

therefore,

volume prism = volume pyramid × 3 = 435.7 × 3 =

= 1,307.1 cm³

Answer:

The answer is

-5.79×10²³,6.88×10‐²³,5.73×10²³,57.8×10²²,5.83×10²³

Step-by-step Explanation:

Answer:

Step-by-step explanation:FIGURE A FIGURE B FIGURE C FIGURE D 2.1.1. Calculate the area of figure A 2.1.2. Calculate the area of figure 2.1.3. Calculate the area of figure C

Sure, here are the calculations for the area of each figure:

Figure A is a rectangle with a length of 4 cm and a width of 3 cm. The area of a rectangle is calculated by multiplying the length and the width, so the area of Figure A is 4×3=12 square centimeters.

Figure B is a triangle with a base of 4 cm and a height of 3 cm. The area of a triangle is calculated by multiplying the base and the height and dividing by 2, so the area of Figure B is (4×3)/2=6 square centimeters.

Figure C is a trapezoid with a top base of 4 cm, a bottom base of 6 cm, and a height of 3 cm. The area of a trapezoid is calculated by averaging the top and bottom bases and multiplying by the height, so the area of Figure C is (4+6)/2×3=15 square centimeters.

Figure D is a circle with a radius of 2 cm. The area of a circle is calculated by multiplying the square of the radius by π, so the area of Figure D is 2

2

π=4π square centimeters.

it will be A .......................................

In the given diagram, we have a pair of parallel lines intersected by a transversal line. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by parallel lines and a transversal.

From the diagram, we can observe the following angle relationships:

Angle A is alternate interior to the angle (4x - 10)°.

Therefore, we can write: A = (4x - 10)°.

Angle B is corresponding to the angle (4x - 10)°.

Therefore, we can write: B = (4x - 10)°.

Angle C is alternate interior to the angle 2x°.

Therefore, we can write: C = 2x°.

Angle D is corresponding to the angle 2x°.

Therefore, we can write: D = 2x°.

Since the sum of angles in a straight line is 180°, we can set up the equation:

A + B + C + D = 180°

Substituting the known values, we get:

(4x - 10)° + (4x - 10)° + 2x° + 2x° = 180°

Simplifying the equation, we can solve for x:

8x - 20 + 4x + 4x = 180

16x - 20 = 180

16x = 200

x = 12.5

Therefore, the value of x is 12.5.

Please note that this solution assumes the given diagram accurately represents the angle relationships.

The value of x is 24.426 degrees when the opposite side is 9 and adjacent side is 20  and value of x is 58.211 degrees degrees when the adjacent side is 17 and hypotenuse is 32

In the given triangle

We have to find the missing angle x

By tan function we know that tan is a ratio opposite side and adjacent side

tanx=9/20

tanx=0.45

x=tan⁻¹(0.45)

x=24.426 degrees

For example 2, we find x by using cosine function which is a ratio of adjacent side and hypotenuse

cosx=17/32

cosx=0.53

x=cos⁻¹(0.53)

x=58.211 degrees

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After calculating the average of numbers here, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

The step-by-step solution to this is given below:

To determine which average is greater, let's calculate the averages of the even and odd numbers separately.

The four even numbers from [tex]8 \ to \ 15 \ are \ 8, 10, 12, and \ 14[/tex]. To find their average, we sum them up and divide by [tex]4[/tex]:

[tex]\[\text{Average of even numbers} = \frac{8 + 10 + 12 + 14}{4} = \frac{44}{4} = 11\][/tex]

The four odd numbers from [tex]8 \ to \ 15 \ are \ 9, 11, 13, and \ 15.[/tex] Similarly, we calculate their average:

[tex]\[\text{Average of odd numbers} = \frac{9 + 11 + 13 + 15}{4} = \frac{48}{4} = 12\][/tex]

Now, the next step will be comparing the two averages, we find that the average of the four odd numbers, [tex]12[/tex], is greater than the average of the four even numbers, [tex]11[/tex].

Therefore, the average of the four odd numbers from [tex]8 \ to \ 15[/tex] is greater than the average of the four even numbers.

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The solution for x, y, and z is x = 2, y = 2, and z = 2.

To solve the equation (35)"4(23)"5(25)"7 = 2"x3"y*5"z, let's break it down step by step:

Simplify the expressions within the parentheses using the power of operator ("^").

[tex](35)"4 = 15^4\\(23)"5 = 6^5\\(2\times5)"7 = 10^7[/tex]

Apply the power rule of exponents, which states that [tex](a^b)^c = a^{(b\times c).[/tex]

[tex]15^4 \times 6^5 \times 10^7 = (15610)^{(4+5+7)[/tex]

Simplify the expression within the parentheses.

[tex](15610)^{16 }= 900^{16[/tex]

Express both sides of the equation in terms of prime factors.

[tex]900 = 2^2 \times 3^2 \times 5^2[/tex]

quate the powers of the prime factors on both sides of the equation.

[tex]2^2 \times 3^2 \times 5^2 = 2"x \times 3"y \times 5"z[/tex]

From this, we can conclude that x = 2, y = 2, and z = 2.

Therefore, the solution for x, y, and z is x = 2, y = 2, and z = 2.

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The polynomial 3x^4 - 3x^2 - 7x is classified as a Cubic Trinomial.

The polynomial 3x^4 - 3x^2 - 7x can be classified as a Cubic Trinomial.

Here's the breakdown of the classification:

Degree: The highest power of the variable x is 4, so the degree of the polynomial is 4. Since the degree is 4, the polynomial is not cubic (which would have a degree of 3) or quintic (which would have a degree of 5).

Number of terms: The polynomial consists of three terms: 3x^4, -3x^2, and -7x. A polynomial with three terms is called a trinomial.

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Answer:Quartic trinomial

Step-by-step explanation:

Don't listen to the other guy, I put cubic and I got the answer wrong thanks to the other guy.

(a) A formula to calculate the amount after n months: 1,500(1 + nx0.0046)

(b)  the amount owed after 14 months = $1596.6

Given that,

Principal amount =  P  = $1,500

interest of grown = R = 5.5%

Now we can write is,

5.5% = 5.5/100

        =  0.055

We know that,

The simple interest formula,

A = P(1 + rt)

Where,

A represents Amount after T years

R represents rate of interest

T is time in year

Now,

Since 1 month = 1/12 years

                        = 0.084

Therefore amount after 1 month be

A = 1,500(1+0.055x0.084)

  = 1,500(1+0.0046)

  = 1506.93

Amount after 2 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1+2x0.0046)

Amount after 3 month be

A =  1,500(1+ 2 x 0.055x0.084)

  = 1,500(1 + 3x0.0046)

Hence amount of  n months = 1,500(1 + nx0.0046)

Hence,

The amount after 14 months,

=  1,500(1 + 14x0.0046)

= $1596.6

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Answer:

x = - 3, x = 1

Step-by-step explanation:

x² + 2x - 3 = 0

consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)

the factors are + 3 and - 1 , since

3 × - 1 = - 3 and + 3 - 1 = + 2 , then

(x + 3)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - 3 , x = 1

Answer: Landing on X and heads, landing on Y and heads, landing on Z and heads, landing on X and tails, landing on Y and tails, landing on Z and tails

Step-by-step explanation:

       There are three possible spinner options and 2 possible coin options. 3 * 2 = 6, leading to 6 possible outcomes.

       The spinner could land on X, Y, or Z.

       The coin could land on heads or tails.

       If we type out all of these possibilities (each spinner section and heads, each spinner section and tails) we end up with;

       ➜ Landing on X and heads

       ➜ Landing on Y and heads

       ➜ Landing on Z and heads

       ➜ Landing on X and tails

       ➜ Landing on Y and tails

       ➜ Landing on Z and tails

X=90 ....angles in a semi-circle

Angle B=A ...Radii

a. The number halfway between 3.6 and 9.6 is 6.6.

b. The number halfway between 1.1 and 1.5 is 1.3.

c. The number halfway between 7.26 and 7.28 is 7.27.

To find the number halfway between 3.6 and 9.6, we can add the two numbers and divide by 2:

(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6

The number halfway between 3.6 and 9.6 is 6.6.

To find the number halfway between 1.1 and 1.5, we can use the same approach:

(1.1 + 1.5) / 2 = 2.6 / 2 = 1.3

The number halfway between 1.1 and 1.5 is 1.3.

To find the number halfway between 7.26 and 7.28, we can apply the same method:

(7.26 + 7.28) / 2 = 14.54 / 2

= 7.27

The number that is between 3.6 and 9.6:

(3.6 + 9.6) / 2 = 13.2 / 2 = 6.6

6.6 is the number that falls between 3.6 and 9.6.

We can apply the same strategy to determine the value that lies between 1.1 and 1.5:

(1.1 + 1.5) / 2 = 2.6 / 2

= 1.3

1.3 is the number that falls between 1.1 and 1.5.

We can use the same procedure to determine the number that is halfway between 7.26 and 7.28:

(7.26 + 7.28) / 2 = 14.54 / 2

= 7.27

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Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.

To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.

The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.

For example, if we let x = 0, we can solve the equation for y:

y - 7 = 3(0 + 9)

y - 7 = 3(9)

y - 7 = 27

y = 27 + 7

y = 34

So, one point on the line is (0, 34).

Alternatively, if we let x = -9, we can solve the equation for y:

y - 7 = 3(-9 + 9)

y - 7 = 3(0)

y - 7 = 0

y = 7

So, another point on the line is (-9, 7).

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I cannot describe the pattern in the sequence of artwork without visual representation.

Let's analyze each pattern:

The pattern appears to be adding 7 to each number to get the next number.

The next three numbers would be:

29, 36, 43.

The pattern alternates between adding 2 and subtracting 1.

The next three numbers would be:

11, 10, 12.

The pattern increments by 3 each time.

The next three numbers would be:

15, 18, 21.

The pattern alternates between squaring and taking the square root of the previous number.

The next three numbers would be:

1, 8, 1.

The pattern doubles each time.

The next three numbers would be:

64, 128, 256.

The pattern multiplies each number by 3 to get the next number.

The next three numbers would be:

243, 729, 2187.

As a text-based AI model, I am unable to draw diagrams.

I can describe the next diagram in each pattern:

The next diagram would consist of three rows, each containing four dots arranged in a square.

The next diagram would consist of a single dot positioned 7 units below the bottom dot of the previous diagram.

The next diagram would consist of two vertical lines with three dots each.

The next diagram would consist of a single dot positioned 4 units above the top dot of the previous diagram.

The next diagram would consist of a row of six dots arranged in a straight line.

The next diagram would consist of four rows, each containing three dots arranged in a square.

A text-based AI model, I am unable to see or analyze images or diagrams.

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The linear graph that represents a proportional relationship is the graph that passes through the origin, which is the second option;

A graph that passes through the points (0, 0), (4, -1)

A proportional relationship is one in which the output value is a multiple of the input value, such that, the graph passes through the origin.

The options in the question are;

The first option; A graph that passes through the points (0, 2.5), (1, 4)

The second option; A graph that passes through the points (0, 0), (4, -1)

The third option; A graph that passes through the points (0, -1), (1, -1)

The fourth option; A graph that passes through the points (0, -3), (1, -2)

The first option; A graph that passes through the points (0, 2.5), (1, 4)

A proportional relationship is a function of the form; y ∝ x

y = k·x

k = y/x

The graph of a function that has a proportional relationship, passes through the point (0, 0), therefore, the option that represents a function that is a proportional relationship is the second option, such that we get;

The ratio of proportionality, k = -1/4

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Answer: quotient: x+7 remainder: -5

Answer:

A) AAS

B) HL

C) SSS

E) SAS

Step-by-step explanation:

We cannot prove the triangles congruent by AAS because we would need another angle pair that is congruent to each other.

We can prove the triangles congruent by HL because the pairs of hypotenuses and shorter legs are shown to be congruent to each other.

We can prove the triangles are congruent by SSS because every side is congruent to its respective pair.

We cannot prove the triangles congruent by HA because we would need another angle pair that is congruent to each other, like with AAS.

We can prove the triangles are congruent by SAS because two pairs of sides in addition to their respective included angles (the right angles) are congruent to each other.

We cannot prove the triangles congruent by LA because we would need to know by the given information that ∠B≅∠E, but it's not provided.

Therefore, A, B, C, and E are the correct answers.

Answer:

a. 30 b. indeterminate, unless you're given the measure of either of the other sides.

Step-by-step explanation:

a. lazy solution: it's a 3-4-5 right triangle scaled up (18 is 3*6, 24 is 4*6, last side will be 5*6= 30. Less than lazy solution: it's a right triangle, pythagorean theorem applies:

[tex]x^2= 18^2+24^2 = 324+576 = 900\\x= 30[/tex]

b.problem is indeterminate as long as you don't know the measure of any of the other sides. the 30-60 triangle is half of an equilateral triangle and x is [tex]\sqrt3[/tex] times the short side, or [tex]\frac{\sqrt3} 2[/tex] times the long side. It's easily shown by mirroring the triangle along the vertical side, and if the short leg measures k, the hypotenuse measures 2k, and the vertical side measures [tex]x^2+k^2=(2k)^2\\x^2+k^2 = 4k^2\\x^2 = 3k^2 \implies x=\sqrt3\ k[/tex]

The measure of angle cbd in regular octagon ABCDEFGH is 22.5°.

We are given that;

The octagon ABCDEFGH

Now,

To find the measure of angle CBD. Since ABCDEFGH is a regular octagon, triangle BCD is an isosceles triangle with BC = BD2. Therefore, the base angles of triangle BCD are congruent and have the same measure. Let x be the measure of angle CBD. Then, we have:

x + x + 135° = 180° (sum of angles in a triangle)

2x + 135° = 180°

2x = 180° - 135°

2x = 45°

x = 45°÷2

x = 22.5°

Therefore, by the angle the answer will be 22.5°.

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The number of choir students that performed in at least 3 concerts is given as follows:

16 students.

An histogram is a graph that shows the number of times each element of x was observed, or the number of observations in each range of a data-set.

Hence, for this problem, the meaning of the histogram is given as follows:

Hence the number of choir students that performed in at least 3 concerts is given as follows:

9 + 4 + 3 = 16 students.

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The six ordered pairs for the function f(x) = -x^2 + 3x + 2 are:

(-2, -8), (-1, -2), (0, 2), (1, 4), (2, 4), (3, 2).

To find six ordered pairs for the function [tex]f(x) = -x^2 + 3x + 2[/tex], we can substitute different x-values into the function and evaluate the corresponding y-values.

Let's choose six x-values and calculate the corresponding y-values:

When x = -2:

[tex]f(-2) = -(-2)^2 + 3(-2) + 2 = -4 - 6 + 2 = -8[/tex]

Therefore, the ordered pair is (-2, -8).

When x = -1:

[tex]f(-1) = -(-1)^2 + 3(-1) + 2 = -1 - 3 + 2 = -2[/tex]

Therefore, the ordered pair is (-1, -2).

When x = 0:

[tex]f(0) = -(0)^2 + 3(0) + 2 = 0 + 0 + 2 = 2[/tex]

Therefore, the ordered pair is (0, 2).

When x = 1:

[tex]f(1) = -(1)^2 + 3(1) + 2 = -1 + 3 + 2 = 4[/tex]

Therefore, the ordered pair is (1, 4).

When x = 2:

[tex]f(2) = -(2)^2 + 3(2) + 2 = -4 + 6 + 2 = 4[/tex]

Therefore, the ordered pair is (2, 4).

When x = 3:

[tex]f(3) = -(3)^2 + 3(3) + 2 = -9 + 9 + 2 = 2[/tex]

Therefore, the ordered pair is (3, 2).

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2/9 is the probability that the teacher will choose two girls

To calculate the probability of choosing two girls from the class

we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes: Since the teacher is choosing two students from a class of 10, the total number of outcomes is given by the combination formula C(10, 2), which is calculated as:

C(10, 2) = 10! / (2!(10 - 2)!) = 10! / (2! × 8!) = (10 × 9) / (2 × 1) = 45

Number of favorable outcomes

We want to choose two girls from the 5 girls in the class.

The number of ways to choose 2 girls from 5 is given by the combination formula C(5, 2), which is calculated as:

C(5, 2) = 5! / (2! × (5 - 2)!) = 5! / (2! × 3!) = (5× 4) / (2× 1) = 10

Therefore, the number of favorable outcomes is 10.

The probability of choosing two girls is given by the number of favorable outcomes divided by the total number of outcomes:

Probability = Number of favorable outcomes / Total number of outcomes = 10 / 45 = 2 / 9

Hence, the probability that the teacher will choose two girls is 2/9.

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