Probability Skill Check
DOOR Numbers
1
2
3
4
5
Coloured Blue, Red, Yellow and Green

What is the probability you will sit in a yellow seat? Give your answer as a fraction.
1/4
But what is the probability you will enter using an odd numbered door and sit in a green seat? Give your answer as a fraction.

Based on the information, the incorrect step is C. step 3.

Step 1: 4(3x – 3y = 6) –3(4x – 7y = 2)

Step 2: 12x – 12y = 24 –12x + 21y = –6

Step 3: 9y = 18

Step 4: y equals 1 over 2

Correct calculation:

3x – 3y = 6 (1)

4x – 7y = 2 (2)

make x the subject in ....(1)

3x - 3y = 6

3x = 6 + 3y

x = 6 + 3y/ 3

x = 2 + y

substitute x = 2 + y into (2)

4x – 7y = 2 (2)

4(2 + y) - 7y = 2

8 + 4y - 7y = 2

8 - 3y = 2

8 + 2 = -3y

10 = -3y

y = 10/-3

y = -3 1/3

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Michael solved the system of linear equations and provided the solution. 3x – 3y = 6 4x – 7y = 2 Step 1 4(3x – 3y = 6) –3(4x – 7y = 2) Step 2 12x – 12y = 24 –12x + 21y = –6 Step 3 9y = 18 Step 4 y equals 1 over 2 In which step did Michael show his first error? Step 2 Step 3 Step 4

Answer: the inequalities for which 0 is a solution are x - 5 ≤ -3 and x/-2 ≥ 0.

Step-by-step explanation: x - 5 ≤ -3 (0 is less than or equal to 2)

x/-2 ≥ 0 (0 is greater than or equal to 0)

In mathematical form, this can be written as:

0 ≤ x - 5 ≤ -3 or x - 5 ≤ 0 and x ≤ -3

A graph of quadrilateral M'N'O'P' after a vertical translation is shown below.

In Mathematics and Geometry, the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of quadrilateral MNOP vertically downward 4 units, the coordinates of quadrilateral M'N'O'P' include the following:

(x, y)                               →                  (x, y - 4)

M (-2, 5)                        →                  (-2, 5 - 4) = M' (-2, 1).

N (-3, 2)                        →                  (-3, 2 - 4) = N' (-3, -2).

O (-5, 2)                        →                  (-5, 2 - 4) = O' (-5, -2).

P (-6, 5)                        →                  (-6, 5 - 4) = P' (-6, 1).

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Answer: A' will be at (-2,0)

Step-by-step explanation:

Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)

Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)

A linear equation which shows a proportional relationship include the following: A. y = 2x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4

Constant of proportionality, k = 2.

Therefore, the required linear equation is given by;

y = kx

y = 2x

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Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.

From the given information, we can form two equations:

7x + 9y = 135 ...(1)

9x + 7y = 137 ...(2)

We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:

63x + 81y = 1215 ...(3)

63x + 49y = 959 ...(4)

Subtracting equation (4) from equation (3), we get:

32y = 256

y = 8

Substituting the value of y in equation (1), we get:

7x + 9(8) = 135

7x + 72 = 135

7x = 63

x = 9

Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.

The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

[tex]A = P(1+r/2)^{2t}[/tex]

[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]

[tex]A = 50,000(1.04)^{20[/tex]

[tex]A = 109,556.15[/tex]

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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Answer:

meaning that you're answer would be $7.34 please make brainliest

Step-by-step explanation:

The completed calculation with regards to the area of the congruent triangles can be presented as follows;

The distance formula indicates;

AM = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, we get;

AM = √((4 - 0)² + (0 - 0)²) = √(4²)

AM = √(4²) = 4

BM = √((x₂ - x₁)² + (y₂ - y₁)²)

BM = √((4 - 4)² + (6 - 0)²) = √(6²)

BM = √(6²) = 6

AM ≅ CM Definition of the midpoint of AC

AM = CM Definition of congruent segments

CM = 4 Substitution property

Area ΔABM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Area ΔCBM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Therefore Area ΔABM = area ΔCBM by congruence

Triangles are congruent if they have the same size and shape.

The details of the reasons for the calculation steps and values are presented as follows;

Definition of midpoint of a segment

The midpoint of a line segment is the point that divides the segment into two parts of the same length

Definition of congruence?

Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement

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The opposite side of the right triangle is determined as 10.6 cm.

The value of x is calculated by applying trigonometry ratio as shown below;

we will use the short form; SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.

sin (62) = x/12

x = 12 sin (62)

x = 10.6 cm

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Answer:

0.38 degrees.

Step-by-step explanation:

C = 2π(53) = 106π km

The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.

d = (44/60) km/min

θ = (d / C) x 360°

θ = [(44/60) / (106π)] x 360°

θ ≈ 0.38°

Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.

Answer: C: 144

Step-by-step explanation:

First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.

Next subtract this from 180 to find the exterior angle.

180- 36 = 144 degrees

thats the meaure of the exterior angle!

Answer:144

First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.

Next subtract this from 180 to find the exterior angle.

180- 36 = 144 degrees

Manuel bought a car for 65% (percentage) of the original price of $7,000, he must have paid $4,550 for the car.

The percentage is a number or ratio that represents a fraction of a whole number or the sum of ratios.

The percentage is computed by dividing one number by another and multiplying the result by 100.

The original price of the car = $7,000

The discount factor = 65% (1 - 35%) or 0.65

The discounted price = $4,550 ($7,000 x 0.65)

Thus, by implication, for receiving a discount of 35% (100% - 65%), Manuel paid $4,550 for the car.

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a) The polar coordinates of point A are (√(18), π/4).

b) The curve is a circle centered at the origin with radius 6.

c) The directed distance is the value of r, which is 6 √(3).

To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:

r = √(x² + y²)

θ = arctan(y/x)

Using the values of point A, we have:

r = √((-3)² + (-3)²) = √(18)

θ = arctan((-3)/(-3)) = arctan(1) = π/4

To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:

x = r cos(θ)

y = r sin(θ)

Using these formulae, we can rewrite the equation as:

r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0

Simplifying this equation, we get:

r = -6 sin(θ) / (1 - cos²(θ))

To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:

r = -6 sin(4 π/3) / (1 - cos²(4 π/3))

r = -6(-√(3)/2) / (1 - (-1/2)²)

r = 6 √(3)

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The key number, ac, is -104.

Key number is the product of the coefficients of the first and last terms. The right binomial factors for a quadratic expression can be determined with its assistance.

We must multiply the coefficient of the quadratic term by the constant term to obtain the key value, ac, which results in:

ac = 13(-8) = -104

Therefore, The key number, ac, is -104.

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There is a financial advantage of $ 1,187,520.

Incremental Costs and Revenues will be as follows

Increment in sales = 82,000 units × 40% = 32,800 units

and, Selling Price

= (32,800 units × $62 per unit)

= $ 2,033,600

Direct materials

= $ 7.50 × 32,800 units

= 246,000

Direct labor

= $ 9.00 × 32800

= $295,200

and, Variable manufacturing overhead

= 2.40 x 32800

= $78, 720

So, the contribution is

= 2,033,600 - (246000 + 285200 + 78720)

= 1,423,680

Now, Variable selling expenses

= 32800 x 3.7

= 121,360

and, Fixed Selling Expenses

= 32800 x 3.5

= 114,800

So, Net income = 1, 187, 520

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The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.

Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.

So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.

The solution is the value of X is, x = 2.

Here, we have,

from the given diagram,

we get,

from triangle ABC,

AB = 5, AC = 6

and, From triangle ADE,

AD = 10, AE = 12

and, both has same angle A,

so, by SAS rule, both are congruent.

we get,

triangle AED ~ triangle ABC

now, we know that,

here, DE = 2 BC

so, x+12 = 2( 4x-1)

or, x+ 12 = 8x -2

or, x = 14/7

or. x= 2

Hence, the value of X is, x = 2.

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The time taken to reach a population of 500 is gotten from  500=50e^0.55t

Exponential growth is a process that increases quantity over time as in the bacterial culture here.

We know that from the question, we have;

P(t)=Poe^rt

P(t) = population at time t

Po= Initial population

r = growth rate

t = time taken

Then we have that;

150 = 50e^2r

3=e^2r

ln3 = 2r

r = ln3/2

r = 0.55

If the rate of growth is 0.55, then to reach a population  of 500;

500=50e^0.55t

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The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.

Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.

Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.

Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.

Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.

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Answer: x < 5, see attached for the graph.

Step-by-step explanation:

   To solve, we will isolate the variable.

Given:

  5x - 15 < 10

Add 15 to both sides of the equation:

  5x < 25

Divide both sides of the equation by 5:

  x < 5

  For the graph, we will use an open circle because this is only less than (<), not less than and equal to.

  Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.

The Volume of Cone is 84.8 m³.

We have,

d = 9 m

r= 4.5 m

H = 4 m

So, Volume of Cone

= 1/3 πr²h

= 1/3 (3.14) (4.5)² (4)

= 1/3 (3.14) (20.25) (4)

= 84.8 m³

Thus, the volume is 84.8 m³.

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Answer:

Step-by-step explanation:

Answer:

  3013.5 cm³

Step-by-step explanation:

Given a ball with a circumference of 56.3 cm, you want to know its volume.

The formula for circumference is ...

  C = 2πr

Solving for radius, we get ...

  r = C/(2π) = 56.3 cm/(2π) ≈ 8.96042 cm

The volume of a sphere is given by ...

  V = 4/3πr³

  V = 4/3π(8.96042 cm)³ ≈ 3013.5 cm³

The ball's volume is about 3013.5 cubic centimeters.

__

Additional comment

Alternatively, we could use the formula ...

  V = C³/(6π²)

to get the same result.

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The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).

Given that:

Width, W = x

Length, L = 6x

Path width, d = 3

The rectangle's area will be given as,

Area of the rectangle = L × W square units

The quadratic function to represent the total area of the park and the path will be given as,

A = (x + 2 · 3) (6x + 2 · 3)

A = (x + 6)(6x + 6)

A = 6(x + 6)(x + 1)

A = 6(x² + 7x + 6)

The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).

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