Megan has two boxes. There are x beads in box A. 7 of these beads are white. The rest of the beads are black. There are x beads in box B. 4 of these beads are white. The rest of the beads are black. She chooses at random a bead from box A. She notes the colour and then places this bead into box B. She then chooses at random a bead from box B. The probability of choosing a white bead from box A and a white bead from box B is 22 Work out the total number of beads in the two boxes:​

The required dimensions are

22. x = 9.45

23. perimeter = 198.2

24. angle NSR = 110

25. x = 10

22. The value of x is solved using Pythagoras theorem

x² = (7.4 + 4.6)² - 7.4²

x² = 144 - 54.76

x = √89.24 = 9.45

23. perimeter of tringle GHI

solving for x

7x + 4 = 12x - 20

x = 4.8

perimeter = 52 + (52 - 15 + 7x + 4) + 15 + 12x - 20

perimeter = 52 + (52 - 15 + 7(4.8) + 4) + 15 + 12(4.8) - 20

perimeter = 198.2

24. angle NSR = 1/2 (170 + 50 )

angle NSR = 1/2 (220) = 110

25.

angle V = 1/2 * 290 = 145

4x - 5 + 145 = 180

4x - 5 + 145 = 180

4x + 140 = 180

4x = 40

x = 10

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The length of  segment BD of the right triangle is 7 units.

The length of  segment BC of the right triangle is  7√2.

The length of each segment of the triangle is calculated applying trig ratio as follows;

The length of segment BD is calculated as follows;

tan 45 = opposite side / adjacent side

The adjacent side of the right triangle is given as 7 units, the opposite side which is the height (BD) is calculated as follows;

tan 45 = BD/7

BD = 7 x tan 45

BD = 7 x 1

BD = 7

The segment BC is calculated as follows;

cos 45 = CD / BC

cos 45 = 7 / BC

BC = 7/ cos 45

BC = 7√2

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The transformations that when applied to a triangle on a coordinate grid that would preserve congruence are

(x, y) -> (x + 7, y - 8)

A reflection of the triangle across the x-axis

Rigid transformations refer to transformations in geometry that preserve shape and size

In other words when an object is transformed using a rigid transformation the object does not change its size or shape hence preserving congruence.

The types of rigid transformations translations rotations and reflections.

The first transformation: (x, y) -> (x + 7, y - 8)

is a translation of 7 units to the right and translation of 8 units down

While a reflection of the triangle across the x-axis also preserves congruence

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Answer:

Tickets Sold: 146

Step-by-step explanation:

Let's assume that the number of adult tickets sold is "x".

According to the problem, the number of student tickets sold is three times the number of adult tickets sold. Therefore, the number of student tickets sold is 3x.

The total number of tickets sold is 584, so we can set up an equation:

x + 3x = 584

Simplifying the equation, we get:

4x = 584

Dividing both sides by 4, we get:

x = 146

Therefore, the number of adult tickets sold is 146.

Answer: 146

Step-by-step explanation:

let x = # of adult tickets sold

let y = # of student tickets sold

x + y = 584

this is because the sum of adult tickets and student tickets is 584.

3x = y

this equation is written because there is 3 times more students there than adults

using substitution, we can find the equation :

x + (3x) = 584

4x = 584

x = 146

since x is equal to the number of adult tickets sold, your answer is 146.

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

We have,

To find the solution to the system of linear inequalities:

2x - 3y < 12

y ≤ 2

We first graph the line 2x - 3y = 12:

To graph the line, we can find the x and y intercepts:

When x = 0, we have -3y = 12, then y = -4, so (0, -4) is a point on the line.

When y = 0, we have 2x = 12, then x = 6, so (6, 0) is a point on the line.

Plot these two points and draw the line passing through them:

Next, we shade the region that satisfies the inequality 2x - 3y < 12:

We can choose a test point not on the line, such as (0,0).

Substitute the coordinates into the inequality:

2(0) - 3(0) < 12, which is true.

Now,

We shade the region that satisfies the inequality y ≤ 2:

We shade the region below the horizontal line y = 2:

Therefore,

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

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y=1/2x-3

"The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point."

Also, 1/2 (m= slope)

Also, rise⬆️/run↔️ is a good way to remember how to graph them. If the "Rise"(1) is positive it will go up. if it is negative it will go down. if the "Run" (2) is positive, youll go right, if it is negative youll go left.

The areas of the triangles are 5 square units and 35 square units

From the question, we have the following parameters that can be used in our computation:

Area = Length * Width/2

Where

Length = L

Width = W

Triangle (a)

L = 2 and W = 5

When the given values are substituted, we have the following equation

Area = 2 * 5/2

Area = 5

Triangle (b)

L = 10 and W = 7

When the given values are substituted, we have the following equation

Area = 10 * 7/2

Area = 35

Hence, the areas of the triangles are 5 square units and 35 square units

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Complete question

Find the area of each triangle using the formula of A=L×W/2​

(a) L = 2 and W = 5

(b) L = 10 and W = 7

The length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three Decimal places.

To find the length of the remaining rope, we need to subtract the sum of the lengths of the two pieces that were cut from the original length of the rope.

Original length of the rope = 8 m

Length of the first piece cut = 15/7 m

Length of the second piece cut = 29/9 m

Therefore, the length of the remaining rope can be found as:

Remaining length = Original length - Length of first piece - Length of second piece

Remaining length = 8 - 15/7 - 29/9

To perform the subtraction, we need to find a common denominator for 7 and 9, which is 63.

Remaining length = 504/63 - 135/63 - 203/63

Remaining length = (504 - 135 - 203)/63

Remaining length = 166/63

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 1.

Remaining length = 166/63 meters

Therefore, the length of the remaining rope is 166/63 meters, or approximately 2.635 meters when rounded to three decimal places.

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Correct equation best represents the relationship between x , the age of the machine in years, and y , the value of the machine in dollars over this 10-year period is,

⇒ y = 500x + 8000

We have to given that;

The graph models the value of a machine over a 10 -year period.

Now, Let two points on graph are, (0, 8000) and (8, 4000)

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Hence,  on substituting the values in above result, we get;

y - 8000 = (4000 - 0) / (8 - 0) (x - 0)

y - 8000 = 500x

y = 500x + 8000

Thus, The correct equation is,

y = 500x + 8000

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The baker would need 47. 25 cups of floor

We need to know that proportion is a form of mathematical comparison with two equations made equal to each other.

From the information given, we have that;

baker used 33 3/4 cups of flour to make 15 batches of cookies

This is represented as;

Convert to improper fractions

135/4 cups = 15 batches of cookies

Then, x cups = 21 batches of cookies

cross multiply the values

15x = 708. 75

Divide both sides by the coefficient of x, we have ;

x = 708. 75/15

x = 47. 25 cups of floor

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Answer:

trapezium

Step-by-step explanation:

it is a quadrilateral in which only one pair of opposite sides is parallel

Answer:

Trapezium

Step-by-step explanation:

That shape is a Trapezium as it is a quadrilateral having one pair of parallel sides.

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Note that

1.BA~CD Given

2.ABCDis a trapezoid Given

3.ABCD is and isosceles trapezoid -  Definition of  of isosceles trapezoid

4. AD~AD -  reflective property

5.6. Triangle BAD ~ triangle CDA  -  SAS Axiom

7.BD~ CA -  CPCTC

The top and bottom sides of an isosceles trapezoid are parallel, but the other two non-parallel sides are the same length. A trapezoid is a quadrilateral having two parallel sides and two non-parallel sides, as we know.

The bases (top and bottom) are perpendicular to one other. The bases (top and bottom) are perpendicular to one other. Congruent angles can be found on either side of the base. Congruent angles can be found on either side of the base.

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The table to set up a System of equations to solve for the number of laps walked and run if the total distance is 24 laps.the correct answer is not listed among the options given.

The table to set up a system of equations to solve for the number of laps walked and run if the total distance is 24 laps:

3 + 5 = A   (the total number of laps walked and run is equal to A)

B + 10 = C   (the total number of laps walked and run is equal to C)

15 + D = 40  (the total number of laps walked and run for the week is 40)

Simplifying each equation, we get:

A = 8

B = 5

C = 15

D = 25

To find how many laps will the participants walk and run if the total distance is 24 laps, we can set up the following proportion:

3x/8 + 5x/15 = 24

Multiplying both sides by 120 (the least common multiple of 8 and 15), we get:

45x + 40x = 2880

Simplifying, we get:

85x = 2880

Dividing both sides by 85, we get:

x ≈ 33.88

Therefore, the participants will walk approximately:

3x/8 ≈ 12.66 laps

And run approximately:

5x/15 ≈ 21.22 laps

Rounding to the nearest whole number, we get:

They will walk 13 laps and run 21 laps.

Therefore, the correct answer is not listed among the options given.

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Answer:

-2

Step-by-step explanation:

The expression with the greatest quotient can be found by computing each expression and comparing the results.

-20 ÷ -5 = 4

8 ÷ -4 = -2

-6 ÷ -3 = 2

12 ÷ -3 = -4

Therefore, the expression with the greatest quotient is -2, since it has the largest absolute value.

17.55% is the probability for any day, the number of special orders sent out will be exactly 5

The given situation describes a Poisson distribution with a mean of 5 special orders per day. The probability of getting exactly 5 special orders in a day can be calculated using the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of special orders, λ is the mean number of special orders per day, and k is the number of special orders we want to find the probability for.

Plugging in the given values, we get:

P(X = 5) = (e^(-5) * 5^5) / 5!

Simplifying this expression, we get:

P(X = 5) = 0.1755

Therefore, the probability of getting exactly 5 special orders in a day is 0.1755 or 17.55%, rounded to four decimal places.

Intuitively, this means that out of many days, we can expect around 17.55% of them to have exactly 5 special orders sent out. The Poisson distribution is commonly used to model the number of events occurring in a fixed period of time, given a known average rate of occurrence. In this case, the Poisson distribution can be used to estimate the likelihood of a particular number of special orders being sent out in a day.

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There are two ways to solve this problem: use the formula for the area of a trapezoid, or break the trapezoid up into 3 shapes.

Formula for the Area of a Trapezoid: A = 1/2(b1 + b2) x h

A = 1/2(17 + 9) x 8

A = 1/2(26) x 8

A = 13 x 8

A = 104 m^2

Trapezoid = 2 right triangles + 1 rectangle

Area of a triangle = 1/2 x base x height

A(triangle) = 1/2 x 4 x 8

A(triangle) = 16

A(both triangles in the trapezoid) = 32 m^2

A(rectangle) = 8 x 9

A(rectangle) = 72 m^2

Total area = 72 + 32 = 104 m^2

Answer: A = 104 m^2

Hope this helps!

The value of x is 3 and angle Q is 39°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A circle theorem states that : angles in thesame segment are equal.

With this theorem is means that angle 13x is equal to angle x +36 .

Therefore;

13x = x +36

collecting like terms

13x -x = 36

12x = 36

divide both sides by 12

x = 36/12

x = 3

therefore the value of angle Q = 13 × 3

= 39°

Therefore the value of angle Q is 39°

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Answer: 40 cups per min = 2.5 gallons per hour

Step-by-step explanation:

Answer:

We can use the law of cosines to solve for c:

c^2 = 20^2 + 15^2 - 2(20)(15)cos(125°)

c^2 = 400 + 225 + 600cos(125°)

c^2 = 625 + 600cos(125°)

c = sqrt(625 + 600cos(125°))

c ≈ 32.7

Therefore, the length of c is approximately 32.7 units.

Answer:

To rotate a point 90 degrees clockwise about another point, you can follow these steps:

1. Subtract the coordinates of the center of rotation from the coordinates of the point you want to rotate to translate the center of rotation to the origin.

A translated point A would be: (5 - 0, 4 - 1) = (5, 3)

2. Perform the rotation by swapping the x and y coordinates and negating the new x-coordinate.

The rotated point A' would be: (3, -5)

3. Add the coordinates of the original center of rotation to the rotated coordinates to translate the origin back to the center of rotation.

The final coordinates of point A' would be: (3 + 0, -5 + 1) = (3, -4)

The volume of this of rectangular container is equal to 19,425 cubic centimeter.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular container = 25 × 37 ×  21

Volume of rectangular container = 19,425 cubic centimeter.

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Complete Question:

A rectangular container is 25cm by 37cm by 21cm. What is the volume of this rectangular container?

The calculated length of the segment WK is (b) 2√5

From the question, we have the following parameters that can be used in our computation:

The right triangle

Where we have

W = (-6, -2)

K = (-2, 0)

The length of the segment WK is calculated as

WK = √[(x2 - x1)² + (y2 - y1)²]

Substitute the known values in the above equation, so, we have the following representation

WK = √[(-6 + 2)² + (-2 - 0)²]

Evaluate

WK = √20

This gives

WK = 2√5

Hence, the length of the segment WK is (b) 2√5

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The experimental probability of rolling a total of 9 on two number cubes is 2/50, or 0.04.

To calculate the experimental probability,we divide the number of successful outcomes by the total   number of trials.

In this case, there were 2 successful outcomes (the sum of the number cubes was 9) and 50 total trials.

Therefore, the experimental probability is

2/50 = 0.04.

It is important to note that this is just an experimental probability, and the actual probability of rolling a total of 9 may be different.

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Answer:

Step-by-step explanation: 78 +3x+x=180 deg.

                                                 4x=180-78

                                                 4x=102/:4

                                                    x=25.5 deg

Step-by-step explanation:

180 = 78° + 3x°

78° + 3x° = 180°

3x°= 180° - 78°

3x = 102°

x = 102°/3

sure the answer is c and a or b but the correct one is c

The area of the parallelogram with vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3) is 90 units².

To find the area of a parallelogram, we need to know the length of one of its bases and its corresponding height. We can find the length of the base by computing the distance between two parallel sides of the parallelogram.

In this case, we can see that sides AB and CD are parallel, and they both have a length of 18 units (6 - (-12) = 18).

To find the height, we need to compute the distance between the parallel sides. We can do this by computing the vertical distance between either AB and CD or AD and BC.

Let's use AD and BC. The vertical distance between A and D is 5 units (2 - (-3) = 5), and the vertical distance between B and C is also 5 units (2 - (-3) = 5). Therefore, the height of the parallelogram is 5 units.

Now we can use the formula for the area of a parallelogram:

Area = base x height

Area = 18 x 5

Area = 90 units²

Therefore, the area of the parallelogram with vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3) is 90 units².

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The solution to the system is x = -4, y = -1.

One can employ the techniques of substitution or elimination to obtain solutions for the given set of equations.

Let's apply the elimination approach in this scenario.

To ensure that the coefficients of x are equal, multiply the first equation by 2 and the second by 3.

6x - 22y = -2,

6x - 15y = -9.

Subtract the second equation from the first:

0x - 7y = 7.

So, y = -1.

Substitute y = -1 into the second equation:

2x - 5(-1) = -3,

2x + 5 = -3,

2x = -8.

So, x = -4.

The solution to the system is x = -4, y = -1.

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The Complete Question:

Solve the system of equations.

3x – 11y = -1

2x – 5y = -3