a) A bag contains red and blue counters only.
Number of red counters : number of blue counters = 3:4

Write down the fraction of the counters that are red.

b) Write down the ratio 12:30 in the form 1:n

Answer:

D

Step-by-step explanation:

The diagram below shows the perpendicular bisector of AB.

Option B is the correct answer.

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Line DF bisects line AB.

The diagram shows the perpendicular bisector of AB.

Thus,

DF is the perpendicular bisector of AB.

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Step-by-step explanation:

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6) ?

Since, A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100,we have to find the value of f(6).

Consider

f(n+1) = f(n)-8

Let n =1, we get

f(1+1) = f(2) = f(1) - 8 = 100-8 = 92

Let n =2, we get

f(2+1) = f(3) = f(2) - 8 = 92-8 = 84

Let n =3, we get

f(3+1) = f(4) = f(3)-8 = 84 - 8 = 76

Let n =4, we get

f(4+1) = f(5) = f(4)-8 = 76 - 8 = 68

Let n =5, we get

f(5+1) = f(6) = f(5) - 8 = 68-8 = 60

Therefore, the value of f(6) is 60.

Answer: C, 60

Step-by-step explanation: Just took the quiz :)

The four capital letters of the alphabet in block style with rotational symmetry are equals to the Z, S, H and N.

A letter is said to have rotational symmetry as an initial if it looks the same when rotated 180 degrees clockwise or counterclockwise. Letters Z, S, H, N, when an object is rotated around its own axis, the shape of the object appears to be the same. This is called second-order rotational symmetry because there is has two 90 degree rotations.

The letter O has first-order rotational symmetry because it looks the same when rotated 90 degrees. Letters can also have axes of symmetry, vertical or horizontal. Examples of letters with vertical lines of symmetry: A, H, I, M, O, T, U, V, W, X, and Y. Examples of letters with horizontal lines of symmetry include B, C, D, E , H, I, K, O, S and X. Hence, required letters are Z, S, H and N.

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The sum of the arithmetic sequence 7, 9, 11, ..., 69 is 1216. To find the sum of the arithmetic sequence 7, 9, 11, ..., 69,

We can use the formula for the sum of an arithmetic sequence:

S = (n/2)(a + L)

where S is the sum, n is the number of terms, a is the first term, and L is the last term.

First, we need to find the number of terms in the sequence. To do this, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, and d is the common difference. In this case, a1 = 7 and d = 2, so the formula becomes:

an = 7 + 2(n - 1)

an = 2n + 5

To find the value of n that corresponds to the last term, we solve for an = 69:

69 = 2n + 5

64 = 2n

n = 32

So there are 32 terms in the sequence.

Now we can use the formula for the sum of an arithmetic sequence to find the sum:

S = (n/2)(a + L)

S = (32/2)(7 + 69)

S = 16(76)

S = 1216

Therefore, the sum of the arithmetic sequence 7, 9, 11, ..., 69 is 1216.

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Answer:

$38.40

Step-by-step explanation:

Answer:

$38.40

Step-by-step explanation:

Yes, there is sufficient evidence to refute the publisher's claim that 20% of their readers own a Rolls Royce at the 0.01 level.

The hypothesis test result indicates that the p-value is less than 0.01, which means the null hypothesis can be rejected at a 0.01 level of significance. Therefore, there is evidence to suggest that the true percentage of Rolls Royce owners among the newsletter publisher's readers is less than 20%. This could have implications for the publisher's advertising strategy and target audience.

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A rectangular prism has 6 faces, 8 vertices and 12 edges.

What is rectangular prism?

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid. A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

If all the faces of the prism are squares then the rectangular prism is a cube. The volume of a rectangular prism is a measure of the space inside the prism.

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Answer:

703.7 in³

Explanation:

Volume of cone =  ⅓ × π × radius² × height

                           = ⅓ × π × 8² × 10.5

                           = 224π

                           = 703.72 in³

                           = 703.7 in³           (rounded to nearest tenth)

Note: If π considered as 3.14, then volume is 703.36 in³.

Answer:

oouu I'm in 7th grade science and I already did this I can help!

There are 27,405 different ways according to the combinations formula ,presenter can select 4 people out of 30.

What is combinations?

Combinations, in mathematics, refer to the selection of items from a larger set without considering their order.

To determine the number of different ways the presenter can select 4 people out of 30, we can use the concept of combinations. Specifically, we can calculate the number of combinations of 30 items taken 4 at a time, denoted as "30 choose 4" or "C(30, 4)".

The formula for combinations is:

C(n, r) = n! / (r!(n - r)!)

where n is the total number of items and r is the number of items to be selected.

Using this formula, we can calculate the number of different ways:

C(30, 4) = 30! / (4!(30 - 4)!) = (30 * 29 * 28 * 27) / (4 * 3 * 2 * 1) = 27,405

Therefore, there are 27,405 different ways the presenter can select 4 people out of 30.

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Answer:

3m -2

Step-by-step explanation:

(10m – 6) – (7m – 4)

Distribute the minus sign

(10m – 6) – 7m + 4

Combine like terms

3m -2

Answer:

Simplifying

1x + 2y = 5

Solving

1x + 2y = 5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

1x + 2y + -2y = 5 + -2y

Combine like terms: 2y + -2y = 0

1x + 0 = 5 + -2y

1x = 5 + -2y

Divide each side by '1'.

x = 5 + -2y

Simplifying

x = 5 + -2y

Step-by-step explanation:

Answer:

I can't Respond since I have no picture to help you or me

Step-by-step explanation:

Without the Picture I can't determine if the triangle ABC is congruent to triangle DEF by SAS, AB=DE

Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

The mathematical procedure for decomposing a complex waveform into simpler waveforms is known as Fourier analysis. It allows for the identification of the individual frequency components that contribute to the overall pattern.

Fourier analysis, named after the French mathematician Jean-Baptiste Joseph Fourier, is a fundamental technique used in many fields, including signal processing, physics, and engineering. It is based on the concept that any complex waveform can be represented as a combination of simpler sinusoidal waveforms. These simpler waveforms are characterized by their frequency, amplitude, and phase.

The procedure involves decomposing a complex waveform into its constituent frequencies by applying the Fourier transform. The Fourier transform converts the waveform from the time domain to the frequency domain, revealing the underlying frequency components. By analyzing the resulting spectrum, which shows the amplitude and phase of each frequency component, one can determine the simpler waveforms that make up the original complex pattern.

Fourier analysis has numerous applications, such as analyzing sound waves, image processing, and data compression. It enables us to better understand and manipulate complex signals by breaking them down into their fundamental building blocks.

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Answer:

The PC 5150 is sold anywhere from $50 - $500 I believe it is a reasonable price since it is an old item and does not work as well as the newer and better ones.

Hope this helped : )

The odds against an event is 4:7

Unfavourable elements for the event = 4

Favourable elements for the event = 7

Total = 4 + 7 = 11

Hence the probability that the event will fail = 4/11.

The rocket reaches at it maximum height at 3.25 seconds.

What is a function?

A mathematical formula, rule, or legislation that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is h(t) = -16t² + 104t + 5

A quadratic function f(x) = ax² + bx +  c is maximum at x = -b/2a

Now compare  -16t² + 104t + 5 with ax² + bx +  c

a = -16, b = 104, c = 5

The maximum value of  h(t) = -16t² + 104t + 5 is at t = -104/(2× (-16)) = 3.25.

The rocket reaches at it maximum height at 3.25 seconds.

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The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.

The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.

Given, the double integral ∫∫yA and the region y = x-6 and x = y²

y = x-6

x = y²

y² = y +6

y² - y - 6 = 0

y² - 3y +2y - 6 = 0

(y-3) (y+2) = 0

y = 3 and y = -2

\(\int\int\limits_\triangle {y} \, dA\\ \\\)

= \(\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}\)

The value for the double integral is 125/12.

Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.

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Yes, it is possible for two different pairs of numbers to have the same geometric mean. It is the nth root of the product of the numbers.

The geometric mean of a set of numbers is the nth root of the product of the numbers, where n is the total number of values in the set. The geometric mean is a measure of central tendency that is useful for calculating the average growth rate, finding a common ratio, or comparing values that are exponentially related.

To illustrate that two different pairs of numbers can have the same geometric mean, let's consider the following examples:

Pair 1: 2 and 8

Pair 2: 4 and 4

For Pair 1, the geometric mean is √(2 * 8) = √16 = 4.

For Pair 2, the geometric mean is √(4 * 4) = √16 = 4.

As we can see, both pairs have the same geometric mean of 4, even though the individual numbers in each pair are different. This shows that different pairs of numbers can have the same geometric mean. However, it is important to note that in general, there are infinitely many pairs of numbers that can have the same geometric mean.

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Based on the given information, we know that the medium-sized jet has a fuselage diameter of 3.8 meters and a loaded mass of 85,000 kilograms. The drag on the airplane is primarily due to the cylindrical shape of the fuselage, and its aerodynamic shaping gives it a drag coefficient of 0.37.

To calculate the drag force on the airplane, we can use the formula:

Drag Force = 1/2 x Density x Velocity^2 x Surface Area x Drag Coefficient

The surface area of a cylinder is given by:

Surface Area = 2 x π x (diameter/2) x length

Assuming a length of 30 meters for the fuselage, we can calculate the surface area as:

Surface Area = 2 x π x (3.8/2) x 30 = 426.43 square meters

Using the given drag coefficient of 0.37 and assuming a cruising speed of 800 km/h (or 222.22 m/s), we can calculate the drag force as:

Drag Force = 1/2 x 1.225 kg/m^3 x (222.22 m/s)^2 x 426.43 m^2 x 0.37
Drag Force = 5,641,613 Newtons

Therefore, the drag force on the medium-sized jet is approximately 5.64 million Newtons. This drag force must be overcome by the jet's engines to maintain its cruising speed.

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The popcorn box would hold 168.75 cubic inches of popcorn when it is full. Rounded to the nearest tenth, the answer is 168.8 cubic inches.

To find the volume of the popcorn box, we need to multiply its length, width, and height. However, we need to make sure that all the dimensions are in the same units before we multiply them.

First, let's convert the mixed numbers to improper fractions:

3 3/4 = 15/4

7 1/2 = 15/2

Now, we have the dimensions in the same units (inches):

Length = 15/4 in

Width = 3 in

Height = 15/2 in

To find the volume, we multiply the three dimensions:

Volume = Length x Width x Height

Volume = (15/4) x 3 x (15/2)

Volume = 168.75 cubic inches

Therefore, the popcorn box would hold 168.75 cubic inches of popcorn when it is full. Rounded to the nearest tenth, the answer is 168.8 cubic inches.

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Answer:

4.8 is the answer!

Step-by-step explanation:

0.6 x 8 = 4.8

6 x 8 = 48

multiply 6 by 8, and move the decimal to the left one time, and get 4.8

Answer: 4.8

Step-by-step explanation: multiply 6*8 (which is 48) then move the decimal point one forward from the back

48.0 (this is before you move the point)

4.8 (this is after)

basically depending on how much numbers you have after the decimal point, that's how much you move forward!

Let me know if you have more questions!

Good luck!

Answer: b2 should be 5 i believe

Step-by-step explanation:

Answer:

B∨2 = 5

Step-by-step explanation:

Hope this helps!

Answer:

it is the abstract science of number, quantity and space, either as abstract concept

Answer:

so what

Step-by-step explanation:

After calculating and conversion of the given vector to component form we get

for part A

−7(u • v) = 64.209

for part B

u • w = 26.353

In order to convert the vectors to component form,

u = 6(cos 60°i + sin60°j) = 6(0.5i + 0.866j) = (3i + 5.196j)

v = 4(cos 315°i + sin315°j) = 4(-0.707i + 0.707j) = (-2.828i + 2.828j)

−7(u • v) = −7[(3)(-2.828) + (5.196)(2.828)] = −7(-8.484 + 14.697)

= 64.209

In order to convert the vectors to component form,

u • w = (6)(cos60°)(-12)(cos330°) + (6)(sin60°)(-12)(sin330°)

= (-36 + 62.353) = 26.353

Hence, u • w is not equal to zero and u and w are not parallel or orthogonal.

After calculating and conversion of the given vector to component form we get

for part A

−7(u • v) = 64.209

for part B

u • w = 26.353

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Answer:

Quadrilateral ABCD is a SQUARE

Step-by-step explanation:

When we are given coordinates (x1, x2) and (y1 , y2) for a Quadrilateral, we solve for the sides using this formula.

√(x2 - x1)² + (y2 - y1)²

A (3, 1), B (4, 4), C (7, 5), D (6, 2)

Side AB = A (3, 1), B (4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 3)² + (4 - 1)²

= √1² + 3²

= √1 + 9

= √10

Side BC = B (4, 4), C (7, 5)

√(x2 - x1)² + (y2 - y1)²

= √(7 - 4)² + (5 - 4)²

= √3² + 1²

= √9 + 1

= √10

Side CD = C (7, 5), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 7)² + (2 - 5)²

= √(-1) ² + (-3)²

= √1 + 9

= √10

Side AD = A (3, 1), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 3)² + (2 - 1)²

= √3² + 1²

= √9 + 1

= √10

From the above calculation,

Side AB = √10

Side BC = √10

Side CD = √10

Side AD = √10

Hence, AB = BC = CD = AD

When all the side of a Quadrilateral are the same or equal to each other, it means the Quadrilateral is a square.

Therefore, Quadrilateral ABCD is a SQUARE

Here, we want to use the given number of 3's to get the answer of 5

Mathe matically, we can have this as;

By adding what we have above , we get 6

Dividing this by 3, we get 2

Then consequently, we add this to 3 and we get 5