A bag contains 48 marbles. The ratio of red marbles to black marbles is 5 to 3. How many RED marbles are in the bag?

The work done in each of the cases is:

B) W =  8,400 N*m

C) W = 17,500 N*m

The work can be defined by the product between the force and the distance translated.

W = Force*Distance

So, if there is a force of 120N and the vehicle moves 70 meters, the work done is:

W = 120N*70m = 8,400 N*m

C) Similar case to the above one, here the force is F = 3.5 KN = 3,500N

And the distance is d = 15m

Then in this case the work done is:

W = 3,500N*15m = 17,500 N*m

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Answer:

list the squares

1x1=1

2x2=4

3x3=9

4x4=16

16  the answer because 1+6=7

hope this helps if you have any questions you can ask

Step-by-step explanation:

Answer:

4's square number : 16

5's square number : 25

32's square number : 1024

40's square number : 1600

49's square number : 2401

50's square number : 2500

Step-by-step explanation:

I might have missed a few but ...

Answer:

We know that our number m is more than -(7 2/3)

Then we must write this as:

m > -(7 2/3)

At most -10 is written as:

m ≤ - 10.

Then the statement:

"A number m is more than -7 2/3 or at most -10" is written as:

m > -(7 2/3) ∨ m ≤ - 10.

Where ∨ means "or".

The graph of this will look like:

A white dot in the point -(7 2/3) and a line that goes to the right. And a black dot at -10, and a line from that that goes to the left.

Remember that white dot means that the element is not a solution, and that is used for the symbols > <

And a black dot means that the element is a solution, is used for the symbols ≤ ≥

Answer:

Step-by-step explanation:

the answer would be m > -7 2/3 or m ≤ - 10.

52 tiles are there in the 25th figure in this pattern.

A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.

A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.

A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.

Any kind of event or object can be connected to the Pattern.

A pattern is referred to as a rule or a way in which a group of numbers is related to one another.

Sometimes a pattern is also referred to as a sequence.

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Please find attached the image of the enlargement of the shape X by a scale factor of -1 created using MS Word, which is a drawing equivalent to option B. The correct option is therefore;

B.

An enlargement transformation is one in which the pri-image object size is scaled about a center of enlargement, using a scale factor, with the sign of the scale factor indicating the direction of the enlargement, which for a +ve sign is on the same side, and for a -ve sign is on the other side of the center of enlargement.

An enlargement by a scale factor of -1, can be obtained by producing the image on the alternate side of the center of enlargement, which with a scale factor of -1, is the same size as the size of the image.

Therefore, the dilation by a scale factor of -1, with the center at the origin, produces an image which is equivalent to a reflection of the original object (pre-image), across the y-axis followed by a reflection across the y-axis.

The image of the object following the dilation will therefore be the mirror image of the mirror image of the object reflected across the y-axis, which takes the shape of a vertically flipped, left flipped F, which is option B

Please find attached a drawing of the shape of the image of the enlargement of shape X by a scale factor of -1, created with MS Word

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The solution to the given system of equations is (x, y, z) = (-3, 1, 0).

We have,

To solve the system of equations, we can use the method of Gaussian elimination or matrix operations.

Let's use the method of Gaussian elimination:

The given system of equations is:

x + y + z = -2 --- (1)

x - y + 2z = -4 --- (2)

x - y + 3z = -4 --- (3)

We can start by subtracting equation (2) from equation (3) to eliminate the variable y:

(x - y + 3z) - (x - y + 2z) = -4 - (-4)

z = 0

Now, we substitute z = 0 back into equation (2) to solve for x and y:

x - y + 2(0) = -4

x - y = -4 --- (4)

Next, we substitute z = 0 into equation (1) to solve for x and y:

x + y + 0 = -2

x + y = -2 --- (5)

Now, we have a system of two equations with two unknowns (x and y). We can solve this system by adding equations (4) and (5) to eliminate y:

(x - y) + (x + y) = -4 + (-2)

2x = -6

x = -3

Substituting x = -3 back into equation (5):

-3 + y = -2

y = 1

So, we have found x = -3, y = 1, and z = 0.

Therefore,

The solution to the given system of equations is (x, y, z) = (-3, 1, 0).

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Answer:

50h+25.5=154

Step-by-step explanation:

Answer: x = -6

Step-by-step explanation: The problem gave us the y value, so we can just substitute it into the equation and solve it.

y = x - 6

y = 2x

2x = x - 6 (substitute the y value into the equation)

1x = -6 (subtract x on each side)

x = -6 (1x is basically saying x so you do not need to divide)

The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

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Answer: the

Step-by-step explanation:

The equation of the given line is y = 2x

The standard equation of a line is y = mx + b

From the graph, we can use the coordinate point (1, 2) and (2, 4)

Get the slope

m = 4-2/2-1

m = 2/1

m = 2

Since the line pass through the origin, hence b = 0

Get the required equation:

y = 2x + 0

y = 2x

Hence the equation of the given line is y = 2x

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Answer:

8 and 4

Step-by-step explanation:

The probability is approximately (b) 0.0062., The probability is approximately (c) 0.0808

For the first question, we know that the life expectancy of the tire is normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. We want to find the probability that a randomly selected tire will have a life of at least 52,500 miles.

To solve this, we need to standardize the value of 52,500 miles using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

z = (52,500 - 40,000) / 5,000 = 2.5

Now we look up the area to the right of z = 2.5 on a standard normal distribution table or use a calculator to find the cumulative probability. The probability is approximately 0.0062. Therefore, the answer is (b) 0.0062.

For the second question, we know that the time it takes to travel from home to the office is normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes. We want to find the probability that the trip takes more than 32 minutes.

Again, we need to standardize the value of 32 minutes using the formula z = (x - μ) / σ.

z = (32 - 25) / 5 = 1.4

Now we look up the area to the right of z = 1.4 on a standard normal distribution table or use a calculator to find the cumulative probability. The probability is approximately 0.0808. Therefore, the answer is (c) 0.0808.

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89 Step-by-step explanation: 12+-3 = 6

Answer: 5,120

Step-by-step explanation:

Your equation is:

v(t) = 320 • 4^t

You are trying to find v(2) so:

t = 2

Plug in 2 for t:

v(2) = 320 • 4²

Solve:

v(2) = 5,120 views

Hope this helps! :)

The complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ.

For (i), the complex exponential Fourier series is given by:

X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where

A₀ = 1/2

Aₙ = (1/2)[cos(2nπ/8) + cos(2nπ/8 + π/2)]

For (ii), the complex exponential Fourier series is given by:

X(ω) = A₀ + ∑[Ancos(nωt + φn) ], where

A₀ = 1

Aₙ = (2/2)[sin(nπ/3) + 3cos(nπ/3 + π/3)]

In conclusion, the complex exponential Fourier series of a signal can be determined by computing the coefficients A₀ and Aₙ. This technique can be used to analyze any periodic signal or system and is invaluable in signal processing, communications, and control engineering.

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Systemic chemotherapy's impact on survival and recurrence in people with high-grade glioma has not been conclusively studied.

Patients undergoing systemic chemotherapy can get their chemotherapy drugs intravenously or orally. The medication may be injected into the body intravenously, or through an IV, or intramuscular, into a muscle (IM).

Some Key features of systemic chemotherapy are-

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\(\csc(90^{\circ}-\theta)\\\\=\sec \theta \\\\=\sqrt{10}\)

Answer:

       \(\frac{2}{7}\)

Step-by-step explanation:

3.5 = \(\frac{7}{2}\)

swap the numerator and denominator (flip the fraction):

reciprocal of \(\frac{7}{2}\) is \(\frac{2}{7}\)

The order of g is a power of 2, Hence G is abelian.

Everything is in order, with the exception of identification.

2, then  a2=e

where  a∈G

 (including identity this time). So,  a−1=a

  for all  a∈G

Hence  ab=(ab)−1=b−1a−1=ba

 for all  a b∈G

For every x∈G

we have x2=e

where e

represents the identity in.

Then x−1=x

Now, let a,b

be two arbitrary elements in G

We have ab=(ab)−1=b−1a−1=ba

Hence G is abelian.

(First equality is true because  ab

is also an element of  G

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Statistical process control technique that permits only 3.4 defects per million opportunities is Six Sigma.

Six Sigma is a statistical technique that emphasizes the necessity of a standardized approach to enhancing and optimizing the efficiency of the production and management processes by reducing the variation and waste within them. It concentrates on controlling a process to ensure that the results of a process are consistent and reliable by using statistical methods. The objective of the Six Sigma process is to produce 3.4 errors or defects per million opportunities. If the process is better than Six Sigma, it is considered more consistent and predictable.
Six Sigma's statistical approach to process control encompasses a range of tools and methods. Six Sigma's primary objective is to increase revenue and profits by developing and delivering high-quality products and services while eliminating defects and reducing waste.
Six Sigma aims to improve quality by detecting and reducing the reasons for variations in production processes. It accomplishes this by developing quality management practices that enable it to assess quality, establish goals, and implement best practices to achieve those goals.
In conclusion, Six Sigma is a process control approach that emphasizes statistical methods for process control and improvement. Six Sigma is used to reduce variability and eliminate waste, and its goal is to achieve 3.4 defects per million opportunities.

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Answer:

this is what the graph will look like but i hope this helps

Step-by-step explanation:

have a safe and happy holiday

The expression log(\(x^{11}\)\(y^5\)/\(z^{13\)) can be written as 11log(x) + 5log(y) - 13log(z) where A = 11, B = 5 and C = -13.

To write the expression log(\(x^{11}\)\(y^5\)/\(z^{13\)) ) in the form Alog(x) + Blog(y) + Clog(z), we need to apply the properties of logarithms. Let's break down the expression step by step:

log(\(x^{11}\)\(y^5\)/\(z^{13\)) )

Using the properties of logarithms, we can rewrite this expression as:

log(\(x^{11\)) + log(\(y^5\)) - log(\(z^13\))

Next, using the exponent property of logarithms, we can further simplify:

11log(x) + 5log(y) - 13log(z)

Now we can see that the expression is in the desired form. Comparing it to Alog(x) + Blog(y) + Clog(z), we can identify the values of A, B, and C:

A = 11

B = 5

C = -13

Therefore, the expression log((\(x^{11}\)\(y^5\)/\(z^{13\))) can be written as 11log(x) + 5log(y) - 13log(z).

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Answer:

2,100

Step-by-step explanation:

(a) Mrs Jeya gave 30 stickers to Group B on Tuesday. (b) Mrs Jeya bought a total of 126 stickers.

(a) Let's first calculate the number of stickers Mrs Jeya had remaining after giving 1/4 of the stickers to Group A. If she had 72 stickers remaining, it means that 3/4 of the original number of stickers is equal to 72. We can set up the equation:

(3/4) * x = 72

To solve for x, we multiply both sides of the equation by 4/3:

x = (72 * 4) / 3 = 96

So Mrs Jeya initially had 96 stickers.

Now, on Tuesday, she gave 5/12 of the remaining stickers to Group B. We know that the remaining number of stickers after giving to Group A was 72. Let's calculate the number of stickers she gave to Group B:

(5/12) * 72 = 30

Therefore, Mrs Jeya gave 30 stickers to Group B on Tuesday.

(b) To determine how many stickers Mrs Jeya bought, we need to add up the stickers she gave to Group A, the stickers she gave to Group B, and the remaining stickers.

Stickers given to Group A: 1/4 * 96 = 24

Stickers given to Group B: 30

Remaining stickers: 72

Total stickers = Stickers given to Group A + Stickers given to Group B + Remaining stickers

              = 24 + 30 + 72

              = 126

Therefore, Mrs Jeya bought a total of 126 stickers.

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Answer:

Here is answer

Step-by-step explanation:

To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.

Let's start by factoring each of the given polynomials:

ax² - (a² + ab)x+ a²b = a(x - b)x

bx² - (b² + bc)x+ b²c = b(x - c)x

cx² - (c² + ac)x + c²a = c(x - a)x

The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.

Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.

Answer:

Part B: (0, -6)

Part C: x = -1

Part D: (-1, -8)

Explanation:

see the attached pdf

Answer:

8√2

Step-by-step explanation:

Notice that this is a 45-45-90 triangle (isosceles right triangle). This type of triangle has a  property where the ratio between side lengths is x : x : x√2, where x√2 is the measure of the two equal legs and is the measure of the hypotenuse.

Since we know the measure of one of the smaller legs is 8, then we can set x in the ratio to 8 -->  8 : 8 : 8√2

Thus, the length of BC (hypotenuse) is 8√2

Answer:

a² + b² = 20

Step-by-step explanation:

Given

(a - b) = 4 ← square both sides

(a - b)² = 4²

a² - 2ab + b² = 16 ← substitute ab = 2

a² - 2(2) + b² = 16

a² - 4 + b² = 16 ( add 4 to both sides )

a² + b² = 20

To find the x-coordinate of the point where the line l intersects the plane x - 3y - z = 9, we need to find the value of x when the coordinates (x, y, z) satisfy both the equation of the line and the equation of the plane.

Since the line l is parallel to the line with vector equation r(t) = 〈2, 4, 1〉 + t〈2, 3, -2〉, we can write the equation of line l as:

x = 2 + 2t

y = 4 + 3t

z = 1 - 2t

Substituting these equations into the plane equation x - 3y - z = 9, we have:

(2 + 2t) - 3(4 + 3t) - (1 - 2t) = 9

Simplifying the equation, we solve for t:

2 + 2t - 12 - 9t - 1 + 2t = 9

-5t - 11 = 9

-5t = 20

t = -4

Substituting t = -4 into the equation x = 2 + 2t, we find:

x = 2 + 2(-4) = -6

Therefore, the x-coordinate of the point where the line l intersects the plane is -6.

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