Your Turn (Activity 3): Calculate the LCM of 54 and 90​

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The correct option is (D) (78-6x)°

The measure of the complement of angle K is 78-6x degrees

In the geometry, angle is defined as the geometrical figure formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.

Some common terms related to angles :

Endpoint  : It is the point where the rays met to each other.

Ray : Ray is the side or line segment on which angle is formed.

Curve : It is a line but not straight i.e. a bended line.

Tangent : A line which touches the surface of curve.

Suppose m is the measurement of any angle . Then we can find the complement by subtracting the measurement of that angle from 90 degree.

i.e. mathematically, complement = 90 - measurement

In the question given,

measurement of K = m∠K = 6x + 12

So, complement of ∠K = 90 - m∠K

                                      = 90 - (6x + 12)

                                      =  78 - 6x

hence, complement of angle K is 78-6x degrees

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The complete question is:

m∠K = (6x + 12). Find the measure of the complement of ∠K.

A) (67-6x)°

B) (102 + 6x)°

C) (112 + 6x)°

D) (78-6x)°

Answer:

I think it is the first one

The probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

The probability of exactly 4 total launches being performed until an unsuccessful launch occurs, we can use the geometric probability formula.

In this case, the probability of a successful launch (p) is 0.7 (since the probability of an unsuccessful launch is 0.3). We want to find the probability of 4 successful launches followed by an unsuccessful launch.

The probability of exactly 4 successful launches followed by an unsuccessful launch can be calculated as follows:

P(4 successful launches followed by an unsuccessful launch) = (p⁴) × (1-p)

P(4 successful launches followed by an unsuccessful launch) = (0.7⁴) × (1-0.7)

P(4 successful launches followed by an unsuccessful launch) = 0.7⁴ × 0.3

P(4 successful launches followed by an unsuccessful launch) = 0.2401 × 0.3

P(4 successful launches followed by an unsuccessful launch) ≈ 0.0720

Therefore, the probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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The expression that is not a solution to the equation \(2^t\) = 10 is \(log_{10} 4\). The correct answer is 3.

In order for an expression to be a solution to the equation \(2^t\)= 10, it must yield the value of t that satisfies the equation when substituted into it. Let's evaluate each option to determine which one is not a valid solution:

(1) \(2/1 log 2\): This expression simplifies to log 2, which is not equal to the value of t that satisfies the equation \(2^t\) = 10.

(2) \(log_2\sqrt10\): This expression can be rewritten as \(log_2(10^{(1/2)}).\) By applying the property of logarithms, we can rewrite it as \((1/2)log_2(10)\). Since \(2^(1/2)\) is equal to the square root of 2, this expression simplifies to \((1/2)log_2(2^{(5/2)})\), which is equal to (5/4).

(3)\(log_{10}4\): This expression does not involve the base 2, so it is not a valid solution to the equation \(2^t\) = 10.

(4)\(log_{10} 4\): This expression simplifies to log 4, which is not equal to the value of t that satisfies the equation \(2^t\) = 10.

Therefore, the expression that is not a solution to the equation \(2^t\)= 10 is (3)\(log_{10}4.\)

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Question

Which expression is not a solution to the equation 2^t = 10 ?

(1)  2/1 log 2

(2) log_2\sqrt10

(3) log_104

(4) log_10 4

Answer:

3 a 2 − a + 10

Step-by-step explanation:

like and 5 star

Answer:

3a^2-a+10

Step-by-step explanation:

...

Answer:

40

Step-by-step explanation:

Henry will take 2/3 or 20 acres and Mitzi will take 1/3 or 10 acres. Leading to it taking 40 hours.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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Answer: 1 7/16

Step-by-step explanation: If you look at a ruler 1 7/8 is just a little behind 1 7/16 while 1 3/4 is far behind. Also 2 1/8 is past where the green line stops.

Answer:

option 1) 1 7/8"

Step-by-step explanation:

its clearly visible that the green line covers 1 unit completely.

but it stops before it can reach 2 units.

check the attachment

it will be at a distance of 1/ 2 units from the "unit 1".

( since 1 and 2 are 1 unit apart their mid point will lie exactly at rhe center that is 1/ 2 = 0.5)

since the "mid point" is at a distance of 0.5 units from "unit 2", second mid point will be at a distance of (1/ 2)/ 2 = 1/ 4 units from "mid point".

since they're 1/ 4 units apart the third mid point will be (1/ 4)/2 units away from "second mid point"

and this is where the green line stops!

we got these points now well just add them up, to get the distance of required point from unit 1.

1/ 2 + 1/ 4 + 1/ 8

= 7/ 8

and this is in centimeters so add a " after it

1 7/ 8"

that is option 1.

The value the seasonal index (SI) for Q4 is 0.63.

To find the seasonal index (SI) for Q4, the first step is to calculate the average of the ratio-to-moving average for each quarter.

The formula for calculating seasonal index is as follows:

Seasonal Index = Average of Ratio-to-Moving Average for a Quarter / Average of Ratio-to-Moving Average for all Quarters

To find the seasonal index (SI) for Q4:

1: Calculate the average of the ratio-to-moving average for Q4.Q4 average = (0.65 + 0.65) / 2 = 0.65S

2: Calculate the average of the ratio-to-moving average for all quarters.All quarters average = (0.87 + 1.30 + 1.50 + 0.65 + 0.77 + 1.36 + 1.35 + 0.65) / 8 = 1.03

3: Calculate the seasonal index for Q4.Seasonal Index for Q4 = Q4 Average / All Quarters Average= 0.65 / 1.03 = 0.6311 (rounded to 2 decimal places)

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The five values in a summary are the median, the lower and upper quartiles, the maximum and minimum values in the data set. Minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), and maximum value are all listed together in this sequence.

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Answer:

x=80

Step-by-step explanation:

100+x=180

x=180-100

x=80

Answer

this

Step-by-step explanation:

is how

Answer: No.

Step-by-step explanation: It's obviously a quiz of some sort. If it's not, then why would it be timed? Please don't do this :(

When we differentiate the function y = f(x) with respect to x, we obtain dy/dx = 10x - 6. The differential of the function is then expressed as dy = (10x - 6)dx.

Let's go through the steps in more detail:

Start with the equation y = f(x).

To find the differential, we differentiate both sides of the equation with respect to x, which gives us dy/dx on the left side and d/dx (5x^2 - 6x) on the right side.

Applying the power rule of differentiation, the derivative of 5x^2 with respect to x is 10x. The derivative of -6x with respect to x is -6.

Combining these derivatives, we get dy/dx = 10x - 6.

The differential of the function is represented as dy = (10x - 6)dx, where dx represents a small change in the x-value and dy represents the corresponding small change in the y-value.

In summary, when we differentiate the function y = f(x) with respect to x, we obtain dy/dx = 10x - 6. The differential of the function is then expressed as dy = (10x - 6)dx.

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There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Multiplying these values, we get 20x3=60. Therefore, it will take 60 unit cubes to completely fill the rectangular prism.

To find the number of unit cubes required to completely fill the rectangular prism, we need to know the total number of unit cubes that can fit inside the prism. We can determine this by counting the number of unit cubes that can fit in one layer of the prism, and then multiplying it by the number of layers in the prism.

Let's assume that the dimensions of the rectangular prism are length (L), width (W) and height (H), and that it is partially filled with unit cubes. We can count the number of unit cubes in one layer of the prism by multiplying L by W. This gives us the area of the base of the prism, which is the number of unit cubes that can fit in one layer.

Next, we need to count the number of layers in the prism. This is simply the height (H) of the prism. Once we have both these values, we can multiply them to find the total number of unit cubes required to fill the prism.

For example, if the dimensions of the rectangular prism are L=4, W=5 and H=3, and it is partially filled with unit cubes, we can count the number of unit cubes in one layer as 4x5=20. The number of layers in the prism is 3. Multiplying these values, we get 20x3=60. Therefore, it will take 60 unit cubes to completely fill the rectangular prism.

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Answer:

\( \frac{4(5 + 2)}{2} = \frac{20 + 8}{2} = \frac{28}{2} = 14\)

I hope I helped you^_^

The gallons of water that a clydsdale drink in 28 days will be 840 gallons.

It should be noted that Clyde's dale drinks about 120 gallons of every 4 days. Therefore, the gallons Frank in a day will be:

= 120 / 4

= 30 gallons

Therefore, the gallons drank for 28 days will be:

= 30 × 28

= 840 gallons.

Therefore, the gallons of water that a clydsdale drink in 28 days will be 840 gallons.

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Answer:

$14.04

Step-by-step explanation:

-21.46 + 35.50 is the same as

35.50 - 21.46 = $14.04

Answer: 14.04

Step-by-step explanation: -21.46 + 35.50 = 14.04

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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The solution to each of the arithmetic sequence are:

1) a₁₀ = 56

2) a₁₀ = 87

3) missing term is 13

4) missing term is 14

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is nth term

d is common difference

1) a = 2

d = 6

a₁₀ = 2 + (10 - 1)6

a₁₀ = 2 + 54

a₁₀ = 56

2) a = 15

d = 8

a₁₀ = 15 + (10 - 1)8

a₁₀ = 87

3) The missing term will be gotten by finding the common difference.

d = (22 - 4)/2

d = 18/2

d = 9

missing term = 4 + 9 = 13

4) The missing term will be gotten by finding the common difference.

d = (53 - 25)/2

d = 28/2

d = 14

missing term = 4 + 9 = 14

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Answer:

Combine like terms on the left side of equation first

then solve the equation normally

Step-by-step explanation:

Answer:

34523

Step-by-step explanation:

345-23=po

If m∠2 =(3x+2)° and m∠3 = 100° and the angle is linear pairs the value of x will be 26°.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that,

m∠2 =(3x+2)°

m∠3 = 100

If the ∠2 and ∠3 are linear pairs the sum of the angles is 180°.

Only when a pair of neighboring angles add up to 180 degrees is the pair referred to be a linear angle. For instance, the sum of the neighboring linear angles of 40 degrees and 140 degrees will equal 180 degrees, making them known as linear angles.

∠2 + ∠3 = 180°

(3x+2) + 100 = 180°

(3x+2) = 180° - 100

(3x+2) = 80

3x = 80 -2

3x =78

x =26

Thus, if m∠2 =(3x+2)° and m∠3 = 100° and the angle is linear pairs the value of x will be 26°.

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There are 6 values of the displacement of the string at x = 5.0 m at 1 s intervals from t = 0 s to t = 6 s.

All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤x≤ 1.

Given

A snapshot graph at t = 0 s of two waves on a string approaching each other at 1 m/s.

The values of the displacement of the string at x = 5.0 m at 1 s intervals from t = 0 s to t = 6 s are,

At t = 0

s,=>Y₀= 0 cm

At t =1

s,=>Y₁= 0 cm

At t = 2

s,=>Y₂= 0 cm

At t =3

s,=>Y₃= 0 cm

At t =4

=>Y₄= 0 cm

At t = 5 s,

=>Y₅=0 cm

At t = 6

s,=>Y₆= 0 cm

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We will have the following:

*First: We determine the measure of angle L:

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario:

The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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