Find the next number in the 4; 2; 1; 2 ....... ​

Torque is the cross product of the distance from the pivot point to the force, denoted by r, and the force applied, denoted by F. τ= r×F, where r is the moment arm, and F is the force. The direction of torque is either clockwise or counterclockwise depending on whether the force causes rotation that is clockwise.

Also, it is denoted by a positive sign for a counterclockwise torque and a negative sign for a clockwise torque.Let's assume that the vector F, acting on a rigid body about pivot point P, creates a moment, i.e., torque. The torque about P is determined by the product of the force magnitude, F, and the perpendicular distance, rm, from point P to the line of action of F.

 That is, τ=rm ×F. If F and rm are known, we may substitute them into the equation to obtain the torque in the direction of rotation.τ = rm × Fsin(θ) where θ is the angle between the two vectors F and rm.Therefore, the torque about P due to F is expressed in terms of rm and F or in terms of r, θ, and F as τ=rm ×Fsin(θ) or τ = rFsin(θ), respectively.

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First, you know that Jackson (let call her J) scored 42 more points than L (Leslie).  What we don't know is how many points L scored so we can use a variable that will be 'x'.

So the equation will be J=42+x.

We also know that the total points is 1,144.

To find out what x is we first subtract 1,144-42.  We then get 1,102.

We are now left with 2x and 1,102 so we divide 1,102 by 2 and get 551.

551=x so now we can plug that in.

J = 551 + 42

Jackson scored 593 points and Leslie scored 551 points

(You can use bar modeling to do solve this problem.  An example of bar modeling is shown below.  

The peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

To model the roof line of Terry's house, we can use the concept of absolute value. The equation for an absolute value function can be written as:

y = |x - h| + k

where (h, k) represents the vertex of the absolute value graph.

In this case, the peak of the roof line is at 24 feet. Since the width of the house is 32 feet, the vertex of the absolute value graph will be at the midpoint of the width, which is 16 feet. Therefore, h = 16.

Since the peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

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Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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Answer:

yes that is

Step-by-step explanation:

Answer:

11 weekends.

Step-by-step explanation:

470.80 = 58.30 + 37.50x

-58.30    -58.30

412.50 = 37.50x

divide both sides by 37.50, and x = 11

Step-by-step explanation:

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The volume of the cone made by rotating this triangle is  5303.57

As isosceles triangle has a base of 15 ft and an altitude of 30 ft

We need to find the volume of the cone made by rotating this triangle

If we rotate

we get a cone of radius of 15/2 = 7.5

we get a cone of height of 30

The area of cone takes up on a three-dimensional plane is known as its volume. A cone's base is round, hence it is formed of a radius and a diameter. The highest point of the cone, which is naturally at the bottom when it comes to ice cream, may then be reached from the center of the base. This point is where the height of the cone is determined.

Volume of the cone is given by the formula πr²h

= 3.14 x (7.5)² x 30

= 5303.57

Therefore, the volume of the cone made by rotating this triangle is  5303.57

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Answer:

y=3x^2+34

3x+y-10=0

Step-by-step explanation:

Rounding off the answer to the nearest dollar, the amount in the account at the end of 10 years is $377,453.

Given that money is transferred continuously into an account at the constant rate of $230,000 per year, and the account earns interest at the annual rate of 3.7% compounded continuously.

We are to find how much will be in the account at the end of 10 years.

To solve this question, we can use the formula for continuous compound interest, which is given as;

A = Pert,

where

A = the balance in the account at the end of the investment period

P = the principal amount (the initial amount invested)

exp = is Euler’s constant ≈ 2.71828

r = the annual interest rate expressed as a decimal

t = the time the money is invested

Using the formula above to solve the question;

P = $230,000r = 0.037

t = 10 years

A = Pert

A = $230000 * e(0.037*10)A = $377,453.06

Rounding off the answer to the nearest dollar, the amount in the account at the end of 10 years is $377,453.

$377,453

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On solving the provided question, we can say that permutation will = 1/2(26) = 13 ways

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

here,

by permutation,

1 through 26

permutation will = 1/2(26) = 13 ways

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The given order of integration is dx first, then dy, and finally dz. To change the order of integration to dz first, then dx, and finally dy, we need to identify the new limits of integration. We can do this by using the given limits of integration and setting up the new integrals. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by looking at the given limits of integration and setting up the new integrals. First, we need to integrate with respect to z, so we set the limits of integration for z from 0 to 1 - 2x.

Next, we integrate with respect to x, so we set the limits of integration for x from 0 to 2y. Finally, we integrate with respect to y, so we set the limits of integration for y from 0 to 1/4.

Putting it all together, we get the equivalent integral with the new order of integration: ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by setting up the new integrals based on the given limits of integration. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

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Answer: 1/10

Step by step explanation:

Hattie's strategy of thinking that her probability of getting the marble increases as the volume of the cake decreases does not make sense.

Hattie's strategy is based on a flawed assumption. In the context of randomly choosing a slice with a hidden marble, the probability of Hattie getting the marble does not change as the volume of the cake decreases.

The distribution of marbles within the cake is fixed regardless of its size. Each slice has an equal chance of containing the marble, irrespective of the remaining volume of the cake.

To illustrate this, consider a simplified scenario with two slices. Initially, the cake is whole, and the probability of Hattie getting the marble is 1/2.

If Hattie chooses the first slice without the marble, the remaining volume decreases, but the probability of the second slice containing the marble remains 1/2.

The volume of the cake does not affect the marble's location or the equal probabilities associated with each slice.

Therefore, Hattie's strategy of thinking her probability increases as the volume of the cake decreases is not rational and does not align with the principles of probability.

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Answer:

3x-y) (2x+5y) b. 12z3-6z²+18z. 6z(2z²-z+3) d. 612-1-2. (3+-2)(2++1) f. 6x²-17x+10 ... 5x²-15x+2= x²+10x-4. 4x²-25x+6=0. (4x-1)(x-6)=0 x= = x=6 x={=,65. 2.

Step-by-step explanation:

thats awnser ...

Parallel lines are lines which are equidistant to each other long every point on both lines.

A line is said to be perpendicular if it crosses another line at exactly 90°. Hence, as depicted in the image attached, TZ is perpendicular to RS.

It is important to note that perpendicular lines always bisect one another and that the slopes of lines that are perpendicular are negative of each other and reciprocals.

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To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.

By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.

Therefore, the optimal assignment would be:

- Person 4 for Job 1 (16 hours)

- Person 2 for Job 2 (18 hours)

- Person 1 for Job 3 (25 hours)

- Person 4 for Job 4 (14 hours)

This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.

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Answer:

7/10 or 0.7 or 70% left.

Step-by-step explanation:

Since he gives 1/5 of the cake to Sali, he gave 1/5 * 30 = 6 cakes away to Sali. Since 10% is 1/10, he gave away 1/10 * 30 = 3 cakes away to Jane. He has a total of 30 - 3 - 6 = 21 cakes left. 21/30 = 7/10, or 0.7, or 70% left.

Answer: 21/30

Explanation this is because 1/5of 30 is 6 and 10 percent of 30 is 3

6+3=9

30-9=21

Therefore Simon has 21/30 cakes left

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Answer:

For all numbers b and c such that the product of c and 3 is b which of the following expression represents the sum of c and 3 in terms of b??A) ...

1 answer

·

13 votes:

Hope this will be helpful to you.If really then mark it as brainleist.......

Step-by-step explanation:

If Lisa spends her income on veggie burgers and pints of soy milk and the price of veggie burgers is three times the price of a pint of soy milk, then when Lisa maximizes her utility she will buy both goods until the marginal utility of veggie burgers is three times the marginal utility of soy milk.

Therefore, if Lisa spends her income on veggie burgers and pints of soy milk and the price of veggie burgers is three times the price of a pint of soy milk, then when Lisa maximizes her utility she will buy both goods until the marginal utility of veggie burgers is three times the marginal utility of soy milk.

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It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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The economic order quantity (EOQ) is a formula used in inventory management to determine the optimal order quantity that minimizes the total cost of inventory. The formula for EOQ is: EOQ = √((2 * Demand * Ordering Cost) / Holding Cost) In this case, the demand is 6,000 units per year, the ordering cost is $100, and the holding cost is $5 per unit.

Plugging in these values into the formula, we get:

EOQ = √((2 * 6000 * 100) / 5)

Simplifying the expression inside the square root:

EOQ = √(2 * 6000 * 100 / 5)

Calculating the numerator:

EOQ = √(1,200,000)

Taking the square root:

EOQ ≈ 1,095.45

Therefore, the economic order quantity (EOQ) is approximately 1,095 units.

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Option A is correct, the experimental probability of not selecting a diamond is 82.5%.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of cards drawn is 40, and the frequency of diamonds drawn is 7.

This means that the frequency of not selecting a diamond is:

40 - 7 = 33

So the experimental probability of not selecting a diamond is:

P(not diamond) = frequency of not selecting a diamond / total number of cards drawn

P(not diamond) = 33/40

P(not diamond) = 0.825

P(not diamond) = 82.5%

Therefore, the experimental probability of not selecting a diamond is 82.5%.

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All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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Janet can customize a car in 630 different ways.

To determine the number of ways Janet can customize a car, we need to multiply the number of options for each customization choice.

Number of car models: 10

Number of exterior colors: 7

Number of interior colors: 9

To calculate the total number of ways, we multiply these numbers together:

Total number of ways = Number of car models × Number of exterior colors × Number of interior colors

= 10 × 7 × 9

= 630

Therefore, the explanation shows that Janet has a total of 630 options or ways to customize her car, considering the available choices for car models, exterior colors, and interior colors.

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The Laplace transform of the given differential equation is: s^2 Y(s) - s y(0) - y'(0) - 15 (s Y(s) - y(0)) + 56 Y(s) = e^(-s)/s * e^(s).

Substituting y(0) = 0 and y'(0) = 1, and simplifying, we get:

Y(s) = (s + 1) / (s - 7) * e^(-s) / s * e^(s - 1)

Using partial fraction decomposition and inverse Laplace transform, we get: y(t) = 9t e^6t - e^t + u(t - 1) * (1/7 * e^(7t - 7) - 1/7 * e^(6t - 6))

In summary, we used the Laplace transform to solve the given initial-value problem of a second-order differential equation with a unit step function on the right-hand side.

The Laplace transform was used to convert the differential equation into an algebraic equation, which was then solved using partial fraction decomposition and inverse Laplace transform to obtain the solution in terms of the given initial conditions and the unit step function.

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Answer:

8h+12=E

h: hours worked

E: total Earnings

The value of x is 93.

What is the exterior angles property of a quadrilateral?

The total of a quadrilateral's outside angles is 360°. Since all convex polygons share this property, their total exterior angles will always add up to 360 degrees.

In the given figure,

The sum of all outside angles=360°

x-11+x+10+31+2x-42=360

4x-12=360

4x=360+12=372

x=372/4 =93

So, the value of x is 93.

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