Does anybody know what 3,600 is as 1 unit less than 4,000???

We can rewrite 3^6 as the product of two whole-number powers of 3 as: [tex]3^4 . 3^2.[/tex]

To rewrite 3^6 as the product of two whole-number powers of 3, we need to find two exponents that add up to 6.

A way to do this is to use the fact that 3^4 = 81, which is close to 3^6.

Specifically, we have:

3^6 = 3^4 * 3^2

We can check that this is true by using the rule for multiplying exponents that states that a^m * a^n = a^(m+n).

Applying this rule, we get:

= 3^4 * 3^2

= 3^(4+2)

= 3^6.

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Okay, let's go through this step-by-step:

1) sin(A) = opposite/adjacent = BC/AB = 18/24 = 3/4

2) cos(A) = adjacent/hypotenuse = AB/AC = 24/30 = 4/5

3) tan(A) = sin(A) / cos(A) = (3/4) / (4/5) = 3/4

4) sec(A) = 1/cos(A) = 1/4/5 = 5/4

5) csc(A) = 1/sin(A) = 1/3/4 = 12/3

In simple terms:

sin(A) = 3/4

cos(A) = 4/5

tan(A) = 3/4

sec(A) = 5/4

csc(A) = 12/3

Let me know if you need more details.

The periodic deposit required to reach the financial goal of $1,000,000 in 45 years with a 6.75% annual interest rate compounded monthly is approximately $541.05.

And,  Amount $292,593.00 comes from deposits and $707,407.00 comes from interest.

For the periodic deposit, we can use the formula:

P = (FV × r) / ((1 + r)ⁿ - 1)

where P is the periodic deposit, FV is the financial goal, r is the interest rate per period, and n is the total number of periods.

Using the given values, we get:

P = ($1,000,000 0.0675) / ((1 + 0.0675/12)^(45x12) - 1)

P ≈ $541.05

So, the periodic deposit required to reach the financial goal of $1,000,000 in 45 years with a 6.75% annual interest rate compounded monthly is approximately $541.05.

And, To determine how much of the financial goal comes from deposits and how much comes from interest, we can calculate the total amount of deposits made over the 45-year period:

Hence, Total deposits is,

P n = $541.05 (45 x 12)

      ≈ $292,593.00

Then we can subtract this amount from the financial goal to get the amount that comes from interest:

Amount from interest = FV - Total deposits

= $1,000,000 - $292,593.00

≈ $707,407.00

So , Amount $292,593.00 comes from deposits and $707,407.00 comes from interest.

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Answer:

Both solutions are valid, and depending on the context of the problem, one or both solutions may be useful in solving for different parameters, such as the maximum height or the time of flight of the projectile.

Step-by-step explanation:

In a projectile motion formula, such as the one that describes the height of an object in motion as a function of time, there are two solutions because the object can reach the same height at two different times during its trajectory.

The negative solution represents the time it takes for the object to reach its maximum height and then start falling back down to the ground. The positive solution represents the time it takes for the object to reach the same height on its way up.

So, both solutions are valid, and depending on the context of the problem, one or both solutions may be useful in solving for different parameters, such as the maximum height or the time of flight of the projectile.

The height of the building , given the shadow that it casts would be 93 meters tall .

Utilizing proportions can be an effective method to tackle this issue. By defining ' h ' as the height of the building responsible for casting a 39.75 meter shadow, we may establish the ensuing proportion :

h / 39. 75 = 3. 2 / 1. 37

Solving for h gives us :

h / 39. 75 = 2. 336

h = 2. 336 x 39. 75

h = 92. 8 56

h = 93 meters tall

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The sample mean for the number of years worked is 12.9, and 35% of the employees in the sample worked for the company for at least 10 years.

To find the sample mean, we need to add up all the years worked and divide by the total number of employees:

8 + 13 + 15 + 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13 = 258

So, the sample mean is 258/20 = 12.9 (rounded to the nearest tenth).

To find the percentage of employees who worked for at least 10 years, we need to count the number of employees who worked for 10 years or more.

From the data, we see that 7 employees worked for at least 10 years (Employee Number: 2, 3, 5, 10, 11, 15, and 19). So, 7 out of 20 employees worked for at least 10 years, which is 35%. Therefore, the answer is 35% (rounded to the nearest integer).

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After 16 minutes of decay, approximately 182.3 grams of the element remains.

To calculate how much of the element remains after 16 minutes of decay, we can use the formula for exponential decay:

A = A₀ * [tex]e^{(-kt)[/tex]

where A is the amount of the element remaining after time t, A₀ is the initial amount of the element, k is the decay constant, and t is the elapsed time.

In this case, we have A₀ = 420 grams, k = 0.118 (since the element decays by 11.8% per minute), and t = 16 minutes. Plugging these values into the formula, we get:

A = 420 * [tex]e^{(-0.118*16)[/tex]

A = 182.3 grams

We round our answer to the nearest 10th of a gram, as requested in the problem.

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question 9.

Based on a cubic modeling equation, the  prediction about this data that is  most reliable is a $70k house would have 1,354 square ft.

Option A is correct.

Question 10.

The second coordinate in a scatterplot of the linearized data and  rounding the answer to the tenth place is 0.8

Option A is correct.

Question 11.

The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168

Option C is correct.

The equation is given as

Log y= 0.75821x+0.03442

We substitute x = 4 into the given equation and solve for y:

log y = 0.75821(4) + 0.03442

log y = 3.07286 + 0.03442

log y = 3.10728

We take the antilogarithm of both sides,

y = 10^(3.10728)

y = 1,168.66

Rounding off, the closest answer is option  (c) 1,168.

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Step-by-step explanation:

See image

The merchant needs to mix 10 pounds of red beans and 10 pounds of black beans to get a mix that costs $3.75 per pound.

We have,

Let's assume that the merchant needs to mix x pounds of red beans and (20 - x) pounds of black beans.

To find the pounds of each variety, we can use the following equation:

= 3.5x + 4(20 - x)

= 3.75(20)

Simplifying the equation.

3.5x + 80 - 4x = 75

-0.5x = -5

x = 10

Therefore,

The merchant needs to mix 10 pounds of red beans and 10 pounds of black beans to get a mix that costs $3.75 per pound.

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The complete question.

A merchant wants to mix red beans that cost $3.5 per pound with black beans that cost $4 per pound to get 20 pounds of a mix that costs $3.75 per pound. How many pounds of each variety should he mix?

The ages of people who can get a driver's license can be represented in three forms as follows;

x ≥ 16

x ≤ 85

16 ≤ x ≤ 85

The ages of people who cannot get a driver's license can be represented in three forms as follows;

x ≤ 16

x ≥ 85

16 ≥ x ≥ 85

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable x denotes the ages of people who wishes to obtain a driver's license, a set of inequality which can be used to represent those who are eligible in three forms include;

x ≥ 16

x ≤ 85

16 ≤ x ≤ 85

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If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross-section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.

What is meant by cross section?

The form we obtain by cutting a straight through an object is called a cross-section.

The shape of the cross section of a cube that is cut into two pieces by a single slice that passes through point A, B, and C depends on the location of these points on the cube.

If points A, B, and C are three nonadjacent vertices of the cube, then the cross section will be a triangle. Specifically, it will be an isosceles triangle with base equal to the length of the edge of the cube and legs equal to the distances between point A and the other two points B and C.

If points A, B, and C are three adjacent vertices of the cube, then the cross section will be a square. Specifically, it will be a square with side length equal to the length of the edge of the cube.

If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.

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It will take Ms. Estrada about 25 hours to complete the mural.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.

In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.

Some common topics in algebra include:

Solving equations and inequalities

Simplifying expressions

Factoring and expanding expressions

Graphing linear and quadratic functions

Using logarithms and exponents

Working with matrices and determinants

First, we need to convert the length of the mural from feet to inches to match the unit of the sections.

20 feet x 12 inches/foot = 240 inches

Then, we need to determine the number of sections in the mural:

240 inches / 8 inches/section = 30 sections

Now, we can find the total time it will take Ms. Estrada to complete the mural:

30 sections x 50 minutes/section = 1500 minutes

Finally, we can convert the time to hours:

1500 minutes / 60 minutes/hour = 25 hours

Therefore, it will take Ms. Estrada about 25 hours to complete the mural.

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The shortest length that rope can be, is 360 cm; such that the rope may be cut into lengths of exactly 18cm long, 30cm long or 40cm long.

A rope is cut into length which may be exactly 18cm long, 30cm long or 40cm long.

The shortest length that rope can be

Considering the individual lengths which are all integers, the shortest length is calculated as the LCM or the Least Common Multiple of the individual lengths that are considered

Factorize the numbers 18, 30 and 40 in the following way.

18 = 2 * 3 * 3

30 = 2* 3 *5

40 = 2* 2* 2* 5

The LCM of  the numbers 18, 30 and 40 is

= 2* 2* 2* 3* 3* 5

= 360

So, the shortest length that rope can be, to make it cut into lengths of exactly 18cm long, 30cm long or 40cm long, is 360 cm.

Therefore, the required shortest length that rope can be, is 360 cm; such that the rope may be cut into lengths of exactly 18cm long, 30cm long or 40cm long.

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this will be the square -

[tex]2 \times \sqrt[5]{4} [/tex]

or 2,63902

The centerline=  459.9

The upper control limit=  852.55.

The lower control limit = 67.25.

We determine the mean to set up the standard limits:

Mean is gotten as :

(465 + 502 + 395 + 488 + 472 + 462 + 524 + 434 + 481 + 386) / 10

mean = 459.9

we then find the Standard Deviation:

Standard Deviation = √variance

variance = ((465-459.9)^2 + (502-459.9)^2 + (395-459.9)^2 + (488-459.9)^2 + (472-459.9)^2 + (462-459.9)^2 + (524-459.9)^2 + (434-459.9)^2 + (481-459.9)^2 + (386-459.9)^2) / 9

variance = 17119.1

Standard Deviation = √(17119.1)

Standard Deviation= 130.88

Hence

Centerline = 459.9

upper control limit  = 459.9 + 3 x (130.88) = 852.55

lower control limit. = 459.9 - 3 x (130.88) = 67.25

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Answer:

Step-by-step explanation:

Given you have collected 70 coins and stamps, and your friend has collected 1/5 as many coins and twice as many stamps, for a total of 95 coins and stamps, you want the numbers of each.

We can let x represent the number of coins you have collected. Then 70 -x is the number of stamps you have collected. The corresponding numbers for your friend are x/5 coins and 2(70-x) stamps. Your friend's collection is ...

  x/5 +2(70 -x) = 95

  -9/5x +140 = 95 . . . . . . . . simplify

  45 = 9/5x . . . . . . . . . . . . . add 9/5x -95

  25 = x . . . . . . . . . . . . . . . . multiply by 5/9

  70 -x = 45

  1/5x = 5

  2(70 -x) = 90

You collect 25 coins and 45 stamps; your friend collects 5 coins and 90 stamps.

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Answer- e^x-1-3

Step-by-step explanation:

Team B has 33 players that weigh more than 200 pounds.

To calculate the percentage, divide the amount by the total value and multiply the result by 100. The percentage is calculated using the formula: (value/total value)100%.

When 80% of the players weigh more than 200 pounds, 20% of the players weigh less than 200 pounds.

We can start by locating 20% of the players:

20% of 41 = 0.20 x 41 = 8.2

So we can guess that there are about 8 players weighing 200 pounds or fewer.

We may subtract this estimate from the total number of participants to obtain the number of players who weigh more than 200 pounds:

41 - 8 = 33

As a result, Team B has 33 players that weigh more than 200 pounds.

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The coordinate of points K, L and M is the location of the points on a coordinate plane

Here, we have,

to determine the missing coordinates:

The given parameters are:

K = (10, )

L = ( ,10)

M = (30, )

The question has missing parameters.

So, I will assume that the line is a perfectly horizontal line.

This means that the y-coordinates of points K, L and M are equal.

The y-coordinate of point L is 10.

So, we have:

K = (10, 10)

L = ( ,10)

M = (30, 10)

Assume that point L is halfway points K and M, then we have:

K = (10, 10)

L = (20, 10)

M = (30, 10)

See attachment for the diagram of the coordinate plane showing the line

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Answer:

4/5

Step-by-step explanation:

2 : 5/2

4/2 : 5/2

4 : 5

The scale factor is:

4/5

Answer:

Step-by-step explanation:

You want to determine the number of solutions to three different systems of equations.

A linear equation is written in standard form when the coefficients are mutually prime, and the leading coefficient is positive:

  ax +by = c . . . . . . GCF(a, b, c) = 1, a > 0

The equations are easiest to compare when they are all written in standard form.

A system will have an infinite number of solutions when the equations are identical.

A system will have zero solutions when it reduces to ...

  (non-zero constant) = 0

A system will have one solution when the equations are different.

A factor of 2 can be removed from the first equation:

  2x -3y = 5

A factor of 3 can be removed from the second equation:

  2x -3y = 5

These equations are identical, so have infinitely many solutions.

Multiplying the first equation by 2 gives ...

  2y = -3x +6

Adding 3x, we have ...

  3x +2y = 6

When we subtract the second equation from this, we get ...

  (3x +2y) -(3x +2y) = (6) -(3)

  0 = 3

These equations have no solution.

These equations are already in standard form, and are different. This system has one solution.

(The exact solution is (x, y) = (0.48, 3.36).)

If the total cost is $39.80, then the number of miles driven is 66 miles.

Here we know that  a truck rental costs $20 plus $0.30 for each mile driven.

Then we can model this with a linear equation where the y-intercept is 20, and the slope is 0.30 (where the independent variable will be the number of miles driven).

Then the total cost is modeled by the linear equation:

y = 20 + 0.3*x

If the total cost is $39.80, then we can solve:

39.8 = 20 + 0.3*x

39.8 - 20 = 0.3*x

19.8/0.3 = x

66  =x

There are 66 miles.

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Answer: see attached image

Step-by-step explanation:

since the distance between each number is split into fourths, that is the interval it is increasing.

5/2 simplified is 2 and 1/2. so you go 2 tick marks after the 2.

-2 and 3/4 goes 3/4 (3 tickmarks) after the -2.

The correct answer is option B. That is the amount of plastic needed for making one plastic cylinder is 57 cm²

A cylinder is a three-dimensional geometric shape that has two congruent circular bases that lie parallel to each other and are connected by a curved surface. It can be thought of as a stack of circles or as a prism with a curved surface. Some common examples of cylinders include soda cans, water bottles, and pipes.

Given that the individual container of bubbles will be a plastic cylindrical tube with a diameter 2 cm and a height of 8 cm.

So radius = diameter/2 = 2/2 = 1 cm.

The surface area of the cylinder = 2πrh + 2πr²

SA = 2π × 1 ×8 + 2π × 1²

SA = 2π + 16π

SA = 18π

Substituting the value of π = [tex]\frac{22}{7}[/tex]

Hence, SA = 18π = 18 × [tex]\frac{22}{7}[/tex] ≈ 56.57

Rounding to the nearest integer, we get:

Answer: B. 57 cm^2.

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a. Using Nearest Neighbor starting in Jerusalem, the value will be 1000km.

b. Using Repeated Nearest Neighbor, the values are attached.

Using Nearest Neighbor starting in Jerusalem, the value will be from A to B to C to D to E to F to A.

This will be:

Total length = 58 + 95 + 35 + 29 + 233 + 241 + 309

= 1000km.

Therefore, Using Nearest Neighbor starting in Jerusalem, the value will be 1000km na using Repeated Nearest Neighbor, the values are attached.

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Answer:

Maliks fruit salad will taste more melony

Step-by-step explanation:

To determine whose fruit salad will taste more "melony," we can calculate the percentage of melon in each fruit salad for Aisha and Malik.

For Aisha's fruit salad:

Total cups of fruit = 4 cups of melon + 1 cup of apple = 5 cups

Percentage of melon = (4 cups of melon / 5 cups of total fruit) x 100%

For Malik's fruit salad:

Total cups of fruit = 13 cups of melon + 3 cups of apple = 16 cups

Percentage of melon = (13 cups of melon / 16 cups of total fruit) x 100%

Now we can calculate the percentages:

Aisha's percentage of melon:

(4 cups of melon / 5 cups of total fruit) x 100% = 80%

Malik's percentage of melon:

(13 cups of melon / 16 cups of total fruit) x 100% ≈ 81.25%

Based on the calculations, Malik's fruit salad has a higher percentage of melon (81.25%) compared to Aisha's fruit salad (80%). Therefore, Malik's fruit salad is likely to taste more "melony" compared to Aisha's fruit salad.

After filling Container B completely, there are approximately 209.56 cubic feet of water left in Container A.

Container A:

Diameter = 14 feet

Radius = Diameter / 2 = 14 / 2 = 7 feet

Height = 11 feet

Volume of Container A = π * (7^2) * 11 ≈ 1,696.46 cubic feet

Container B:

Diameter = 10 feet

Radius = Diameter / 2 = 10 / 2 = 5 feet

Height = 19 feet

The volume of Container B = [tex]π * (5^2) * 19[/tex] ≈ 1,486.90 cubic feet

Now, let's find out how much water is left in Container A after filling Container B completely.

Water left in Container A = Volume of Container A - Volume of Container B

Water left in Container A ≈ 1,696.46 - 1,486.90 ≈ 209.56 cubic feet

So, after filling Container B completely, there are approximately 209.56 cubic feet of water left in Container A.

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Answer:

vertical because they are right across from each with the same degrees