Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.

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).)

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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To calculate the gross profit, we need to subtract the cost of goods sold (COGS) from the revenue generated by sales. The revenue generated by sales can be found by multiplying the number of printers sold by the selling price of each printer, which is $1,750.

Revenue generated by sales = 26 x $1,750 = $45,500

The cost of goods sold for each printer is $975, so the total cost of goods sold for all 26 printers is:

Total cost of goods sold = 26 x $975 = $25,350

Therefore, the gross profit can be calculated as:

Gross profit = Revenue generated by sales - Total cost of goods sold

Gross profit = $45,500 - $25,350

Gross profit = $20,150

The gross profit is $20,150.

To calculate the net income, we need to subtract all operating expenses from the gross profit. The operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month).

Total operating expenses = $3,000 + $50 + $550

Total operating expenses = $3,600

Therefore, the net income can be calculated as:

Net income = Gross profit - Total operating expenses

Net income = $20,150 - $3,600

Net income = $16,550

The net income is $16,550.

In summary, the gross profit is the revenue generated by sales minus the cost of goods sold, which in this case is $20,150. The net income is the gross profit minus all operating expenses, which in this case is $16,550.

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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?

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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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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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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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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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.

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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An equation to match the graph include the following: f(x) = |x - 1| - 1.

In Mathematics and Geometry, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x) = |x|, g(x) would be created by translating f(x) the parent function one units to the right and one units downward as follows;

f(x) = |x|

g(x) = |x - 1| - 1

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The logarithm of 6.373log4.948/sqrt(0.004636) is approximately 2.2022

Logarithm is the inverse operation of exponentiation. It is a function that tells you what power you need to raise a given base to in order to get a certain value.

The logarithm of a number x with respect to  base a is denoted as logₐ(x).

For example, if we have a base of 2 and a value of 8, we can write:

log₂(8) = 3

Going back to our question, we can apply the basic knowledge of logarithm to solve the question.

First, simplify the expression:

6.373log4.948/sqrt(0.004636)

= 6.373 * log(4.948) / sqrt(0.004636)

= 6.373 * 1.6941 / 0.068

= 159.50

Now, we can find the logarithm of 159.50.

log(159.50) ≈ 2.2022

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this will be the square -

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

or 2,63902

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 probabilities are given as follows:

4. A. 1/2.

5. B. 3/7.

6. C. 3/13.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

For item 4, we have that out of 30 trials, an Alaskan Malamute won 15 times, hence the probability is given as follows:

p = 15/30

p = 1/2.

For item 5, we have that out of 42 trials, a Siberian Husky was chosen 18 times, hence the probability is given as follows:

p = 18/42

p = 3/7.

For item 6, we have that out of 52 cards in a deck, 12 are pictures, hence the probability is given as follows:

p = 12/52

p = 3/13.

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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.

Answer:

1 = y^2 - 2

y^2 = 3, so y = -√3

Answer:

60.5 m

Step-by-step explanation:

We can use the arc length formula to calculate the length of highlighted arc. Let the numerical measure of the highlighted arc be known as C, the angle measure be known as [tex]\theta[/tex], and r as the radius of the circle.

Given variables:

Plug in all the variables into the formula and solve for the letter C.

[tex]\boxed{\text{Formula: C = }{2\pi r\huge{\text(}\frac{\theta}{360}\huge\text{)}}}[/tex]

[tex]\implies C = }{2\pi (11)\huge{\text(}\dfrac{315}{360}\huge\text{)}}}[/tex]   [tex]\implies C = }{22\pi \huge{\text(}\dfrac{315}{360}\huge\text{)}}} = 60.5 \ \text{m}[/tex]

Therefore, Option A is the correct option.

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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The zeros of the function f(x) = (-x - 2)(-2x - 3) are x = -2 and x = -3/2, listed from least to greatest.

Given the function in the question:

f(x) = ( -x - 2 )( -2x - 3 )

To determine the zeros of the function f(x), we need to solve the equation f(x) = 0.

f(x) = ( -x - 2 )( -2x - 3 )

0 = ( -x - 2 )( -2x - 3 )

( -x - 2 )( -2x - 3 ) = 0

We can set each factor equal to zero and solve for x:

( -x - 2 ) = 0

-x - 2 = 0

-x = 2

x = -2

( -2x - 3 ) = 0

-2x - 3 = 0

-2x = 3

x = -3/2

Therefore, the zeros are x = -2 and x = -3/2.

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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 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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Answer- e^x-1-3

Step-by-step explanation:

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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Answer:

4/5

Step-by-step explanation:

2 : 5/2

4/2 : 5/2

4 : 5

The scale factor is:

4/5

The graph that represents the equation is:

The graph shows an upward parabola with vertex (2, -6) and passes through (-1, 7), (0, 0), (4, 0), and (5, 7).

Option B is the correct answer.

We have,

The equation y = (3/2)x² - 6x represents an upward parabola since the coefficient of x² is positive.

Now,

The vertex of the parabola.

x = -b/2a,

where a and b are the coefficients of x² and x, respectively.

So,

a = 3/2 and b = -6

x = -(-6)/(2(3/2)) = 6/3 = 2.

Plugging x = 2 into the equation,

We get y = 3/2(2)² - 6(2) = -6,

so the vertex is (2, -6).

We can eliminate options A and C since their vertices are not (2, -6).

Now,

To check which of the remaining options fits the equation, we can plug in the given points and see if they satisfy the equation.

Option B gives:

When x = -1, y = 3/2(-1)² - 6(-1) = 7

When x = 0, y = 3/2(0)² - 6(0) = 0

When x = 4, y = 3/2(4)² - 6(4) = 0

When x = 5, y = 3/2(5)² - 6(5) = 7.5

So option B fits the equation, and is the graph that represents

y = (3/2)x² - 6x.

Therefore,

The graph that represents the equation is:

The graph shows an upward parabola with vertex (2, -6) and passes through (-1, 7), (0, 0), (4, 0), and (5, 7).

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The function that would match the graph shown below is given as follows:

y = -5(x³ + 7x² + 8x - 16).

The function is defined using the Factor Theorem, as we have the x-intercepts of the graph, hence we can write the function as a product of it's linear factors.

Considering the x-intercepts, the roots are given as follows:

Hence, considering the leading coefficient a, the function is defined as follows:

y = a(x + 4)²(x - 1)

y = a(x² + 8x + 16)(x - 1)

y = a(x³ + 7x² + 8x - 16).

When x = 0, y = 80, hence the leading coefficient a is obtained as follows:

-16a = 80

a = -5.

Hence the function is:

y = -5(x³ + 7x² + 8x - 16).

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