What is the measure of angle ABC?

The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.

The smallest number that has 1, 2, 3, 4, 5 as factors is 60. This number is called the LCM (Least Common Multiple) of the given numbers.The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of these numbers. We can find the LCM of more than two numbers by following the below procedure:Firstly, find the LCM of two numbers.

This will be the smallest number that is a multiple of both these numbers. Then, find the LCM of this number and the third number. This will be the smallest number that is a multiple of all the three numbers. Repeat the same process for other numbers until we have found the LCM of all the given numbers.

Here, the given numbers are 1, 2, 3, 4, and 5.LCM of 1 and 2 is 2.LCM of 2 and 3 is 6.LCM of 6 and 4 is 12.LCM of 12 and 5 is 60.

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Answer:

(-6, 4/3, 7)

Step-by-step explanation:

To solve the system of equations, we can use elimination or substitution. Here, we will use elimination:

First, we can eliminate z by adding the first and third equations:

x - 3y - 5z = 7

6x + 5y - 6z = 85

7x + 2y = 92

Next, we can use the second equation to eliminate z from the second equation:

6y + z = 27

-6z from both sides:

6y = -6z + 27

Divide both sides by 6:

y = -z/6 + 9/2

Now, we can substitute y = -z/6 + 9/2 into the equation 7x + 2y = 92:

7x + 2(-z/6 + 9/2) = 92

7x - z/3 + 9 = 92

7x - z/3 = 83

Multiplying both sides by 3 to eliminate the fraction:

21x - z = 249

We now have two equations:

7x + 2y = 92

21x - z = 249

To eliminate x, we can multiply the first equation by 3 and subtract it from the second equation:

21x - z = 249

- (3 * (7x + 2y = 92))

-----------------------------------------------------------------

-13x - 6z = -215

Solving this equation for z, we get:

-13x - 6z = -215

6z = 13x + 215

z = (13/6)x + 35 + 1/3

Now we can substitute this value of z into one of the equations to solve for y. Let's use the second equation:

6y + z = 27

6y + [(13/6)x + 35 + 1/3] = 27

6y + (13/6)x + 35 + 1/3 - 27 = 0

6y + (13/6)x + 8 + 1/3 = 0

6y + (13/6)x = -25/3

y = (-13/36)x - (25/18)

Finally, we can substitute these values for x, y, and z into one of the original equations to check our work. Let's use the first equation:

x - 3y - 5z = 7

x - 3[(-13/36)x - (25/18)] - 5[(13/6)x + 35 + 1/3] = 7

x + (13/12)x + (25/6) - (65/6)x - 175 - (5/3) = 7

-51x/12 - 215/6 = 7

-17x/4 - 35/2 = 7

-17x/4 = 21/2

x = -6

Substituting this value of x into the expressions we found for y and z, we get:

y = (-13/36)x - (25/18) = (13/6) - (25/18) = 4/3

z = (13/6)x + 35 + 1/3 = -(13/6)*6 + 35 + 1/3 = 7

the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.

The formula to find the recommended amount of mulch for a circular flower bed is:

Mulch = π * r^2 * d

Where r is the radius of the flower bed and d is the desired depth of the mulch.

Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:

Mulch = π * (20 feet)^2 * 0.5 feet

Mulch = π * 400 square feet * 0.5 feet

Mulch = 200π cubic feet

To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:

Mulch ≈ 200 * 3.14

Mulch ≈ 628 cubic feet

Rounding to the nearest tenth, we get:

Mulch ≈ 628.3 cubic feet

Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

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Yes, the figure shown in the xy-coordinate plane is a parallelogram because side OP is parallel to side TS and side OT is parallel to side PS

In order for any quadrilateral to be considered a parallelogram, two pairs of its parallel sides must be equal (congruent). Therefore, we would determine the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For side OP, the slope is given by:

Slope (m) = (b - 0)/(a - 0)

Slope (m) = b/a.

For side TS, the slope is given by:

Slope (m) = (0 - )/(c - (a + c))

Slope (m) = -b/-a = b/a

Therefore, side OP is parallel to side TS.

For side OT, the slope is given by:

Slope (m) = (0 - 0)/(c - 0)

Slope (m) = 0.

For side PS, the slope is given by:

Slope (m) = (b - b)/((a + c) - c)

Slope (m) = 0

In conclusion, the figure shown above is a parallelogram because side OT is parallel to side PS and side OP is parallel to side TS.

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Answer:

95.2 square yards

Step-by-step explanation:

8(3) + 2(1/2)(3)(7.2) + 2(1/2)(8)(6.2)

= 24 + 21.6 + 49.6 = 95.2 square yards

Answer: We have:

(5i√3)² = (5i)²(√3)² = -25(3) = -75

Therefore, the square of 5i√3 is -75.

Step-by-step explanation:

The square of the complex number of 5i√3 is 75.

A complex number is the sum of a real number and an imaginary number.

To find the square of the complex number, 5i√3, we use the following Steps below

Step1: Square the expression

Step 2: use the law of surd to seperate each of the terms in the expression

Note: In complex number notation,

Therefore,

Hence, square of 5i√3 is 75

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The equation of line perpendicular to y=x-5 passing through (-3,9) is y=-x+6.

Two distinct lines intersecting each other at 90 degrees or at a right angle are called perpendicular lines

To find the equation of a line perpendicular to y = x - 5, we need to first determine the slope of the original line. The slope of a line in slope-intercept form (y = mx + b) is the coefficient of x, so in this case, the slope of the original line is 1.

Since we want to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1.

So, the slope of the perpendicular line is -1, and we also know that it passes through the point (-3,9).

We can use the point-slope form of a line to write the equation of the perpendicular line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values we know, we get:

y - 9 = -1(x - (-3))

Simplifying this expression, we get:

y - 9 = -x - 3

Adding 9 to both sides, we get:

y = -x + 6

Therefore, the equation of the line perpendicular to y = x - 5 and passing through the point (-3,9) is:

y = -x + 6

So the answer is option 1: y = -x + 6.

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The total number of ways five of them to sit in a row of chairs under the given condition is equal to 152 ways.

Use the principle of inclusion-exclusion to solve this problem.

Let us first consider the case where Alice sits next to Bob or Carla.

Now, treat Alice, Bob, and Carla as a block, which can be arranged in 3! = 6 ways.

Within this block, Alice can sit in two different positions,

And Bob and Carla can sit in the remaining two positions.

There are 6 x 2 = 12 ways for Alice to sit next to Bob or Carla.

Now,

Let us consider the case where Derek sits next to Eric.

Treat Derek and Eric as a block,

which can be arranged in 2! = 2 ways.

Within this block,

Derek can sit in two different positions,

And Eric can sit in the remaining position.

There are 2 x 2 = 4 ways for Derek to sit next to Eric.

However,

Double-counted the case where Alice sits next to Bob or Carla AND Derek sits next to Eric.

Treat Alice, Bob, Carla, Derek, and Eric as two blocks,

which can be arranged in 2! x 3! = 12 ways.

Within each block,

There are 2 ways to arrange the people.

There are 12 x 2 x 2 = 48 ways for both conditions to be satisfied.

Using the principle of inclusion-exclusion,

The total number of ways for the five of them to sit in a row of chairs under these conditions.

Total

= total number of ways - number of ways Alice sits next to Bob or Carla - number of ways Derek sits next to Eric + number of ways both conditions are satisfied

= 5! - 12 - 4 + 48

= 152

Therefore, there are 152 ways for the five of them to sit in a row of chairs under these conditions.

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2.6 *  10⁻⁶  F  is the capacitance.

What is a capacitor short answer?

A capacitor is a component used in electrical circuits to hold charges. The idea behind how a capacitor functions is that when an earthed conductor is moved close to a conductor, its capacitance increases noticeably.

                                      As a result, a capacitor contains two plates with equal and opposing charges that are spaced apart. Two conductors that are near to one another and are isolated from one another make up a capacitor, a device for storing electrical energy. The parallel-plate capacitor is a straightforward illustration of such a storage device.

We have realtion Q=CV  

where Q is charge ,  C is capacitance and V is voltage.

C=Q/V

C=(2500 *  10⁻⁶)/960

C= 2.6 *  10⁻⁶  F

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Although the statements are not clearly written, the proof that ΔABC ≅EFG is:


AC = EG - Given

BA = FE - Given

BC = FG - Given

∠ABC = ∠EFG - Given

∠BAC = ∠FEG - Given

∠BCA = ∠FGE - Given

Thus, ΔABC ≅EFG  on the bases of the S-S-S Angle postulate or the A-A-A congruence postulate.

The S-S-S Angle Postulate and the A-A-A Congruence Postulate are both mathematical principles used to prove that two triangles are congruent (having the same size and shape).

The S-S-S Angle Postulate states that if two triangles have three sides that are congruent to the corresponding sides of another triangle, then the triangles are congruent.

The A-A-A Congruence Postulate, on the other hand, states that if two triangles have three angles that are congruent to the corresponding angles of another triangle, then the triangles are congruent.

Both of these postulates are fundamental to the study of geometry and are used to prove a wide range of geometric theorems and relationships.

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The ratio of false positives to false negatives in this scenario is 3.5.

3.5 is the correct answer. False positives are lightning detector activations when there is no lightning in the area. False negatives are lightning detector not activations when there is lightning in the area. To calculate the ratio of false positives to false negatives, divide the false positives (7%) by the false negatives (2%). 7/2 = 3.5. Therefore, the ratio of false positives to false negatives in this scenario is 3.5.

The ratio of false positives to false negatives in this scenario is 3.5.

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Answer:

i took the test :)

Step-by-step explanation:

3.5

Answer:

y = 3x + 11

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (- 2, 5 )

m = [tex]\frac{5-2}{-2-(-3)}[/tex] = [tex]\frac{3}{-2+3}[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 2, 5 )

5 = 3(- 2) + c = - 6 + c ( add 6 to both sides )

11 = c

y = 3x + 11 ← equation of line

Answer:the answer would be around 300 or 314

if you have 100ft in a circle and divided the space using the equation it what you get .

Step-by-step explanation:

The remaining credit after 50 minutes of calls is[tex]$19.68[/tex].To calculate the remaining credit after 50 minutes of calls, the linear function is substituted with the given value of 50 for TCT.RC = -0.14 × 50 + 33.68 RC = 19.68

The linear function representing the credit remaining on a phone card (in dollars) with respect to the total calling time (in minutes) is given by:Remaining Credit (RC) = m × Total Calling Time (TCT) + c where m is the gradient and c is the intercept.To solve for the linear function, two points are needed. The two points are:(24, 21.88) and (38, 20.6)Substituting the values into the linear function, the gradient (m) is calculated to be -0.14 and the intercept (c) is calculated to be 33.68.Therefore, the linear function representing the credit remaining on a phone card (in dollars) with respect to the total calling time (in minutes) is:RC = -0.14 × TCT + 33.68.To calculate the remaining credit after 50 minutes of calls, the linear function is substituted with the given value of 50 for TCT.RC = -0.14 × 50 + 33.68 RC = 19.68.Therefore, the remaining credit after 50 minutes of calls is [tex]$19.68.[/tex]

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Step-by-step explanation:

The volume of a rectangular box is given by the formula:

Volume = length x breadth x height

In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:

Volume = a x 2b x 3c

= 6abc

Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.

Answer:

The solution to the equation is -7

Step-by-step explanation:

I hate these kinds of Questions but it all comes down to how you mathematically interpret it.

Answer:

67.466%

Step-by-step explanation:

No. of people aged below 14 years old= 60,094

No. of people aged between 15 and 64 years old= 212,468

No. of people aged above 65 years old= 42,362

Age Dependency Ratio= No. of people aged between 15 and 64 years old

                                          /Total People

                                       = [tex]\frac{212,468}{60,094+212,468+42,362}[/tex] × 100

                                       = [tex]\frac{212,468}{314,924}[/tex] × 100

                                       = 67.466%

∴ the Age Dependency Ratio is 67.466%.

The width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.

Given that:

Area, A(x) = 2x³ + 6x² + 5x + 15

Length, L = x + 3

The formula for the area of a rectangle is:

A = length x width

A(x) = (x + 3) · W

A(x) / (x + 3) = W

W = (2x³ + 6x² + 5x + 15) / (x + 3)

W = [2x²(x + 3) + 5x(x + 3)] / (x + 3)

W = [(2x² + 5)(x + 3)] / (x + 3)

W = 2x² + 5

Therefore, the width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.

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Answer:

70 stamps are from North America

Step-by-step explanation:

All I did was add the percentages together

35+20+10= 65

I then took 65% of 200 to get 70.

Answer:37c − 32d

2:7p+3w

Step-by-step explanation:

Answer:

1. c - 5d

2. 7p + 3w

Step-by-step explanation:

1.)

5c - 8d - 4c + 3d =

5c + -8d +-4c + 3d

Combine like terms:

(5c + -4c) +(-8d + 3d) =

c - 5d

2.)

6p - 2w + p + 5w =

6p + -2w + p + 5w

Combine like terms:

(6p + p) + (-2w + 5w) =

7p + 3w

Answer:

arc length ≈ 29.32 mm

Step-by-step explanation:

arc length is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{80}{360}[/tex]

     = 2π × 21 × [tex]\frac{8}{36}[/tex]

    = 42π × [tex]\frac{2}{9}[/tex]

   = [tex]\frac{42\pi (2)}{9}[/tex]

   ≈ 29.32 mm ( to the nearest hundredth )

Answer:

We can use the continuous compound interest formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), and t is the time (in years). We can rearrange this formula to solve for t:

t = ln(A/P) / r

where ln is the natural logarithm function.

Using the given values, we have:

P = 920

A = 2310

r = 0.047

So,

t = ln(2310/920) / 0.047

t ≈ 18.8 years

Rounding to the nearest year, it would take about 19 years for the value of the account to reach $2310.

Answer:

19 years

Step-by-step explanation:

The cost of 5 tables and 6 chairs would be Rs. 1200.

Let the cost of one table be x and the cost of one chair be y.

From the given information, we have the following two equations:

2x + 3y = 3200 ... equation (1)

4x + 10y = 3200 ... equation (2)

To solve for x and y, we can multiply equation (1) by 2 and subtract it from equation (2) to eliminate x:

4x + 10y = 3200

(4x + 6y = 6400)

4y = -3200

Solving for y, we get:

y = -800

Substituting y = -800 into equation (1), we get:

2x + 3(-800) = 3200

Simplifying and solving for x, we get:

2x - 2400 = 0

2x = 2400

x = 1200

Therefore, the cost of one table is Rs. 1200, and the cost of one chair is Rs. -800 (which means the cost of one chair is Rs. 800 with a negative sign indicating a decrease from the original cost of Rs. 1200).

To find the cost of 5 tables and 6 chairs, we can simply multiply the cost of one table by 5 and the cost of one chair by 6 and add them:

Cost of 5 tables = 5 * Rs. 1200 = Rs. 6000

Cost of 6 chairs = 6 * Rs. (-800) = Rs. -4800 (or Rs. 4800 with a negative sign indicating a decrease from the original cost of Rs. 800)

Total cost = Rs. 6000 + Rs. (-4800) = Rs. 1200

Therefore, the cost of 5 tables and 6 chairs is Rs. 1200.

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Answer:

2x

Step-by-step explanation:

it is x+x or 2x, since if x>=0, the absolute value of x is just x, then we can say that it is x+x without the absolute value symbols. :)

Answer:

1) 3rd one down   1  7/12 ( the one you've selected well doneee)

2)pretty sure its also the 3rd one down ( don't come for me if its wrong)

Step-by-step explanation:

4 1/6 = 25/6

5  3/4= 23/4

25/6   x4=    100/24

23/4  x 6 = 138/24

138/24  - 100/24  = 38/24

divide by 2:

19/12= 1   7/12

You will pay $2.90 in sales tax in California for a pair of jeans that costs $40.

At the time of sale, a tax known as sales tax is applied to the cost of products or services. The state, county, or city where the transaction occurs determines the tax rate, which is often expressed as a percentage of the purchase price. The vendor is responsible for collecting sales tax and remitting it to the relevant government body. Sales taxes are levied in order to raise money for the government and pay for essential services like infrastructure, healthcare, and education. Because it is based on the quantity of goods or services consumed rather than income or wealth, sales tax is a sort of consumption tax.

Given that, sales tax in California is 7.25%.

Thus,

Sales tax = price of jeans x sales tax rate

Sales tax = $40 x 0.0725

Sales tax = $2.90

Therefore, you will pay $2.90 in sales tax in California for a pair of jeans that costs $40.

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Answer:

Here is an ad campaign to promote Ray and Kelsey's roller coaster

Step-by-step explanation:

(Opening shot of the roller coaster with screaming riders)

Voiceover: "Get ready for the ride of your life!"

(Cut to Ray and Kelsey, standing in front of the roller coaster)

Ray: "Hey, I'm Ray, and this is Kelsey. We're the creators of the most thrilling roller coaster in town."

Kelsey: "Our coaster is packed with twists, turns, and loops that will leave you screaming for more!"

Ray: "Come on down to the amusement park and experience the thrill for yourself."

Kelsey: "Our coaster is perfect for adrenaline junkies who love a good rush!"

(Cut back to the roller coaster with more screaming riders)

Voiceover: "Don't miss out on the ride of a lifetime. Come ride Ray and Kelsey's roller coaster today!"

(Optional closing shot of the roller coaster with a tagline: "Are you brave enough?")

If preparing an interview or report, here is a script.

Interviewer: "So, Ray and Kelsey, tell us about your new roller coaster."

Ray: "Well, it's the most thrilling coaster in town. We wanted to create a ride that would really get people's hearts racing."

Kelsey: "Our coaster has twists, turns, and loops that will leave riders screaming for more. It's perfect for anyone who loves a good adrenaline rush."

Interviewer: "What inspired you to create this coaster?"

Ray: "We both love roller coasters, and we wanted to create something that would be just as exciting as our favorite rides."

Kelsey: "We spent months designing and testing the coaster to make sure it was the best it could be."

Interviewer: "What can riders expect when they ride your coaster?"

Ray: "They can expect a thrilling ride that will leave them breathless."

Kelsey: "Our coaster is perfect for anyone who loves a good rush. We can't wait for everyone to experience it for themselves."

The completed chart for a one-time investment made in the amount of $9,200 is attached below.

For Annually compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.06)¹⁵

A = $9,200 (1.06)¹⁵

A = $22,048.34

For Semi-Annually compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.03)³⁰

A = $9,200 (1.03)³⁰

A = $21,214.29

For Quarterly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.015)⁶⁰

A = $9,200 (1.015)⁶⁰

A = $20,947.34

For Monthly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.005)¹⁸⁰

A = $9,200 (1.005)¹⁸⁰

A = $20,812.09

For Weekly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.0012)⁷⁸⁰

A = $9,200 (1.0012)⁷⁸⁰

A = $20,756.54

For Daily compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.0002)⁵⁴⁷⁵

A = $9,200 (1.0002)⁵⁴⁷⁵

A = $20,726.55

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Image transcribed:

1. Fill in the chart for the following investment.

A one-time investment is made in the amount of $9,200 for 15 years at an APR of 6%.

Compound Interest: A = P (1 + i)", where A is the final amount, P is the principal invested, i is the interest rate per compounding period, and n is the number of compounding periods.