a rectangular table top is three times as it is wide. it's width is 2 meters. what is the area of the table top

Answer:

y = 3(2)^x

Step-by-step explanation:

If we look at the x and y values, we see that the xs' increase by 1 each time, while the ys' double (12*2 = 24, 24 *2 = 48 etc.).

Because the value doubles each time, we know that this is an exponential equation, and the base (b) is 2.

The general form (as shown) is y = a(b)^x, where a is the initial value (y-intercept or value of y when x = 0) and b is the base.

We can find a by plugging in one x and y coordinate and 2.

For example, we can use (1, 6) to solve for a:

[tex]y=a(b)^x\\6=a(2)^1\\6=a(2)\\3=a[/tex]

Answer:

Step-by-step explanation:

Distribute.

4xb and 4x-0.17b

C. 4b - 0.68b

The expressions are not equal and the explanation is wrong because the index forms have different exponential values.

The correct answer is  14^-1/3

Equivalent expressions are known as expressions that are the same solution but differ in the mode of their arrangement.

From the information given, we have the index forms;

(14^0/14^3)^1/3=14^-2/3

It is important to note that exponents with zero equals 1.

Then, we have that;

1/14^1/3 = 14 ^-2/3

Take the inverse of the exponent

14^-1/3 is not equal to 14^-2/3

Hence, the correct answer is 14^-1/3

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The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

Let x(t) and y(t) be the solution of the linear system of differential equations:

[tex]$\frac{dx}{dt} = ax + by$[/tex]

[tex]$\frac{dy}{dt} = cx + dy$[/tex]

with initial conditions x(0)=5 and y(0)=3.

The general solution of the system of differential equations can be written as:

[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]

where X0 = 5 and Y0 = 3.

Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:

[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]

[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]

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The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.

One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.

In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.

To start, we'll find a common denominator for all the terms in the expression.

The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.

Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.

96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.

Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.

So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.

Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.

The final equivalent expression is

=> 104/120a + 107/120b + 15/120 - 90/120

=> (104 + 107 + 15 - 90)/120a + (107/120)b

=> 136/120a + 107/120b.

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Answer: -2

Step-by-step explanation: use the slope formula.

The wing span of the 1:40 model Phantom II is 18.31 inches.

A unit conversion is a conversion with different units of measurements of same quantity. It is a process with multiple steps that involves multiplication or division by particular factor.

Wingspan of real Phantom II =465''(in millimeter)

1 inch = 2.54 cm⇒25.4 mm.

465''=[tex]\frac{465}{25.4}[/tex]

       = 18.31 inches.

Hence, wingspan of the model 1:40 model Phantom II in inches is 18.31.

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The expression to find the total number of stickers bought by Mark is x = 9s.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The number of sheets of stickers Mark bought is denoted by the variable = s.

The number of stickers on each sheet is = 9

Let the total number of stickers be x.

Use the arithmetic operation of multiplication.

Then the expression will be -

Total number of stickers = Number of sheets of stickers × Number of stickers on each sheet

Substitute the values into equation -

x = s × 9

x = 9s

Therefore, the expression is obtained as x = 9s

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The correct answer is:

Function f is translated to the right 7 units.

Function f is translated down 4 units

Step-by-step explanation:

Volume.

[tex]v = lwh[/tex]

[tex]l = 20 \: w = 18 \: h = 0.5[/tex]

We just multiply these three numbers.

[tex](20)(18)(.5) = 180[/tex]

[tex]180 {ft}^{3} [/tex]

The solution of the given problem of triangle comes out to be tan ∠A = 0.25.

Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners.

Here,

Since △ABC is a right triangle with m∠C = 90°, we know that m∠A + m∠B = 90°.

Using the fact that tan ∠B = opposite/adjacent, we can set up a ratio using a common factor, x, for the opposite and adjacent sides of ∠B:

tan ∠B = 0.25 = opposite/adjacent = x/4x

Simplifying the right side, we get:

0.25 = x/4x = 1/4

Multiplying both sides by 4x, we get:

x = 4

So the opposite side of ∠B has length x = 4, and the adjacent side has length 4x = 16.

Using the Pythagorean theorem, we can find the length of the hypotenuse of △ABC:

c² = a² + b²

c² = 4²+ 16²

c² = 256

c = √256

c = 16

Now, we can use the fact that tan ∠A = opposite/adjacent to find tan ∠A:

tan ∠A = opposite/hypotenuse = 4/16 = 1/4

Therefore, tan ∠A = 0.25.

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The given information states that the machine produces good pieces with a probability of 0.96, which means that there is a 0.04 probability of getting a bad piece.

To calculate the probability of getting two bad pieces in a row, we multiply the probabilities of each individual bad piece:

0.04 * 0.04 = 0.0016

So the chances of getting two bad pieces are 0.0016, or 0.16%. This means that out of 100 tries, you would expect to get two bad pieces in a row 0.16 times.

It's vital to remember that independent events, like obtaining two terrible pieces, have probabilities that are determined by multiplying the individual possibilities.

This is based on the idea of the multiplication rule of probability, which states that the likelihood of two unrelated events occurring simultaneously is the sum of the probabilities of each event occurring separately.

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Time is 9:42 a.m. when they meet will at the starting point again.

We have, Cheko and Sharko started running at the same time and starting point. The shape of ground or stadium is circular. Time taken by Cheko to complete the one round of stadium

= 7 minutes

Time taken by Sharko to complete the one round of stadium = 6 minutes.

At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM ( 7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are the following, 7 = 1×7

=> 6 = 2× 3 × 1

So, LCM (6,7 ) = 2×3×7×1 = 42 minutes

Thus, the again starting time = 9:00 a.m. + 42 minutes = 9: 42 a.m.

Hence, the required time is 9: 42 a.m.

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Step-by-step explanation:

what is the question ?

without an actual question I can only "daydream" things about this information.

EB is the diameter, FB is therefore the radius.

since FB = 3 units, EB = 2×FB = 2×3 = 6 units.

the arc angle AB = 120°.

if you need to express the angle in radians, remember :

360° (the full circle) = 2pi

120° = 360/3 = 2pi/3

the arc angle AE is the supplementary angle to AB (both together have 180° or 2pi/2 = pi).

180 = AB + AE = 120 + AE

AE = 180 - 120 = 60°

60° = 360/6 = 2pi/6 = pi/3

the arc angle BC = 45°.

45° = 360/8 = 2pi/8 = pi/4

the arc angle CD = 30°

30° = 360/12 = 2pi/12 = pi/6

the arc angle ED is the supplementary angle to BC and CD.

180 = ED + BC + CD = ED + 45 + 30 = ED + 75

ED = 180 - 75 = 105°

105° = pi - pi/4 - pi/6 = 12pi/12 - 3pi/12 - 2pi/12 = 7pi/12

the sum of

AB + BC + CD = 2pi/3 + pi/4 + pi/6 =

= 4×2pi/12 + 3pi/12 + 2pi/12 =

= 8pi/12 + 3pi/12 + 2pi/12 = 13pi/12

so, nothing fits to any of your answers.

again, I am not sure what problem you need to solve here.

maybe you can build your answer out of the various pieces I gave you here.

Answer:

10²

Step-by-step explanation:

assume you typed 10.4 million

so 10³/10.4 ≈ 10²

So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).

In geometry, a shape's perimeter is sometimes referred to as its total length. By adding up the lengths of all of an object's sides and borders, one can determine the circumference of something such as a form. The perimeter of a form can be calculated by adding up all of the edges' lengths. For instance, a rectangular with dimensions of 24 yards long as well as 15 yards wide will have a 78 yard perimeter.

Here,

To find the perimeter of the octagon, we need to determine the length of each side of the octagon.

First, let's find the length of the diagonal of the smaller square. We can use the Pythagorean theorem:

d²=4² + 4²=

d² = 16+16 =32

d = √32

=> d = 4√2

​

This diagonal of the smaller square is also the side length of the overlapping square.

Next, let's find the length of one of the sides of the larger square that overlaps with the smaller square. Since the length of the larger square is 6cm, the side length of the overlapping region (part of the larger square that overlaps with the smaller square) is:

6 - 4√2

Finally, the length of one of the sides of the octagon is the sum of the side lengths of the two squares that overlap, minus the side length of the overlapping square (since this side is counted twice):

=> 6 + 6 - 4√2 - 4√2 - (6 - 4√2)

Therefore, the perimeter of the octagon is:

=>8 (12 - 6√2) = 96 - 48√2

So the perimeter of the octagon is approximately 45.25 centimeters (rounded to two decimal places).

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Answer:

  gh280,854

Step-by-step explanation:

You want the total income after 3 and half years of a man and a woman who receive a monthly salary of gh3725 and gh2962 respectively.

You can add up the income from each of the months for each of them, or you can use multiplication to simplify the problem.

The total income each month is ...

  gh3725 +gh2962 = gh6687

The total received in 42 months is ...

  42 × gh6687 = gh280,854

Their total income after 3 1/2 years is gh280,854.

__

Additional comment

There are 12 months in a year, so ...

  3×12 +1/2×12 = 36 +6 = 42

months in 3 1/2 years.

Answer:

6

Step-by-step explanation:

The number completes the sequence is 6

Answer:

Doris and Miguel will have the same amount after 6 weeks.

Step-by-step explanation:

if 6 is the amount of weeks and 114 is the savings, then the point that the lines will cross at represents 114 dollars after 6 weeks. this means that after six weeks, both doris and miguel will have 114 dollars.

Answer:

The correct equation you're looking for is the first choice: [tex]\frac{240 miles}{5 hours}[/tex] = 48 miles  per hour.

Step-by-step explanation:

The formula to show the relationship between rate, time, and distance is [tex]rt=d[/tex], where [tex]r[/tex] represents the rate of change, [tex]t[/tex] represents time, and [tex]d[/tex] represents the total distance. Since you are given the distance and time, and are looking for the rate of change, then you need to divide the total distance traveled by the time it took to travel that distance, so the correct equation is [tex]\frac{240miles}{5hours}[/tex] = 48 miles per hour.

Have a great day! Feel free to let me know if you have any more questions :)

He must sell 520 units from the second shipment in order to have sold 80 percent of all of the unit.

This is mathematical equations.

The salesman sold 75% of 800 units, so he sold 0.75 * 800 = 600 units from the first shipment.

The salesman wants to sell 80% of all the units, which is a total of 0.80 * (800 + 600) = 0.80 * 1400 = 1120 units.

To find out how many units he must sell from the second shipment, we subtract the number of units he has already sold from the number of units he wants to sell:

1120 units - 600 units = 520 units.

Therefore, the salesman must sell 520 units from the second shipment in order to have sold 80% of all the units.

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A number which is 15 more than twice a number is 37 is 11.

Let the number be N.

Let's set up the equation.

A number is 15 more than twice a number is 37,

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

So the number which is 15 more than twice a number is 37 is 11.

A number system is a means of representing numbers. It is a method of representing numbers in a set of numbers consistently by using digits or other symbols. Each number receives a unique representation as well as information about the arithmetic and algebraic structure of the numbers. Addition, subtraction, multiplication, and division are just a few of the mathematical operations we may carry out using it.

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The relevant angle relationship in the diagram is that the total angle of line JKEF = the total angle on line JHGF.

The value of X = 20

The measures of ZJAH and ZGAH = 60° and 100° respectively.

To find the value of X, the angle of the straight line = 180°

Therefore, 3x+5x+X = 180

180 = 9x

X = 180/9

X = 20

Therefore the measures of <JAH = 3 × 20 = 60°

the measure of <GAH = 5×20 = 100°

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Answer:

4) 175

5) 2

6) 72

7) 48

8) 45

9) 5

10) 18

11) 3

12) 10

13) 30

14) 12

15) 1

16) 2

17) 2

18) 8

Step-by-step explanation:

The easiest way to do this is to cross-multiply.

Ans:

Q4. 175

Q5. 2

Q6. 72

Q7. 48

Q8. 45

Q9. 5

Q10. 18

Q11. 3

Q12. 10

Q13. 30

Q14. 12

Q15. 1

Q16. 2

Q17. 2

Q18. 8

On solving the provided question, we can say that the area of the picture of the flyer in the newspaper is = 36 square inches.

The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.

he original flyer has an area of = 576 square inches.

The Picture Noah prints will be a dilation of the flyer using a scale factor of 1/4.

Scale factor k=1/4

So the area of the picture of the flyer in the newspaper is

A = 576 X k^2

A = 576*1/4*1/4

A = 36 sq in.

the area of the picture of the flyer in the newspaper is = 36 square inches.

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The same field can be mowed in 3 hours by 2 gardeners.

A soccer field may be mowed by 6 gardeners in 2 hours, meaning each one works at a rate of 1/6 of the field per hour.

We must ascertain the rate at which the field can be mowed in 3 hours, which is 1/3 of the field every hour, in order to establish the number of gardeners required to mow the same field in that amount of time.

We divide this rate by the rate of each gardener, which is 1/6 of the field each hour, to determine the required number of gardeners, resulting in the equation 1/3 / 1/6 = 2.

Hence, 2 gardeners can mow the same field in 3 hours.

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The first six terms of the sequence are 1, 1, 2, 3, 5 and 8. The solution has been obtained by using arithmetic progression.

What is arithmetic progression?

In an arithmetic progression (AP) sequence of numbers, there is always the same amount of difference between any two subsequent integers. Arithmetic Sequence is another name for it.

We are given a sequence as a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + a[tex]_{n-2}[/tex] where a₀ = 0 and a₁ = 1.

So, the first term is a₁ = 1

The second term is

a₂ = a₂₋₁ + a₂₋₂

a₂ = a₁ + a₀

a₂ = 1

The third term is

a₃ = a₃₋₁ + a₃₋₂

a₃ = a₂ + a₁

a₃ = 1 + 1

a₃ = 2

The fourth term is

a₄ = a₄₋₁ + a₄₋₂

a₄ = a₃ + a₂

a₄ = 2 + 1

a₄ = 3

The fifth term is

a₅ = a₅₋₁ + a₅₋₂

a₅ = a₄ + a₃

a₅ = 3 + 2

a₅ = 5

The sixth term is

a₆ = a₆₋₁ + a₆₋₂

a₆ = a₅ + a₄

a₆ = 5 + 3

a₆ = 8

Hence, the first six terms of the sequence are 1, 1, 2, 3, 5 and 8.

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Answer:

5.06%

Step-by-step explanation:

x = cost of living....then increase it 2 %

       1.02 x   = new cost of living      now increase this 3 %

           (1.03) 1.02x = 1.0506x     which equates to 5.06% increase in 2 years