What is the radius of a circle with a circumference of 64 feet?

If Tito took a loan of $10000 from a bank to be repaid within 4 years, at 12% Simple interest per annum, then, he will have to pay overall $4800 as interest to the bank over 4 years and a total payment of $14800 at the end of the 4th year to repay and close off the loan.

As per the question statement, a bank charges 12% Simple interest per annum on cash loans to its clients and Tito took a loan of $10000 from the same bank to be repaid within 4 years.

We are required to calculate the overall interest Tito has to pay to bank if he repays and closes the loan at the end of 4th year, and also to calculate the total payment required to repay and close off the loan at the end of the 4th year.

To solve this question, we need to know the formula to calculate the interest amount in case of simple interest which goes as

Interest (I) \(=(\frac{P*R*T}{100} )\)

where, "P" = Principle amount of Loan,

"R" = Rate of simple interest charged on the principle per annum, and

"T" = Time period within which, the loan is to be repaid.

Here, (P = 10000), (R = 12%) and (T = 4). Then, the overall interest Tito will have to pay at the end of 4th year  = \((\frac{10000*12*4}{100}) = (100*12*4)=(48*100)=4800\)

And total amount to be paid to repay and close of the loan at the end of 4th year will be = $[4800 + 10000] = $14800.

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In order to determine the recursive and explicit rule for the values given in the table, first find the arithmetic constant of the sequence by subtracting a pair of consecutive values of f

Answer:

2m³ + 9m² - 19m - 11

Step-by-step explanation:

3f(m) - 2g(m)

= 3(3m² - 5m + 1) - 2(- m³ + 2m + 7) ← distribute parenthesis

= 9m² - 15m + 3 + 2m³ - 4m - 14 ← collect like terms

= 2m³ + 9m² - 19m - 11

The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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Answer

3*9=27

27/ 1/5

5.25

Step-by-step explanation:

5.25=5 1/4

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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Answer:

500 markers

Step-by-step explanation:

Multiply 5000 by 1/10

\(5000*\frac{1}{10} \\\\= \frac{5000}{10}\\\)

Simplify (dividing the numerator and denominator by 10)

\(\frac{5000}{10} \\= \frac{500}{1}\\= 500\)

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The corresponding particular solution to the system of differential equations :

X(t) = -6e^(-12t)(1, 1) + 6e^(2t)(3, -1)

The eigenvalue method involves finding the eigenvalues and eigenvectors of the matrix associated with the system of differential equations.

        X' = AX

        where X is a column vector with the variables x1 and x2,

        X' is the derivative of X with respect to t,

        and A is the coefficient matrix given by:

       A = [ -13 9

                 -5 1  ]

       det(A - λI) = 0

       where I is the identity matrix and λ is an eigenvalue.

        λ = -12, 2

For each eigenvalue, we solve for the corresponding eigenvector by setting up a system of equations and solving for the unknowns. For λ = -12, the eigenvector is (1, 1), and for λ = 2, the eigenvector is (3, -1).

       X(t) = c1e^(-12t)u1 + c2e^(2t)u2

where c1 and c2 are constants and u1 and u2 are the eigenvectors corresponding to the eigenvalues -12 and 2, respectively.

       X(0) = [3  3] = c1u1 + c2u2

       c1 = -6, c2 = 6

        X(t) = -6e^(-12t)(1, 1) + 6e^(2t)(3, -1)

This is the final solution to the system of differential equations.

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To find the function n(t) that models the population of bacteria after t hours, we can use the exponential growth formula:

n(t) = n0 * e^(kt)

Where:

n(t) is the population after t hours,

n0 is the initial population size,

e is the base of the natural logarithm (approximately 2.71828),

k is the growth rate constant.

We can determine the value of k using the given information. After 1 hour, the bacteria count is 9500, which is the population at time t = 1. Plugging these values into the equation:

\(9500 = 1100 * e^(k*1)\)

To find k, we can divide both sides by 1100:

9500/1100 = e^k

Now, we can solve for k by taking the natural logarithm (ln) of both sides:

ln(9500/1100) = ln(e^k)

ln(9500/1100) = k

Now we have the value of k. We can plug it back into the exponential growth formula to obtain the function n(t):

\(n(t) = 1100 * e^(ln(9500/1100) * t)\)

To find the population after 1.5 hours, we can substitute t = 1.5 into the equation:

\(n(1.5) = 1100 * e^(ln(9500/1100) * 1.5)\)

To find the number of hours when the number of bacteria will reach 20,000, we can set n(t) equal to 20,000 and solve for t:

\(20,000 = 1100 * e^(ln(9500/1100) * t)\)

Finally, to sketch the graph of the population function, plot the values of t on the x-axis and the corresponding values of n(t) on the y-axis using the equation n(t) = 1100 * e^(ln(9500/1100) * t). The resulting graph will show the exponential growth of the bacteria population over time.

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Answer:

-9x-9.5

Step-by-step explanation:

-5x-15-4x+6.5

-9x-9.5

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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Answer:

blue

Step-by-step explanation:

270° moves by 3 quadrants

Answer:

Blue

Step-by-step explanation:

Rotate 1/2 circle (180°) counterclockwise and you go through the yellow to the green.

Go another 1/4 circle (90°) and you get to the blue.

180° + 90° = 270°

Tan x = opposite side / adjacent side

opposite side: 21

Adjacent side: 28

Replacing:

Tan x = 21/28

Answer:

12

Step-by-step explanation:

The solution that correctly shows the slope calculation to enable Dorothy show that △PQR is a right triangle

Right triangles are triangles with have perpendicular relationships

The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals  then they are perpendicular and the triangle is a right triangle

Using point PQ

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 5) / (-1 - -2)

m = -4

Using point QR

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 1) / (7 - -1)

m = 2/8 = 1/4

Comparing the slopes shows that slopes calculated are negative reciprocals

-4 and 1/4

Therefore the triangle is a right triangle

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To find out how many flowers will be in each centerpiece, we can divide the total number of flowers by the number of centerpieces:

Total number of flowers: 1,064

Number of centerpieces: 28

Number of flowers in each centerpiece = Total number of flowers / Number of centerpieces

Number of flowers in each centerpiece = 1,064 / 28 = 38

Therefore, there will be 38 flowers in each centerpiece.

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Answer: 38

Step-by-step explanation:

The question is asking you to divided.

1064 divided by 28 = 38

So there will be 38 flowers in each centerpiece

Answer

1) A dilation with a scale factor < 1 will reduce/decrease the size of the pre-image.

2) A dilation with a scale factor > 1 will enlarge/increase the size of the pre-image.

Step-by-step Explanation

Dilation refers to enlarging or reducing the size of an image. And the scale factor determines how much the image is reduced or enlarged.

- A scale factor of 1 means the image is neither enlarged or reduced.

- A very large scale factor (greater than 1) indicates that the size of the image is enlarged compared to the size of the original image.

- A very small scale factor (less than 1) indicates that the size of the image is reduced compared to the size of the original image.

So, for the question,

1) A dilation with a scale factor < 1 will reduce/decrease the size of the pre-image.

2) A dilation with a scale factor > 1 will enlarge/increase the size of the pre-image.

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Answer:

\(e\frac{4}{3}\) will be the exponential expression.

Step-by-step explanation:

We have to choose a number between 0 ad 10 and has to be odd to be base say 3

And even number between 0 ad 10 to be exponent  say 4.

So the exponential expression will be : \(e\frac{4}{3}\)

According to the information given above expression is the required expression.

Answer:

43

Step-by-step explanation:

Answer:

The price of bus after 4 yrs is Rs.1652400

Step-by-step explanation:

Present price of car = Rs.3000000

We are given that the price of bus depreciated the first two yrs by 10%

So, The price after first two years =\(3000000(1-0.1)^2=2430000\)

Now the price of bus depreciated by 15%

So, The price after third year = 2430000-0.15(2430000)=2065500

Now the price of bus depreciated by 20%

The price after fourth year =2065500-0.2(2065500)=1652400

Hence the price of bus after 4 yrs is Rs.1652400

This is of Both

Range = Highest - Lowest data

Range = 45 - 10

Range = 35

Only A

Range = 45 - 10

Range = 35

Only B

Range = 40 - 15

Range = 25

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Answer:

Step-by-step explanation:

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

no te entiendo, puedes escribir la pregunta completa

We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:

Step 1 - Picture a

Step 2 - Picture b

Step 3 - Picture c

Step 4 - Picture c.

Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.

The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.

A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.

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Answer:

Step-by-step explanation:

Percentages can be expressed as decimals. Percentage of something can be found by multiplying the number by the decimal.

20% = 0.20

20%(18.5)
0.20(18.5)
3.7

Since this is a 20% increase, we will add this to the original value.

18.5 + 3.7 = 22.2

Answer:

y= 21

Step-by-step explanation:

2*10+1= y

20+1= 21

y = 21

The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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Answer: y = 2x − 4

The correct answer is B) y = 2x − 4

Step-by-step explanation:

Move all terms that don't contain y to the right side and solve:

y = −4 + 2x

Then reorder −4 and 2x:

y = 2x − 4

Final answer is:

B) y = 2x − 4