Which scenario best expresses a 400% increase?

Answer:

A ≈ 34.91 m²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × \(\frac{40}{360}\) ( r is the radius )

  = π × 10² × \(\frac{1}{9}\)

  = \(\frac{100\pi }{9}\)

  ≈ 34.91 m² ( to 2 decimal places )

Answer:

(round 35m²)

Step-by-step explanation:

360° : 40° = 9  

Area of Circle Formulas · Area = π × r2, where 'r' is the radius

Area = π × r2

Area = π × 10²

Area = π × 100

Area = 3.14 × 100

Area = 314 m²

314 : 9 = 34.88m² (round 35m²)

Answer: the first one

Step-by-step explanation: it has nothing to do with the function

Answer:

i don't know, i just want to know if you got it right

Step-by-step explanation:

The correct statement (C) "Mr. Jones will have more money because he invested for a longer period of time" is correct.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

\(\rm A = P(1+\dfrac{r}{n})^{nt}\)

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

It is given that:

Mr. Jones and Mr. Smith both plan to retire in 5 years.

From the formula:

The rate of interest is the same for both cases.

The duration for Mr. Jones is 20 years

The Initial investment amount for Mr. Jones = $250

The duration for Mr. Smith is 10 years

The initial investment amount for Mr. Smith = $500

Mr. Jones will have more money because he invested for a longer period of time.

Thus, the correct statement (C) "Mr. Jones will have more money because he invested for a longer period of time" is correct.

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Answer:

C.

Step-by-step explanation:

WE need to convert the given equations  into the standard form

(x - a)^2 + (y - b)^2 = r^2 where r = the radius.

x^2 + y^2 + 12x - 20y+ 132 = 0

(x + 6)^2 - 36 + (y - 10)^2 - 100 = -132

(x + 6)^2 + (y - 10)^2 = -132 + 36 + 100 = 4

giving a radius of 2

x^2 + y^2 + 12x - 20y + 55 = 0

will give a right hand side of -55 + 36 + 100 = 81  giving radius 9.

x^2 + y^2 - 12x+ 20y + 127 = 0

- gives right hand side of -127 + 36 + 100 = 9 giving a radius of 3.

Answer:

The answer is C I hope this helps

The number of cylindrical can will be 163 i.e. C.

What exactly is a cylinder?

In geometry, a cylinder is one of the fundamental 3d forms with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

The cylinder's total surface area (TSA) is equal to the sum of its curved surface area and the area of its two circular bases. The volume of a three-dimensional cylinder is the space it occupies (V).

TSA=2πr²+2πrh, where r is the radius and h is the height.

Volume=πr²h

Now,

Volume of cone shaped cup=1/3*π*r²*h

here diameter=7 so r=3.5, h=10

so V=1/3*π*3.5*3.5*10

and there are total 900 cups

So total volume of drink=π*3.5*3.5*10*300

and Volume of cylinderical cans=πr²h

r=7.5, h=30

V=π*7.5*7.5*30

So let number cans required to fill cups = x

then π*7.5*7.5*30 * x=π*3.5*3.5*10*300

x=163.3≈163

Hence,

           The number of cylindrical can will be 163.

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The p-value represents the probability of observing a sample mean as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true.

To determine whether the population mean life span for Honolulu is less than 77 years, we can conduct a hypothesis test using the given information. Let's set up the hypotheses:

Null Hypothesis (H0): The population mean life span for Honolulu is greater than or equal to 77 years.

Alternative Hypothesis (Ha): The population mean life span for Honolulu is less than 77 years.

To find the p-value, we would need additional information such as the sample mean and standard deviation. Without those values, we cannot directly calculate the p-value. However, we can describe the process of hypothesis testing.

To test the hypothesis, we would collect a sample of life spans in Honolulu, calculate the sample mean and standard deviation, and perform a one-sample t-test or z-test depending on the sample size and information available. This test would yield a test statistic and corresponding p-value.

A small p-value (less than the significance level, typically 0.05) would provide evidence to reject the null hypothesis in favor of the alternative hypothesis, suggesting that the population mean life span for Honolulu is indeed less than 77 years.

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Equation of a line:

9x - 7y = -63

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

Answer

x-intercept: −7; y-intercept: 9

The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x

From the question, we have the following parameters:

Dimension of sheet = 8 inches by 12 inches

Also from the question, we understand that:

He cuts equal squares from each corner.

The cut-out length from the sheet would represent the height of the box

Represent this cut-out length with x

So, we have

Height = x

The width and the length are then represented as

Width = Initial width - 2x

Length = Initial length - 2x

So, we have

Width = 12 - 2x

Length = 18 - 2x

The volume of a box is the product of its dimensions

In this case, we have

Width = 12 - 2x

Length = 18 - 2x

Height = x

So, we have

Volume = Width * Length * Height

Substitute the known values in the above equation So, we have the following equation

V = (12 - 2x)(18 - 2x)x

So, the volume function is V = (12 - 2x)(18 - 2x)x

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The set of real numbers includes both rational and irrational numbers.


1. Real numbers: Real numbers include all rational and irrational numbers. They can be represented on a number line and are not limited to whole numbers or integers.

2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. They can be written in the form a/b, where a and b are integers and b is not equal to 0. For example, 3/4, -2/5, and 0.6 are all rational numbers.

3. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers. They cannot be written in the form a/b. Examples of irrational numbers include √2, π (pi), and e.

Therefore, the set of real numbers includes both rational and irrational numbers.

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The absolute maximum and minimum value of f on [π/4, 7π/4] are 2.1523 and -2.2160 respectively.

Given function is f(t) = t cot(1/2t) on [π/4, 7π/4].

To find the absolute maximum and minimum value of the given function f(t), let's follow the following steps:

Step 1: Find the critical numbers of f(t) on the given interval. Critical number is a number in the interval where the derivative is zero or undefined.

Step 2: Find the values of f(t) at the critical numbers, end points of the interval.

Step 3: Compare all the values found in Steps 1 and 2 to determine the absolute maximum and minimum of the function f(t) on the given interval.

1) First find the critical numbers of f(t) on the given interval:

Using the chain rule and product rule,differentiate

f(t) = t cot(1/2t)  w.r.t t :

f′(t) = cot(1/2t) – (t/2) csc^2(1/2t)

Critical numbers occur where f′(t) = 0 or is undefined.

Therefore, we solve cot(1/2t) – (t/2) csc^2(1/2t) = 0 ...[1]

Note that the function cot(1/2t) is defined on the interval [π/4, 7π/4] if and only if 1/2t ≠ kπ for integer k.

So, we solve [1] only for those values of t which are not multiple of π.

For simplicity, let's write x instead of 1/2t.

Now, we have, cot x - (2x)^-1 = 0i.e. cot x = 1/2x

Now, graph of cot x and y = 1/2x are shown below:

The x-coordinate of the intersection points of the two graphs are the solutions of the equation cot x = 1/2x.

There are two solutions on the interval [π/4, 7π/4]: x = 1.20256 and x = 5.44148

Therefore, the corresponding critical numbers t are t = 1/(2x) and t = 1/(2x) = 1.65214 and t = 11.01182 (approximate to five decimal places).

2) Now, find the value of f(t) at the critical numbers and end points of the interval:

f(π/4) = (π/4) cot(π/8)

≈ 0.76537f(7π/4)

= (7π/4) cot(7π/8)

≈ -0.76537

f(1.65214) = 1.65214 cot 0.82607

≈ 2.1523

f(11.01182) = 11.01182 cot 5.50591

≈ -2.2160

Therefore, absolute maximum of f(t) on the interval [π/4, 7π/4] is 2.1523 and it occurs at t = 1.65214.

Absolute minimum of f(t) on the interval [π/4, 7π/4] is -2.2160 and it occurs at t = 11.01182.

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Answer:

hmm..

Step-by-step explanation:

If a user is using a faulty HDMI cable, possible symptoms the user may experience include:

No display Blank screen Display with flickers Audio issues Selecting the right kind of HDMI cable is critical when it comes to getting the most out of your High-Definition entertainment experience.

Why to choose best HDMI cables?

HDMI cables can be found at any electronics store or online but, with so many choices and so much technological jargon, how do you know which one to choose? There are numerous types of HDMI cables on the market, but the majority of consumers are concerned about finding the best one. To select the best HDMI cable, users should look for the length of the cable and the type of cable. Different kinds of HDMI cables may result in different problems that could affect the user's experience, such as the symptoms mentioned above.

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To determine the value of n, we need to equate the probabilities and solve for n. Let's set up the equation: Therefore, the value of $n$ is 12.

There are n-1 ways to choose the first ball (since it can be any number from 1 to n except n itself). For each of these choices, there are n-3 ways to choose the second ball (again, any number except the first chosen number and its consecutive number). Similarly, for each pair of chosen balls, there are n-5 ways to choose the third ball, and so on.

Therefore, the probability of not drawing any pair of consecutive numbers is given by:
(n-1)(n-3)(n-5)...(3)(1) / n(n-2)(n-4)...(4)(2)

The probability of drawing exactly one pair of consecutive numbers can be calculated as follows:There are n-2 ways to choose the position of the pair of consecutive numbers (since it can start from any position except the first and last position). For each choice, there are (n-1) ways to choose the actual pair of consecutive numbers. For the remaining n-3 balls, there are (n-3)(n-5)...(3)(1)

ways to choose them such that no other pair of consecutive numbers is drawn.

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Answer:

number of glasses he bought = 60

Step-by-step explanation:

Let the variable x represent the number of glasses he bought

Total cost of x glasses at Rs. 12 each = 12x

5 glasses broke so remaining number of glasses = x- 5

He sold this quantity of glasses for Rs. 16 each

Total sale price of (x - 5) glasses = 16(x - 5)

Total profit = Total sales - Total cost = 160

=> 16(x - 5) - 12x = 16

Expand brackets for 16(x - 5): 16x - 16 x 5 = 16x - 80

Therefore we get

16x - 80- 12x = 160

4x - 80 = 160

Add 80 on both sides:

4x -80 + 80  = 160 + 80

4x = 240

x = 240/4 = 60

Answer:

5.2z

Step-by-step explanation:

When you are adding any variables of the same power, like we have in this problem, you can just add any co-efficients.

3.1 + 2.1 = 5.2

So 3.1z + 2.1z = 5.2z

Answer:

9

Step-by-step explanation:

total is 30

spent is $9

this is total money minus the amount of the picture frame

30-9

21 divide by 3

the total sum of journals bought was 9

Answer:

sin D = 0.25

Step-by-step explanation:

If ∠E = 90°, it means that the triangle is a right angle triangle.

Thus, hypotenuse will be the longest side which will be DC = 65

Since we are given CE = 16 and ED = 63, I have attached a diagram showing this triangle.

From the diagram, since we are looking for sin ∠D, we can say that;

sin D = opposite/hypotenuse

Now, opposite = CE = 16

Hypotenuse = CD = 65

Thus;

sin D = 16/65

sin D = 0.2462

Approximating to the nearest hundredth gives;

sin D = 0.25

Ans5

Step-by-step explanation:

5

Answer:

Exact Form:

61/12

Decimal Form:

5.083 with 3 repeating

Mixed Number Form:

5   1/12

Step-by-Step Explanation:

-5/3×3/8 = -5/8

-5/8+3/8= -1/4

-1/4+6/9=5/12

5/12+14/3=61/12

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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Answer:

ima guess $262.50

Step-by-step explanation:

There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

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Answer:

20!

Step-by-step explanation:

Isosceles triangles have 2 angles are the same. Since we can't do 140, because interior angles of a triangle equal 180, then we need to subtract 140 from 180. 180-140=40. 40/2 because of 2 angles=20. 20 is the angle.

Answer:

20

Step-by-step explanation:

Explanation

Step 1

The middle number is 6 and the last number is -7.

Factoring means we want something like

We need two numbers that...

Add together to get 6

Multiply together to get -7

c

The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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The vertex is at (3, -16), so we conclude that:

For a general quadratic function:

\(y = a*x^2 + b*x + c\)

The vertex is at:

\(x = -b/2a\)

In our case, we have:

\(f(x) = -x^2 + 6x - 25\)

So the x-value of the vertex is:

\(x = -6/2*(-1) = 3\)

And the y-value of the vertex is:

\(f(3) = -(3)^2 + 6*3 - 25 = -9 + 18 - 25 = -16\)

So the vertex is at (3, -16)

Also, notice that the function has a negative leading coefficient, which means that the vertex is a maximum.

From that, we conclude that the range is:

f(x) ≤ -16.

And the domain like in all quadratic functions is the set of all real numbers.

The graph can be seen below.

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Answer:

500

Step-by-step explanation: