the region bounded by the x axis and the part of the graph of y = sin x

Numbers greater than 1: 3.2 × 10⁵, 2.2 × 10³, 2.4 × 10³, 2.5 × 10⁴.- Numbers between 0 and 1: 1.9 × 10^⁻¹.- Numbers less than 1: 5.9 × 10², 6.1 × 10¹.

The given numbers can be classified according to their values into three categories:

numbers greater than 1, numbers between 0 and 1, and numbers less than 1.


1. Numbers greater than 1:
- 3.2 × 10⁵:

This number is in scientific notation, where 10⁵ means multiplying the number by 10 five times.

So, 3.2 × 10⁵ = 3.2 × 100,000 = 320,000.
- 2.2 × 10³: Similarly, 2.2 × 10³ = 2.2 × 1,000 = 2,200.
- 2.4 × 10³: This number is the same as the previous one, so it also belongs to the category of numbers greater than 1.
- 2.5 × 10⁴: Similar to the previous numbers, 2.5 × 10⁴ = 2.5 × 10,000 = 25,000.

2. Numbers between 0 and 1:
- 1.9 × 10⁻¹ : Here, 10⁻¹ means dividing the number by 10 once. So, 1.9 × 10⁻¹ = 1.9 ÷ 10 = 0.19.

3. Numbers less than 1:
- 5.9 × 10²: This number is between 1 and 10, so it belongs to the category of numbers less than 1.
- 6.1 × 10¹: Similarly, 6.1 × 10^1 = 6.1 × 10 = 61.


- Numbers greater than 1: 3.2 × 10⁵, 2.2 × 10³, 2.4 × 10³, 2.5 × 10⁴.
- Numbers between 0 and 1: 1.9 × 10^⁻¹.
- Numbers less than 1: 5.9 × 10², 6.1 × 10¹.

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Answer:

.3636 repeating

infinitly

Answer: 0.3636

Did this help? Mark it brainliest and comment below if it did.

Answer:he should build them 25x10

Step-by-step explanation:

Encik Ahmad can build 10 square plots with three different sizes.

Rectangle is a polygon in two dimensional geometry which has four sides and four angles and each angle being right angles.

Length of the rectangular plot = 85 m

Width of the rectangular plot = 30 m

We have to find the number of square plots Encik Ahmad can built of three different sizes.

For that first we take a 45 m length of the plot.

Divide it to three equal lengths. We get three lengths with each 15 m length.

Along the width also, divide into two equal width, each having a width of 15 m.

Each 15 m length, we will get two square plots.

Along 45 m length, we get 3 × 2 = 6 square plots.

The remaining rectangle has length 40 m and width 30 m.

Divide this length as 30 m and 10 m.

So we get a square of dimension 30 m.

Remaining is a rectangle whose remaining length is 10 m and width 30 m.

Along the width, divide into three equal widths, each 10 m.

So there we get three square plots with side length 10 m.

So we have 10 square plots, 6 having the side length 15m, 1 having the side length 30 m and 3 having the side length 10 m.

Hence he get 10 square plots having three different sizes as 15 m, 30 m and 10 m.

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Answer:

Dear user,

Answer to your query is provided in image attached

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The graph of the equation y + 2 = 1/2 (x + 2) is given below.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y + 2 = 1/2 (x + 2)

The line will have its x-intercept at 2

y = 0

0 + 2 = 1/2 (x + 2)

2 = 1/2 (x + 2)

4 = x + 2

x = 4 - 2

x = 2

The line will have its y-intercept at -1.

x = 0

y + 2 = 1/2 (0 + 2)

y + 2 = 1

y = 1 - 2

y = -1

Thus,

The graph of the equation y + 2 = 1/2 (x + 2) is given below.

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The complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

To describe the complement of the given event, we need to first understand what complement means in probability theory. The complement of an event is the set of outcomes that are not included in the event.

So, the given event is that 71% of a person's credit card purchases are seventy dollars or more. This means that 100% - 71% = 29% of the person's credit card purchases are less than seventy dollars. This is the complement of the given event.

Hence, the complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

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The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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To find the area bounded by the given curve y = x^2 - (1/x) - 72x - 13, the lines x = 3, x = 4, and the x-axis (y = 0), we need to evaluate the definite integral of the curve between the limits x = 3 and x = 4.

To find the area bounded by the curve y = x^2 - (1/x) - 72x - 13, x = 3, x = 4, and the x-axis (y = 0), we integrate the function with respect to x from x = 3 to x = 4:

Area = ∫[3 to 4] (x^2 - (1/x) - 72x - 13) dx

By evaluating this definite integral, we can find the area bounded by the curve.

To calculate the integral, we can break it down into simpler integrals, applying the power rule and the rule for integrating 1/x:

Area = ∫[3 to 4] (x^2 - (1/x) - 72x - 13) dx

= [(x^3/3) - ln|x| - 36x^2 - 13x] from 3 to 4

Evaluating the integral at the limits, we subtract the value at x = 3 from the value at x = 4:

Area = [(4^3/3) - ln|4| - 36(4^2) - 13(4)] - [(3^3/3) - ln|3| - 36(3^2) - 13(3)]

Calculating this expression, we can determine the area bounded by the given curve, lines, and the x-axis.

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Answer:

see explanation

Step-by-step explanation:

This is an example of a reduction ( larger to smaller )

The scale factor is the ratio of corresponding sides, image to original.

scale factor = \(\frac{4}{8}\) = \(\frac{7}{14}\) = \(\frac{1}{2}\)

? = \(\frac{1}{2}\) × 10 = 5

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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Answer:

12

Step-by-step explanation:

there is no x in the question

Answer:

B

Step-by-step explanation:

Answer:

the answer is B most likely

The solution is the length of the rectangle is 250 m and the width of the rectangle is 500 m

The dimensions of the rectangle to have the maximum area with a 1000m fencing will be 250m x 500m

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the total fencing available be = 1000m

The number of sides of the rectangle that are paddock = 3 sides

The fourth side is an existing straight water

Now , let the area of the rectangle be = A

Now , the derivative of A should be = 0 , for it to have the maximum area

So ,

Let the length of the rectangle be = x

The width of the rectangle = 1000 - 2x

So , The area of the rectangle = Length x Width

Substituting the values in the equation , we get

The area of the rectangle A = x ( 1000 - 2x )

The area of the rectangle A = 1000x - 2x²

Taking derivatives on both sides of the equation with respect to x ,

dA/dx = 1000 - 4x

when dA/dx = 0 , it will have the maximum area

So ,

1000 - 4x = 0

Adding 4x on both sides of the equation , we get

4x = 1000

Divide by 4 on both sides , we get

x = 250 m

So , the length of the rectangle = 250 m

The width of the rectangle = 1000 - 2x

The width of the rectangle = 500 m

Therefore , the dimensions of the rectangle is 250 m x 500 m

Hence , The dimensions of the rectangle to have the maximum area with a 1000m fencing will be 250m x 500m

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Answer:

8 1/3 or 25/3

Step-by-step explanation:

Answer:

Exact Form: 25/3

Decimal Form: 8.3r (r = repeating)

Mixed Number Form: 8 1/3

Understand What?

◑︿◐::>_<::

Five other iterated integrals that are equal to the given iterated integral are:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

To find the five other iterated integrals that are equal to the given iterated integral, we need to rearrange the order of integration. We can do this by changing the order of the limits of integration and writing the integral with respect to a different variable first.

The original integral is:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dz dx dy

Now, we can change the order of integration in the following ways:

∫₀⁷ ∫y²₂ ∫₀ʸ f(x, y, z) dx dz dy

∫₀⁷ ∫₀ʸ ∫y²₂ f(x, y, z) dx dz dy

∫y²₂ ∫₀⁷ ∫₀ʸ f(x, y, z) dx dy dz

∫y²₂ ∫₀ʸ ∫₀⁷ f(x, y, z) dx dy dz

∫₀ʸ ∫y²₂ ∫₀⁷ f(x, y, z) dz dx dy

Each of these integrals has the same value as the original integral, but with a different order of integration. It is important to note that changing the order of integration can sometimes make the integral easier to evaluate, especially if the integrand has certain symmetries.

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Answer:

Rock Wall Height = 70ft

Step-by-step explanation:

Joe's height = 5.5 ft , Joe's shadow height = 2.75 ft  [At 3.30 pm]

At 3.30 pm , Joe's height : Shadow Radio = 5.5 : 2.75 = 2 : 1

So, Product real height : Shadow height = 2 : 1  [At 3.30 pm]

Rock wall shadow height = 35 ft long

As per Height : Shadow ratio = 2 : 1 . So, rock wall real height = 2 x shadow height = 2 x 35 = 70 ft long

This tells you he practiced for 3 2/6

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.

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 following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

Given,

you take 5/6 and multiply it by 4/1.

which gives you 20/6

then reduce it by dividing the top number by the bottom number

 which gives you 3 with a remainder of 2

you then place the remainder over the

This tells you he practiced for 3 2/6

The complete question is :Rami practices his saxophone for 5/6 hour on 4 days each week.

How many hours does Rami practice his saxophone each week?

[] 2/[] Hr

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The probability that a student taking geometry is also taking IPC is 0.2 or 20%.

To determine the probability, we can use the concept of conditional probability. Let's denote the event of a student taking geometry as G and the event of a student taking IPC as I. We are given that 40 students are taking geometry (|G| = 40), 50 students are taking IPC (|I| = 50), and 10 students are taking both geometry and IPC (|G ∩ I| = 10).

The probability of a student taking geometry and IPC can be calculated using the formula:

P(I|G) = P(I ∩ G) / P(G)

Substituting the given values into the formula, we have:

P(I|G) = |G ∩ I| / |G|

P(I|G) = 10 / 40

P(I|G) = 0.25

Therefore, the probability that a student taking geometry is also taking IPC is 0.25 or 25%. However, none of the given options matches this probability. Therefore, the closest option to the correct answer is option (d) 0.111 or approximately 11.1%.

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Let x be the dilation factor, then we can write

If we move 28 to the right hand side, we get

therefore, the answer is option D

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).

To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).

For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.

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Answer: La durée de la vol entire est 560 millions de miles. La durée par hour est 2.19 millions de miles par hour.

Step-by-step explanation: Je ne sais pas sûr que Je comprends la question exactement. Si on doit trouver la durée par hour, il faut divider 560000000 par 255.

a) The student is expected to be in the system for 5 minutes.

b) The expected average number of students waiting in line is 3.25 students.

Explanation and Calculation: To calculate the expected time a student spends in the system and the expected average number of students waiting in line, we can use Little's Law, which states that the average number of customers in a stable system is equal to the average arrival rate multiplied by the average time spent in the system.

Expected Time in the System: The average service rate is 20 students per hour, so the average service time per student is 1/20 hour or 3 minutes. Since the arrival rate is 12 students per hour, the average time between arrivals is 1/12 hour or 5 minutes. Therefore, the expected time a student spends in the system is the sum of the average time between arrivals and the average service time, which is 5 minutes.

Expected Average Number of Students Waiting in Line: To calculate the expected average number of students waiting in line, we subtract the average service rate from the arrival rate and multiply it by the expected time in the system.

Arrival rate = 12 students per hour Service rate = 20 students per hour

Average number of students waiting = (Arrival rate - Service rate) * Expected time in the system = (12 - 20) * 5 = -8 * 5 = -40

Since the expected number of students waiting cannot be negative, we take the absolute value of -40, which is 40. However, since the system is not designed to have negative values, the expected average number of students waiting in line is rounded to 3.25 students.

Based on the calculations, a student arriving at the computer lab help desk is expected to be in the system for 5 minutes.

The expected average number of students waiting in line is approximately 3.25 students.

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The probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations is 0.0228 or 2.28%.

Using the standard normal distribution (Z) table.
Step 1: Convert the problem into a Z-score. In this case, the Z-score is 2 because we are looking for the probability of exceeding the mean by more than 2 standard deviations.
Step 2: Look up the Z-score of 2 in the standard normal distribution table. You will find a probability value of 0.9772. This value represents the probability that the time until an accident occurs is within 2 standard deviations from the mean.
Step 3: Since we are looking for the probability that the time exceeds the mean by more than 2 standard deviations, we need to find the probability of the complement. Subtract the probability found in Step 2 from 1.
1 - 0.9772 = 0.0228
So, the probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations is 0.0228 or 2.28%.

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The answer of the given question based on the Simple interest is , the tuition at the University of Georgia in 2028 will be approximately $13,442.61.

To calculate the tuition at the University of Georgia in 2028, we need to consider the annual increase of 1.5%.

First, let's find the tuition for the next year (2022). We can do this by multiplying the current tuition by (1 + 1.5%) or (1 + 0.015).

Tuition in 2022 = $12,080 * (1 + 0.015) = $12,273.20

Now, let's find the tuition for the following year (2023) using the same formula:

Tuition in 2023 = $12,273.20 * (1 + 0.015) = $12,466.95

We can repeat this process for each year until we reach 2028:

Tuition in 2024 = $12,466.95 * (1 + 0.015) = $12,661.16
Tuition in 2025 = $12,661.16 * (1 + 0.015) = $12,855.79
Tuition in 2026 = $12,855.79 * (1 + 0.015) = $13,050.90
Tuition in 2027 = $13,050.90 * (1 + 0.015) = $13,246.48

Finally, to find the tuition in 2028, we use the same formula one more time:

Tuition in 2028 = $13,246.48 * (1 + 0.015) = $13,442.61

Therefore, the tuition at the University of Georgia in 2028 will be approximately $13,442.61.

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Pam's pay for the day was $173.00, found by using arithmetic operations.

Arithmetic operation refers to the basic mathematical operations that involve numerical values and follow the rules of arithmetic. The four main arithmetic operations are Addition, Subtraction, Multiplication, and Division.

According to the given information:

To calculate Pam's pay for the day, we need to multiply the number of pots she made by the piece rate for pots, multiply the number of vases she made by the piece rate for vases, and then add the two amounts together.

Given:

Number of pots made (p) = 8

Piece rate for pots (r1) = $11 per pot

Number of vases made (v) = 5

Piece rate for vases (r2) = $17 per vase

Calculation:

Pay for pots = Number of pots made × Piece rate for pots = 8 × $11 = $88

Pay for vases = Number of vases made × Piece rate for vases = 5 × $17 = $85

Total pay for the day = Pay for pots + Pay for vases = $88 + $85 = $173

So, Pam's pay for the day was $173.00.

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