Area of Composite Shapes
Can someone explain how to find this? I'm not sure I understand. Thanks <3

The inequality to find the possible widths of the roped-off section is: w ≤ 4.9.

We can make use of the fact that the manager can only use a rope that is 25 meters in length and that the section's length is fixed at 7.6 meters.

Let's write 'w' (in meters) to represent the width of the roped-off area.

If we assume that we must rope off all four sides, we may calculate the total length of rope required for the portion to be roped off:

Length of rope = 2 * (width + length)

Substituting the given values:

Length of rope = 2 * (w + 7.6)

According to the problem, the manager can use no more than 25 m of rope. Therefore, we can set up the following inequality:

2 * (w + 7.6) ≤ 25

Simplifying the inequality:

2w + 15.2 ≤ 25

Subtracting 15.2 from both sides:

2w ≤ 9.8

Dividing both sides by 2:

w ≤ 4.9

Therefore, the inequality to find the possible widths of the roped-off section is: w ≤ 4.9.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

y intercept = (0,4)

Answer:

0,4 i think

(sorry if i am wrong)

The function df(x, y) = (y^2 - xy)dx - x^2 dy is an inexact differential.

To determine if a function is exact or inexact, we need to check if its partial derivatives with respect to x and y satisfy the condition ∂M/∂y = ∂N/∂x, where df(x, y) = M(x, y)dx + N(x, y)dy.

In this case, we have M(x, y) = y^2 - xy and N(x, y) = -x^2. Calculating the partial derivatives, we find:

∂M/∂y = 2y - x

∂N/∂x = -2x

Since ∂M/∂y is not equal to ∂N/∂x (2y - x ≠ -2x), the function df(x, y) = (y^2 - xy)dx - x^2 dy is inexact.

Next, we can test the integrating factor 1/(xy^2) to see if it produces an exact differential. The integrating factor is denoted by μ(x, y) and is given by μ(x, y) = e^(∫(∂M/∂y - ∂N/∂x)/N dx). If the resulting expression becomes an exact differential, the integrating factor is successful.

In this case, the integrating factor μ(x, y) = e^(∫(2y - x)/(-x^2) dx) = e^(-2y/x). However, integrating factor μ(x, y) does not produce an exact differential, and hence, it is not a suitable integrating factor for this function.

Lastly, the expression H(g) represents the enthalpy change of a substance g. The notation Hˉ∘(2000 K) - Hˉ∘(0 K) indicates the difference in enthalpy between the substance at 2000 Kelvin and 0 Kelvin. To calculate this difference, additional information or a specific equation relating enthalpy change to temperature is needed. Without further details, it is not possible to provide a numerical calculation for Hˉ∘(2000 K) - Hˉ∘(0 K) for H(g).

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Answer:

The measure of a using the law of sines is 36 approximately.

the Department of Education receives about 65 percent of the federal funds transferred to state governments.

First, you need to identify what type of information is being asked for in the question. In this case, the question is asking which department receives a certain percentage of federal funds transferred to state governments.

Next, you need to research the answer. You can find the answer to this question by looking at the U.S. Department of Education website or other reliable sources.

The answer is that the Department of Education receives about 65 percent of the federal funds transferred to state governments.

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"Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

Statistics is the art and science of learning from data. It involves collecting, organizing, analyzing, interpreting, and presenting data to gain insights and make informed decisions. In the 4th edition of the book "Statistics: The Art and Science of Learning from Data," you can expect to find a comprehensive exploration of these topics.

This edition may cover important concepts such as descriptive statistics, which involve summarizing and displaying data using measures like mean, median, and standard deviation. It may also delve into inferential statistics, which involve making inferences and drawing conclusions about a population based on a sample.

Additionally, the book may discuss various statistical techniques such as hypothesis testing, regression analysis, and analysis of variance (ANOVA). It may also provide real-world examples and case studies to illustrate the application of statistical methods.

When using information from the book, it is important to properly cite and reference it to avoid plagiarism. Be sure to consult the specific edition and follow the guidelines provided by your instructor or institution.

In summary, "Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

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Answer:

B

Step-by-step explanation:

He was accepted to UCLA's School of Management

Answer:

El que pesa distinto es aquel que causa un desnivel en la balanza.

Step-by-step explanation:

Sabemos que una balanza tiene dos lados en los cuales podemos poner peso, si la balanza está equilibrada, ambos lados están a la misma altura, de lo contrario, habrá un desnivel entre ambos lados.

Puesto que solo podemos emplear la balanza 3 veces, debemos crear tres grupos de cuatro personas, que dentro de cada una cada mitad, conformada por dos personas, es colocada en un lado de la balanza. Si la balanza está equilibrada, entonces todo ese grupo está integrado por personas del mismo peso, pero si esta desequilibrada, una persona de alguno de los dos subgrupos.

En ese caso, se procede a sacar a dos personas, una por cada lado de la balanza, si el desbalance desaparece, entonces alguna de las dos personas que salió tiene un peso distinto, pero si el desbalance persiste, entonces es causante del desbalance se encuentra en aún en la balanza.

En conclusión, el que pesa distinto es aquel que causa un desnivel en la balanza.

Answer:

(4x^2-5) x (2x^2-9)

Step-by-step explanation:

01.) Write -46x^2 as a difference

8x^4-10x^2-36x^2+45

02.) Factor out 2x^2 from the expression

8x^4-10x^2 -36x^2+45

2x^2 * (4x^2-5) - 36x^2+45

03.) Factor out -9 from the expression

2x^2 * (4x^2-5) - 9(4x^2-5)

2x^2 *(4x^2-5)-9(4x^2-5)

04. Factor out 4x^2-5 from the expression

(4x^2-5) *(2x^2-9)

To find the length of the parametric curve given by x(t) = -12t^2 + 24t and y(t) = -4t^3 + 12t^2, where t goes from 0 to 1, we can use the arc length formula for parametric curves:

L = ∫[a,b] √((dx/dt)^2 + (dy/dt)^2) dt

In this case, we have x(t) = -12t^2 + 24t and y(t) = -4t^3 + 12t^2. Let's find dx/dt and dy/dt:

dx/dt = d/dt(-12t^2 + 24t)
= -24t + 24

dy/dt = d/dt(-4t^3 + 12t^2)
= -12t^2 + 24t

Now, let's substitute these derivatives back into the arc length formula:

L = ∫[0,1] √((-24t + 24)^2 + (-12t^2 + 24t)^2) dt

Simplifying the expression inside the square root:

L = ∫[0,1] √(576t^2 - 1152t + 576 + 144t^4 - 576t^3 + 576t^2) dt
= ∫[0,1] √(144t^4 - 576t^3 + 1152t^2 - 1152t + 576) dt

Now, we can integrate this expression. However, the integral of a general quartic polynomial is quite complex and involves elliptic integrals. Therefore, the exact closed-form solution for the integral is not readily available.

To find an approximate numerical solution, we can use numerical integration methods such as Simpson's rule or the trapezoidal rule. These methods involve dividing the interval [0,1] into smaller subintervals and approximating the integral over each subinterval. Using numerical integration software or programming, we can approximate the length of the curve.

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Answer:

d

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Your answer is Toys and treats

Answer:

x=9/4

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:i think its 115 degres

Step-by-step explanation:

If two dice are rolled, then the chances that the sum of the spots is 6 is option (b) 5/36

To calculate the probability of rolling a sum of 6 with two dice, we need to count the number of possible outcomes that add up to 6 and divide that by the total number of possible outcomes when rolling two dice.

There are five possible outcomes that add up to 6:

1 and 5

2 and 4

3 and 3

4 and 2

5 and 1

And there are a total of 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes and there are 6 × 6 = 36 possible pairs of outcomes.

Therefore, the probability of rolling a sum of 6 with two dice is:

5/36

Therefore, the correct option is (b) 5/36.

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L over 3 equals 9; L = 27 feet.

Answer:

The third one

the Length (L) is 27 since L/3

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Hai!

You would make 110$

Brainliest maybe?

The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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Answer:

the project has been completed.

Step-by-step explanation:

5/18 +4/18 + 9/18 = 18/18 or 1

so therefore no one has to complete the project, as it has already been completed

An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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It is true that education can often be a key factor in higher earnings potential.

Obtaining a higher level of education can provide individuals with additional skills, knowledge, and qualifications that are valued in the job market.

However, it's important to note that earning potential can vary based on several factors, including the field of study, location, job market conditions, individual experience, and skills.

The figure you mentioned, $30,400 per year, represents the median earnings of high school graduates according to a U.S. Census Bureau study. This figure provides a general idea of the earnings potential for individuals with a high school diploma. However, it's worth noting that this amount can vary significantly depending on factors such as the industry, job position, and individual circumstances.

Obtaining higher levels of education, such as a college degree or advanced degrees, tends to be associated with higher earning potential. On average, individuals with a bachelor's degree tend to earn more than those with just a high school diploma. However, it's important to keep in mind that individual circumstances and choices can also play a role in determining earnings.

Additionally, it's worth noting that education is not the only factor that influences earning potential. Other factors such as work experience, skills, networking, and personal motivation can also impact one's ability to earn higher wages.

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Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

In this case we must apply the properties of supplementary angles and opposite angles.

1 .

opposite angles

∠ 1 = 120 °

supplementary angles

∠ 1 + ∠ 2 = 180

120 + ∠ 2 = 180

∠ 2 = 180 - 120

∠ 2 = 60 °

The same properties can be applied in the other exercises to solve them.

The solution is:

∠ 1 = 120 °

∠ 2 = 60 °

==============================================

Work Shown:

If you save 40%, then you pay 100% - 40% = 60% of the original price

final price = 60% of original price

final price = 0.60*(original price)

840 = 0.60x

0.60x = 840

x = 840/0.60

x = 1400

The ring was originally £1400 before the discount.

The percentage of pregnancies last shorter than 38 weeks is (c) 30.85%.

We can use the normal distribution formula to calculate the percentage of pregnancies that last shorter than 38 weeks:

z = (x - μ) / σ

where z is the z-score, x is the value we are interested in (in this case, x = 38), μ is the mean (μ = 39), and σ is the standard deviation (σ = 2).

Substituting the values, we get:

z = (38 - 39) / 2 = -0.5

We can now use a standard normal distribution table or a calculator to find the percentage of values that fall below the z-score of -0.5. The area to the left of -0.5 is approximately 30.85%.

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To find the area bounded by the polar curve r=e^−θ/12 in the given sector, we use the formula A = ∫a b 1/z,2 dθ. Here, a=π/2 and b=π, and z=e^−θ/12. So, we have A = ∫π/2 π 1/(e^−θ/6) dθ. Therefore, the area of the region bounded by the polar equation r=e^−θ/12 in the sector π/2 ≤θ≤π is 1 - e^(-π/24).

To solve this integral, we use the substitution u=-θ/12, which gives us du/dθ = -1/12, or dθ = -12du. Substituting this and e^u for e^−θ/12, we get A = ∫−π/24 0 e^u * (-12)du.
Evaluating this integral, we get A = [e^u] from −π/24 to 0 = e^0 - e^(-π/24) = 1 - e^(-π/24). So, the area of the region bounded by the polar equation r=e^−θ/12 in the given sector is 1 - e^(-π/24).
In conclusion, the area of the region bounded by the polar equation r=e^−θ/12 in the sector π/2 ≤θ≤π is 1 - e^(-π/24).

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Answer:

y = -3/2x + 3

The given point is (3,2).

The transformation is a rotation 90° clockwise around the point (0,1).

The rule for this transformation would be

So, the transformation would be

Therefore, the final position of the given point is (3,-3).