When the sun is 62° above the horizon, a building casts a shadow 18 m long. How tall is the building?

Answer:

i have the answer but you just have to calculate the answer is 5

The differential equation y''+2y'+3y=0 is a second order linear differential equation. Therefore, option a is the correct answer.

What is a linear differential equation?

A differential equation is said to be linear if its dependent variable and all its derivatives occur only in the first degree and are not multiplied together. This means that the dependent variable and its derivatives appear as separate variables.

For example, the following differential equation is linear:

y′′(x) + xy′(x) + y(x) = 0

On the other hand, a nonlinear differential equation is one that involves powers or products of the dependent variable or its derivatives. For example:

y′′(x) + (y(x))² = 0

What is a second order differential equation?

A differential equation is said to be of the second order if it contains two derivatives of the dependent variable. For example, the differential equation:

3y′′(x) + 2y′(x) + y(x) = 0

is a second order differential equation.

What is the solution to a second order linear differential equation?

The general solution to a second order linear differential equation of the form:

y′′(x) + p(x)y′(x) + q(x)y(x) = 0 is given by:

y(x) = c₁y₁(x) + c₂y₂(x)

where y₁(x) and y₂(x) are two linearly independent solutions of the differential equation.

The constants c₁ and c₂ are found by applying initial or boundary conditions that specify the values of y and its derivative at one or more points in the domain of the differential equation.

Hence, the differential equation y''+2y'+3y=0 is a second order linear differential equation. Therefore, option a is the correct answer.

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The functions are arranged/combined as follows

21. 595

22. 6a² + 25ab - 3b² + 6

23. 2b - 2

24. 7x² - 5xy + y²

25. 3x - 24y - 4

Descending powers involves making the highest power to be the first term

The equations are solved one after the other as follows

21.

720 + 40 - 60 - 120 + 15 = 595

22.

25ab + 6a² - 3b² + 6 =

6a² + 25ab - 3b² + 6

23.

= 3a + 2b - 3a + 1 - 3

= 3a - 3a + 2b + 1 - 3

= 2b - 2

24.

= 3x² - 2xy + 4x² - 3xy + y²

= 7x² - 5xy + y²

25.

= 2x + x + 25y - y - 4

= 3x - 24y - 4

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The least expensive rectangular storage container without a lid, with a volume of 10 cubic meters, has a length three times its width.  The total cost of the least expensive box is $750.  

Let's assume the width of the rectangular container is x meters. According to the given information, the length of the base is three times the width, so the length is 3x meters. The height of the box can be determined by dividing the volume by the area of the base, giving us a height of 10/(3x^2) meters.  

The cost of the base can be calculated by multiplying the area of the base (3x * x = 3x^2) by the cost per square meter ($20). Therefore, the cost of the base is 3x^2 * $20 = $60x^2.

The cost of the sides can be calculated by finding the area of the four sides (2 * 3x * 10/(3x^2) + 2 * x * 10/(3x^2)), which simplifies to 20/x. Multiplying this by the cost per square meter ($10) gives us a cost of $200/x.

To find the total cost, we sum the cost of the base and the cost of the sides: $60x^2 + $200/x. To minimize the cost, we can take the derivative with respect to x, set it equal to zero, and solve for x. The result is x = √(100/3). Substituting this value back into the cost equation, we find the minimum cost is approximately $750.

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A 95% confidence interval for the estimated proportion of Canadians who refused the H1N1 vaccination can be calculated as follows:

Let p be the true proportion of Canadians who refused the vaccination.

The sample proportion is estimated by:

p_hat = 700 / 1000 = 0.7

The standard error of the sample proportion is:

SE = sqrt(p_hat * (1 - p_hat) / 1000) = sqrt(0.7 * 0.3 / 1000) = 0.0247

Using a normal approximation and a z-score of 1.96 (corresponding to a 95% confidence level), the confidence interval can be calculated as:

p_hat +/- z * SE = 0.7 +/- 1.96 * 0.0247 = [0.6511, 0.7489]

So, with 95% confidence, we can estimate that the true proportion of Canadians who refused the H1N1 vaccination lies between 0.6511 and 0.7489.

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Answer:

I don't know what the question is, but 7.5 miles in 1/4 hour is equal to 30 mph.

The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

First five terms of the recursive sequence defined by a1 = 2, a2 = 3, and an = an-2 * an-1.
1. First term (a1): Given as 2.
2. Second term (a2): Given as 3.
3. Third term (a3): To find a3, use the formula an = an-2 * an-1. In this case, n = 3, so a3 = a1 * a2 = 2 * 3 = 6.
4. Fourth term (a4): Similarly, to find a4, use the formula with n = 4. So a4 = a2 * a3 = 3 * 6 = 18.
5. Fifth term (a5): Finally, to find a5, use the formula with n = 5. So a5 = a3 * a4 = 6 * 18 = 108.
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

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c. 11%. This means that the average forecasted demand deviates from the actual demand by approximately 11%.

The Mean Absolute Percent Error (MAPE) measures the accuracy of a forecast by calculating the percentage difference between the actual demand and the forecasted demand. To calculate the MAPE, you can follow these steps:

1. Calculate the absolute percent error (APE) for each day by subtracting the forecasted demand from the actual demand, taking the absolute value of the difference, and dividing it by the actual demand. Here are the APE values for each day:
  Day 1: |(16-20)/16| = 20%
  Day 2: |(19-20)/19| = 5.26%
  Day 3: |(21-20)/21| = 4.76%
  Day 4: |(21-20)/21| = 4.76%
  Day 5: |(22-20)/22| = 9.09%
  Day 6: |(17-20)/17| = 17.65%

2. Calculate the mean of the APE values by summing them up and dividing by the total number of days:
  (20% + 5.26% + 4.76% + 4.76% + 9.09% + 17.65%)/6 ≈ 10.98%

3. Finally, multiply the mean APE by 100 to convert it into a percentage. This gives us the MAPE:
  10.98% * 100 = 10.98%

Therefore, the MAPE for the given dataset is approximately 10.98%.

c. 11%. This means that the average forecasted demand deviates from the actual demand by approximately 11%.

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hope it helps. ...........

Based on the calculations, the sample standard deviation is equal to 4.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{\bar x\;-\;u}{\delta}\)

Where:

In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:

Note: Variance, δ² = 16

Taking the square root of the variance, we have:

Standard deviation, δ = √16

Standard deviation, δ = 4.

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Complete Question:

A sample of n=225 scores has \(\bar x\) = 103 and δ² = 16. What is the sample standard deviation?

In order to determine what type of model is being referred to, more context is needed. However, if the model is being used in a scientific or analytical context, it is likely that the model would be either statistical or mathematical.

A statistical model is a mathematical representation of data that describes the relationship between variables. A mathematical model, on the other hand, is a simplified representation of a real-world system or phenomenon, using mathematical equations to describe the relationships between the different components. These types of models are often used in fields such as engineering, physics, and economics, and can be used to make predictions or test hypotheses. In some cases, models may also incorporate simulations or physical components, but this would depend on the specific context and purpose of the model.

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Answer:

150 ft

Step-by-step explanation:

Hence, the sum of the fixed expenses ($75 + $25 = $100) and the expressions variable charges ($15 per person) would equal the total cost for catering.

Mathematically speaking, you can multiply, divide, add, or subtract. This is how an expression is constructed: Math operation, expression, and numerical value Functions, parameters, and numbers make up a mathematical expression. It is feasible to use opposing words and phrases. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical operation between them. As an instance, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.

Finding the slope of the line will allow you to compute the rate of change for Smokey Joe's catering. The slope in this instance is $15, which indicates that the price will rise by $15 for each extra person served. The variable cost that Smokey Joe's incurs every person served is represented by this rate of change.

If Smokey Joe's charges a $25 delivery fee, this will be an extra set expense that they will pay no matter how many customers they serve. Hence, the sum of the fixed expenses ($75 + $25 = $100) and the variable charges ($15 per person) would equal the total cost for catering.

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For the year in which they earned $176,500, the partners will receive $52,950, $35,300, and $88,250 respectively.

Here let the partners be A, B, and C.

According to the question, A: B: C = 3: 2: 5

This implies that if the profits are divided into

3 + 2 + 5 = 10 equal parts, 3 of those parts will go to A, 2 of those parts will go to B and 5 of those parts will go to C.

Here the profits for the year are $176,500.

Now dividing them into 10 equal parts will give us the value of each part to be

$176, 500/10 = $17,650

Hence A will receive $17,650 X 3 = $52,950

B will receive $17,650 X 2 = $35,300

C will receive $17,650 X 5 = $88,250

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Answer:

\(-\sqrt{2}\)

Step-by-step explanation:

Note that:

\(a^2-2ab+b^2=(a-b)^2 = 4ab \\ \\ a^2 + 2ab+b^2 = (a+b)^2 = 8ab \\ \\ \implies \frac{a+b}{a-b}=\frac{\sqrt{8ab}}{-\sqrt{4ab}}=-\sqrt{2}\)

Answer:

\(\sf \dfrac{a+b}{a-b}= -\sqrt{2}\)

Step-by-step explanation:

\(\sf a^2 + b^2 = 6ab \qquad where\:\:0 < a < b\)

Basic formula:

\(\sf (a + b)^2 = a^2 +b^2 +2ab\)

\(\sf (a - b)^2 = a^2 + b^2 -2ab\)

solve for a + b

\(\sf \rightarrow a^2 + b^2 = 6ab\)

\(\sf \rightarrow (a+b)^2-2ab = 6ab\)

\(\sf \rightarrow (a+b)^2 = 6ab+2ab\)

\(\sf \rightarrow (a+b)^2 = 8ab\)

\(\sf \rightarrow a+b = \pm \sqrt{8ab}\)

solve for a - b

\(\sf \rightarrow a^2 + b^2 = 6ab\)

\(\sf \rightarrow (a-b)^2 + 2ab = 6ab\)

\(\sf \rightarrow (a-b)^2 = 6ab-2ab\)

\(\sf \rightarrow (a-b)^2 = 4ab\)

\(\sf \rightarrow a-b = \pm \sqrt{4ab}\)

Now solve for (a + b)/(a - b)

\(\sf \rightarrow \dfrac{a+b}{a-b}= \dfrac{\pm\sqrt{8ab} }{\pm\sqrt{4ab} }\)

\(\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt\dfrac{8ab }{4ab}\)

\(\sf \rightarrow \dfrac{a+b}{a-b}= \pm \sqrt{2}\)

As, the value of b is greater than the value of a and both the values a  and b are greater than 0. It turns the value of expression negative as the denominator will be always evaluated to negative integer and the numerator value always > 0. So, the answer will be negative, -√2.

\(\sf \rightarrow \dfrac{a+b}{a-b}= - \sqrt{2}\)

To perform a hypothesis test on the proportion of people who subscribe to a cable television service versus others, we need to check the following conditions:

1. Random Sampling: Ensure that the sample is randomly selected, which means each person has an equal chance of being selected. This is important to avoid biases and ensure the sample is representative of the population.

2. Independence: If sampling without replacement, the sample size (n) should be less than 10% of the population size (N) to assume independence. This is called the 10% Rule. Independence is important because the outcome of one person's choice should not affect another person's choice.

3. Normality: We need to ensure that the sampling distribution of the sample proportion (p-hat) is approximately normal. This can be checked using the success-failure condition, which states that both np and n(1-p) should be greater than or equal to 10. This ensures that the distribution is sufficiently normal to apply the z-test.

To help the student, remind them to:

1. Verify that the sample is random.
2. Check the independence condition by confirming the sample size is less than 10% of the population size.
3. Check the normality condition by calculating np and n(1-p) and making sure both values are greater than or equal to 10.

It is crucial to check these conditions because if they are not met, the hypothesis test's results may not be valid or reliable. Meeting these conditions ensures that the statistical methods applied are appropriate and provide accurate results for making conclusions.

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Answer:

Terrence made $30 more than Teresa.

Step-by-step explanation:

Giving the following information:

Terrence earns $450 per week.

Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.

First, we need to structure the total income formula for each:

Terrence= 450

Teresa= 300 + 0.06*x

x= sales

Now, for $2,000 sales of books:

Terrence= $450

Teresa= 300 + 0.06*2,000= $420

A chart that is recommended as an alternative to a pie chart is a - stacked column chart. A chart that is recommended as an alternative to a pie chart is a stacked column chart. Question 24: A data visualization tool that updates in real time and gives multiple outputs is called - a data dashboard.

A data visualization tool that updates in real time and gives multiple outputs is called a data dashboard. What is a scatter plot? A scatter plot is a type of diagram used to display two variables on a two-dimensional plot. The positioning of data points on a scatter plot graphically depicts the correlation between the two variables. To construct a scatter plot, two variables (independent and dependent variables) are plotted on a graph.

The independent variable is plotted on the horizontal (x) axis and the dependent variable is plotted on the vertical (y) axis. A point is plotted for each pair of values, and the pattern of the points suggests a relationship between the two variables.A scatter plot is useful in displaying the correlation between two variables. The correlation is positive if the points are in an upward direction. The correlation is negative if the points are in a downward direction. A lack of correlation, or random points, is suggested by a scatter plot with no apparent pattern.

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You will need amount of 1.5 cups of butter if you plan to use 3 cups of flour in your recipe.

To calculate how much butter is needed for 3 cups of flour in a recipe, start by identifying that the recipe requires a ratio of 1 cup of butter for every 2 cups of flour. To get the amount of butter needed for 3 cups of flour, multiply 1 cup of butter by 1.5. This will give you 1.5 cups of butter, which is the amount needed for 3 cups of flour.  Therefore, you will need 1.5 cups of butter if you plan to use 3 cups of flour in your recipe.  To ensure accuracy, it is recommended to measure the ingredients carefully and double check your calculations before proceeding.

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Answer:

x = 13

Step-by-step explanation:

x = 7 + 8 - 2

x = 7+6 = 13

just move 2 to the other side

Answer:

the second answer is correct

Step-by-step explanation:

Answer:

8 1/3 feet need to be purchased

Step-by-step explanation:

if it's a square garden and we know the length of one side is 3 1/4 ft then the other three sides are also 3 1/4 ft

as an improper fraction, 3 1/4 equals 13/4

to get the total amount of fencing needed we can multiply 13/4 and 4

13/4 x 4/1 = 13

so 13 feet in total is needed but he already has 4 2/3 so we must subtract

4 2/3 from 13

we can change 13 to become 12 3/3 before we subtract

12 3/3 - 4 2/3 equals 8 1/3

Answer:

Hello,

Step-by-step explanation:

1/4 of an circle - the triangle

\(Area=\dfrac{\pi*26^2}{4} -\dfrac{26^2}{2} \\\\=169*(\pi-2)\approx{192,93}\)

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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On dividing the circumference and the diameter of our Jack-o-Lantern we will get π.

A Jack-o-Lantern can be considered spherical in shape.

The circumference of a #D shape is the intersection of the 3D shape with any plane passing through its center.

Hence the circumference of a jack-o-lantern will be the perimeter of the circle that has been cut through its center.

Let the radius of our Jack-o-lantern be r cm.

The formula of a circumference of a sphere is 2πr

where r is the radius of the sphere.

The diameter of a sphere is twice its radius.

Therefore, the diameter of our jack-o-lantern will be

2r cm.

By dividing the circumference and the diameter we get

2πr cm / 2r cm

= π

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The total weight is 18.5 kilograms

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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