The base of the cone has a radius of 4.5 inches. The height of the cone is 16 inches.

If the cone shown above is sliced by a plane that passes through the center of the base, and also passes through the top vertex, what is the area of the cross-section of the cone?

The Lame furniture company business must produce at least 50 chairs and 0 tables to maximize profits.

We denote by "x" and "y" respectively the number of chairs and tables produced by the company.

The constraints of the problems are,

5x + 9y ≤ 300 (labor constraint)

12x + 24y ≤ 800 (mahogany constraint)

The goal is to maximize the profit and the proposition can becomes:

Profit = 900x + 1300y

We can use linear programming to solve this problem First, we can draw the constraints on a coordinate plane and color the feasible region (the region that satisfies all the constraints)

We can get from Each vertex in the graph evaluates the objective function to determine the maximum profit,

(0 , 0) : Profit = 0

(0, 33.33) : Profit = 43.333

(20, 10): Profit = 29,000

(50, 0): Profit = 45,000

Therefore, the firm must produce 50 chairs and 0 tables to maximize profit.

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Answer:

8.795 is exactly half way between them

Step-by-step explanation:

That is the difference between them

The present value of the annuity at the end of year 7 is approximately $47,069.08.

To calculate the present value of an ordinary annuity, we can use the formula:

PV = PMT * [(1 - (1 + r)⁻ⁿ) / r],

where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, the annual payment is $4,500, the interest rate is 8%, and the number of periods is 16. However, the payments start at the end of year 8 and continue until the end of year 23, which means there is a delay of 7 years.

Using the formula, the present value at the end of year 7 can be calculated as:

PV = $4,500 * [(1 - (1 + 0.08)⁻¹⁶) / 0.08] = $47,069.08.

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Answer:

x = 64

Step-by-step explanation:

90 + x + 26 = 180

116 + x = 180

x = 180 - 116

x = 64

Answer:

x=64

Step-by-step explanation:

x and 26 are complementary, which means they add to 90 degrees.

x+26=90

We want to find x, so we have to get x by itself. 26 is being added on to x. To undo this, subtract 26 from both sides, because subtraction is the opposite of addition.

x+26-26=90-26

x=90-26

x=64

So, x is 64 degrees

In a statistical problem, a population consists of all items of interest in a statistical problem.The correct option in this case is option C - all items of interest in a statistical problem.

Population refers to the complete set of observations or items for which inferences are being made in statistical inference. It's the group that researchers are interested in studying, and it's the group to which they hope to extend their conclusions.

In statistics, the population is the entire collection of individuals, objects, or measurements that researchers are interested in studying. Researchers utilize statistical techniques to make inferences about population parameters based on data obtained from samples.

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It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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Answer:  76 Sodas and 40 hot dogs

Step-by-step explanation:

Let S and H represent the numbers of Sodas and Hot dogs.

We are told that:

S + H = 116

We also see that:

H = S - 36

==

Take the second equation's value for H (S - 36) and use it in the first:

S + H = 116

S + (S-36) = 116

2S = 152

S = 76

and therefore H = S - 36, or 40.

76 + 40 = 116  [Checks]

76 Sodas and 40 hot dogs

Answer:

  C) no: The packs of socks are marked up to $7 and then discounted to $4.20

Step-by-step explanation:

You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.

When the $5 cost is marked up by 40%, the resulting price is ...

  $5 + 0.40×5 = $5 +2 = $7.

The socks are marked up to $7.

When the $7 price is marked down by 40%, the resulting price is ...

  $7 - 0.40×7 = $7.00 -2.80 = $4.20

The socks are discounted to $4.20.

Answer:

We conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:

Step-by-step explanation:

Given

A number t multiplied by -4 is at least −2/5

To determine

Write the sentence as an inequality.

For the inequalities, when we mention 'at least', we can term it as 'greater than or equal to' symbol such as '≥'.

It is stated that A number t multiplied by -4 is at least −2/5.

Let 't' be the number.

Multiplying t by -4 is: -4t

Thus,  A number t multiplied by -4 is at least −2/5 will be written as:

-4t ≥ -2/5

Therefore, we conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:

Answer:

C

Step-by-step explanation:

\(\frac{480}{3000}\) x 105,000,000 = 16,800,000

A sample in which each individual in the population has an equal chance to be selected is a "simple random sampling".

A subset of such a statistical population called a simple random sample is one where each member has an equal chance of being chosen. A straightforward random sample is intended to offer an objective depiction of a group.

Some key features of simple random sampling are-

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Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

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Answer:

x=50

Step-by-step explanation:

To find the angle on the bottom left you would subtract 180-149 and get 31.

Then you would add 31 and 99 to get 130.

Then subtract 180-130 to get x=50 because all triangles equal 180 if you add all of the angles together.

Answer:

4

Step-by-step explanation:

25- 9.5 is 15.5 and 4 ×3.75 is 15 you would have still have .5 cents

Answer:

answer is c

Step-by-step explanation:

Mark my answer as brainliest

Answer:

2n +11

Step-by-step explanation:

4n+11−2n

Combine like terms

4n -2n +11

2n +11

Answer:

2n+11

Step-by-step explanation:

The term "income" refers to the money that an individual earns or receives in exchange for their work or services.

In this case, the panhandler is making $15 to $20 per day on the streets, which can be considered his income. The terms "prestige," "status," and "wealth" are not relevant in this context.
                                             A panhandler who makes $15 to $20 per day on the streets and you want to know whether this is his A) wealth, B) income, C) status, or D) prestige.

The answer is B) income. The money a panhandler makes per day can be considered his daily income.

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The clockwise rotation about the origin from the pre-image to the image​ include the following: a rotation of 90° clockwise.

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Additionally, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

Next, we would apply a rotation of 90° clockwise to the coordinate of triangle ABC as follows;

(x, y)                               →            (y, -x)

Coordinate A = (1, 1) → Coordinate A' = (1, -(1)) = (1, -1)

Coordinate B = (1, 4) → Coordinate B' = (4, -(1)) = (4, -1)

Coordinate C = (5, 1) → Coordinate C' = (1, -(5)) = (1, -5)

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Numerical analysis is a mathematical method that uses computational algorithms and mathematical models to approximate complex mathematical problems. Its applications can be found in various fields, including science, engineering, and finance, to solve practical problems.

Civil engineering is a branch of engineering that deals with the design, construction, and maintenance of the built environment. Differential equations play a crucial role in civil engineering, as they can be used to model various physical phenomena, such as heat transfer, fluid dynamics, and structural analysis.When solving differential equations numerically, one can use various numerical methods, such as Euler's method, Runge-Kutta method, and the finite difference method. These methods rely on the principle of discretization, which involves breaking down the problem into smaller, more manageable parts, and approximating the solution at each point.As your friend is a civil engineering student, they would be interested in the numerical solution of differential equations. The numerical solution of differential equations is an essential tool in engineering design and analysis. By using numerical methods, civil engineers can simulate the behavior of complex systems, such as bridges, dams, and buildings, and optimize their designs to ensure their safety and durability.

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Answer:

(-(23/3), -(11/3))

Step-by-step explanation:

x=y-4

2x-5y=3

=====

2x-5y=3

2(y-4)-5y=3 [Substitute (y-4) for x in the 2nd equation]

2y - 8 -5y = 3

-3y = 11

y = -(11/3)

y = -3 2/3

Use this in the 1st equation to find x:

x=y-4

x=-(11/3)-4

x = -(11/3)-(12/3)

x = -(23/3)

x = -7 2/3

See graph attached.

Answer:

True.

Step-by-step explanation:

The distributive property of real numbers says

a(b + c) = ab + ac. Here, the number outside multiplies the numbers only in the parentheses. Therefore the statement is true. The number located outside can be applied to only numbers in parentheses.

Answer:

True

Step-by-step explanation:

The coefficient of determination is a statistical measure that indicates the proportion of variability in the dependent variable that can be explained by the independent variable(s) in a regression model. It is also known as R-squared and is expressed as a fraction between 0 and 1. The closer the value is to 1, the better the fit of the model.

The coefficient of determination can be thought of as the fraction of variability that can be accounted for by the slope of the regression model. The slope is the change in the dependent variable per unit change in the independent variable. In other words, it represents the rate of change in the dependent variable due to a change in the independent variable.

Therefore, a higher coefficient of determination means that a larger proportion of the variability in the dependent variable is explained by the slope of the regression model. This is important because it provides information on the accuracy and usefulness of the model. If the coefficient of determination is low, it may indicate that the model is not a good fit for the data and needs to be revised.
In conclusion, the coefficient of determination is a crucial measure in regression analysis that helps to assess the proportion of variability in the dependent variable that can be explained by the slope of the regression model. It is expressed as a fraction between 0 and 1 and provides important information on the accuracy and usefulness of the model.
In other words, it represents the proportion of the total variability in the dataset that the model is able to explain.

The coefficient of determination ranges from 0 to 1, with values closer to 1 indicating that the regression model is better at explaining the variability in the data. When interpreting R-squared, keep in mind that a higher value doesn't always imply a good model, as it can sometimes be due to overfitting.

To calculate R-squared, you would first fit a regression model to your data. The regression model typically consists of a slope, which represents the rate of change between the independent variable (x-value) and dependent variable (response), and an intercept, which is the point where the regression line crosses the y-axis.

Once the model is fit, you can compute the sum of squares due to regression (SSR) and the total sum of squares (SST). The coefficient of determination is then found by dividing SSR by SST.

R-squared = SSR / SST

By understanding the coefficient of determination, you can evaluate the effectiveness of a regression model in accounting for the variability in the data and make informed decisions based on its performance.

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Answer:

33.02 cm in 13inches

Step-by-step explanation:

Answer:

42 quarts

Step-by-step explanation:

There are 4 quarts in one gallon, so you'd just multiply.

Answer:

the correct answer is A.

Step-by-step explanation:

Hope it will help you..

The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".

Given:

Length of the garden = 24 feet

Diagonal of the garden = 30 feet

Using the Pythagorean theorem, we can set up the following equation:

\(24^2\) + \(w^2\) = \(30^2\)

Simplifying:

576 + \(w^2\) = 900

Subtracting 576 from both sides:

\(w^2\) = 900 - 576

\(w^2\) = 324

Taking the square root of both sides:

w = √324

w = 18

So, the width of the garden is 18 feet.

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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.

Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.

The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).

The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.

In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

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The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The confidence interval provides a range of values within which the true population mean height is likely to fall with a 95% level of confidence. It does not provide information about individual orangutans' heights or the sample mean's precise location within the interval.

Therefore, The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

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