(b) the water level drops at a rate of 0.1 cm per hour. at what rate is the radius of the water decreasing when the depth is 4 cm? round your answer to four decimal places.

Answer: The expression for number of faces of a pyramid =1+n

Step-by-step explanation:

A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .

Its base describe the number of other faces of it.

For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....

So the total number of faces in a pyramid = base + lateral faces

If a pyramid has n sides therefore it give rise to n lateral faces such that

The total number of faces in a pyramid= 1+n .

The total number of faces of the pyramid is [tex]n+1[/tex].

A pyramid is a three-dimensional structure whose lateral sides converge to a single step at the summit, roughly forming a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any other polygon shape.

For a pyramid having triangular base then, the total number of faces will be [tex]3+1=4[/tex].

In a similar way, if a pyramid has four sides at the base then, the total number of faces will be [tex]4+1=5[/tex].

Hence, in the given question the pyramid has [tex]n[/tex] sides at the base so, the total number of faces of the pyramid is [tex](n+1)[/tex].

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The student's questions relate to high school-level mathematics, such as using a graphing calculator for probability distribution calculations, the practice of mental arithmetic, and understanding significant figures and rounding. Some problems also touch on algebraic thinking and the application of mathematics in real-world contexts.

The student is asking several questions that pertain to solving mathematical problems and making calculations, which fall within the subject of Mathematics. It's apparent that the questions involve using a graphing calculator, understanding probability distributions, mental arithmetic, and solving equations. This level of mathematics typically corresponds to High School curriculum.

For instance, the student mentions using a graphing calculator to find a probability with a binomial distribution (binompdf), which indicates a familiarity with statistical functions and probability theory. The second part of the series includes an arithmetic puzzle meant to encourage mental math skills by breaking down a problem into more manageable parts. Another problem gives insight into significant figures and decimal places, suggesting the topic of precision and rounding in measurements or calculated results.

Additional parts of the problems focus on making estimates and using ratios for time calculations, implying topics potentially from an algebra or pre-calculus course, with a touch on the real-world application of mathematics and the flexibility and multiple methods within the mathematical process.

Answer:

The water will be 4 times more as compared to the original.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

f(n)= -6.5n +14.5

f(1)= 8, f(n+1) = f(n) - 6.5

Step-by-step explanation:

the arithmetic sequence 8, 1.5, –5, –11.5 . . .

First term is 8

Now we find difference between the terms

1.5 - 8= -6.5

-5-1.5= -6.5

difference is -6.5

The formula is f(n)= a1 + (n-1)d

where a1 is the first term and d is the difference

f(n)= 8 + (n-1)(-6.5)

f(n)= 8 -6.5n+6.5

f(n)= -6.5n +14.5

To get recursive formula we use

f(n+1) = f(n)+ difference

f(1)= 8, f(n+1) = f(n) - 6.5

The functions that represent the arithmetic sequence is given by:

f(n) = –6.5n + 14.5

f(n+1) f(n) – 6.5, f(1) = 8

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In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the nth term is given by:

[tex]f(n) = a_1 + (n-1)d[/tex]

The sequence can also be represented by a recursive sequence, given by:

[tex]f(1) = a_1[/tex]

[tex]f(n+1) = f(n) - d[/tex]

In this sequence:

Thus, the possible representations are:

[tex]f(n) = a_1 + (n-1)d[/tex]

[tex]f(n) = 8 - 6.5(n-1)[/tex]

[tex]f(n) = 8 - 6.5n + 6.5[/tex]

[tex]f(n) = -6.5n + 14.5[/tex]

And

[tex]f(1) = a_1[/tex]

[tex]f(n+1) = f(n) - d[/tex]

[tex]f(1) = 8[/tex]

[tex]f(n+1) = f(n) - 6.5[/tex]

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The minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

[tex]f(x,y)=2x^2+3y^2-4x-2, g(x,y)=x^2+y^2-16.[/tex]

[tex]f_x (x,y)=4x+0-4-0=4(x-1)[/tex]

[tex]f_y (x,y)=0+6y-0-0=6y[/tex]

[tex]4(x-1)=0, x=1[/tex]

[tex]6y=0, y=0.[/tex]

So, critical points of [tex]f(x,y)[/tex] is [tex](1,0)[/tex].

Put this in [tex]g(x,y)=x^2+y^2-16[/tex].

[tex]g(1,0)=1^2+0^2-16=-15<0[/tex].

So, critical point is in the interior point of the given region.

[tex]g_x (x,y)=2x+0-0=2x[/tex]

[tex]g_y (x,y)=0+2y-0=2y[/tex]

Let there is a parameter [tex]\lambda[/tex] such that [tex]f_x = \lambda g_x[/tex] and [tex]f_y = \lambda g_y[/tex].

[tex]4(x-1)=\lambda (2x)[/tex] and [tex]6y=\lambda (2y)[/tex]

So, [tex]2(x-1)=x\lambda[/tex] and [tex]\lambda=3[/tex]

So, [tex]2(x-1)=3x[/tex]

So, [tex]-2=x[/tex]

Put [tex]x=-2[/tex] in [tex]x^2+y^2=16[/tex], to determine the value of [tex]y[/tex].

[tex](-2)^2+y^2=16[/tex]

[tex]y^2=12[/tex]

[tex]y=\pm 2\sqrt{3}[/tex]

So, the obtained possible extrema are [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

Now, find [tex]f(x,y)[/tex] at [tex](1,0), (-2, -2\sqrt{3}),[/tex] and [tex](-2, 2\sqrt{3})[/tex].

[tex]f(1,0)=2(1)^2+3(0)^2-4(1)-2[/tex]

[tex]=2-4-2[/tex]

[tex]=-4[/tex]

[tex]f(-2,-2\sqrt{3})=2(-2)^2+3(-2\sqrt{3})^2-4(-2)-2[/tex]

[tex]=8+36+8-2[/tex]

[tex]=50[/tex]

[tex]f(-2,2\sqrt{3})=2(-2)^2+3(2\sqrt{3})^2-4(-2)-2[/tex]

[tex]=8+36+8-2[/tex]

[tex]=50[/tex]

So, the minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].

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Vail Ski Shop won't receive any credit because the payment did exceed the discount period. Vail's outstanding balance is $716, calculated by subtracting the partial payment from the original invoice.

The $1,201 invoice dated July 8 with 2/10, 1/15, n/60 terms means that Vail Ski Shop receives a discount  if paid within certain time periods, specifically a 2% discount if paid within 10 days, a 1% discount if paid within 15 days, and full payment is required within 60 days. However, since Vail made a partial payment of $485 on July 22, the days had already exceeded both the 10 and 15-day discount periods. This implies that Vail should not receive any credit.

To calculate Vail's outstanding balance, we would subtract the amount Vail has paid partially from the original invoice. So, the calculation would be $1,201 - $485 which equals $716. Therefore, Vail's outstanding balance would be $716.

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A standard deviation of zero in a data set signifies that all data points are identical, with no variation among them.

When calculating one variable statistics, if you find that the standard deviation is equal to zero, it means that all of the data points in the set have the same value. There is no spread or variability within the data, as standard deviation measures how much each number in a set differs from the mean of the data set. Since all numbers are the same, they all equal the mean, resulting in zero deviation.

If owners of a business must spend less than $140 on supplies. They have already spent $60. Now they want to buy chairs that cost $20 each. Let x represent the number of chairs they can buy. Then they can buy any number of chairs fewer than 4.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given,

owners of a business must spend less than $140 on supplies.

They have already spent $60.

They want to buy chairs that cost $20 each.

Let x represent the number of chairs they can buy.

60+20x<140

Now solve for x

20x<140-60

20x<80

Divide both sides by 20

x<80/20

x<4

Hence they can buy any number of chairs fewer than 4

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To solve this problem, we use the formula:

z = (x – u) / s

where z is the z score value which can be obtained from the tables, x is the sample value, u is the mean = 6.3 min, and s is the std dev = 2.2 min

at P value = 0.90, the z = 1.28, finding for x:

x = z s + u

x = 1.28 * 2.2 + 6.3

x = 9.116

at P value = 1.0, the z = 3.49, finding for x:

x = z s + u

x = 3.49 * 2.2 + 6.3

x = 13.978 ~ 14

Therefore the longest 10% calls last about 9.1 minutes to 14 minutes

Answer:

That huy is wrong... the answer is negetive! People

Step-by-step explanation:

The absolute error of the veterinarian's estimate is 0.5 kg, and the percent error is approximately 5.3% when rounded to the nearest tenth.

The question given asks us to find the absolute error and the percent error of a veterinarian's estimate of a puppy's weight. To calculate the absolute error, we take the actual weight of the puppy (9.5 kg) and subtract the veterinarian's estimate (9 kg), which gives us an absolute error of 0.5 kg. To find the percent error, we divide the absolute error by the actual weight and multiply by 100, resulting in a percent error of about 5.3% when rounded to the nearest tenth.

Here is the step-by-step breakdown:

The bakery takes up 1/10 of the total shopping center space. Since the shopping center is 4,500 square feet, the bakery is 450 square feet.

To determine the size of the bakery in square feet, we need to calculate 1/10th of the total shopping center's area. The shopping center is 4,500 square feet in total. So, the calculation would be:

Here's the step-by-step calculation:

Therefore, the bakery takes up 450 square feet of space within the shopping center.