Which number when rounded to the nearest hundredth is 37.62?

A. 37.612
B. 37.618
C. 37.627
D. 37.626

We need to find the volume of the pyramid.

We know that the pyramid has the same base area as the prism since they have the same base: a rectangle with dimensions a and b.

Also, both the figures have the same altitude c.

The volume V₁ of the prism is given by the formula:

And the volume V₂ of the pyramid is given by the following formula:

We know that the prism has a volume of 39 units³. Thus, we have:

Then, using this information into the formula for the volume of the pyramid, we obtain:

Therefore, the volume of the pyramid is 13 units³.

Answer:

13 units

Step-by-step explanation:

Answer:

i got

\( - \frac{11}{12} \)

I do not know if I'm right please tell me me if I'm wrong

Rewrite the sums as

\(\displaystyle S_2 = \sum_{k=1}^n \frac{k^2}{2k^2 - 2nk + n^2} = \sum_{k=1}^n \frac{\frac{k^2}{n^2}}{\frac{2k^2}{n^2} - \frac{2k}n + 1}\)

and

\(\displaystyle S_3 = \sum_{k=1}^n \frac{k^2}{3k^2 - 3nk + n^2} = \sum_{k=1}^n \frac{\frac{k^2}{n^2}}{\frac{3k^2}{n^2} - \frac{3k}n + 1}\)

Now notice that

\(\displaystyle \lim_{n\to\infty} \frac{S_2}n = \int_0^1 \frac{x^2}{2x^2 - 2x + 1} = \frac12\)

and

\(\displaystyle \lim_{n\to\infty} \frac{S_3}n = \int_0^1 \frac{x^2}{3x^2 - 3x + 1} = \frac{9 + 2\pi\sqrt3}{27}\)

and the important point here is that \(\frac{S_2}n\) and \(\frac{S_3}n\) converge to constants. For any real constant a, we have

\(\displaystyle \lim_{n\to\infty} \frac{\ln(an)}n = 0\)

Rewrite the limit as

\(\displaystyle \lim_{n\to\infty} \sqrt[n]{S_2 \times S_3} = \lim_{n\to\infty} \exp\left(\ln\left(\sqrt[n]{S_2 \times S_3}\right)\right) \\\\ = \exp\left(\lim_{n\to\infty} \frac{\ln(S_2) + \ln(S_3)}n\right) \\\\ = \exp\left(\lim_{n\to\infty} \frac{\ln\left(n \times \frac{S_2}n\right) + \ln\left(n \times \frac{S_3}n\right)}n\right)\)

Then

\(\displaystyle \lim_{n\to\infty} \sqrt[n]{S_2 \times S_3} = e^0 = \boxed{1}\)

A plot of the limand for n = first 1000 positive integers suggests the limit is correct, but convergence is slow.

Answer:

  (a)  3x +y = 2

Step-by-step explanation:

You want the equation y = -3x +2 written in standard form.

The standard form of a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.

To put the given equation into that form, we can add 3x to both sides:

  3x +y = 3x -3x +2

  3x +y = 2

Answer:

5000000+800000+30000+4000+800+40+6

Step-by-step explanation: this is correct

The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

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Disclaimer:

The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

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Answer:

I think its 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Outline

You could have 2 values. The way to get them is to take the square root of 25, c is double the value you get for the first step.  Why 25? Well you only have 1 other choice and that is the 1 that is in front of the x^2. That's not very helpful.

Formula

c = ± 2*sqrt(25)

Solution

c = ± 2 * sqrt(25)

c = ± 2 * 5

c = ± 10

Comment

Where does the ± come from?

You need to get + 25

If you have (x - 5)(x - 5) the last term will be -5 * - 5 = 25

Similarly you get the same result with (x + 5)(x + 5)

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.

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Answer: The correct answer is A. they lie in the same plane.

Step-by-step explanation:

If four points are coplanar, it means they all lie in the same plane. This is because a plane is defined as a two-dimensional flat surface that extends infinitely in all directions, and any four non-collinear points uniquely define a plane.

Option B is not correct because three points being coplanar does not necessarily imply that a fourth point will also be coplanar with them.

Option C is not correct because collinear points lie on the same straight line, not on the same plane.

Option D is not correct because if points are not in the same plane, they are not coplanar.

Answer:

\(3x + 6y = 1200\) is the correct linear equation.

Step-by-step explanation:

Given:

Time taken to manufacture an office chair = 3 hours

Number of office chairs produced = \(x\)

Time taken to manufacture an office desk = 6 hours

Number of office desks produced = \(y\)

Let us calculate, Total Time taken to manufacture \(x\) chairs.

Suppose we manufacture 2 chairs, time taken = 3 hours + 3 hours i.e. = 6 hours

Suppose we manufacture 3 chairs, time taken = 3 hours + 3 hours + 3 hours i.e. = 9 hours

Now, we are manufacturing \(x\) number of chairs so we have to add 3 for \(x\) number of times:

OR

simply multiply 3 with \(x\).

i.e. Total time taken in producing \(x\) chairs = 3\(x\) hours

Similarly Total time taken in producing \(y\) desks = 6\(y\) hours

We have a total of 1200 hours to produce this type of office chairs and desks:

So, 1200 = Total time taken in producing \(x\) chairs + Total time taken in producing \(y\) desks

Putting the values, we get the following:

\(3x+6y=1200\) is the correct linear equation for the situation.

Answer:

Step-by-step explanation:

You could use a distance formula or pythagorean theorem (which is where the distance formula comes from) but if you look at these points this line is just literally a flat straight horizontal line. You could count squares on a graph or visualize in your head that it goes from -4 to 3. See image.

Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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The reasonable domain for the function f(x) = -2/3x + 4 in this situation is B. 0 ≤ x ≤ 6

In this question, we have:

Function, f(x) = -2/3x + 4

Where

x is the bottles of hand sanitizer per month

The function f(x) cannot be less than 0

So, we have

-2/3x + 4 = 0

This gives

-2/3x = -4

Solve for x

x = 6

This means that x cannot exceed 6

Hence, the domain is (b) . 0 ≤ x ≤ 6

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

d = 5

Step-by-step explanation:

For:

(X1, Y1) = (2, 3)

(X2, Y2) = (2, 8)

Distance Equation Solution:

d=(2−2)2+(8−3)2−−−−−−−−−−−−−−−√

d=(0)2+(5)2−−−−−−−−−√

d=0+25−−−−−√

d=2–√5

d=5

Answer: -12

Step-by-step explanation: -4 * 3 = -12

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Answer: It snowed 3.5 inches on Monday and Tuesday combined.

Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow

Hope this helped!

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer: x=14 y=10

Step-by-step explanation:

The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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Simplifying the expression 15at +3bt + 5ax + bx, we get (3t + x)(5a + b)

from the question, we have the following parameters that can be used in our computation:

15at +3bt + 5ax + bx

Factor the expression

So, we have

3t(5a + b) + x(5a + b)

Factor out 5a + b from the expression

So, we have

(3t + x)(5a + b)

Hence, the solution is (3t + x)(5a + b)

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The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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Answer:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Step-by-step explanation:

1 2 33

Convert them all into decimals. Percent is just 0.--, and the fraction you can calculate out which gives: 0.625=5/8,0.64=64%

5/8

64%

0.65

Answer:

0+0

Step-by-step explanation:

0+0=0 and 7x0=0

Answer:

0+0

Step-by-step explanation:

0+0=0 7x0=0

Answer:

75%

Step-by-step explanation:

100/64*48=75%