Find the volume of the sphere. Use 3.14 for n. Round to the nearest tenth. radius= 6ft.​

Answer:

n=5

Step-by-step explanation:

First cross multiply to get:

36n = 180

Divide both sides by 36

36n/36 = 180/36

n=5

Maria will need approximately 2209.6 square cm of paper to cover the entire container.

The formula for the surface area of a cylinder is A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.

To find the surface area of the container, we can plug in the given values for r = 11 and h = 21:

A = 2π(11²) + 2π(11)(21)

A = 2π(121) + 2π(231)

A = 242π + 462π

A = 704π

We can approximate π as 3.14, then

A ≈ 704 × 3.14

Apply the multiplication operation, and we get

A = 2,210 square cm

Thus, the surface area of a cylinder is approximately 2,210 square cm.

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Answer:

\(4\frac{2}{3}\) miles each day

Step-by-step explanation:

Divide the total number of miles traveled by the total number of days. This will give the number of miles traveled per day

14/3 = 4.667 = 4 2/3

Answer:

.................................................2

each day they traveled 4 ----      miles you have to divide 14 by 3

.................................................3

hope this helps ☺

The size of the city in 10 years is equal to 29,802.32

Given the following data:

To calculate the size of the city in 10 years:

In this exercise, you're required to determine the size of this city in the next ten (10) years.

Mathematically, the exponential growth of a population is given by this formula;

\(P = a(1+r)^t\)

Where:

Substituting the given parameters into the formula, we have;

\(P = 3200(1+0.25)^{10}\\\\P = 3200(1.25)^{10}\\\\P = 3200 \times 9.3132\)

P = 29,802.32

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The absolute deviation of each of the data values are 4, 1 and 3 respectively.

The absolute deviatuon gives the distance of any given value in a dataset to the mean value. The absolute deviation is always positive as it does not consider the side to which the value belongs.

Absolute deviation = |value - mean|

Mean = 4

Absolute deviation of 0 = |0 - 4| = 4

Absolute deviation of 3 = |3 - 4| = 1

Absolute deviation of 7 = |7 - 4| = 3

Hence, The absolute deviation of each of the data values are 4, 1 and 3 respectively.

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A parametrization of path C is x= 4t and y = 8t

Line segments on nearly trivial to parametrize. It is often it easiest to do in interval t∈ [0,1]

Then we just need to think about what we need to add to each first coordinate to get the second

Since, 0+ 4 = 4  and 0+ 8 = 8

So, parametrization is

=> x = 4t

y = 6t

(b) To evalute the line integral, we have to derivate parametrize

dx/dt = 4

dy/dt = 8

So, the differential line element is

\(ds = \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}\)

=> √(4)²+(8)²

=> 4√5

Integrating ,

\(\int\limits_{c} {x^2 + y^2} \, ds\\ = \int\limits^1_0 {(4t)^2 + (8t)^2 } 4\sqrt{5} \,dt\\=4\sqrt{5} [\frac{80}{3} t^3]^{1}_{0}\\\)

Putting the limits

=> 285.51

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The graph of the equation g(x) = 2(x + 1) - 2 on the coordinate plane is added as an attachment

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

g(x) = 2f(x + 1) - 2

Also, we have

f(x) = 2x

Recall that, we have

g(x) = 2f(x + 1) - 2

Using the above as a guide, we have the following:

f(x) = 2x

Add 1 to x

So, we have

f(x + 1) = 2(x + 1)

Subtract 2 from the function

So, we have

f(x + 1) - 2 = 2(x + 1) - 2

Substitute f(x + 1) - 2 = 2(x + 1) - 2 in g(x) = 2f(x + 1) - 2

g(x) = 2(x + 1) - 2

Next, we plot the graph of the function

See attachment for the graph

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9514 1404 393

Answer:

  -11/2x -5/12

Step-by-step explanation:

Eliminate parentheses and collect terms.

  9/4 -2(4x +4/3) +5/2x . . . . given

  = 9/4 -8x -8/3 +5/2x

  = (-16/2 +5/2)x +27/12 -32/12 . . . . use common denominators

  = -11/2x -5/12

Answer:

The answer is 6720

Step-by-step explanation:

(210 x 2) x 2) x 2) x 2) x 2) = 6720

Step by step its:

210 x 2 = 420

420 x 2 = 840

840 x 2 = 1680

1680 x 2 = 3360

3360 x 2 = 6720

Answer:

1050 Students

Step-by-step explanation:

You can do 210 x 2 which gets you 420, and is 2 of the 5 years in total.

Next you can do 420 x 2, which is 840, and gets you 4 of the 5 years in total ( including the first steps years).

Then you can do 210 x 2, which we know is 420, and add it to 210 which we know is 1 year, and it gives you 1050, the total.

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Answer:

D. The sum of the angles is 90°.

Step-by-step explanation:

The definition of complementary angles is that their measures add to 90°.

The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2

How to solve a function?

If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:

g(x) = a(4) raise to the power x-k/2

where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:

f(x) = g(x)/2

Substituting the expression for g(x) into this equation and simplifying, we get:

4raise to the power x - 6 = a(4)raise to the power x-k/2

To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:

f(0) = 4 - 6 = -5

f(1) = 4- 6 = -2

Using the equation g(x)/2 = f(x), we can write:

g(0)/2 = -5

g(1)/2 = -2

Substituting the expression for g(x) into these equations, we get:

a(4) raise to the power -k/2 = -10

a(4) raise to the power 1-k/2 = -4

Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":

(4)raise to the power -k/2 / (4)  raise to the power 1-k/2 = -10 / -4

Simplifying this equation, we get:

4.raise to the power(1-k/2) = 5

Taking the logarithm of both sides (with base 4), we get:

1-k/2 = log4(5)

Solving for "k", we get:

k = 2 - 2 log4(5)

Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":

a = -10 / (4)   raise to the power  -k/2

Substituting the numerical value of "k", we get:

k = 2 - 2 log4(5) ≈ 0.872

a = -10 / (4) raise ti the power  -k/2 ≈ 2.323

Therefore, the equation for the transformed function g(x) is:

g(x) = 2.323 (4)raise to the power x-0.872/2

or equivalently:

g(x) = 1.1615 (4) raise to the power -x0.872

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Answer:

g(x) = 1/2 (4)^x - 3

Step-by-step explanation:

A vertical compression by a factor of 1/2

means that the entire function f is multiplied by 1/2:

1/2 f (x) = 1/2 (4^x - 6)

= 1/2 (4)^x - 3

The equation of the line in the standard form exists 3x - y = 2.

The equation of a line is a representation of a line on an x-y plane that illustrates the relationship between x and y for each point on the specific line. When x and y are variables and a, b, and c are constants, a line has the standard form ax + by = c.

Y = mx + b is the slope-intercept form of a line, where x and y are variables, m is the line's slope, and b is the line's y-intercept.

The one-point formula reads: y - y₁ = m(x - x₁). to describe the equation of a line traveling through the point (x1, y1) and having a slope of m.

We are asked to graph a line with a slope = -3, passing through the point (1, -5).

We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (1, -5).

Substituting these values in the equation y - y₁ = m(x - x₁), we get

Let the equation be y - -5 = -3(x - 1)

simplifying the equation, we get

y = -3x + 3 - 5

y = -3x - 2

3x - y = 2

The equation of the line in the slope-intercept form exists y = -3x - 2

The equation of the line in the standard form exists 3x - y = 2.

We draw the locations (1,-5) (because it is obvious that the line goes through this location) and (0, 2) (since the y-intercept is at 2 and the line passes through the point (0, 2)) in order to graph this line. We draw a line connecting these places, then we expand it on both sides to create the necessary line.

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Answer:

5/24

Step-by-step explanation:

-5/12+5/8

-10/24+15/24

5/24

Answer:m<k+m<k=180+167-133=100

Step-by-step explanation:

Answer:

$246

Step-by-step explanation:

the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

The area of the shaded region is 24x² - 78x + 33.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side².

We have,

Two squares:

Smaller square:

Side = x + 4

Larger square:

Side = 5x - 7

Now,

Area of the shaded region.
= Area of the bigger square - Area of the smaller square

= (5x - 7)² - (x + 4)²

= 25x² - 70x + 49 - x² - 8x - 16

= 24x² - 78x + 33

Thus,

24x² - 78x + 33 is the area of the shaded region.

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The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The gcf is 12, so you'll divide 12 to both the 48 and the 180.

So it'll look like this...

\(12(4e+15)\)

P.S. don't forget to the "e"

If you want to check if you're right just distribute the 12 and you should get 48e + 180 if you didn't you did something wrong.

Answer:

Step-by-step explanation:

This is a proof.  You need to use theorems and definitions to get to your answer.  You cannot make any assumptions without a definition for it.  You can you use the information that you have proven from previous statements.

m<1 = m<2                               Given

QP = QR                                   Given

m<3 = m<4                               Vertical Angles

m<1 + m<3 + m<P = 180          Triangle Sum Theorem

m<P = 180 - m<1 - m<3            Subtraction

m<P = 180 - m<2 - m<3           Substitution

m<2 + m<4 + m<R = 180         Triangle Sum Theorem

m<R = 180 - m<2 - m<4           Subtraction

m<R = 180 - m<2 - m<3           Substitution

m<P = m<R                               Transitive

m<Q = m<Q                             Reflexive

ΔQTP ≅ ΔQTR                        ASA

We proved that the triangles are congruent by proving an angle, a side and another angle are the same.

<Q and <Q same

QR and QP same, this was give

<R = <P same through proof    

Answer:49 miles per hour

Step-by-step explanation: 14 miles times 35 miles = 490

but the 0 will not matter so steve was going 49 miles per hour

HOPE THIS HELPS YOU:)

The approximate arc length is,

⇒ s = 3.665  units

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, We know that;

The arc length (s) is given by,

⇒ s = r·θ

Here, We have;

r = 1

θ = 7π / 6

Hence, We get;

s = 1 × 7π/6

s = 3.665  units

Thus, The approximate arc length is,

⇒ s = 3.665  units

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Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

B) 15 hours, 34 minutes

2:12 + 15 hours = 5:12 A.M

5:12 + 34 minutes = 5:46 A.M

9514 1404 393

Answer:

  4) ΔEFG ~ ΔECD

  6) Not Similar

Step-by-step explanation:

4) Shortest to longest sides are ...

  EF : FG : GE = 14 : 16 : 20 = 7 : 8 : 10 (reduced)

  EC : CD : DE = 7 : 8 : 10

The triangles have the same side length ratios, so are similar.

  ΔEFT ~ ΔECD

__

6) Shortest to longest, the given sides have ratios ...

  UT : TV = 71 : 84 (reduced)

  GT : TH = 60 : 72 = 5 : 6 (reduced)

The side ratios are different, so the triangles are NOT SIMILAR.

Answer:

part 1. Use side ratios to determine if the triangles in each pair of similar. If so complete the similarity statement. NO LINKS!!!