Solve for 2 in the diagram below.
120°
32°
T=

Answer:

192 [tex]ft^2[/tex]

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

[tex]\pi[/tex] is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]

2. [tex]Surface\ Area = 4\pi r^2[/tex]

Given volume is 256 ft³.

[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]

So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].

Answer:

192

Step-by-step explanation:

Answer:

because this is equal to the given matrix, the given matrix is symmetric.

Step-by-step explanation:

A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.

Answer:

A. 44º

Step-by-step explanation:

The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:

1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given

2) [tex]a = b[/tex], [tex]c = d[/tex] Given

3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.

4) [tex]c + d + e = 180^{\circ}[/tex] Given.

5) [tex]b + c = 90^{\circ}[/tex] Given.

6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)

7) [tex]a = 44^{\circ}[/tex] Algebra

8) [tex]b = 44^{\circ}[/tex] By 2)

9) [tex]b= f[/tex] Alternate internior angles.

10) [tex]f = 44^{\circ}[/tex] By 8). Result

Hence, the answer is A.

The correct answer is $750

Explanation:

The total of food the Masmin family spend according to the graph is 15%. Now, to know the amount of money this represents, it is necessary to find the 15% of $5000, which is the total budget. The steps to do this are shown below.

1. To calculate the percentage of a given number, first, write all values

5000 = 100%

 x       =  15%

2. Use cross multiplication, this means you multiply 5000 by 15 and x by 15

x 100 = 75000

3. Solve the equation to find x or the 15% of 5000

x = 75000 ÷ 100

x = 750

Answer:

x = 7

Step-by-step explanation:

The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.

7x - 7 = 4x + 14

3x = 21

x = 7

Answer:

There are six terms in the series

Step-by-step explanation:

We can see that n starts from 0, and ends at 5. There are therefore 6 terms in this series - as 0 is included. Therefore there will be 6 terms in this series, not 5.

There are six terms in the given series.

Answer:

(a) The mean of the weight of the mice is 50.26 grams.

(b) The standard deviation of the weight of the mice is 14.08 grams.

Step-by-step explanation:

(a)

The mean is given as follows:

[tex]\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/tex]

    [tex]=\frac{5026}{100}\\\\=50.26[/tex]

Thus, the mean of the weight of the mice is 50.26 grams.

(b)

Compute the standard deviation as follows:

[tex]s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}][/tex]

  [tex]=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08[/tex]

Thus, the standard deviation of the weight of the mice is 14.08 grams.

Answer:

[tex]\boxed{Slope = 0}[/tex]

Step-by-step explanation:

Hey there!

We’ll y = -2 creates a horizontal line,

and horizontal lines have a slope of zero.

Slope = 0

Hope this helps :)

Answer:

The slope of a linear equation is always the coefficient of the x value when the equation is solved for y. Since we don't have an x value on this expresion, the coefficient of x is 0. Hence, the slope of the line is 0.

Answer:

1. Jan checks the weather.  It is 27 degrees outside.  Jan did chores for two hours.  After Jan was done, she checked the weather again.  The temperature had decreased 11 degrees.

2. (See screen shot below.)

Step-by-step explanation:

1.  It doesn't have to be as complicated as I made it.  You can just say that the weather started out with 27 degrees, and decreased later on.  Remember, decreased means subtracted and 27+(-11) is the same as 27-11 because when a + and - are together - always wins.  So no.1 wants you to say something got subtracted.

2. On the number line, make a dot at 29 because it said it was 29 degrees.  Then drag the dot at the number 29 to 13 because it said it decreased 16, so it is 19 minus 16 which is 13.

Answer:

[tex]\large \boxed{\sf \bf \ \ 12 \ \ }[/tex]

Step-by-step explanation:

Hello, we can see that this shape is ...

...at the left, a right triangle of side = 2

   area = (2*2)/2 =2

... at the middle, a square of side = 2

   area = 2*2 = 4

... at the right, a right triangle of sides 2 and 6

   area= (2*6)/2 = 6

So the total is 2 + 4 + 6 = 12

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

option A is correct

4x.2x²+4x.(-2)+1.2x²+1.(-2)

hope this will help :)

Answer:

A.  4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)

Step-by-step explanation:

(4x + 1)(2x² – 2)

apply the FOIL method

= 4x * 2x² + 4x( -2) + 1 * 2x² + 1 * (-2)

Answer:

x + 2y = 8.

Step-by-step explanation:

Line goes through (-4, 0) and (4, -4).

The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.

Since we are looking for the equation of the line parallel to that line, the slope will be the same.

We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.

3 = (-1/2) * 2 + b

b - 1 = 3

b = 4.

So, we have y = -1/2x + 4.

1/2x + y = 4

x + 2y = 8.

Hope this helps!

ANSWEAr

x + 2y = 8

because it is

No, that is not a function.

To be a function, each different input (x) needs a different output (y)

In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.

Answer: no

Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.

Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.

Ask yourself, do any of the ordered pairs

in this relation have the same x-coordinate?

Well by looking at this relation, we can see that two

of the ordered pairs have the same x-coordinate.

In this case, the x-coordinate of 3 appears twice.

So no, this relation is not a function.

Step-by-step explanation:

To find the value of y when z = 14 we must first find the relationship between them

The statement

y varies directly as z is written as

y = kz

where k is the constant of proportionality

when y = 180

z = 10

180 = 10k

Divide both sides by 10

k = 18

The formula for the variation is

y = 18z

When z = 14

y = 18(14)

Hope this helps you

Answer:

{-14, 16}

Step-by-step explanation:

The coefficients of this quadratic are a = 1, b = -2 and c = -224.

Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.

Thus, the roots (solutions) are

      -(-2) ± 30

x = -----------------  =  {-14, 16}

             2

Answer:

10y+1

Step-by-step explanation:

The perimeter is the three sides added together

3y+5+6y+y-4=

10y+1

Answer:

[tex]\huge\boxed{P_\triangle=10y+1}[/tex]

Step-by-step explanation:

The formula of a perimeter of a triangle:

[tex]P_\triangle=a+b+c[/tex]

We have:

[tex]a=3y+5,\ b=6y,\ c=y-4[/tex]

Substitute:

[tex]P_\triangle=(3y+5)+(6y)+(y-4)=3y+5+6y+y-4[/tex]

Combine like terms:

[tex]P_\triangle=(3y+6y+y)+(5-4)=10y+1[/tex]

Assuming the cube is closed, you can use the divergence theorem:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]

where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].

We have

[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]

so the flux is 0.

Answer:

a =4,b=2, c=3

Step-by-step explanation:

Answer:

The answer is 20

Step-by-step explanation:

Answer: $1.83

Step-by-step explanation:

1. Solve this problem: 1+2+4+6+8+10+12+14+16+18+20+22+24+26. There are 15 numbers for 15 days. You want to solve this because each day is doubled. For example: first day is 1 cent, second day is 2 cents, third day is 4 cents, and so on.

2. Answer is 183 cents.

3. Convert 183 cents to dollars.

4. Your answer is $1.83.

Hope it helps!

Answer:

$1.83.

You start with one cent, and add two more cents after that day.

Answer:

His own problem to his explanation

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]

Given: Mean = 191  and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

Answer:

number 3

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

The given system of the equations is,

-2x + 4y - 3z = 10 ------(1)

x - 2y + z = 8 -------(2)

If the system of equations has the solution as (a, b, c),

Which shows,

x = a, y = b and z = c

Multiply equation (2) by 2 and add it to equation (1),

2(x - 2y + z) + -2x + 4y - 3z = 10 - 16

2x - 2x - 4y + 4y + 2z - 3z = 10 - 16

-z = -6

z = 6

Therefore, z = c = 6 will be the answer.

Option (3) will be the correct option.

Answer:

Step-by-step explanation:

The nth term of the sequence is

A(n) = 5n + 7

To find the (n+1)st term substitute n+1 into the general equation

That's

For (n + 1)st term

A(n+1) = 5(n+ 1) + 7

A(n+1) = 5n + 5 + 7

Hope this helps you

[tex] n^{\text{th}} \text{ term is } 5n+7 [/tex]

forget n for a while.

let's call it t .

The [tex] t^{\text{th}} \text{ term is } 5t+7 [/tex]

agreed? I don't think there should be a problem.

you're asked what's the [tex](t+1)^{\text{th}}[/tex] term.

let's call it u . so just like we did before,

[tex] u^{\text{th}} \text{ term is } 5u+7 [/tex]

but we know, [tex]u=t+1[/tex]

So, [tex]5u+7=5(t+1)+7=5t+12[/tex]

does that answer your question?

Answer:

Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.

Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.

Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.

Step-by-step explanation:

Answer:

Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.

hope this answer helps u

pls mark as brainliest .-.

Answer:

The  probability is [tex]P(X > 20 ) = 0.8[/tex]

Step-by-step explanation:

From the question we are told that

  The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $18 and $28 per share.

Given that the stock is uniformly distributed then the probability that the stock price will be more than $20 is mathematically evaluated as

       [tex]P(X > 20 ) = 1 - P(X < 20 )[/tex]

Since it is uniformly distribute  between $18 and $28 per share then we can solve is as follows

=>     [tex]P(X > 20 ) = 1 - [\frac{ 20 - 18 }{28 -18} ][/tex]

=>    [tex]P(X > 20 ) = 0.8[/tex]

Answer:

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, the critical point of the function occurs at its turning point i,e at f'(x) = 0

First we have to differentiate the function as shown;

[tex]f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\[/tex]

[tex]Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1[/tex]

Hence the critical numbers of the function are (2, -1)

Answer: The answer in a is No while the answer in b is Yes

Step-by-step explanation:

Find the explanation in the attached file.

Answer:

d = s x t

Step-by-step explanation:

The formula for distance.