The following data shows the number of stage shows 20 students of a class watched in a month:


1 7 4 4 3 2 7 8 1 19 20 22 20 19 16 16 19 13 1 13


Which histogram represents this data?
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 7, the second goes to 6, the third goes to 4, and the last goes to 3.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 3, the second goes to 4, the third goes to 6, and the last goes to 7.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 7, the second goes to 3, the third goes to 4, and the last goes to 6.
A histogram titled Number of Stage Shows Students Watch is shown. The horizontal axis is labeled Number of Stage Shows Watched with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Number of Students with values from 0 to 10 at intervals of 1. The first bin goes to 3, the second goes to 7, the third goes to 6, and the last goes to 4.

The two parabolas intersect for

[tex]8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2[/tex]

and so the base of each solid is the set

[tex]B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}[/tex]

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, [tex]|x^2-(8-x^2)| = 2|x^2-4|[/tex]. But since -2 ≤ x ≤ 2, this reduces to [tex]2(x^2-4)[/tex].

a. Square cross sections will contribute a volume of

[tex]\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x[/tex]

where ∆x is the thickness of the section. Then the volume would be

[tex]\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}[/tex]

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

[tex]\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x[/tex]

We end up with the same integral as before except for the leading constant:

[tex]\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx[/tex]

Using the result of part (a), the volume is

[tex]\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}[/tex]

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

[tex]\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x[/tex]

and using the result of part (a) again, the volume is

[tex]\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}[/tex]

The surface area of the square pyramid is: 451 cm²

The lateral surface area of the square pyramid = 330 cm²

Surface area = a² + 2al, where a is the base edge and l is the slant height.

Lateral Surface Area =  2al.

Given the following:

Surface area = a² + 2al = 11² + 2(11)(15)

Surface area = 451 cm²

Lateral Surface Area =  2al = 2(11)(15)

Lateral Surface Area = 330 cm²

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The lateral and surface area of a square base pyramid with side length of 11 cm and slant height of 15 cm are 330 cm² and 451 cm².

surface area = A + 1 / 2 ps

where

Therefore,

surface area = 11² + 1 / 2 × (11 × 4) × 15

surface area = 121 + 1 / 2 × 44 × 15

surface area = 121 + 330

surface area = 451 cm²

lateral area = 1 / 2 ps

lateral area = 1 / 2 × 44 × 15

lateral area = 330 cm²

learn more on lateral and surface area here; https://brainly.com/question/23857644

Answer: 18,840*pi

Step-by-step explanation:

The volume of a globe would be 4/3*pi*radius^3 so that would be 4/3*14,130= 18840*pi or approximately 59,187.6055

Linear equations are typically organized in slope-intercept form:

[tex]y=mx+b[/tex]

To find linear equations in slope-intercept form:

We're given:

First, determine the slope of the line.

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line

⇒ Plug in the given points (2,6) and (4,16):

[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]

⇒ Therefore, the slope of the line is 5. Plug this back into the general form:

[tex]y=5x+b[/tex]

Now, determine the y-intercept.

[tex]y=5x+b[/tex]

⇒ Plug in one of the given points:

[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]

⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:

[tex]y=5x-4[/tex]

[tex]y=5x-4[/tex]

Answer:

  (d)  112 m²

Step-by-step explanation:

The area of a parallelogram is given by the formla ...

  A = bh . . . . . . where b is the base length and h is the height

__

Here, the base is divided into parts, but their total length is 5m+9m = 14m. The height is given as 8m, so the area is ...

  A = (14 m)(8 m) = 112 m²

The area of the parallelogram is 112 square meters.

__

Alternate solution

You can also figure this as the sum of the areas of the two triangles and that of the center rectangle.

  A = 2(1/2bh) +bh

  A = 2(1/2(5 m)(8 m)) +(9 m)(8 m) = 40 m² +72 m² = 112 m²

Answer:

56

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

9x² + 10 = 5

⇔ 9x² = 5 - 10

⇔ 9x² = -5

This is impossible because 9x² > 0 and -5 < 0

Answer:

384.29 in²

Step-by-step explanation:

The radius of these circles is 5 in.

- As the radii are equal, and 4 of them are used to make up the side of the square. [20 ÷ 4 = 5]

To find the area of circle, you use the formula [tex]\pi r^{2}[/tex]

[tex]\pi[/tex] · (5)² = 25[tex]\pi[/tex]

The area of the square equals the length x width

20 · 20 = 400

To find the area of the shaded region, subtract these values.

400 - 25[tex]\pi[/tex] ≈ 389.29 in²

Answer:

x = 108 , y = 72

Step-by-step explanation:

x and 108 are alternate exterior angles and are congruent , then

x = 108

x and y are same- side exterior angles and sum to 180° , that is

x + y = 180

108 + y = 180 ( subtract 108 from both sides )

y = 72

Answer:

  [tex]X=\left[\begin{array}{cc}-5&2\\0&8\\8&1\end{array}\right][/tex]

Step-by-step explanation:

Solving the given matrix equation, we find ...

  X = (1/4)(C - B)

These operations, subtraction and multiplication by a scalar, are done on a term-by-term basis. A calculator or spreadsheet can do these for you.

For example, the middle right term (row 2, col 2) is ...

  (38 -6)/4 = 32/4 = 8

Answer:

[tex]X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]

Step-by-step explanation:

[tex] Given \:\: B=\begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix} \: and\: C=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]

To Solve: 4X + B = C

[tex]\implies 4X + \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}- \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12-8 & 6-(-2)\\-1 -(-1)& 38-6\\24-(-8) & -6-(-10)\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -12-8 & 6+2\\-1 +1 & 38-6\\24+8 & -6+10\end{bmatrix}[/tex]

[tex]\implies 4X =\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]

[tex]\implies X =\frac{1}{4}\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]

[tex]\implies X =\begin {bmatrix} \frac{-20}{4} & \frac{8}{4}\\\\\frac{0}{4}& \frac{32}{4}\\\\ \frac{32}{4} & \frac{4}{4}\end{bmatrix}[/tex]

[tex]\implies X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]

Answer:

The housewife purchased 8 chairs

Answer:

A: Service Fee = $55
   Hourly Rate = $ 73
B: $288

Step-by-step explanation:

A: the service rate increases by $5 per year, so year 8 would be $20 more than year 4 (5*4)
  The hourly rate increases by $3 per year, so year 8 would be $12 more than year 4 (3*4)

B. Service fee for year 9 would be $60 ($5 more than year 8) and the hourly rate would be $76 per hour ($3 more than year 8). This gives you Service Fee + (Hourly rate * 3) = $60 + ($73*3) = $60 + $228 = $288

Answer:

[tex]\displaystyle k = \frac{1}{32}\ln\frac{1}{2} \approx -0.02166[/tex]

Step-by-step explanation:

The decay formula is given by:
[tex]\displaystyle P(t) = P_0e^{kt}[/tex]

Where k is some constant, P₀ is the initial population, and t is the number of years.

Because the substance has a half-life of 32 years, P(t) = 1/2P₀ when t = 32. Substitute:
[tex]\displaystyle \frac{1}{2}P_0 = P_0 e^{k(32)}[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} \frac{1}{2} & = e^{32k} \\ \\ \ln\left(e^{32k}\right) & = \ln\left(\frac{1}{2}\right) \\ \\ 32k & = \ln\frac{1}{2} \\ \\ k & = \frac{1}{32}\ln\frac{1}{2} \\ \\ &\approx -0.02166\end{aligned}[/tex]

In conclusion, the value of k is about -0.02166.

The value of k in the exponential decay formula is k = 0.022

To find the constant k in the decay formula for the radioactive substance, we can use the formula for exponential decay, which is given by:

N(t) = N₀*exp(-kt)

where:

The half-life of the substance is the time it takes for half of the substance to decay, which is 32 years in this case. So, after one half-life, N(t) = N₀ / 2.

Now, let's set up the equation for one half-life:

N(t) = N₀ * exp(-k * 32)

Since N(t) = N₀ / 2 after one half-life, we can write:

N₀ / 2 = N₀ * e^(-k * 32)

Now, divide both sides by N₀:

1/2 = exp(-k * 32)

To solve for k, take the natural logarithm (ln) of both sides:

ln(1/2) = -k * 32

k = ln(1/2) / -32

k = 0.022

Learn more about half-life at:

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#SPJ3

Answer:

.1, 1.2, 0, 1.5, 0, 1.4 // 19.2, .8, 70.2, .7, 4791.7, .7

Step-by-step explanation:

The first set is if you meant the first number divided BY the second and the second set of numbers is if you meant it vice versa. If it was worded better I could understand better.

Answer:

58π mi.

Step-by-step explanation:

The diameter of the circle = the hypotenuse of the right triangle ( by the angle subtended by a diameter theorem).

By Pythagoras:

diameter^2 = 40^2 + 42^2

=  3364

Diameter = 58 mi.

Now the circumference

= diameter * π

= 58π mi.

Answer:

Step-by-step explanation:

no, because positive 4 is 8 more than negative 4.

Answer:

one positive n one negative equals a positive

Step-by-step explanation:

no?

Answer:

11 feet

Explanation:

Here given:

====================

Solving steps:

⇒ 1/2 * (15 + b) * 7.6 = 98.8

⇒ (15 + b) * 7.6 = 197.6

⇒ (15 + b) = 26

⇒ b = 11 ft

Let unknown be x

Answer:

ITS B because sqrt 11 is 3.something

Step-by-step explanation:

Answer:

like terms: (3n,-n),(7,-3)

Step-by-step explanation:

Answer:=2n+2

Step-by-step explanation:

3n+7-n-3=2n+2

Answer:

i think it b i dont know for sure

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

the range is the y values of the line.

so it would be [3, 6]

Answer: 147.2

Step-by-step explanation:

(8+15) = 23

23 x 6.4= 147.2

Answer: 147.2

Step-by-step explanation: 8+15= 23 so 23*6.4 is 147.2

Answer: 4

Step-by-step explanation: how i know by guessing

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Scalar factor Multiplication in Matrix.

So from the above matrix, -3A , is just simply multiplying the -3 to every element of the matrix, so we get as,

===> -3A = | -9 -18 |

| -24 -21 |

| -6 6 |

hence the correct option is B.

○ 2,350 square feet

○ 2,450 square feet

○ 2,500 square feet

● 2,400 square feet answer

Step-by-step explanation:

wellcome

rip

Answer: X is 11,

Step-by-step explanation:

Hope it helps you