Two same-sized triangular prisms are attached to a rectangular prism as shown below.
If a = 20 cm, b = 13 cm, c = 12 cm, d = 5 cm, and e = 8 cm, what is the surface area of the figure?
a 1,208 square centimeters
b 1,592 square centimeters
c 1,004 square centimeters
d 1,400 square centimeters

[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]

so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]

Answer:

2a(7b+5)

Step-by-step explanation:

yeah-ya....... right?

The current depth of the hole is at least 20 feet below ground level.

Inequality is an expression that shows the non equal comparison of numbers and variables.

Let d represent the current depth of the hole.

To be at least 40 feet below ground level, he need more than 2 times its current depth.

2d < -40

d < -20

Hence the current depth of the hole is at least 20 feet below ground level.

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Answer:

20 feet below

Step-by-step explanation:

Answer:

I think its D

Step-by-step explanation:

The dot starts on -2 and decreases so the answer would = -2 or be less than -2 :)

Answer:

y = 18 when x = 3

Step-by-step explanation:

y is directly proportional to x^2, meaning:

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

where a is the proportion between them. We're given the values for both x and y, so plug those in and solve for a:

[tex]8=a(2)^2\\8=a4\\2=a\\a=2[/tex]

Now you can use a to solve for y when x is 3:

[tex]y=ax^2\\y=(2)(3)^2\\y=2(9)\\y=18[/tex]

Answer:

x=25/6

Step-by-step explanation:

3x+11=9x-14

11=6x-14

25=6x

x=25/6

Answer:

[tex]x=\cfrac{25}{6}[/tex]

or

[tex]x=4.16[/tex]

Step-by-step explanation:

[tex]3x+11=9x-14[/tex]

[tex]3x+11-11=9x-14-11[/tex]

[tex]3x=9x-25[/tex]

[tex]3x-9x=9x-25-9x[/tex]

[tex]-6x=-25[/tex]

[tex]\cfrac{-6x}{-6}=\cfrac{-25}{-6}[/tex]

[tex]x=\cfrac{25}{6}[/tex]

Have a good day!

Answer:

34

Step-by-step explanation:

20% of 70 + 80% of 25 = 14 + 20 = 34.

Answer:

61

Step-by-step explanation:

Assuming a linear relationship between the percent chance for rain and the number of attendees, the number is 20% of the way from 70 (0% chance) to 25 (100% chance).

The expected number of people with a 20% chance of rain would be 61.

(hope it helps)

71.8

71.841:

The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.

In order to round, we need to remember how to round numbers:

First, 4<5, meaning that 4 is less than 5.

#1 above is stating that the number to the left of 4 stays the same.

If we use that rule:

71.8 is our answer.

Answer:

$290,000

Step-by-step explanation:

Total cost = total variable cost + fixed cost

= 5000×328 + 120000

= 1640000+120000

=1760000 $

The jeans maker earns in total = 5000 × 410

= 2050000 $

So the income is

= 2050000 – 1760000 = 290000 $ ( Answer)

If the number of units is 5,000. Then the income will be $290,000.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

A pants producer is planning another line of pants. These pants will sell for $410 per unit and cost $328 per unit in factor expenses to make. Fixed costs complete $120,000.

Let 'x' be the number of units. Then the equation is given as,

Income = Selling cost - Variable cost - Fixed cost

Income = $410 x - $328 x - $120,000

Income = $82 x - $120,000

If the number of units is 5,000. Then the income is calculated as,

Income = $82 (5,000) - $120,000

Income = $410,000 - $120,000

Income = $290,000

More about the function link is given below.

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Answer:

Integers

The set of numbers including all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero)

Answer:

Step-by-step explanation:

Assumed the dimensions of the top and bottom parts are identical.

Since the cylindrical part has total height of 1.8 cm and the hemisphere volume is transferred to bottom part and the cone part is still full, the value of h is the difference of the total height of cylinder and full part of the top section of cylinder:

Find the volume of sand in the bottom part. It consists of a hemisphere and a cylinder of 1.5 cm height.

Total sand in the bottom part:

Time taken:

Answer:

$572

Step-by-step explanation:

Answer:

LQ = 5

Median = 6

Step-by-step explanation:

[tex]\frac{n+1}{2}[/tex] gives us 5.5, so we do the average of position 5 and 6. This gives us 6, so the median is 6.

Now we find the median of the bottom half of the numbers, which is 5, so the LQ is 5.

Now we find the median of the upper half of the numbers, which is 7, so the UQ is 7.

Answer:

Step-by-step explanation:

Let the price is x.

With 17% discount it becomes:

The number we need is 0.83

Solution,

Assume That The Price is x

When Will Put It in Equation,

[tex] \frak{ \bigstar}{ \rm{ {We \: Will \: Get,}}}[/tex]

Hence, Required Price is “0.83”

Answer:

74.2

Step-by-step explanation:

53 x .4 = 21.2

21.2 + 53 = 74.2

Answer:

1 1/5

Step-by-step explanation:

Answer:

19 x 23.5 x 4

Step-by-step explanation:

4 * x * (x + 4.5) =1800

Divide both sides by 4

x * (x + 4.5) = 450

Use distributive property

x^2 + 4.5x = 450

Move all terms to one side

x^2 + 4.5x - 450 = 0

Use quadratic formula to solve   a = 1, b = 4.5, c = -450

-4.5 +- [tex]\sqrt{4.5^2 - 4 * 1 * -450}[/tex]/2

=-4.5 + - [tex]\sqrt{1820.25}[/tex] / 2

= -4.5 +- 42.664 / 2

=19.08 and -23.582. You can't have a negative length, so it is 19.08, or 19

19 x 23.5 x 4

Answer with step-by-step explanation:

A: 207

We know that percentage is out of 100, so we can divide 460 by 100 to find 1%, which is 4.6. We also know 45% percent of teenagers like comedies, so we multiply 4.6 by 45, or 207. 207 teenagers like comedies.

B. 80 teenagers

We know that 50% of teens Hannah surveyed like thrillers. We also know that 40 teenagers like thrillers. Using multiplication, we can multiply 40 by 2, since 50% is half, we need to multiply by 2 to get the total number of teenagers. Hannah surveyed 80 teenagers.

C. Jamie went to the candy store and spent his entire allowance of $20 on candy. His friends gave him $5 more dollars, so he bought candy with that too. He spent 125% of his allowance on candy.

The number of teenagers who like comedy is 207, and The total number of teenagers Hannah surveyed is 100.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Given:

Netan surveyed 460 teenagers, He found that 45% of the teenagers surveyed like comedies,

(a) Calculate the number of teenagers who like comedy as shown below,

The number of teenagers who like comedy = 45 × 460 / 100

The number of teenagers who like comedy = 207

(b) Calculate the total number of teenagers as shown below,

The total number of teenagers × 50% = 40

The total number of teenagers = 40 × 100 / 40

The total number of teenagers = 100

To know more about percentages:

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[tex]f[/tex](x) = 0.20x + 35 : 29.5

Answer:

the answer u r looking for is 144

Step-by-step explanation:

if u know who this is i will follow u

hint: its from avatar tla

only the first person that answers!!!

Answer:

about 5.1 units

Step-by-step explanation:

to find the length between two points you can use the pythaogorean theorem

5^2 + 1^2 = c^2

25 + 1 = c^2

26 = c^2

c is about 5.09901

rounding to the nearest tenth we get 5.1

Answer:

Focus on planting trees and and getting healthier soil, improve energy efficiency and not use so much pesticides using natural ways to plant things.

Step-by-step explanation:

Answer:

tank 1 : 19 gallons

tank 2 : 42 gallons

Step-by-step explanation:

tank 1 : x

tank 2 : 2x+4 ( 4 more than twice the other )

x + ( 2x + 4 ) = 61

3x + 4 = 61 [ add x + 2x = 3x ]

3x = 57 [ subtract 4 on both sides ]

x = 19 [divide 3 on both sides ]

tank 1 : 19 gallons

tank 2 : 42 gallons

Answer:

15 installments

Step-by-step explanation:

3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex]   400 - 20*(n - 1)

Answer:

i have no clue

Step-by-step explanation:

i said this bc apparently i have to help someone to get help and i just wanna finish this math homework lol

Answer:

Step-by-step explanation:

Answer:

P=14

Step-by-step explanation:

Since P depends on two variables x and y as the sum of the two, then;

P = 3+ 11

P = 14

we have: -10/4 = -2.5 ⇒ -2 > -2.5 > -3

ANSWER : -2 and -3

ok done. Thank to me :>

Answer:

c. copy an angle.

there's no angle in this as far as I can see.