A booth at the circus is taking donations for the children's hospital. They noticed on Saturday that more than 217 people donated money. Women averaged a donation of $18, and men averaged a donation of $16. Which system of inequalities could be used to determine the number of women (w) and men (m) who donated, if no more than $3,702 was donated?

Answer:

height of pyramid = 3 cm

height of prism = 9 cm

Step-by-step explanation:

Square Pyramid

surface area of 4 triangular sides of the pyramid = [tex]2a\sqrt{\dfrac{a^2}{4}+h^2}[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm

[tex]\implies \textsf{SA}=2\cdot8\sqrt{\dfrac{8^2}{4}+h^2}[/tex]

            [tex]=16\sqrt{16+h^2}[/tex]

Square Prism

surface area of square prism with one base = [tex]a^2+4ah[/tex]

(where [tex]a[/tex] is the base edge and [tex]h[/tex] is the height)

Given [tex]a[/tex] = 8 cm and [tex]h[/tex] = 3h

[tex]\implies \textsf{SA}=8^2+4\cdot 8\cdot 3h[/tex]

Total surface area

total SA = SA of pyramid + SA of square prism

Given total SA = 432 cm²

[tex]\implies 432=16\sqrt{16+h^2}+64+96h[/tex]

[tex]\implies 368=16\sqrt{16+h^2}+96h[/tex]

[tex]\implies 368=16(\sqrt{16+h^2}+6h)[/tex]

[tex]\implies 23=\sqrt{16+h^2}+6h[/tex]

[tex]\implies 23-6h=\sqrt{16+h^2}[/tex]

[tex]\implies (23-6h)^2=16+h^2[/tex]

[tex]\implies 529-276h+36h^2=16+h^2[/tex]

[tex]\implies 35h^2-276h+513=0[/tex]

[tex]\implies (h-3)(35h-171)=0[/tex]

[tex]\implies h=3, h=\dfrac{171}{35}[/tex]

Inputting both values of [tex]h[/tex] into the equations for SA:

when [tex]h = 3[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+3^2}=80 \ \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(3)=352 \ \sf cm^2[/tex]

[tex]\textsf{total SA}=80+352=432 \ \sf cm^2[/tex]

when [tex]h=\dfrac{171}{35}[/tex]:

[tex]\textsf{pyramid}=16\sqrt{16+(\frac{171}{35})^2}=101.0285714... \sf cm^2[/tex]

[tex]\textsf{square prism}=64+96(\frac{171}{35})=533.0285714... \ \sf cm^2[/tex]

[tex]\textsf{total SA}=101.0285714...+533.0285714... =634.0571428... \ \sf cm^2[/tex]

Therefore, h = 3 only (since the total area is 432 cm²)

⇒ height of pyramid = 3 cm

⇒ height of prism = 3h = 3 × 3 = 9 cm

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle

Step-by-step explanation:

Answer:

Tjats is baout the circumfrence of nonsensical poop

Step-by-step explanation:

Answer:

what ever the first person have answer

Step-by-step explanation:

1. ∠EBC = x (Theorem One: The angle at the centre of the circle is twice the angle at the circumference subtended on the same arc. You already have this one labelled)

2. ∠FCD = x (F rule / corresponding angles are equal)

3. ∠CAE = x (Theorem Two: Angles at the circumference subtended by the same arc are congruent)

4. ∠BED = ∠DCF = ∠FCD = x (Theorem Fifteen: The exterior angle of a cyclic quadrilateral is congruent to the interior opposite angle)

5. ∠CDF = ∠BED = x (F rule / corresponding angles are equal)

6. ∠CAE = ∠OAE = ∠OEA = x  (CAE and OAE are the same angles, OF and OA are radii, thus they must both be equivalent in magnitude, therefore making the triangle ΔAOE isosceles. Base angles of an isosceles triangle are always equal, since we knew ∠OAE from '3.' was x, we found that ∠OEA was also x)

Answer:

4. F

5.C

6.G

7.D

8.A

9.E

10.B

Step-by-step explanation:

The savings account of a person shows the amount which is immediately available to the person and this helps to create budgets and control spending.

This refers to the way data is arranged by showing the figures in columns for easy reading and calculations.

Please note that your question is incomplete so I gave you a general overview to help you get a better understanding of the concept.

Read more about tables here:

https://brainly.com/question/24040786

Answer:

= 196 cm^2

Step-by-step explanation:

A= bh

= 14X14

= 196 cm^2

Answer:

24

Step-by-step explanation:

24

The total number of different costumes possible is 24 if  Anita has a costume wardrobe that consists of 2 pairs of tights, 3 T-shirts, and 3 scarves.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Anita has a costume wardrobe that consists of 2 pairs of tights (1 white pair and 1 black pair), 3 T-shirts (1 pink, 1 blue, and 1 green), and 3 scarves (1 silver, 1 gold, and 1 white).

The costume consists of either a pair of tights or a T-shirt with a scarf:

In this case total number of ways = 2×3×3 = 18

Pair of tights and a T-shirt without a scarf:

In this case total number of ways = 2×3 = 6

Total number of different costumes are possible:

= 18 + 6

= 24

Thus, the total number of different costumes possible is 24 if  Anita has a costume wardrobe that consists of 2 pairs of tights, 3 T-shirts, and 3 scarves.

Learn more about permutation and combination here:

https://brainly.com/question/2295036

#SPJ2

Answer:

463.70 or 500.45

Answer:

C, D and E

Step-by-step explanation:

Given equation:

[tex]\dfrac35(30x-15)=72[/tex]

Use the distributive law  [tex]a(b-c)=ab-ac[/tex]:

[tex]\implies \dfrac35\cdot30x- \dfrac35\cdot15=72[/tex]

[tex]\implies \dfrac{3 \cdot30}5x- \dfrac{3 \cdot15}5=72[/tex]

[tex]\implies \dfrac{90}5x- \dfrac{45}5=72[/tex]

[tex]\implies 18x- 9=72[/tex]  ←  option c

Factor out common term 3:

[tex]\implies 3(6x- 3)=72[/tex]  ←  option d

Solve [tex]18x- 9=72[/tex]:

[tex]\implies 18x- 9+9=72+9[/tex]

[tex]\implies 18x=81[/tex]

[tex]\implies \dfrac{18x}{18}=\dfrac{81}{18}[/tex]

[tex]\implies x=4.5[/tex]  ←  option e

Step-by-step explanation:

-2 (4a + 4b) + 5a > -35

-8a -8b + 5a > -35

-3a -8b > -35

for a

-3a > -35 + 8b

a < -35 + 8b ÷ -3

a < 35 - 8b ÷ 3

for b

-3a - 8b > -35

-8b > -35 + 3a

b < -35 + 3a ÷ -8

b < 35 - 3a ÷ 8

Answer:

b) [tex]a_{n}[/tex] = 2 + 2/5n

Step-by-step explanation:

Given :-

a = 12/5

d = 2/5

To Find :-

[tex]a_{n}[/tex]

Solving :-

[tex]a_{n}[/tex] = a + (n - 1)d

= 12/5 + 2/5n - 2/5

= 2 + 2/5n

Solution :-

b) [tex]a_{n}[/tex] = 2 + 2/5n

Answer:

2.2360679775

Step-by-step explanation:

Answer:

2.2360679775

Step-by-step explanation:

Answer:

0.00000049

I believe this is right if not I apologize

Answer:

can't solve this

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's tricky because everybody is used to seeing 50+50=100

50+50=100 Its simple but when u put it like that it makes at trickier and people think its 90 or 103

Answer:

The sum of a number and its additive inverse is equal to 0.

Step-by-step explanation:

Answer:

3. 15 outcomes

5. 72 outcomes

Step-by-step explanation:

5 x 3 = 15

(2 x 3) x 12 = 72

2 x 3 = 6

6 x 12 = 72

Answer:

108 i think

Step-by-step explanation:

Answer:

108 inch.

Step-by-step explanation:

To make it a bit easier, I calculated the area of each side of the prism that was shown.

1. Start with the triangular sides: 3 × 4/2 = 6. Since there are two triangular surfaces, you add them together. In the end, you have 12 inch.

2. Calculate the surface with the dimensions 8 in. with 5 in.: 8 × 5 = 40 inch.

3. Calculate the surface with the dimensions 4 in. with 8 in.: 4 × 8 = 32 inch.

4. Calculate the surface with the dimensions 3 in. with 8 in.: 3 × 8 = 24 inch.

5. Last step - add all the results together: 12 + 40 + 32 + 24 = 108 inch.

Hope it helped!!

Answer:

It would be $45.00.

Step-by-step explanation:

50 divided by 10 would be 5. Subtract that from 50 to get 45.

Answer:

$45.00

Step-by-step explanation:

If an item cost $50 and the discount is 10% then:

Convert 10% to a decimal

10/100 = .1

.1 * $50 = $5

The discount is $5, subtract the discount from the original amount.

$50 - $5 = $45

The item would cost $45.00 after the discount.

Answer:

Y=45 X=90

Step-by-step explanation:

B is equal to C so it would be 45. Since the whole triangle must be 180 you subtract 45 and 45 from 180 and you get 90. Another way to tell C and B are the same is the 2 little lines on the sides.

Answer:

y=45°(angles opposite to equal sides are equal)

x+y+45=180(sum of the interior angles of a triangle is 180)

x+45+45=180

y+90=180

y=180-90

y=90

Step-by-step explanation:

Answer:

I don't know which letter answer it is because it is unclear in the question, but the answer is:

28/100 for the fraction

0.28 for the decimal

Answer:

Dear Friend here is your answer.

Answer: C) Draw segment TU and point R on segment TU.

The construction he set up so far is pretty much almost done. If he draws a ray through points T and U (with T as the endpoint), then ray TU combines with ray TS to get angle STU. This angle is congruent to angle BCD.

The point R is introduced so that we call this angle STR instead of angle STU, but it's the same basic idea. You could also replace "ray" with "line" or "line segment" to get the same basic construction of copying an angle.

Answer:

100

Step-by-step explanation:

Lets solve this the easiest way possible :)

120/6 = 20

Now since they sold 5/6 of these copies, lets multiply the 20 by 5 to figure out how much they sold.

20 x 5 = 100

They sold 100 copies :)

Hope this helps!!!

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

100

Step-by-step explanation:

5     120

-----   ------

6          1

=

600

-------   =  100

6

Answer:

20% discount

Step-by-step explanation:

Given the following question:

20% of 400

To find the answer we will use the formula to calculate percentages, once we have that answer we then subtract it from the original price to see if we have the same new price as the question.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times40}{100}[/tex]
[tex]20\times40=8000[/tex]
[tex]8000\div100=80[/tex]
[tex]=80[/tex]

Subtract from the original price:
[tex]400[/tex]
[tex]400-80=320[/tex]
[tex]=320[/tex]

The dress has a "20% discount."

Hope this helps.

Answer:

16 ounces

Step-by-step explanation:

x, quantity of the 5%

24-x, quantity of the 20%

5%x + 20%(24-x) = 10% of 24

.05x + .20(24-x) = .10 * 24

.05x + 4.8 - .20x = .10 * 24

4.8 -.15x = 2.4

2.4 = .15x

.15x = 2.4

x = 2.4/.15

x = 16