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2 years ago

15

Tom has 50 coins consisting of quarters and dimes. The combined value of coins is $8.30. How many dimes and quarters does Tom ha

ve:
dimes
quarters

1 answer:

klio [65]2 years ago

6 0

Answer:

thirty two quarters and three dimes

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A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha

netineya [11]

Answer:

$(a)\ Area = 195\pi$

$(b)\ Volume = 700\pi$

Step-by-step explanation:

Given

$h = 12$

$d_1 = 10$ --- lower diameter

$d_2 = 20$ --- upper diameter

Solving (a): The curved surface area

This is calculated as:

$Area = \pi l(r_1 + r_2)$

Where

$r_1 = 0.5 * d_1 = 0.5 * 10 = 5$ --- lower radius

$r_2 = 0.5 * d_2 = 0.5 * 20 = 10$ --- upper radius

And

$l = \sqrt{h^2 + (r_1 - r_2)^2$ ---- l represents the slant height of the frustrum

$l = \sqrt{12^2 + (5 - 10)^2$

$l = \sqrt{12^2 + (-5)^2$

$l = \sqrt{144 + 25$

$l = \sqrt{169$

$l = 13$

So, we have:

$Area = \pi l(r_1 + r_2)$

$Area = \pi * 13(5 + 10)$

$Area = \pi * 13(15)$

$Area = 195\pi$

Solving (b): The volume

This is calculated as:

$Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))$

This gives:

$Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))$

$Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))$

$Volume = \frac{1}{3}\pi * 12 * (175)$

$Volume = \pi *4 * 175$

$Volume = 700\pi$

6 0

2 years ago

What is the area of the shaded part of the figure?

adoni [48]

Oh all u do is just do the triangle the subtract the square from that

8 0

2 years ago

Simplify the numerical expression:<br> (5^4) (5^2)<br> A. 5^-10<br> B. 5^2<br> C. 5^-6<br> D. 5^-2

alexgriva [62]

Answer: A is the answer

3 0

2 years ago

Part A: Consider the equation x + 7 = 16. Which number from the set {5, 7, 9, 11} makes the equation true?

wel

Part A: Substitute/plug in each number into the equation to see which number will make the equation true.

x + 7 = 16 Plug in 5 into "x"

5 + 7 = 16

12 = 16 5 doesn't make the equation true because it equals 12 not 16

x + 7 = 16 Plug in 7 into "x"

7 + 7 = 16

14 = 16 7 doesn't make the equation true because it equals 14 not 16

x + 7 = 16 Plug in 9 into "x"

9 + 7 = 16

16 = 16 9 makes the equation true because it equals 16

Part B: Plug in 9 into "x" in the inequality to see if it still makes it true.

x + 7 < 16 [x plus 7 is less than 16]

9 + 7 < 16

16 < 16 [16 is less than 16] The same number would not make the inequality true because 16 can't be less than itself.

To figure out which numbers satisfy the inequality, plug it into the inequality:

x + 7 < 16 Plug in 5 into "x"

5 + 7 < 16

12 < 16 5 does satisfy the inequality because 12 is less than 16

x + 7 < 16 Plug in 7 into "x"

14 < 16 7 does satisfy the inequality because 14 is less than 16

x + 7 < 16 Plug in 11 into "x"

11 + 7 < 16

18 < 16 11 doesn't satisfy the inequality because 18 isn't less than 16

3 0

2 years ago

Find f(1/3) if f(n) =3n

hichkok12 [17]

Answer:

f(1/3) = 1

Step-by-step explanation:

Plug 1/3 in for n

f(1/3) = 3(1/3)

Now simplify

f(1/3) = 1 { 3(1/3) = (3/1)(1/3) = 3/3 = 1 }

6 0

2 years ago

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