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Vanyuwa [196]
3 years ago
12

1/6 students are wearing blue shirts, and 2/3 are wearing white shirts. There are 36 students. How many students are wearing shi

rts that arent blue or white?​
Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
8 0

Answer:

6 students are wearing shirts that aren't blue or white

Step-by-step explanation:

1/6 + 2/3 = 5/6  

5/6 are wearing either blue or white so 1/6 isn't wearing blue or white

there are 36 student and 1/6 means 36 divided by 6

36 divided by 6 = 6

Mnenie [13.5K]3 years ago
6 0
I need point ugh but yeah good luck with that
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Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

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

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

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

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

\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}}

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

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

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

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

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

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

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

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

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

\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}}

7 0
2 years ago
The triangle area is 90ft^2 and the height is 10 what's the base
Sidana [21]
Area of triangle = 1/2 x base x height
Let the base be "b"

90 = 1/2 x 10 x b
90 = 5b
b = 18 ft

Base = 18 ft
4 0
3 years ago
Write an expression that is equivalent to three over four (5z+ 16)
anygoal [31]
     3
------------
4(5z+16)

I'm assuming you want to include all of the numbers
3 0
3 years ago
Read 2 more answers
Callie has 6 yards of green fabric and 4 yards of white fabric.
DedPeter [7]

Answer:

16 feet left

Step-by-step explanation:

one yard = 3 feet

so:

6 yards = 18 feet

24 inches = 2 feet

18 feet - 2 feet = 16 feet

7 0
3 years ago
Evaluate the expression 21 ÷ 3 + 8 − 4.<br><br> A) 19<br><br> B) 17<br><br> C) 15<br><br> D) 11
nirvana33 [79]

Answer:

D

Step-by-step explanation:

We will use the order of operations to evaluate the expression.

From left to right , Multiplication/Division followed by Addition/Subtraction.

21 / 3 + 8 - 4

= 7 + 8 - 4

= 15 - 4

= 11

Therefore, the answer is D

5 0
1 year ago
Read 2 more answers
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