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wolverine [178]
3 years ago
12

24 swimmers are swimming in the pool. 9 of them are female. What fraction of swimmers are male?

Mathematics
1 answer:
Korolek [52]3 years ago
7 0

Answer:

15/24 or 5/8

Step-by-step explanation:

Well 9 are female

The rest of the 24 has to be male so

24-9=15

15/24 or 5/8

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16. What are the values of a and b?
MrMuchimi

Answer:

  a = 20; b = 2√101

Step-by-step explanation:

The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...

  200/a = a/2

  400 = a^2

  √400 = 20 = a

Then, by the Pythagorean theorem, the value of b can be found:

  b = √(a^2 + 2^2) = √(400 +4) = √4·√101

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4 0
2 years ago
Which value represents a horizontal shift (left and right) in the following function y=a*sin(bx-c)+d
grigory [225]
The value is C because it represents the shift

5 0
3 years ago
A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six
kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

V = Length \times Width \times Height \\\\

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

Width = 3 - 2x \\\\

The length of the shaded region is given by

Length = \frac{1}{2} (5 - 3x) \\\\

So, the volume of the box becomes,

V =  \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V =  \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V =  \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V =  \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

a = 18 \\\\b = -38 \\\\c = 15 \\\\

x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 +  19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\

Volume of the box at x= 1.59:

V =  \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\

Volume of the box at x= 0.53:

V =  \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0
3 years ago
What is (2+y)³ written out?
Aleksandr-060686 [28]
{ \left( 2+y \right)  }^{ 3 }\\ \\ =\left( 2+y \right) \left( 2+y \right) \left( 2+y \right) \\ \\ =\left( 2+y \right) \left( 4+4y+{ y }^{ 2 } \right)

\\ \\ =2\left( 4+4y+{ y }^{ 2 } \right) +y\left( 4+4y+{ y }^{ 2 } \right) \\ \\ =8+8y+2{ y }^{ 2 }+4y+4{ y }^{ 2 }+{ y }^{ 3 }\\ \\ ={ y }^{ 3 }+6{ y }^{ 2 }+12y+8
5 0
3 years ago
A single serving of jello requires 1/8 cups of sugar. How much sugar is needed for 6 servings?
sp2606 [1]
Hi there!

3/4 of sugar is needed for 6 servings.

1/8 x 6 = 6/8 simplify it and you get 3/4.

So 3/4 is your answer.

Hope this helps ;D
7 0
2 years ago
Read 2 more answers
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