Answer:
<u>The solution of this system of equation is ( 3, - 8)</u>
Step-by-step explanation:
1. Let's solve the system of equations:
First equation:
x + 2y = - 13
x = - 13 - 2y
Second equation:
12x + 5y = -4
12 * (- 13 - 2y) + 5y = - 4 (Replacing x with - 13 - 2y)
-156 -24y + 5y = - 4
-24y + 5y = - 4 + 156 (Like terms)
-19y = 152
y = - 152/19
<u>y = -8</u> (Dividing by 19)
Solving x
x + 2y = -13
x + 2 (- 8 ) = - 13
x - 16 = - 13
x = - 13 + 16
<u>x = 3</u>
2. Proving that x = 3 and y = - 8 are correct:
12x + 5y = -4
12 * 3 + 5 * -8 = -4
36 - 40 = - 4
- 4 = - 4
<u>We proved that x = 3 and y = - 8 are correct</u>
The cubic centimeter one container can hold is 2,878.33 cm³.
<h3>What is the cubic centimeter one
container can hold ?</h3>
In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.
Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)
Volume of the cylinder = πr²h
Where:
- π = 3.14
- r = radius
- h = height
3.14 x 5² x 30 = 2355 cm³
Volume of a hemisphere = (2/3) x π x r³
2 x (2/3 x 3.14 x 5³) = 523.33 cm³
Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³
To learn more about the volume of a hemisphere, please check: brainly.com/question/26840364
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Answer:
(a) 93.19%
(b) 267.3
Step-by-step explanation:
The population mean and standard deviation are given as 502 and 116 respectively.
Consider, <em>X</em> be the random variable that shows the SAT critical reading score is normally distributed.
(a) The percent of the SAT verbal scores are less than 675 can be calculated as:
Thus, the required percentage is 93.19%
(b)
The number of SAT verbal scores that are expected to be greater than 575 can be calculated as:
So,
Out of 1000 randomly selected SAT verbal scores, 1000(0.2673) = 267.3 are expected to have greater than 575.
