There are 600 people on a cruise ship.The over 30s and the 30 and unders are in the ratio 4:1.
30% of the over 30s are female.
Work out how many of the over 30s are male.
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males over 30
Answers
Step-by-step explanation:
600 people is the total number of people.
with a given ratio of 4:1 we know that this total number of people is basically split into 5 (4 + 1) equal units.
each of the 5 units is therefore
600 / 5 = 120 people.
the "over 30s" are 4 of these units = 4 × 120 = 480 people.
the "30 and under" are 1 unit = 120 people.
30% of these 480 "over 30" people are female.
that leaves under normal circumstances 100 - 30 = 70% of these 480 "over 30" people to be male.
100% = 480
1% = 100%/100 = 480/100 = 4.8
70% = 1% × 70 = 4.8×70 = 48×7 = 336 people.
there are 336 males over 30 on that ship.
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which of the following expressions does not contain any like terms? a. 2x^2+3x-4x+2 b. xy+yz-17 c. x^3+x^2-2x-x^2 d. 14+8+y
If (x1, y1) and (x2, y2) are distinct solutions to the system of equations shown above, what is the sum of the y1 and y2?
Answers
Solving the system we can see that the sum of the y-values of the two solutions is 139.
How to get the sum of y₁ and y₂?
Let's solve the system of equations.
y = 10 + 16x − x²
y = 3x + 50
We can write this as a single quadratic equation:
10 + 16x - x² = 3x + 50
10 + 16x - x² - 3x - 50 = 0
-x² + 13x - 40 = 0
Using the quadratic formula we will get the two solutions for x:
So the two solutions are:
x = (-13 + 3)/-2 = 5
x = (-13 - 3)/-2 = 8
Evaluating the linear equation in these two values we will get y1 and y2.
if x = 5
y₁ = 3*5 + 50 = 65
if x= 8
y₂ = 3*8 + 50 = 74
The sum is:
65 + 74 =139
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Final answer:
The distinct solutions to the system of equations are (5, 65) and (8, 74), and the sum of the y-values is 139.
Explanation:
To find the sum of y-values of the distinct solutions to this system of equations, first, you need to set the two equations equal to each other to find the x-values of the solutions:
10 + 16x − x^2 = 3x + 50.
Then, solve the resulting equation for x:
x^2 - 13x + 40 = 0.
This is a quadratic equation, and it can be solved either by factoring or using the quadratic formula. The solutions for x result in:
x = 5 and x = 8.
These are the two distinct x-values for the intersections of the graphs of the two equations. To find the corresponding y-values, plug these x-values into either of the original equations. We'll use the simpler equation, y = 3x + 50:
For x = 5, y = 65 and for x = 8, y = 74.
Therefore, the distinct solutions to the system of equations are (5, 65) and (8, 74). Finally, the sum of y1 and y2 is 65 + 74 = 139.
Learn more about System of Equations here:
#SPJ1
Answers
Answers
34 + 108 + 65 = 207
360-207 = 153
Your unknown angle is 153 degrees
1. 2(x2 + 5) = 60 1.
2. 2x2 + 10 = 60 2.
3. 2x2 = 50 3.
4. x2 = 25 4.
5. x = ±5 5.
Answers
2(x²+5)=60
<==>x²+5=30 (divided teh 2 members by the positive 5 :keep the equality)
<==>x²-25=0 (substract 25 from 2 members)
<==>(x-5)(x+5)=0 (remarquable product a²-b²=(a+b)(a-b))
<==> x= 5 or x=-5 (a product if null if one at least of its factor is null)
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