Answer:
Every week, the mass of the sample is multiplied by a factor of 0.81
Step-by-step explanation:
Let's rewrite the base and find the expression whose exponent is just ttt.
(0.97)7t+5=(0.97)7t⋅(0.97)5=(0.977)t⋅(0.97)5
Therefore, we can rewrite the modeling function as follows.
M(t)=(0.97)5⋅(0.977)t
According to this model, the mass of the sample is multiplied by 0.977 every week. Rounding this to two decimal places, we get 0.977≈0.81.
Its 9 because it includes f(x)
Solving a system of equations we will see that we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
<h3>
How many liters of each solution do we need to use?</h3>
First, we need to define the variables:
- x = liters of the 35% acid used.
- y = liters of the 80% acid used.
We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
If you want to learn more about systems of equations:
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A triangle will be produced from the intersection of the vertical plane and pyramid. The correct options are triangles and trapezoid.
<h3>What is a triangle?</h3>
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
Given that a vertical plane passes through a pyramid that has a horizontal base. Therefore, when the vertical plane and the pyramid meets or intersect the two dimensional figure that will be produced when the two intersect is triangle. It can also be trapezoid if the vertical plane does not intersect exactly in mid of the pyramid.
Hence, a triangle or a trapezoid will be produced from the intersection of the vertical plane and pyramid.
Learn more about Triangle here:
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(3) 62.5% cuz u take the total number of the students and u divide it by the number of students between 60 to 65
