If f(x)=2x+1f(x)=2x+1f, left parenthesis, x, right parenthesis, equals, 2, x, plus, 1 and g(x)=x^2+7g(x)=x 2 +7g, left parenthes
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After two bites, the weight of the hamburger is recorded at 160g.
Each bite removes 20% of the burger's total weight, so to uncover the weight prior to the bites, we calculate it based on the percentage that remains.
The initial weight stands at 160g. Given that 20% of the weight was lost during a bite, we should divide this weight by the remaining percentage after the bite:
After a bite, 80% of the burger is what remains. Convert this percentage into a decimal by dividing it by 100:
Now, let's divide the original weight by this figure:
Before the second bite, the weight of the hamburger was 200g.
The same method will apply for the first bite. Initially, it weighed 200g, with 80% still intact after the initial bite. Since 80% converts to 0.8 in decimal form, divide 200 by 0.8:
Thus, the original weight of the hamburger prior to any bites was 250 grams.
Each bite removes 20% of the burger's total weight, so to uncover the weight prior to the bites, we calculate it based on the percentage that remains.
The initial weight stands at 160g. Given that 20% of the weight was lost during a bite, we should divide this weight by the remaining percentage after the bite:
After a bite, 80% of the burger is what remains. Convert this percentage into a decimal by dividing it by 100:
Now, let's divide the original weight by this figure:
Before the second bite, the weight of the hamburger was 200g.
The same method will apply for the first bite. Initially, it weighed 200g, with 80% still intact after the initial bite. Since 80% converts to 0.8 in decimal form, divide 200 by 0.8:
Thus, the original weight of the hamburger prior to any bites was 250 grams.
Response:
Events A and B exhibit independence.
Detailed explanation:
We are provided with
The multiplication principle applicable to events A and B
A correct assertion regarding events A and B is necessary for this principle to hold.
It is understood that for two events A and B to be independent
Consequently, the probability
Thus, the correct assertion concerning events A and B for the application of this principle is stated as
Events A and B are independent.
The diagram is not available, so I included a supplementary figure.
Response:
The segments ST and UT are equal in length.
Detailed explanation:
As seen in the additional figure
∵ ST and UT act as tangents to circle K at points S and U respectively
∵ SK and UK are the radii of circle K
- A tangent is perpendicular to the radius at the point where it touches the circle.
Thus, ST ⊥ KS at point S
Thus, m∠KST = 90°
Thus, UT ⊥ KU at point U
Thus, m∠KUT = 90°
Therefore, m∠KST = m∠KUT
In triangles KST and KUT
∵ KS = KU because they are both radii
∵ m∠KST = m∠KUT confirms the equality
∵ KT is common to both triangles
- Therefore, the triangles are congruent according to the HL criterion
∴ Δ KST ≅ KUT as per the HL criterion
- Thus, from the congruency result
∴ ST = UT
The segments ST and UT are equal in length.
