William is taking the 25-question, multiple choice American Mathematics Competition. Each question has five answer choices. Will
1 answer:
Given that <span>William guesses random answers for the last four questions and that e</span><span>ach question has five answer choices.</span><span>
The probability that he gets an answer correct </span>is 1 / 5.
The probability that he did not get an answer correct is 4 / 5.
The probability that he will not get any of the 4 questions correctly is
Therefore, the probability that he gets at least one of the 4 questions correctly is
The probability that he gets an answer correct </span>is 1 / 5.
The probability that he did not get an answer correct is 4 / 5.
The probability that he will not get any of the 4 questions correctly is
Therefore, the probability that he gets at least one of the 4 questions correctly is
You might be interested in
Exterior angle theorem and properties of the isosceles triangles are used
prove the specified relations.
Correct responses:
9. ΔPAT ~ ΔPTB by AA similarity postulate
15. ║
by basic proportionality theorem
9. A two column proof is presented as follows;
Statement Reasons
1. ∠PTA = ∠B 1. Given
2. ∠PAT = ∠ATB + ∠B 2. Exterior angle of a triangle theorem
3. ∠BTP = ∠ATB + ∠PTA 3 Angle addition postulate
4. ∠BTP = ∠ATP + ∠B 4. Substitution property of equality
5. ∠PAT = ∠BTP 5. Substitution property
6. ΔPAT ~ ΔPTB 6. AA similarity postulate
The Angle-Angle, AA, similarity postulate states that two triangles are similar if two angles in one triangle are each equal to two angles in the other triangle.
15. A two column proof is presented as follows;
Statement Reasons
1. Given
2. ∠1 ≅ ∠G 2. Given
3. ΔKHG is an isosceles triangle 3. Definition
4. HK = HG 4. Legs of an isosceles triangle
5. Substitution property
6. ║
6. BPT, Basic Proportionality Theorem
Basic Proportionality Theorem, BPT, states that if a line parallel to one of the sides of a triangle, intersects the other two sides, then the line divides the other two sides in the same proportion.
Learn more about basic proportionality theorem, AA similarity postulate here:
Answer:
Step-by-step explanation:
Given
Required
Determine
The implication of the question is to solve for
Given that
and
would be
Collect Like Terms
Open Bracket
Collect Like Terms
You need to write an equation for each.
For Andre, he has 100 dollars, and every week gets 5 dollars more. You add the 5 dollars, and Since you don't know how many weeks it has been, use a variable.
For Elena, she has 10 dollars, and gets 20 each week.
Now that you know that it has been 4 weeks, you can plug in 4 for the variable for weeks.
Andrew:
Elena
Andrew has more money in this time.
To find when they have the same amount, equal their expressions to each other. This means that they will have the same amount (because they are equalled) and you can solve to find the variable, which means the weeks that they are equal at.
Bring the like terms to each side by canceling them out. Since you have positive 10, then subtract 10 to each side. You have 5w, so subtract 5w to each side.
The answer will simplify down to 6 weeks.