A biology test is worth 100 points and has 36 questions. a. Multiple-choice questions are worth 2 points each and essay questions are worth 6 points each. How many questions of each type are on the test?

b. Your friend says that it is possible for the multiple-choice questions to be worth 4 points each. Is your friend correct? Explain.

The test contained 29 multiple choice questions and 7 essay questions.

Let x represent the number of multiple questions and y represent the number of essay questions.

Given that there are a total of 36 questions, hence:

x + y = 36    (1)

Also, the test is worth a total of 100 points, hence:

2x + 6y = 100   (2)

Solving equation 1 and 2 simultaneously gives:

x = 29, y = 7

Therefore the test contained 29 multiple choice questions and 7 essay questions.

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(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

--- Number of questions

--- Points

Solving (a): Number of question of each type.

Make E the subject of formula in

Substitute 36 - M for E in

Collect Like Terms

Divide both sides by -4

Substitute 29 for M in

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

would be:

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

Subtract 116 from both sides

Make x the subject

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

Your friend is incorrect.

coins of silver or gold

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet