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TEA [102]
3 years ago
12

Your math teacher tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth

2 points each and word problems are worth 5 points. How many of each type of question are there?​

Mathematics
1 answer:
rusak2 [61]3 years ago
4 0
If we assume that
x isthe number of multiple choice questions, and y is the number of word problems, we can write a system of equations like:
{ x + y = 38
{ 2x + 5y = 100

If we multiply the first equation by -2 we get:
{ -2x-2y = -76
{ 2x + 5y = 100

Now if we add both equations we get only equation with 1 unknown (y) :

3y = 24 ⇒ y = 8

Substituting the calculated value to the first equation we get:

x + 8 = 38 ⇒ x = 30

The solution:
{ x = 30
{ y = 8

means that:
The test had 30 multiple choice questions, and 8 word problems.
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6. If the net investment function is given by
Pachacha [2.7K]

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

  • (a) The capital formation from the end of the second year to the end of the fifth year is approximately <u>298.87</u>.

  • (b) The number of years before the capital stock exceeds $100,000 is approximately <u>46.15 years</u>.

Reasons:

(a) The given investment function is presented as follows;

I(t) = 100 \cdot e^{0.1 \cdot t}

(a) The capital formation is given as follows;

\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot  e^{0.1 \cdot t}} + C

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

\displaystyle  \mathbf{\left[1000 \cdot  e^{0.1 \cdot t}} + C \right]^t_0} = 100,000

Which gives;

\displaystyle 1000 \cdot  e^{0.1 \cdot t}} - 1000 = 100,000

\displaystyle \mathbf{1000 \cdot  e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000

\displaystyle e^{0.1 \cdot t}} = 101

\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15

The number of years before the capital stock exceeds $100,000 ≈ <u>46.15 years</u>.

Learn more investment function here:

brainly.com/question/25300925

6 0
2 years ago
Which of the following functions have a vertical asymptote for values of Ø such that cos Ø = 1?Select all that apply.
igomit [66]

Answer:

y=\cot \theta and y=\csc \theta

Step-by-step explanation:

Note that if \cos \theta=1, then \sin \theta=0.

Functions y=\cos \theta,\ \ y=\sin \theta do not have vertical asymptotes at all.

Vertical asymptotes have functions y=\tan \theta,\ \ y=\cot \theta,\ \ y=\sec \theta,\ \ y=\csc \theta.

Functions y=\tan \theta and y=\sec \theta have the same vertical asymptotes (when \cos \theta =0).

Functions y=\cot \theta and y=\csc \theta have the same vertical asymptotes (when \sin \theta =0). See attached diagram

3 0
3 years ago
What is the significance of having short-term ínvestrnents?
Lesechka [4]

Answer:

You can cancel your investment without wasting a lot of money.

Step-by-step explanation:

Short-term means that you dont have it for a long time, so you could basically wait it out and then cancel.

(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I answer.) If this answer helped you please consider giving it brainliest. If my answer was wrong and you got marked wrong for it, I deeply apologize and hope you will forgive me, since everyone makes mistakes sometimes. If you need me to elaborate on my answer or give further explanation on it, please ask and I will do so. If you need to explain your reasoning on your work feel free to use my words- word for word- without crediting me, the answer was made for you anyways! Hope yall learn from my answer and it helps you in the future with assignments, quizzes, test’s, and more! <3 me

4 0
2 years ago
Read 2 more answers
Find an equation for the nth term of the arithmetic sequence. -13, -8, -3, 2, ...
Nikitich [7]
Https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.798537.html
3 0
3 years ago
Read 2 more answers
Triangle ABC is a right triangle. The legs of the triangle are AB = 6 cm and BC = 12 cm. Find the measure of angle A.
Mnenie [13.5K]

Answer:

63.4°

Step-by-step explanation:

Given that AB and BC are the legs of the right triangle, then opposite to angle A is side BC and adjacent to angle A is side AB.

By definition, the tangent of angle A is:

tan(∠A) = opposite leg / adjacent leg

tan(∠A) = BC/AB

tan(∠A) = 12/6

∠A = arctan(2)

∠A = 63.4°

8 0
3 years ago
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