MATHEMATICS HIGH SCHOOL

Select the correct answer.Mary deposited $350 in a bank account that promises 2.8 percent interest compounded continuously. Approximately how many years will it take to reach a balance of $500?

A.
1.43 years

B.
2.80 years

C.
5.55 years

D.
12.77 years

Answers

Answer 1

Answer:

Answer:

2.80 years

Step-by-step explanation:

beacause it is simple that it will take option B . You

don't have to worry .

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Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.

Answers

The rectangle with a certain area and the smallest perimeter
is always a square.

343 = 7³

If the area is 343 m², then the rectangle with the smallest perimeter
is the square with sides of

√343 = (7)^ ¹·⁵ = 7 √7 meters

Final answer:

To find the dimensions of a rectangle with the smallest possible perimeter given an area of 343 m², we must determine the dimensions that will minimize the sum of the lengths of the four sides. The dimensions of the rectangle are 7 m by 49 m.

Explanation:

To find the dimensions of a rectangle with the smallest possible perimeter given an area of 343 m², we must determine the dimensions that will minimize the sum of the lengths of the four sides. Since the perimeter is the sum of the lengths of the opposite sides of a rectangle, we can rewrite the perimeter formula as P = 2l + 2w, where l represents the length and w represents the width.

Now, let's solve for the dimensions:

1. Start with the formula for the area of a rectangle: A = lw.

2. Substitute the given area: 343 = lw.

3. Rewrite the perimeter formula: P = 2l + 2w.

4. Express one variable in terms of the other using the area formula: l = 343/w.

5. Substitute the expression for l in the perimeter formula: P = 2(343/w) + 2w.

6. Simplify the equation: P = (686/w) + 2w.

7. To find the minimum perimeter, differentiate the equation with respect to w and set it equal to zero: 0 = (686/w²) + 2.

8. Solve the equation for w: (686/w²) + 2 = 0. Subtract 2 from both sides: 686/w² = -2. Multiply both sides by w²: 686 = -2w².

9. Divide both sides by -2: -343 = w². Take the square root of both sides (ignoring the positive value since the width cannot be negative): w = -√343 = -7.

10. Substitute the value of w back into the area formula: 343 = l(-7). Solve for l: 343 = -7l. Divide both sides by -7: l = 343/-7 = -49.

Since both dimensions cannot be negative, we ignore the negative values and take the absolute values of w and l: w = 7 and l = 49.

Therefore, the dimensions of the rectangle with an area of 343 m² and the smallest possible perimeter are 7 m by 49 m.

Learn more about Dimensions of a rectangle here:

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When critiquing an observational study, which four factors should be analyzed?A.Methodology, Results, Discussion, Conclusion
B.Introduction, Results, Discussion, Conclusion
C.Introduction, Methodology, Results, Discussion
D.Methodology, Causes, Results, Discussion

this was in my math class, so that is why the subject is mathematics. Any help would be greatly appreciated.

Answers

Answer:

The correct answer is option C. Introduction, Methodology, Results, Discussion

Step-by-step explanation:

When critiquing an observational study, the following four factors should be analyzed == Introduction, Methodology, Results, Discussion.

Critiquing means the evaluation of any theory in a detailed and analytical way. This method is also called the IMRaD format.

Answer:

Option:A

Step-by-step explanation:

The observation study involves

1) Methodology:

"Methodology is the philosophical framework within which the research is conducted or the foundation upon which the research is based”

2) Result:

Results section is just a presentation of the data. The results need to be presented in enough detail for someone not familiar with the scientific paper to understand them.

3) Discussion:

It unrolls the main results, explain their meanings. Put there the new questions and perspectives, describe the most interesting points for the entire field. Define the possible answers, write down why and how and what for, your suggestions.

4)Conclusion:

It is a summary of the discussion or the whole work. You can put there the main points and results, their factual meaning for the field and a possible further direction. I like to describe this as "discussion's points and facts without the discussion."

Help me with this question

Answers

Answer:

37.2

Step-by-step explanation:

when you turn the small triangle LMN to its right angle to cover the right angle of KLM, you find that they are similar triangles.

therefore the corresponding side lengths are at the same ratio.

LM/KM = MN/LN

LM = 24

MN = 13

we can get LN via Pythagoras of the small triangle

LN² + MN² = LM²

LN² + 13² = 24²

LN² = 24² - 13² = 576 - 169 = 407

LN = sqrt(407) = 20.174241

now back to our main problem

24/KM = 13/sqrt(407)

24×sqrt(407)/13 = KM = 37.2

What are the measurements of the listed angles? (numbers only) Box 1 - Angle B Box 2 - Angle C

Answers

Answer:

speak spanish soy ecuatoriana no se entiende plis

How do you write 35 over 20 As a percentage

Answers

In order to write $(35)/(20)$ as a percentage, we must first convert the fraction into a decimal. We can do that simply by dividing.

35 / 20 = 1.75

In order to convert a fraction to a decimal, we must multiply it by 100

1.75 * 100 = 175%

$(35)/(20)$ as a percentage is 175%.
Hope that helped =)

Well, first you have to make it to a decimal, dividing 35 into 20, which is 1.75, and now you convert THAT into a percentage, which would be 175%, because we have to multiply it by 100.
I hope I helped! =D

Suppose a varies directly as b, and a=7 when b=2 find b when a =21

Answers

because α varies directley to β
$\alpha = k \beta$
(k = constant)

α=7 when β=2
7= 2k
k= $(7)/(2)$

so when α=21
21= $(7)/(2)$ b
b= 6

Final answer:

To solve for 'b' when 'a' = 21 in a direct variation relationship where 'a' = 7 when 'b' = 2, first determine the constant of proportionality. Then, insert 'a' into the formula and solve for 'b'. The solution of 'b' would be 6.

Explanation:

In this scenario, we are given that a varies directly as b, which means we can state this relationship as a = kb, where k is a constant of proportionality. Initially, we're given that a = 7 when b = 2. From this, we can find that k = a / b, so k = 7 / 2 = 3.5. Therefore, our direct variation equation is a = 3.5b.

When a = 21, we can substitute this into the direct variation equation and solve for b. Thus, 21 = 3.5b, and by dividing both sides by 3.5, we can find that b = 6.