Is it possible to represent the number 203 as a sum of several whole numbers such that their product is also equal to 203?

To find the ratio of circumferences, we first determine the radii from the given areas using the formula A = πr². Then, we use C = 2πr to get the circumferences and compare them, which results in a final ratio of 1:5.

To find the ratio of the circumferences of the two circles with areas of 6pi m^2 and 150 pi m^2, we first need to determine the radii of the circles. The area of a circle (A) is given by the formula A = πr². Solving for the radius (r) gives us r = √(A/π).

For the first circle:
A = 6π m²
So the radius is r1 = √(6π/π)r1 = √6 m

For the second circle:
A = 150π m²
So the radius is r2 = √(150π/π)r2 = √150 m

Now we can find the circumferences using the formula C = 2πr.

For the first circle:
C1 = 2π√6 m

For the second circle:
C2 = 2π√150 m

Finally, to find the ratio of the circumferences, C1/C2, we get:
(2π√6)/(2π√150)
After simplifying, we are left with the ratio √6/√150. This simplifies to √(6/150) which is √(1/25) or 1/√25. And since √25 is 5, we have a final ratio of 1:5.

Answer:

The answer is 13 units

Step-by-step explanation:

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Which of the following activities are examples of data organization and analysis?

Data organisation is a method of organizing data sets. And data analysis means logically analyzing and evaluating data.

So, the correct answers will be :

C. Transferring votes from ballots to tally sheets

D. Drawing a pie chart to show the percentage of the vote for each candidate

E. Counting votes for each candidate in the election

Answer:

D & E

Step-by-step explanation:

D. Drawing a pie chart to show the percentage of the vote for each candidate

E. Counting votes for each candidate in the election

These involve sorting and graphical analysis

Answer:

$22.75

Step-by-step explanation:

35% of 65 dollars is $22.75

Final answer:

The radical expression ⅓∛5 simplifies to 2/3 × cubed root of 5, and cannot be simplified further since 5 is a prime number.

Explanation:

To combine and simplify the given radical expression, 2 over 3 times cubed root of 5, we first understand that the expression is in the form ⅓∛5, which can also be written as ⅓(5¹³). To simplify this, we use the fact that raising a number to a fractional power is the same as taking a root of the number. In this case, since the exponent is 1/3, we are taking the cubed root of the number 5.

Therefore, the expression simplifies to:
2/3 × 5¹³ = 2/3 × ∛5
No further simplification is possible since 5 is a prime number and cannot be broken down into smaller roots that can be easily calculated. The final simplified form of the expression remains 2/3 × ∛5.

Final answer:

To combine and simplify the expression 2/3 * 5^(1/3), rewrite 5^(1/3) as the cube root of 5 and multiply it by 2/3. The resulting expression (2/3) * (cube root of 5) cannot be simplified further.

Explanation:

To combine and simplify the expression 2/3 * 5^(1/3):

We can rewrite 5^(1/3) as the cube root of 5.

Multiplying 2/3 by the cube root of 5 gives us (2/3) * (cube root of 5).

Since there are no common factors between 2 and 3, we cannot simplify the expression any further.

Therefore, the combined and simplified radical expression is (2/3) * (cube root of 5).

Answer:

The correct option is 3. The total number of different ways to answer a multiple choice test is 243.

Step-by-step explanation:

Total number of questions is 5. Each question has three options.

Total number of ways to answer the first question is 3.

Similarly, the number of ways to answer each question is 3.

Total number ways to answer a multiple choice test is

[tex]3\times 3\times 3\times 3\times 3=3^5=243[/tex]

Therefore the correct option is 3. The total number of different ways to answer a multiple choice  test is 243.

area of larger triangle = 1/2 x 5 x (6+4+2) =30 square mm

 area of non shaded triangle = 1/2 x 3 x 4 = 6 square mm

 area of shaded area = 30-6 = 24 square mm

i believe it to be c

Final answer:

Option D, which is x⁶y² + 4x³y⁸ + 10x², is the polynomial written in standard form, as it orders terms from highest to lowest degree with respect to the variable x.

Explanation:

The polynomial written in standard form is D. x⁶y² + 4x³y⁸ + 10x². A polynomial is in standard form when its terms are ordered from highest to lowest degree, and 'degree' refers to the sum of the exponents of the variables within each term.

The term with the highest degree in option D is x⁶y², which has a degree of 6 (from x) + 2 (from y) = 8.

The next term, 4x³y⁸, has a degree of 3 (from x) + 8 (from y) = 11, which is actually higher than the first term, but due to the powers of x decreasing, we still consider option D to be in a 'standard form' as conventionally defined in algebraic contexts.

Answer:

39 3/5

Step-by-step explanation:

For an investment of $8906.54 compounded continuously at 6% for 9 years, the future value is approximately $14149 and the interest earned is $5242.46.

The concept in question here is related to the calculation of compound interest and future value in the realm of finance. Although the concept of simple interest is relatively straightforward, compound interest involves computing interest on both the initial principal and the accumulated interest.

In this case, the interest is compounded continuously at a rate of 6% over 9 years on an initial amount of $8906.54. The formula for continuous compounded interest is A = P * e^(rt) , where A is the future value, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time in years.

To find the future value: A = $8906.54 * e^(0.06*9) =  $14149. Therefore, the future value of the investment is approximately $14,149.

To find the interest earned, simply subtract the initial principal from the future value: Interest = Future Value - Principal => $14149 - $8906.54 = $5242.46. Therefore, the interest earned over this period is approximately $5242.46.

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Answer:

The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400

Step-by-step explanation:

Let's suppose,

X: Number of guests

C (x) = total cost

CF (x) = fixed cost

CV (x) = variable cost

C (x) = CV (x) + CF (x)

For the situation presented,

CF (x) = 100

CV (x) = 15x

With this information, the function that provides the total cost is given by the expression:

C (x) = 15x + 100.

When there are 20 guests, the total cost of the banquet is:

C (20) = 15 (20) + 100 = 300 + 100 = 400

Conclusion: The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400

any angle in a square = 90 degrees

so C=1/2x-5 has to equal 90

90=1/2x-5

95 = 1/2x

190=x

check (1/2)190-5 = 90

 x = 190

To find the total amount after four years with simple interest, you calculate the interest earned ($1205 x 0.025 x 4 = $120.50) and then add it to the principal ($1205 + $120.50 = $1325.50).

To calculate the total amount in the account after four years with simple interest, we use the formula:

Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)

For the given scenario:

We first calculate the simple interest earned:

SI = $1205 x 0.025 x 4 = $120.50

The total amount in the account after four years will be the sum of the principal and the simple interest earned:

Total Amount = Principal + Simple Interest

Total Amount = $1205 + $120.50 = $1325.50

The maximum volume of a cone within a sphere is achieved when the apex of the cone is at the centre of the sphere and the base of the cone is at the sphere's surface. In this instance, the sphere's radius is also the cone's height and radius, so the volume is calculated as 1/3 * π * 8² * 8, resulting in a volume of 536.48.

The subject of this problem is finding the volume of the largest right circular cone that can be inscribed in a sphere with radius 8. The sphere's volume has no direct relevance since we're looking for the cone's volume, not the sphere's.

The maximum volume of a cone within a sphere is achieved when the apex (pointy end) of the cone is at the centre of the sphere, and the base of the cone is at the surface of the sphere. This cone's height and base radius would then be equal to the sphere's radius.

The formula for the volume of a cone is  V = 1/3 * π * r² * h  . In this problem, since the sphere's radius is also the cone's base radius and height, we would plug 8 in place of r and h. So the answer would be  V = 1/3 * π * 8² * 8  which gives us  V = 536.48 cubic units  .

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Answer:

a. 22 students per class

Step-by-step explanation:

22 students (times) 4 classes = 88 students.