Find the time for an investment to double at the given annual interest rate, compounded continuously. (Round your answer to two decimal places.)

3.5%

Answer:

  B)  108°

Step-by-step explanation:

You want the interior angle measure for a regular pentagon.

The interior angles of a regular n-gon will have measure ...

  180° -360°/n

When n = 5, the interior angles have measure ...

  180° -360*/5 = 180° -72° = 108°

The interior angles of a regular pentagon are 108°.

__

Additional comment

The 360°/n comes from the fact that the sum of exterior angles for any convex polygon is 360°. For a regular n-gon, those exterior angles are congruent, so each is 360°/n. The interior angle is its supplement.

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Answer:

- Hello Risap!

\( \large{ \tt{ \green❊ \pink { \: S \: O \: L \: U \: T \: I \: O \: N} \green { \: ❊}}}\)

\( \large {\tt{✢ \: SP = MP - dis\% \: of \: MP}}\)

\( \large{ \tt{⟶ \: 1760 = MP - 12\% \: of \: mp}}\)

\( \large{ \tt{⟶ \: 1760 = MP - \frac{12}{100} \: mp }}\)

\( \large{ \tt{⟶ \: 1760 = \frac{100 \: MP - 12 \: mp}{100} }}\)

\( \large{ \tt{⟶ \: 88 \: MP = 176000}}\)

\( \large{ \tt{⟶ \: MP= \frac{176000}{88} }}\)

\( \large{ \tt{⟶ \: MP = Rs \: 2000}}\)

\( \large{ \boxed{ \boxed{ \tt{⤳ \: OUR \: FINAL \: ANSWER : \boxed{ \red{ \tt{MP = Rs \: 2000}}}}}}}\)

For any positive integer n, the theorem states that the integer 8^n + 13 is divisible by 7. This means that when we raise 8 to any positive power and add 13, the resulting number will always be divisible by 7.

To understand why 8^n + 13 is divisible by 7 for any positive integer n, we can use the concept of modular arithmetic. Modular arithmetic deals with remainders when dividing numbers. In this case, we are interested in divisibility by 7.

Let's examine the pattern when we raise 8 to different powers and add 13:

- For n = 1: 8^1 + 13 = 8 + 13 = 21, which is divisible by 7.

- For n = 2: 8^2 + 13 = 64 + 13 = 77, which is divisible by 7.

- For n = 3: 8^3 + 13 = 512 + 13 = 525, which is divisible by 7.

We can observe that for each value of n, 8^n + 13 results in a number that is divisible by 7. This pattern continues for any positive integer n.

To provide a more formal explanation, we can use modular arithmetic notation. The statement can be expressed as: 8^n + 13 ≡ 0 (mod 7). This notation means that 8^n + 13 leaves a remainder of 0 when divided by 7, or in other words, it is divisible by 7.

This theorem can be proven using mathematical induction, where we show that the statement holds for n = 1, and assuming it holds for a particular value of n, we prove that it also holds for n + 1. The proof involves manipulating the expression 8^n + 13 using the properties of modular arithmetic.

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Complete question:

Main theorem. Assume that n is any positive integer. Then the integer \(8^{n}\)+13 is divisible by 7.

Answer:

Answer:

r = 6 in

Step-by-step explanation:

The volume of a cylinder of radius r and height or length h is

V = πr²h.

Here, we need to solve for the radius; we get:

     V

------------- = r²

     πh

                                       904.23 in³

This works out to    r² = ----------------- = 35.97 in²

                                            π(8 in)

Finally, take the square root of this result to find the radius, r:

r = √35.97 in² = 6 inches

Using greater than sign or number line, we can show the numbers from greatest to least as 35/4 > √72 > 25/3 > 8.4

To arrange numbers from greatest to least, you would first find the largest number and place it at the beginning of the list. Then, you would compare the remaining numbers and place the next largest number after the first. You would continue this process until all of the numbers are arranged in order from largest to smallest.

In this problem, we can arrange the number from greatest to least and assigning the greater than sign to show the decrease in number. We dan also use the concept of number line to show how the numbers are placed.

From the data given,

35/4 > √72 > 25/3 > 8.4

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Answer:

$3,100

Hope this helps!!

Step-by-step explanation:

We can use the distance formula. Solution shown below. I hope this helps! :)

Answer:

\(\boxed{x_1 = \frac{2}{3} ~~or~~x_2 = 1}\)

.

Step-by-step explanation:

\((3x - 2)(5x - 4) = (3x - 2)^2\)

\(15x^2 - 12x - 10x + 8 = 9x^2 - 12x + 4\)

\(15x^2 - 22x + 8 - 9x^2 + 12x - 4 = 0\)

\(6x^2 - 10x + 4 = 0\) → divide both segment by 2

\(3x^2 - 5x + 2 = 0\)

\((3x - 2)(x - 1) = 0\)

\(3x - 2 = 0\)

\(3x = 2\)

\(x = \frac{2}{3}\)

.

\(x - 1 =0\)

\(x = 1\)

=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

15.23 m

Step-by-step explanation:

The problem given describes the shape of a right angled triangle.

From the diagram below:

The height of the tree is the opposite = 6 m

The distance of the flower from the base of the tree = adjacent = 14 m

The distance the bird must fly to get from the nest to the flower = hypotenuse = h

According to Pythagoras rule:

\(hyp^2 = opp^2 + adj^2\)

Therefore:

\(h^2 = 6^2 + 14^2\\\\h^2 = 36 + 196\\\\h^2 = 232\\\\h = \sqrt{232} \\\\h = 15.23 m\)

The bird will have to fly 15.23 m to get from its nest to the flower in a direct path.

The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.

As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

Amadou misses 2% of the free throws he attempts in a season, he missed 32,

Calculate the total number of throws as shown below,

2% of x = 32

Here, x is the total number of throws,

0.02 × x = 32

x = 32 / 0.02

x = 1600

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The solution for x is x = (y + 49)/7.

Given that an equation 7x - 49 = y, we need to determine the equation in for of x,

To solve for x in the equation 7x - 49 = y, we'll isolate x on one side of the equation.

Here's the step-by-step process:

Start with the given equation: 7x - 49 = y.

Add 49 to both sides of the equation to isolate the term with x:

7x = y + 49.

Divide both sides of the equation by 7 to solve for x:

(7x)/7 = (y + 49)/7.

Simplify:

x = (y + 49)/7.

Therefore, the solution for x is x = (y + 49)/7.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The assumption underlying the independent samples t-test is that the scores must be drawn from a normally distributed population. Option A is correct.

A t-test is a statistical method that determines whether two groups of observations are significantly different from one another. When comparing the means of two populations, the t-test is commonly used. The t-test is used to determine whether two groups' means are significantly different when the samples are drawn from normally distributed populations with equal variances.

The t-test is a powerful tool for determining whether a sample is significantly different from a population or whether two samples are significantly different from one another. The independent samples t-test, as opposed to the dependent samples t-test, is a t-test that compares the means of two independent groups. In this situation, the groups are separate and distinct.

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Answer:

D: an irregular quadrilateral​

Step-by-step explanation:

def not a rhombus : A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal.

def not a pentagon, cause it's got only 4 sides.

def not a regular quadrilateral which must have 4 equal sides, and 4 equal angles, and its diagonals must bisect each other. Square is the only quadrilateral that satisfies all these conditions.

only D: An irregular quadrilateral is a quadrilateral with four sides that are not regular or the same.

The options are given as follows:

a. H0: fragrance opinion is not independent of gender; Ha: fragrance opinion is independent of gender

b. H0: gender = fragrance opinion; Ha: gender \(\neq\) fragrance opinion

c. H0: fragrance opinion is independent of gender; Ha: fragrance opinion is not independent of gender

d. H0: gender \(\neq\) fragrance opinion; Ha: gender = fragrance opinion

The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The answer is option (d).

H0: gender \(\neq\) fragrance opinion

Ha: gender = fragrance opinion

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Answer:

5:2

Step-by-step explanation:

Start with what the question is asking for, which is the ratio of math problems to minutes.

With ratios "to" also means ":", so you can change it to math problems : minutes.

Then, substitute the numbers for the labels. Math problems = 10 and minutes = 4, so now you have 10:4

Lastly, to simplify the ratio, find the greatest common factor, in this case 2, and divide both sides, which gives you your answer 5:2

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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The equation of Henry's equation is y = 2x + 3

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation of Adriana is given as

y = 2x + 4

From the question, we understand that:

Henry's equation has the following properties:

This is represented as:

y = 2x + 4 - 1

Evaluate the difference

y = 2x + 3

Hence, the equation of Henry's equation is y = 2x + 3

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Answer:

  85,999,999.999 999 909

Step-by-step explanation:

The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.

The numbers in standard form are ...

  86,000,000 = 8.6×10^7

  0.000000091 = 9.1×10^-8

Their difference is ...

  86,000,000 -0.000000091 = 85,999,999.999 999 909

In scientific notation, this is ...

  8.599 999 999 999 990 9×10^7

Answer:

4x+20

Step-by-step explanation:

Bottom length is:

x

Second length is:

2x+8

Last length is:

x+12

Perimeter is adding up all of these lengths:

x+2x+8+x+12:

Simplify:

4x+20

Answer:

300 plus 40 plus 8 plus 0.5 plus 0.06 plus 0.002

If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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Answer:

-84

Step-by-step explanation:

A quotient is the result of division.

n / 6 = -14

You do the inverse operation of division, which is multiplication.

The equation is x/6 = -14 and the value of the unknown number is -84.

Given the parameters:

The quotient of a number and 6 is -14.

Let x represent the unknown number.

Hence:

The quotient of a number and 6 will be x/6.

Next, the quotient is -14

Hence:

x/6 = -14

Therefore, the equation is x/6 = -14.

To solve for x, we cross multiply:

x/6 = -14/1

x = 6 × -14

x = -84

Therefore, the value of x is -84.

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The control limits help to separate common and special causes from each other.

Control lines are the horizontal lines drawn on the control chart. A control chart has several components. It has two control limits. They are represented by dashed lines. The lower one is called the lower control limit (LCL) and the upper one is called the upper control limit (UCL).

The control limits help us mark the highest (by UCL) and lowest (by LCL) error that is bearable. All those errors that occur between UCL and LCL are common errors/variations while the errors that occur above UCL or below LCL are the products with assignable causes variations.

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The product(s) of an acid-base mechanism depend on the specific reactants involved. Without knowing the reactants, it is not possible to provide a definitive answer.

However, in general, acid-base reactions involve the transfer of a proton (H+) from an acid to a base, resulting in the formation of a conjugate acid and a conjugate base. The conjugate acid is formed by the acceptance of the proton, while the conjugate base is formed by the donation of the proton.

It is important to note that without specific reactants, it is impossible to determine the exact products of an acid-base mechanism. The nature of the reactants and their acid-base properties determine the specific products formed in a given reaction.

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The given compound inequality is

Notice that the solution for x would be all real numbers less than 4, and greater than or equal to 13. If we graph this solution, it would be