if q is inversely proportional to r squared and q=30 when r=3, find r when q=1.2

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We have to write an equivalent fraction of 15 using fifteenths.

2/15

So let multiply by 5 .

2 / 15 x  5/ 5 = 10/75

Thus, 10/75 is equivalent expression.

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Answer:

did you ever did the answer

Step-by-step explanation:

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

To ensure that there is an equal number of glass bears in each group, Mrs. Dryson constructed a total of 17 groups, which can be calculated using arithmetic operations.

What is arithmetic operations?

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

As given in the question,

Mrs. Dryson divided her collection of 52 glass bears into equal groups and She had one bear left over

The steps listed below can be used to calculate the total amount of Mrs. Dryson's products:

Step 1: Arithmetic operations can be utilized to calculate Mrs. Dryson's overall output.

Step 2: Keep in mind that there are 52 glass bears in all, and after separating them into equal groups, she was left with just one bear.

Step 3 - The total bear population to divide into groups of an equal number is calculated as follows:

= 52 - 1 = 51

Step 4: The number that is divided by 51 such that the result is an integer is 3.

Step 5 - As a result, Mrs. Dryson created a total of the following groups:

= 51/3 = 17.

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By looking at the vertical asymptote, we can see that the rational function graphed is the one in option C:

\(F(x) = \frac{1}{(x + 1)^2}\)

Here we can see that we have a vertical asympthote at x = -1, and we can see that bot sides go upwards.

Then we have a denominator of the form:
(x + 1)²

So the denominator becomes zero when x = -1, and thus we have the asymptote.

The only option with that denominator is the one we can see in C, which is:

\(F(x) = \frac{1}{(x + 1)^2}\)

That is the function on the given graph.

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For given triangle, x is 4√5 using Pythagorean theorem.

What is Pythagorean Theorem?

Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.

The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.

The Pythagoras Theorem formula is presented in the definition as:

Perpendicular² + Base² = Hypotenuse²

c² = a² + b²

Now,

Given that perpendicular =19

Hypotenuse=21

then Base²=21²-19²  using Pythagoras theorem

Base=√441-361

=√80

=4√5

Hence,

          x is 4√5

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If Adam and Simon start on bicycle trips from the same point at the same time and Adam travels east at 8mph and Simon travels south at 6mph then after 4.28 hours the distance between them is 60 miles.

Speed is the distance an object covers in a particular time period. It can be calculated as under:

Speed=Distance/ Time.

We have been given the speed of Adam and Simon as 8 mph and 6 mph and we are required to find the time taken by both to be 60 miles apart.

Time=Distance/speed

We cannot find individually but we can find the average time.

Time=60/(6+8)

=60/14

=2.28 hours

Hence if If Adam and Simon start on bicycle trips from the same point at the same time and Adam travels east at 8mph and Simon travels south at 6mph then after 4.28 hours the distance between them is 60 miles.

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Step-by-step explanation:

(a) The lower limit of the 90% confidence interval can be calculated using the formula:

lower limit = sample mean - margin of error

Plugging in the given values, we have:

lower limit = 7.43 - 1.32

lower limit = 6.11 (rounded to 2 decimal places)

Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.

(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.

Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:

500 * 0.9 = 450

So, approximately 450 of these confidence intervals would contain the population mean.

Answer:

uhm b but don't fully believe me if someone else answers i suggest using theirs

Step-by-step explanation:

The price after discount will be $92.82

What does math's % mean?

Percentages are fundamentally fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

The percentage can be calculated by dividing the value by the total value and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.

given data

Price at launch: $123.75

10% off = 25%

Let's calculate the discount's amount.

= 25/100*123.75

= 0.25*123.75

=$30.93

Consequently, the shoe's price is

=123.75-30.93

=$92.82

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Step-by-step explanation:

m<2= 180-90-41= 49°

m<4=90°

m<5=41

m<9=36°

Answer:

c.60

Step-by-step explanation:

Answer:

B. Share them with the office to celebrate a job well-done.

Step-by-step explanation:

This is a question about ethics.

There are 3 dozen doughnuts, which is equal to 36 doughnuts, probably enough to go round the office of the newsroom.

The feature profile from yesterday was a team work, you were not the only one involved, since the doughnut was brought to the newsroom, it is ethical that you share them with the office to celebrate a job well-done. This shows that you appreciate the team work put together by the whole office.

As noble and benevolent as taking the doughnut to the homeless center, it wont be ethical in this situation.

Answer:

2-and-a-half pounds

10 / 4 = 2.5

Answer:

  457

Step-by-step explanation:

The general term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

where a1 is the first term (-26), and d is the common difference (7).

The 70th term of your sequence can be found by putting the numbers into this formula:

  a70 = -26 +7(70 -1) = -26 +483

  a70 = 457

The 70th term of the sequence is 457.

Answer (3x−2)(3x+2)^2

Step-by-step explanation:

Answer:

1. C

2. B

3. D

4. A

Step-by-step explanation:

1. As mentioned in the last sentence of the passage, the main goal of the problem is to figure out how long it took John to get ready.

2/3/4. The goal is to find the amount of time John took to get ready and to obtain that time you need to use 6:10-5:30=n. After solving the number sentence, you should get 40 minutes.

Based on the cross-price elasticity of Demand, we can conclude that good X and good Y are substitutes.

Let's calculate the cross-price elasticity of demand using the given information:

a. Find the percentage change in quantity demanded of good Y:

Percentage Change in Quantity Demanded of Good Y = (New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded * 100

Percentage Change in Quantity Demanded of Good Y = (6250 - 5000) / 5000 * 100 = 25%

b. Find the percentage change in the price of good X:

Percentage Change in Price of Good X = (New Price - Initial Price) / Initial Price * 100

Percentage Change in Price of Good X = (5 - 4) / 4 * 100 = 25%

Now, we can calculate the cross-price elasticity of demand:

Cross-Price Elasticity of Demand = Percentage Change in Quantity Demanded of Good Y / Percentage Change in Price of Good X

Cross-Price Elasticity of Demand = 25% / 25% = 1

b. Based on the calculated cross-price elasticity of demand, we can determine the types of goods:

If the cross-price elasticity of demand is positive (as in this case, where it is 1), it indicates that the two goods are substitutes. This means that when the price of good X increases, the quantity demanded of good Y also increases, suggesting that consumers view these goods as alternatives to each other.

Therefore, based on the cross-price elasticity of demand, we can conclude that good X and good Y are substitutes.

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Answer:

Step-by-step explanation:

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

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Answer:

314 square centimeters

Step-by-step explanation:

Answer:

ok so it could be Careful because think about it 10000x 0.01...

Answer:10,000

Step-by-step explanation:

Answer:

\(-(a+1\frac{3}{4}b)\)

Step-by-step explanation:

Perimeter of a polygon = Sum of the measures of all sides of the polygon

For the given trapezoid,

Perimeter = \(1\frac{1}{2}a+1\frac{1}{2}b+1\frac{1}{2}a+2\frac{3}{4}b\)

By combining similar terms,

Perimeter = \((1\frac{1}{2}+1\frac{1}{2})a+(1\frac{1}{2}+2\frac{3}{4})b\)

                 = \((1+\frac{1}{2}+1+\frac{1}{2})a+(1+\frac{1}{2}+2+\frac{3}{4})b\)

                 = (2 + 1)a + \((3+\frac{1}{2}+\frac{3}{4})b\)

                 = 3a + \((3+\frac{2}{4}+ \frac{3}{4})b\)

                 = 3a + \((3+\frac{5}{4})b\)

                 = 3a + \((3+1+\frac{1}{4})b\)

                 = 3a + \(4\frac{1}{4}b\)

For rectangle,

Perimeter = 2(Length + Width)

                 = 2(2a + 3b)

Difference between the perimeter of trapezoid and rectangle,

= (3a + \(4\frac{1}{4}b\)) - 2(2a + 3b)

= (3a - 4a) + (\(4\frac{1}{4}b\) - 6b)

= -a + \((4+\frac{1}{4}-6)b\)

= -a + \((\frac{1}{4}-2)b\)

= -a + \((\frac{1}{4}-\frac{8}{4})b\)

= -a - \(\frac{7}{4}b\)

= \(-(a+1\frac{3}{4}b)\)

Answer:

first three terms are -5 , 2, and 9

Step-by-step explanation:

term(n) = a + (n-1)d

term5 = a+ 4d = 23

term12 = a + 11d = 72

subtract them

7d = 49

d = 7

sub into a+4d = 23

a + 28 = 23

a = -5

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

80 degrees

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees.  Let x be the third angle

37+63+ x = 180

Combine like terms

100 + x = 180

Subtract 100 from each side

100+x-100 = 180-100

x = 80

Answer:

21

Step-by-step explanation:

2^3=8

7x6=42

42x8=336

336/ (10.6+5.4)

336/ 16= 21

Answer 21

Answer:

it's b

Step-by-step explanation:

just took the test

Answer:

2 dozen = $576

1 dozen = 12 donuts

2 dozen = 24 donuts

to find how much each donut costs, we have to divide the total cost with the total amount of donut, so 576 divide 24, which equals to $24

so each donut cost $24

If twelve people each bought 2 dozen donuts then the cost of each donut is $2.2.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Twelve people each bought 2 dozen donuts.

So, each people bought (2×12) = 24 donuts.

∴ The total number of donuts is,

= (24×12).

=  264 donuts.

∴ The cost of each donut is $(576/262).

= $2.2

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Answer:

y=0.5x + 5

Step-by-step explanation:

The points are (0,5) and (-10,0)

to find the slope do

0-5/-10-0 = 5/10 = 1/2 = 0.5

next plug one of the points into point slope formula

y-y1=m(x-x1)

lets use the point (-10,0)

y1=0

x1= -10

m= 0.5

y-0=0.5(x- -10)

y = 0.5(x+10)

distribute the 0.5

y=0.5x+5