Convert X^2 + Y^2 = 16 to polar form

Answer:

\(4(4b - 8) - \frac{3}{8} \\ 16b - 32 - \frac{3}{4} \\ \frac{64b - 128 - 3}{8} \\ \frac{64b - 131}{8} \)

hope this will help you

The value of x is 1

Given that,

AB=DE

AC=DF

∠CAB=∠FDE

So by the triangle property of SAS, ΔABC and the ΔDEF are equal means ΔABC≅ΔDEF.

And we know that if two triangles are equal then by their properties their respective sides and angles will also be equal to each other.

So we can write that,

⇒13x-12=7x-6

⇒13x-7x=12-6

⇒6x=6

⇒x=1

Therefore the value of x is 1.

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Answer:

Rs 6900

Step-by-step explanation:

To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.

The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:

Taxable Income = Early Income - Tax-Free Allowance

Taxable Income = 150,000 - 100,000

Taxable Income = 50,000

Now, we can calculate the tax amount based on the given tax rates:

For the first 20,000 rupees, the tax rate is 12%:

Tax on First 20,000 = 20,000 * 0.12

Tax on First 20,000 = 2,400

For the remaining taxable income (30,000 rupees), the tax rate is 15%:

Tax on Remaining 30,000 = 30,000 * 0.15

Tax on Remaining 30,000 = 4,500

Finally, we add the two tax amounts to get the total tax she should pay in a year:

Total Tax = Tax on First 20,000 + Tax on Remaining 30,000

Total Tax = 2,400 + 4,500

Total Tax = 6,900

Therefore, the girl should pay 6,900 rupees in tax in a year.

Answer:

6.25

Step-by-step explanation:

divide the volume value by 8

Using the linear equations the punch bowl had 2.75 cups of punch in it before Felicia added 12 cups of punch to it.

Let's assume that the punch bowl had x cups of punch before Felicia added 12 cups of punch to it.

After Felicia added 12 cups of punch, the total amount of punch became x + 12 cups.

Then, when two guests served themselves 1.25 cups and 2 cups of punch, respectively, the total amount of punch in the bowl became:

x + 12 cups - 1.25 cups - 2 cups = x + 8.75 cups.

We know that the punch bowl contained 11.5 cups of punch after this. So we can write:

x + 8.75 cups = 11.5 cups

Subtracting 8.75 from both sides, we get:

x = 2.75 cups

Therefore, the punch bowl had 2.75 cups of punch in it before Felicia added 12 cups of punch to it.

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The question is -

The punch bowl at Felicia’s party is getting low so she adds 12 cups of punch to the bowl. Two guests serve themselves 1.25 cups and 2 cups of punch. The punch bowl now contains 11.5 cups of punch. How many cups were in the punch bowl before Felicia refilled it?

Answer:

99π/4 sq ft

Step-by-step explanation:

Area = (110/360)\(\pi 9^{2}\)

        =  99π/4

Step-by-step explanation:

6(3n - 4)

= 6(3n) - 6(4) (by distributive law)

= 18n - 24.

Given that a company budgeted 5 1/4 hours to complete a project, determine how much time they spent on research if they spent 1/3 of the total budget.

First, convert the budget from hours into minutes.

5 1/4 hours = 315 minutes

1 hour = 60 min

1/4 hour = 15 min

60 x 5 = 300

300 + 15 = 315

Then, divide the minutes by 3 or multiply it by 1/3.

315 / 3 = 105

315 x 1/3 = 105

Lastly convert to a mixed number.

1 3/4 hour

Thus, the company plans to spend 1 3/4 hours or 1 hour and 45 minutes on research.

The cost of the trainers in pounds which is $60 in the USA is £44.94

What is exchange rate?

The exchange rate between the dollar and the pound sterling is the amount at which both currencies exchange hands, I mean the amount of pound sterling that is given in lieu of $1, in this case, for every $1, the amount of pound sterling that is equivalent to it is £0.749, which means that on the basis of the exchange rate the value of trainers in pounds can be determined as shown in details below:

$1 = £0.749

$60=60*£0.749

$60=cost a pair of trainers=£44.94

In short, a pair of trainers selling for $60 in the USA should cost £44.94 based on the exchange rate of $1 = £0.749

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Answer:

9

Step-by-step explanation:

There are 9 x's above 1 letter mailed.

The Probability that at least one person did not choose Coke is 7/10.

According to the statement

we have given that the in a consumer survey, 10 people were asked to choose a cola among Coke, Pepsi, and RC.

And we have to find the probability that at least one person did not choose Coke.

So, for this purpose, we have know that the

Probability is the chance that a given event will occur.

In probability, at least mean the minimum value that should occur once a random event happens.

And

the number of person which take part in a survey = 10

Number of items to choose = 3

The probability that the all person choose cola = 3/10

And

we know that the at least probability is:

at least probability = 1 - simple probability

So,

Probability that at least one person did not choose Coke = 1 - Probability that all person did choose Coke

Substitute the values in it then

Probability that at least one person did not choose Coke = 1 - 3/10

Probability that at least one person did not choose Coke = 7/10.

So, The Probability that at least one person did not choose Coke is 7/10.

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Answer:

77 years old

Step-by-step explanation:

The 95% confidence interval for the mean tip percentage is (3.49, 4.22)

Confidence interval is the two-sided limit consisting of the lower limit and the upper limit and the value between the two limits is the parameter value.

For this question, we have given a graph of the data, so we only need to see the data and interpret that to answer the question.

First, since confidence interval is 95% so we must see 2.5% limit for two side or equal to 0.025.

For the lower limit, see upper value of dot plot then see separate lowest 0.025 of data is 3.491 or 3.49.

For the upper limit, see lower value of dot plot then see separate highest 0.025 of data is 4.224 or 4.22.

Thus, the 95% confidence interval is (3.49, 4.22) for the mean tip percentage.

Your question is incomplete, but most probably your full question was (image attached)

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If Alice has $50 and spends 4/5 of her money, she spends $40.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.

Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.

To find out how much Alice spends, we can multiply her total money ($50) by 0.8

= $50 x 0.8

Multiply the numbers

= $40

Therefore, Alice spends $40.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Alice has $50 and spends 4/5 of her money. How much does Alice spend?

Step-by-step explanation:

Draw points at

(-1, -4)

(0, -2)

(1, 0)

(2, 2)

(3, 4)

Then draw a line through those points and that should do it.

This is the graph for the equation.

Answer:

-27.89%, the portfolio loses about 28% of its value every year on average.

Step-by-step explanation:

The annual growth-rate is -52.90%

The annual growth rate can be calculated using the formula:

i = (1 - (final value / initial value)^(1/n)) x 100%

Where "final value" is the current value of the portfolio, "initial value" is the original value of the portfolio, "n" is the number of years, and "i" is the annual growth rate.

In this case, the portfolio drops to one-tenth of its former value, which means the final value is 1/10 or 0.1 times the initial value. The time period is 6 years. So we have:

i = (1 - (0.1)^(1/6)) x 100%
i = (1 - 0.471) x 100%
i = 52.9%

Therefore, the annual growth rate is -52.9% (since the portfolio has decreased in value). Rounded to two decimal places, the answer is -52.90%.

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Answer:

Step-by-step explanation:

Factor to solve.

12a2 + a – 35 = 0

>Multiply the first and the last, 12 and -35

     (12)(-35) = -420

>  Find 2 numbers that multiply to -420 but add to middle term, 1

       -20 and +21 multiply to -420 but adds to 1

>Replace the middle term with -20 and 21

      12a² + a – 35 = 0

       12a² + 20a -  21a – 35 = 0

>Group the first 2 and last 2 terms

      ( 12a² + 20a) (-  21a – 35) = 0

>Take out GCF from each of the groupings

      4a ( 3a + 5) -7(3a + 5) = 0

>Take out GCF (3a + 5)

      ( 4a - 7) ( 3a + 5) = 0

>Set each =0 and solve for a

       ( 4a - 7) = 0                      ( 3a + 5) = 0

          a=7/4                                  a = -5/3

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is 35/138

Probability is the measure of that how likely is an event can occur.

Probability of an event = Favorable outcomes of the event / total outcomes

Multiplication rule of probability states that probability of two events happening at the same time = (probability of one event )*(probability of another event )

Given that A cooler contains 14 bottles of water and 10 bottles of lemonade. Colleen randomly selects 2 bottles from the cooler

Total bottle = 14 +10 = 24

Let E be the event that Colleen selects a bottle of water first

Probability of E = 14/24

Let F be an event that Colleen selects bottle of lemonade when at the same time a bottle of lemonade is already taken out  

Probability of F = 10/23

Therefore , The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is

= Probability of E * Probability of F = (14/24)*(10/23) =35/138.

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Answer:

372

Step-by-step explanation:

Since we know the total weight which is 714 and we know the weight of one garden which is 342, all we need to do now is subtract:

714 - 342 = 372

The radius of the cone is approximately 0.99917 inches when the volume of the cone is 527.52 cubic inches.To find the radius of the cone, we need to use the formula for the volume of a cone, which is:

V = (1/3)πr^2h

where V is the volume, π is the mathematical constant pi (approximately 3.14), r is the radius, and h is the height of the cone. We are given that the volume of the cone is 527.52 cubic inches, so we can substitute that value into the formula:

527.52 = (1/3)πr^2h

We don't know the height of the cone, but we can simplify the formula by multiplying both sides by 3:

1582.56 = πr^2h

Now we can solve for r. We know that π is approximately 3.14, so we can substitute that value:

1582.56 = 3.14r^2h

We still don't know h, but we can eliminate it by dividing both sides by r^2:

1582.56/r^2 = 3.14h

Now we can solve for h:

h = 1582.56/(3.14r^2)

We can substitute this value for h back into the original formula:

527.52 = (1/3)πr^2h

527.52 = (1/3)πr^2(1582.56/(3.14r^2))

Simplifying this equation, we get:

527.52 = 1582.56/3

Multiplying both sides by 3, we get:

1582.56 = 1582.56

This is true, so we know that our calculation is correct. Now we just need to solve for r:

527.52 = (1/3)πr^2h
527.52 = (1/3)πr^2(1582.56/(3.14r^2))
527.52 = 526.9468r^2
r^2 = 0.998344
r = 0.99917 (rounded to the nearest hundredth)

Therefore, the radius of the cone is approximately 0.99917 inches when the volume of the cone is 527.52 cubic inches.

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Answer:

10.7a-8.1b

Step-by-step explanation:

Answer: 24.3a - 8.1 + 0.29

Step-by-step explanation:

YOUR WELCOME

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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To show that for any string w ∈ L(G) of length n ≥ 1, exactly 2n − 1 steps are required for any derivation of w in a context-free grammar (CFG) in Chomsky normal form (CNF), we can prove it by induction.

First, let's consider the base case when n = 1. In this case, w consists of a single terminal symbol. Since the CFG is in CNF, the derivation for w will consist of a single production rule that directly produces the terminal symbol. Thus, in this case, exactly 1 step is required, which is equal to 2n − 1 = 1.

Now, let's assume that for any string of length k < n, the number of steps required for its derivation is 2k − 1. We will prove that for a string w of length n, the number of steps required for its derivation is 2n − 1.

Since the CFG is in CNF, any production rule in the derivation can either introduce two non-terminals or substitute a non-terminal with a terminal symbol.

Therefore, for a string of length n, the total number of steps required for its derivation is n + (n - 1) = 2n - 1.

By induction, we have shown that for any string w ∈ L(G) of length n ≥ 1 in a CFG in CNF, exactly 2n − 1 steps are required for any derivation of w.

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Answer:

Bond

Step-by-step explanation:

A promissory note or a promise to repay a certain amount of money at some point in the future is basically a bond.

A bond is a debt security that represents a loan made by an investor to a borrower, which is usually a corporation or government agency. It is a fixed-income investment, meaning that the borrower promises to pay a specific amount of interest over a set period of time and return the principal amount of the loan on the date of maturity. Bonds are issued for various purposes, such as raising capital, funding new projects, or refinancing debt.

CD (Certificate of Deposit) is a savings instrument issued by a bank or credit union that generally pays a fixed rate of interest over a set term. Mutual fund is an investment vehicle that pools money from multiple investors to purchase a portfolio of securities, such as stocks, bonds, or both. Stock is an ownership share in a company that represents a claim on part of the company's assets and earnings.

Answer:

I am pretty sure

-

x=9.6

Step-by-step explanation:

the two angles are corresponding which means they are equal to eachother.

you set the equations equal to eachother and then solve how you would a normal algebra problem.

1. add negative nineteen to the other side

2. subtract 3x to the other side

3. 3x=29

4. -

x= 9.6

Answer:

they are congruent

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

He spent 4/5 out of 5/5

4/5 = 36 to find the whole we cross multiply the equation

let x represent the whole

4/5 = 36/x

5*36 = 4x

180 = 4x divide both sides by 4

x = 45

If Gas prices are typically marked up for holiday travel. If the prices are marked up 10% and the regular price is $2.45,  the price after the mark-up is $2.70.

Frist step is to find the marked-up price using this formula

Markup price = Markup percentage × Regular price

Let plug in the formula

Markup price = 10% × $2.45

Markup price = $0.245

Now  let find the price after markup  using this formula

Price after markup = Regular price + Markup price

Let plug in the formula

Price after markup = $2.45 + $0.245

Price after markup = $2.695

Price after markup = $2.70 ( Approximately)

Therefore $2.70 is the price after marked-up.

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