Please help my son with #3

Answer:

[tex]\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})[/tex]

Step-by-step explanation:

Conversion of parametric form of ( r , θ ) to rectangular coordinate can be done by using the formula ( rcosθ , rsinθ ).

Here we need to convert (-4, pi/3) in to rectangular coordinate form.

Which can be converted to rectangular coordinate form as

         [tex]\left ( -4cos\left ( \frac{\pi}{3} \right),-4sin\left ( \frac{\pi}{3} \right)\right )=\left ( -4\times \left ( \frac{1}{2} \right),-4\times \left ( \frac{\sqrt{3}}{2} \right)\right )=(-2,-2\sqrt{3})[/tex]

[tex]\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})[/tex]

The rectangular coordinates of the point (-4, pi/3) is:

This refers to the system which is used to find out the position of points in a geometric element.

First of all, we have to convert to parametric form

Next, we have to convert (-4, pi/3) in to rectangular coordinate form.

(-4 x (1/2), -4 x ([tex]\sqrt{3}[/tex]/2)) = n(-2, -2 [tex]\sqrt{3}[/tex])

After the conversion,

This would bring the rectangular coordinate form to:

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Answer:

The next town is 62.5 miles away.

Step-by-step explanation:

Scale problems can be solved by a simple rule of three.

The scale on a map is 2 cm=25 miles

This means that for each 2cm we measure on the map, the real distance is 25 miles.

Dave measured the distance to the next town at 5cm. Hoiw many miles away is the next town?

How many miles are 5 cm. So

2cm - 25 miles

5cm - x miles

[tex]2x = 25*5[/tex]

[tex]x = 62.5[/tex]

The next town is 62.5 miles away.

Answer:

The interest paid will be $9.946 ≈ $9.95.

Step-by-step explanation:

p = 1256.34

r = [tex]9.5/12/100=0.007917[/tex] (monthly)

Now, given is :

A late payment fee of $29.00 is added to the principal if you pay after 5/28. You make a payment for $200.00 on 5/28.

As the payment is made on the last date, so no extra charge will be paid. So, it is simple interest of [tex]1256.34\times0.007917=9.946[/tex]

Hence, the interest paid will be $9.946 ≈ $9.95.

1 cubic inch=16.39 cubic cm. 1 yard=36 inches. 36 x 2.11=75.96 cubic inches.

75.96 cubic in x 16.39 = 1244.9844 = 1.24 x 10³ cubic cm.

I believe this is correct

Answer:

1,613,219.190 cm^3

Step-by-step explanation:

There is 1 inch per every 2.53 cm, we just need to do the multiplication to the square:

[tex](\frac{2,11yards^3}{x})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})=\frac{764,558,8579cm^3*2,11yd^3}{1yd^3}\\x=1,613,219.190 cm^3[/tex]

SO now we know that 2,11 yards^3 are equal to 1,613,219.190 cm^3

Answer:

Its C. x2 + 12x + 4x + 48

on edg

3 one-pound bags;2 three-pound bags

Answer

Find out the  how many of each size bag did you buy .

To proof

Let us assume that the one-pound bags = x

Let us assume that the three-pound bags = y

As given

if you buy 5 bags

than the equation becomes

x +  y = 5

As given

a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50

if you buy 5 bags and spend $17

than the equation becomes

2x + 5.50y =  17  

2x + 5.50y = 17

than the two equation are

2x + 5.50y = 17 and x +  y = 5

mulitply  x +  y = 5 by 2 and subtracted from 2x + 5.50y = 17

2x - 2x + 5.50 y - 2y = 17 - 10

3.5y = 7

[tex]y = \frac{7}{3.5}[/tex]

y = 2

put y = 2 in  x +  y = 5

x = 5 -2

x = 3

Therefore  one-pound bags of peanuts bags are 3 and three-pound bags of peanuts bags are 2 .

Hence proved

Answer:

11.33%

Step-by-step explanation:

Amount of salt which Larry has to mix= 15 grams

In 210 gm of salt solution, content of salt= 5%

Amount of salt in salt solution= 5 % of 210 grams

Amount of salt in salt solution= [tex]\frac{5}{100}[/tex] of 210 grams

Amount of salt in salt solution= [tex]\frac{21}{2}[/tex]

Amount of salt in salt solution= 10.5 grams

Now the 15 grams of salt have to mix with 5% of salt solution

Total amount of salt= 15+ 10.5

Total amount of salt = 25.5 gram

Total amount of salt solution=15+ 210= 225 grams

Percentage of salt in new solution=[tex]\frac{amount of new salt}{ amount of new solution}[/tex] ×100

Percentage of salt in new solution=[tex]\frac{25.5}{ 225}[/tex] ×100

Percentage of salt in new solution= 0.13333×100

Percentage of salt in new solution= 11.33%  (approx)

Hence, the correct answer is 11.33%

To solve this problem, we have to make use of the z statistic. The formula for z score is:

z = (x – u) / s

where x is the sample value = 18,000 to 30,000, u is the sample mean = 30,000, and s is the standard deviation = 10,000

at x = 18,000

z = (18,000 – 30,000) / 10,000 = - 1.2

at x = 30,000

z = (30,000 – 30,000) / 10,000 = 0

So find for the P at values of z = -1,2 and z = 0.

P (z = - 1.2) = 0.1151

P (z = 0) = 0.5000

The proportion in between is the difference:

P (18,000 < x < 30,000) = 0.5000 – 0.1151 = 0.3849

So about 38.49% can be expected to travel 18,000 to 30,000 miles in a year

Using z-scores and the normal distribution, we can calculate that approximately 38.49% of trucks can be expected to travel between 18 and 30 thousand miles in a year.

This problem involves the normal distribution in mathematics, particularly statistics. Given that the distance travelled per truck per year is normally distributed, we can calculate the proportion of trucks that may be expected to travel between 18 and 30 thousand miles in a year using z-scores.

The first step is to calculate the z-scores for the two distances we are concerned with. The z-score is a measure of how many standard deviations an element is from the mean. Given a mean of 30 thousand miles and a standard deviation of 10 thousand miles, the z-score for 18 thousand miles is (18 - 30) / 10 = -1.2, and the z-score for 30 thousand miles is (30 - 30) / 10 = 0.

You then need to find the area between these two scores on a standard normal distribution table, which gives you the proportion of trucks likely to travel this distance. Looking up -1.2 and 0 in a standard normal table gives us values of 0.1151 and 0.5000 respectively. The difference between these two areas (0.5000 - 0.1151) is 0.3849, or 38.49% when expressed as a percentage. Thus, we can expect approximately 38.49% of trucks to travel between 18 and 30 thousand miles in a year.

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Ali's dog weighs 48 pounds.

We have,

Let's assume the weight of Ali's cat is represented by the variable "x".

According to the given information,

Ali's dog weighs 8 times as much as her cat.

Therefore, the weight of Ali's dog can be expressed as 8x.

We are also given that together the two pets weigh 54 pounds.

So we can set up an equation:

x + 8x = 54

Combining like terms:

9x = 54

To find the value of x, we divide both sides of the equation by 9:

9x/9 = 54/9

Simplifying:

x = 6

Therefore, Ali's cat weighs 6 pounds.

To find the weight of Ali's dog, we can substitute the value of x back into the expression for the weight of the dog:

Weight of the dog = 8x = 8 * 6 = 48 pounds

Thus,

Ali's dog weighs 48 pounds.

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Final answer:

Mr. Smith should deposit $119,631.97 now to have $500,000 in his bank account after 16 years, assuming a 10% annual compound interest rate.

Explanation:

To calculate how much Mr. Smith should deposit now to attain his retirement goal of $500,000 in 16 years with an annual compound interest rate of 10%, we use the formula for the present value of a future sum, which is:

PV = FV / (1 + r)^n

Where:

PV is the present value (the amount to deposit now)

FV is the future value (the desired amount in the account)

r is the annual interest rate (as a decimal)

n is the number of years

Plugging in Mr. Smith's values, we have:

PV = $500,000 / (1 + 0.10)^16

Calculating the denominator first:

(1 + 0.10)^16 = 1.10^16 = 4.1772

Now, divide the future value by this amount:

PV = $500,000 / 4.1772
= $119,631.97

Therefore, Mr. Smith should deposit $119,631.97 now to reach his goal of $500,000 in 16 years with a 10% annual compound interest rate.

Catholic Church felt threatened by the heliocentric theory of the Universe as Church as church felt that it will reduce its authority over the commons. Authority of the Church was at its highest peak during the era and these inventions were challenging its teaching and beliefs.

Further Explanations:

Chronicles of the Catholic Church began with Christ and his pedagogy, while its continuation of the Christian community was established by disciple of Jesus. It was considered that Bishops were successors to Jesus apostles and the Church leaders are its successor to Saint Peter. They even were practicing the power of regional assembly to resolve the doctrinal and policy issues.  

The theory of heliocentric was given by Galileo Galleli for which he was trialed and condemned by the Catholic Church in 1633. His discoveries were opposing the Church as it pronouncedheliocentrism to be precisely heretical. Books on Heliocentrism were banned and Gallelio was even forced to stop his teaching defending Heliocentric theories.

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Answer Details

Grade:High School

Subject:  History

Chapter:Catholic Church

Keywords:Catholic Church, Christ,  pedagogy, Christian community, Bishops, Saint Peter, Galileo Galleli, Catholic Church, Heliocentrism, doctrinal

Given

James and his friend earn $8 per hour.

James works 10/1-2 hours his first week.

And  James agreed to pay his friend 1/10 of his salary

10.5*8=84 1/10 or 10% of $84=$8.40.

primarily based on this, the common salaried individual works 2,080 (forty x fifty-two) hours every 12 months. To decide your hourly salary, divide your annual revenue by 2,080. in case you make $75,000 a year, your hourly wage is $ seventy-five,000/2080, or $36.06. if you work 37.5 hours a week, divide your annual earnings by way of 1,950 (37. five x fifty-two).

To calculate annual earnings, begin by using figuring out how many hours you figure in every week. in case you paint different hours every week, use the common number of hours you work. subsequent, multiply your hourly revenue with the aid of the range of hours you work per week. eventually, multiply that wide variety via 52 to find your annual earnings.

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