A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?

Answers

Answer 1

Answer:

3181 yards.

Step-by-step explanation:

All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin V / v = sin G / g.

It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:

sin 100 / 4510 = sin 44 / x.

Cross multiplying gives:

x*sin 100 = 4510*sin 44

Making x the subject gives:

x = (4510*sin 44)/sin 100.

x = 3181 yards (to the nearest yard).

Therefore, Norman and Voyager are 3181 yards apart from each other!!!

Answer 2

The required distance between the Norman and the Voyager is 3181 yards.

Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.

What are trigonometric equations?

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°

sin(100) / 4510 = sin(44) / x.

x = 3181.12

x ≈ 3181 yards

Thus, the required distance between the Norman and the Voyager is 3181 yards.

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Related Questions

In a certain company, 74 employees were hired in the last 5 years. If
this represents 43% of the current number of employees, then how
many current employees does the company have?

- list the steps please & thank you!

Answers

You have to be able to take the written words and turn them into a workable equation. 74 employees is 43% of the current number, which you don't know. The word "is" means = , the 43% is written as .43, the word "of" means to multiply and the current number of employees, what you're looking for, is your unknown x. So translating those words into an equation looks like this:
74 = .43x. And dividing both sides by .43 you get that the current number of employees is 172.09, or just 172

Final answer:

To find the total number of employees in the company, set up and solve the equation, 0.43 * X = 74. Solving this provides approximately 172 employees

Explanation:

In order to answer this question, we need to use the concept of percentages. Here are the steps:

Since we know 74 employees represent 43% of all employees, we set up the equation: 0.43 * X = 74, where X is the total number of employees in the company. Solving the equation for X leads us to the answer. We divide both sides of the equation by 0.43, which gives us X = 74/0.43. Calculating the right side of the equation, we find X is approximately 172, so there are approximately 172 employees in the company.

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A sofa is on sale for 26% off. The sale price is $629 . What is the regular price?

Answers

100% - 26% = 74%

74% ..............$629
100% ..............?

629 x 100/74 = 850

answer
regular price is $850

The regular price is $850 hope this helped

The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test? Show your work. A. List the two equations B. Find each type of question

Answers

x is 2 pt questions
y is 4 pt questions
x+y=34
2x+4y=80
Multiply the top equation by -2 to use elimination technique
-2x-2y=-68
Then combine the two equations (x is cancelled out)
2y=12
y=6
If there are 6 four point questions, there must be 28 two point questions to get a total of 34 questions.

A pizza parlor sold 38 1/8 pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?

Answers

38*8 = 304

304 + 1 =305 slices were sold

8(38 1/8)

8(38)+8(1/8)

304+1

305 slices.

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. (remember, m is a factor of n if m divides n evenly.)

Answers

This is the following condition in order to get the specific output for this specific problem: if is_a_prime(n): is_prime = True Now all you have to do is write is_a_prime().

For the hard code for this problem:

if n == 2:
is_prime = True
elif n % 2 == 0:
is_prime = False
else:
is_prime = True
for m in range (3, int (n * 0.5) + 1, 2):
if n % m == 0:
is_prime = False
break.

To add, a high-level programming language that is widely used for general-purpose programming, created by Guido van Rossum and first released in 1991 is called Python.

Below is the solution of assign true to is_prime if n has no factors other than 1 and itself.

Further explanation

Python is an interpreted, high-level, general-purpose programming language. Python is created by Guido van Rossum and first released in 1991. Its design philosophy emphasizes code readability. Python is a more productive language than Java because it is an interpretive language which is accompanied by elegant syntax and it makes an excellent choice for scripting and rapid application development in many areas. Python is a general-purpose, versatile and popular because it is concise and easy to read, and it is also a good language to have in any programmer’s stack as it can be used for everything such as web development, software development, data science applications.

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. And remember, m is a factor of n if m divides n evenly. So:

if n == 2:

is_prime = True

elif n % 2 == 0:

is_prime = False

else:

is_prime = True

for m in range (3, int(n**0.5)+1, 2):

if n % m == 0:

is_prime = False

Learn moreLearn more about python https://brainly.com/question/4331067Learn more about python IDLE or similar environment https://brainly.com/question/6280029Learn more about python function https://brainly.com/question/9806744

Answer details

Grade: 9

Subject: mathematics

Chapter: python

Keywords: python, integer, factors, python IDLE, is_prime

Three times a number added to seven is 22

Answers

3x+7=22

3x=15

x=5

the number is 5

Breanna works in the mall and her hours increase during busy shopping times of the year. Breanna has a plan to save $25 each week for 5 weeks, and then increase that amount by $20 for the next 7 weeks during the busy time, then go back to $25 per week. If Breanna’s plan is to save $540, how many weeks total will she need to save?
a.
11 weeks
b.
16 weeks
c.
22 weeks
d.
23 weeks

Answers

The math I used is probably not the quickest way, but for me, the easiest.
25*5=125 25+20=45 45*7=315 125+315=440 25*4=100 440+100=540 5+7+4=16
B is your answer.

Answer:

Number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

Step-by-step explanation:

As given

Breanna works in the mall and her hours increase during busy shopping times of the year.

Breanna has a plan to save $25 each week for 5 weeks.

Thus

Breanna saves in first 5 weeks = Amount saves per weeks in next 5 weeks × Number of weeks .

= $25 × 5

= $ 125

Increase that amount by $20 for the next 7 weeks during the busy time.

Thus

Amount saves per weeks for next 7 weeks = Amount saves per weeks in first 5 weeks + Increase in amount .

= $25 +$ 20

= $ 45

Breanna saves in next 7 weeks = Amount saves per week× Number of weeks .

Put all the values in the above

= $45 × 7

= $ 315

As given

Breanna saves $25 per week.

If Breanna’s plan is to save $540 .

Let us assume last weeks in which Breanna saves $25 per weeks be x .

Breanna saves in last x weeks = Amount saves for next x weeks × Number of weeks .

= 25 × x

= 25x

Equation becomes

Breanna saves in first 5 weeks + Breanna saves in next 7 weeks + Breanna saves in last x weeks = Total saving amount .

125 + 315 + 25x = 540

440 + 25x = 540

25x = 540 - 440

25x = 100

[tex]x = \frac{100}{25}[/tex]

x = 4 weeks

Thus

Total number of weeks Breanna saves = 5 weeks + 7 weeks + 4 weeks

= 16 weeks

Therefore the number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

One weekend, a newsstand sold twice as many Sunday papers as Friday papers. The Sunday paper costs $1.50, and the Friday paper costs $0.75. How many Sunday papers were sold if the newsstand took in $116.25?

Answers

1.50s + 0.75f = 116.25
2f = s

1.50(2f) + 0.75f = 116.25
3f + 0.75f = 116.25
3.75f = 116.25
f = 116.25/3.75
f = 31...31 friday papers

2f = s
2(31) = s
62 = s <=== 62 sunday papers

Answer:

Step-by-step explanation:

John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.

Answers

Let a_0 = 100, the first payment. Every subsequent payment is the prior payment, times 1.1. In order to represent that, let a_n be the term in question. The term before it is a_n-1. So a_n = 1.1 * a_n-1. This means that a_19 = 1.1*a_18, a_18 = 1.1*a_17, etc. To find the sum of your first 20 payments, this sum is equal to a_0+a_1+a_2+...+a_19. a_1 = 1.1*a_0, so a_2 = 1.1*(1.1*a_0) = (1.1)^2 * a_0, a_3 = 1.1*a_2 = (1.1)^3*a_3, and so on. So the sum can be reduced to S = a_0 * (1+ 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) which is approximately $5727.50

Question help a robotic rover on mars finds a spherical rock with a diameter of 1313 centimeters. the rover picks up the rock and lifts it 1515 centimeters straight up. the rock has a specific gravity of 5.255.25. the gravitational acceleration on mars is 3.73.7 meters per second squared. if the robot's lifting arm has an efficiency of 3535% and required 1212 seconds to raise the rock 1515 centimeters, how much power (in watts) did the arm use?

Answers

Due to apparent doubling of numbers in the question, assume
diameter=13 cm/2=0.065m
h=15 cm=0.15m
rho=5.25*1000=5250 kg/m^3
eta=35%=0.35 [efficiency]
t=12 s
g=3.7 m/s^2

mass, m=rho*V=rho*(4pi/3)(r^3)
=5250 kg/m^3 * (4pi/3)(0.065)^3 m^3
=1.922 kg

Work done in lifting h=0.15m
W=mgh
=1.922pi kg * 3.7 m/s^2 * 0.15 m
=1.067pi kg (m/s)^2
=1.067pi J

Average power required, with efficiency eta=0.35
P=(W/t)/eta
=(1.067pi J )/ (12 s) /0.35
=0.254pi J/s
=0.798W (approx.)

What are the X intercepts of a parabola with vertex (6,27) and y intercept of (0,-81)?

Answers

so hmm let's see if we can get the parabola's equation

if we assume a vertical parabola, "y" in x-terms.... then

[tex]\bf \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{we know that } \begin{cases} h=6\\ k=27 \end{cases}\implies y=a(x-6)^2+27 \\\\\\ \textit{we also know the y-intercept } \begin{cases} x=-81\\ y=0 \end{cases}\implies 0=a(-81-6)^2+27 \\\\\\ -27=a(-87)^2\implies \cfrac{-27}{(-87)^2}=a\implies -\cfrac{3}{841}=a\\\\ -------------------------------\\\\ \boxed{y=-\cfrac{3}{841}(x-6)^2+27}[/tex]

now, to get the x-intercepts, we simply set y = 0

[tex]\bf 0=-\cfrac{3}{841}(x-6)^2+27\implies -27=-\cfrac{3}{841}(x-6)^2 \\\\\\ \cfrac{-27\cdot 841}{-3}=(x-6)^2\implies 7569=(x-6)^2\implies \pm\sqrt{7569}=x-6 \\\\\\ \pm 87=x-6\implies \pm 87+6=x\implies x= \begin{cases} 93\\ -81 \end{cases}[/tex]

and... since the y = 0, then (93, 0) and (-81, 0)

Find the value of x
A 41
B 44
C 46
D 36

Answers

This time it's cosine.

Cosine is the adjacent/hypotenuse. In this case, the adjacent is 15 and hypotenuse is 21.

15/21, or like 5/7.

Now put that into a fancy calculator with the [tex]cos^{-1} [/tex] thing or something like that and then you have the answer, or around 44 degrees.

simplify the expression by using a double angle formula

cos^2 4theta-sin^2 4theta

Answers

Double angle formula for cos(2x) is
cos(2x)=cos^2(x)-sin^2(x)

Substitute x=4theta, then
cos(8theta)=cos^2(4theta)-sin^2(4theta)
=>
cos^2(4theta)-sin^2(4theta) = cos(8theta)

What is the solution to the equation 0.8m − 4 = −0.8m?

Answers

m= 2.5 that's the solution for m for them to be equal

0.8m − 4 = −0.8m
0.8m + 0.8m = 4
1.6m = 4
m = 4 /1.6
m = 2.5

It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

Answers

Final answer:

To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, approximately 187 samples are needed.

Explanation:

To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, we need to determine the required sample size. In this case, we can use the formula for sample size determination, which is:

n = (Z^2 * σ^2) / E^2

Where:

n is the required sample sizeZ is the Z-score associated with the desired confidence level (99% corresponds to a Z-score of approximately 2.58)σ^2 is the variance of the GPAs (given as 1.44)E is the desired margin of error (0.25)

Plugging in the values, we get:

n = (2.58^2 * 1.44) / 0.25^2

n ≈ 186.43

Therefore, we need a sample size of approximately 187 to estimate the mean GPA within a margin of error of 0.25 at a 99% confidence level.

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D=6.3cm what is the circumference and area of the circle

Answers

Circumference = 2pir
=2×pi×1.6
=10.05

Area= pir^d
=pi × 6.3
=19.79

Describe the relationship between the similarity ratio of two triangles and the ratio of their areas.

Answers

[tex]\bf \textit{let's say the sides ratio is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{s_1}{s_2} \\\\\\ \textit{then the ratio of their areas is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{(s_1)^2}{(s_2)^2}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}[/tex]

Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 50 km/h. After six hours, the velocity of the car is 54 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equation obtained in Part A for the first seven hours? (5 points)

Answers

part A)

[tex]\bf \begin{array}{ccllll} hours(x)&velocity(y)\\ -----&-----\\ 2&50\\ 6&54 \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 50}})\quad % (c,d) &({{ 6}}\quad ,&{{ 54}}) \end{array}[/tex]

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{54-50}{6-2}\implies \cfrac{4}{4}\implies 1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-50=1(x-2)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-50=x-2\implies \boxed{y-x=48}\impliedby \begin{array}{llll} standard\\ form \end{array}[/tex]

part B)

well, to graph a LINEar equation, since it's just a LINE, you simply need two points to graph a line, and since we know that y - x = 48.... if you want to know what's "y" when x = 7? or 7 hours, well

y - (7) = 48
y = 48 + 7
y = 55

so.. that's the point for the 7th hour, 7, 55, and you can pick any other point above, and graph it away.

what is the area of a circle with a radius of 7 inches

Answers

Area formula is A=πr2
A=3.1416(radius)2 (radius is 7)
A=3.1416(49)
A=153.94
The area is 153.94 inches.
Hope that was helpful :)

Answer is provided in the image attached.

To make the two triangles below similar, what would the values of x and y have to be?

Answers

i dont really remember how to solve this since i done this some time ago the angles must be the same i would say d since 5 the bigger triangle is five times bigger

~ hope this helps ~

First, y and 40 degrees would have to be the same; thus, y = 40 degrees.

Second, form and solve the ratio (x/25) = (6/30). 30x=25(6)=150. Thus, x=5.

py+7=6y+q
what is the answer for this question (linear equations with unknown coefficients)?

Answers

Assuming your solving for y:
py+7=6y+q
-6y -7 -6y -7
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)

Answer:

The required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]py+7=6y+q[/tex]

We need to simplify the equation and convert it into a linear equation with unknown coefficients.

Subtract 6y from both sides.

[tex]py - 6y + 7 = q[/tex]

Subtract 7 from both sides.

[tex]py - 6y = q - 7[/tex]

Take y common from left side.

[tex]y(p-6) = q-7[/tex]

Divide both sides by p-6.

[tex]y =\frac{(q-7)}{(p-6)}[/tex]

Hence, the required equation is [tex]y =\frac{(q-7)}{(p-6)}[/tex].

solve for y 6y-8=3y-2

Answers

6y-8 =3y-2

subtract 3y from both sides

3y-8 = -2

add 8 to both sides

3y=6

y=6/3 =2

y = 2

If 5 workers can pave 10 driveways in 30 days, how many days would it take 20 workers to pave 38 driveways?

Answers

Given that 5 workers can pave 10 driveways in 30 days, then:
let x be the number of days that can take 20 workers to complete 38 drive ways;
therefore:
proportion of work completed by 5 workers will be:
5*30/10
=15
proportion of work completed by 20 workers will be:
20*x/38
The time taken for 20 workers to complete 38 driveways will be:
15=20/38x
x=15*38/20
x=28 1/2
The answer is 28.5 days

help find the answer to this question

Answers

First, find the area of the entire traingle using the formula bh/2.
18*9/2=81 cm^2
Then subtract the area of the smaller triangle within the larger one (white triangle). It has the same base but a height of only 4.
18*4/2=36 cm^2
81-36=45
Final answer: 45 cm^2

Suppose that an individual has a body fat percentage of 17.9% and weighs 132 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.

Answers

f=132(17.9/100)

f=2362.8/100

f=23.628

f≈23.6 pounds (to nearest tenth of a pound)

Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018? a. 70% b. -27% c. -17% d. -75%

Answers

Using linear function concepts, it is found that the industry’s percent change from 2008 to 2018 will be of:

b. -27%

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.

In this problem:

The industry had 63.1 thousand jobs in 2008, hence b = 63.1.This number is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018, hence m = -1.7.

Thus, the function is:

y = -1.7x + 63.1.

In 2018, which is 10 years after 2008, the value of the function is:

y(10) = -1.7(10) + 63.1 = 46.1.

The percent change is given by the change divided by the initial value, hence:

(46.1 - 63.1)/63.1 = -27%

Hence option b is correct.

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The correct answer is b. -27%.

To solve this problem, we need to find the number of jobs in 2018 and then calculate the percent change from 2008 to 2018.

Given information:

- Number of jobs in 2008: 63.1 thousand

- Average annual rate of decline: 1.7 thousand jobs per year

- Time period: 2008 to 2018 (10 years)

Step 1: Find the total decline in jobs from 2008 to 2018.

Total decline in jobs = Average annual rate of decline × Number of years

Total decline in jobs = 1.7 thousand × 10 years = 17 thousand jobs

Step 2: Find the number of jobs in 2018.

Number of jobs in 2018 = Number of jobs in 2008 - Total decline in jobs

Number of jobs in 2018 = 63.1 thousand - 17 thousand = 46.1 thousand jobs

Step 3: Calculate the percent change from 2008 to 2018.

Percent change = (Change in value / Original value) × 100%

Percent change = ((46.1 - 63.1) / 63.1) × 100%

Percent change = (-17 / 63.1) × 100%

Percent change ≈ -27%

Therefore, the industry's percent change from 2008 to 2018 is approximately -27%.

Number of jobs in 2018 = [tex]46.1\text{ thousand} \\[/tex]

Percent change from 2008 to 2018 = [tex]-27\%[/tex]

Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. How many spare tires of this same variety must carried so that a trip of 15,000 miles can just be completed.

Answers

3 spare tires are needed. This works if you rotate the tires every 5,000 miles.

Tire A, B, C, D (and spare is E F G)
first 5,000 miles you use tire A B C D
second 5000 miles you use tire B C D E
third 5000 miles you use A E F G

Each tires is used no more than twice (10,000 miles).

today there are 3,659 thousand elementary and secondary teachers employed in a certain country. this number is expected to increase to 3,856 thousand by next decade. what is the percent increase?

Answers

percent increase = (new number - original number) / original number...* 100
= (3856 - 3659) / 3659...* 100
= 197 / 3659....* 100
= 0.0538 * 100
= 5.38% <==

Help Please question in the file.

Answers

check the picture below.

palace help me solve these two equations 14, 15

Answers

14)

check the picture below... so.. is just a semi-circle and a rectangle, nothing fancy, get their area, sum them up.

15)

so... the voter turnout, is referring to, what's the percentage that voted, which year has the highest percentage... well, we simply check the percentage of the value provided from the total eligible voters, keeping in mind that, all eligible voters are the 100%

so.. for 1944

[tex]\bf \begin{array}{ccllll} amount&\%\\ ------&----\\ 86,607,000&100\\ 47,976,670&x\\ \end{array}\implies \cfrac{86,607,000}{47,976,670}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 47,976,670}{86,607,000}\implies x\approx 55.39583405498[/tex]

for 1984

[tex]\bf \begin{array}{ccllll} amount&\%\\ -----&-----\\ 167,727,000&100\\ 92,659,000&x \end{array}\implies \cfrac{167,727,000}{92,659,000}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 92,659,000}{167,727,000}\implies x\approx 55.2439380660239[/tex]

Other Questions

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