Answer:
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
Step-by-step explanation:
a)The variable "weekly time spent watching television" is normally distributed and is skewed right.
b) Mean = x` 2.35 hours
Standard deviation = s/√n = 1.93/√40=1.93/6.3245553= 0.3051598
c) P(2<X<3) = P (2-2.35/ 0.3051598< Z< 3 -2.35/ 0.3051598)
= P ( -1.14694 < Z <2.13003)
= 0.3729 + 0.4830
=0.8559
So the probability is 0.8559
(0.8559 we check the value of 2.13 from the normal distribution tables and add with the value of 1.14 to get the in between value -1.14694 < Z <2.13003)
d) Here n = 35 , s= 1.93 , mean = 2.35 and x= 1.89
So Putting the values
P (X ≤ 1.89) = P (Z ≤ 1.89- 2.35/ 1.93 / √35)
= P ( Z ≤ -0.238341/ 5.9160797)
= P ( Z ≤ -0.04028)
= 0.5 - 0.0159
= 0.4841
Similarly again subtracting from 0.5 the value from normal distribution table to get less than or equal to value.
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
The mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes 0.4841 internet users watch less TV.
It is given that the amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials.
It is required to find the standard deviation and probability.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We know the formula for standard error:
[tex]\rm SE = \frac{s}{\sqrt{n} }[/tex]
Where 's' is the standard error
and n is the sample size.
In the question the value of s = 1.93 hours
and sample size n = 40
[tex]\rm SE = \frac{1.93}{\sqrt{40} }\\[/tex]
SE = 0.3051597
For the probability between 2 and 3 hours.
= P(2<X<3)
[tex]\\\rm =P(\frac{2-x)}{s} < Z < \frac{3-x)}{s})\\\\\rm = P(\frac{(2-2.35)}{0.3051598} < Z < \frac{(3-x)}{0.3051598})\\\\[/tex] (because the mean value x is 2.35)
=P(-1.14694 <Z < 2.13003)
=0.3729+ 0.4830 ( values get from Z table for -1.14 and 2.13 )
=0.8559
For P(X≤1.89)
[tex]\rm P(Z\leq \frac{(x'-x)}{\frac{s}{\sqrt[]{n} } } )\\\\\rm P(Z\leq \frac{(1.89-2.35)}{\frac{1.89}{\sqrt[]{35} } } )[/tex]
= P(Z ≤ -0.04028)
= 0.5 - 0.0159
=0.4841
Based on the result of 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5.
Thus, the mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes internet users watch less TV.
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Which plane figure generates a cylinder when it rotates about the dashed line?
Answer:
It is a rectangle
Solve fora - 26 = - 2w Simplify your answer as much as possible
Answer:
w = 13
if you have any questions just ask!
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 4
The area of a surface between a plane and a cylinder is evaluated using the integral [tex]\int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex]. So, the area of the given surface is [tex]\frac{4\pi}{3}\sqrt{14}[/tex]
Given that
[tex]x + 2y + 3z =1[/tex]
[tex]x^2 + y^2 = 4[/tex]
Make z the subject in [tex]x + 2y + 3z =1[/tex]
[tex]3z = 1 - x - 2y[/tex]
[tex]z = \frac{1}{3}(1 - x - 2y)[/tex]
The surface area is calculated using the formula:
[tex]Area = \int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex]
Where: [tex]dA = rdr \times d\theta[/tex]
[tex]z = \frac{1}{3}(1 - x - 2y)[/tex]
Calculate [tex]\frac{dz}{dx}[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(0 - 1 - 2 \times 0)[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(0 - 1 - 0)[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(- 1)[/tex]
[tex]\frac{dz}{dx}= -\frac{1}{3}[/tex]
Calculate [tex]\frac{dz}{dy}[/tex]
[tex]\frac{dz}{dy}= \frac{1}{3}(0 - 0 - 2 \times 1)[/tex]
[tex]\frac{dz}{dy}= \frac{1}{3}(- 2)[/tex]
[tex]\frac{dz}{dy}= -\frac{2}{3}[/tex]
Because the plane is inside [tex]x^2 + y^2 = 4[/tex], then the region of z is:
[tex]D = \{(r,\theta) | 0 \le r \le \sqrt{4}, 0 \le \theta \le 2\theta\}[/tex]
[tex]D = \{(r,\theta) | 0 \le r \le 2, 0 \le \theta \le 2\theta\}[/tex]
[tex]Area = \int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex] becomes
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{(\frac{-1}{3})^2 + (\frac{-2}{3})^2 + 1} } \, dA[/tex]
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{1}{9} + \frac{4}{9} + 1} } \, dA[/tex]
Take LCM
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{1+4+9}{9}} } \, dA[/tex]
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{14}{9}} } \, dA[/tex]
Evaluate the square root of 9
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\frac{\sqrt{14}}{3} } \, dA[/tex]
Remove the constant
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 \int\limits^{2}_0 { dA}[/tex]
Recall that: [tex]dA = rdr \times d\theta[/tex]
So, we have:
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 \int\limits^{2}_0 { rdr \times d\theta}[/tex]
Integrate
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{r^2}{2} |\limits^{2}_0 \ d\theta}[/tex]
Expand
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{2^2 - 0^2}{2} \ d\theta}[/tex]
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{4}{2} \ d\theta}[/tex]
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { 2 \ d\theta}[/tex]
Integrate
[tex]Area = \frac{\sqrt{14}}{3}[2\pi]|\limits^{2\pi}_0[/tex]
Expand
[tex]Area = \frac{\sqrt{14}}{3}[2 \times 2\pi - 0][/tex]
[tex]Area = \frac{\sqrt{14}}{3}[4\pi - 0][/tex]
[tex]Area = \frac{\sqrt{14}}{3}[4\pi][/tex]
[tex]Area = \frac{4\pi}{3}\sqrt{14}[/tex]
Hence, the area of the surface is: [tex]\frac{4\pi}{3}\sqrt{14}[/tex]
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An investment of $8,000 earns interest at an annual rate of 7% compounded continuously. Complete parts (A) and (B) below. Click the icon to view the derivatives of exponential and logarithmic functions.
(A) Find the instantaneous rate of change of the amount in the account after 2 year(s). $ (Round to two decimal places as needed).
(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000. $ (Round to two decimal places as needed).
Answer:
A. [tex]\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}[/tex]
B. [tex]\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }[/tex]
Step-by-step explanation:
Given that:
An investment of Amount = $8000
earns at an annual rate of interest = 7% = 0.07 compounded continuously
The objective is to :
A) Find the instantaneous rate of change of the amount in the account after 2 year(s).
we all know that:
[tex]A = Pe^{rt}[/tex]
where;
[tex]A = (8000) \ e ^{0.7t}[/tex]
The instantaneous rate of change = [tex]\dfrac{dA}{dt}[/tex]
[tex]\dfrac{dA}{dt} = \dfrac{d}{dt}(8000 \ e ^{0.07t} )[/tex]
[tex]= 8000 \dfrac{d}{dt}e^{0.07 \ t}[/tex]
[tex]\dfrac{dA}{dt}= 8000 (0.07)e^{0.07 \ t}[/tex]
[tex]\dfrac{dA}{dt}= 560 e^{0.07 \ t}[/tex]
At t = 2 years; the instantaneous rate of change is:
[tex]\dfrac{dA}{dt}|_{t=2}= 560 e^{0.07 \times 2}[/tex]
[tex]\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}[/tex]
(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000.
Here the amount = 12000
[tex]12000 = (8000)e^{0.07 \ t}[/tex]
[tex]\dfrac{12000 }{8000}= e^{0.07 \ t}[/tex]
[tex]1.5= e^{0.07 \ t}[/tex]
㏑(1.5) = 0.07 t
0.405465 = 0.07 t
t = 0.405465 /0.07
t = 5.79
[tex]\dfrac{dA}{dt}= 560 e^{0.07 \ t}[/tex]
At t = 5.79
[tex]\dfrac{dA}{dt}|_{t = 5.79}= 560 e^{0.07 \times 5.79}[/tex]
[tex]\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }[/tex]
The following is a list of 5 measurements. 19,30,20,10,17 Suppose that these 5 measurements are respectively labeled.
Answer:
For example, suppose we weigh five children. ... 5. ∑ i=1 xi. = x1 + x2 + x3 + x4 + x5. = 10 + 12 + 14 + 8 + 11. = 55. ... We also use sigma notation in the following way: 4 ... j2 = 12 + 22 + 32 + 42 = 30.
Missing: 17 | Must include: 17Summary measures for this data set are ... 17 18. 19 20. Observedresult. 0. 1. 0. 1. 1. 0. 1. 0. 1. 1. Total so far. 4. 5. 5. 6 ... 5. 10. 15. 20. 25. 30. 35. 40 . Toss. Figure S2.1 Proportion P, 40 tosses of a coin.
Series is defined as sum of sequences. The sum of the sequence given is 96
Sequence and seriesSeries is defined as sum of sequences
Given the sequence below
19,30,20,10,17
The given su notation denotes the sum of the first five terms of the sequence.
Take the sum
Sum = 19+30+20+10+17
Sum = 96
Hence the sum of the sequence given is 96
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Wich expression is equivalent?
Answer:
2.56p
Step-by-step explanation
Because the variable is the same for every input, and are all addition, you can just all them all together. You must remember p = 1p
Hope this helps!
-The Business Man
Answer:
2.26p
Step-by-step explanation:
0.7p + p + 0.56 p (The coefficient is 1)
0.7p + 1p + 0.56p (Collect the like terms)
(0.7 + 1 + 0.56)p
Calculate the sum
And this brings you to your answer: 2.26p
Find the area of the shaded figure.
Answer:
8500 ft²
Step-by-step explanation:
First we need to find the area of the non shaded region within this shaded region. To find the area of this non shaded rectangle, use the formula base×height.
20×100=2000 ft².
Now we need to find the height and width of the shaded region which is,
25+25+20=70 Height
25+25+100=150 Width
mutiply these numbers 150×70=10500 ft²
Now we just need to subtract that inside area.
10500-2000=8500 ft²
Ella purchase 350 pallets of flowers there are 152 flowers on each pallet how many flowers did Ella purchase?
Answer:
53,200
Step-by-step explanation:
350 pallets times 152 flowers each is 53,200 flowers in total
Please give brainliest thanks
Answer:
53,200
Step-by-step explanation:
I saw the other guys answer
A rectangular Persian carpet has a perimeter of 220 inches the length of the carpet is 22 inches more than the width what are the dimensions of the carpet
Answer:
length= 65 inches
width= 45 inches
Step-by-step explanation:
65 plus 65= 130
45 plus 45= 90
130 plus 90= 220 in.
ASAP what is 46x78+(56-43)247.Our teacher gave us random problems cuz we were horrible
Answer: 6,799
Step-by-step explanation:
A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $90,000. If it wins one of the races, it will be worth $55,000. If it loses both races, it will be worth only $15,000. The man believes there is a 30% chance that the horse will win the first race and a 40% chance that it will win the second one. Assuming that the two races are independent events, find the man's expected profit.
The expected profit of the man from the horse race is $22,400.
Given data:
To find the man's expected profit, calculate the probability of each outcome and multiply it by the corresponding profit.
To determine the probability of each outcome based on the given information:
Probability of winning both races = 0.30 * 0.40
Probability of winning both races = 0.12
Probability of winning one race = 0.30 * 0.60 + 0.70 * 0.40
Probability of winning one race = 0.46
Probability of losing both races = 0.70 * 0.60
Probability of losing both races = 0.42
Next, calculate the expected profit for each outcome:
Profit from winning both races = $90,000 - $20,000
Profit from winning both races = $70,000
Profit from winning one race = $55,000 - $20,000
Profit from winning one race = $35,000
Profit from losing both races = $15,000 - $20,000
Profit from losing both races = -$5,000 (a loss of $5,000)
Now, determine the man's expected profit by multiplying the probability of each outcome by the corresponding profit and summing them up:
Expected profit = (0.12 * $70,000) + (0.46 * $35,000) + (0.42 * -$5,000)
Expected profit = $8,400 + $16,100 - $2,100
Expected profit = $22,400
Hence, the man's expected profit is $22,400
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Between which two positive integers does ;33 lie?
A pitcher's arm rotates at a speed of
7
77 degrees per millisecond
(
degrees
ms
)
(
ms
degrees
)left parenthesis, start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, m, s, end text, end fraction, right parenthesis.
At what speed does the pitcher's arm rotate in
degrees
s
s
degrees
start fraction, start text, d, e, g, r, e, e, s, end text, divided by, start text, s, end text, end fraction?
Answer:
7000
Step-by-step explanation:
1000x7
Answer:
7000
Step-b7y-step explanation:
Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alpha = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are $61,000,000, $92,000,000, $48,000,000, and so onBudget(x) 61 92 48 36 135 58 93Gross(y) 69 62 53 58 627 144 42a. What are the null and alternative hypotheses?i) H_0: rho = 0, H_1: rho < 0ii) H_0: rho = 0, H_1: rho notequalto 0iii) H_0: rho notequalto 0, H_1: rho = 0iv) H_0: rho = 0, H_1: rho > 0b. Construct a scatterplot. Choose the correct graph below.c. The linear correlation coefficient r is.d. The test statistic t is.e. The P-value is.
Answer:
The answers are below
Step-by-step explanation:
1. H0: rho = 0
H1: rho not equal to 0
2. I will add the scatter plot as an attachment
3. ΣX = 523,
ΣY = 1055
ΣX² = 46023
ΣY²= 430407
ΣXY = 111448
n = 7
The correlation coefficient r =
r = 7(111448)-(523)(1055)/√7(46023)-(523)² × √7(430407)-(1055)²
r = 780136-551765/√322161-273529√3012849-1113025
= 228371/220.53*1378.34
= 228371/303965.32
r = 0.751
4. Test statistics
t = r√n-2/√1-r²
= 0.751√5/√0.5640
= 1.679/0.660
= 2.543
5. P value
Degrees of freedom n-2 = 5
T dist(2.543,5,2)
The p value is less than 0.05 so we reject null hypothesis. There is enough evidence to show a linear correlation between budgets and gross receipts.
Help me pleseeeeeee asappppp
Answer:
(-2.5, -10)
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Step 1: Plug in
x = (-2 + -3)/2
y = (-8 + -12)/2
Step 2: Evaluate
x = -5/2
y = -20/2 = -10
Step 3: Format into coordinates
(-5/2, -10)
Step 4: Convert to decimal
(-2.5, -10)
Point W has coordinates (4, -7). If it is reflected over the y-axis. What are the coordinates of its image? (4, -7) (-4, 7) (-4, -7) (4, -7)
Answer:
(-4, -7)
Step-by-step explanation:
reflection over the y-axis means the x-value becomes the opposite (+ → - or - → +)
(4, -7) → (-4, -7)
Answer:
(-4, -7)
Step-by-step explanation:
1mm66 converted in height inches
Answer:
0.065354330709 inch
Step-by-step explanation:
1 millimeter is equal to 0.03937007874 inches, so 1.66 mm is 0.065354330709 inches.
This comes from the definition 1 inch = 2.54 cm
so 1 inch = 25.4 mm. Divide by 25.4 and get:
0.03937007874 inch = 1 mm
What is 400,000 in scientific notation?
Answer:
Hello! I hope I am correct!
Step-by-step explanation:
Answer:
4x 10^5
Make it into decimal
Decimal form:4.00000
Now count the zeros in 4.00000
There is 5 zeros and 4 (4 is the first number)
Formula: Ax10^{B}
Answer: 4x10^{5}
That’s how you get your answer.
Hope this helps!
By: BrainlyAnime
A password contains three digits, such as 175. How many different passwords can be formed?
Answer:
157,517,715,751,571.Therefore,5 more passwords can be formed
Ivan is an artist. He creates 1 sculpture for every 5 paintings. If he has created 30 paintings, how many sculptures has he created?
Answer: Ivan has created 6 sculptures.
Step-by-step explanation:
If Ivan creates 1 sculpture for every 5 paintings and he makes 30 paintings.
30 divided by 5 =6
30 being the total
5 being how much for one
6, the answer, being for the total amount of sculptures.
Which expression is the exponential form of
Answer:
it would be the second one cause i picked it and it was right
Step-by-step explanation:
Sheryl purchased a plot of land for $32,500. The land appreciates about 4.9% each year. What is the value of the land after eleven years?
Appreciates means increases.
Appreciation formula:
Future value = starting value x (1 + interest rate) ^ time.
Future value = 32,500(1+0.049)^11
Value in 11 years = $55,006.46
What is two more than 4 times a number is -18 translated and solved
Answer:
n=-5
Step-by-step explanation:
Let "n" represent the unknown number.
So, the equation asks for 4n and two more, or +2, that is all equal to -18.
So, your equation will be:
[tex]4n+2=-18[/tex]
First, subtract 2 from both sides:
[tex]4n+2-2=-18-2\\4n=-20[/tex]
Then, divide both sides by 4:
[tex]\frac{4n}{4}=\frac{-20}{4}\\n=-5[/tex]
Therefore, n=-5.
-3(k-8)-(k+5)=23
please explain how to do this
You are buying a car whose price is $22,500. Which of the following options will you choose? Explain.
a. You are given a factory rebate of $2000, followed by a dealer discount of 10%.
b. You are given a dealer discount of 10%, followed by a factory rebate of $2000.
Let f(x) = x-2000 and let g(x) = .9x Which option is represented by the composite f(g(x))? Which option is represented by the composite g(f(x)) ?
Answer:
Option B
Step-by-step explanation:
Option A
1. $22500 - $2000 = $205002. $20500 - 10% = $20500*0.9 = $18450This is g(f(x)) since the first step is same f(x) and the second step is g(x)
Option B
1. $22500 - 10% = $22500*0.9 = $202502. $20250 - $2000 = $18250This is f(g(x)) since the first step is g(x) and the second one f(x)
This option is better as 10% discount is applied to full price and final price is less.
find the mean of 1.8, 1.7, 1.3, 1.1, 1.2, 1.6, 1.8,
Answer:
Sum: 10.5 Arithmetic mean (Simple Average):1.5 Median: 1.6 Range: 0.7 Variance: 0.09 Standard Deviation: 0.09 =0.29
The answer is 0.29
hope this helped
Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 14 based on earlier studies.
Answer: 67
Step-by-step explanation:
Formula to calculate sample size: [tex]n=(\dfrac{z^*\times s}{E})^2[/tex] , where s = standard deviation on prior studies , z* = two tailed critical value for confidence level , E = margin of error
Given: E = 4 , s= 14 and confidence level = 98%
Z-value for 98% confidence = 2.326
Then, required sample size: [tex]n=(\dfrac{2.326\times 14}{4})^2=(8.141)^2=66.275881\approx67[/tex]
Hence, the required sample size = 67 .
Sample size required to estimate the mean score on a standardized test is 67.
The confidence level (C) = 98% = 0.98
α = 1 - C = 0.02
α/2 = 0.02/2 = 0.01
The z score of α/2 is the same as the z score of 0.49 (0.50 - 0.01) which is equal to 2.33
Given that:
Standard deviation (σ) = 14, margin of error (E) = 4, n = sample size, hence:
[tex]E=z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\4=2.33*\frac{14}{\sqrt{n} } \\\\\sqrt{n}=8.155\\\\n=67[/tex]
Hence the sample size required to estimate the mean score on a standardized test is 67.
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Amy invested $300 in the bank and a year later has $343.70. By what percent has the amount changed?
44% increase
13% increase
15% increase
87% increase
Answer:
15
Step-by-step explanation:
i just know
Answer:
15
Step-by-step explanation:
just took the quiz
Graph the line with the slope -3/4 passing through the point (4,-1)
Answer:
Step-by-step explanation:
Plot the point (4, -1) in the 4th Quadrant.
The slope (-3/4) tells us what to do next:
With your pencil point initially on (4, -1), move it 4 units to the right, to (8, -1).
With your point initially on (8, -10, move it down 3 units, to (8, -4). Plot (darken) (8, -4).
Draw a line through (4, -1) AND (8, -4)
The equation of a line for the given slope and the coordinate point is 4y=-3x+8.
Given that, the line with the slope -3/4 passes through the point (4,-1).
We need to find the line of equations.
What is slope intercept form?The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis. Let us consider a straight line of slope 'm' and y-intercept 'b'. The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.
Now, substitute m=-3/4 and the point (4,-1) in y = mx + b and find the value of b.
That is, -1 = -3/4 (4)+b
⇒b=2
Then the equation becomes y=-3/4 x+2
⇒4y=-3x+8
Therefore, the equation of a line for the given slope and the coordinate point is 4y=-3x+8.
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4. Both the Galapagos Islands and the island of Naura are on the Equator, but the Galapagos Islands are at 90.30◦W whereas the island of
Nauru is at 166.56◦E. How far is it from the Galapagos Islands to
Nauru traveling over the Pacific ocean along the Equator, correct to
the nearest km ?
Answer:
Distance between Nauru and Galapagos islands = 11525 Km to the nearest Km
Step-by-step explanation:
The angle between the two Islands is given as X
X = (180 - 166.56) + (180 - 90.30)
X = 13.44° + 89.70°
X = 103.14
Distance between the islands = length of the arc with angle X subtended at the center of the earth of radius R.
Length of arc = (X/360) × 2πR
Where, R, radius of the earth = 6400 Km
Length of arc = (103.14/360) × 2π × 6400 Km
Length of arc = 11525.48 Km
Therefore, distance between Nauru and Galapagos islands = 11525 Km to the nearest Km