Answers
The function on the graph can't be a sin, then the correct option is:
y = A*cos(k*x) + C
Which equation matches the graph?
We know that the graph is either of the equation:
y = B*sin(k*x) - C
Or
y = A*cos(k*x) + C
Now, notice that there is a maximum at x = 0
And we also know that:
sin(0) = 0
cos(0) = 1
Then the option with the sin can be discarded, as it does not have a maximum at x = 0.
The correct option is:
y = A*cos(k*x) + C
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Related Questions
Complete the table representing a linear function.
Answers
Answer:
x y
1 0
2 10
5 40
10 90
Step-by-step explanation:
In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).
Therefore, when x is 2, y will be 10.
To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.
Answer:
Step-by-step explanation:
(1,0) (5,40)
Using these coordinates we find the line equation y=mx+b:
[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]
We substitute the value of coordinate (1,0) into equation (1):
[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]
Divide both parts of the equation by 10:
[tex]10=x\\\\Thus, (10,90)[/tex]
x | y
-----------------
1 | 0
------------------
2 | 10
------------------
5 | 40
------------------
10 | 90
Griffin wants to go hiking, but the weather is not cooperating. Right now, there is 2 inches of snow on the ground and snow is falling at a rate of 0.25 in/hr. (a) Write the linear equation that represents the represents the total amount of snow, y, after x amount of hours. (b) How much snow will be on the ground after 4 hours? You must use your equation above to solve, and you must show all of your work. (c) If Griffin does not want to be hiking when there is 6 inches of snow on the ground, how long does he have to complete his hike? Do you think he will finish his hike in time? You must use your equation above to solve, and you must show all of your work.
Answers
a) The linear function is:
y = 2 + 0.25x.
b) The amount of snow on the ground after 4 hours will be of 3 inches.
c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the unit rate of change of the output y by the input x.b is the y-intercept of the function, which is the numeric value of the output y when the input x assumes a value of zero.In this problem, the values of these coefficients are given as follows:
b = 2, which is the initial amount of snow on the ground.m = 0.25, which is the hourly rate of snow.Hence the equation is:
y = 2 + 0.25x.
After four hours, the amount of snow on the ground will be of:
y = 2 + 0.25(4) = 2 + 1 = 3 inches.
The time until the amount reaches 6 inches is of:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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Suppose you know that f(x) is an odd function on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5.
List ALL intervals on which the function f(x) is concave up and ALL intervals on which the function f(x) is concave down; explain how you know these to be correct
Answers
The intervals for the concavity of the odd function are given as follows:
Concave down: x < -5, -3 < x < 0, 3 < x < 5.Concave up: -5 < x < -3, 0 < x < 3, x > 5.What are even and odd functions?The definition of even and odd functions depends on the relation between f(x) and f(-x), as explained as follows:
In even functions, we have that the statement f(x) = f(-x) is true for all values of x.In odd functions, we have that the statement f(-x) = -f(x) is true for all values of x.If none of the above statements are true for all values of x, the function is neither even nor odd.In this problem, we have that the function is odd, hence the following statement is true:
f(-x) = -f(x) for all values of x.
This means that the concavity intervals are exchanged, hence:
f(x) is concave down on -3 < x < 0, as it is concave up of 0 < x < 3.f(x) is concave down on x < -5, as it concave up on x > 5. f(x) is concave up on -5 < x < -3, as it is concave down of 3 < x < 5.More can be learned about even and odd functions at https://brainly.com/question/13048723
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms. What is the percent of the decrease in the size of the sugar order?
somebody hwelp pwease
Answers
Answer:
40% decrease
Step-by-step explanation:
[tex]\frac{1090-654}{1090}[/tex] = .4 x 100 to make a percent equals 40%
Answer:There is no decrease from 2,820 kilograms to 2,820 kilograms.
The percent of decrease in the size of the sugar order is 0%.
Step-by-step explanation:
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
Answers
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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Stanley thinks of a positive number, n, which is less than 1. He adds this number to its reciprocal and gets 2.05. Work out the value of n. Give your answer as a fraction in its simplest form.
Answers
The value of n is given by either 4/5 or 16/25.
Given that the positive number is n which is n<1.
Reciprocal of the number is = 1/n
Addition of the number and the reciprocal is 2.05.
So the suitable equation for this,
n + 1/n = 2.05
[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]
So the number can be either 4/5 or 16/25.
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Help please! 15 points!!!!! give me an answer!!!!!
Billy has 15 apples he eats 3 ands sells 4 for $4 dollars each, How many apples are left. And what's Billy's total profit at the end of the day?
Answers
Answer:
Step-by-step explanation:
7*5
Answer:
he got 8 apples left and made a profit of 16
Step-by-step explanation:
The values of a and r in the series 3 + 12 + 48 + are
a. a = 3, r = 4 c. a = 3, r = –4
b. a = 4, r = 3 d. a = 4, r = –3
Answers
Option a is correct.
The first term, a is 3;
Common ratio, r = +4;
What is Geometric Series?
The total of a geometric sequence's finite or infinite terms is known as a geometric series. The analogous geometric series is a + ar + ar2 +..., arn-1 + for the geometric sequence a, ar, ar2,..., arn-1,... The word "series" is known to mean "sum." The geometric series specifically refers to the total of phrases with a common ratio between every pair of neighboring terms. Geometric series can be of two different types: finite and infinite.
In the given question, we have:
The series: 3 + 12 + 48 +
So, here the first term (a) = 3;
The second term = +12;
and, we know that the common ratio in the geometric series is the ratio of the second term and the first term.
So,
Common ratio, r = [tex]\frac{12}{3}[/tex]
r = 4;
so, The common ratio will be the same everywhere. So, It will be 4 in all the cases.
And, The first term, a is 3;
Hence,
Option a is correct.
The first term, a is 3;
Common ratio, r = +4;
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Need answers for these questions.
Answers
The future value of $8904.56 compounded semi annually is $13,468.95 The interest earned is approximately $4,564.39
The future value of $8904.56 compounded continuously is $66,185.90.
The interest earned is approximately $57,281.34.
What are the future values and the interests?When an investment is compounded semi annually, it means that both the amount that was invested and the interest that has already been earned increases in value twice in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = semi annual interest rate = annual interest rate / number of compounding = 6% / 2 = 3%m = number of compoundingN = number of yearsFV = 8904.56 x 1.03^(7 x 2) = $13,468.95
Interest = future value - amount invested
$13,468.95 - $8904.56 = $4,564.39
When an amount is compounded continusoly, it increases in value infinitely over the investment time horizon.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFV = 8904.56 x e^0.06 x 7 = $66,185.90
Interest = future value - amount invested
$66,185.90 - 8904.56 = $57,281.34
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20 points and brainliest <3 (added photo)
Answers
The measure of angles are
∠a = 48 degrees, it is an acute angle∠b = 140 degrees, it is an obtuse angle∠c = 324 degrees, its a reflex angleThe sum of angles around a point is equal to 360 degrees
The consider the angle a
The equation will be
∠a + 312 = 360 degrees
∠a = 360 - 312
∠a = 48 degree
The angle a is less than 90 degrees then it is an acute angles
Consider the angle b
∠b + 220 = 360
∠b = 360 -220
∠b = 140 degrees
Angle b is greater than 90 degrees and less than 180 degrees then it is an obtuse angle
Consider the angle c
∠c + 36 = 360
∠c = 360 - 36
∠c = 324 degrees
Angle c is grater than 180 degrees and less than 360 degrees then it is a reflex angle
Hence, the measure of angles are
∠a = 48 degrees, it is an acute angle∠b = 140 degrees, it is an obtuse angle∠c = 324 degrees, its a reflex angleLearn more about angles here
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If
a + 86 = 48,
what is
a − 86?
Answers
Answer:-48
Step-by-step explanation:
a + 85 = 48
first we need to find what a
86-48=a
a=38
now we calculate
a-86?
38 - 86 = -48
Answer:
a - 86 = -124
Step-by-step explanation:
a + 86 = 48
a = 48 - 86
a = -38
Then:
a - 86 = -38 - 86
= -124
Given: x-5> -10.
Choose the solution set.
Answers
The solution set. for the given inequality : x-5> -10. is (-5, ∞]
An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
We need to find the solution set for x-5> -10.
x - 5 > - 10
x > -10 + 5
x > -5
The solution set = (-5, ∞]
Therefore, the solution set. for the given inequality : x-5> -10. is (-5, ∞]
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Triangle EFG is similar to triangle HIJ. Find JH. Round your answer to
the nearest tenth if necessary. Figures are not drawn to scale.
Answers
The length of the side JH in the triangle ΔHIJ is 97.9.
We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.
Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".
IJ ∝ FG
IJ = k*FG
k = IJ/FG
k = 47/12
The side JH is proportional to the side GE.
JH = k*GE
x = (47/12)*25
x = 97.9
Hence, the length of the side JH is 97.9 units.
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I need help with this please help me
Answers
The measurement of angles ∠1 is 126° and ∠2 is 154°.
According to the question,
We have the following information:
We have a figure of two triangles and some of the measurements of the angles are given.
We know that the sum of three angles of a triangle is 180°.
So, for the larger triangle, we have the following expression:
96+30+third angle = 180
Third angle = 180-126
Third angle = 54°
We know that sum of angles on a straight line is 180°.
So, we have:
∠1+54 = 180
∠1 = 180-54
∠1 = 126°
Now, finding the sum of angles in smaller triangle:
126+28+third angle = 180
Third angle = 180-154
Third angle = 26°
Now, angle 2 and this angle will make a straight line.
∠2+26 = 180
∠2 = 180-26
∠2 = 154°
Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.
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At his most recent medical checkup, a boy was 40 inches tall. Currently, he is 46 inches tall. What percent taller is the boy now?
im not smart at this lol
Answers
Answer:
15%
Step-by-step explanation:
15%*40=46
Answer:
15%
Step-by-step explanation:
[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]
The boy was 40 inches tall so that means 40 inches is the old value
The boy is currently 46 inches tall now, so 46 is the new value
Plug these values into the equation:
[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]
Simplify:
[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]
[tex]Percent of change =\frac{600}{ 40} \\[/tex]
[tex]Percent of change =15[/tex]
I hope this answers your question :)
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (−4,1)
Answers
Answer:
[tex]y=-43x-173[/tex]
Step-by-step explanation:
[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]
In the figure, A.ABC is congruent to AADC t the square ABCD is dilated by a factor of 2 to form ABCD, what
ASCO to the area of ABCD?
A 2:1
B 3:1
c. 4:1
d 5:1
Answers
Answer:
C. Trust me on this one, it is an easy one.
In triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6°. Determine the measure of the exterior angle to ∠X.
25.65°
41.25°
82.45°
97.55°
Answers
The measure of the exterior angle to triangle X is D. 97.55°.
How to calculate the angle?It is important to note that the sum of the angles in a triangle is 180°.
In this case, triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6.
The exterior angle to X will be:
= Total angle - (43.85 + 38.6)
= 180 - 82.45
= 97.55°
In conclusion, the correct option is D.
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Answer:
I got the answer d when I took the test
Step-by-step explanation:
I hope this helps...
6 eggs in 7 months Remember to write your answer with the unit rate per something. Round to the hundredths place if necessary. PLS HELP
Answers
The unit rate which correctly corresponds to.the given rate; 6 eggs in 7 months is; 0.86 eggs per month.
What is a unit rate?A unit rate as the name implies is one in which case a given quantity is expressed in terms of one unit of the other quantity.
Such units are expressed as; a per b.
On this note, since the given rate is; 6 eggs in 7 months.
It follows that the rate can be expressed as;
6 eggs / 7 months
= 6/7 eggs per month.
= 0.85714 eggs per month.
And ultimately, when rounded to the nearest hundredth; we have; 0.86 eggs per month.
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19. Barney divides a rectangle into fourths.
Show two ways he could do this. That’s the space or something in the picture
Answers
Answer:
slice it in the middle in the top and bottom or do it corner to corner.
Step-by-step explanation:
1. have 2 braincells
2. put them toghether and think.
can you help me use compatible numbers to find two estimates of 478/12 i will give you 100000 points
Answers
Answer:
48
Step-by-step explanation:
The penguins at the zoo eat 2 5/8 pounds of fish each day. The zookeeper bought 5 1/4 pounds of fish. How many days will the fish last?
Answers
5 1/4 = 21/4 = 42/8
42 is double 21 so it will last 2 days
José is climbing a mountain. Using a rope, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. How far from the top of the cliff is he after 14 minutes?
Enter the correct answer in the box.
Please help this is due tomorrow
Answers
The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.
What is an elevation?An elevation simply means the height above sea level.
In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:
= 12.2 × 4
= 48.8 feet
He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:
= 3.6 × 10
= 36 feet.
Therefore, the change in elevation will be:
= Elevation up - Elevation down
= 36 - 48.8
= 12.8 feet.
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what is 2 1/2 + 1 1/8 + 1 1/4 - 1 1/2
Answers
Answer:
27/8 or 3.375 or 3 3/8
Step-by-step explanation:
if I make 11 dollars an hour and i worked 20 hours for 4 days, how much would I earn?
Answers
Answer: I think you would earn $8.35 per hour
Step-by-step explanation:
Answer: $880
Step-by-step explanation:
As I understand you are working 20 hours a day for 4 days.
[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880
Please help!
You are playing a game where you must spin a spinner that is numbered 1–8 on equal parts. What is the probability that you would get an odd number twice in a row?
25%
50%
12.5%
6.25%
Answers
The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%
Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
How to get the probability of the spinning?
From the analysis, the spinning is done twice from numbers 1-8
this means that in ever row, each number appears double.
The sample size is 8x8=64
1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8
2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8
3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8
4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8
5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8
6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8
7,1 7,2 7,3 7,4 7,5 7,6 7,7 , 7,8
8,1 8,2 8,3 ,,8,4 ,,, 8,5 ,,8,6 8,7,,, 8,8
The required outcome is 8
These outcomes are
1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8=8 outcomes
Probability of and event is
P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]
P(E)=[tex]\frac{8}{64}[/tex]
P(E)=[tex]\frac{1}{8}[/tex]
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Answer: 25%
Step-by-step explanation:
You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%
For questions 9-11, find the values of x and y if l || m.
Answers
The values of x and y using angle relationships are as follows:
x = 9, y = 13x = 22, y = 15x = 7, y = 24How to find angles in parallel line cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
Therefore, the angle relationship can be used to find the value of x and y in the diagram.
In the diagram, l and m are parallel lines and are cut by a transversal line.
Therefore,
10.
10x - 17 = 8x + 1(alternate exterior angles are congruent)
10x - 8x = 1 + 17
2x = 18
x = 18 / 2
x = 9
8x + 1 + 6y + 29 = 180(sum of angles on a straight line is 180 degrees)
72 + 1 + 29 + 6y = 180
102 + 6y = 180
6y = 180 - 102
6y = 78
y = 78 / 6
y = 13
11.
7x - 30 = 5x + 14(Corresponding angles)
Corresponding angles are congruent.
7x - 5x = 14 + 30
2x = 44
x = 44 / 2
x = 22
3y + 11 + 7x - 30 = 180(sum of angles on a straight line)
3y + 11 + 7(22) - 30 = 180
3y + 11 + 154 - 30 = 180
3y = 180 - 11 - 154 + 30
3y = 45
y = 45 / 3
y = 15
12.
7y - 23 = 23x - 16 (vertically opposite angles)
7y - 23x = 7
8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)
31x - 37 = 180
31x = 180 + 37
31x = 217
x = 217 / 31
x = 7
7y - 23(7) = 7
7y = 7 + 161
7y = 168
y = 168 / 7
y = 24
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Y is inversely proportional to the square of x. If Y = 5 when x = 3, then Y=1 4/5
, when x is.
Answers
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}[/tex]
Given (x – 7)2 = 36, select the values of x :x = 13 x = 1 x = –29 x = 42
Answers
The solution to the equation given as (x - 7)² = 36 are x = 1 and x = 13
How to determine the values of x?From the question, the equation is given as
(x - 7)² = 36
To start with, we take the square roots of both sides
This gives
x - 7 = ±6
Add 7 to both sides of the equation
So, we have
x = 7 ± 6
Evaluate the like terms
x = 1 and x = 13
Hence, the values of x are x = 1 and x = 13
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La duración de las llamadas telefónicas de larga distancia realizadas desde una central telefónica tiene distribución normal con media de 130 segundos y desviación estándar de 30 segundos. Si en un día cualquiera se realizaron 500 llamadas telefónicas desde esta central, ¿cuál es la probabilidad que la duración total de estas llamadas supere las 18 horas? Considere independencia en la duración de las llamadas.
El valor de la probabilidad es: ______ (escriba su respuesta con tres decimales)
Answers
The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:
0.618 = 61.8%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for n instances of a normal variable, the mean is of [tex]\mu n[/tex] and the standard deviation is of [tex]\sigma\sqrt{500}[/tex]Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:
[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]
Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:
3600 x 18 = 64800.
The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64800 - 65000)/670.82
Z = -0.3.
Z = -0.3 has a p-value of 0.382.
1 - 0.382 = 0.618 = 61.8% probability.
TranslationThe problem says that:
Telephone calls are normally distributed with mean of 130 seconds and standard deviation of 30 seconds.A sample of 500 calls is taken.The problem asks for the probability that the total duration of these calls is greater than 18 hours.Calls are independent.More can be learned about the normal distribution at https://brainly.com/question/25800303
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