Answers
Answer:
See below.
Step-by-step explanation:
1)
For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:
[tex]f(x)=2(3)^x[/tex]
The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.
2)
Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:
[tex]f(x)=10(2)^x[/tex]
The 10 represents the initial amount while the 2 represents the rate.
3)
I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.
4)
To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:
For Amber:
Day 3:
[tex]f(3)=3(4)^3=192[/tex]
Day 10:
[tex]f(10)=3(4)^{10}=3,145,728[/tex]
For Ben:
Day 3:
[tex]f(3)=2(3)^3=54[/tex]
Day 10:
[tex]f(10)=2(3)^{10}=118,098[/tex]
And for Carter:
Day 3:
[tex]f(3)=10(2)^3=80[/tex]
Day 10:
[tex]f(10)=10(2)^{10}=10,240[/tex]
5)
Amber's new graph of:
[tex]f(x)=3(4)^x+45[/tex]
will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.
6)
On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.
7)
If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.
Answer:
Here is the slope:
[tex]y = zy + dsince m = 0c = 9[/tex]
Hope this helps
Related Questions
zoey inflates 24 balloons for decorations at the middle school dance. if zoey inflated 15% of the total number of balloons for the dance, how many balloons are there total?
Answers
Answer:
160 balloons
Step-by-step explanation:
Step 1: State what is known
She blew up 24 balloons
She only inflated 15%
We want to find the total amount of balloons
Let the total balloons equal "x"
Step 2: Write you equation
[tex]0.15x=24\\\frac{0.15x}{0.15} =\frac{24}{0.15} \\x = 160[/tex]
Therefore there are 160 balloons in total
the perimeter of a square ground is 128m
find it's area
Answers
Answer:
The answer is
1024 m²Step-by-step explanation:
Perimeter of a square = 4l
Area of a square = l²
where
l is the the length of one side
To find the area we must first find the length of the square using the perimeter
Perimeter = 128m
Substitute the value into the formula for finding the perimeter and find the length
That's
[tex]128 = 4l[/tex]
Divide both sides by 4
length = 32 m
So the area of the square is
A = 32²
We have the final answer as
Area = 1024 m²Hope this helps you
consider 8x^2-48x=-104 factor the trinomial and simplify
(x+_)^2=_
Answers
Answer:
[tex](x-3-2i)(x-3+2i)[/tex]
Steps:
[tex]8x^2-48x=-104[/tex]
[tex]8x^2-48x+104=0[/tex]
Divide both sides by 8
[tex]x^2-6x+13=0[/tex]
But we can't factor it.
Using the Quadratic Formula to calculate the roots:
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$x=\frac{-(-48)\pm \sqrt{(-48)^2-4\cdot 8\cdot 104}}{2\cdot 8}$[/tex]
[tex]$x=\frac{48\pm32i}{16}$[/tex]
[tex]x_1=3+2i\\x_2=3-2i[/tex]
The answer might be
[tex](x-(3+2i))(x-(3-2i))[/tex]
[tex](x-3-2i)(x-3+2i)[/tex]
On three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to
achieve an average score of 95%?
A.94%
B.97%
C.96%
D.95%
Answers
Answer:
B
Step-by-step explanation:
To achieve an average of 95% on 4 tests, the sum of the scores Olivia gets must be 95 * 4 = 380. Right now, the sum of her scores is 89 + 98 + 96 = 283 so she must get at least a 380 - 283 = 97% on her last test.
Katie walks 2 ft forward and 5 ft backwards. Find her displacement traveled.
Answers
Step-by-step explanation:
It is given that, Katie walks 2 ft forward and 5 ft backwards. We need to find her displacement traveled.
The difference between final position and the initial position is equal to displacement. It is the shorted path covered.
Let forward is +x and backward is -x
Initial position of Katie = +2 ft
Final position of Katie = -5 ft
Displacement = final position - initial position
= -5 - 2
Displacement = -7 ft
So, her displacement is 7 feet in backward direction.
The first four numbers hexa said were 16 32 48 and 64 if she keep counting this way what is the 99th Number hexa will say
Answers
Answer:
316,912,650,057,057,350,374,175,801,344
Step-by-step explanation:
You can see that this sequence is geometric so you need to know the geometric sequence which is [tex]x_{n} =r^{n-1}[/tex] and if you plug in every thing you get [tex]x_{n}[/tex]=[tex]2^{99-1}[/tex] which would be [tex]2^{98}[/tex] which is 316,912,650,057,057,350,374,175,801,344
* Required
Farmer Joe separates his apple tree farm into 10 regions. He counts the number
of apples produced in two of the regions and uses that estimate to predict the
number of apples produced on the whole farm. This is sampling. *
simple
stratified
cluster
systematic
Answers
Systematic
Got it right on test
The information depicted is an example of cluster sampling.
From the information given, Farmer Joe separates his apple tree farm into 10 regions and then counts the number of apples that are produced in two of the regions and uses that estimate to predict the number of apples produced on the whole farm, this illustrates cluster sampling.
Cluster sampling is when researchers divide a population into smaller groups that are called clusters and then randomly select from the population.
Read related link on:
https://brainly.com/question/17255201
Does anyone know this?
Answers
Answer:
The answer is "c"
Step-by-step explanation:
What is the approximate value of sin C?
Please help! Urgent
Answers
Answer:
B. 0.36
Step-by-step explanation:
Given:
Right ∆ABC,
AB = 5
BC = 13.93
CA = 13
Required:
Value of sin C
SOLUTION:
[tex] sin(C) = \frac{opposite}{hypotenuse} [/tex]
Opposite = 5
Hypotenuse = 13.93
[tex] sin(C) = \frac{5}{13.93} [/tex]
[tex] sin(C) = 0.3589 [/tex]
[tex] sin(C) = 0.36 [/tex]
the answer would be B, 0.36
Elaine has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 in wide 12 in long and 5 cm deep. ( 1 gallon=231 in^3, 1 inch=2.54cm)
Answers
Answer:
b. The paint will not fill the tray by 5.22 in3.
Step-by-step explanation:
The computation is shown below:
First we have to determine the volume of tray by using the following equation
[tex]V = L \times W \times H[/tex]
Now transform this from dimensions to inches
Now putting the values,
[tex]V = 10\times12\times (5\times(\frac{1}{2.54})) \\\\As\ 5 cm = 5 \times (\frac{1}{2.54})[/tex]
the volume would be equivalent to the
236.22 inches^3
Now 1 gallon is 231 inches^3
So, the remaining would be
= 236.22 - 231
= 5.22^3
Therefore the correct option is b.
Hence, all the other options are wrong
56. In a specific region of the country, the amount of a customer's water bill, W, is directly proportional to the
average daily temperature for the month, T, the lawn area, A, and the square root of F, where Fis the family size,
and inversely proportional to the number of inches of rain, R. In dne month, the average daily temperature is
78°F and the number of inches of rain is 5.6. If the average family of four who has a thousand square feet of laws pays $72.00 for water for that month, estimate the water bill in the same month for the average family of six who
has 1500 ft of lawn.
Formula=
Solve for k
Solve for w
Answer=
Answers
Answer:
Approximately
W=132.29
Step-by-step explanation:
W=k(TA√F)/R
T=78°F
R=5.6 inches
F=4
A=1000 square feet
W=$72
Solve for k
W=k(TA√F)/R
72=k(78*1000*√4)/5.6
72=k(78,000*2) / 5.6
72=k(156,000) / 5.6
72*5.6 =156,000k
403.2=156,000k
k=403.2/156,000
=0.002585
Solve for w when F=6, A=1500, T= 78, R=5.6 inches
W=k(TA√F)/R
W=0.002585(78*1500*√6) / 5.6
=0.002585(78*1500*2.4495) / 5.6
=0.002585(286,591.5) /5.6
=740.8390 / 5.6
=132.2927
W=132.2927
Approximately 132.29
The length of a rectangle is 3 inches greater than the width.
A. Write a polynomial that represents the area of the rectangle.
B. Find the area of the rectangle when the width is 4 inches.
Answers
Answer:
A - x (x+3) = Area of the rectangle
B- 28 inches squared
Step-by-step explanation:
B- using the formula from A
x = 4
x + 3 = 4 +3 = 7
4 times 7 is 28
Answer: 28ins²
Step-by-step explanation:
From the question, let the width of the rectangle = xins.
Therefore, the breadth = ( x + 3 )ins.
(A) The area of the rectangle which is L x B = x( x+ 3 )
= (x² + 3x)ins² . In polynomial.
(B) The area of the rectangle if the width is 4ins, that is if x = 4ins.To find the area, we substitute for x in the area above
= 4² + 3 x 4
= 16 + 12
= 28ins²
A box contains 10 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below. a. All are defective b. None are defective Answers has to be a fraction
Answers
Answer:
1. 1/120
2. 7/24
Step-by-step explanation:
n = 10
Number of defective = 3
1. Probability of all defective =
(Number of defective/n) x (number of defective -1/n -1)...(number of defective -n/n-1)
=3/10 x 2/9 X 1/8
= 6/720
= 1/120
2. probability of none defective
Since 3 are defective, those that are not defective = 7
The probability is therefore:
7/10 x 6/9 x 5/8
= 210/720
= 7/24.
PLEASE HELP ASAP NEED NOW !!! For the given word problem, identify the rate of change.
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
(1 point)
a. $2.78
b. g
c. $18
d. 1
Answers
Answer:
6½ gallons
Step-by-step explanation:
Givem the cost of 1gallon of gas = $2.78. . If Cory buys $18 of gas, we are to find the number of gallons did he buy. To do that we will use the equality method as shown;
$2.78 ,= 1gallon
$18 = x gallon
Cross multiply
2.78 × x = 1×18
2.78x = 18
Divide through by 2.78
2.78x/2.78 = 18/2.78
.x = 6.5
Hence Cory buys about 6½ gallons of gas for $18
help me out here pleaseee
Answers
Answer:
Wednesday: 45 - 18
Thursday: 55 - 22
Step-by-step explanation:
18*2.5=45
55/5=11
11*2=22
Answer:
Trees Planted Unknown Value = 45
Trees Harvested Unknown Value = 22
Step-by-step explanation:
Plants : Harvest
= 5 : 2
= x : 18
= 5 * x : 2 * x
= 5 * x : 18 / 2
= 5 * x : 9
= 5 * x : x
= 5 * x : 2 * x
= 5 * 9 : 2 * 9
= 45 : 18
Trees planted value = 45
Plants : Harvest
= 5 : 2
= 55 : y
= 5 * y : 2 * y
= 55 / 5 : 2 * y
= 11 : 2 * y
= y : 2 * y
= 5 * y : 2 * y
= 5 * 11 : 2 * 11
= 55 : 22
Trees harvested value = 22
I really hope this helps! Tell me if I am incorrect!
A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if they were working together? Group of answer choices
Answers
Answer:
x=3 15/16 hours together
Step-by-step explanation:
the painter paints 1/7 of the house in 1 hour
the assistant paints 1/9 of the house in 1 hour
x=# of hours it takes them together to paint the house
(1/7)x+(1/9)x=1 (job finished)
multiply both sides by the LCM which is 63
63(1/7)x+63(1/9)x=63(1)
9x+7x=63
16x=63
x=63/16
x=3 15/16 hours together
Pritam. Sarah and Emily share some money in the ratios 3: 6:4
Sarah gets S15 more than Emily.
Work out the amount of money that Pritam gets.
Answers
Answer:
Pritam gets $22.50
Step-by-step explanation:
Ratios
Pritam =3
Sarah=6
Emily=4
The ratio between Sarah and Emily = 6:4
=3:2
If Sarah gets $15 more than Emily
Then,
Sarah gets $45
Emily gets $30.
The ratio between Pritam and Sarah = 3:6
= 1:2
Since Sarah gets $45,
Pritam gets half as much= $45 / 2
=$22.50
ASAPPP How do I explain what's the difference in the meaning of the "+1" in the following equations: f(x)=2x^2+5x+1. and g(x)=2(x+5)^2+1 ??????
Answers
Answer:
The +1 in f(x) is the y intercept
The +1 in g(x) is the y coordinate of the vertex
Step-by-step explanation:
For f(x), plugging in x = 0 leads to
f(x) = 2x^2+5x+1
f(0) = 2(0)^2+5(0)+1
f(0) = 1
Showing that (0,1) is the y intercept of f(x).
The same is not true for g(x)
g(x) = 2(x+5)^2+1
g(0) = 2(0+5)^2+1
g(0) = 51
-------------------------------
The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is
y = a(x-h)^2+k
with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.
Ms. Baker was measuring yarn for a project and
had 2.4 feet of red yarn. She needed this piece of
yarn cut into thirds. How long is each piece of yarn?
Answers
Answer:
2.4/3
8 Feet of yarn
This is because we're asking of one third of the original amount so we divide it by three.
Need help Giving 13 points
Answers
Answer:
Read Exp:
Step-by-step explanation:
1.) 4 is the Base and 8 is the Exponent.
2.) 9^4 = 9 x 9 x 9 x 9 = 6561.
3.) (-5)^2 = -5 x -5 = 25.
4.) 3^3 = 3 x 3 x 3 = 27.
5.) (1/2)^5 = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.03125
Have to change it to a simplified fraction:
* 1/32
Gwen says that the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4. Is Gwen correct? Explain why or why not.
Answers
Answer: No
Step-by-step explanation: no because one is negative 1 3/4 and the other one isint in the negatives
The sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 by cumulative property.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There are summations with an infinite set of parameters.
The summation is to add or subtract any two or more terms by doing that operation we will get a new result which could be big or small depending upon the number.
Cumulative property is the property summation states;
x + y will be equal to y + x ⇒ x +y = y + x
Now given,
The sum of -1 3/4 and 2 1/2 ⇒ -1 3/4 + 2 1/2
By cumulative property,
-1 3/4 + 2 1/2 = 2 1/2 + -1 3/4
The difference between 2 1/2 and 1 3/4 ⇒ 2 1/2 - 1 3/4
Hence "The sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 by cumulative property".
For more information about summation,
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A boat takes twice as long to travel 5 km upstream as it does travel 3km downstream in a river that flows at a rate of 2 kph. At what speed does the boat travel in still water?
Answers
Answer: 22 kph
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> [tex]\dfrac{5}{2(x-2)}=t[/tex]
Downstream equation: 3 = t(x + 2) --> [tex]\dfrac{3}{x+2}=t[/tex]
Set the equations equal to each other to solve for x:
[tex]\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x[/tex]
Step-by-step explanation:
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> \dfrac{5}{2(x-2)}=t
2(x−2)
5
=t
Downstream equation: 3 = t(x + 2) --> \dfrac{3}{x+2}=t
x+2
3
=t
Set the equations equal to each other to solve for x:
\begin{gathered}\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x\end{gathered}
2(x−2)
5
=
x+2
3
Cross multiply:
5(x+2)=3⋅2(x−2)
Distribute:
5x+10=6x−12
Isolate x:
10=x−12
22=x
What type of number is 8/2?
Answers
Answer:
Step-by-step explanation:
8/2
Numerator is bigger than denominator. So it is improper fraction and rational number
Rational numbers are any number that can be written in p/q form
Answer:
it should be improper fraction
Step-by-step explanation:
because the numerator is greater than the denominator.
Hope it helps :)
What are the solutions to the following equation? x²+8x+15=0
Answers
The value of x is = -5, -3
PLEASE HELP ME!! The deepest point of Lake Titicaca in South America is -922 feet relative to its surface. The deepest point is 11,542 feet above sea level. What is the elevation of this lake?
Answers
Answer:
12,464 ft
Step-by-step explanation:
I assume that the elevation of the lake is the altitude at the surface of the water.
The surface of the lake is 922 ft above the deepest point of the lake.
11,542 ft + 922 ft = 12,464 ft
if the sides of a square measure 10 square root 6 units then find the length of the diagonal
Answers
Answer:
Length of the diagonal = 20√3 units
Step-by-step explanation:
Given:
Side of square = 10√6 units
Find:
Length of the diagonal
Computation:
Using Pythagorean theorem.
Length of the diagonal = √2(a)²
Length of the diagonal = √2(10√6)²
Length of the diagonal = √1200
Length of the diagonal = 20√3 units
Which of the following is equal to 393,500? 3.935 × 10 -5 3.935 × 10 5 0.3935 × 10 -6 39.35 × 10 -4
Answers
Answer:
3.935 x 10^5.
Step-by-step explanation:
There are five digits after the first 3 so it will be 10^5.
The answer is 3.935 x 10^5.
393500 equals 3.935×10⁵
What is an exponent?If we write xⁿ then we mean to say that x is multiplied n times.
The exponent of a number says how many times the number is multiplied by itself.
How to calculate?393500=3.935×100,000=3.935×10⁵
Hence, 393500=3.935×10⁵
Learn more about exponents here- https://brainly.com/question/5497425?referrer=searchResults
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What type of number is -4pi
A) whole number
B) Integer
C) Rational
D) Irrational
Answers
Answer: D
Step-by-step explanation:
Irrational numbers cannot be expressed as a ratio of two integers.
Answer:
D only
Step-by-step explanation:
|-12-(-8)|= simply expression
Answers
Step by step:
First, get rid of the parenthesis.
| -12 + 8 |
Then, add up the two numbers.
| -4 |
The absolute value of -4 equals 4 because it makes number become positive. So, the answer is 4.
Hope this helps! Please tell me if I did anything wrong, thank you and have a great day!!
The time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. Find the time for each event.
Answers
Answer:
(a) the time for the event of the highest 5% is 15.29 minutes.
(b) the time for the event of the lowest 50% is 12 minutes.
(c) the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.
(d) the time for the event of the lowest 80% is 13.68 minutes.
Step-by-step explanation:
We are given that the time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes.
Let X = the time required to cook a pizza at a neighborhood pizza joint.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 12 minutes
[tex]\sigma[/tex] = standard deviation = 2 minutes
(a) We have to find the time for the event of the highest 5%, that means;
P(X > x) = 0.05 {where x is the required time}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-12}{2}[/tex] ) = 0.05
P(Z > [tex]\frac{x-12}{2}[/tex] ) = 0.05
Now, in the z table, the critical value of x that represents the top 5% of the area is given as 1.645, i.e;
[tex]\frac{x-12}{2}=1.645[/tex]
[tex]{x-12}=1.645\times 2[/tex]
x = 12 + 3.29 = 15.29 minutes.
Hence, the time for the event of the highest 5% is 15.29 minutes.
(b) We have to find the time for the event of the lowest 50%, that means;
P(X < x) = 0.50 {where x is the required time}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.50
P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.50
Now, in the z table, the critical value of x that represents the lowest 50% of the area is given as 0, i.e;
[tex]\frac{x-12}{2}=0[/tex]
[tex]{x-12}=0[/tex]
x = 12 + 0 = 12 minutes.
Hence, the time for the event of the lowest 50% is 12 minutes.
(c) We have to find the time for the event of the middle 95%, that means we have to find the time for the event of 2.5% and above 97.5%;
Firstly, the time for the event of the lowest 2.5%, i.e;
P(X < x) = 0.025 {where x is the required time}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.025
P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.025
Now, in the z table, the critical value of x that represents the lowest 2.5% of the area is given as -1.96, i.e;
[tex]\frac{x-12}{2}=-1.96[/tex]
[tex]{x-12}=-1.96 \times 2[/tex]
x = 12 - 3.92 = 8.08 minutes.
Firstly, the time for the event of the below 97.5%, i.e;
P(X < x) = 0.975 {where x is the required time}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.975
P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.975
Now, in the z table, the critical value of x that represents the top 2.5% of the area is given as 1.96, i.e;
[tex]\frac{x-12}{2}=1.96[/tex]
[tex]{x-12}=1.96 \times 2[/tex]
x = 12 + 3.92 = 15.92 minutes.
Hence, the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.
(d) We have to find the time for the event of the lowest 80%, that means;
P(X < x) = 0.80 {where x is the required time}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.80
P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.80
Now, in the z table, the critical value of x that represents the lowest 80% of the area is given as 0.8416, i.e;
[tex]\frac{x-12}{2}=0.8416[/tex]
[tex]{x-12}=0.8416 \times 2[/tex]
x = 12 + 1.68 = 13.68 minutes.
Hence, the time for the event of the lowest 80% is 13.68 minutes.