For every 4 songs on Mary's playlist, 3 of the songs are longer than 5 minutes.
Complete the table of values to compare the total money spent to tickets purchased.
Total Number of Songs on Playlist
Number of Songs Longer Than 5 Minutes
8
32
40
136
Answers
we were told that in every 4 songs on the playlist, 3 of the songs are longer than 5
so if in for 4 songs, 3 is longer than 5
for 8 songs,
we divide the the number of songs in the playlist by 4 in other to get the numbers of 4 in it then muliply by the number of songs longer than 5
for 8 songs on the playlist:
= 8/4 X 3
= 2 X 3
= 6
For 32 songs on the playlist
= 32/4 X 3
= 8 X 3
= 24
For 40 songs on the playlist
= 40/4 X 3
= 10 X 3
= 30
For 136 number of songs on the playlist
= 136/4 X 3
= 34 X 3
= 102
so in completing the table:
Total Number of Songs on the Playlis Number of songs longer than 5min.
8 6
32 24
40 30
136 102
Related Questions
Match the number with the correct description.
PLEASE HELP
Answers
Answer:
Answers on attached image
Step-by-step explanation:
Transformations that preserve shape and size are called rigid motions. Find a definition of just the word rigid using the internet and write it below.
Answers
Simply put,
Rigid means not moving.
In transformations, rigid motions are transformations that preserve distance.
Write equation for graph ?
Answers
The equation for parabolic graphed function is y = [tex]-3x^{2} -24x-45[/tex].
What is parabola graph?
Parabola graph depicts a U-shaped curve drawn for a quadratic function. In Mathematics, a parabola is one of the conic sections, which is formed by the intersection of a right circular cone by a plane surface. It is a symmetrical plane U-shaped curve. A parabola graph whose equation is in the form of f(x) = ax2+bx+c is the standard form of a parabola.
The given graph has 2 intercept at x axis x = -3, x = -5
y = a (x+3) (x+5)
using the intercept (-4, 3)
3 = a (-4 +3)(-4+5)
3 = a (-1)(1)
a =-3
y = -3(x+3)(x+5)
y = -3 [x(x+5) +3(x+5)]
y = [tex]-3x^{2}-24x-45[/tex]
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Solve the inequality
And how do I graph Graph the solution below:
Answers
Answer:
Step-by-step explanation:
to solve, divide both sides by -3/2 to isolate x
you'll get x>1.5
to graph, make a ray pointing right from 1.5 with an open dot
Please help i need the answers for a test and how to work em out for the future
Answers
Given: The angles as shown in the image
[tex]\begin{gathered} m\angle DEY=105^0 \\ m\angle DEF=27x+3 \\ m\angle YEF=6x+3 \end{gathered}[/tex]To Determine: The measure of angle DEF
Solution
It can be observed that
[tex]\begin{gathered} m\angle DEY+m\angle YEF=m\angle DEF \\ Therefore \end{gathered}[/tex][tex]\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=\frac{105}{21} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} m\angle DEF=21x+3 \\ =21(5)+3 \\ =105+3 \\ =108 \end{gathered}[/tex]Question 12
Given:
[tex]\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}[/tex]To Determine: The measure of angle HIU
Solution:
It can be observed that
[tex]m\angle UIJ+m\angle HIU=m\angle HIJ[/tex][tex]\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-\frac{14^0}{2} \\ x=-7^0 \end{gathered}[/tex]Therefore, the measure of angle HIU would be
[tex]\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}[/tex]Hence, the measure of angle HIU is 30⁰
Graph the reflection of the polygon in the given line
Answers
Let:
[tex]\begin{gathered} A=(-3,2) \\ B=(1,-1) \\ C=(-2,-2) \\ D=(-4,-1) \end{gathered}[/tex]After the reflection over y = -x:
[tex]\begin{gathered} A->(-y,-x)->A^{\prime}=(-2,3) \\ B->(-y,-x)->B^{\prime}=(1,-1) \\ C->(-y,-x)->C^{\prime}=(2,2) \\ D->(-y,-x)->D^{\prime}=(1,4) \end{gathered}[/tex]Find the maximum value:13, 18, 27, 12, 38, 41, 32, 15, 32
Answers
We can find the maximum value by creating a list of the provided numbers from the smallest to the largest.
[tex]12,13,15,18,27,32,32,38,41[/tex]As we see on the list, the last number and the largest is 41. Some tools are used to solve this kind of problem like the diagram of leaves and stems, a table os fre
Lulu the Lucky puts chests of gems into her treasure vault.
Each chest holds the same number of gems. The table
below shows the number of gems Lulu received from
three different adventures and the number of chests she
needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between
g, the number of gems, and c, the number of chests.
Answers
The equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
What are equations?A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, the equation representing the relation of 'g' and 'c':
We can observe that:
600/2 = 3001500/5 = 3004800/16 = 300So, we can conclude that:
g/c = 300300c = gTherefore, the equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
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Cost of a pen is two and half times the cost of a pencil. Express this situation as a
linear equation in two variables.
Answers
The equation to illustrate the cost of a pen is two and half times the cost of a pencil is C = 2.5p.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the cost of a pen is two and half times the cost of a pencil.
Let the pencil be represented as p.
Let the cost be represented as c.
The cost will be:
C = 2.5 × p
C = 2.5p
This illustrates the equation.
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When you purchase a T.V., the size refers to the diagonal measurement of the screen. If
the 46 inch TV has a square screen, what is the approximate length and width? Round
your answer to the nearest tenth.
Answers
TV Dimensions (Diagonal) Screen Width
46 inch TV 40.1 inches + Bezel
A TV's screen size is determined by measuring the panel diagonally from one corner to the other. The TV's bezels and other exterior surfaces are not included in this. There are numerous models in a certain size group.
What does diagonal screen size mean?A screen's size is often determined by the diagonal, or the distance between its opposite corners, which is typically measured in inches. To distinguish it from the "logical image size," which characterizes a screen's display resolution and is measured in pixels, it is also often referred to as the physical image size.
Start at the top-left corner and measure diagonally down to the bottom-right corner using a measuring tape. Do not include the bezel (the plastic, metal, or glass edge), if any, when measuring the screen alone.
because the units are too large to be offered by furlongs and fathoms. Since the United States does not use the metric system, while television was being invented, American engineers used the units they were most accustomed to.
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Drew has a video game with five differentchallenges. He sets the timer to play his gamefor 10.75 minutes. He spends the same amountof time playing each challenge. How long doesDrew nlay the fifth challenge?
Answers
For each game, Drew spends 10.75 minutes, this means in total Drew spends
[tex]5\cdot10.75\text{ minutes}[/tex]this product gives
[tex]5\cdot10.75=53.75\text{ minutes}[/tex]then, in the fifth challenge Drew spends 53.75 minutes
Solve the equation for w.
4w + 2 + 0.6w = −3.4w − 6
No solution
w = 0
w = 1
w = −1
Answers
Answer:
w = -1
Step-by-step explanation:
Given equation:
[tex]4w + 2 + 0.6w=-3.4w-6[/tex]
Add 3.4w to both sides:
[tex]\implies 4w + 2 + 0.6w+3.4w=-3.4w-6+3.4w[/tex]
[tex]\implies 4w + 2 + 0.6w+3.4w=-6[/tex]
Subtract 2 from both sides:
[tex]\implies 4w + 2 + 0.6w+3.4w-2=-6-2[/tex]
[tex]\implies 4w +0.6w+3.4w=-6-2[/tex]
Combine the terms in w on the left side of the equation and subtract the numbers on the right side of the equation:
[tex]\implies 8w=-8[/tex]
Divide both sides by 8:
[tex]\implies \dfrac{8w}{8}=\dfrac{-8}{8}[/tex]
[tex]\implies w=-1[/tex]
Therefore, the solution to the given equation is:
[tex]\boxed{w=-1}[/tex]
Given that,
→ 4w + 2 + 0.6w = -3.4w - 6
Now the value of w will be,
→ 4w + 2 + 0.6w = -3.4w - 6
→ 4.6w + 2 = -3.4w - 6
→ 4.6w + 3.4w = -6 - 2
→ 8w = -8
→ w = -8/8
→ [ w = -1 ]
Hence, the value of w is -1.
What is the slope of a line parallel to the line whose equation is 12x – 15y = 315.Fully simplify your answer.
Answers
Answer:
4/5
Explanation:
Definition: Two lines are parallel if they have the same slope.
Given the line:
[tex]12x-15y=315[/tex]Determine the slope of the given line by expressing it in the slope-intercept form (y=mx+b), where m is the slope:
[tex]\begin{gathered} 12x-15y=315 \\ \text{ Add 15y to both sides of the equation} \\ 12x-15y+15y=315+15y \\ 12x=315+15y \\ \text{ Subtract 315 from both sides:} \\ 12x-315=315-315+15y \\ 12x-315=15y \\ \text{ Divide all through by 15} \\ \frac{15y}{15}=\frac{12}{15}x-\frac{315}{15} \\ y=\frac{4}{5}x-21 \end{gathered}[/tex]• The slope of the line, m = 4/5.
Since the lines are parallel, they have the same slope.
Hence, the slope of a line parallel to the line whose equation is 12x – 15y = 315 is 4/5.
Use the graph to answer the question.Find the interval(s) over which the function is decreasing.A. (-infinity,-2)U(5,infinity)B. (-infinity,-2)U(-2,1)U(5,infinity)C.infinity,-2)U(-2,-1)U(-1,1)U(5,infinity )D. (1,5)
Answers
Okay, here we have this:
Considering the provided graph, and that a function is decreasing when as x increases, "y" decreases, we obtain the following:
The intervals over which the function is decreasing are:
(infinity,-2)U(-2,-1)U(-1,1)U(5,infinity )
Finally we obtain that the correct answer is the option C.
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
A. y = -250x + 3750
B. $2125
Step-by-step explanation:
A.
(5, 2500), (7, 2000)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2000 - 2500 -500
m = ----------------- = ---------------------- = ---------- = -250
x₂ - x₁ 7 - 5 2
y - y₁ = m(x - x₁)
y - 2500 = -250(x - 5)
y - 2500 = -250x + 1250
+2500 +2500
-------------------------------------
y = -250x + 3750
B.
y = -250x + 3750
y = -250(6.50) + 3750
y = -1625 + 3750
y = 2125
(6.50, 2125)
I hope this helps!
Evaluate the expression shown: 30-3²-2+7
Answers
Answer:
=26
Step-by-step explanation:
30−32−2+7
=30−9−2+7
=21−2+7
=19+7
=26
8. (03.07 MO)Solve x2 - 10x = -21. O x = 7 and x = 3O x = -7 and x = 3O x = -7 andx = -3O x = 7 and x = -3
Answers
Given:
Quadratic equation
[tex]x^2-10x+21=0[/tex]To find:
Values of x satisfying given equation.
Explanation:
Roots of equation of type
[tex]ax^2-bx+c=0[/tex]roots will be (x-a)(x-b) and x = a,b.
Solution:
We will factorize equation as:
[tex]\begin{gathered} x^2-10x+21=0 \\ x^2-7x-3x+21=0 \\ (x-3)(x-7)=0 \\ x=3,\text{ 7} \end{gathered}[/tex]Hence, 3 and 7 are values of x.
rounded 425.652 to the hundredths place
Answers
Since the given number is 425.652
The hundredth digit is the 2nd number right at the decimal point
It is 5
To round to the nearest hundredth, we will look at the digit right to it
1. If it is 0, 1, 2, 3, or 4 we will ignore it and write the number without change except by canceling that digit
2. If it is 5, 6, 7, 8, or 9 we will cancel it and add the digit left to it 1
Since the right digit to the digit 5 is 2, then we will remove it and do not change the digit 5 (case 1), then
The number after rounding should be 425.65
The answer is 425.65
The number of bacteria in a culture increased from 27,000 to 105,000 in five hours. When is the number of bacteria one million if:a) Does the number increase linearly with time?b) The number increases exponentially with time?
Answers
We have the following situation regarding the growth of bacteria in a culture:
• The given initial population of bacteria is 27,000
,• After 5 hours, the population increases to 105,000.
Now, we need to find the moment when that population is one million if:
• The population increases linearly with time
,• The population increases exponentially with time
To find the time in both situations, we can proceed as follows:
Finding the moment when the population is one million if it increases linearly with time1. We need to find the equation of the line that passes the following two points:
• t = 0, population = 27,000
,• t = 5, population = 105,000
2. Then the points are:
[tex]\begin{gathered} (0,27000)\rightarrow x_1=0,y_1=27000 \\ (5,105000)\rightarrow x_2=5,y_2=105000 \\ \end{gathered}[/tex]3. Now, we can use the two-point form of the line equation:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \\ y-27000=\frac{105000-27000}{5-0}(x-0) \\ \\ y-27000=\frac{78000}{5}x=15600x \\ \\ y=15600x+27000\rightarrow\text{ This is the line equation we were finding.} \end{gathered}[/tex]4. We can see that the population is given by y. Then if y = 1,000,000, then we need to solve the equation for x as follows:
[tex]\begin{gathered} 1000000=15600x+27000 \\ \\ 1000000-27000=15600x \\ \\ \frac{(1000000-27000)}{15600}=x \\ \\ x=62.3717948718\text{ hours} \\ \\ x\approx62.3718\text{ hours} \end{gathered}[/tex]Therefore, if the population increases linearly with time, the number of bacteria will be one million around 62.3718 hours.
Finding the moment when the population is one million if it increases exponentially with time1. In this case, we also need to find the equation that will give us the time when the number of bacteria is one million. However, since the equation will be exponential, we have:
[tex]\begin{gathered} y=a(1+r)^x \\ \\ a\rightarrow\text{ initial value} \\ \\ x\rightarrow\text{ number of time intervals that have passed.} \\ \\ (1+r)=b\text{ }\rightarrow\text{the growth ratio, and }r\rightarrow\text{ the growth rate.} \end{gathered}[/tex]2. Now, we can write it as follows:
[tex]\begin{gathered} a=27000 \\ \\ x=5\rightarrow y=105000 \\ \\ \text{ Then we have:} \\ \\ 105000=27000(b)^5 \\ \end{gathered}[/tex]3. We can find b as follows (the growth factor):
[tex]\begin{gathered} \frac{105000}{27000}=b^5 \\ \\ \text{ We can use the 5th root to obtain the growth factor. Then we have:} \\ \\ \sqrt[5]{\frac{105000}{27000}}=\sqrt[5]{b^5} \\ \\ b=1.31209447568 \end{gathered}[/tex]4. Then the exponential equation will be of the form:
[tex]\begin{gathered} y=27000(1.31209447568)^x \\ \\ \text{ To check the equation, we have that when x = 5, then we have:} \\ \\ y=27000(1.31209447568)^5=105000 \end{gathered}[/tex]5. Now, to find the time when the number of bacteria is one million, we can proceed as follows:
[tex]\begin{gathered} 1000000=27000(1.31209447568)^x \\ \\ \frac{1000000}{27000}=1.31209447568^x \end{gathered}[/tex]6. Finally, we need to apply the logarithm to both sides of the equation as follows:
[tex]\begin{gathered} ln(\frac{1000000}{27000})=ln(1.31209447568)^x=xln(1.31209447568) \\ \\ \frac{ln(\frac{1000000}{27000})}{ln(1.31209447568)}=x \\ \\ x=13.2974595282\text{ hours} \end{gathered}[/tex]Therefore, if the population increases exponentially with time, the number of bacteria will be one million around 13.2975 hours.
Therefore, in summary, we have:
When is the number of bacteria one million if:
a) Does the number increase linearly with time?
It will be 62.3718 hours
b) The number increases exponentially with time?
It will be around 13.2975 hours
A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Answers
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]I need help with a math problem. I linked it below
Answers
According to the distributive property of multiplication:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Then,
[tex]\begin{gathered} -6(x+5)=12 \\ -6x-6\cdot5=12 \\ -6x-30=12 \end{gathered}[/tex]To find x, add 30 to both sides:
[tex]\begin{gathered} -6x-30+30=12+30 \\ -6x=42 \end{gathered}[/tex]And divide both sides by -6:
[tex]\begin{gathered} \frac{-6}{-6}x=\frac{42}{-6} \\ x=-7 \end{gathered}[/tex]Answer:
- 6x - 30 = 12
x = -7
Rewrite the polynomial in standard form: 2x + 7x^2 - 3+ x^3
Answers
The given polynomial is
[tex]2x+7x^2-3+x^3[/tex]The standard form refers to organizing the terms where the exponents are placed in decreasing order.
[tex]x^3+7x^2+2x-3[/tex]while eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour. on average, how many customers arrive in each 10 minutes interval?
Answers
In every 10 minutes an average of 3 customers will arrive to the pizza station
Given,
The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.
We have to find the average number of customers arrives in each 10 minutes.
Here,
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P (X = x) = (e^-μ × μ^x) / x!
Where,
The number of successes is x.
The Euler number is e = 2.71828.
μ is the average over the specified range.
Now,
Rate of 18 customers per hour;
μ = 18 n
n is the number of hours.
Number of customers arrive in each 10 minutes
10 minutes = 10/60 = 1/6
Then,
μ = 18 x 1/6 = 3
That is,
In every 10 minutes an average of 3 customers will arrive to the pizza station.
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How do I solve it and what would be the answer
Answers
The quotient is x² + 4x + 3
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Explanation:[tex](x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2)}[/tex][tex]\begin{gathered} x\text{ - 2 = 0} \\ x\text{ = 2} \\ \\ \text{coefficient of }x^3+2x^2\text{ - 5x - 6:} \\ 1\text{ 2 -5 -6} \\ \\ We\text{ will divide the coefficients by 2} \end{gathered}[/tex]Using synthetic division:
[tex]\begin{gathered} (x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2) = }\frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}} \\ \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}\text{ = quotient + }\frac{remai\text{ nder}}{\text{divisor}} \\ \\ The\text{ coefficient of the quotient = 1 4 3} \\ \text{The last number is zero, so the remainder = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}=1x^2\text{ + 4x + 3 + }\frac{0}{x\text{ - 2}} \\ \text{quotient }=\text{ }x^2\text{ + 4x + 3} \end{gathered}[/tex]For a (x - 2) to be a factor of x³ + 2x² - 5x - 6, it will not have a remainder when it is divided.
Since remainder = 0
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Dante is arranging 11 cans of food in a row on a shelf. He has 7 cans of beans, 3 cans of peas, and 1 can of carrots. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Answers
Given:
The number of cans of food =11
The number of cans of beans=7
the number of cans of peas=3
the number of cans of carrots=1
Condition : two cans of the same food are considered identical.
To arrange the n objects in order,
[tex]\begin{gathered} \text{Number of ways= }\frac{n!}{r_1!r_2!r_3!} \\ =\frac{11!}{7!3!1!} \\ =\frac{39916800}{30240} \\ =1320 \end{gathered}[/tex]Answer: the number of ways are 1320.
$1750 is invested in an account earning 3.5% interest compounded annualy. How long will it need to be in an account to double?
Answers
Given :
[tex]\begin{gathered} P\text{ = \$ 1750} \\ R\text{ = 3.5 \%} \\ A\text{ = 2P} \\ A\text{ = 2}\times\text{ 1750 = \$ 3500} \end{gathered}[/tex]Amount is given as,
[tex]\begin{gathered} A\text{ = P( 1 + }\frac{R}{100})^T \\ 3500\text{ = 1750( 1 + }\frac{3.5}{100})^T \\ \text{( 1 + }\frac{3.5}{100})^T\text{ = }\frac{3500}{1720} \end{gathered}[/tex]Further,
[tex]\begin{gathered} \text{( 1 + }\frac{3.5}{100})^T\text{ = 2} \\ (\frac{103.5}{100})^T\text{ = }2 \\ (1.035)^T\text{ = 2} \end{gathered}[/tex]Taking log on both the sides,
[tex]\begin{gathered} \log (1.035)^T\text{ = log 2} \\ T\log (1.035)\text{ = log 2} \\ T\text{ = }\frac{\log \text{ 2}}{\log \text{ 1.035}} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} T\text{ = }\frac{0.3010}{0.0149} \\ T\text{ = 20.20 years }\approx\text{ 20 years} \end{gathered}[/tex]Thus the required time is 20 years.
a. Draw any obtuse angle and label it angle AXB. Then draw ray XY so that it bisects < AXB.b. if m AXB = 140°, then what is m ZYXB?
Answers
The obtuse angle is shown in the diagram below:
The word, "bisect" means to divide an angle into 2 equal parts. Given that ray XY bisects angle AXB, it mean that it divides it into two equal halves. Theregfore, angle YXB is 140/2 = 70 degrees
Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.
Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs.
a. Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.
Answers
Using the normal distribution and the central limit theorem, the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is:
[tex]P(3.5 \leq \bar{X} \leq 4.25) = 0.7482[/tex]
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of each review are given as follows:
[tex]\mu = 4, \sigma = 1.2[/tex]
For the sampling distribution of sample means of size 16, the standard error is given as follows:
[tex]s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is the p-value of Z when X = 4.25 subtracted by the p-value of Z when X = 3.5, hence:
X = 4.25:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.25 - 4)/0.3
Z = 0.83.
Z = 0.83 has a p-value of 0.7967.
X = 3.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (3.5 - 4)/0.3
Z = -1.67.
Z = -1.67 has a p-value of 0.0475.
Hence the probability is:
0.7967 - 0.0485 = 0.7482.
The statement is:
[tex]P(3.5 \leq \bar{X} \leq 4.25)[/tex]
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George filled up his car with gas before embarking on a road trip across the country. The capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven. Make a table of values and then write an equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
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Given that the capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven.
[tex]\begin{gathered} G_{\circ}=12 \\ m=-2 \end{gathered}[/tex]slope m is negative since the gas is reducing every hour.
Writing the equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
[tex]\begin{gathered} G=G_{\circ}+mt \\ G=12+(-2)t \\ G=12-2t \end{gathered}[/tex]The equation for G is;
[tex]G=12-2t[/tex]Calculating the number of gallons remaining in the tank after 0,1,2 and 3 hours, we have;
[tex]\begin{gathered} G=12-2t \\ at\text{ t=0}; \\ G_0=12-2(0)=12 \\ at\text{ t=1}; \\ G_1=12-2(1)=10 \\ at\text{ t=2}; \\ G_{2_{}}=12-2(2)=12-4=8 \\ at\text{ t=3;} \\ G_3=12-2(3)=12-6=6 \end{gathered}[/tex]Completing the table, we have;