a) The minimum 75% of commuters in Boston has a commute time within 2 standard deviation of the mean.
b) The minimum 60.93% of commuters in Boston has a commute time within 1.6 standard deviation of the mean.
c) Commute times within 1.4 standard deviation are lie between 15.48 to 38.72.
Explanation:
Given that
The mean of the commute time to work for a resident of Boston is 27.1 minutes.the standard deviation of the commute time is 8.3 minutes.To find
a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?c) What are the commute times within 1.4 standard deviation?So, according to the question
We know that
The minimum percentage within k standard deviations of the mean,= (1- [tex]\frac{1}{k^2}[/tex] )×100
a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of the mean?
The minimum percentage within 2 standard deviations of the mean,= (1- [tex]\frac{1}{2^2}[/tex] )×100
= (1- [tex]\frac{1}{4}[/tex] )×100
= ( [tex]\frac{4-1}{4}[/tex] )×100
= [tex]\frac{3}{4}[/tex] ×100
= 3 × 25
= 75%
b) What minimum percentage of commuters in Boston has a commute time within 1.6 standard deviation of the mean?
The minimum percentage within 1.6 standard deviations of the mean,= (1- [tex]\frac{1}{1.6^2}[/tex] )×100
= (1- [tex]\frac{1}{2.56}[/tex] )×100
= ( [tex]\frac{2.56-1}{2.56}[/tex] )×100
= [tex]\frac{1.56}{2.56}[/tex] ×100
= 1.56 × 39.06
= 60.93%
c) What are the commute times within 1.4 standard deviation?
Within 1.4 standard deviations,commute times = 27.1 ± (1.4×8.3)
= 27.1 ± 11.62
for + sign,
= 27.1 + 11.62
= 38.72
for - sign,
= 27.1 - 11.62
= 15.48
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At a point on the ground 15ft from the base of a tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. Find the height of the tree.
At a point on the ground 15ft from the base of a tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. Find the height of the tree.
The height of the tree is 8ft.
Given that,
A right triangle has two legs, which are height and (15 feet) from the base.
The hypotenuse is 15 feet from the base to the top of the tree.
or 2(height) + 1ft.
Let us take a as height of the tree; b=distance from base=15 ft; c=hypotenuse=2a+1ft
The area of the square created on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on the triangle's legs:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]a^{2} +(15ft)^{2}=(2a+ 1ft) ^{2}[/tex]
[tex]a^{2} +225ft^{2}=4a^{2} +4a+1\\ 0=3a^{2}+4a-224\\ 0=(a-8)\times(3a+28)\\[/tex]
Now,
a-8=0 (or) 3a+28=0
a=8 (or) a=[tex]\frac{-28}{3}[/tex]
Therefore, The height of the tree is 8ft.
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The cold water tap can fill a container two hours faster than the hot water tap. The two taps together can fill a container in 80 minutes. How long does it take each tap to fill the container on its own?
Answer:
4 hours and 2 hoursStep-by-step explanation:
Let the time for cold tap be c and hot tap be h.
Convert2hrs = 120 minSet equationsThe cold water tap can fill a container two hours faster than the hot water tap:
c - h = 120The two taps together can fill a container in 80 minutes:
1/c + 1/h = 1/80Solve the system by substitutionc = h + 1201/c + 1/h = 1/801/(h + 120) + 1/h = 1/80(h + h + 120)/(h(h+120)) = 1/8080(2h + 120) = h(h + 120)160h + 9600 = h² + 120hh² - 40h - 9600 = 0h² - 40h + 400 = 10000(h - 20)² = 100²h - 20 = 100 (taking positive root only, since time is positive value) h = 120 min = 2 hrsFind cc = 120 + 120 = 240 min = 4 hrsPractice Another
A city lot has the shape of a right triangle whose hypotenuse is 4 ft longer than one of the other sides. The perimeter of the lot is 440 ft. How long is each side of the lot?
short leg
ft
long leg
ft
hypotenuse
ft
Short leg:___________ft
Long Leg:___________ft
Hypotenuse:___________ft
The length of each sides of the right triangle are as follows:
short leg = 27 ftlong leg = 90 fthypotenuse = 94 ftHow to find the sides of a right triangle?The shape of the city lot is a right triangle.
The hypotenuse side is 4 ft longer than one of the other side.
The perimeter of the lot is 440 ft.
Therefore, using Pythagoras theorem,
let
x = the other side
y = the second leg
x² + y² = (x + 4)²
x² + y² = (x + 4)(x + 4)
x² + y² = x² + 4x + 4x + 16
x² + y² = x² + 8x + 16
y² = 8x + 16
Hence,
x + x + 4 + y = 440
2x + y + 4 = 440
2x + y = 436
2x + y = 436
y = 436 - 2x
y² = 8x + 16
(436 - 2x)(436 - 2x) = 8x + 16
190096 - 872x - 872x - 4x² = 8x + 16
190096 - 1744x - 4x² = 8x + 16
4x² + 1752x -190080 = 0
4(x² + 438x - 47520) = 0
x² + 438x - 47520 = 0
Therefore,
x = 90 and x = - 528
Therefore, the hypotenuse side is 94 ft.
94² - 90² = y²
y = √8836 - 8100
y = √736
y = 27.1293199325
y = 27 ft
Therefore, the short leg, long leg and hypotenuse are 27 ft, 90 ft and 94 ft.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6 and each adult ticket sells for $9. There was a total of $747 in revenue from the sale of 98 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
Answer:
x + y = 989x + 6y = 747==============================
Let the number of adult tickets be x and student tickets be y.
Set equationsNumber of tickets:Adult tickets + student tickets = 98x + y = 98Amount of revenue:Total of adult tickets = 9x, total of student tickets = 6y9x + 6y = 747Numbers that can be written as a power in more than one way
Numbers that can be written as a power in more than one way is known as exponents .
WHAT ARE EXPONENTS?A sign that denotes raising to a power that is placed above and to the right of a mathematical expression. for example , [tex]2^{a}[/tex].
The mathematical procedure known as exponentiation, abbreviated as bn, involves the base number (b) and the exponent (or power) number (n). In English, it is pronounced "b (raised) to the (power of) n." [1] Exponentiation is the process of repeatedly multiplying bases, where n is a positive integer, and the product is known as bn.
The exponent is typically denoted by a superscript to the right of the base. The term "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most simply, "b to the nth," is used to describe bn.
CALCULATIONNumbers that can be written as a power in more than one way is known as exponents .
These numbers are basically written to save time to multiply the same number multiple times .
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List some TV shows or movies with permissive parents.
Answer: full house,fairly oddparents, the simsons
edit^^^ a movie is clueless or even mean girls
Step-by-step explanation:
(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)
Answer:
The correct answer would be,
= 10m^3 + 8m^2 - 10m - 0.8
Step-by-step explanation:
First you subtract the m^3 terms :
> 7m^3 + 3m^3
> 10m^3
Then you subtract m^2 , in this case we only have 1 m^2 :
> 8m^2
Then you subtract the m terms :
> -m - 9m
> -10m
The lastly you subtract the last terms :
> 2.8 - 3.6
> -0.8
= 10m^3 + 8m^2 -10m -0.8
(Make sure to distribute the negative before you solve it.) Just a point!!
Answer:
10m³+8m²-10m-0.8
Step-by-step explanation:
(7m³ +8m²-m+2.8)-(-3m³ +9m+3.6)
Use the sign to open the bracket we have;
7m³ +8m²-m+2.8+3m³-9m-3.6
bring like terms together
7m³+3m³+8m²-9m-m-3.6+2.8
Simplifying we have;
10m³+8m²-10m-0.8
hope it helps...
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Miraawesome
Ay-Jiuan can buy 12 songs for $10, or she
can pay $0.85 per song. Which option has the lesser price per song?
Answer: The 12 songs for $10
Step-by-step explanation: 12 / 10 = 1.2 while 12 / 0.85 = 14.11
Find the edge length of the cube.
Answer:
The volume of a cube is the edge length cubed (S^3)
To find the edge length when the volume is known find the cubic root of the volume.
Step-by-step explanation:
Edge = ∛1/27
Edge = 1/3 ft.
Find the slope of a line that passes through (4.5,3.5) and (9.5,5.5)
M =
[tex](\stackrel{x_1}{4.5}~,~\stackrel{y_1}{3.5})\qquad (\stackrel{x_2}{9.5}~,~\stackrel{y_2}{5.5})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5.5}-\stackrel{y1}{3.5}}}{\underset{run} {\underset{x_2}{9.5}-\underset{x_1}{4.5}}}\implies \cfrac{2}{5}[/tex]
What is the solution to r/-3 = 12? A. r=-36 B. r= -4 C. r=4 D. r=36 (1 point)
Choose the number phrase that correctly matches the word phrase “18 less 6.”
18 x 6
18 + 6
6 – 18
18 – 6
First try was incorrect
Rew decided to purchase some dubbles (x) and totts (y). Altogether,
he planned to buy at most 7 items.
Write an inequality, in standard form, to model this relationship.
Answer:
x + y ≤ 7
(if that doesn't work, 0 ≤ x + y ≤ 7)
Rew wants to buy 7 items or less, so the number of dubbles and totts combined can't be bigger than 7, and is therefore less than or equal to 7.
What is the next fraction in this sequence? Simplify your answer.
1/3, 1/9, 1/27, 1/81,
Submit
...
Answer:
1/243
Step-by-step explanation:
Each denominator is multiplied by 3 from the last one
3 x 3 = 9
9 x 3 = 27
27 x 3 = 81
81 x 3 = 243
Find the value of PT if
PT=4x+1 and 7x-8
Answer:
4x+8+7x-8
Step-by-step explanation:
4x+7x+8-8
11x+0
11x.
PLEASE HELP!!! DUE TMRW!!!
The values of the required parameters based on the analysis of the dataset are as follows;
X MIN = 0
X MAX = 2
X Scl = 0.5
Y MIN = 0
Y MAX = 110
Y Scl = 20
What is a dataset?A dataset is a presentation of a collection of data. In a tabular form, a dataset is arranged such that each column of the table presents the data of a specific variable.
The table of values in the question are presented as follows;
d [tex]{}[/tex] p
0 [tex]{}[/tex] 110
0.25 [tex]{}[/tex] 90
0.5 [tex]{}[/tex] 80
0.75 [tex]{}[/tex] 75
1 [tex]{}[/tex] [tex]{}[/tex] 75
1.25 [tex]{}[/tex] 40
1.5 [tex]{}[/tex] 40
1.75 [tex]{}[/tex] 10
2 [tex]{}[/tex] 0
Please find attached a plot of the data in the table presented in the question
X MIN is the minimum x-value obtained from the set of x-values, which is the minimum value of the domain of the data in the table.
From the table in the question; X MIN = 0
X MAX is the maximum x-value obtained from the set of x-values of the data in the table, which is also the maximum x-value of the range of input values in the table.
The maximum x-value in the table, X MAX = 2
X scl is the scale the specification of the distance between consecutive tick marks on the x-axis.
The distance between tick marks on the x-axis of the attached graph, X Scl = 0.5
Y MIN is the minimum y-value obtained from the set of y-values, which is the minimum value of the range of the data presented in the table
The Y MIN obtained from the table is 0
Y MAX is the maximum y-value obtained from the y-values of the data in the table, which is the maximum value of the range of the data in the table
The maximum y-value, Y MAX = 110
Y Scl is the distance between consecutive tick marks on the y-axis of the graph of the data
The Y Scl of the y-axis of the attached graph Y Scl = 20
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HELP
Graph the following system of inequalities on the coordinate plane. You will need to explain your
work. Each correct line graphed WITH the correct explanation and shading is worth 2 points.
> − −
+ ≤
> −
See attachment for the graphs of the inequalities
How to graph the system of inequalities?To do this, we analyze and plot each inequality at a time
Having said that, we have
Inequality 1: y > -3x - 2
Here, we have
y > -3x - 2
The inequality > implies that the right-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a dotted line
Inequality 2: 4x + 5y ≤ 20
Here, we have
4x + 5y ≤ 20
The inequality ≤ implies that the left-hand side of the origin will be shaded
Also, it means that the line of the inequality will be a closed line
Inequality 3: y > -4
Here, we have
y > -4
The inequality > implies that the upper part of the origin will be shaded
Also, it means that the line of the inequality will be a dashed line
See attachment for the graphs of the inequalities
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solve for y : 3x-2y+12>0
Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
[tex]y < \frac{3x}{2} +6[/tex]
The table lists the eight human blood types.
It also shows how blood types determine who a person can donate blood to and receive blood from.
Blood type
A+
B+
AB+
AB-
A-
B-
0+
0-
Can donate to
A+, AB+
B+, AB+
AB+
AB+, AB-
A+, A-, AB+, AB-
B+, B-, AB+, AB-
(a) X = 1
(b) x = 0
A+, B+, AB+, 0+
All blood types
Can receive from
A+, A-, 0+, 0-
B+, B-, 0+, 0-
All blood types
A-, B-, AB-, 0-
A-, O-
B-, 0-
0+, 0-
0-
Let U be the set of all eight human blood types.
U=(A-, B-, AB+, AB-, A-, B-, 0-,0-)
Let X be the set of blood types that type AB- cannot receive blood from.
Let I be the set of blood types that type B+ can donate blood to.
Find the sets below. Write each answer in roster form or as 2.
CE
D
AB-
0.0 Ø
8+
AB+
The average rate of change of
f from x =2 to x =5
is _________ -5/4 is incorrect
Answer:
-1 or -3/3
Step-by-step explanation:
Average rate of change = slope
x = 2 x = 5
(2,3) (5,0)
Slope formula: y₂-y₁/x₂-x₁
(0-3)/(5-2) = -3/3 or -1
A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. What is the capacity of the tank (in hL)?
The capacity of the full tank is 16 hectolitre. percentage problem.
A gasoline tank contains 9.6 hectolitres (hL) when it is 60% full. when the tank is 100% full that is the capacity of the tank.
so, the capacity of the full tank is 9.6x(100/60) = 16 hL.
this a percentage problem. In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number; it has no unit of measurement.
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Answer this question please
Answer:
[tex] \sf (- \infty, 58] [/tex]
Step-by-step explanation:
Express as interval = [tex] \sf (- \infty, 58][/tex]
the difference between compound interest and simple interest on the same sum of rupees 8000 for 2 year is rupees 20 find the rate of interest ?
Answer:
5%
Step-by-step explanation:
You want the interest rate that makes the difference between compound and simple interest on ₹8000 for two years be ₹20.
Interest formulasThe formula for the value of an account earning simple interest is ...
A = P(1 +rt) . . . . P earning interest rate r for t years
The formula for the value of an account earning compound interest is ...
A = P(1 +r)^t . . . . P earning interest rate r for t years
ApplicationWe want the difference in these amounts over 2 years to be ₹20.
8000(1 +r)^2 -8000(1 +2r) = 20
1 +2r +r^2 -(1 +2r) = 20/8000 . . . . . divide by 8000, expand the square
r^2 = 1/400 . . . . . . simplify
r = 1/20 = 5% . . . . . take the square root
The rate of interest is 5% per year.
Robbie opens an account at a local bank by depositing $100. The account pays 2.4% interest, compounded weekly. He deposits $100 every week for 3 years.
b. Write the future value function if x represents the number of weeks.
c. Use a graphing calculator to graph the future value function.
d. Using the graph, what is the approximate balance after 2 years?
The equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
Robbie depositing= $100
Interest=2.4%
Time=3 years.
According to given question we have
P = periodic payment = $100 / week
r = interest rate = 2.4%, compounded weekly
t = 3 years
x = 52 weeks (# of times interest is compounded per year)
To write a equation we have
B = Future Value
[tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex]
Therefore, the equation of the future value function if x represents the number of weeks is [tex]= P((1+r/x)^{nt} - 1)/(r/x)[/tex].
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Find the equation of the line with slope m=- 3 that contains the point (9, - 15) Use fractions in your response, not decimals
Answer:
y = - 3x + 12
Step-by-step explanation:
Slope intercept form of line
y = mx + b where m = slope, b = y-intercept
==> y = -3x + b is the equatin
To find b, plug in values for point x = 9, y =-15 and solve for b
-15 = -3(9) + b
-15 = -27 + b
Add 27 both sides
-15 + 27 = b
12 = b
b = 12
Equation is
y = - 3x + 12
Three angles add up to 180 degrees, angle one has a measure of 8x+8, angle two has a measure of 8x+8 and angle three has a measure of 2x+8.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
The first angle will be 77.33°.
How to calculate the angle?It should be noted that the total angles will be 180°.
This will be illustrated as:
8x + 8 + 8x + 8 + 2x + 8 = 180
18x + 24 = 180
18x = 180 - 24
18x = 156
x = 8.667
The first angle will be
= 8x +8
= 8(8.667) + 8
= 77.33°
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One pizza will feed 4 people. How many pizzas are needed for 36 people?
pizzas
Answer:
9 Pizzas
Step-by-step explanation:
What is the standard form of 2y =6x + 4
Answer: solve for x
x=[tex]\frac{y-2}{3}[/tex]
solve for y
y=3x+2
Step-by-step explanation:
solve for x
2y=6x+4
Swap sides so that all variable terms are on the left hand side.
6x+4=2y
Subtract 4 from both sides.
6x=2y−4
Divide both sides by 6.
6
6x
Dividing by 6 undoes the multiplication by 6.
[tex]x=\frac{2y-4}{6}[/tex]
Divide −4+2y by 6.
x=[tex]\frac{y-2}{3}[/tex]
solve for y
2y=6x+4
The equation is in standard form.
2y=6x+4
Divide both sides by 2.
[tex]\frac{2y+2}{2} =\frac{6x+4}{2}[/tex]
Dividing by 2 undoes the multiplication by 2.
[tex]y=\frac{6x+4}{2}[/tex]
Divide 6x+4 by 2.
y=3x+2
5/8 of the pens in a box are blue pens. 4/5 of the remaining are red pens.what fraction of the pens are red ?
A rain gauge collected 0.2 inches of
rain in 30 minutes. If it keeps
raining at the same rate, what is the
total time it will take to collect 1
inch of rain?
Answer:
you're answer will be 2 hours and 30 minutes
Step-by-step explanation:
i hope that helps you! :))