The mean of the commute time to work for a resident of Boston is 27.1 minutes. Assume that the standard deviation of the commute time is 8.3 minutes.

a) What is the minimum percentage of commuters in Boston has a commute time within 2 standard deviation of themean?

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?

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].

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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See attachment for the graphs of the 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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Answer:

4x+8+7x-8

Step-by-step explanation:

4x+7x+8-8

11x+0

11x.

Answer:

you're answer will be 2 hours and 30 minutes

Step-by-step explanation:

i hope that helps you! :))

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

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

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

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

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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[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]

Answer:

[tex] \sf (- \infty, 58] [/tex]

Step-by-step explanation:

Express as interval = [tex] \sf (- \infty, 58][/tex]

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

​

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.

The 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

We 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.

Answer:

9 Pizzas

Step-by-step explanation:

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.

Answer: The 12 songs for $10

Step-by-step explanation: 12 / 10 = 1.2 while 12 / 0.85 = 14.11

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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The first angle will be 77.33°.

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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Answer:

Step-by-step explanation:

Let the time for cold tap be c and hot tap be h.

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:

Numbers that can be written as a power in more than one way is known as 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.

Numbers 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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The length of each sides of the right triangle are as follows:

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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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.

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:

==============================

Let the number of adult tickets be x and student tickets be y.

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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Answer: full house,fairly oddparents, the simsons

edit^^^ a movie is clueless or even mean girls

Step-by-step explanation:

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]