The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and plan 2 charges $17 per month plus $0.03 per call. Use and inequality to find the number of monthly calls for which plan is more economically than plan 2

The probability that at least 75 students arrive at the library is 0.1440.

From the information, the undergraduate library at State U tends to have 33.4 students enter every hour during normal operation.

The expected number of students for the two hours will be:

= 2 × 33.4

= 66.8

The probability that at least 75 students arrive at the library will be:

P(x >= 75) = 1 - P(x <= 74)

This will be looked at in the distribution table

= 1 - 0.8560

= 1.440

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The average payment of Tim worker is $52.71   .

The Average of n numbers can be defined as sum of n numbers divided by n .

For Example : Average of 2,4,5,9 is

=(2+4+5+9)/4

=20/4

=5

In the question ,

it is given that

Sum of amount Tim Worker received = $158.14

number of payments received = 3

So the Average payment for Tim worker can be calculated using the formula

Average = (Sum of payment)/(number of payment)

Substituting the values of Sum of payment and number of payment , we get

Average = 158.14/3

= 52.71

The average payment of Tim worker is $52.71   .

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Answer:

$52.71

Hope It Helps. (HIP).

Answer:

189.7

Step-by-step explanation:

Hope it helps! =D

The distance expression of the number of units between points A and B is √[(-2 - 3)^2 + (5 - 5)^2]

From the question, we have the following parameters:

This means that

A = (-2, 5)

B = (3, 5)

The distance between the points is calculated as

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Where

A = (x1, y1) = (-2, 5)

B = (x2, y2) = (3, 5)

Substitute the known values in the above equation

So, we have

Distance = √[(-2 - 3)^2 + (5 - 5)^2]

The question does not imply that the we simplify the above expression

So, we leave the expression unsimplified

Hence, the expression of the distance between A and B is √[(-2 - 3)^2 + (5 - 5)^2]

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linear; translation up 4 units

The given function is:

g(x) = x + 4

This is of the form:

y = mx + c

where m is the slope and c is the y-intercept

Therefore, g(x) is a linear function

The parent function is:

g(x) = x

g(x) = x + 4 means that the function is translated up 4 units

The percentage of students that score between 400 and 600 on the verbal SAT is 11%.

It should be noted that from the information, SAT scores are normed so that, in any year, the mean of the verbal or math test score should be 500 and the standard deviation is 100.

Therefore, the percentage of students score between 400 and 600 on the verbal SAT will be:

Z = (625 - 500) / 100

Z = 125 / 100

Z = 1.25.

We will then look at the z table. This will be:

P(Z > 1.25) = 0.11

The percentage is 11%.

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Volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

As given,

Volume of solid of revolution formed by rotating about the x-axis region between the graph of f(x)= x /2:

Volume = π∫[f(x)]²dx  

⇒Volume =π∫(x/2)²dx

⇒Volume =(π/4)∫x²dx

⇒Volume =(π/4) (x³/3)

                 =(π/12)(x³)

x axis between x=2 and x=5

Volume =(π/12)(125-8)

             =117π/12 unit³

Therefore, volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.

The complete question is:

Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of

f(x)= x /2

and the x axis between x=2 and x=5.

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The domain of f⁻¹(x) is (9,∞).

The function we have is

f(x) = 4x² + 9 for x ≤ 0

Now, let us find the inverse of the function f(x),

To find the inverse of f(x),

Replacing f(x) with f(y)

f(y) = 4y² + 9

Now the equation is,

x = 4y² + 9

y² = (x-9)/4

y = √(x-9)/2

The inverse of f(x) is,

f⁻¹(x) = √(x-9)/2

The domain of √(x-9)/2 can be found as,

(x-9)>0

x>9

The domain of f⁻¹(x) is (9,∞).

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When the graph of a proportional connection passes through the origin, the ratio in the proportional relationship can be found.

The connection is proportional if the graph is a line through the origin. This relationship is non-proportional unless the line or ray is non-proportional. K = y/x is the formula for the constant of proportionality. The formula for the slope of a straight line with respect to the origin is the same as this.

If the graph is a line or lines through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it will not be proportional. Also, anything that is not linear is not proportional

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Answer:

He raised 51 dollars

Step-by-step explanation:

If for every 5 points he raised 3 dollars he would have raised 51 dollars because he had 85 points.

The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.

The average speed is the ratio of total length traveled to total time taken to travel that length. Average speed is the total distance travelled per time.

Average speed = the total distance / total time

Given that Noah's average speed is 6mph

From the above formula, to determine miles run is average speed x time

The Total miles he ran in 1 hour = 6 x 1 = 6 miles

Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles

Total miles he ran in 1 and 1/3 hours = 6 x 4/3 = 8 miles

The formula for the total time:  total distance / average speed

The Time it took Noah to run 1 and 1/2 miles = 3/2 ÷ 6 = 1/4

Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2

Time it took Noah to run 4 and 1/2 miles = 9/2 ÷ 6 = 3/4

The miles he ran in 4/3 hours at a constant speed of 6 miles per hour is 8 miles.

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The complete question is

Noah is running a portion of a marathon at a constant speed of 6 mph. Complete the table to predict how long it would take him to run different distances at that speed and how far he would run in different time intervals.

Time in hours Miles traveled at 6mph

1.

1/2

1 1/3

1 1/2

9

4 1/2

Answer:

(9x^3+x^2-6x+5) is the answer to algebra equation

Answer:

The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min

Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min

Step-by-step explanation:

[tex]\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}[/tex]

The surface area of a sphere of radius r is given by:

[tex]\\S = 4\pi r^2\\[/tex]

The rate of change of surface area is given by
[tex]\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\[/tex]

[tex]\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}[/tex]

We are given that [tex]\text{$\dfrac{dr}{dt}$}[/tex] = 70 cm/min and asked to find rate of change of S when r = 40 cm

Substituting these values into the equation for [tex]\dfrac{dS}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min[/tex]

In absolute values

Answer:

Step-by-step explanation:

x-84/6

As we can see in the card, on Monday the worker clocked in at 08:15 and clocked out at 12:15. This means they worked 4 hours.

They then clocked in at 13:00 and clocked out at 17:30. This means they worked for 4 and a half hours.

Since they earn a wage of $14.50/h, they earned:

So that day they earned $123.25

Answer:

i think it is 7 but not sure

Step-by-step explanation:

GCF of 28 and 35 is the largest possible number that divides 28 and 35 exactly without any remainder. The factors of 28 and 35 are 1, 2, 4, 7, 14, 28 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 28 and 35 - prime factorization, Euclidean algorithm, and long division.

Answer:

C). Or SAS~with 3/2 proportionate sides.

Step-by-step explanation:

You can tell because the similar angle shows which sides should be proportional to the other on the corresponding triangle, and of those sides, 6/4 = 10.5/7

Easily simplifying to 3/2 both times to find the rate at which the side lengths where changed.

Hope this helps.

To convert the number given in base 7 to a bse 10 number we follow the procedure shown, that is, we need to multiply each number by the appropiate power of seven (given by their position) and then add them, then we have that:

Therefore:

(a) 291/2020

Divide the total for the 10-14 year column by the total.

(b) 77/465

There are 465 people from the east, 77 of which were loyal for 10 to 14 years

(c) 437/1010

There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.

(d) 145/376

376 people are from the West, (45+100)=145 of which are at least 10.

(e) 32/157

157 people were loyal for less than a year, 32 of which were from the East.

(f) 53/157

157 people were loyal for less than a year, 53 of which were from the South.

(g) 433/465

465-32=433 people were loyal for at least 1 year out of the 465 people from the East.

(h) 335/376

376-41=355 people were loyal for at least 1 year out of the 376 people from the West.

G(x) = [tex]x^{2}[/tex] + 4 is the transformation of f(x)=[tex]x^{2}[/tex] represented by g.

The change mentioned comes from f(x)=[tex]x^{2}[/tex], g(x) = x² + 4

The value of h determines the horizontal shift. The formula for the horizontal shift is g(x)=f(x+h). The graph has been moved left by h units.

g(x)=f(x-h)

The graph is moved right by h units.

The graph is not moved left or right in this instance because h=0.

No Horizontal Shift

The value of k determines the vertical shift. The formula for the vertical shift is g(x)=f(x)+k. The graph has been raised k units.

g(x)=f(x)-k The graph is moved k units downward.

Shift vertically up four units.

When g(x)=-f, the graph is mirrored on the x-axis (x)

No reflection on the x-axis

When g(x)=f, the graph is mirrored on the y-axis (x)

No reflection on the y-axis

Depending on the value of a, compressing and expanding.

When an exceeds 1, the line is extended vertically.

In the range 0 to 1, an is vertically compressed.

Vertical Stretch or Compression: None

Compare the transformations and make a list.

No Horizontal Shift

Shift vertically up four units.

No reflection on the x-axis

No reflection on the y-axis

Vertical Stretch or Compression: None

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Answer:

A

Step-by-step explanation:

.

Notice that the values for w are multiples of 9, and their respective factor is expressed on the values of z. Therefore, the equation to describe the relationship between w and z is w=9z

Answer:

15 + m = 60; m = 45 minutes

Step-by-step explanation:

Hello!

According to the question He had a total of 60 minutes to complete the entire exam. He spent 15 minutes on Part 1 of the exam. how much time he had left to complete Part 2.

Let's make an equation where the time spent on part 1 which is 15 + m which is minutes remaining for part 2 is equal to Total minutes which is 60 minutes

So, if we put it together;

15 + m = 60

So, let's solve for m

15 + m = 60

Substract 15 from both sides

15 - 15 + m= 60 - 15

m = 45

So, the equation is 15 + m = 60 and he had 45 minutes of time remaining to complete part 2.

ANSWER

EXPLANATION

We want to find how much chicken stock will be needed in quarts.

To convert a value from cups to quarts, we have to divide it by 4.

Therefore, the amount of chicken stock needed, in quarts, is:

That is the answer.

As given by the question

There are given that the expression

Now,

Multiply by 5 on both side of the equation

So,

Hence, the value of a is 110.

The federal income tax is levied against the yearly profits of people, companies, and other legal entities. The overall federal income tax payment of this individual will be $4126.

The federal income tax is levied against the yearly profits of people, companies, and other legal entities. Federal income taxes are due on all compensation, including salaries, monetary gifts from employers, business profits, tips, winnings from gaming, bonuses, and unemployment benefits.

Income taxes are levied by the federal government and the majority of states in the US. Income taxes, which may be incurred as income increases, are produced by applying a tax rate to taxable income, which is the total income less allowable deductions.

The overall federal income tax payment of this individual exists $970 + $3,156 = $4126.

The taxable income of the individual will be $4126.

Therefore, the correct answer is option C. $4,126.

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Answer:

2:3

Step-by-step explanation: