A phone company offers two monthly plans. Plan A costs $16 plus an additional $0.18 for each minute of calls. Plan B costs $28 plus an additional $0.14 for each minute of calls.

The equation represented by the graph is f(x) = -3x + 6

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'b' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable.

the straight line cuts the axes at (0,6) and (2,0)

Equation of straight line in slope-intercept form is f(x) = mx + c

when x = 0 f(x) = 6

6 = m(0) + c

c = 6

when x = 2, f(x) = 0

0 = 2m + c

2m = -c, but c = 6

2m= -6

m = -6/2

m = -3

Equation of line becomes f(x) = -3x + 6

In conclusion f(x) = -3x + 6 is the equation that is represented by the graph.

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}[/tex]

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

[tex]\theta = 100^\circ - 42^\circ = 58^\circ[/tex]

Thus the resulting speed is obtained as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54[/tex]

The resulting angle of the plane is then obtained as follows:

[tex]\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)[/tex]

Hence:

[tex]\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)[/tex]

[tex]\angle = 59.87^\circ[/tex]

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

What is permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.

So, the number of desired cases are,

= [tex]\frac{7_P_3(24)^4}{2} = 34836480[/tex]

Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

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Answer:

Fossil

are impressions of plants or animals embedded in rock and preserved. They may be in the form of a body or trace.

The age of the fossils is determined by the Radioactive carbon dating technique in which the half-life of carbon and found radioactive elements is determined to calculate the age of a fossil

There are "P(20, 10) - P(15, 10)" options (ways) to distribute the coupons so that at least one woman receives a coupon.

What do you mean by permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

There are P(20, 10) ways to distribute the coupons if they are different, with the only restriction being that no more than one coupon can be given to a shopper. To ensure that all of the coupons go to the guys, there are P(15, 10) ways to distribute them. In order to ensure that at least one coupon is given to a woman, there are P(20, 10) - P(15, 10) options to distribute the coupons.

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Complete Question

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.

If the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?

The formula of time is time: distance/speed

Time is an important concept in physics, and it can be expressed in a variety of ways. The most common way to describe time is with the equation t = d/s, where t is time, d is the change in position of an object, and s is the speed of the object. This equation is known as the time-distance formula.  The time-distance formula can be used to calculate the time it takes for an object to travel a certain distance., also the time-distance formula can also be used to calculate the distance an object travels in a certain amount of time.

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The option that describes the viable solution for the system is D.

all real number values, with x >=0 and y>=0​

Here we have the following system of inequalities:

-y ≤ 3x + 4

-3x - 3y ≤ 9

We can rewrite the second inequality to get:

-3y ≤ 9 + 3x

-y ≤ 9/3 + 3x/3

-y ≤  3 + x

Then our system of inequalities becomes:

-y ≤  3 + x

-y ≤ 3x + 4

So, as long as x and y are both positive or 0, the system is true (this is a rough estimation), but that is enough to conclude that the correct option is D.

all real number values, with x >=0 and y>=0​

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Answer:

No, A and B do not have the same solution.

To find the solution to A, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting x from both sides of the equation and then adding 2 to both sides. This gives us:

4x + 2 - x = 6 - x + 2

3x = 8

x = 8/3

To find the solution to B, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting 2 from both sides of the equation. This gives us:

5x + 2 - 2 = 6 - 2

5x = 4

x = 4/5

As we can see, the solutions to A and B are different, so A and B do not have the same solution. The solution to A is x = 8/3, and the solution to B is x = 4/5.

Step-by-step explanation:

Answer:

k=7

Step-by-step explanation:

k*3-9=12

3k-9=12

3k=12+9

3k=21

k=[tex]\frac{21}{3}[/tex] cross out 21 and 3

k=7

The slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.  

What is the slop of the line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the points (-8, 2) and (-11, 3),

Slop (m) = ?

The slope formula is:

m =  (y₂-y₁) ÷ (x₂-x₁)

so here,

m = (3 - 2) ÷ (-11 - (-8))

m = 1 ÷ (-3)

m = -1/3

Hence, the slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.  

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Answer:

Without knowing the values of the variables in the given expression, it is impossible to determine the value of the expression. In general, the expression is a combination of a number (A), two variables (b and c), and an exponent (2). The value of the expression will depend on the values of these variables and the operations that are performed on them. For example, if A=3, b=2, and c=4, then the value of the expression would be:

(3^2 * 2 * 4^2) - 5

Which is equal to 29. However, if the values of the variables were different, then the value of the expression would also be different. Therefore, it is impossible to determine the value of the expression without knowing the values of the variables.

Step-by-step explanation:

Answer:

(3^2 * 2 * 4^2) - 5, hope it helps.

A Rubik's Cube puzzle variation is called Square-1. You must be familiar with the fundamental notation used to denote the puzzle's various moves and positions in order to read the puzzle.

The face serves as the fundamental unit of notation in Square-1. A Square-1 puzzle has four faces, and each face is identified by a letter: U denotes the top face, D the bottom face, F the front face, and B the back face.

You must specify the face you are turning and the direction you are turning it in order to signify a move. For instance, a move like "U" turns the top face in a clockwise direction, whereas "U'" turns it in a counterclockwise direction.

You can adjust the puzzle with a few more complex moves in addition to the fundamental ones. For instance, the move "r" denotes moving the right face in a clockwise direction, while "r'" denotes turning it in a counterclockwise direction.

You can manipulate the problem to find the solution by combining these movements and employing them in various combinations. Reading and utilizing the notation for Square-1 requires effort, but with persistence and time, you may learn to solve the puzzle fast and effectively.

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Answer: 13.1

Step-by-step explanation:

(2.5)+(7*9)/(5) = 2.5+63/5 = 65.5/5 = 13.1

Answer:

13.1

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{m+(7 \cdot 9)}{n}[/tex]

To determine the value of the given expression when m = 2.5 and n = 5, substitute the given values into the expression and solve.

[tex]\begin{aligned}m=2.5, n=5 &\implies \dfrac{2.5+(7 \cdot 9)}{5}\\\\&\implies \dfrac{2.5+63}{5}\\\\&\implies \dfrac{65.5}{5}\\\\&\implies \dfrac{65.5 \cdot 2}{5 \cdot 2}\\\\&\implies \dfrac{131}{10}\\\\&\implies 13.1\end{aligned}[/tex]

The given events A and B are not independent events.

What is probability?

As there is no information given on the probability if selecting Box 1 and Box 2, thus we assume the event of selecting any of the boxes as equi-probable

P(A) = 1/2 * 3/11 + 1/2 * 2/3 = 31/66

P(B) = 1/2

P(A|B) = 2/3

Thus, we can see that P(A|B) is not equal to P(A)

So, the events A and B are not independent events.

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The original activity of the sample can be calculated using the equation A=A0e^(-kt), where A0 is the initial activity, k is the decay constant, and t is the elapsed time.

1. Identify the given values: Half-life (t1/2) = 3.8 days, Activity level (A) = 0.17 bq/L, and Elapsed time (t) = 5.0 days.

2. Calculate the decay constant (k) using the equation k = ln(2)/t1/2.

k = ln(2)/3.8 days

k = 0.1815

3. Calculate the original activity (A0) using the equation A0 = A/e^(-kt).

A0 = 0.17 bq/L/e^(-0.1815)

A0 = 0.21 bq/L

Therefore, the original activity of the sample was 0.21 bq/L.

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Answer:

420

Step-by-step explanation:

60 x 7 = 420

Answer: 420

Step-by-step explanation:

If you have 7 songs on each CD then you have 60 CD'S just take 7 and times it by 60.

Answer: Yes, he is correct

Step-by-step explanation:

[tex]\frac{1}{3}*\frac{2}{2}=\frac{2}{6} +\frac{1}{6}=\frac{3}{6}[/tex] The (*) means x or multiply

Answer: -4

Step-by-step explanation:

Answer:

88

Step-by-step explanation:

Answer: The speed was 4.1 MB/sec.

We first find the amount that was transferred within the first 125 seconds:

549-36.5=512.5

Now we divide this by 125, the number of seconds:

512.5/125 = 4.1

The speed of the transfer is 4.1 megabytes per second.

It took 235 seconds for the drive to be completely filled.

Step-by-step explanation:

The distance between the ships changing at 3.00 p.m is 12.2 mile/mph.

What do you mean by differentiation?

A derivative of a function with respect to an independent variable is what is referred to as differentiation. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.

A function of x would be y = f(x). Next, the formula for the rate of change of "y" per unit change in "x" is as follows:

dy / dx

It is given that ship A is 8 miles west of ship B and ship a is sailing north at 10mph and ship b is sailing south at 7mph

Let x and y be the initial position of the ships A and B

Let  x be the distance between A and x

y as the distance between B and x

z as the distance between A and B

Using pythagoras theorem,

[tex]z^{2} =x^{2} +y^{2}[/tex]

Differentiating both sides wrt t,

2z dz/dt = 2x dx/dt + 2y dy/dt

Divide the equation by 2

z dz/dt = dx/dt + dy/dt --- (1)

dx/dt = 10 mile/mph

dy/dt = 7 mile/mph

When t = 3 hours,

x = 30, y = 21 and

z = [tex]\sqrt{x^{2} +y^{2} }[/tex]

Substituting the values

z = √([tex]30^{2} +21^{2}[/tex])

z = √(900 + 441)

z = √1341 = 36.6

Substituting it in equation (1)

36.6 dz/dt =30×10+ 21×7

dz/dt = 447/36.6

dz/dt = 12.2 mile/mph

Therefore, the distance between the ships changing at 3.00 p.m is 12.2 mile/mph.

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By using percentage, it can be calculated that-

Sticker price of the car =  $14291.75

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage

For example 11% means [tex]\frac{11}{100}[/tex] . Here 11 is expressed as a fraction of 100

This is a word problem on percentage

Base price of the car = $15455.40

Cost of option = $585

Destination charge = $675

The dealer's cost is 85% of the base and 82% of the options

Sticker price of the car = [tex]\frac{85}{100}\times 15455 + \frac{82}{100} \times 585 + 675[/tex]

                                      = 13137.09 + 479.7 + 675

                                      = $14291.75

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The results obtained by using proportions to calculate are:

A) Valerie takes (4.995 ≅) 5 hours to drive to work on average after 10 days.

B) Valerie takes (9.4911 ≅) 9.5 hours to drive a total of 224.2 miles to work.

C) Valerie takes (20.98 ≅) 21 days to drive a total of 247.8 miles to work.

Proportions are the two ratios that are related by equality between them. I.e., w : x = y : z

We can rewrite them as

w/x = y/z or wz = xy

By using this relation, we can solve any of the variables.

It is given that,

Valerie takes, on average, 30 mins, to drive the 11.8 miles to her job every day.

So, from this, we can find the time taken by her for driving 1-mile using proportions.

I.e.,

for 11.8 miles → 30 min

then 1 mile → X min

⇒ 11.8 : 1 = 30 : X

⇒ 11.8X = 30

∴ X = 30/11.8 = 2.54 mins

A) The time it takes for her to drive to work on average after 10 days:

for 10 days, she drives 11.8 × 10 = 118 miles

So, the time taken for 118 miles × 2.54 min = 299.72 min

We know that for 60 min it is 1 hour, then for 299.72 min, it is 4.995 hours that is on average Valerie takes 5 hours to drive for 10 days.

B) The time it takes for her to drive a total of 224.2 miles to work:

We know that for 1 mile she takes 2.54 min, then for 224.2 miles, she takes 224.2 × 2.54 = 569.468 min

That means 569.468 min/60 = 9.49 hours ≅ 9.5 hours

Thus, she takes 9.5 hours to drive 224.2 miles.

C) The number of days she takes to drive a total of 247.8 miles to work:

We know that for 1 mile she takes 2.54 min, then for 247.8 miles, she takes 247.8 × 2.54 = 629.412 min

If she takes 30 min to drive per day, then the number of days for 629.412 min is

= 629.412 min/30 = 20.98 days ≅ 21 days.

Thus, she takes 21 days for driving 247.8 miles.

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Triangle ABC to triangle A'B'C' is enlarged by the dilation.

Dilation is the process of enlarging a shape, figure, or line. In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.

The query leads us to believe that:

Triangle A'B'C' is created by enlarging triangle ABC.

The diagram also demonstrates that triangle A'B'C"s side lengths are longer than ABC's.

The dilation is hence an augmentation

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Answer:

The dilation is an enlargement because the image, triangle A'B'C', is larger than the pre-image, triangle ABC.

Step-by-step explanation:

edge 2023

1) 20 more ants there are in ant colony A than in ant colony B

2) The growth rate of ant colony A is 12%

3) The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

1)   colony A :

  Number of ants = 210

    colony B:

   Number of ants = 190 ( from the graph )

Find the difference: 210 - 190 = 20 ants

So, 20 more ants there are in ant colony A than in ant colony B

2 )  Exponential growth function: y= a(b)^x

b= 1+ r , r is the growth rate as decimal

We have a(x)=210(1.12)^x

b= 1.12 = 1+0.12

So, r= 0.12 = 12%

3 )  (x,y) = (1,220)

y= a(b)^x  

=> 220 = 190(b)^1

=> b= 220/190 = 1.15

b= 1+r

r= b - 1 = 1.15 - 1 = 0.15 = 15%

The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

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1) 20 more ants there are in ant colony A than in ant colony B

2) The growth rate of ant colony A is 12%

3) The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

1)   colony A :

Number of ants = 210

colony B:

Number of ants = 190 ( from the graph )

Find the difference: 210 - 190 = 20 ants

So, 20 more ants there are in ant colony A than in ant colony B

2)  Exponential growth function: y= a(b)^x

b= 1+ r , r is the growth rate as decimal

We have a(x)=210(1.12)^x

b= 1.12 = 1+0.12

So, r= 0.12 = 12%

3) (x,y) = (1,220)

y= a(b)^x  

=> 220 = 190(b)^1

=> b= 220/190 = 1.15

b= 1+r

r= b - 1 = 1.15 - 1 = 0.15 = 15%

The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

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Answer:

A ; B ; D

Step-by-step explanation:

5t + 9

for commutative property

9 + 5t

5t = 5 x t

5 · t + 9

(5 x t) + 9

Answer: It's either 60 or 232

Note: I'm not that good, in problem solving but i thought i can try.

Message: If this helps, let me know by giving me a thanks! :)

Using the provided equation and derivative for the rate, The initial value is 100 and the rate is 40.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

y= 40x + 100

x=0 for initial value, We get y=100.

apply derivative on y with respect to x , We get

[tex]\frac {dy}{dx} =40[/tex]

rate =40

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