The total number of gallons of water in the tank, T, after w weeks can be represented by the equation T = -15w + 275. Which of the following is the best interpretation of the number 275 in the equation?

The expression that can be use to represent the amount owned on rental is 0.1x + 25y

Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.

The expression that can be use to represent the amount owned on rental can be represented as follows:

let

x = number of miles driven

y = number of days

Let's convert cent to dollars

100 cents  = 1 dollars

10 cents = ?

cross multiply

amount in dollars = 10 / 100 = 0.1 dollars

Therefore,

the expression = 0.1x + 25y

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16

Step-by-step explanation:

square root of 121 is 11

cube root of 125 is 5

11+5=16

therefore the answer is 16

Answer:

[tex]A=20 units^2[/tex]

Step-by-step explanation:

I would separate out the shape into two equal right triangles over a square.  The total area can then be found by adding these areas together:

[tex]A_t=2A_\Delta +A_s\\A_t=2(\frac{1}{2}bh)+(s)^2\\b=2 units\\h=2units\\s=4units\\A_t=2[\frac{1}{2}(2units)(2units)]+(4units)^2\\A_t=4units^2+16units^2\\A_t=20units^2[/tex]

Answer:

----------------------------

If the given function is f(x), then rules of translation by b units are:

Our function and its image are:

Therefore we have translation left by 3 units.

Correct choice is D.

Answer:

Translate each point of the graph of h(x) 3 units left.

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

Given functions:

[tex]h(x)= \log_6 x[/tex]

[tex]m(x)= \log_6(x+3)[/tex]

As m(x) = h(x+3),  to graph the function m(x), translate the function h(x) 3 units left.

Answer:

15095.39

Step-by-step explanation:

[tex]13000(1+(0.03)/4)^{(4)(5)} \approx 15095.39[/tex]

Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex] is 2020 and [tex]\int^{70}_{10}v(t)dt[/tex] means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

From the given question,

An initial height of 0 feet at time t=0 seconds.

The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.

(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate [tex]\int^{70}_{10}v(t)dt[/tex].

[tex]\int^{70}_{10}v(t)dt[/tex]

A midpoint Riemann sum with 3 sub intervals so, n=3

∆t= (70-10)/3

∆t = 60/3

∆t = 20

Intervals: (10, 30), (30,50), (50,70)

Midpoint:      20        40         60

Midpoint Riemann Sum

[tex]\int^{70}_{10}v(t)dt[/tex] = ∆t[v(20+v(40)+v(60)]

From the table

[tex]\int^{70}_{10}v(t)dt[/tex] = 20[22+35+44]

[tex]\int^{70}_{10}v(t)dt[/tex] = 20*101

[tex]\int^{70}_{10}v(t)dt[/tex] = 2020

(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight [tex]\int^{70}_{10}v(t)dt[/tex].

It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.

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The domain when the maximum number of people allowed in the movie theater is 60 people would be: B. 0 ≤ x ≤ 60.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Since the maximum number of people that are allowed in the movie theater is 60 people, we can logically deduce that the input values (x-values) for its function is less than or equal to 60. Therefore, the domain of the function on this graph is given by:

Domain = [0, 60]

Domain = 0 ≤ x ≤ 60.

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Complete Question:

The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.

40 ≤ y ≤ 160

0 ≤ x ≤ 60

40 ≤ x ≤ 160

0 ≤ y ≤ 60

Answer:

the answer is 0 is less than or equal to x which is less than or equal to 60

Step-by-step explanation:

Domain is the x value

Since the max amount of people is 60, and people is x value the answer i put above is a reasonable domain.

Hope this helps!

By using the properties of parallel lines, it can be proved that

[tex]\angle[/tex]1 [tex]\cong \angle[/tex]8 by the substitution property.

What are parallel lines?

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Given that e || f and g is a transversal,

We know that

[tex]\angle[/tex]4 [tex]\cong \angle[/tex]5 [by the alternate interior angles theorem]

We also know that

[tex]\angle[/tex]1 [tex]\cong \angle[/tex]4 and [tex]\angle[/tex]8 [tex]\cong \angle[/tex]5 by the vertically opposite angle

So [tex]\angle[/tex]1 [tex]\cong \angle[/tex]8 by the substitution property.

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Complete Question

Given that e parallel f and g is a transversal, we know that angle 4 is-congruent-to angle 5 by the alternate interior angles theorem. we also know that angle 1 is-congruent-to angle 4 and angle 5 is-congruent-to angle 8 by the ________. therefore, angle 1 is-congruent-to angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

Answer:

15095.39

Step-by-step explanation:

[tex]13000(1+(0.03)/4)^{(4)(5)} \approx 15095.39[/tex]

Yes it is reasonable to save that the farm’s glass recycling could pay for their fuel oil.

Recycling is the process of turning trash into new products and materials. This idea frequently takes the recovery of energy from waste materials into account. The capacity of a substance to regain the qualities it had in its initial state determines how recyclable it is.

Both the environment and your community may benefit from recycling. It protects natural resources, minimizes greenhouse gas emissions, cleans up the air and water, and conserves energy.

In this question, there is a benefit to recycling. That is, the farm would be able to save more fuel. Hence it pays for the costs of fuel.

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If the value of the car is depreciates 20% at the end of the first year and 12% at the end of every year after the first year, the value of the car after 3 years will be $15488

The cost of the car = $25000

The percentage of depreciate at the end of the first year = 20%

Then the new cost  will be

= 25000 - (25000×20/100)

= 25000 - 5000

= $20000

For the next two years the value will depreciates by 12%

Then the final value = [tex]20000(1-\frac{12}{100})^2[/tex]

= 20000 × 0.7744

= $15488

Hence, the value of the car at the end of the third year is $15488

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Answer:

b = amount of boys

g = amount of girls

f = amount spent in first intermission

s = amount spent in second intermission

c = cake cost

x = coke cost

b = 16

g = 14

f = 76

s = 74

c = 2

x = 3

Step-by-step explanation:

cg + xb = f

xg + cb = s

f - 2 = s

b + g = 30

b > g

To solve for the variables, you just have to guess and check.

(2 x 14) + (3 x 16) = 76

(3 x 14) + (2 x 16) = 74

76 - 74 = 2

16 + 14 = 30

16 > 14

If the inequality which can be used to determine x is 7.25 + 23.25x ≤ 170 and the number of people who can go the amusement park is 7

The maximum amount that he can spend = $170

The cost of the parking ticket = $7.25

The cost of the ticket including tax = $23.25 per person

Then the inequality will be

7.25 + 23.25x ≤ 170

Subtract both side of the inequality by 7.25

23.25x ≤ 162.75

Divide both side of the inequality by 23.25

23.25x / 23.25 ≤ 162.75/23.25

x ≤ 7.006

Hence, the inequality is 7.25 + 23.25x ≤ 170 and 7 people can go to the amusement park

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Answer:

-------------------------------

Find y:

Answer:

cost of television: $924

Cost of DVD player: $308

Step-by-step explanation:

we make a system of equations

T- television

D- dvd played

t+d=1232

3d=t

3d+d=1232

4d=1232

/4.  /4

d=308

Dvd player costs $308

Now to find television

3(308)=t

924=t

Television costs $924

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The speed of Buddy is 2 miles per hour

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

let the speed of Andy  be x so that Buddy speed when Andy loses 3 miles per hour is  1/2(x-3)

distance between them is 48 miles, time between them is 4 hours

so speed between them is 48/4 = 12 miles per hour

so that,

x + 1/2(x - 3) = 12

multiply through by 2

2x + x -3 = 24

3x = 24 -3

3x = 21

x = 21/3

x = 7 miles per hour

Buddy's speed = 1/2(7 - 3) = 2 miles per hour

In conclusion Buddy's speed is 2miles per hour

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The amounts of each solution needed are given as follows:

The percentage of paint when 5 liters of the thinned solution are added is of:

62%.

The variables to the system of equations are given as follows:

The painted needs 20 liters, hence:

x + y = 20.

The solution is 65%, hence:

0.5x + 0.75y = 0.65 x 20

0.5x + 0.75y = 13.

From the first equation, we have that:

x = 20 - y.

Hence the amount of liters of the 75% solution is obtained as follows:

0.5(20 - y) + 0.75y = 13.

0.25y = 3

y = 3/0.25

y = 12 liters.

Then the amount of liters of the 50% solution is of:

x = 20 - y = 20 - 12 = 8 liters.

When 5 liters of the 50% solutions are added, there would be 13 liters of the 50% solution, then the percentage would be of:

P = (0.5 x 13 + 0.75 x 12)/25 = 0.62 = 62%.

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Answer:

[tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]

Step-by-step explanation:

when a line is parallel the slope is the same for both

y=mx+b is slope intercept form where m is slope and b is intercept

we know the slope is 2/3 so to find b we just fill it in with coordinates

-2=2/3(-5)+b

-2=-10/3+b

+10/3 +10/3

4/3=b

y=2/3x+4/3

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The value of each small coin(p) is 2.

The value of each large coin(p+5) is 7.

What is an equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation.

It is given that the value of each small coin is denoted as 'p' and large coins worth extra 5 points.

then, the value of each large coin will be ' p+5 '

she collected 102 coins out of which 100 coins are collected as small coins, So the rest 2 coins will be large coins.

∴ Total points value = (value of each small coin × small coins) + (value of large coins × large coins)

                         214 = [p × 100] + [(p+5) × 2]

                         214 = 100p + 2p + 10

                         214 - 10 = 102p

                         204 = 102p

                         p = 204/102 = 2.

Hence, Value of each small coin is 2 and value of each large coin is 7 i.e. ( 2+5).

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The percentage of her commission from the sales was 2.2%

percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Commission = $58,399

sales = $2,654,500

Percentage commission = [tex]\frac{commission}{sales}[/tex] x 100%

Percentage commission = [tex]\frac{58399}{2654500}[/tex] x 100%

Percentage commission = 2.2%

In conclusion, the percentage commission is 2.2%

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Answer:

First option

Step-by-step explanation:

Hope this helps

Answer:

y = 2x + 1

Step-by-step explanation:

The slope intercept form is represented in: y=mx+b

m = slope

b = y-intercept

let's find slope:

(1, 3)(-3, -5)

m = -5 - 3 / -3 - 1 = - 8 / -4 = 2

Therefore,

let's find b using (1, 3)

y = 2x + b

3 = 2 + b

b = 1

y = 2x + 1

When Mandy tossed a fistful of silver coins into the air, then picked up the 23 coins that landed heads up, this isn't a random sample of the coins.

In statistics, a simple random sample is a subset of individuals chosen at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.

A simple random sample is a subset of a population chosen at random. This sampling method gives each member of the population an exact equal chance of being chosen, reducing the risk of selection bias.

In this case, Mandy only picked heads, this isn't a random sample since it's biased.

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The statement about the original and transformed triangles that must be true is The triangles are congruent.

Triangles are congruent when they have the same size and shape but face opposite directions. Triangles do not change size or shape as a result of translation and rotation.

This means that if a triangle is translated and then reflected, the result will still be congruent with the first triangle. If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. So two triangles are congruent if all of their sides are the same—side, side, side.

In conclusion, the correct option is B.

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main answer:  line integral  by the two following methods [tex]xy dx x^{2} dy c[/tex]

supporting answer: A line integral in Calculus is an integral in which the function to be integrated is evaluated along a curve. A path integral, curve integral, or curvilinear integral are all names for a line integral. This article will go over the definition of the line integral, formulas, examples, and how to use line integrals in real life

body of the answer : given

line integral xy dx x^{2} dy c

c is counter clockwise

according to greens theorem

∫ₐpdx+qdy

∫∫ₓdq/dx-dp/dq

we evaluate the 1st line integral from (0,0) to (0,4)

an equation  of straight  line joining (0,0) and (0,4)in the xy plane is y=4

l₁=∫⁰₄ x(4)dx+ x²(4)=∫⁰₄ 4xdx+4x²

=[4.x²/2+4x³/3]₄⁰

=4(16)/2+4(64)/3

=32+256/3

=117

we evalute second integral from (0,4)to (3,0)

an equation of straight line joining (0,4)and(3,0)in xy plain is x=3 dx=0

the second line integral now becomes

l₂=∫³₀ (3)y(0)+3²dy

=∫³₀ 9dy

=27

we now evaluate the third line integral from  (3,0) to (3,4)

an equation  of straight line joining (3,0)and (3,4) in xy plain is y=4,dy=0

the third integral now becomes,

l₃=∫³₃ x(0)dx+ x²(4)

=∫³₃ 4x²

=4*9=36

36-36=0

now evalute the 4th line integral from (3,4) to(0,0)

an equation of straight line joining from (3,4) to (0,0) in xy plane is x=0

∫₄⁰(3)y(0)+ 9dy

∫⁰₄ 9dy

=9*4=36

sum of all line integral=36+27+0+117

=180

final answer:therefore ∫ₐ pdx +qdy

∫∫ₓdq/dx-dp/dq=180

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Line integral by the two following methods  is 180

What is integral calculus?

A line integral in Calculus is an integral in which the function to be integrated is evaluated along a curve. A path integral, curve integral, or curvilinear integral are all names for a line integral. This article will go over the definition of the line integral, formulas, examples, and how to use line integrals in real life

Given

line integral xy dx x^{2} dy c

c is counter clockwise

According to greens theorem

∫ₐpdx+qdy

∫∫ₓdq/dx-dp/dq

We evaluate the 1st line integral from (0,0) to (0,4) an equation of straight  line joining (0,0) and (0,4)in the xy plane is y=4

l₁=∫⁰₄ x(4)dx+ x²(4)=∫⁰₄ 4xdx+4x²

=[4.x²/2+4x³/3]₄⁰

=4(16)/2+4(64)/3

=32+256/3

=117

We evaluate second integral from (0,4) to (3,0)

an equation of straight line joining (0,4) and (3,0) in xy plain is x=3 dx=0

the second line integral now becomes

l₂=∫³₀ (3)y(0)+3²dy

=∫³₀ 9dy

=27

We now evaluate the third line integral from  (3,0) to (3,4)

an equation  of straight line joining (3,0)and (3,4) in xy plain is y=4,dy=0

the third integral now becomes,

l₃=∫³₃ x(0)dx+ x²(4)

=∫³₃ 4x²

=4*9=36

36-36=0

Now evaluate the 4th line integral from (3,4) to(0,0)

an equation of straight line joining from (3,4) to (0,0) in xy plane is x=0

∫₄⁰(3)y(0)+ 9dy

∫⁰₄ 9dy

=9*4=36

Sum of all line integral=36+27+0+117

=180

Therefore ∫ₐ pdx +qdy

∫∫ₓdq/dx-dp/dq=180

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The domain of the relation is {-9, 1, 3, 8, 9}

All the values that go into a relation or a function are called the domain.

Given is a relation, (-3, -7), (8, -7), (1, 10), (-9, -8) and (9, -6)

The domain of a function or relation is the set of all possible independent values the relation can take.

Hence, the domain of the relation is {-9, 1, 3, 8, 9}

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Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

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Total kinetic energy that is generated will be 2025 joules

What is kinetic energy?

The K.E. of an object is that the energy that it possesses because of its motion. it's outlined because the work required to accelerate a body of a given mass from rest to its expressed velocity.

Main body:

According to question :

mass = 2 kg

velocity = 45 m/s

formula for kinetic energy = (1/2) mv²

substituting these values in formula,

K.E. = (1/2) 2* 45²

K.E. = 45²

K.E. = 2025 joules.

Hence kinetic energy generated is 2025 joules.

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a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

Answer:

9a(-3a² + a - 5)