Ellis is going on a tour that costs $65 while on vacation. He was told to bring $118 to pay for the cost of the tour and dinner. Which of the following inequalities represents the money Ellis can spend on dinner?

A. $118 + d < $65
B. $118 + d > $65
C. $65 + d > $118
D. $65 + d < $118

Answer:

Step-by-step explanation:

Identity used:  (a +b)³ = a³ + b³ + 3ab(a +b)

       p + q = -2  ------------------(I)

Both sides take cube,

        (p +q)³ = (-2)³          

a = p and b =q

  p³ + q³ + 3pq(p +q) = -8

  p³ + q³ + 3pq*(-2)   = - 8        {From (I)}

  p³ + q³  - 6pq         = -8

                  p³ + q³    = -8 + 6pq

             p³ + q³   + 8 = 6pq

Hence, proved.

By using the midpoint approach, the price elasticity of demand between each of the given prices are:

The price elasticity of demand measures the responsiveness of the quantity demanded by a consumer with respect to a specific change in price of the product, all things being equal (ceteris paribus).

By using the midpoint approach, the price elasticity of demand between each of the given prices is given by:

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (15 - 5)/[(15 + 5)/2]/(25 - 30)/[(25 + 30)/2]

Price elasticity of demand = 1/-0.1818

Price elasticity of demand = 5.50.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (25 - 15)/[(25 + 15)/2]/(20 - 25)/[(20 + 25)/2]

Price elasticity of demand = 0.5/-0.2222

Price elasticity of demand = 2.25.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (35 - 25)/[(35 + 25)/2]/(15 - 20)/[(15 + 20)/2]

Price elasticity of demand = 0.33/-0.2857

Price elasticity of demand = 1.17.

Price elasticity of demand = (Q₂ - Q₁)/[(Q₂ + Q₁)/2]/(P₂ - P₁)/[(P₂ + P₁)/2]

Price elasticity of demand = (45 - 35)/[(45 + 35)/2]/(10 - 15)/[(10 + 15)/2]

Price elasticity of demand = 0.25/-0.4

Price elasticity of demand = 0.63.

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Answer:

See below ~

Step-by-step explanation:

⇒ t represents the years after 1992

⇒ So, in 1992, t = 0

⇒ Apply in the formula

⇒ n(0) = 89e^(0.02 × 0)

⇒ n(0) = 89e⁰

⇒ n(0) = 89,000,000

The rat population in 1992 was 89,000,000.

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

⇒ Number of years after 1992 : 2003 - 1992 = 11

⇒ Substitute for t in the formula

⇒ n(11) = 89e^(0.02 × 11)

⇒ n(11) = 89e^(0.22)

⇒ n(11) = 89 × 1.24607673

⇒ n(11) = 110,900,829 rats

The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.

Answer:

(a) 89,000,000 rats

(b) 110,900,829 rats

Explanation:

Given equation:

To find the initial population (1992):

insert t = 0

To find the rat population in 2003 (after 11 years):

insert t = 11

Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

Answer:

10 1/2

Step-by-step explanation:

divide 7/10 which is 0.7 then multiply that by 5 which is 3.5

then divide 4/10 which is 0.4 then multiply that by 5 which is 2, but add 5 which is 7.

then combine all of that together which is 3.5+7= 10.5

then convert that into a fraction which is 10 1/2

Answer:

1347 hours

Step-by-step explanation:

Assuming the income is net income (total after taxes etc.):

To calculate the number of hours to be worked to save enough to buy the car, divide the cost of the car by hourly net income:

[tex]\begin{aligned}\implies \textsf{Number of hours to work} & = \dfrac{\textsf{Cost of car}}{\textsf{hourly net income}}\\\\& = \sf \dfrac{17500}{13}\\\\& = \sf 1346.1538...\end{aligned}[/tex]

We have to round the number up to 1347 hours, as only $17,498 will be saved if 1346 hours are worked.

The average working week is approximately 40 hours, therefore to calculate how many weeks it would take to earn enough money to purchase the car, divide the number of hours by 40:

⇒ 1347 ÷ 40 = 33.675

So it would take 34 weeks, working an average of 40 hours a week and not spending any of the money earned, to save enough to purchase the car.

Total hours

Round to the next whole instead of nearest whole to avoid depicit

In most of the countries the average working hours per week is

Total weeks

Answer:

Negative thirty

Step-by-step explanation:

Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are having two equations:-

2x - 4y = 5

6x - 3y=10

When we multiply the first equation by -3 the equation will become as follows:-

-6x  +  12y = - 15

6x   -  3y  =   10

By adding both the equations one variable will be eliminated:-

9y = - 5

Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.

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Answer:

[tex]x = - 3 \: and \: y = - 11[/tex]

Step-by-step explanation:

L

[tex]since \: y = 2x - 5(equation \: 1) \: \\ [/tex]

[tex]substitute \: for \: y \: in \: equation \: 2 \: (6x + 7 = y)[/tex]

[tex]6x + 7 = y \\ 6x + 7 = 2x - 5 \\ collect \: like \: terms \\ 6x - 2x = - 5 - 7 \\ 4x = - 12 \\ x = \frac{ - 12}{4} \\ x = - 3[/tex]

[tex]substitute \: for \: x in \: equation \: 1[/tex]

[tex]y = 2x - 5 \\ y = 2( - 3) - 5 \\ y = - 6 - 5 \\ y = - 11[/tex]

Answer:

[tex]y = 2.x = \frac{1}{11} [/tex]

[tex] \binom{x - 56x + 7 = y}{y = 2} [/tex]

_______________________

1. Substitute y = 2 :

[tex](x - 56x + 7 = 2)[/tex]

2. Simplify :

[tex]( - 55x + 7 = 2)[/tex]

3. Isolate x for [tex]( - 55x + 7 = 2) : x = \frac{1}{11} [/tex]

4. The solution of the system of equations are :

[tex]y = 2.x = \frac{1}{11} [/tex]

Answer:

1st mechanic:20hours

2ndmechanic:15hours

Step-by-step explanation:

1stmechanic:20hours=20x95

                                   =$1900

2nd mechanic:15hours=15x110

                                     =$1650

total=$1900+$1650

       =$3550

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

Exponential decay obeys the equation

[tex]m(t) = m_0 e^{-kt}[/tex]

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

[tex]m(t) = m_0 e^{-kt}[/tex]

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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The value of the length DF is 17

The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.

So, we have:

AB = AD

AC = A F

BC = DF

Given that BC = 17;

The equation BC = DF becomes

17 = DF

Rewrite as:

DF = 17

Hence, the value of the length DF is 17

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Answer:

See below

Step-by-step explanation:

Interest   3%   in decimal form is  .03

  interest in ONE year    7000 * .03

         interest in SEVEN years   7000 * .07 * 7

           this is added to the original deposit of 7000

              to become   7000 + 7000 * .03 * 7

                                        or  7000 ( 1 + .03*7 )

                                              or   7000 ( 1.21 ) = $ 8470

IF the interest is compounded

   the money in the account will be    7000 ( 1+.03)^7  

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

The answer is A

[tex]y = - x - 6 \\ 0 = - x - 6 \\ x = - 6[/tex]

so x intercept : (-6,0)

and slope is negative

Hope it helps

Please give brainliest

The equation of line which a slope is -1 and an x-intercept of (-6,0) will be;

⇒ y = - x - 6

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The slope of the line = - 1

And, The x-intercept = (- 6, 0)

Now,

Let the equation of line;

⇒ y = - x - 6

Slope (m) = dy/dx = - 1

And, The x - intercept is find as;

Put y = 0;

⇒ y = - x - 6

⇒ 0 = - x - 6

⇒ x = - 6

Thus, The correct equation is,

⇒ y = - x - 6

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Any proper CDF [tex]F(x)[/tex] has the properties

• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]

• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]

and so

[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]

[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]

Answer:

4 pints

Step-by-step explanation:

Therefore each can would contain 8/2 =  4 pints

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Please feel free to comment, ask questions, give feedback, or correct me if I am wrong!

Have a great day!

:)

Answer:

3-x is the inverse of f(x)=x-3

Answer:

wait I will edit and answer it in a few minutes

[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]

Now, since the base on both sides are equal, therefore their exponents are equal as well ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x} = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{6}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{1}{2} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:x = 0.5[/tex]

Hope you got the required Answer ~

Answer:

a

x

2

+

b

x

+

c

=

0

the two roots of the equation take the form

x

1

,

2

=

−

b

±

√

b

2

−

4

a

c

2

a

So, start by adding

−

5

to both sides of the equation to get

2

x

2

+

x

−

5

=

5

−

5

2

x

2

+

x

−

5

=

0

Notice that you have

a

=

2

,

b

=

1

, and

c

=

−

5

. This means that the two solutions will be

x

1

,

2

=

−

1

±

√

1

2

−

4

⋅

2

⋅

(

−

5

)

2

⋅

2

x

1

,

2

=

−

1

±

√

41

4

You can simplify this if you want to get

x

1

=

−

1

+

√

41

4

≅

1.35078

and

x

2

=

−

1

−

√

41

4

≅

−

1.85078

Answer:

(2x-2)=

     +2 =+2

(2x)=2

----------

    2

x= 1

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

(x+5)=

   -5=-5

x= -5

Step-by-step explanation:

You just need to separate the variable from the numbers

To solve the theorem, we will  take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides

Pythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides

For instance, let;

According to the theorem above, mathematically;

c² = a² + b²

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Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

Answer:

Hi! I think you are referring to the Pythagorean Theorem.

Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.

The formula is a squared + b squared = c squared

If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:

3 squared + 4 squared = x squared

(Let x =  the longer side)

3 squared = 9

4 squared = 16

9+16 = x squared

25 = x squared

x =  5

So there you go, that's the Pythagorean theorem.

Let me know if this helped!

Answer:

a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Step-by-step explanation:

The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

55/16 cups or 3.4375 cups

Step-by-step explanation:

there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes

Answer:

A

Step-by-step explanation:

tan60=opp/adj

tan60=15/x

15tan60=x

25.98=x (when you calculate 15 root 3 it is the same number)

Answer:

16x^6(3x^5)

48x^11

Answer:

C)

Step-by-step explanation:

f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]  ,  a=8, b= - 16, c= - 15

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]