Nick estimates that 50% of his income goes toward living expenses. Of the rest 50% goes to paying for his car and 25% of what is left goes to. his other expenses. IF nick has $300 remaining at the end of the month how much does he earn?

For item a, the linear functions are given as follows:

1. y = 1.5x.

2. y = 0.5x - 1.

3. y = -0.5x + 1.

4. y = -1.5x - 1.

For item B, we have that:

1. The functions are:

a. y = 2x + 3.

b. y = 0.5x - 1.

2. The unit rates(slopes) are:

a. 2

b. 0.5.

A linear function is modeled by:

y = mx + b

In which:

In graph 1, the function goes through (0,0), hence b = 0, and through point (2,3), hence the slope is:

m = (3 - 0)/(2 - 0) = 3/2 = 1.5.

Hence the function is:

y = 1.5x.

In graph 2, the function goes through (0,-1), hence b = -1, and through point (2,0), hence the slope is:

m = (0 - (-1))/(2 - 0) = 1/2 = 0.5.

Hence the function is:

y = 0.5x - 1.

In graph 3, the function goes through (0,1), hence b = 1, and through point (2,0), hence the slope is:

m = (0 - 1)/(2 - 0) = -1/2 = -0.5.

Hence the function is:

y = -0.5x + 1.

In graph 4, the function goes through (0,-1), hence b = -1, and through point (2,-4), hence the slope is:

m = (-1 - (-4))/(0 - 2) = -3/2 = -1.5.

Hence the function is:

y = -1.5x - 1.

In table a, the function goes through (0,3), hence b = 3, and through point (1,5), hence the slope is:

m = (5 - 3)/(1 - 0) = 2.

Hence:

y = 2x + 3.

The unit rate, which is the slope, is of 2.

For table b, the function goes through (2,0) and (6,2), hence the slope is:

m = (2 - 0)/(6 - 2) = 1/2 = 0.5.

Hence:

y = 0.5x + b.

When x = 2, y = 0, hence we can find b as follows.

0 = 0.5(2) + b

b = -1.

Thus:

y = 0.5x - 1.

The unit rate is of 0.5.

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Answer:

there is no mode

Step-by-step explanation:

Using the above exponent rule,  the value of t in the given equality [tex]5^3/ 5^9 = 5^t[/tex] will be t = -6.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]

WE need to find the value of t in the given equality 5^3/ 5^9 = 5^t

Using the above exponent rule, we get

[tex]5^{3 -9 }= 5^t\\\\5^{-6}= 5^t[/tex]

Therefore, compairing both the side we get;

t = -6.

Hence the value of t in the given equality[tex]5^3/ 5^9 = 5^t[/tex]will be t = -6.

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Answer:

250%

Step-by-step explanation:

divide both sides by 0. 4 so A/0.4=B then rearrange so then its (1/0.4)xA=B then divide so its 2.5A=B and obviously 2.5= 250/100 so that makes the answer 250%

is that better?

No The extraneous solution of this equation

The given equation is

    [tex]\sqrt{3x + 13}[/tex] - 5 = x

    [tex]\sqrt{3x + 13 }[/tex] = x + 5

We have to find the value of x, so we need to square both sides of the equation

   [tex](\sqrt{3x + 13} )^{2}[/tex] = [tex](x + 5)^{2}[/tex]

  3x + 13 = [tex]x^{2}[/tex] + 10x + 25

  [tex]x^{2}[/tex] + 7x + 12 = 0

 [tex]x^{2}[/tex] +  4x + 3x + 12= 0

x( x + 4) + 3( x + 4) =0

(x + 4) ( x + 3 ) = 0

x = - 3, -4

To find the value of the extraneous solution we need to put both the value of x in the equation

x = -3

[tex]\sqrt{(3 * -3) + 13}[/tex] - 5 = -3

[tex]\sqrt{-9 + 13}[/tex] - 5 = -3

[tex]\sqrt{4}[/tex] - 5 = -3

2 - 5 = -3

-3 = -3

Now

x = -4

[tex]\sqrt{(3 * -4 ) + 13}[/tex] - 5= -4

[tex]\sqrt{-12 +13}[/tex] - 5 = -4

[tex]\sqrt{1}[/tex] - 5 = -4

-4 = -4

Hence we get that the value of x is the solution to the equation.

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Answer: A $14 dollar meal with a 20% tip would be $16.80. The tip would be $2.80.

Step-by-step explanation:

People generally tip 15-20% of the bill. To calculate the tip multiply the total check by 1 plus the decimal percentage tip you'd like to leave. If you wanted to leave a 20% tip, you would add 1 to 0.20 to get 1.20. Multiply 14 by 1.20 to get the total amount you'd leave including the tip which would be $16.80.

Hope this helps!

It will take the reporter 7 minutes to type the document

The reporter can type 215 words in one minute

The reporter wants to type a document that is 1505 words long

The amount of time it will take the reporter to type a document that is 1505 long can be calculated as follows

215 = 1

1505 = x

cross multiply both sides to get the value of x

215x= 1505

divide both sides by the coefficient of x which is 215

215x/215 = 1505/215

x= 7

Hence the reporter will use 7 minutes to type out the 1505 word document

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The inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

We are given the function:

f (x) = 15 - 3 x

Now, we need to find the inverse of the function.

For this, first we write the function as:

y = 15 - 3 x

Now, we will find the function in terms of x

3 x + y = 15

3 x = 15 - y

x = 5 - y/3

So, the inverse will become:

f ⁻¹ (x) = 5 - x/3

g (x) = 5 - x/3

Now, for one one function:

g (x₁) = g (x₂)

5 - x₁/3 = 5 - x₂/3

- x₁ / 3  = - x₂ / 3

x₁ = x₂

So, it is one - one.

So, the inverse is also a function as every element of x only has one image in y.

Therefore, the inverse of the function f (x) = 15 - 3 x is f ⁻¹ (x) = 5 - x/3 which is also a function.

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They travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

This is solved by unitary method.

Distance travelled by (4 and 2/3) or 14/3 gallons of gas = 143 miles.

So, we get that for 1 gallon of gas it will be given as:

Distance travelled by 1 gallon of gas = 143 miles × 3/14

= 30.64 miles

So, they travel at 30.64 miles per gallon of gas when they drove 143 miles and used 4 2/3 gallons of gas.

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The image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)

To plot the image of point Q under the translation we need given information.

The translation is given as:

(x,y) -> (x+1,y+2)

The point Q is located at

(-4,4)

So, the image would be:

(x,y) -> (-4+1,4+2)

Evaluate

(x,y) -> (-3,6)

Hence, the image of point Q under the translation at (x,y) -> (x+1,y+2) is (-3,6)

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Answer: -5/8

Step-by-step explanation:

The intensity level of the earthquake was compared to the intensity level of each earthquake below

1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.

2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.

3) The earthquake at New Madrid was of greater intensity than earthquake at  Charlottesville.

4) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.

In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values.

The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle.

A typical use of the greater than sign is to compare two values, where the first  is greater than the second, or one is greater than the other.

The greater than sign is an approximation of a closing square bracket.

Hence, The magnitude of the earthquake was compared to each earthquake's magnitude above.

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The question is incomplete. The complete question is

In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.

1. magnitude 7.7 in San Francisco, California, in 1906

2. magnitude 9.5 in Valdivia, Chile, in 1960

3. magnitude 3.2 in Charlottesville, in 2001

4. magnitude 6.9 in Kobe, Japan, in 1995

Answer:

Step-by-step explanation:

[tex]\sqrt{25+9}[/tex] =

[tex]\sqrt{34}[/tex] =

≈5,83095    (5,8309518948453)

The lifetime cost of Ellen's dishwater is $1,030.44

What is Number system?

A system of writing to express the number is called number system.

Given that;

Cost of dishwasher before sales tax 9.22% is = $315

And, Sales tax = 9.22%

Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043

And, Average of 10 times per week for the next 6 years before replacing it.

Since, There are 52 weeks in a year.

So, Average uses is calculated as,

10  * 52  * 6 = 3120

Since, cost for water = $0.09

Cost for electricity = $0.13

Total cost per uses = $0.22

Hence, Cost of uses = 0.22 * 3120 = $686.40

Now, Purchase cost = $344.043

And, Cost of uses =  $686.40

Hence, Lifetime cost =  $344.043 + $686.40 = $1,030.443

So, The lifetime cost of Ellen's dishwater is $1,030.44.

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Answer:

27^4

2.74*10^2

4.27*10^2

Step-by-step explanation:

in exponential notation the number is expressed like this.

Answer:

Step-by-step explanation:

The given function → f(x) = x⁵ - 3x³ is odd in nature.

A function f(x) is even if f(−x) = f(x) and is odd if f(−x) = − f(x).

Given is the function -

f(x) = x⁵ - 3x³

In order to find f(-x), replace 'x' by '-x' in f(x) -

f(x) = x⁵ - 3x³

f(-x) = (-x)⁵ - 3(-x)³

f(-x) =  - x⁵ + 3x³

f(-x) =  3x³ -  x⁵

Now -

f(-x) ≠ f(x)

So, it is not a even function.

In order to find '-f(x)', multiply f(x) by '-1' -

f(x) = x⁵ - 3x³

- f(x) = - (x⁵ - 3x³) = - x⁵ + 3x³ = 3x³ - x⁵

Now -

f(-x) = -f(x)

So, it is a odd function.

Therefore, the given function → f(x) = x⁵ - 3x³ is odd in nature.

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Answer:

y1=-4/3, y2=1/2

Step-by-step explanation:

Answer:

A) Vertical angles are congruent

B) 40 and b are vertical angles and c and a are vertical angles.

C) <a = 40

<b = 140

<c = 140

Step-by-step explanation:

A straight angle is a straight line.  It is 180°

The integers that will make the inequality false are integers greater than 3

The inequality expression is given as

5x + 6 ≤ 2x + 15

Collect the like terms.

So, we have

5x - 2x  ≤ -6 + 15

Evaluate the like terms.

So, we have

3x ≤ 9

Divide both sides of the expression by 3

So, we have

x ≤ 3

Hence, the integers that will make the inequality false are integers greater than 3

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The number of chair being set up for a round table in a party is 6.

The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is called as probability.

Given that,

Banquet table rentals are often suited for less formal gatherings as opposed to round tables for formal ones.

Banquet tables are typically 4 feet, 6 feet, or 8 feet long and 30 inches wide. 8-foot tables

The most widely utilized dimension for guest seats. 4 chairs are present.

Eight people can sit comfortably at an 8-foot table.

Although seating can be provided at 4 and 6 foot tables

These sizes are often employed for different objectives.

4 guests may fit comfortably at a 4 foot banquet table, and 6 guests can

Banquet table can comfortably sit 6.

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If the variation is direct, then the value of y decreases with a decrease in x and increases when x increases.

On the other hand side, if we are following inverse variation then the value of y will decrease if x increases and increase if x decreases.

If there is a constant k that is nonzero and such that y = kx, then the variable y fluctuates directly as x. The expression y = kx is referred to as a direct variation equation, and the variable constant is denoted by the number k.

A function with the following equation as its definition is known as an inverse variation: xy = k , where k is a constant real integer that is not zero. There are several instances when one quantity changes as another does so indirectly.

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The amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively

Let the amount invested in the growth fund, income fund and money market fund be x, y and z respectively

As per the question, the company invested twice as much in the income market as in the money market

Therefore,

y = 2z

Equations will be:

x + 2z + z = 50000

12/100x + (8/100)*2z + 5/100z = 4500

Solving the equations

x + 3z = 50000

12x + 21z = 450000

Multiplying the first equation by 7 for equating

7x + 21z = 350000

12x + 21z = 450000

Equating these two we get

5x = 100000

x = 20000

Putting x = 20000 in 7x + 21z = 350000

z = 10000

2z = 20000

So, the amount invested in the growth fund, income fund and money market fund is 20000, 20000 and 10000 respectively

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Answer:

Figure Y is not a rotation of figure X because the length of individual side is different.

Step-by-step explanation:

Figure Y is not a rotation of figure X because the length of individual side is different.

The relationship a linear function and the equation is y = -3x + 24

The table of values is given as

Number of Clubs      Free Time (hours)

1                                         27

2                                         24

3                                          21

4                                           18

A linear relationship is any relationship with a constant rate

From the above table, we can see that as x increases by 1, y decreases by 3

This means that

Slope = Rate = -3

Hence, the relationship a linear function

In (a), we have

Slope = -3

Also, we have

Number of Clubs      Free Time (hours)

1                                         27

Reduce the above parameters by the constant rate

So, we have

Number of Clubs      Free Time (hours)

0                                      24

1                                         27

The above means that

y-intercept = 24

A linear equation is represented as

y = Slope * x + y-intercept

So, we have

y = -3x + 24

Hence, the equation is y = -3x + 24

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Answer:

1111/2500

Step-by-step explanation:

we have constructed the given quadrilateral.

The dimensions of the quadrilateral are:

WX = 4 cm

XY = 3.5 cm

YZ = 5 cm
WZ = 5.5 cm

∠ x = 75°

First draw a line segment  WX = 4 cm.

Now from the point X, construct an angle of 75°.

Now, on the ray of that angle, mark an arc that is 3.5 came long and mark the intersection point as Y

Now, from point Y, draw an arc of 5 cm and from point W draw an arc of 5.5 cm.

Mark their intersecting point as Z

Join WZ and YZ

The quadrilateral is formed.

Therefore, we have constructed the given quadrilateral.

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Answer:  The three medians of the triangle are concurrent. The point of concurrency is called the centroid. Point A is the centroid of the triangle.

Step-by-step explanation:

Answer:

Centroid.

Step-by-step explanation:

This point is where the three medians of a triangle meet. The median in a triangle is the line between a vertex and the opposite side.