Financial Goals: Tutorial
Part C
? Question
Diego's cash flow is the difference of his monthly income, $3,000, and his total expenses, $2,715. Which equation
correctly represents Diego's cash flow?
O cash flow = $2,715 - $3,000
O cash flow = $3,000-$2,715
O $3,000 = $2,715 - cash flow
$3,000 = cash flow-$2,715
Submit
25 of 37 Save & Exit
Σ
Sign out
Sep 6
7:56

Answer:

f(x) = $65x + $50

f(4.5) = $342.5

  The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.

Step-by-step explanation:

         We will write a function where x is the hours. Since you pay $65 for every hour, we will multiply $65 by x. Next, there is a fee of $50 so we will add that onto the end.

     f(x) = $65x + $50

         Now, we will plug 4.5 into the function for x and solve.

     f(x) = $65x + $50

     f(4.5) = $65(4.5) + $50

     f(4.5) = $292.5 + $50

     f(4.5) = $342.5

         The real-world interpretation of f(4.5) would be an emergency service call where they have to work for 4.5 hours.

7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified line, 7y+2=3x-5, is the next step.

To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.

Check for (2,-1/7)

Connect it to 7y+2=3x–5.

7(-1/7)+2=3(2)-5

-1+2=6-5

1=1

Which is correct; as a result, this point is on the line 7y+2=3x-5.

Verify (3,-2/7)

Connect it to 7y+2=3x–5.

7(-2/7)+2=3(3)-5

-2+2=09-5

1=4

Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.

Connect it to 7y+2=3x–5.

7(-1)+2=3(0)-5

-7+2=0-5

-5=-5

Which is correct; as a result, this point is on the line 7y+2=3x-5.

Verify (1, -4, 7)

Connect it to 7y+2=3x–5.

7(-4/7)+2=3(1)-5

-4+2=3-5

-2=-2

This is why I'm making this point

lies on the line 7y+2=3x-5 that is presented.

Verify (-1, -10/7)

Connect it to 7y+2=3x–5.

7(-10/7)+2=3(-1)-5

-10+2=-3-5

-8=-8

Which is correct; as a result, this point is on the line 7y+2=3x-5.

To learn more about line Visit : https://brainly.com/question/11557045

#SPJ9

From the given graph the value of μ is 530 and the value of σ is 15.

In the Normal Curve the value at which the shape of the graph is highest is called it's mean(μ) and the value on the left of mean is μ-σ and the value on the right of the mean is μ + σ .

In the Given question

the shape of the graph is highest at 530,

hence the value of mean(μ) = 530.    ....(i)

we know that the value on the left of mean is μ-σ .....(ii)

From the graph the value to the left of mean(μ) is 515.    ...(iii)

Equating equation (ii) and (iii) we get ,

μ-σ = 515

Substituting the value of  μ from equation (i) we get ,

530 - σ = 515

σ = 530 - 515

σ = 15

Therefore , From the graph the value of μ is 530 and the value of σ is 15.

Learn more about Normal Curve here

https://brainly.com/question/27978164

#SPJ1

The missing coordinate can either be - 16 or 8.

Let the missing coordinate be x.

Now, we know that the distance between (-3, -4) and (6, x) is 15.

Using the distance formula, we get that:

Distance² = (x₂ - x₁)² + (y₂ - y₁)²

Substituting the values in the formula, we get that:

15² = (6 + 3)² + ( x + 4)²

225 = 9² + x² + 16 + 8 x

225 = 81 +x² + 16 + 8 x

225 = x² + 8 x + 97

x² + 8 x - 128 = 0

x² + 16 x - 8 x -128 = 0

x ( x + 16) - 8 ( x + 16) = 0

(x + 16)(x - 8) = 0

x = -16 or x = 8.

Therefore, the missing coordinate can either be - 16 or 8.

Learn more about distance formula here:

https://brainly.com/question/7243416

#SPJ9

Answer:

Step-by-step explanation:

Given function:

[tex]y=\dfrac{x-3}{x^2-2x-3}[/tex]

The domain is the set of all possible input values (x-values).

Factor the denominator of the function:

[tex]\implies y=\dfrac{x-3}{(x-3)(x+1)}[/tex]

The domain of the given function is restricted as the function is undefined when the denominator equals zero, and when both the numerator and denominator equal zero.  

Therefore, the function is undefined when x = -1 and x = 3.

Therefore, the domain is (-∞, -1) ∪ (-1, 3) ∪ (3, ∞).

The range is the set of all possible output values (y-values).

As the domain is restricted, the range is also restricted.

Therefore, the range is (-∞, 0) ∪ (0, ¹/₄) ∪ (¹/₄, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Point Discontinuity (holes): When a rational function has a factor with an x that is in both the numerator and the denominator.

Therefore, there is a point discontinuity at x = 3.

Infinite Discontinuity: A vertical asymptote occurs when the denominator of a rational function is zero. This is considered an infinite discontinuity when the graph exists on both sides of the asymptote.

Therefore, there is an infinite discontinuity at x = -1.

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & =\dfrac{x-3}{x^2-2x-3}\\\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{(x^2-2x-3)(1) - (x-3)(2x-2)}{\left(x^2-2x-3\right)^2}\\\\ & = \dfrac{(x-3)(x+1)-(x-3)(2x-2)}{\left((x-3)(x+1)\right)^2}\\\\& = \dfrac{(x-3)[(x+1)-(2x-2)]}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{(x-3)(-x+3)}{(x-3)^2(x+1)^2}\\\\ & = \dfrac{-(x-3)^2}{(x-3)^2(x+1)^2}\\\\& = \dfrac{-1}{(x+1)^2}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{-1}{(x+1)^2} & = 0\\ -1 & \neq 0\end{aligned}[/tex]

Therefore, there are no stationary points and no minimum/maximum points.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0\\\implies \dfrac{-1}{(x+1)^2} & > 0\\ \dfrac{1}{(x+1)^2} & < 0\\ \textsf{If $\dfrac{1}{a} < 0$ then $a < 0$}:\\(x+1)^2 & < 0\\ \textsf{As $(x+1)^2\geq 0$, no solution.}\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0\\\implies \dfrac{-1}{(x+1)^2} & < 0\\ \dfrac{1}{(x+1)^2} & > 0\\ \textsf{If $\dfrac{1}{a} > 0$ then $a > 0$}:\\(x+1)^2 & > 0\\ \end{aligned}[/tex]

[tex]\textsf{For $a^n > 0$, if $n$ is even then $a < 0$ or $a > 0$}[/tex]

[tex]\implies x+1 < 0 \implies x < -1[/tex]

[tex]\implies x+1 > 0 \implies x > -1[/tex]

Combine the intervals:

(-∞, -1) ∪ (-1, ∞)

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)

Range: [0, ∞)

Continuity: Point discontinuity (hole) at x = 3.

Infinite discontinuity (vertical asymptote) at x = -1.

None

Decreasing function: (-∞, -1) ∪ (-1, ∞)

Symmetry: Neither

Answer:

52/129

Step-by-step explanation:

Answer:2/3

Step-by-step explanation:

The solution to each division problem is;

1) 4

2) 2

3) 3

4) 3

5) 3

1) We are given the expression;

(5 * 3) * ___ = 60

To get the blank answer, we will divide both sides by (5 * 3) to get;

60/(5 * 3) = 4

2) We are given the expression;

4 *( ___ * 9) = 72

To get the blank answer, we will divide both sides by (4 * 9) to get;

72/(4 * 9) = 2

3) We are given the expression;

7 * (2 * ___) = 42

To get the blank answer, we will divide both sides by (7 * 2) to get;

42/(7 * 2) = 3

4) We are given the expression;

(___ * 5) * 5 = 75

To get the blank answer, we will divide both sides by (5 * 5) to get;

75/(5 * 5) = 3

5) We are given the expression;

(3 * 3) * ___ = 27

To get the blank answer, we will divide both sides by (3 * 3) to get;

27/(3 * 3) = 3

Read more about Multiplication of Numbers at; https://brainly.com/question/10873737

#SPJ1

Answer: Sue fills 32/3 (Decimal form = 10.6667 containers)

Step-by-step explanation: 8 divided by 3/4 equals 32/3. If you need it in decimal form it's 10.6667

Please heart this or rate it :)

Answer:

10 2/3 containers BUT can only fully fill 10 containers

Step-by-step explanation:

to solve this equation you need to divide 8 by 3/4

8 / 3/4

that is

8/1 / 3/4

when dividing fractions you must flip the second number and multiply both numbers together

8/1 * 4/3

32/3 is your answer

or

10 2/3

she can fully fill 10 containers

Answer:

x=6

Step-by-step explanation:

2(x+3)-8=10

use 2 to multiply the one in the bracket

(2x+6)-8=10

group like terms

2x-2=10

send all constant terms to one side of the equation

2x=10+2

2x=12

divide both side by the coefficient of x

2x/2=12/2

x=6

Answer:

7561413

Step-by-step explanation:

6561413+1000000=    Equals Calculator Answer/////7561413

Answer:

7561413

Step-by-step explanation:

The calculator it equals 7561413

There are 5548 students majoring in computer science.

This problem is related to percentage we have to calculate the number of students with the percentage given. After multiplying the percent given to the total number of students we will get the required number of students.

Given that the total number of students in the university class is =7600

Also 73% of students are majoring in computer science.

Number of students majoring in computer science is = (73/100) of 7600

                                                                                   = 73×76

                                                                                   = 5548 students

So, the total number of students majoring in computer science is 5548.

To learn more about percentage visit the link:

https://brainly.com/question/14979505

#SPJ9

The simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3

The expression is given as:

3^2018 + 3^2015 / 3^2017 + 3^2016

Factor out 3^2015 in the expression

So, we have

3^2015(3^3 + 1)/3^2015(3^2 + 3)

Cancel out the common factor

(3^3 + 1)/(3^2 + 3)

Evaluate the exponents

(27 + 1)/(9 + 3)

This gives

28/12

Simplify

7/3

Hence, the simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

1, 0.75, 1.25, 3, 0

Step-by-step explanation:

To find the value of the function, we find the y coordinate of the point with the given x value.

Brief The Question Please, Thank You

The percent of the days in month that the cash will run out is given as: 23.33%. See the computation below.

Money put in ATM per day=$7750

We have to find the percent of days in a month you should expect to run out of cash.

From the given information

There are 7 days in which you run out cash more than $7750

Assuming that the total number  of days in a month = 30

Hence, we can arrive at the above value by saying:
(Corresponding days/Total number of Days) * 100

From we above we state:

(7/30) * 100

= 23.33%

Learn more about percentages:
https://brainly.com/question/24304697
#SPJ1

Step-by-step explanation:

ok, let's try this again. we need to explain congruence then in its details as an implicit part of the proof, as everything boils down to that.

due to AE = FC we also know that ED = BF.

because as ABCD is a parallelogram, it means AD = BC (and AB = DC).

and AD || BC, AB || DC.

as AD = AE + ED and BC = BF + FC, it means that

AE + ED = BF + FC

with AE = FC we can then simplify to

ED = BF.

as AD || BC, so is also ED || BF.

since the distance from E to D is the same as for B to F, it means that EB and DF must be equidistant to each other, and that means they are parallel.

and because ED || BF, that also means that both line segments are equidistant from each other, and that means that the connections between their end points (EB and DF) must have the same lengths.

therefore, the shape is a quadrilateral with 2 pairs of parallel and equally long line segments. and that is the definition of a parallelogram.

so, BEDF is a parallelogram.

Answer:

y= -3x-4.

Step-by-step explanation:

1) the slope-interception form is:

y=slope*x+i, where i - interception;

2) using the given two points it is possible to calculate the slope:

[tex]slope=\frac{5+1}{-3+1}=-3;[/tex]

then the required equation has the form:

y=-3x+i;

3) in order to calculate the 'i', it is enough to substitute the coordinates of the one point into this form of the required equation:

-1=-3*(-1)+i; ⇒ i=-4.

4) finally, the required equation is:

y=-3x-4.

P.S. the suggested way is not the shortest one.

The area of the region inside the rectangle that surrounds the square is; 162 square meters

We are given that;

Side length of square = 6 m

Width of rectangle = 11 m

Length of rectangle = 18m

Thus;

Area of rectangle = width * length = 11 * 18 = 198 square meters

Area of square = side * side = 6 * 6 = 36 square meters

Area of region inside rectangle not inside square = (area of rectangle) - (area of square) = 198 - 36 = 162 square meters

Read more about Area of rectangle at; https://brainly.com/question/25292087

#SPJ1

Answer: f'(x)=6x

Step-by-step explanation:

f'(x)= lim (h->0) [f(x+h) - f(x)] /h

f'(x)= lim (h->0) [3(x+h)^2 + 1 - (3x^2 + 1)] /h

f'(x)= lim (h->0) [3(x^2+2hx+h^2) + 1 - 3x^2 - 1] /h

f'(x)= lim (h->0) [3x^2+6hx+3h^2 - 3x^2] /h

f'(x)= lim (h->0) [6hx+3h^2] /h

f'(x)= lim (h->0) [6x+3h]

f'(x)= [6x+3(0)]

f'(x)=6x

The quotient of A = - 210 and B = - 15 is 14.

The Euclid's Division Lemma says when a number 'a' is divided by a number 'b' gives the quotient to be 'q' and the remainder to be 'r' then the following relation -> a = bq + r exists, where 0 ≤ r < b.

Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]

Given two numbers A = - 210 and B = - 15

The resultant quotient when A is divided by B can be calculated using Euclid's division lemma. Initially, we will assume remainder [r] = 0.

If the quotient is in decimals, we will change the remainder according to it else if the quotient is a whole number, the remainder will remain 0.

Using Euclid's division lemma -

Dividend [a] = Divisor [b] × Quotient [q] + Remainder [r]

- 210 = - 15 x q + 0

- 210 = - 15 x q

q = - 210 / - 15 = 14

Since, the quotient is a whole number, the remainder will remain zero.

Therefore, the quotient of A = - 210 and B = - 15 is 14.

To solve more questions on Divisions, visit the link below-

https://brainly.com/question/18052636

#SPJ1

The minuend and the subtrahend of 696 - 275 can be decomposed to give;

600 + 90 + 6

-

200 + 70 + 5

400 + 20 + 1

The decomposition into place values is chosen because of ease of reinforcing knowledge.

The decomposition method of subtraction involves decomposing the subtrahend, which is the smaller number and the place value of the numbers can be simply subtracted from the minuend.

In the subtraction, 696 - 275, the minuend is 696, while the subtrahend is 275.

Decomposing the subtrahend, gives;

275 = 200 + 70 + 5

Decomposing the minuend, gives;

696 = 600 + 90 + 6

The subtraction expression in the question, 696 - 275 gives;

696

-275

The above can therefore be decomposed as follows;

600 + 90 + 6

-

200 + 70 + 5

400 + 20 + 1

400 + 20 + 1 = 421

Therefore;

696 - 275 = 421

The reason the decomposition into place values of each digit is chosen is so as to make use of the easier understanding of subtracting numbers that are multiples of 10.

Learn more about subtraction in mathematics here:

https://brainly.com/question/4721701

#SPJ1

Answer:

greatest -( 9/36, -21/28, -7 )- smallest

Answer:

9/36

-7

-21/28

Step-by-step explanation:

You actually had them in the correct order

Answer:

The width is 3 feet and the height is 6 feet.

Step-by-step explanation:

Answer:

4cm

Step-by-step explanation:

the ratio of the two scales is 100,000:300,000 which simplifies to 1/3

1/3 x 12 =4

Answer: Parentheses

Step-by-step explanation: Parentheses always go first because if you look at the work PEMDAS, P= parentheses, E= exponents, M= Multiplication, D= division, A= addition, and S= subtraction.

Answer:

5250.

Step-by-step explanation:

Consistent = Population of deer increases 5% each year.

This year = 5000

105% of 5000 = 5250