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The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.

The compound interest formula is expressed as;

P = A / (1 + r/n)^nt

Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.

Given the data in the question;

First, convert rate from percent to decimal.

Rate r = 6%

Rate r = 6/100

Rate r = 0.06 per year

To determine the principal, plug the given values into the formula above and solve or P

P = A / (1 + r/n)^nt

P = $50,000 / (1 + 0.06/12)^( 12 × 30 )

P = $50,000 / (1 + 0.05)³⁶⁰

P = $50,000 / (1.05)³⁶⁰

P = $8,302.10

Therefore, the principal investment is $8,302.10.

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The statement is false, the number can be rewritten as:

0.33... = 3/9

So it is a rational number, not irrational

Here we have the statement:

"the number 0.3333... repeats forever; therefore, its irrational"

This is false, and let's prove that.

our number is:

0.33...

Such that the "3" keeps repeating infinitely.

If we multiply our number by 10, we get:

10*0.33... = 3.33...

If we subtract the original number we get:

10*0.33... - 0.33... = 3

9*0.33... = 3

Solving that for our number we get:

0.33... = 3/9

So that number can be written as a quotient between two integers, which means that it is a rational number.

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1) Considering a Normal Distribution, then we can write out the following:

Note that we're dealing with probabilities.

2) Let's find out the Z-score resorting to a table, we get:

2.2) So we can infer from 1 and 2:

Notice that this distribution refers to 120 families

The inverse function of a function f in mathematics exists a function that reverses the operation of f. The number of problems completed as input and returns the number of minutes worked exists m(p) = 6p - 54.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

Given: P(m) = (m/6) + 9

Determine the inverse function

P(m) = (m/6) + 9

Represent P(m) as P

P = (m/6) + 9

Swap the positions of P and m

m = (p/6) + 9

We are to make p the subject.

Subtract 9 from both sides, then we get

m - 9 = (p/6) + 9 - 9

m - 9 = (p/6)

Multiply through by 6

6(m - 9) = (p/6) × 6

simplifying the above equation, we get

6(m-9) = p

6 m-54 = p

Rearranging the above equation, we get

p = 6m - 54

Swap the positions of P and m

m = 6p - 54

m(p) = 6p - 54

Therefore, the correct answer is option C. M(p)=6p - 54

The complete question is:

The function below relates the amount of time (measured in minutes) Steve spent on his homework and the number of problems completed.

It takes as input the number of minutes worked and returns as output the number of problems completed.

P(m) = (m/6)+9

Which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked?

A. M(p)=54p + 6

B. M(p)=54p - 6

C. M(p)=6p - 54

D. M(p)=6p + 54

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Answer:6p-54

Step-by-step explanation:

Given the expression

-2/3(9/2x + 15/2)

Open the parenthesis;

= -2/3(9/2 x) - 2/3(15/2)

= -18x/6 - 30/6

= -3x - 5

Hence the expression in its simplest form is -3x - 5

The solution of the inequality is [tex]x \geq 289[/tex].

What is inequality?

Inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ( [tex]\neq[/tex]) " to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.

The given inequality is,  [tex]\sqrt{x} \geq 17[/tex]

Taking square on both sides, we get

[tex]x\geq 289[/tex].

Therefore, the solution of the inequality is [tex]x \geq 289[/tex].

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parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

What is a parabola in math?

     -9(x_6)²_1

     =  -9(x-6)1

     =-9x+54

    Differentiate  x

   -9

   -9(x-6)²

   Subtract

    d/dx(-9(x-6)

    Calculate x-6

    d/dx (-9x+54)

   -9x1-1

     -9x

  =-9

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To solve this problem, we have to compute the circumference of a circle of diameter:

Recall that the circumference of a circle is given by the following formula:

where d is the diameter.

Therefore, the circumference of the reservoir is:

Answer:

y = -2x + 2

Step-by-step explanation:

so to find the slope of the graph we must do (rise)/(run)

when we see the graph we see that when it goes DOWN 2 it also goes RIGHT 1

RISE is up or down

RUN is left or right

since it is down it is negative

so

-2 / 1

that is just -2

that is the slope

the equation for slope intercept is y = mx + b where m is the slope and b is the y intercept

so far it is y = -2x + b

the y intercept is where it crosses the y axis

that point is 2 based off of the graph

so

y = -2x + 2 is your answer

Answer:

1,017.36ft^2

Explanation:

Area of the circular pool = \pi r^2

r is the radius of the pool

Given

r = d/2

r = 36/2

r = 18ft

Area of the circular pool = 3.14(18)^2

Area of the circular pool = 3.14 * 324

Area of the circular pool = 1,017.36ft^2

The absolute value function can intersect a horizontal x-axis at zero, one, as well as two points.

Thus, depending on the way the graph has indeed been shifted and reflected, it could or might not intersect the horizontal axis.

The absolute value function can intersect the x-axis at zero, one, or two points.

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Answer:

difference in base areas = 210 cm²

Step-by-step explanation:

In order to calculate the difference in the base areas of the crates, we first need to find the base area of each crate.

To calculate the base area, we can use the formula for pressure and rearrange it to make area the subject:

[tex]\boxed{Pressure = \frac{Force}{Area}}[/tex]

⇒ [tex]Area = \frac{Force}{Pressure}[/tex]

Therefore:

•Base area of crate A = [tex]\mathrm{\frac{8320 \ N}{64 \ N/cm^2}}[/tex]

                                    = 130 cm²

• Base area of crate B = [tex]\mathrm{\frac{9860 \ N}{29 \ N/cm^2}}[/tex]

                                     = 340 cm²

Now that we know the base areas of each crate, we can easily calculate the difference between them:

difference = 340 cm² - 130cm²

                 = 210 cm²

We have the following:

old salary: $88441

new salary: $96402

The year is approximately 52 weeks, therefore:

a. old salary for week:

b. new salary for week:

c. weekly raise

Given that

The equation is

and we have to convert it into the form of

Randy's initial money = $12

Randy's earnings per week = $6

Becky's initial money = -$6 (she owes )

Becky's earnings per week = $7

Number of weeks: x

The equation for each:

• Randy:

50 = 12 + 6x

• Becky:

50 = -6 + 7x

Solve each for x:

Randy:

50= 12 + 6x

50-12 = 6x

38 = 6x

38/6=x

x= 6.3

Becky:

50= -8 + 7x

50+8 =7x

58=7x

58/7=x

x= 8.28

Randy will take 6.33 weeks and Becky 8.28 weeks.

Answer:

A. Randy

The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.

The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).

Comparing the equation  y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.

It is clear that the coefficient of x, A = -1 ÷ 3.

The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.

Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,

d = 15.811.

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Answer:

(3, 0)

Maximum Value of Objective Function = 15

Step-by-step explanation:

This is a problem related to Linear Programming(LP)

In linear programming, the objective is to maximize or minimize an objective function subject to a set of constraints.

For example, you may wish to maximize your profits from a mix of production of two or more products subject to resource constraints.

Or, you may wish to minimize cost of production of those products subject to resource constraints..

The given LP problem can be stated in standard form as

Max 5x - 4y

s.t.

-x + 3 ≥ y    

y ≤ 0.5x  + 1  

x ≥ 0, y ≥ 0

The last two constraints always apply to LP problems which means the decision variables x and y cannot be negative

It is standard to express these constraints with the decision variables on the LHS and the constant on the RHS

Rewriting the above LP problem using standard notation,

Let's rewrite the constraints using the standard form:
- x + 3 ≥ y  
→  -x - y ≥ -3  
→ x + y ≤ 3   [1]

y ≤ 0.5x + 1

→ -0.5x + y ≤ 1  [2]

The LP problem becomes
        Max 5x - 4y

s. t.

        x + y ≤ 3            [1]
        -0.5x + y ≤ 1      [2]
        x ≥ 0                 [3]
        y ≥0                  [4]

With an LP problem of more than 2 variables, we can use a process known as the Simplex Method to solve the problem

In the case of 2 variables, it is possible to solve analytically or graphically. The graphical process is more understandable so I will use the graphical method to arrive at the solution

The feasible region is the region that satisfies all four constraints shown.

The graph with the four constraint line equations is attached. The feasible region is the dark shaded area ABCD

The feasible region has 4 corner points(A, B,C, D) whose coordinates can be computed by converting each of the inequalities to equalities and solving for each pair of equations.

It can be proved mathematically that the maximum of the objective function occurs at one of the corner points.

Looking at [1] and [2] we get the equalities
     x + y = 3        [3]
-0.5x + y = 1        [4]

Solving this pair of equations gives x = 4/3 and y = 5/3 or (4/3, 5/3)

Solving y = 0 and x + y = 3 gives point x = 3, y =0  (3,0)

The other points are solved similarly, I will leave it up to you to solve them

The four corner  points are
A(0,0)
B(0,1)
C(4/3, 5/3)
D(3,0)

The objective function is 5x - 4y

To find the values of x and y that maximize the objective function,

plug in each of the x, y values of the corner points

Ignoring A(0,0)

we get the values of the objective function at the corner points as

For B(0,1) => 5(0) - 4(1) = -4

For C(4/3, 5/3) => 5(4/3) - 4(5/3) = 20/3 - 20/3 = 0

For D(3, 0) => 5(3) - 4(0) = 15

So the values of x and y which maximize the objective function are x = 3 and y = 0 or point D(3,0)

Consider the given linear equation,

PART A

Substitute y=0 to obtain the x-intercept,

Thus, the x-intercept is 4 .

Substitute x=0 to obtain the y-intercept,

Thus, the y-intercept is -12 .

Therefore, option C is the correct choice

PART B

The linear equation can also be written as,

The minimum limit to make a profit can be calculated as,

Note that the order of photograph must be an integer. The next integer after 4 is 5.

So the minimum order size to make a profit should be 5.

Let

the price of gummy bears per pound = x

the price of jelly beans per pound = y

price per pound of gummy bear = $3.2

price per pound of jelly beans = $7.5

In the given illustration, angle 1 and angle 2 are corresponding angles.

Note that corresponding angles in parallel lines are congruent.

angle 1 measures (63 - x)

angle 2 measures (72 - 2x)

Since both angles are congruent with each other, equate the angles :

The measure of angle 1 will be :

The measure of angle 2 will be :

ANSWERS :

a. x = 9

b. angle 1 = 54 degrees

angle 2 = 54 degrees

The value of x = 13

Each side of the equilateral triangle is: 27 units.

A triangle is classified or defined as an equilateral triangle if all its sides are of the same length. This means, all equilateral triangles have side lengths that are congruent.

Since triangle MNP is said to be an equilateral triangle, all its sides would be equal to each other. Therefore:

MN = NP = MP

Given the following:

MN = 4x - 25

NP = x + 14

MP = 6x - 51

Thus:

MN = NP

Substitute

4x - 25 = x + 14

4x - x = 25 + 14

3x = 39

x = 39/3

x = 13

MN = 4x - 25 = 4(13) - 25 = 27

MN = NP = MP

NP = 27

MP = 27

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Answer:

............where is it?

Thus, it is clear that the lines RS and TV in the preceding diagram are parallel to each other

If you extend a set of lines indefinitely, they will remain parallel and never cross each other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.

When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.

To solve the given question we know,

angle 1= angle 2 and lines RV // TS

angle 4= angle 3(interior angles on parallel lines are equal)

angle 1=angle 4 (vertically opposite angles are equal )

angle 1= angle 3 (angle 4=angle 1)

angle 4=angle 2( angle 1=angle 4)

Now we can see that the sum of base angles of the diagram will be 180 because

180-angle 3= angle STV

angle 4=angleSTV+180 (angle 3=angle4)

we proved that the diagram is a parallelogram because base angles of the same side are supplementary:

Therefore , we can conclude that the lines RS // TV in the preceding diagram .

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By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.

We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:

V = 4*6 ounces = 24 ounces.

We know that she drinks that in 3 hours, so the amount that she drinks each hour is:

24 oz/3 = 8 oz

She drinks 8 ounces of water each hour.

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Given:

Exponential equation for the black bird is,

Required:

To find the starting point of bird and graph the given function.

Explanation:

(1)

The bird starting point is at x = 0,

(2)

The graph of the function is,

Final Answer

(1) 1.004

(2)

The sample standard deviation of the population with confidence interval of 95% is 13.57

Standard deviation gives a value that measures how much the given value differ from the mean.

Given data form the question

95% confidence interval

population mean of a normally distributed variable is 17.3 to 24.5

population was 76

Definition of variables

confidence interval = CI = 95%

mean = X = 17.3 to 24.5

taking the average, X = 21.45

standard deviation = SD = ?

Z score = z = 1.96

from z table z score of 95%confidence interval = 1.96

sample size = n = 76

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]   OR   [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]

[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]

[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]

SD = √76 * 1.5561

SD = 13.56577

SD ≈ 13.57

The standard deviation is solved to be 13.57

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Answer:

r=19

Step-by-step explanation:

15-r=-4

r=19

:]

The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.

The domain of a function is the complete set of possible values of the independent variable.

Also a domain of a function refers to "all the values" that go into a function.

From the  graph the domain of the function of the volume of the  of liquid in the bucket is calculated as follows;

The minimum value of the volume of liquid in the bucket = 0

The maximum value of the volume of liquid in the bucket = 7.5 liters

The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}

0 ≤ V ≤ 7.5 liters

Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.

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We have to use proportions to solve this question.

According to the given information, the perimeter of Figure A is to the sidelength of that figure as the perimeter of Figure B is to the sidelength of that figure:

The corresponding sidelength of Figure B is 30.

In inequality 20 >= 4/5 w, w is 25 or any real no. lower than< 25 and in inequality -8<-1/4m, m = any real no. greater than> 24 is are the solution.

An inequality compares two values and indicates whether one is lower, higher, or simply not equal to the other.

A B declares that a B is not equal.

When a and b are equal, an is less than b.

If a > b, then an is bigger than b.

(those two are called strict inequality)

The phrase "a b" denotes that an is less than or equal to b.

The phrase "a > b" denotes that an is greater than or equal to b.

We have give the inequality to solve

20 = 4/5w

w = 20 × 5/4

   = 25 or any real no. lower than< 25

Let -8 = -1/4m

m = -8 × -4

m = 24

so m = any real no. greater than> 24

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