After 9 years in an account with a 3.9% annual interest rate compounded continuously, an investment is worth a total of $17,757.16. What is the value of the principal investment? Round the answer to the nearest penny. $8,103.08 $5,256.41 $12,500.75 $12,530.37

a) The earnings of Portfolio 1 are given as follows: $679.5.

b) The Portfolio with the greatest earnings is: Portfolio 1.

The earnings are found by the sum of the multiplication of the equivalent decimal of the return by the investment.

The equivalent decimals are given as follows:

Then the earnings of the Portfolio 1 are given as follows:

0.028 x 1425 - 0.0155 x 1380 + 0.117 x 3400 + 0.0849 x 3100 = $679.5.

The earnings of the Portfolio 2 are given as follows:

0.028 x 4500 - 0.0155 x 3600 + 0.117 x 2150 + 0.0849 x 1980 = $489.86.

Hence Portfolio 1 earned the most, as 679.5 > 489.86.

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Answer:

Step-by-step explanation:

You'd multiply them by setting them correctly. When you multiply them you'd get 1.12 (don't know if you wanted the answer or just wanted to know how to multiply them)

Answer: 1.12 is the answer

Step-by-step explanation:

for an example here !

The required probability that 2 or fewer students are left-handed in a random sample of 65 students from the school is 0.0360.

Let X be a random variable which denotes the number of students who are left handed out of a sample of 65 students.

Here we have 65 students, therefore the number of trials would be 65. It would be reasonable to assume that the probability of one student being left handed is independent of any other student.

Therefore, the trials are independent.

There are only two possible outcomes for each trial i.e, either success or failure. The probability of success for each trial is 0.1

Hence we can say that X follows a binomial distribution with n = 65 and p = 0.1

X ~ Bin(65,0.1)

We need the probability that 2 or fewer students are left handed. This is given as :

P(X≤2)

we shall use the BINOM.DIST() function to find this

The syntax is given as:

= BINOM.DIST(number_s,trials,probability_s,cumulative)

Here,

number_s denotes the number of success required (2 in this case)

trials is the number of trials(65 in this case)

Probability_s is the probability of success in each trial (0.1 in this case)

cumulative, if true indicates the CDF or false if the PDF of X(TRUE in this case)

Hence the function which we use is

= BINOM.DIST(2,64,0.1,TRUE)

on running this code in any cell of excel, we get the probability as 0.035973

The required probability is 0.0360

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The function A is a linear function.

The function B is not a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Function A.

The coordinates:

(0, 1), (1, 0), (2, -1), (3, -2), (4, -1)

The rate of change of a linear function between any two points is the same.

Rate of change:

= (0 - 1) / (1 - 0) = -1/1 = -1

= (-1 - 0) / (2 - 1) = -1/1 = -1

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

The function A is a linear function.

Function B.

The linear function graph is a straight line.

Function B graph is not a straight line.

Thus,

Function A is a linear function but function B is not a linear function.

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The price paid by Jason for the gallons of gas he used for the trip is $2.15per gallon of gas.

As given in the question,

Reading of odometer in the starting of trip = 42,876.1

Reading of odometer in the end of trip = 43,156.1

Total distance covered by Jason on his trip = 43,156.1 - 42,876.1

                                                                         = 280 miles

Average miles per gallon of Jason's car = 35 miles per gallon

Gallons of gas used by Jason on his trip = 280 / 35

                                                                   = 8 gallons

Amount of money used to fill gas = $17.20

Price of the gas per gallon = 17.20 / 8

                                            = $2.15 per gallon of gas.

Therefore, the price paid by Jason for the per gallon of gas is equal to $2.15 per gallon of gas.

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Answer: y = 3x + 2

Step-by-step explanation:

Let's start with what we know. To calculate the slope, we do:
(y1 - y2)/(x1 - x2)

So, for this equation we get:

(5 - 2)/(3-0)

We get 3/3, so the slope = 1. So far, we have:

y = 3x + b

Let's use one of our coordinates to plug this in:

2 = 0 + b

So b = 2.

So our final equation is:
y = 3x + 2

At 99%, the confidence level will be (26.03,33.97)

given that

random sample n = 20

mean = 30

standard deviation = 6.2

the degree of freedom

df = n-1

   = 20-1

   =19

"t" at confidence level 99%, will be:

[tex]\alpha[/tex] = 1 - 0.99

  =0.01

[tex]\alpha[/tex]/2 = 0.01/2

     =0.005

t×[tex]\alpha[/tex]×df = t× 0.005 × 19

   By using the student table, we get

 = 2.861

The margin of error will be:

E = t[tex]\alpha[/tex]/2df× ([tex]\frac{s}{\sqrt{n} }[/tex])

   = 2.861 ×[tex]\frac{6.2}{\sqrt{20} }[/tex]

  = 3.97

At 99%, confidence interval will be:

=x - E < μ < x + E

=30 - 3.97 < μ < 30 + 3.97

=(26.03,33.97)

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Types of  built in functions are;

Standard library functions and User-defined functions.

Given,

Built in functions;

A built-in function is one that is pre-installed in a programing language, software program, or other user-accessible tool. For instance, the SUM function is a built-in feature of most spreadsheet programs that sums up all the cells in a row or column.

There are two types of function in C programming: Standard library functions and User-defined functions.

Standard library function;-

These are defined in header lines.

Eg; A standard library function called printf() is used to display formatted output on a screen (display output on the screen). The header file stdio.h has a definition for this function.

Therefore, we must use #include stdio.h> to include the stdio.h header file in order to use the printf() method.

User- defined functions;

As needed, you can also build functions. User-defined functions are those that the user has created.

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Answer:

1. FY and FT

Step-by-step explanation:

1. Which sides form angle F?

Answer: FY and FT

Sides FY and FT form the sides of ΔFYT for which ∠F is the included angle.

A triangle is a polygon having three vertices and three edges. Sum of the interior angles of a triangle is 180°.

There are three sides and three angles for the triangle.

For ΔFYT given here, FY, YT and FT are the edges or sides of the triangle. ∠F, ∠Y and ∠T are the angles of this triangle formed at vertices F, Y and T respectively.

∠F is formed by the edges FT and FY

∠Y is formed by the edges FY and YT

∠T is formed by the edges YT and FT

Hence, sides of the triangle FYT for which angle F is the included angle are FT and FY.

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The amount of money invested at the rate [tex]2\frac{1}{4}[/tex]% is $8500 and the amount of money invested at the rate 2% is $3000.

Given that, Phyllis invested $11,500, a portion earning a simple interest rate of [tex]2\frac{1}{4}[/tex] % per year and the rest earning a rate of 2% per year.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Let x be the amount invested at [tex]2\frac{1}{4}[/tex] =2.25% per year

Now, S.I= (x×2.25×1)/100

= 0.0225x

Then, (11,500-x) be the amount invested at 2% per year

S.I =((11,500-x)×2×1)/100

=(11,500-x)×0.02

= 230-0.02x

After one year the total interest earned on these investments was $251.25.

Now, 0.0225x+230-0.02x=251.25

⇒ 0.0025x+230=251.25

⇒ 0.0025x=21.25

⇒ x=21.25/0.0025

⇒ x=$8500

So, 11,500-x=$3000

Therefore, the amount of money invested at the rate [tex]2\frac{1}{4}[/tex]% is $8500 and the amount of money invested at the rate 2% is $3000.

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If the heights of five dogs are 400 mm, 370 mm, 470 mm, 330 mm and 500 mm. Then the standard deviation of the heights of the dogs is:

c) 70 mm

Given:

five friends were comparing the height of their dogs.

the heights at the shoulders were 400mm, 370mm, 470mm, 330mm and 500mm.

we are asked to find out the standard deviation of the heights of these dogs = ?

First find mean :

(400+ 370+470 + 330 + 500)/5

Mean = 2070/5

Mean = 414

standard deviation = √∑(xi - mean)²/N-1

= √(400-414)²+(370-414)²+(470-414)²+(330-414)²+(500-414)²/4

= √(14)²+(-44)²+(56)²+(-84)²+(86)²/4

= √196+1936+3136+7056+7396/4

= √19720/4

= √4930

= 70.21

rounding it to the nearest integer.

= 70 mm

Hence we get the required standard deviation as 70 mm.

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Answer:

20:3 ratio

Step-by-step explanation:

Answer:20 horses to 3 cows or 20:3

Step-by-step explanation:

The answer would be 20:3. If you notice that Both 40 and 6 can be divided by 2 so you would divide 40 by 2 and get 20 as your answer. And for the next you would divide 6 by 2 getting 3. So your ratio would be 20 horses to 3 cows or 20:3. I hope you were able to understand and I hope this helps you! I'm so sorry I didn't see your question earlier!

Answer:

It's a good idea to make a savings plan for all of your regular expenses, as well as any unexpected expenses that may come up. This can include things like housing costs, groceries, utilities, transportation costs, insurance premiums, and debt payments. It can also be helpful to save for larger expenses that you know are coming up, such as a vacation or a home repair. By making a plan for your savings, you can ensure that you have the funds available to cover all of your expenses, both expected and unexpected.

The solution for the given inequality is 1 < m ≤ 4. The graph for the obtained solution set is shown below.

Two expressions are related by comparative operations like 'less than or 'greater than or 'less than or equal or 'greater than or equal. Then that equation is said to be an "inequality equation".

For example, a < k ≥ b, etc.

The given inequality equation is

-2 < 3m - 5 ≤ 7

On adding 5 to the inequality, we get

-2 + 5 < 3m - 5 + 5 ≤ 7 + 5

⇒ 3 < 3m ≤ 12

On dividing by 3, we get

⇒ 3/3 < 3m/3 ≤ 12/3

⇒ 1 < m ≤ 4

Therefore, the solution set for the given inequality is (1, 4].

The obtained solution set is shown on the number line here.

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Answer:

A

Step-by-step explanation:

In an ordered pair, the coordinates are (x,y)

The only answer that describes a coordinate with an (x,y) that matches the table is A

The area of the shaded sector is 9π unts²

The term "turn" also refers to a 360° rotation. Angles between 0° and 360° are calculated. We require a circle's circumference, which is equal to 2 r r, where r is the circle's radius.

In any circle of radius r, the ratio of the arc length ℓ to the circumference equals the ratio of the angle θ subtended by the arc at the center and the angle in one revolution. Thus, measuring the angles in radians, ℓ2πr=θ2π⟹ ℓ=rθ.

Find the diagram attached

Given the following

Radius = 6

Theta = pi/2 = 90°

Area of the sector = theta/360×πr²

Area if the sector = 90/360 × π(6)²

Area of the Sector = 1/4 × 36π

Area of the sector = 9π unts²

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Step-by-step explanation:

To find the values of the trigonometric functions, we need to know the angle whose cosine, sine, etc. we are trying to find. In this case, we are given that the cosine of the angle is 3/5, but we are not told the measure of the angle itself. We can find the values of the other trigonometric functions using the given value of the cosine, but we must first express the value in radians.

Since the cosine of an angle is equal to the x-coordinate of the point on the unit circle that is located on the terminal side of the angle, we can find the value of the angle in radians by finding the inverse cosine (cos^-1) of 3/5. In other words, we want to find the angle such that the cosine of the angle is 3/5.

The inverse cosine function is denoted by cos^-1, so we can write:

$\cos^{-1}(3/5) = \theta$

where $\theta$ is the measure of the angle in radians.

To find the value of the other trigonometric functions, we can use the following relationships:

$\cos^2\theta = 1 - \sin^2\theta$

$\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{1 - \cos^2\theta}{\cos^2\theta}$

$\csc^2\theta = \frac{1}{\sin^2\theta}$

$\sec^2\theta = \frac{1}{\cos^2\theta}$

$\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\cos^2\theta}{1 - \cos^2\theta}$

We can now plug in the value of $\theta$ that we found earlier and use these relationships to find the values of the other trigonometric functions:

a. $\cos\theta = \cos(\cos^{-1}(3/5)) = \frac{3}{5}$

b. $\sin^2\theta = 1 - \cos^2\theta = 1 - (\frac{3}{5})^2 = \frac{4}{25}$

c. $\cos^2\theta = (\frac{3}{5})^2 = \frac{9}{25}$

d. $\tan^2\theta = \frac{\sin^2\theta}{\cos^2\theta} = \frac{\frac{4}{25}}{\frac{9}{25}} = \frac{4}{9}$

e. $\csc^2\theta = \frac{1}{\sin^2\theta} = \frac{1}{\frac{4}{25}} = \frac{25}{4}$

f. $\sec^2\theta = \frac{1}{\cos^2\theta} = \frac{1}{\frac{9}{25}} = \frac{25}{9}$

g. $\cot^2\theta = \frac{\cos^2\theta}{\sin^2\theta} = \frac{\frac{9}{25}}{\frac

The slope of the line in the table given is 11

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table

m = 1172 - 864 / 72 - 44

m = 11

The slope of the line is 11

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The radius of a circle having the equation x² + y² + 8x - 6y + 21 = 0 is 2  units .

In the question ,

it is given that ,

the circle is having the equation ⇒ x² + y² + 8x - 6y + 21 = 0 ,

we know that ,

general equation of circle is written as x² + y² + 2fx + 2gy + c = 0 ;

so , radius of circle is calculated using the below formula ,

radius = √(f² + g² - c)

On comparing,  given equation of circle with general equation of circle ,

we get , the values of f = 4 and g = -3 .

So after substituting the values of f , g and c in the radius formula ,

we get ,

radius = √(16 [tex]+[/tex] 9 - 21)

= √(16 [tex]+[/tex] 9 - 21)

= √(25 - 21) = √4 = 2 .

Therefore , the given circle has radius = 2 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0  ?

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Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. Constants and variables can both be used in an algebraic expression.

Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.

4x + 3y - 8 , x - 4, and so forth.

These expressions are represented by variables, constants, and coefficients that are unknown. The combination of these three words is referred to as an expression. It should be noted that, in contrast to an algebraic equation, an algebraic expression lacks sides and the equal sign.

In mathematics, addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

According to the given information

Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

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For straight lines l1 and l2 to be parallel, the value of x will be 4/3

Given that:

A machine is set to make parallel cuts on stone tiles.

Line l2 has equation y = 3/4

Line l1 has gradient -(3x-4)/8

Since y = 3/4. It is a horizontal line and the gradient of a horizontal line is 0. Also, if the straight lines l1 and l2 are parallel, then their will be the same. Thus:

-(3x-4)/8 = 0

-(3x-4) = 0

3x - 4 = 0

3x = 4

x = 4/3

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Answer:

c(x) = 5.50 + 21.60x

Step-by-step explanation:

To start, we are told that the service fee of 5.50 is added to the set price per ticket. So we can automatically eliminate B and D

Now, to find how much it costs per ticket, we have to divide 108.00 by 5 since we are told that it costs $108 to buy 5 tickets

108.00/5 = 21.60

This means that it costs $21.60 per baseball ticket

So the third answer choice is correct

The slope of the line passing through the two points [tex](1,2)[/tex] and [tex](3,8)[/tex] is [tex]\frac{3}{1}[/tex] i.e. [tex]3[/tex]

The formula for finding the slope when two points are given

[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{8-2}{3-1} \\y=\frac{6}{2} \\y=\frac{3}{1}\\y=3[/tex]

The slope of the line is [tex]3[/tex]

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the probability that alex and jose end up on the same team is 44.4%

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

there are two kids in the group, Alex and his best friend Jose.

alex and Jose end up on the same team

Since the order of students in the team is not important so the combination will be used.

The number of ways of selecting 5 students out of 10 is

C(10,5) = 252

Rest of 5 students will go into team B. Therefore, the number of elements in the sample space is 252.

P(Alex and Jose are in one team) = 112 / 252 = 0.4444

Hence the probability that Alex and Jose end up on the same team is 44.4%

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The price for the monthly fee will be;

⇒ x = $9.99  

And, The price per movie rental will be;

⇒ y = $2.99

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Yolanda is charged $21.95 for her monthly fee and 4 movie rentals.

And, Jeffrey is charged $30.92 for the same monthly fee and 7 movie rentals.

Now,

Let the price for the monthly fee = x

And, The price for the movie rental = y

Hence, We can formulate the expression for Yolanda;

⇒ x + 4y = $21.95

And,  We can formulate the expression for Jeffrey;

⇒ x + 7y = $30.92

Subtract equation (ii) from (i), we get;

⇒ 7y - 4y = $30.92 - $21.95

⇒ 3y = $8.97

⇒ y = $2.99

And, x + 4y = $21.95

x + 4 × 2.99 = 21.95

x + $11.96 = $21.95

x = $21.95 - $11.96

x = $9.99

Thus, The price for the monthly fee = $9.99  

And, The price per movie rental = $2.99

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The quadratic equation 7 · x · (2 ·x + 5) = 0 have the points x₁ = 0 and x₂ = - 5 / 2 as its x-intercepts.

In this problem we must determine the the x-intecerpts of a quadratic equation, that is, the values of x such that A · x² + B · x + C = 0. This question can be resolved by means of algebra properties. First, write the quadratic equation:

7 · x · (2 ·x + 5) = 0

Second, expand the expression and simplify until standard form is found:

7 · x · (2 ·x + 5) = 0

14 · x² + 35 · x = 0

Third, complete the square:

x² + (35 / 14) · x + 25 / 16 = 25 / 16

(x + 35 / 28)² = 25 / 16

Fourth, clear the variable x:

x + 35 / 28 = ± 5 / 4

x = - 35 / 28 ± 5 / 4

x = - 5 / 4 ± 5 / 4

The points x₁ = 0 and x₂ = - 5 / 2 are the x-intercepts of the quadratic equation 7 · x · (2 ·x + 5) = 0.

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Assuming that Nathalie's weight is still measured in pounds and ounces and that she has not lost or gained any weight since her birth, we can calculate her current weight as follows:

A) Nathalie weighs 7 pounds and 9 ounces at birth, which is equal to 7.5625 pounds. If she now weighs 12 times as much, she weighs 7.5625 * 12 = 90.75 pounds. In ounces, this is equal to 90.75 * 16 = 1452 ounces.

B) To calculate the percentage increase in Nathalie's weight, we need to first calculate the increase in her weight, which is equal to 90.75 - 7.5625 = 83.1875 pounds. We can then divide this increase by her original weight of 7.5625 pounds and multiply by 100% to express the result as a percentage: (83.1875 / 7.5625) * 100% = 1103.9%. This means that Nathalie's weight has increased by more than 1100% since she was born.

The 350 percent is less than the cube root of 50.

Here given two numbers,

∛50 and 350%

To compare the numbers we have to make to to simplest fraction,

∛50

The radical form of the cube root of 50 is ∛50, and the exponent form is (50)⅓ . The prime factorization of 50 is 2 x 5 x 5,

so the cube root of 50 in its simplest radical form is ∛50 .

50 cube root : 3.684031499

350%

The number 350% can be expressed as ,

350 / 100

350/100 = 3.5

So by comparing 3.684031499 and 3.5, 3.684031499 is larger

So ∛50 is larger than 350%

Therefore 350% is < ∛50.

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Answer:

350 percent is less than the cube root of 50

Step-by-step explanation: