Choose all of the values that are equivalent to

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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Answer:2x^2+23

Step-by-step explanation:

7x^2+3-5x^2+20    (distribute (-5) to x^2 and (-4))

2x^2+3+20              (combine like terms)

2x^2+23

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 mentioned data 100 kilometres in an hour is the speed of rate of object.

The 100 kilometres represents distance and an hour indicates the time. The complete data in the sentence is indicative of coverage of 100 kilometres in an hour by whatever the object is, which is not mentioned in the question.

However, writing distance with respect to time indicates the rate or speed. Widely applicable, it can anything. Few examples of its indication are rate of descending or ascending of plane, kite, lift or any other object. It can refer to the speed of person, car, train or other such objects or animals holding capacity to travel.

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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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a)  The average score on the original exam is 76

b) The average score after 2 months = 67.41

c) The average score after 11 months = 56.574

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

For this case we know that the average scores for the class are given by the following model:

[tex]f(t) =76 - 18 log_{10} (t+1)[/tex] , 0≤ t ≤ 12

Where t is in months. The graph attached illustrate the function for this case

And for this case we can answer the questions like this:

Part a

We just need to replace t =0 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (0+1)[/tex] = 76

Part b

We just need to replace t =2 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (2+1)[/tex] = 67.41

Part c

We just need to replace t =11 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (11+1)[/tex] = 56.574

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Question:

Students in a mathematics class were given an exam and then tested monthly with an equivalent exam. The average scores for the class are given by the human memory model f(t) = 76 − 18 log10(t + 1), 0 ≤ t ≤ 12 where t is the time in months. Verify your answers in parts (a), (b), and (c) using a graphing utility.

(a) What was the average score on the original exam (t = 0)? f(0) =

(b) What was the average score after 2 months? (Round your answer to one decimal place.) f(2) =

(c) What was the average score after 11 months? (Round your answer to one decimal place.) f(11) =

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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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 domain of the linear function that models the volume is:

D: 0 ≤x ≤640

The correct option is the fourth one, counting from the top.

Here we have the following linear function:

V(x) = 640 - x

V(x) represents the volume of water left in the bucket, while x represents the amount of water that has leaked from the bucket.

The domain will represent the possible values of x.

first, the smaller value of x.

It is x = 0, and it represents the moment before the leak started, when the bucket was completely full and had a volume of:

V(0)=  640 ounces.

The largest possible value of x is x = 640, which is the case where all the water in the bucket has come out.

Then the domain is:

D: 0  ≤x ≤640

Finally, the correct option is the last one.

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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:

There are 6 large blue marbles, so there are 8 + 6 - 6 = 8 ways to choose a large blue marble or a large marble.

There are 10 blue marbles (6 large blue marbles and 4 small blue marbles), so there are 10 + 8 - 6 = 12 ways to choose a blue marble or a large marble.

Therefore, there are 8 + 12 = <<8+12=20>>20 ways to choose a blue marble or a large marble.

Step-by-step explanation:

Answer: 24 different ways.

Step-by-step explanation: Hope it helps, please pick brainliest!

Answer:

Step-by-step explanation:

This is not a valid proof, as it simply repeats the given statement without providing any justification or reasoning. To prove that AB CD, we need to use logical reasoning and the properties of lines and angles to show that the statement is true.

One way to prove this statement is to consider the angles of the quadrilateral ZBZD. Since ZBZD is a quadrilateral, it has four angles. We are given that ZB is parallel to AD and that BC is parallel to AD. This means that the angles formed by these lines must be equal.

Additionally, since ZBZD is a quadrilateral, the sum of its angles must be 360 degrees. Therefore, if the angles formed by ZB and AD are equal, and the angles formed by BC and AD are equal, then the angles formed by ZB and BC must also be equal.

Therefore, we can conclude that ZB and BC are parallel, which means that AB CD. This completes the proof.

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

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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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

Using the slope formula, we know that the relationship between AB and CD is that they are (C) parallel.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

A line's steepness can be determined by looking at its slope.

The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

So, formula: m = y2 - y1/x2 - x2

For AB:

m = y2 - y1/x2 - x2

m = -5+2/3-1

m = -3/2

For CD:

m = y2 - y1/x2 - x2

m = 5-2/5-7

m = -3/2

The two lines have equal slopes, and when slopes are equal, lines are said to be parallel.

Therefore, using the slope formula, we know that the relationship between AB and CD is that they are (C) parallel.

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Correct question:
Determine the relationship of AB and CD gave the following points: A (1, -2), B (3, -5), C (7, 2), and D (5, 5).

a. Neither

b. Perpendicular

c. Parallel

Step-by-step explanation:meow

Answer:

100

Step-by-step explanation:

Use Pemdas or Order of Operations:

First in the brackets:

3+2=5
next in the brackets:

45 - 5 = 40

Now you get the equation:

3 x 20 + 40

First solve 20 x 3:

60; +40 = 100

Thus 100 is your total.

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.

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

Answer:

w + 18 = 22

Step-by-step explanation:

HC = 18 lb

HC + GD = 22 lb

GD + HC = 22

GD + 18 = 22

w + 18 = 22

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 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 supplied regular polygon's solitary outside angle measures 32.5 degrees.

additionally, we must determine the size of a single external angle.

As a result, the polygon that is presented has 11 sides.

What does the term "exterior angle" mean?

In a rectilinear figure, the angle between a side and its neighboring side stretched outward.

360 degrees is the sum of all outside angles.

By dividing 360 by the total number of sides, we must determine the size of a single outside angle.

As a result, the supplied regular polygon's solitary exterior angle has a measure of 32.5 degrees.

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As per the double integral, the flux of the vector is 2√11(6z + 1) + 176

What is double integral small definition?

In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.

And it is calculate by the formula as Flux= ∫∫F⋅ndS

Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.

And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.

As per the formula of flux of vector, it can be written as,

=>Flux =  ∫∫(1i + 1j + 3k) . 2 dS

When we integrate this one the we get,

=> Flux = 2√11(6z + 1) + 176

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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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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 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 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 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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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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