Shown in the equation are the steps a student took to solve the simple interest formula A=P(1+rt) for r

For the given polynomial the roots can't have multiplicity, and the polynomial is:

p(x) = (x - 2)*(x - 3)*(x - 5).

Here we know that we have a cubic polynomial (of degree 3) with the following zeros:

2, 3, and 5.

Can any of the roots have multiplicity?

No, because a cubic polynomial can have at maximum 3 zeroes, and here we already have 3.

Now let's get the polynomial

Remember that a cubic polynomial with zeros a, b, and c can be written as:

p(x) = (x - a)*(x - b)*(x - c)

Then the polynomial in this case is:

p(x) = (x - 2)*(x - 3)*(x - 5).

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we have the exponential formula

so

we have

A=182 million ------> initial value (value of P when the value of t=0)

The year 1994 is when the value ot t=0

so

year 2002 -----> t=2002-1994=8 years

For t=8 years, P=186 million

substitute the value of A in the formula

Now

substitute the values of t=8 years, P=186 million

the formula is equal to

Estimate the population in 2004

t=2004-1994=10 years

substitute the value of t in the formula

therefore

The next figure illustrates the problem

x is computed as follows:

tan(12°) = opposite/adjacent

tan(12°) = 2/x

x = 2/tan(12°)

x = 9.4 ft

y is computed as follows:

sin(12°) = opposite/hypotenuse

sin(12°) = 2/y

y = 2/sin(12°)

y = 9.6 ft

Input data

7h + 3

Procedure

A term is a single mathematical expression.

3 = is a single term.

It is simply a numerical term called a constant.

7h = is also a single term. , The coefficient of the first term is 7

Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:

The answers are as follows:

The last answer is:

Given:-

A survey on the nationality of the student in the St Thomas international school is conducted and the results are shown.

To find if two students are randomly selected, what is the probability that both of them are European and if one student is randomly selected, what is the probability that a student is not Asian.

So now the total number of students are,

So now the probability of getting European is,

So the probability is,

So now the probability is asian is,

So the probability that it is not asian is,

so the required probability is,

Given:

The number of quarters = 27

The number of dimes = 21

The number of Nickels = 24

The number of Pennies = 28

Required:

Find the probability to obtain a penny.

Explanation:

The total number of coins = 27 + 21 + 24 +28 = 100

The probability of an event is given by the formula:

The number of penny = 28

Final Answer:

The probability of obtaining Penny is 0.28.

The scale factor is basically by what we need to multiply the original to get the dilated one.

Simple.

We can see that the original one is Trapezoid WXYZ and the dilated one is W'X'Y'Z'.

THe dilated trapezoid is definitely bigger than original. So the scale factor should be larger than 1.

One side of original is "6" and the corresponding side of dilated trapezoid is "14".

So, what we have to do to "6", to get "14"??

This is the scale factor!

To get 14, we have to multiply 6 with, suppose, "x", so:

Hence, SF is 7/3

Part 1:

The probability that a single randomly selected value is greater than 231.1 equals one minus the probability that it is less or equal to 231.1:

P(x > 231.1) = 1 - P(x ≤ 231.1)

Now, to find P(x ≤ 231.1), we can transform x in its correspondent z-score, and then use a z-score table to find the probability:

x ≤ 231.1 => z ≤ (231.1 - 203.6)/35.5, because z = (x - mean)/(standard deviation)

z ≤ 0.775 (rounding to 3 decimal places)

Then we have:

P(x ≤ 231.1) = P( z ≤ 0.775)

Now, using a table, we find:

P( z ≤ 0.775) ≅ 0.7808

Then, we have:

P(x > 231.1) ≅ 1 - 0.7808 = 0.2192

Therefore, the asked probability is approximately 0.2192.

Part 2

For the next part, since we will select a sample out of other samples with size n = 16, we need to use the formula:

z = (x - mean)/(standard deviation/√n)

Now, x represents the mean of the selected sample, which we want to be greater than 231.1. Then, we have:

z = (231.1 - 203.6)/(35.5/√16) = 27.5/(35.5/4) = 3.099

P(x > 231.1) = 1 - P(x ≤ 231.1) = 1 - P(x ≤ 231.1) = 1 - P( z ≤ 3.099) = 1 - 0.9990 = 0.0010

Therefore, the asked probability is approximately 0.0010.

Consider the given function,

Solve for x=-3 as,

Thus, the value of f(-3) is 0.2987 approximately.

Solve for x=-1 as,

Thus, the value of f(-1) is 2.2073 approximately.

Solve for x=0 as,

Thus, the value of f(0) is 6 .

Solve for x=1 as,

Thus, the value of f(1) is 16.3097 approximately.

Solve for x=3 as,

Thus, the value of f(3) is 120.5132 approximately.

Step 1

Given;

Required; To find the zeroes by factoring

Step 2

Find two factors that when added gives -5x and when multiplied give -6x

Factoring we have and replacing -5x with -6x and x we have

Graphically the x-intercepts are;

The x-intercepts are;-1/3,2

Hence, the answer is the zeroes and x-intercepts are the same, they are;

The possible values for any probability are between zero and one. With this in mind we conclude that A, B, C and E are allowed probabilities

EXPLANATION

Let's see the facts:

Austin and Carly deposit: $500

Interest rate= 1%

Compounding period = monthly

Total number of years = 2

Given the Compounding Interest Rate formula:

n is the compounding period

t is the number of years

r is te interest rate in decimal form

Replacing the given values will give us:

Solving the power:

Answer: Austin and Carly will be able to spend $510.09.

Hey there!

[tex]g+6g\\g=9,h=4[/tex]

[tex]4(h)+6(9(g))[/tex]

[tex]4+6(9)[/tex]

[tex]=58[/tex]

Hope this helps!

Solution

The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero. {...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...} The set of integers is sometimes written J or Z for short. The sum, product, and difference of any two integers is also an integer.

The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals. All the whole numbers are also integers, because integers include all the positive and negative numbers

The integers are real numbers

Therefore the numbers are list of integers

Given:

There are given the function:

Explanation:

According to the question:

We need to draw the graph of the given equation:

So,

The graph is:

vertical asymptotes are (-1,1)

And,

The horizontal asymptotes is

y = 0.

Answer: serbia

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Line A:

point 1 (2,7)

point 2 (-1,10)

Line B:

point 1 (-4,7)

point 2 (-1,6)

Line C:

point 1 (6,5)

point 2 (7,9)

Step 02:

perpendicular lines:

slope of the perpendicular line, m’

m' = - 1 / m

Line A:

slope:

Line B:

slope:

Line C:

slope:

m' = - 1 / m ===> none of the slopes meet the condition

The answer is:

there are no perpendicular lines

Answer:

9x+b

Step-by-step explanation:

We have the next system of equations

We can sum both equations we can eliminate one variable

then we isolate the x

Therefore x=-1 then we substitute the value of x in order to find the value of y in the second equation

Then we simplify

Then we isolate the y

ANSWER

x=-1

y=0

Given the equation:

Multiplying both sides by 2

So, the answer will be option B) 12

start identifying the slope and y-intercept for each high school.

The slope represents the growth for each year, in this case for high school A is 25 and for high school B is 50.

The y-intercept is the number of students that are enrolled currently, in this case for A is 400 and for B is 250.

The complete equations in the slope-intercept form are

Continue to graph the equations

High school B is projected to have more students in 8 years.

Given two matrices

We will solve for the resultant matrix -B - 1/2A.

This operation is represented as

Let's simplify the matrices further based on scalar operations that can be done here. The B matrix will be multiplied by -1 while the A matrix will be multiplied by 1/2. We now have

Now, we apply the subtraction of matrices to the simplified matrix operation above. We have

Hence, the resulting matrix for the operation -B - 1/2A is

Answer: D(12)

Step-by-step explanation: To find the opposite it the number you would do -12= -12 x -1 = 12

Add the two expressions together;

The first option is the correct answer

The inverse function table of the function is given by the image at the end of the answer.

A function y = f(x) is composed by the following set of cartesian points:

(x,y).

In the inverse function, the input of the function represented by x and the output of the function represented by y are exchanged, meaning that the coordinate set is given by the following rule:

Thus, the points that will belong to the inverse function table are given as follows:

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Answer:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]

Step-by-step explanation:

The inverse of the graph of a function is its reflection in the line y = x.

Therefore, the mapping rule to find the inverse of the given ordered pairs is:

Therefore:

Completed table:

[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} \vphantom{\dfrac12} x &-8 &-4.5 & -4&0 \\\cline{1-5} \vphantom{\dfrac12} f^{-1}(x) &-2 & -1& 0&2 \\ \cline{1-5}\end{array}[/tex]

Answer:

(a) P = 0.0167

(b) P = 0.9833

(c) P = 0.0093

Explanation:

To answer these questions, we will use the binomial distribution because we have n identical events (13 households) with a probability p of success (27% still have a traditional phone landline). So, the probability that x families has a traditional phone landline can be calculated as

Replacing n = 13 and p = 27% = 0.27, we get:

Part (a)

Then, the probability that no families have a phone landline can be calculated by replacing x = 0, so

Part (b)

The probability that at least one family has a phone landline can be calculated as

Part (c)

The probability that at least eight families have a phone landline can be calculated as

So, each probability is equal to

Then, the probability is equal to

P(x≥8) = 0.0093

Therefore, the answers are

(a) P = 0.0167

(b) P = 0.9833

(c) P = 0.0093