Answer:
Nonexamples of base and exponent in math would be any mathematical expressions that do not involve raising a base to an exponent. For example, 2 + 3 or √4 do not involve base and exponent.
An example of coefficient and exponential form is 5x², where 5 is the coefficient and x² is the exponential form. A nonexample could be x²/5, which does not have a coefficient in front of the exponential form.
An example of expanded form is 5x + 2, where the expression is fully written out. The standard form of the same expression would be 2 + 5x. A nonexample of expanded form is 2(x + 3), where the expression is not fully written out.
Examples of exponent laws include the product rule (a^m * a^n = a^(m+n)), quotient rule (a^m / a^n = a^(m-n)), and power rule ((a^m)^n = a^(mn)). A nonexample of an exponent law could be the sum of powers rule, which does not exist in traditional exponent laws.
The solutions for all the parts are given below.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by 'a' times to itself.
So, a is the exponent of m.
1) Non-examples of a base and exponent in math would be: "2 + 3" or "5 - 7" as these are expressions and not a base raised to an exponent.
2) An example of a coefficient and exponential form would be "2x^3" where 2 is the coefficient and x^3 is the exponential form. A nonexample would be "3x + 2" as it is an expression and not in exponential form.
3) An example of an expanded form would be 235 = 2 x 100 + 3 x 10 + 5 x 1, where each digit is multiplied by its corresponding place value. An example of standard form would be 235 written as is, without being broken down into its place values. A nonexample of expanded form would be 235 written as 2 + 3 + 5, as this is not a multiplication of the digits with their place values.
4). Examples of exponent laws include:
Product law: aᵇ x aⁿ = a⁽ᵇ ⁺ⁿ⁾
Quotient law: [tex]a^m / a^n = a^{(m-n)}\\[/tex]
Power law: [tex](a^m)^n = a^{(m \times n)}[/tex]
Negative exponent law: [tex]a^{(-n)} = 1/a^n[/tex]
Zero exponent law: [tex]a^0 = 1[/tex].
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6 typists working 5 hours a day can type the manuscript of a book in 16 days. How many days will 4 typists take to do the same job? each working 6 hours a day?
Answer:
Let's begin by finding the total work required to complete the manuscript of the book:
Total work = (Number of typists) x (Number of hours per day) x (Number of days) = 6 x 5 x 16 = 480
Now let's find the work done by 4 typists working 6 hours per day:
Work done by 4 typists = (Number of typists) x (Number of hours per day) x (Number of days) = 4 x 6 x d
where d is the number of days required to complete the manuscript.
Since the amount of work done is the same in both cases, we can set the two equations equal to each other and solve for d:
6 x 5 x 16 = 4 x 6 x d
Simplifying this equation, we get:
480 = 24d
Dividing both sides by 24, we get:
d = 20
Therefore, it will take 4 typists working 6 hours per day a total of 20 days to complete the manuscript of the book.
Step-by-step explanation:
Solve question
answer is csca+seca
Show the steps
The solution to the trigonometric expression is given as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
How to solve the trigonometric expression?The trigonometric expression for this problem is defined as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)).
The tangent and the cotangent are represented as follows:
tan(x) = sin(x)/cos(x).cot(x) = cos(x)/sin(x).Hence:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)[1 + sin(x)/cos(x)] + cos(x)[1 + cos(x)cot(x)]
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)+sin²(x)/cos(x) + cos(x) + cos²(x)/sin(x)
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = [sin²(x)cos(x) + sin³(x) + sin(x)cos²(x) + cos³(x)]/(sin(x)cos(x))
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
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find the distance between each pair of points on the coordinate plane
Answer:
give full question please its not full
reagan wanted to paint so she invested $500 several years later,she has earned $2000 in interest. how long did reagan invest the money if she earned a simple interest rate of 5% ?
Regan invested the money for 8 years at simple interest to earn $2000.
What is the difference between simple interest and compound interest?Simple interest is calculated on the loan amount or principle amount, whereas compound interest is calculated using both the principal amount and the interest that has accrued over the course of a prior period or particular time. Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period.
The simple interest is given as:
SI = Prt
where I is the interest earned.
P is the principal, = 500.
is the interest rate = 5% = 0.05.
t is the time (in years).
Substituting the values:
2000 = 500 * 0.05 * t
t = 8 years
Hence, Regan invested the money for 8 years at simple interest to earn $2000.
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reflection across x=1 Graph has GHIJ and yx at points
The vertices of the image after the transformation are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
How to perform the transformationGiven that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
The reflection is given as
Reflection across x = 1
The rule of this reflection is
(x, y) = (-(x - 2a), y)
Where
Reflection across x = a = 1
So, we have
G' = (-(1 - 2), -3), H = (-(5 - 2), -2), I' = (-(3 - 2), -5) and J' = (-(3 - 2), -1)
Evaluate
G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
Hence, the image of the reflection are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
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Complete questionWhat are the coordnate of the reflection across x = 1 of GHIJ such that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.
Can someone give a step by step explanation on how to find the Z score? I know how to find X but I need help with mostly Z.
So the lowest possible score to qualify for the police academy is 225.6.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
Here,
To find the Z-score, you will need to use the following formula:
Z = (X - μ) / σ
where:
X = the raw score you are trying to find
μ = the population mean (in this case, 200)
σ = the population standard deviation (in this case, 20)
To find the lowest possible score to qualify, you need to find the score that corresponds to the 90th percentile (i.e., the top 10%).
To do this, you can use a standard normal distribution table or a calculator that has a normal distribution function.
Here are the steps:
Find the Z-score that corresponds to the 90th percentile.
You can use a standard normal distribution table to find this value. Look for the row that corresponds to the first digit(s) of the percentile (in this case, 9) and the column that corresponds to the second digit (in this case, 0.0). This will give you the Z-score that corresponds to the 90th percentile, which is approximately 1.28.
Alternatively, you can use a calculator that has a normal distribution function. For example, in Excel, you can use the formula =NORM.S.INV(0.9) to find the Z-score that corresponds to the 90th percentile.
Plug in the values for μ, σ, and Z into the formula for Z-score:
Z = (X - μ) / σ
Rearranging the formula, we get:
X = Z * σ + μ
Substituting the values we know, we get:
X = 1.28 * 20 + 200
X = 225.6
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The Gross Domestic Product (GDP) of a country in the first quarter of 2014 was $1.5489*107. Rewrite the GDP in standard notation
We can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
In scientific nοtatiοn, a number is expressed as the prοduct οf a decimal number between 1 and 10 (called the cοefficient) and a pοwer οf 10 (called the expοnent). The expοnent indicates hοw many places the decimal pοint needs tο be mοved tο οbtain the οriginal number.
In the given number, $1.5489*107$, the cοefficient is 1.5489, and the expοnent is 7, which means the decimal pοint needs tο be mοved 7 places tο the right tο οbtain the οriginal number.
Therefοre , we can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
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How many particles in
9.89 moles of Carbon?
The number of particles in 9.89 moles of carbon is solved to be
5.95 x 10^24 particlesHow to find the number of particles in 9.89 moles of carbonTo determine the number of particles in 9.89 moles of carbon, we can use Avogadro's constant, which is defined as the number of particles (atoms or molecules) in one mole of a substance.
Avogadro's constant is approximately 6.02 x 10^23 particles per mole.
So, the number of particles in 9.89 moles of carbon is:
= 9.89 moles x (6.02 x 10^23 particles/mole)
= 5.95 x 10^24 particles
Therefore, there are approximately 5.95 x 10^24 particles in 9.89 moles of carbon.
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Question 4 of 10
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
g(x) =
10
|f(x)=x²
6
E
Option B. g(x)=(x-2)²is the equation of blue graph.
A graph: what is it?A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.
The red graph is represented by the function:
f(x)=x²
Also, we need the formula for the blue graph.
We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.
An example of a horizontal transition is:
f(x-h) where h is the quantity we shift (to the right).
h = 2 since we moved two units to the right.
Our new role will thus be:
g(x)=f(x-2)=(x-2)²
Therefore:
g(x)=(x-2)²
Our response is B.
Notes:
A denotes a downward vertical movement of two units.
C (assuming it is x²) denotes a two-unit vertical displacement upward.
And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.
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the complete question is:
The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x2
g(x) = ?
9(x) =
O A. g(x) = x² - 2
B. g(x) = (x - 2)2
c. g(x) = x + 2
D. Q(x) = (x + 2)2
Image is attached below;
Which of the following explains how to find the area of the shaded region shown?
Find the area of the inner and outer trapezoids, and add them together.
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
Count the shaded grid squares and estimate the number of partially shaded squares.
Find the area of the outer trapezoid.
Part B
Find the area in square units.
Answer:
Step-by-step explanation:
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
[tex]A=\frac{1}{2} (a+b)h[/tex]
[tex]A_o=\frac{1}{2} (6+2)6=24[/tex]
[tex]A_i=\frac{1}{2} (4+2)3=9[/tex]
Total area = 24 - 9 =15 square units
Consider the following function.
r(x)=4−32x
Step 2 of 2 : Find two points on the line to graph the function.
We can plot (0, 4) and (1, -28) points on a coordinate plane and draw a straight line passing through both points to graph the function.
What is a coordinate plane?
A coordinate plane, also known as a Cartesian plane, is a two-dimensional plane that is used to plot points and graph mathematical equations. It consists of two perpendicular number lines called the x-axis and the y-axis. The x-axis is the horizontal line, with positive values to the right of the origin (0) and negative values to the left of the origin. The y-axis is the vertical line, with positive values above the origin and negative values below the origin. The x-coordinate gives the horizontal position of the point, and the y-coordinate gives the vertical position of the point. By plotting points on a coordinate plane, we can graph lines, curves, and other mathematical functions. It is a fundamental tool in mathematics, science, and engineering for visualizing and analyzing relationships between variables.
To find two points on the line of the function r(x) = 4 - 32x, we can simply choose any two values of x and find the corresponding values of r(x).
For example, when x = 0:
r(0) = 4 - 32(0) = 4
So one point on the line is (0, 4).
When x = 1:
r(1) = 4 - 32(1) = -28
So another point on the line is (1, -28).
Therefore, we have two points on the line: (0, 4) and (1, -28).
We can plot these points on a coordinate plane and draw a straight line passing through both points to graph the function.
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answer:
see explanation
Step-by-step explanation:
Part A is correct
Part B
student A solved the system correctly
Part C
student B made the error from step 3 to step 4 , that is
step 3 : 3x - 5x + 150 = 114
step 4 : - 2x + 150 = 114 ( should be - 2x not 2x was the error made )
step 5 : - 2x = 114 - 150 = - 36
step 6 : - 2x = - 36 ( divide both sides by - 2 )
x = 18
substitute x = 18 into y = - x + 30 ( from step 1 )
y = - 18 + 30 = 12
Answer : (18, 12 ) which is the answer student A obtained correctly
I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?
Answer: The circumference would be 62.83
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
You are making an initial deposit of $1000 in an account that yields 5% interest quarterly (four times a year).
Following the pattern given above, find your year-end balance. (Show calculations for all four quarters and round to the nearest
penny) 15 pts
Answer: The interest rate per quarter is 5%/4 = 1.25%.
At the end of the first quarter, the balance is:
$1000 + $1000(1.25%) = $1000 + $12.50 = $1012.50
At the end of the second quarter, the balance is:
$1012.50 + $1012.50(1.25%) = $1012.50 + $12.66 = $1025.16
At the end of the third quarter, the balance is:
$1025.16 + $1025.16(1.25%) = $1025.16 + $12.82 = $1037.98
At the end of the fourth quarter, the balance is:
$1037.98 + $1037.98(1.25%) = $1037.98 + $13.00 = $1050.98
Therefore, the year-end balance is $1050.98 (rounded to the nearest penny).
Step-by-step explanation:
Which statement is true about the circumstance of a circle?
Answer:
The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter
Step-by-step explanation:
What are the coordinates of the point on the directed line segment from (-6,4) to
(9,-8) that partitions the segment into a ratio of 5 to 1?
The required point's coordinates are (0,3).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The required point's coordinates are (0,3).
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Which algebraic expression is equivalent to the expression below? 3 ( 5 x + 7 ) − 6 ( 4 − 2 x )
Answer:
3(5x+7)-6 (4-2x)
15x+21-24+12x = 27x-3
or
15x+21-6+4-2x = 13x+19
Consider a sequence generated by the
formula f(n) = 4n - 7 starting with n =3.
Generate the terms f(1), f(2), f(3), f(4), f(5)
Can you please give a detailed explanation so I can understand
The sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
What is functions?A function is typically denoted by a symbol, such as "f(x)", where "x" is the input value and "f(x)" is the output value. The input value is sometimes referred to as the "argument" of the function.
The formula f(n) = (4n - 7) generates a sequence of numbers when we plug in different values of "n". To generate the terms f(1), f(2), f(3), f(4), f(5) we need to substitute each value of n into the formula and evaluate the expression.
Starting with n = 1, we can generate the terms as follows:
f(1) = (4 × 1 - 7) = -3
f(2) = (4 × 2 - 7) = 1
f(3) = (4 × 3 - 7) = 5
f(4) = (4 × 4 - 7) = 9
f(5) = (4 × 5 - 7) = 13
So the sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
Each term in the sequence is found by plugging in a different value of "n" into the formula f(n) = (4n - 7). The first term, f(1), is found by plugging in n = 1, the second term, f(2), is found by plugging in n = 2, and so on.
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Determine the circumference of the base of the tin?
By answering the given question, we may state that We can apply the formula if we know the radius: C = 2πr where the radius r is.
what is diameter?In geometry, a circle's diameter is any straight line segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. The diameter of a sphere can be defined using either idea. The diameter is the length of the line perpendicular to the two points at either end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.
We must know the base's diameter or radius in order to calculate the circumference of the tin.
If we know the diameter, we can apply the following formula to determine the circle's circumference:
C = πd
where d is the diameter and C is the circumference.
We can apply the formula if we know the radius:
C = 2πr
where the radius r is.
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If 80% of a number is 304 and 15% of the same number is 57, find 95% of that number.
Answer:
95% of that number is 361
Step-by-step explanation:
Let's start by finding the actual value of the number.
If 80% of a number is 304, we can set up the equation:
0.8x = 304
To solve for x, we can divide both sides by 0.8:
x = 380
So the number is 380.
Now we can use the second piece of information to find 15% of the number:
0.15(380) = 57
This confirms that our value for x is correct.
Finally, we can use this information to find 95% of the number:
0.95(380) = 361
Therefore, 95% of the number is 361.
Data shown in a frequency table could be displayed in which of the following graphs?
A) line graph
B)line plot
C)bar graph
D)stem-and-leaf plot
Multiple choice
Answer: I think line plot and bar graph
Step-by-step explanation:
the lowest form of 28 upon 36 is ........... ( with explanation pls)
Answer:
To find the lowest form of 28 upon 36, we need to simplify or reduce the fraction to its lowest terms. This can be done by finding the greatest common factor (GCF) of the numerator (28) and the denominator (36) and dividing both by it.
First, we can find the prime factors of 28 and 36:
28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3
Next, we can identify the common factors, which are 2 and 2.
To find the greatest common factor, we need to multiply the common factors together. In this case, 2 × 2 = 4, so the greatest common factor is 4.
Now we can divide both the numerator and the denominator by the GCF:
28 ÷ 4 = 7
36 ÷ 4 = 9
Therefore, the lowest form of 28 upon 36 is 7/9.
Step-by-step explanation:
Factor the expression
ax+ay+az +3x+3y+3z
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 3
5
11
16
19
Car sales, y (in hundreds) 2
3
8
9
6
According to the given problem, the linear regression line for the given data is y = -0.65 + 0.26x
What is linear regression?
Linear regression is a statistical method used to find the relationship between a dependent variable (y) and one or more independent variables (x). It assumes that there is a linear relationship between the variables, meaning that changes in the independent variable(s) are associated with proportional changes in the dependent variable.
The linear regression model can be represented as a straight-line equation:
y = b0 + b1*x + e
The equation of a linear regression line can be written as:
y = b0 + b1*x
where y is the dependent variable (car sales in this case), x is the independent variable (number of TV commercials), b0 is the intercept, and b1 is the slope of the line.
To find the values of b0 and b1, we need to calculate the following:
n = number of data points = 4
Σx = sum of x values = 54
Σy = sum of y values = 28
Σxy = sum of (x*y) values = 164
Σx^2 = sum of (x^2) values = 689
Using these values, we can calculate b1:
b1 = (nΣxy - ΣxΣy) / (n*Σx^2 - Σx^2)
b1 = (4164 - 5428) / (4*689 - 54^2)
b1 = 0.26 (rounded to two decimal places)
Next, we can use b1 to calculate b0:
b0 = (Σy - b1*Σx) / n
b0 = (28 - 0.26*54) / 4
b0 = -0.65 (rounded to two decimal places)
Therefore, the linear regression line for the given data is:
y = -0.65 + 0.26x
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Five lemonades and two cookles cost $1.50. Two lemonades and five cookles cost $2.70. How much does one cookle and one lemonade cost?
Answer:
50¢/cookie, $1.00/lemonade
Step-by-step explanation:
Let l = cost of one lemonade
c = cost of one cookie
We have:
5l + 2c = 1.50 -------> 10l + 4c = 3.00
2l + 5c = 2.70 -------> 10l + 25c = 13.50
-----------------------
21c = 10.50
c = .50
5l + 2(.50) = 1.50
5l + 1.00 = 1.50
5l = 5, so l = 1.00
Each cookie costs 50¢, and each lemonade costs $1.00.
Jayla is training for the Seaview sprint race she runs the same route in her neighborhood every day and she makes her go on 80% of the time she plans to run every day for the next 10 days how likely that will she make her goal every day
If Jayla makes her goal 80% of the time, we can say that she has a probability of 0.8 of achieving her goal on any given day.
The probability of Jayla making her goal every day for the next 10 days can be calculated by multiplying the probability of her achieving her goal on each day.
Assuming each day's result is independent of the previous day, the probability of Jayla making her goal every day for the next 10 days is:
0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.1073741824
So, there is approximately a 10.7% chance that Jayla will make her goal every day for the next 10 days.
FInd the next three terms of 240,-120,60
The next three terms of the sequence 240,-120,60 are -30, 15 and -7.5
What is the next three terms?240, -120, 60
From observation, the second term is found by halving the first term and multiplying by negative
The third is found by halving the second term and multiplying by negative.
The fourth term = negative third term divided by half
= -(60/2)
= -30
The fifth term = negative fourth term divided by half
= -(-30/2)
= 15
The sixth term = negative fifth term divided by half
= -(15/2)
= -7.5
Hence, the next terms of 240, -120, 60 are -30, 15 and -7.5
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Select ALL the correct answers.
Chris is taking a trip to a certain town and wants to know what the residents of the town think about the restaurants there. It would not be possible to ask all 500 residents, so Chris plans on surveying a random sample of 50 residents in the population.
Select the survey methods that would result in Chris obtaining a random sample.
Surveying the first 25 women and 25 men he met at a grocery store.
Surveying every 10th woman and every 10th man at a local diner.
Surveying every 10th woman and every 10th man from a list of people living in the town.
Surveying one person from every 10th home in the town.
Surveying the first 50 people he saw at the airport as he got off the plane.
Chris can obtain a random sample of 50 residents by surveying the first 25 women and 25 men at a grocery store, surveying every 10th woman and every 10th man from a list of people living in the town, surveying one person from every 10th home in the town, or surveying the first 50 people he saw at the airport as he got off the plane.
Random sampling is an important method used to obtain a representative sample of the population of interest. Random sampling involves selecting a sample of elements from a population in such a way that each element has an equal probability of being selected. This ensures that the sample is not biased in any way and that it is representative of the population.In order to obtain a random sample, Chris could use a variety of methods. He could survey the first 25 women and 25 men he met at a grocery store, survey every 10th woman and every 10th man from a list of people living in the town, survey one person from every 10th home in the town, or survey the first 50 people he saw at the airport as he got off the plane.Each of these methods would result in a sample of 50 people that is randomly selected from the population of 500 residents. This would ensure that the sample is representative of the population and that the results of the survey are not biased in any way. Furthermore, the sample size of 50 is large enough to be considered representative of the population of 500.
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Suppose I took a survey of 324 people at the school. The survey showed that 120 people like dogs, 150 like cats, and 98 like both.
Make a two way table representing the above data.
If a person does not like dogs, what is the probability that they do not like cats
The probability that they do not like cats given that person does not like dogs: 13/51.
Explain about the vein diagram?A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not.Total people : 324.
People like dogs D: 120
Probability P(D) = 120/324
Probability Not like dogs P(D') = 1 - 120/324 = 204/324
People like cats C: 150
Probability P(C) = 150/324
Probability who don't like digs but like cats:
P(C ∩ D') = 52/ 324
Probability that they do not like cats given that person does not like dogs:
P(C'/D') = 1 - P(C ∩ D')/P(D')
P(C'/D') = 1 - (52/324) /(204/324)
P(C'/D') = 1 - 52/204
P(C'/D') = 152/204 = 13/51
Thus, the probability that they do not like cats given that person does not like dogs: 13/51.
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Suppose you borrow $4900 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $175 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$
$4900
$4719.94
1.75% Interest
on Prior Balance
$
$
$
$80.98
Monthly Payment
$175
$175
$175
$175
Ending Balance
$
$
57
$
$4900
$4719.94
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
What is annual interest rate?Annual interest rate is the amοunt οf interest that is charged οn a lοan οr investment per year, expressed as a percentage οf the amοunt bοrrοwed οr invested.
Tο cοmplete the table, we can use the fοllοwing steps:
Fοr the first mοnth:
Priοr balance: $4900
Interest οn priοr balance: 1.75% οf $4900 = $85.75 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4900 + $85.75 - $175 = $4710.75 (rοunded tο the nearest cent)
Fοr the secοnd mοnth:
Priοr balance: $4710.75
Interest οn priοr balance: 1.75% οf $4710.75 = $82.46 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4710.75 + $82.46 - $175 = $4628.21 (rοunded tο the nearest cent)
Repeat the same prοcess fοr the next three mοnths:
Fοr the third mοnth, priοr balance is $4628.21, interest οn priοr balance is $80.89, mοnthly payment is $175, and ending balance is $4549.10.
Fοr the fοurth mοnth, priοr balance is $4549.10, interest οn priοr balance is $79.34, mοnthly payment is $175, and ending balance is $4469.69.
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
Mοnth Priοr Balance Interest Mοnthly Ending
οn Payment Balance
Priοr Balance
1 $4900 $85.75 $175 $4710.75
2 $4710.75 $82.46 $175 $4628.21
3 $4628.21 $80.89 $175 $4549.10
4 $4549.10 $79.34 $175 $4469.69
5 $4469.69 $77.78 $175 $4389.72
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