Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Males who got a C = 4
Total amount of people who got a C = 20
[tex]\frac{4}{20}[/tex]
[tex]\frac{4}{20}[/tex] simplifies to [tex]\frac{1}{5}[/tex]
What is the 95% confidence interval for the mean number of years of education for lower-class respondents?
the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968).
what is mean number ?
In mathematics and statistics, the "mean" typically refers to the arithmetic average of a set of numbers. To find the mean of a set of numbers, you add up all the numbers in the set and divide the total by the number of numbers in the set.
In the given question,
To calculate the 95% confidence interval for the mean number of years of education for lower-class respondents, we need the sample mean, sample standard deviation, sample size, and the t-value for the 95% confidence level with (n-1) degrees of freedom. Here are the steps to calculate the interval:
Collect the sample data of the number of years of education for lower-class respondents.
Calculate the sample mean and the sample standard deviation (s) of the data.
Determine the sample size (n) of the data.
Look up the t-value for the 95% confidence level with (n-1) degrees of freedom. For example, if the sample size is 50, then the degrees of freedom are 49, and the t-value for a 95% confidence level is 2.009 (using a t-distribution table or software).
Calculate the margin of error (ME) using the formula:
ME = t-value x (s / √(n))
Calculate the lower and upper bounds of the confidence interval using the formulas:
Lower bound = x- ME
Upper bound = x + ME
For example, suppose we have a sample of 100 lower-class respondents with a mean of 10 years of education and a standard deviation of 2 years. The degrees of freedom are 99, and the t-value for a 95% confidence level is 1.984 (using a t-distribution table or software).
ME = 1.984 x (2 / √(100)) = 0.3968
Lower bound = 10 - 0.3968 = 9.6032
Upper bound = 10 + 0.3968 = 10.3968
Therefore, the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968). We can interpret this interval as follows: we are 95% confident that the true mean number of years of education for all lower-class respondents is between 9.6032 and 10.3968 years.
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1. The law of demand predicts that
a. the more consumers purchase a good, the greater the demand for the good
b. consumers are willing to buy more of a good at a lower price than at a higher price
c. as prices go up, the quantity of a particular good that consumers will buy also rises
d. consumers are willing to buy more of a good at a higher price than at a lower price
2. The function of price in a market system
a. is a way of adjusting the balance between the forces of supply and demand
b. acts as an incentive to producers to either increase or decrease the quantity supplied
c. is a means of rationing the available supply among those who demand it
d. all of these
3. A key advantage of the corporate form of business organization is
a. that the business lives on even if the owners of the business die
b. limited liability of stockholders
c.
the ability to raise significant amounts of financial capital
d.
all of these
1) consumers are willing to buy more of a good at a lower price than at a higher price Option B
2) All of these
3) All of these
What is the law of demand?An economic theory known as the law of demand states that, all other things being equal, if a good or service's price rises, consumers will demand fewer units of it, and vice versa.
Price and quantity demanded are inversely related, to put it another way. This is a fundamental concept in economics and plays a key role in shaping market behavior and pricing strategies.
The price system is a way of adjusting the balance between the forces of supply and demand. A key advantage of the corporate form of business organization is the ability to raise significant amounts of financial capital.
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The tolerance for a ball bearing is 0.01. if the true diameter of the bearing is be 2.0 inches and the measured value of the diameter is x inches, express the tolerance using absolute value notation.
The value of the absolute difference can be expressed as | x - 2 | ≤ 0.01.
What is the expression of the tolerance?
The tolerance for the ball bearing is given as 0.01 inches.
Let x = measured value of the diameter in inches
The absolute difference between x and the true diameter of 2 inches of the ball bearing must be less than or equal to the tolerance of 0.01 inches.
The value of the absolute difference can be expressed using absolute value notation as follows;
| x - 2 | ≤ 0.01
Thus, the inequality above, express the absolute value of the difference between x and 2, which is less than and equal to 0.01.
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Complete the table for the following function y = 3 Superscript x x -3 -2 -1 0 1 2 3 y One-third 1 3 Graph the function and describe what the graph looks like. a. Increases in Quadrant III b. Increases from left to right c. Decreases from left to right d. Decreases in Quadrant II
The correct answer is to increase from left to right. The correct option is B.
To complete the table for the function [tex]y = 3^x - 3[/tex],
x y
-3 1/27
-2 1/3
-1 0
0 2
1 6
2 18
3 54
To graph the function, we can plot the points from the completed table on a coordinate plane and connect them with a smooth curve.
The graph of the function [tex]y = 3^x - 3[/tex] looks like an exponential function that increases from left to right, passing through the point (0, 2) on the y-axis. The graph is concave up and approaches the x-axis but never touches it.
Therefore, the correct answer is to increase from left to right. The correct option is B.
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The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
Caleb calculated the simple interest on $500 for 1 year rate of 5,5% per year. What is the interest earned ?
Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.
Explanation:
The interest earned by Caleb on $500 for 1 year at a rate of 5.5% per year can be calculated using the simple interest formula:
I = P * r * t
where I is the interest earned, P is the principal (starting amount), r is the annual interest rate as a decimal, and t is the time period in years.
Plugging in the given values, we get:
I = 500 * 0.055 * 1
I = 27.50
Therefore, Caleb earned an interest of $27.50 on $500 for 1 year at a rate of 5.5% per year.
Use the calculator to find each angle measure round to the nearest DEGREE
Need 15 and 16 answers need asap
Answer:
15. 53.13 16. 66.592
Step-by-step explanation:
Used a calculator
HELP DOING CORRECTIONS DUE IN A HOUR GIVING BRAINLIEST AND 20 POINTS
x = 12 times square root 2 (45 45 90 triangle)
y = 6 times square root 2 (30 60 90 triangle)
Given m||n, find the value of x.
t
(8x-7)
(x+16)°
Required value of x is 3.29.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equal sign. Equations can be used to describe a variety of phenomena, from physical laws to economic relationships.
Equations can be solved by manipulating the expressions on each side of the equal sign to isolate the variable being solved for. The solutions to an equation can be represented as a single value, a range of values, or even an infinite number of solutions.
To find the value of x, we need to solve the equation,
(8x-7) = (x+16)°
First, we can simplify the equation by removing the degree symbol and writing it as:
8x - 7 = x + 16
Next, we can isolate the variable x on one side of the equation by subtracting x from both sides and adding 7 to both sides:
8x - x = 16 + 7
Simplifying, we get:
7x = 23
Finally, we can solve for x by dividing both sides by 7:
x = 23/7
Therefore, the value of x is approximately 3.29 (rounded to two decimal places).
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Correct question is " Find the value of x where (8x-7) = (x+16)°".
Barb is saving money to buy a house in ten years. This is an example of a(n) goal. O A. medium-term OB. short-term OC. unrealistic O D. long-term
Answer: long term
Step-by-step explanation: I got it right on the test
assume you are realtor in bradenton, florida. you have recently obtained a listing of selling prices of the homes that have sold in that area in the last 6 months.you wish to organize those data so you will be able to provide potential buyers with useful information statistic question
To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?
What is Average Selling Price?The average selling price is a statistical measure that represents the total sum of all selling prices divided by the number of items being sold. It provides a useful indication of the typical or central value of a dataset.
According to the given information:
Fom the given information we can frame a question -
To know more aboutWhat is the average selling price of homes in Bradenton, Florida over the last 6 months?
To calculate the average selling price of homes in Bradenton, Florida over the last 6 months, you would need to:
1) Gather the selling prices of all the homes that have sold in the area over the last 6 months.
2) Add up all of the selling prices to get a total sum.
3) Divide the total sum by the number of homes that have sold to get the average selling price.
For example, if there were 100 homes sold in the last 6 months, and the total sum of their selling prices was $25,000,000, then the average selling price would be:
Average Selling Price = Total Sum / Number of Homes Sold
Average Selling Price = $25,000,000 / 100
Average Selling Price = $250,000
Therefore, the average selling price of homes in Bradenton, Florida over the last 6 months is $250,000.
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For the given data we've Number of class = 5, minimal value = 67900, Maximum value = 321550, Class range = 50730. The histogram, frequency polygon, and accretive frequency polygon are as shown.
What's histogram?In a graphic representation of data called a histogram, a set of nonstop numerical data is distributed in a given way. Each cube's area is related to the frequency of data values being within a given interval or caddy. It consists of a sequence of blocks or bars. The y- axis displays the frequency or count of values that fall inside each interval, while thex-axis displays the range of values that are divided up into intervals or lockers. Large data sets can be visually summarised using histograms, which can also be used to spot patterns and trends as well as outliers or unanticipated figures.
For the given data we have
Number of class = 5
minimal value = 67900
Maximum value = 321550
Class range = Range/ Number of class
= 321550- 67900/ 5
= 50730
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The complete question is:
Unit 9 lesson1 7th grade math math nation
Match the following. Match the items in the left column to the items in the right column.
1. set builder notation
2. element
3. set
4. line graph
5. inequality
6. real number
a shorthand way to write a set
(less than), (greater than), (less than
or equal to), (greater than or equal to)
visual tool used to illustrate solution
sets
a collection or group of objects
indicated by braces, (
a member of a set
positive or negative, rational or
irrational numbers including zero
The items in the left column should be matched with the items in the right column as follows;
Set builder notation: a shorthand way to write a set.
Inequality: (less than), (greater than), (less than or equal to), (greater than or equal to).
Line graph; visual tool used to illustrate solution sets.
Set: a collection or group of objects indicated by braces, { }.
Element: a member of a set.
Real number: positive or negative, rational or irrational numbers including zero.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.
In conclusion, a set simply refers to a collection or group of elements (objects) that is always indicated by curly braces, { }.
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Choose any dataset (from any online resource). Describe any variable on the dataset where you can apply CLT for mean and CLT for proportions.
Here is a possible dataset with variables for which the central limit theorem could be applied:
A dataset of customer spending at different retail stores.
Variable for which CLT for mean could be applied:
Average monthly spending per customer. As the number of customers at each store increases, the sample mean spending will approach a normal distribution.
Variable for which CLT for proportions could be applied:
Proportion of customers who spend over $200 per month. Even with a small number of customers at each store, the proportion will be approximately normally distributed as the sample size increases due to the CLT for proportions.
The central limit theorem states that the sampling distribution of the sample mean and sample proportion will be normally distributed for large sample sizes, regardless of the original distribution. So these variables from the retail dataset would satisfy that condition. Please let me know if you would like any clarification or have a different dataset in mind. I can provide additional examples.
Give a recursive defintition for the following set or ordered pairs of positive integers (a|b means that a is a factor of b): [tex]S =[/tex]{[tex](a,b)|a[/tex]∈[tex]Z^+, b[/tex]∈[tex]Z^+, a + b[/tex] is odd}
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.
Think about how to solve this problem in general. How can you assure that the sum [tex]a+b[/tex] is odd?
Think about this, what happens when you sum two even numbers? The result is even or odd?
[tex]2+6 = 8 \ \text{(even)}[/tex]
[tex]10+12 = 22 \ \text{(even)}[/tex]
And what happens when you sum two odd numbers ? The result will be even or odd? Look
[tex]3+7 = 10 \ \text{(even)}[/tex]
[tex]5+11 = 16 \ \text{(even)}[/tex]
Therefore to assure that [tex]a+b[/tex] is odd, one of them has to be odd and one of them has to be even, that is why
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.
Which point is collinear to the point (0, 0)? ○ A) (1,0) OB) (3,2) OC) (4,1) OD) (1,3)
Answer:
A) (1, 0)
Step-by-step explanation:
The point (0, 0) lies on the x-axis and y-axis, so any point that lies on either axis will be collinear to it. Therefore, the answer is A) (1, 0).
Hope this helps!
Kylie, a youth leader at a summer camp, is making clear slime for an activity with the kids. She is placing the slime in 2-ounce plastic containers with lids. If Kylie can mix up the slime and fill 75 containers in 50 minutes, how long will it take her to make the slime and fill up 450 of the 2-ounce plastic containers?
A. 6 hours
B. 5 hours
C. 4 hours
D. 9 hours
Therefore, the answer is (B) 5 hours. We can start by finding out how long it takes Kylie to fill one 2-ounce container. we can get by forming equation .
what is equation ?
In mathematics, an equation is a statement that two expressions are equal. An equation can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots.
In the given question,
We can start by finding out how long it takes Kylie to fill one 2-ounce container. To do this, we can set up a proportion:
75 containers / 50 minutes = 1 container / x minutes
Solving for x, we get:
x = (50 minutes) / (75/1) = 0.67 minutes per container
Now we can use this information to find how long it will take Kylie to fill 450 containers:
450 containers × 0.67 minutes per container = 301.5 minutes
So it will take Kylie 301.5 minutes to make the slime and fill up 450 containers. We can convert this to hours by dividing by 60:
301.5 minutes / 60 minutes per hour = 5.025 hours
Rounding to the nearest hour, we get 5 hours.
Therefore, the answer is (B) 5 hours.
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What is the range of the function y=e^4x?
O Y <0
O Y > O
O y <4
O y>4
The range of the function y=e⁴ˣ is y>0
The range of the function y=e⁴ˣ is the same as the range of any exponential function:
y > 0
The function can take on any positive value, but will never be 0 or negative.
It has a horizontal asymptote of y=0.
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Consider the following functions.
[tex]f(x)=x+3[/tex] and [tex]g(x)=\frac{x+5}{3}[/tex]
Step 2 of 2: Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x). Round your answer to two decimal places, if necessary.
Answer:
To find the formula for (g∘f)(x), we need to first evaluate g(f(x)):
g(f(x)) = g(x+3) = (3(x+3)+5)/3 = (3x+14)/3
So, (g∘f)(x) = (3x+14)/3
To find the domain for (g∘f)(x), we need to consider any restrictions on x that would make the function undefined. The only possible restriction is if the denominator of (3x+14)/3 is zero, which occurs when 3x+14=0. Solving for x, we get x=-14/3. Therefore, the domain of (g∘f)(x) is all real numbers except -14/3, or (-∞, -14/3) U (-14/3, ∞).
Rob and Ashley are riding their bicycles uphill. Currently, Rob is 5.7 km from the top and climbing at 0.24 km/min. Ashley is 4.5 km from the top and riding at 0.17 km/min. Estimate when Rob will be closer to the top than Ashley
After approximately 17.14 minutes, Rob will be closer to the top than Ashley.
How to solve the problemRob's distance from the top = 5.7 - 0.24t
Ashley's distance from the top = 4.5 - 0.17t
We want to find the time t when Rob's distance from the top is less than Ashley's distance:
5.7 - 0.24t < 4.5 - 0.17t
Now, we'll isolate the t variable by adding 0.17t to both sides and subtracting 4.5 from both sides:
0.07t > 1.2
t > 1.2 / 0.07
t > 17.14
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Find each length. Round to the nearest hundredth. Show work.
13.
78⁰
20
X
14.
32
18
The measure of side length x in triangle 13 and 14 are 20.45 and 15.26 respectively.
What are the lengths of the triangles marked x?The figures in the image are right-triangle.
To find the measure of x, we use the trigonometric ratio.
In question 13)
Angle θ = 78°
Opposite to angle θ = 20
Hypotensue = x
Note that: sine = opposite / hypotensue
sin( 78 ) = 20 / x
Solve for x
x = 20 / sin( 78 )
x = 20.45
in question 14)
Angle θ = 32°
Adjacent to angle θ = x
Hypotensue = 18
Note that: cosine = adjacent / hypotensue
cos( 32 ) = x / 18
Solve for x
x = cos( 32 ) × 18
x = 15.26
Therefore, the value of x is 15.26.
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The one-to-one functions g and h are defined as follows.
The functions and their composites are g⁻¹(6) = 2, h⁻¹(x) = 7x + 8 and (h⁻¹ o h)(1) = 1
Evaluating the functions and their compositesThe one-to-one functions g and h are defined as follows.
g = {(-4, -1), (1, -6), (2, 6), (6, 7)
Also, we have
h(x) = (x - 8)/7
Solving the functions expressions, we have
g⁻¹(6)
This means that we find x when g(x) = 6
From the ordered pairs, we have
g⁻¹(6) = 2
Next, we have
h⁻¹(x)
This means that we calculate the inverse function of h(x)
So, we have
h(x) = (x - 8)/7
This gives
x = (y - 8)/7
7x = y - 8
y = 7x + 8
So, we have
h⁻¹(x) = 7x + 8
Lastly, we have
(h⁻¹ o h)(1) = h⁻¹(h(1))
Using the rule
(h⁻¹ o h)(x) = h⁻¹(h(x)) = x
We have
(h⁻¹ o h)(1) = 1
Hence, the value of (h⁻¹ o h)(1) is 1
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Please answer question
The equation of the line perpendicular to the tangent line is y = -x + 5.
How to calculate the valueSince the given tangent line has a slope of 1, the line perpendicular to it will have a slope of -1 (the negative reciprocal). The point (2, 3) is on the line, so we can use the point-slope form of a line to write the equation:
y - 3 = (-1)(x - 2)
y - 3 = -x + 2
y = -x + 5
Therefore, the equation of the line perpendicular to the tangent line is y = -x + 5.
To find the point where the tangent line touches Circle N, we need to find the intersection point of the tangent line and Circle N. Since the tangent line has a slope of 1, we know that the line passing through the center of the circle and the point of tangency (point D) will be perpendicular to the tangent line. Let (x,y) be the coordinates of point D. Then the equation of the line passing through (x,y) and (2,3) is:
(y - 3) / (x - 2) = -1
y - 3 = -x + 2
y = -x + 5
We can substitute this equation into the equation of Circle N to get:
(x - 2)^2 + (y - 3)^2 = r^2
(x - 2)^2 + (-x + 2)^2 = r^2
2x^2 - 8x + 8 + 4 = r^2
2x^2 - 8x + 12 = r^2
Now we can substitute the equation of the line into the above equation to eliminate y:
2x^2 - 8x + 12 = (y - 3)^2
2x^2 - 8x + 12 = (-x + 2)^2
2x^2 - 8x + 12 = x^2 - 4x + 4
x^2 - 4x - 8 = 0
Using the quadratic formula, we find that:
x = 2 ± 2√3
Since the circle is tangent to the line y = x + 7, we know that the y-coordinate of point D must be equal to x + 7. Therefore, the coordinates of point D are:
(2 + 2√3, 9 + 2√3) or (2 - 2√3, 5 - 2√3)
The distance from the center of Circle N to point D is the radius of the circle. Using the coordinates of point D found above, we can calculate the distance as follows:
r = sqrt((2 + 2√3 - 2)^2 + (9 + 2√3 - 3)^2)
r = sqrt(16 + 8√3)
r = 4√3 + 4
Therefore, the radius of Circle N is 4√3 + 4.
Using the center and radius of Circle N, we can write the equation of the circle as:
(x - 2)^2 + (y - 3)^2 = (4√3 + 4)^2
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How do you write 9.6522 as a percentage
Answer:
965.22%
Step-by-step explanation:
To write 9.6522 as a percentage, we can multiply it by 100 and add the percent symbol (%):
9.6522 * 100% = 965.22%
Therefore, 9.6522 is equal to 965.22% as a percentage.
Hope this helps!
Answer:
Step-by-step explanation:
41.67 is the answer brainlist and verifed answer
22. An airplane pilot approaches an airport with an angle of depression of 11°. His current elevation is 20,000ft.
Find the ground distance from the airplane to the airport to the nearest 100ft.
20,000 ft
11⁰
X
22.
Please help and show work
Answer: x=102900 feet.
Step-by-step explanation:
The horizontal line extending from the airplane is parallel to the ground. Therefore, the angle of elevation (the angle opposite to the side measuring 20,000 ft) is also 11°. In addition, the angle opposite to x is 90-11=79°. Then, you can use the law of sines to solve for x.
[tex]\frac{sin11}{20000} =\frac{sin79}{x}[/tex]
Solve for x. x=102891. Rounded, 102900.
Or, you can use the tan function. [tex]tan11=\frac{20000}{x}[/tex]
Solve for x. Rounded, x=102900.
Josh's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Josh $5.80 per pound, and type B coffee costs $4.10 per pound. This month, Josh made 138 pounds of the blend, for a total cost of $652.50. How many pounds of type B coffee did he use?
Josh used 87 pounds of type B coffee in the blend.
What is equation?
An equation is a statement that two expressions are equal. It typically contains variables, which are quantities that can take on different values, and constants, which are quantities that have a fixed value. Equations can be used to describe relationships between different quantities and to solve problems by finding the values of variables that satisfy the equation.
For example, the equation 2x + 3 = 7 states that the expression 2x + 3 is equal to the expression 7.
Let's say that Josh used x pounds of type A coffee, and y pounds of type B coffee in the blend.
From the problem statement, we know that the total amount of coffee in the blend is 138 pounds, so x + y = 138.
The cost of the blend is $652.50, so 5.8x + 4.1y = 652.5.
We can use these two equations to solve for y, the number of pounds of type B coffee used.
First, we can solve for x in terms of y from the first equation,
x + y = 138
x = 138 - y
Then we can substitute this expression for x into the second equation,
5.8x + 4.1y = 652.5
5.8(138 - y) + 4.1y = 652.5
800.4 - 5.8y + 4.1y = 652.5
1.7y = 147.9
y = 87
Therefore, Josh used 87 pounds of type B coffee in the blend.
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For the function f(x)=−1(2/3)^x , what is the y -intercept?
Responses
a -1
b -2/3
c 2/3
d 1
The y-intercept of the function is -1. (option a).
In mathematics, a function is a rule that assigns each input (or argument) of a set, to a unique output (or value) of another set. In this case, the function f(x) is given by f(x)=−1(2/3)^x.
To find the y-intercept of a function, we need to evaluate the function at x=0. This is because the y-intercept is the point at which the graph of the function intersects the y-axis, and the y-axis is where x=0.
To find the y-intercept of the function f(x)=−1(2/3)ˣ, we need to evaluate the function at x=0. This gives us:
f(0) = -1(2/3)⁰
f(0) = -1(1)
f(0) = -1
This means that the graph of the function intersects the y-axis at the point (0,-1).
Hence the correct option is (a).
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Si al 15% del 20% de 5N le agregamos el 30% del 50% de 2N obtenemos 270. Calcula N.
The value of N in the algebraic equation is 600.
How to calculate N in the algebraic equation?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. We have:
(15/100 * 20/100 * 5N) + (30/100 * 50/100 * 2N) = 270
0.15N + 0.3N = 270
0.45N = 270
N = 270/0.45
N = 600
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Question in English
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. Calculate N.
Solve this system please.
FOR 35 POINTS
I WILL AWARD BRANLIEST
Answer: x=1 y=2 z=1
Step-by-step explanation:
Add the first 2 equations to eliminate y (easiest to eliminate)
2x + y - 3z = 1
x - y + 2z = 1
3x -z = 2 => 3x - z = 2
Multiply the 2nd equation by 3 to eliminate y again with the 3rd equation
(You want to eliminate same variable but using the 3rd equation)
3(x - y + 2z = 1)
3x - 3y + 6z = 3
Now add that to 3rd equation
3x - 3y + 6z = 3
x + 3y - z = 6
4x + 5z = 9 => 4x + 5z =9
Now you want to eliminate another variable from the 2 equations you just found(equations in bold above
To do that I will multiply the top one by 5
5(3x - z = 2)
15x - 5z = 10
Now add that to the other equation
15x - 5z = 10
4x + 5z = 9
19x =19
19x=19 solve for x
x=1
Now substitute that into one of the added equations to solve for z
3x - z = 2
3(1) - z = 2 simplify
3 - z = 2
-z = -1
z = 1
Now subsitute x and z into one of the original equations
2(1) + y - 3(1) = 1 simplify
2 + y - 3 = 1
-1 + y = 1
y=2
When abraham was born his parents put 2000 into an account that yielded 1.2%
When abraham was born his parents put 2000 into an account that yielded 1.2%, Abram will receive $2,213.10 on his 16th birthday.
To calculate how much Abram will receive on his 16th birthday, we need to use the compound interest formula:
A = [tex]P(1 + r/n)^{(nt)[/tex]
Where:
A = the amount Abram will receive
P = the principal amount (initial investment) = $2,000
r = the annual interest rate = 1.2% = 0.012
n = the number of times the interest is compounded per year = 2 (semi-annually)
t = the number of years = 16/2 = 8 (since interest is compounded twice a year)
Plugging in the values, we get:
A = $2,000(1 + 0.012/2)¹⁶
A = $2,000(1.006)¹⁶
A = $2,000(1.10655)
A = $2,213.10
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Complete question is:
When Abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi-annually. When he turns age 16, his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?