Answer:
A. positive slope.
Step-by-step explanation:
In the least square linear regression of Y on X, the straight line of best fit is given by,
[tex]Y_{s} = \mu_{Y} + \rho \times \frac {\sigma_{Y}}{\sigma_{X}} \times (X - \mu_{X})[/tex] ------------------(1)
[where [tex]Y_{s}[/tex] is the estimated value of Y]
Clearly, here,
Slope pf the line = [tex]\rho \times \frac {\sigma_{Y}}{\sigma_{X}}[/tex]---------------------------------(2)
Y- intercept = [tex]\mu_{Y} - \rho \times \mu_{X} \times \frac {\sigma_{Y}}{\sigma_{X}}[/tex]-----------------(3)
and,
X - intercept = [tex]\mu_{X} - \mu_{Y} \times \frac {\sigma_{X}}{\rho \times \sigma_{Y}}[/tex]----------------(4) [putting [tex]Y_{s} = 0[/tex] in (1) and taking the value of X]
So,
since [tex]\sigma_{Y}, \sigma_{X} > 0[/tex]
[since [tex]\sigma_{Y} = 0[/tex] or [tex]\sigma_{X} = 0[/tex] will result in a degenerate distribution, hence these cases are discarded]
so, correlation coefficient = [tex]\rho[/tex] > 0 implies
A. positive slope. [as evident from (1)]
clearly from (3) and (4) all the other options are false.
Final answer:
A least squares line of best fit with a positive correlation coefficient always has a positive slope, reflecting the positive relationship between the independent and dependent variables. The y-intercept can be positive or negative and is not determined by the correlation.
Explanation:
The question is asking about the characteristics of a least squares line of best fit when there is a positive correlation coefficient. A positive correlation coefficient means that as the value of the independent variable (x) increases, the value of the dependent variable (y) also increases. From this, it follows that the slope of the line ( he m term in the equation) is positive - reflecting the concept that the slope represents the relationship between two variables, with a positive slope indicating a positive relationship.
The y-intercept (the b term in the equation) could be positive or negative, as it represents where the line crosses the y-axis when x is 0, and this point doesn't affect the direction of the relationship between the variables, just the starting level of the dependent variable. Therefore, the correct answer to the question is simply A. positive slope, as this is the only feature guaranteed by a positive correlation coefficient.
is abc = dce? justify your answer below, please explain why! please help :)
Answer:
Step-by-step explanation:
∡ECD = 90°
∡DCA= 90°
∡BCA=90°
∡BCE =90°
⇔ ABC=DCE
a toy store orders jigsaw puzzles for 3 and sells them for 4.50, what is the percent of markup? Round your answer to the nearest tenth of a percent ,if necessary a) 20% b) 33.3% c) 50% d)66.7
Answer:
C
Step-by-step explanation:
THe markup is the difference between the Selling Price and Cost.
As a percentage, we would get the markup in terms of cost.
First,
Selling Price = 4.50
Cost = 3.00
So,
Markup = SP - Cost = 4.50 - 3.00 = 1.50
As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:
1.50/3 = 0.5 * 100 = 50%
THe markup is 50%
C is the correct answer.
Answer:
C
Step-by-step explanation:
The markup is the difference between the Selling Price and Cost.
As a percentage, we would get the markup in terms of cost.
First,
Selling Price = 4.50
Cost = 3.00
So,
Markup = SP - Cost = 4.50 - 3.00 = 1.50
As a percentage, we would divide the markup by cost and then multiply the answer by 100. That's:
1.50/3 = 0.5 * 100 = 50%
The markup is 50%
C is the correct answer.
Melissa bought 3 loaves of freshly baked bread at a specialty bread shop. She paid twice as much for the whole grain bread as for the French bread, and $2.50 more for the cinnamon raisin bread than for the whole grain bread. She spent a total of $11.25 for the 3 loaves. If f represents the price of a loaf of French bread, which equations describe this situation? Select two answers
A.
f + f + (f + 2.50) = 11.25
B.
f + 2f + (f + 2.50) = 11.25
C.
f + 2f + (2f + 2.50) = 11.25
D.
2f + 2.50 = 11.25
E.
5f = 8.75
Answer:
Option C.
Option E.
Step-by-step explanation:
Let be "f" the price of a loaf of French bread, "w" the price of the grain bread and "c" the price of the cinnamon raisin bread.
We know that Melissa paid twice as much for the whole grain bread as for the French bread. This can be represented with this equation:
[tex]w=2f[/tex] [Equation 1]
Since she paid $2.50 more for the cinnamon raisin bread than for the whole grain bread, we can write this equation:
[tex]c=w+2.50[/tex] [Equation 2]
The total amount of money she spent was $11.25, then:
[tex]f+w+c=11.25[/tex] [Equation 3]
Now you must substitute the Equation 1 into the Equation 2:
[tex]c=2f+2.50[/tex] [Equation 4]
Substituting the [Equation 1] and the [Equation 4] into the [Equation 3], you get:
[tex]f+2f+(2f+2.50)=11.25[/tex]
If you simplify the equation, you get:
[tex]5f=8.75[/tex]
The correct equations that describe this situation are: A. f + f + (f + 2.50) = 11.25 and D. 2f + 2.50 = 11.25.
Explanation:The correct equations that describe this situation are:
f + f + (f + 2.50) = 11.252f + 2.50 = 11.25To solve this problem, let's assign variables to represent the prices. Let f be the price of a loaf of French bread. According to the information given, the whole grain bread costs twice as much as the French bread, so its price is 2f. The cinnamon raisin bread costs $2.50 more than the whole grain bread, so its price is (2f + 2.50). The total cost of the 3 loaves is $11.25, so we can set up the equations:
f + f + (f + 2.50) = 11.252f + 2.50 = 11.25Simplifying these equations gives us the correct choices A and D.
When 1,250 Superscript three-fourths is written in simplest radical form, which value remains under the radical?
2
5
6
8
The value remains under the radical is 8 ⇒ last answer
Step-by-step explanation:
Let us revise how to write the exponent as a radical
[tex]a^{\frac{m}{n}}[/tex] can be written as [tex]\sqrt[n]{a^{m}}[/tex]To simplify the radical factorize the base "a" to its prime factorsExample:
[tex](54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}[/tex] , Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 = [tex]2(3)^{3}[/tex][tex]\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}[/tex]2² can not go out the radical because 2 is less than 3 not divisible by 3[tex]3^{6}[/tex] can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical[tex]\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}[/tex]Now let us solve your problem
∵ [tex]1250^{\frac{3}{4}}=\sqrt[4]{1250^{3}}[/tex]
- Factorize 1250 to its prime factors
∵ 1250 = 2 × 5 × 5 × 5 × 5
∴ [tex]1250=2*5^{4}[/tex]
∴ [tex]\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}[/tex]
∵ 2³ can not go out the radical because 3 < 4 and not divisible by it
- [tex]5^{12}[/tex] can go out the radical because 12 can divided by 4
∵ 12 ÷ 4 = 3
∴ [tex]5^{12}[/tex] can go out the radical as 5³
∴ [tex]\sqrt[4]{1250}=5^{3}\sqrt[4]{2^{3}}[/tex]
∴ [tex]\sqrt[4]{1250}=125\sqrt[4]{8}[/tex]
∴ The value remains under the radical = 8
The value remains under the radical is 8
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Answer:
8
Explanation:
Egde 2020
Hope this helps :)
A scientist has two solutions which she has labeled solution A and solution B. Each contains salt. She knows that solution A is 30% salt and solution B is 55% salt. She wants to obtain 60 ounces of mixture that is 45% salt. How many ounces of each solution should she use?
Answer:
A= 24 ounces and B= 36 ounces.
Step-by-step explanation:
Given: Solution A contain 30% salt= 0.30 salt.
Solution B contain 55% salt= 0.55 salt.
New mixture should be of 60 ounces with 45% salt.
Let x be the amount of mixture for solution A. Let y be the amount of mixture of solution B.
Scientist need to to obtain 60 ounce of mixture from solution A and B.
∴ [tex]x+y= 60\ ounces[/tex]
y= [tex]60-x[/tex] equation 1
Now, solving to get final solution.
∴ [tex]0.3x+0.55y=0.45\times 60\ ounces[/tex]
Substituting the value of y from equation 1
⇒ [tex]0.3x+ 0.55\times (60-x)= 27[/tex]
⇒ [tex]0.3x+33-0.55x= 27[/tex]
⇒ [tex]-0.25x= -6[/tex]
∴ x= 24 ounces
Next, finding y
y= 60-x
∴ y= [tex]60-24= 36\ ounces.[/tex]
y= 36 ounces.
Now, we can say scientist would require 24 ounces of solution A and 36 ounces of solution B to obtain mixture of 60 ounces with 45% salt.
Eli took out a 20-year loan for $135,000 at 4.8% interest, compounded
monthly. If his monthly payment on the loan is $876.09, how much of his first
payment went toward note reduction?
O A. $876.09
B. $336.09
O
c. $540.00
D. $420.48
Answer:
B. $336.09
Step-by-step explanation:
Monthly payment = $876.09
Interest rate = 4.8%
Convert the annual interest rate to monthly rate = 4.8% / 12
Monthly rate = 0.4% or 0.004
Amount going towards interest payment = 0.004* loan amount
Interest = 0.004 * 135,000
Interest = $540
Therefore, from the monthly payment of $876.09 , $540 goes towards paying interest and the balance is the note reduction;
Note reduction = $876.09 - $540 = $336.09
Answer:
336.09
Step-by-step explanation:
this is the right anwser
Three times a number increased by ten is equal to twenty less than six times the number. Find the number
Let the number be x. "Three times a number increased by 10" is mathematically translated as
3x + 10
"is equal" is mathematically translated as twenty less than six times the number" is mathematically translated as
6x - 20
The whole sentence "Three times a number increased by ten is equal to twenty less than six times the number" is translated as
3x + 10 = 6x - 20
We now solve the above linear equation to find the number x
3x - 6x = - 20 - 10
- 3x = - 30
x = 10
Check answer
Three times a number increased by ten : 3 × 10 + 10 = 40
Twenty less than six times the number : 6 × 10 - 20 = 40
Final answer:
The simple linear equation given can be solved by defining the unknown number as 'x', setting up the equation, and solving for 'x'. After isolating x on one side, the result is that x equals 10.
Explanation:
The question is a classic example of a simple linear equation in one variable. We can define a variable, let's call it x, to represent the number in question. The problem statement translates to the equation:
3x + 10 = 6x - 20
Now, let's solve for x by isolating it on one side of the equation:
Subtract 3x from both sides:
10 = 3x - 20
Add 20 to both sides to get:
30 = 3x
Finally, divide both sides by 3 to find x:
x = 10
Therefore, the number we are looking for is 10.
There are 12 pupils in a class.
They are each asked whether they have a brother or a sister.
9 say they have a brother.
7 say they have a sister.
2 say they have neither.
Fill in the Venn diagram.
Answer:
The value in box of circle B is 3 and the value in box which belongs in both circle B and S is 6 and value which belongs in circle S is 1 and the value of box outside both the circle is 2.
Step-by-step explanation:
In given Venn diagram
ε = class of 12 pupils
pupils who have brother B = 9
pupils who have sister S = 7
pupils who have neither brother nor sister = 2
Hence the Venn diagram is drawn in the attachment for your reference.
n(E) =12
n(neither B nor S) = 2
So, n(B or S)= n(E) - n(neither B nor S)= 12-2=10
n(B) = 9
n(S) = 7
Now, addition theorem,
n(B or S) = n(B) + n(S) - n(B and S)
[tex]10=9+7-n(B\ and \ S)\\n(B\ and \ S) = 6[/tex]
So the value in box which is in both circle B and S is 6.
So the Box which contains only brothers = n(B) - n(B and S) = 9 - 6 = 3
Value in box of circle B is 3.
So the Box which contains only Sisters = n(S) - n(B and S) = 7 - 6 = 1
Value in box of circle S is 1.
There are 12 pupils in a class so, the number of pupils having both brother and sisters are 6 and the pupils had either brother or sister are 10.
Given :
There are 12 pupils in a class.9 say they have a brother. 7 say they have a sister. 2 say they have neither.Given that there are pupils in a class that is, n(E) = 12
Pupils who have brother, n(B) = 9
Pupils who have sister, n(S) = 7
Pupils who have neither brother nor sister, n(neither B nor S) = 2
So, n(B or S) = n(E) - n(neither B nor S)
= 12 - 2 = 10
n(B or S) = 10
Now, through the addition theorem:
n(B or S) = n(B) + n(S) - n(B and S)
10 = 9 + 7 - n(B and S)
n(B and S) = 6
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In January Jennifer was allowed to use 150 text messages. If she is allowed to use the same amount of text messages every month. How many text messages would she have used in all by the month of August?
She would have used 1200 messages in all by the month of August.
Step-by-step explanation:
Messages allowed per month = 150
There will be 8 months starting from January to August, therefore,
Time period = 8 months
Messages in 8 months = Messages per month * Time period
[tex]Messages\ in\ 8\ months=150*8\\Messages\ in\ 8\ months=1200[/tex]
She would have used 1200 messages in all by the month of August.
Keywords: Multiplication
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15. Which of the following equations was
used to graph the line shown?
A. y=6 + x
B. y=6 - x
C. y=x- 6
D. y=6x
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c (m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0)
m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1
Note the line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 or y = 6 - x ⇒ B
Please help thank you!!
Answer:
the answer is A 6.1
Step-by-step explanation:
Kayla is buying fruit for packed lunches. She needs to buy an assortment of at least 15 apples and oranges and spend less than $20.00. Apples (x) cost $0.65 each, an oranges (y) cost $0.78 each. Which system of linear inequalities models this situation?
Final answer:
The system of linear inequalities for Kayla's fruit purchase is x + y ≥ 15 to represent the quantity of fruit, and 0.65x + 0.78y < 20 to represent the budget constraint.
Explanation:
The student's question is asking for a system of linear inequalities that would model the situation in which Kayla wants to buy at least 15 fruits consisting of apples and oranges, without spending more than $20. Given that apples (x) are $0.65 each and oranges (y) are $0.78 each, we can set up the following inequalities:
x + y ≥ 15
0.65x + 0.78y < 20
The first inequality represents the requirement that Kayla needs to buy at least 15 pieces of fruit. The second inequality represents the constraint that she needs to spend less than $20 on her purchase.
Find the length of RS
Answer:
grab a ruler and put the 0 on the inches side up to the R and she what it's at when it hits S and do it again at T
Somebody help quick please
Answer:
106°
Step-by-step explanation:
For the equilateral ΔBCD all angles are 60° (180/3 = 60).
m∠ADB is 67° Since the triangle is isosceles the base angles are =.
m∠ ABD will be 180 - (67+67) = 46°.
m∠DBC = 60° so m∠ABC = 46 + 60 = 106°
Answer:
For the equilateral ΔBCD all angles are 60° (180/3 = 60).
m∠ADB is 67° Since the triangle is isosceles the base angles are =.
m∠ ABD will be 180 - (67+67) = 46°.
m∠DBC = 60° so m∠ABC = 46 + 60 = 106°
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Step-by-step explanation:
Henry and his children went into a grocery store and where they sell peaches for $2
each and mangos for $1.25 each. Henry has $20 to spend and must buy no less than
10 peaches and mangos altogether. If Henry decided to buy 4 peaches, determine all
possible values for the number of mangos that he could buy. Your answer should be a
comma separated list of values. If there are no possible solutions, submit an empty
answer.
Answer:
6, 7, 8, 9
Step-by-step explanation:
There ya go. The numbers of possible amounts of mangos he could buy without exceeding his budget.
The possible values of mangos if, The cost of peaches is $2, The cost of the mangos is $1.25, and the Total money is $20, are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
What is equation?
A formula known as an equation uses the equals sign to denote the equality of two expressions. In other terms, it is a mathematical statement stating that "this is equivalent to that."
Given:
The cost of peaches =$2,
The cost of the mangos = $1.25,
Total money = $20,
Write the equation, if Henry buys 10 peaches,
10 × 2 + 1.25x = 20
Here, x is the number of mangos,
1.25x = 20 - 20
x = 0
Write the equation when Henry buys 4 peaches,
4 × 2 + 1.25x = 20
8 + 1.25x = 20
x = 20 - 8 / 1.25
x = 9.6 or 9 mangos
Thus, Henry can buy a maximum of 9 mangos if he buys at least 4 peaches.
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What is x^5 times x^2 without exponents
Answer:
x^7
Step-by-step explanation:
(x^5)(x^2)=x^(5+2)=x^7
Please answer this correctly is the answer
3:37pm
6:37pm
8:37pm
5:37pm
Answer: 5:37
Step-by-step explanation:
The answer is d/5:37pm
Step-by-step explanation:
2:07+2:30=4:37
Cheyenne is 1 he ahead
4:37+1:00=5:37
Wich ratio is not equivalent to the other 3?
Ⓐ 2/3. Ⓑ 6/9
Ⓒ12/15. Ⓓ 18/27
Answer:
c 12/15
Step-by-step explanation:
Because you have to multiply 3 to the denominator and what ever you do to the denominator u have to do to the numerator so If u did 3 time 5 it would be 15 but if u do 5 time 2 it would be 10 not 12 because the unit rate fraction is 2/3 so u multiply 3 to each denominator and numerator since 2/3 is the unit rate fraction
Csc of 0°
Not sure how to find it
Answer:
undefined
Step-by-step explanation:
csc(x) = 1/sin(x)
csc0 = 1/sin0
sin0 = 0
1/0 = undefined
What is the unknown term.
in the seqpence 4.5, 5.4,____7.2
A.6.2 or B. 63
Answer:
6.3
Explanation:
To get from 4.5 to 5.4, you need to add 0.9. If you add 0.9 two more times, you get 7.2. Therefore, the middle term should be 6.3. I don't know if you made a typo and forgot the decimal when writing the options cause it says "63", but I believe the answer is 6.3.
Graph the solutions of the inequality
Answer:
The graph in the attached figure
Step-by-step explanation:
Graph the solution of the inequality
[tex]t\leq -4[/tex]
we know that
The solution is the interval ---> (-∞,-4]
All real numbers less than or equal to -4
In a number line the solution is the shaded area at left of t=-4 (closed circle, because the number -4 is included in the solution))
using a graphing tool
The graph in the attached figure
Evaluate the expression for x = 5, y = 3, and z = 1/4 . 5x−6y+20z4yz Enter your answer in the box.
To evaluate the given expression 5x−6y+20z4yz, for x = 5, y = 3, and z = 1/4, we substitute the given values and apply the order of operations to solve the problem.
Explanation:The question requires us to evaluate the mathematical expression given as 5x−6y+20z4yz with provided values of x = 5, y = 3, and z = 1/4. Let us substitute the values into the expression as follows:
First, replace each 'x', 'y', 'z' in the expression with the given values:
= 5×5 - 6×3 + 20×(1/4) / (4×3×(1/4))
= 25 - 18 + 20 / (3)
= 7 + 20/3
Finally, you can calculate the exact numerical result depending on whether you are allowed to leave it as an improper fraction or if you need to convert it to a mixed number or decimal form.
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Nathan estimated 67*36 by finding 70*40. Nathan’s estimate be greater than or less than the actual product? Explain.
Answer:
Nathan's estimate would be greater than the actual product.
Step-by-step explanation:
Let a, b, c, d be natural numbers such that a<c and b<d
Multiplying a positive number on both sides doesn't affect the inequality
⇒a×b < c×b and c×b < c×d
⇒a×b < c×d
Here 67<70 and 36<40
∴67×36<70×40
Hence, Nathan's estimate would be greater than the actual product.
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (4,80) and (7,140) to find the number of soda bottles the machine can make each minute.
This is a mathematics problem involving the calculation of the slope of a line graph. The machine produces 20 soda bottles per minute as concluded from the given coordinates (4,80) and (7,140).
Explanation:The subject of this question falls under Mathematics, specifically the topic of linear relationships or functions. The task is to calculate the rate at which soda bottles are made per minute using the given coordinates of the graph, (4,80) and (7,140).
First, we need to calculate the slope of the line represented by these points since the slope corresponds to the number of soda bottles produced per minute. In a linear relationship, the slope of the line can be found using the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (x1, y1) is (4,80) and (x2, y2) is (7,140). Plugging these values into the slope formula, we get: slope = (140 - 80) / (7 - 4) = 60 / 3 = 20.
So, the machine produces 20 soda bottles per minute.
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HELP WITH THIS???????????????????Will mark brainliest
Answer:
(1,c) (2,b) (3,A)
Step-by-step explanation:
May be right or worng i just read thought it better.
N - 5 is greater than or equal too -2. Solve plz!!!
Answer:
n > 3
Step-by-step explanation:
n - 5 > -2
Add 5 to both sides
n > 3
-5 is neither greater or equal to -2.
-2 is greater than -5.
Or, if you meant if 5 is greater than or equal to -2, then 5 is greater than -2.
Edit: Oh, wait nevermind I didn't see the N there
How do I delete my answer?
the line for the dunking machine was twice as long as the cake walk line the line for the Cakewalk was one third of the length of the line for the hoop shoot if there were 12 people in line for the hoop shoot how many people were in line for the dunking machine
Answer:
Total number of people in the line for the dunking machine is 8.
Step-by-step explanation:
Here, let us assume the number of people in the line for hoop shoot = 12
So, the number of people in the line for cakewalk
= One- Third of the number of people in line for Hoop Shoot
= [tex]\frac{1}{3} \times 12 = 4[/tex]
Also, the number of people in the line for dunking machine
= 2 x ( The number of people in line for Cakewalk)
= 2 x 4 = 8
Hence, the total number of people in line for the dunking machine is 8.
Final answer:
To find the number of people in line for the dunking machine when given the number in line for the hoop shoot, we calculate the cake walk line as one-third of the hoop shoot line, then double that for the dunking machine line, resulting in 8 people.
Explanation:
Given that the line for the dunking machine was twice as long as the cake walk line and that the cake walk line was one-third the length of the hoop shoot line, we can derive the relationship between the numbers of people in line for each activity.
First, since there were 12 people in line for the hoop shoot, and given that the cake walk line was one-third of this, the cake walk had 12 / 3 = 4 people in line.
Next, since the dunking machine line was twice as long as the cake walk line, it had 4 × 2 = 8 people in line.
The sum of 4 times a number and 7 equals 9
Answer:
0.5
Step-by-step explanation:
0.5 x 4 = 2, 2 + 7 = 9
Answer:n=1/2
Step-by-step explanation:
4n+7=9
-7 -7
4n=2
divide by 4 on both sides
n=1/2
The volume of a cube is 15.625cm3. Find the length of its edge
The edge of cube is: 2.5 cm
Step-by-step explanation:
Let V be the volume of cube
V = 15.625 cm^3
Let x be the side of the cube then
[tex]V = x^3\\15.625 = x^3[/tex]
Taking cube root on both sides
[tex]\sqrt[3]{x^3} = \sqrt[3]{15.625} \\x = 2.5\ cm[/tex]
The edge of cube is: 2.5 cm
Keywords: Volume, Cube
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Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4%
per year. How much did he invest at each rate if his annual return totaled $144?
Mr. Jackson invested $800 at 6% per year and $ 2400 at 4 % per year
Solution:Mr. Jackson invested a sum of money at 6% per year, and 3 times as much at 4% per year.
Let the sum invested be ‘a’ and ‘3a’ at 6% per year and 4 % per year respectively
Also, his annual return totaled $144
We can form following equation on the basis of question:-
[tex]\begin{array}{l}{\text { Then, } \frac{a \times 6 \times 1}{100}+\frac{3 a \times 4 \times 1}{100}=\$ 144} \\\\ {\frac{6 a}{100}+\frac{12 a}{100}=144} \\\\ {\frac{6 a+12 a}{100}=144} \\\\ {\frac{18 a}{100}=144} \\\\ {18 a=14400} \\\\ {a=14400 \div 18}\end{array}[/tex]
a = $800
The amount of money invested at 6% = a = 800
The amount of money invested at 4 % = 3a = 3(800) = 2400
So, the amount of money invested at 6% is $800 and the amount of money invested at 4% is $ 2400
To determine the amounts Mr. Jackson invested, the problem was solved by setting up a simple equation and solving for x, which represents the amount at 6% interest. Mr. Jackson invested $800 at 6% and $2400 at 4% to receive a total annual return of $144.
Explanation:The question involves solving a system of linear equations to find how much Mr. Jackson invested at two different interest rates if his total annual return is $144. To solve the problem, let's define the amount invested at 6% per year as x and the amount invested at 4% as 3x, since the latter is three times as much.
The interest from the investment at 6% would be 0.06x, and the interest from the investment at 4% would be 0.04 × 3x. Since these add up to $144, we can write the equation:
0.06x + 0.04 × 3x = 144
Solving this equation:
Multiply the 0.04 by 3x to get 0.12xAdd the two products together: 0.06x + 0.12x = 0.18xDivide both sides by 0.18 to find x: x = 144 / 0.18x = $800Since x represents the amount at 6%, Mr. Jackson invested $800 at 6% and $2400 at 4% because the investment at 4% is three times as much.