(a) 58 = 2(w + 5 + w)
(b) I. The width of the rectangle is 12 cm.
II. The length of the rectangle is 17 cm.
III. The area of the rectangle is 204 cm².
Let's solve the problem step by step:
(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:
Perimeter = 2(length + width)
Substituting the values, we have:
58 = 2(w + 5 + w)
Simplifying the equation, we get:
58 = 2(2w + 5)
(b) Now let's solve for the width and length of the rectangle:
I. To find the width, we solve the equation:
58 = 2(2w + 5)
Dividing both sides by 2, we get:
29 = 2w + 5
Subtracting 5 from both sides, we have:
24 = 2w
Dividing both sides by 2, we find:
w = 12 cm
Therefore, the width of the rectangle is 12 cm.
II. To find the length, we substitute the value of the width into the equation:
Length = w + 5 = 12 + 5 = 17 cm
Therefore, the length of the rectangle is 17 cm.
III. The area of the rectangle can be calculated using the formula:
Area = length × width
Substituting the values, we have:
Area = 17 cm × 12 cm = 204 cm²
Therefore, the area of the rectangle is 204 cm².
For more questions on area, click on:
https://brainly.com/question/2607596
#SPJ8
The better definition of Intersection is:
OA system that has at least one solution.
O Where lines cross over each other. The lines have a common point.
OA value we can put in place of a variable (such as x) that makes the equation true.
OA system that has no solutions.
Answer:
Where lines cross over each other. The lines have a common point.
Assume that at the current exchange rate, the British pound is worth $1.65 in American dollars. You have some dollar bills and several British pound coins. There are 17 items altogether, which have a total value of $20.25 in American dollars. How many American dollars and how many British pound coins do you have?
Answer:
So we have $11.64 in American dollars and £5 in British pound coin
Step-by-step explanation:
To solve this problem, we can use a system of equations. Let x be the number of American dollars and y be the number of British pound coins. Then we have:
x + y/1.65 = 20.25 (since each British pound coin is worth 1.65 American dollars)
x = 17 - y (since there are 17 items altogether)
Substituting the second equation into the first, we get:
(17 - y) + y/1.65 = 20.25
Multiplying both sides by 1.65, we get:
28.05 - y + y = 33.4125
y = 33.4125 - 28.05
y = 5.3625
Therefore, we have 5 British pound coins and:
x = 17 - y = 17 - 5.3625 = 11.6375
nt- Maths ACSF Level 3
Your mum has saved $12,000 and has agreed to give you a share.
Would you rather have
1/5 or 1/10
Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answer:
[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]
Step-by-step explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,
[tex]\cos(105\°)[/tex]
Using the angle sum identity for cosine.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]
Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.
[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]
Now applying the identity.
[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]
Now utilizing the unit circle.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]
[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]
Now simplifying...
[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]
Find the length of side a. 13, 5 B on a right triangle
In a right triangle, the length of side "a" is 12.
The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, can be used to find the length of side "a" in a right triangle with sides of 13 and 5 units.
Let's assign "a" as the unknown side. According to the Pythagorean theorem, we have the equation: [tex]a^{2}[/tex] = [tex]13^{2}[/tex] - [tex]5^{2}[/tex].
Simplifying the equation, we get [tex]a^{2}[/tex] = 169 - 25, which becomes [tex]a^{2}[/tex] = 144.
To solve for "a," we take the square root of both sides: a = √144.
The square root of 144 is 12. Therefore, side "a" has a length of 12 units.
In summary, using the Pythagorean theorem, we determined that side "a" in the right triangle with side lengths 13 and 5 units has a length of 12 units.
Know more about Pythagorean theorem here:
https://brainly.com/question/343682
#SPJ8
What is the slope of the Line y=-3x+2
Answer:
m = -3
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
The equation is y = -3x + 2
m = -3
So, the slope of the line is -3
Answer:
The slope is -3
Step-by-step explanation:
You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and the y-intercept.
y=mx+b, Where m is the slope and b is the y-intercept.
Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)
For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it
Answer:
Step-by-step explanation:
To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:
Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.
Subtract q(x) from p(x) to get (p - q):
(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)
= 5x^2 - x - 3 - 2x^2 - 4x + 3
= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)
= 3x^2 - 5x
Now, calculate the inner product of (p - q) with itself using the given inner product formula:
{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)
= 5(3)(3) + 4(-5)(-5) + 3(0)(0)
= 45 + 100 + 0
= 145
Therefore, the value of {p - q, p - q} is 145.
need help with tshdjkdkdndndndndkd
The length of this line segment is: B. 2√13 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(4 + 2)² + (1 + 3)²]
Distance = √[(6)² + (4)²]
Distance = √[36 + 16]
Distance = √52
Distance = 2√13 units.
Read more on distance here: brainly.com/question/12470464
#SPJ1
Cecilia se compra un libro con la cuarta parte de su dinero y un cómic con la mitad del dinero que le quedaba. Al salir de la librería se da cuenta que le sobraron $8. ¿Cuál es la ecuación para conocer la cantidad de dinero que tenía en un inicio?
The equation to determine the initial amount of money Cecilia had is x = 0.
Let's denote the initial amount of money Cecilia had as "x" dollars.
According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.
Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.
Since she had $8 left, we can set up the equation:
((x - (1/4)x) - ((1/2)x - 8)) = 8
To simplify the equation, we can first combine like terms:
(x - (1/4)x - (1/2)x + 8) = 8
Now, let's solve the equation step by step:
(x - (1/4)x - (1/2)x + 8) = 8
Multiplying the fractions by their common denominator, which is 4, we get:
(4x - x - 2x + 32) = 32
Simplifying further:
(x + 32) = 32
Subtracting 32 from both sides:
x = 0
Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.
for such more question on initial amount
https://brainly.com/question/17438795
#SPJ8
HELPPPPPP ME PLEASEEEEE!!
Answer:
Step-by-step explanation:
The quadratic formula is y=ax^2+bx+c
If we move everything to the left side of the equation,
-6x^2=-9x+7 becomes
-6x^2+9x-7=0
a=-6, b=9, c=-7, so the third answer choice
Find the value of the combination. 10C0 0 1 10
The formula to find the value of a combination is
[tex]C(n, r) = n! / (r!(n-r)!),[/tex]
where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1
In the combination,
n = 10 and r = 0,
so the formula becomes:
C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1
This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.
For more question combination,
https://brainly.com/question/1301954
Devaughn's age is three times Sydney's age. The sum of their ages is 80 . What is Sydney's age?
[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]
Sum up ;
[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]
So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years
Answer:
Sydney= 20, Devaughn= 60
Step-by-step explanation:
Let Sydney's age be 'x'
Devaughn's age = 3 times x = 3x
We Know That
The sum of their ages is 80.
So,
3x + x = 80
4x = 80
If we shift the 4 to the 80 side
x = 80/4
x = 20
So, Sydney's age is 20
Therefore, Devaughn's age =
3x = 3 times x
= 3 times 20
= 60
An import company brought into the country some amplifiers that cost sh. 3,750-each. The government imposed an import duty of 125% and a sales tax of 20 %. If the company decided to make a 10% profit on the sales, calculate the selling price of each amplifier.
Answer:
To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.
Cost of each amplifier: sh. 3,750
Import duty of 125% on the cost:
Import duty = 125% of sh. 3,750
= 125/100 * sh. 3,750
= sh. (125/100 * 3,750)
= sh. 4,687.50
Cost of each amplifier including import duty:
Total cost = Cost + Import duty
= sh. 3,750 + sh. 4,687.50
= sh. 8,437.50
Sales tax of 20% on the total cost:
Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50
= sh. (20/100 * 8,437.50)
= sh. 1,687.50
Total cost including sales tax:
Total cost = Total cost + Sales tax
= sh. 8,437.50 + sh. 1,687.50
= sh. 10,125
Desired profit margin of 10% on the total cost:
Profit = 10% of Total cost
= 10/100 * sh. 10,125
= sh. (10/100 * 10,125)
= sh. 1,012.50
Selling price of each amplifier:
Selling price = Total cost + Profit
= sh. 10,125 + sh. 1,012.50
= sh. 11,137.50
Mia makes $15.50 per hour. For the Memorial holiday she worked 6 hours and 30 minutes on Friday. On Saturday, she worked for 1 hour and 10 minutes less than she did on Friday and on Monday she worked 4 hours and 10 minutes. How much money did Mia make for the Memorial holiday?
Answer:
$248.00
Step-by-step explanation:
Hours worked on Friday: 6 hr and 30 min = 6.5 hr
Money earned on Friday: $15.5/hr x 6.5 hr = $100.75
Hours worked on Saturday: 6.5 hr - 1.167 hr = 5.33 *10 min = 10/60 = 0.1667 hr
Money earned on Saturday: $15.50 x 5.33 hr = $82.67
Hours worked on Monday: 4.167 hr
Money earned on Monday: $15.50/hr x 4.167 hr = $64.58
Total money made: 100.75 + 82.67 + 64.58 = $248.00
please answer i am stuck
The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).
The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:
-x + 20y = 87
-x + 10y = 37
y = 5
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(5) = 87
x = 100 - 87
x = 13
-x + 10(5) = 37
x = 50 - 37
x = 13
Therefore, the system of equations has only one solution (13, 5).
For the year when the population are all the same for three countries, we have:
x = 2010 + (13 - 10)
x = 2013
Read more on solution and equation here: brainly.com/question/25858757
#SPJ1
Please i give 25 points
in this chart, × is the length of a persons forearm in centimeters and y is the persons height in centimeters. the question is if someones forearm (x) is 24.5 cm, how tall would they be? how do i find this? and how would i make a linear regression graph? thanks
The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.
How to construct and plot the data in a scatter plot?In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;
y = 3.01x + 89.63
Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;
y = 3.01x + 89.63
y = 3.01(24.5) + 89.63
y = 163.375 ≈ 163.38 centimeters.
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
a. Find the slope of x^3+y^3-65xy=0 at the points (4,16) and (16,4).
b. At what point other than the origin does the curve have a horizontal tangent line?
c. Find the coordinates of the point other than the origin where the curve has a vertical tangent line.
a. The slope of the curve at the point (4,16) is approximately 1.165, and at the point (16,4) is approximately -0.496.
b. The curve has a horizontal tangent line at the points(0,0) and (3,27).
c. The curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).
How is this so?a. To find the slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.
Differentiating the equation with respect to x, we have -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.
For the point (4,16) -
3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0
48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0
508(dy/dx) = 592
(dy/dx) = 592/508
(dy/dx) ≈ 1.165
For the point (16,4) -
3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0
768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0
(-992)(dy/dx) = 492
(dy/dx) = 492/(-992)
(dy/dx) ≈ -0.496
Thus, the slope of the curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.
b. To find the point where the curve has a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.
This means the slope is zero and the tangent line is horizontal.
From the derivative we obtained earlier -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
Setting dy/dx equal to zero -
3x² - 65y = 0
Substituting y = x³/65 into the equation -
3x² - 65(x³/65) = 0
3x² - x³ = 0
Factoring out an x² -
x²(3 - x) = 0
This equation has two solutions - x = 0 and x = 3.
hence, the curve has a horizontal tangent line at the points(0,0) and (3,27).
c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s) where the derivative is undefinedor approaches infinity.
From the derivative -
3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0
To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.
Setting the denominator equal to zero: -
65x = 65y
x = y
Substituting this condition back into the original equation -
x³ + x³ - 65x² = 0
2x³ - 65x² = 0
x²(2x - 65) = 0
This equation has two solutions - x = 0 and x = 65/2.
Therefore, the curve has a vertical tangent line at the points (0,0)
and(65/2, (65/2)³).
Learn more about slope:
https://brainly.com/question/3493733
#SPJ1
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses
Answer:
37
Step-by-step explanation:
x=-4
=2(5-(-4)2+1
=2(5+4)2+1
=2(9)2+1
=18(2)+1
=36+1
=37
A store has a sale with 20% off every item. When you enter the store, you receive a coupon that states that you receive an additional 30% off. Is this equal to a 50% discount? Explain your answer
Answer: Nope
Step-by-step explanation:
No, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.
To understand why, let's consider an example with an item priced at $100.
If there is a 20% discount applied initially, the price of the item would be reduced by 20%, which is $100 * 0.20 = $20. So the new price after the first discount would be $100 - $20 = $80.
Now, if there is an additional 30% discount applied to the $80 price, the discount would be calculated based on the new price. The 30% discount would be $80 * 0.30 = $24. So the final price after both discounts would be $80 - $24 = $56.
Comparing the final price of $56 to the original price of $100, we can see that the total discount is $100 - $56 = $44.
Therefore, the total discount received is $44 out of the original price of $100, which is a discount of 44%, not 50%.
Hence, receiving a 20% discount followed by an additional 30% discount does not result in a total discount of 50%.
Colin and Paul have played 38 tennis matches.
Colin has won 20 times.
Paul won the rest.
a) Estimate the probability that Colin wins.
b) Estimate the probability that Paul wins.
Answer:
P(Colin) = 20/38
P(Paul) = 18/38
Step-by-step explanation:
Colin won 20 times out of 38, so the probability that he wins would be 20/38 (or 10/19 simplified).
Paul won 18 times out of 38, so the probability that he wins would be 18/38 (or 9/19 simplified).
Answer:
a) Probability of Colin winning = 10/19
b) Probability of Paul winning = 9/19
Step-by-step explanation:
Total number of matches = 38
Colin won 20,
Paul won the rest so, 38 - 20 = 18
Paul won 18 matches,
From this data, we calculate the probabilities of Colin or Paul winning,
a) Estimate the probability that Colin wins.
Colin won 20 out of 38 matches, so his probability of winning is,
20/38 = 10/19
Probability of Colin winning = 10/19
b) Estimate the probability that Paul wins
Paul won 18 out of 38 matches, so his probability of winning is,
18/38 = 9/19
Probability of Paul winning = 9/19
Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students.
Part A
Write an expression for how many pencils she has left after giving them out to her students.
A.
100
−
2
×
(
22
−
19
)
B.
100
−
2
×
22
−
19
C.
100
−
2
×
22
−
2
×
19
D.
100
−
22
−
19
Part B
Does she have enough pencils to give each of her students 2?
Yes or no
, she has
15,18,37,59
More or fewer
than she needs.
Answer:
Part A:
The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:
A. 100 - 2 × (22 - 19)
Part B:
To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.
If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.
Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.
Yes, she has enough pencils to give each of her students 2.
She has 18 more than she needs.
Purchasing a Car
Now you have to decide how to save enough money to purchase a used car in three years. You have the
$1000 that you saved up and you plan to continue working. According to your estimates, you can save an
additional $60 per month to put towards the car purchase. After conducting some research at the banks,
you have decided on two options (see below). You need to figure out which option will yield the most
money after the three years.
Option #1-CD for 3 years
Interest rate of 3% compounded monthly.
No money can be added to the CD.
However you can save your money on the side.
Option # 2-CD for 1 year
Interest rate of 2% compounded quarterly.
You can add money at the end of each year.
You will renew it each year for 3 years.
Work Shown:
Answer:
Step-by-step explanation:
To determine which option will yield the most money after three years, let's calculate the final amount for each option.
Option #1 - CD for 3 years:
Principal (initial investment) = $1000
Interest rate = 3% per year (compounded monthly)
No additional money can be added
To calculate the final amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
For Option #1:
P = $1000
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
A = $1000 * (1 + 0.03/12)^(12*3)
Calculating the final amount for Option #1, we get:
A = $1000 * (1 + 0.0025)^(36)
A ≈ $1000 * (1.0025)^(36)
A ≈ $1000 * 1.0916768
A ≈ $1091.68
Option #2 - CD for 1 year:
Principal (initial investment) = $1000
Interest rate = 2% per year (compounded quarterly)
Money can be added at the end of each year
To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.
First Year:
P = $1000
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1000 * (1 + 0.02/4)^(4*1)
A ≈ $1000 * (1.005)^(4)
A ≈ $1000 * 1.0202
A ≈ $1020.20
At the end of the first year, the total amount is $1020.20.
Second Year:
Now we add an additional $60 to the previous amount:
P = $1020.20 + $60 = $1080.20
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1080.20 * (1 + 0.02/4)^(4*1)
A ≈ $1080.20 * (1.005)^(4)
A ≈ $1080.20 * 1.0202
A ≈ $1101.59
At the end of the second year, the total amount is $1101.59.
Third Year:
Again, we add $60 to the previous amount:
P = $1101.59 + $60 = $1161.59
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1161.59 * (1 + 0.02/4)^(4*1)
A ≈ $1161.59 * (1.005)^(4)
A ≈ $1161.59 * 1.0202
A ≈ $1185.39
At the end of the third year, the total amount is $1185.39.
Comparing the final amounts:
Option #1: $1091.68
Option #2: $1185.39
Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.
please answer ASAP I will brainlist
The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).
The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:
-x + 20y = 129
-x + 10y = 59
y = 7
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(7) = 129
x = 140 - 129
x = 11
-x + 10(7) = 59
x = 70 - 59
x = 11
Therefore, the system of equations has only one solution (11, 7).
For the year when the population are all the same for three countries, we have:
x = 2010 + (11 - 10)
x = 2011
Read more on solution and equation here: brainly.com/question/25858757
#SPJ1
GEOMETRY 100 POINTS
TY
Answer:
A.
Step-by-step explanation:
In this case, we have to use tan ([tex]\frac{opposite}{adjacent}[/tex] because we are asked for the opposite side (x) given the adjacent side (20 m).
So tan(75)=[tex]\frac{x}{20}[/tex]
Solve for x
x = 20 * tan(75)
x = 74.641...
x = 74.64 m
Answer:
The height is 74.64 meters
Step-by-step explanation:
We have a ΔABC with ∠B = 75°, hypotenuse = AB
[tex]cos\; 75\textdegree = \frac{\sqrt{3} -1}{2\sqrt{2} }\\\\\frac{1}{cos\; 75\textdegree} = \frac{2\sqrt{2} }{\sqrt{3} -1}[/tex]
cos B = adjacent/hyppotenuse
⇒ hypotenuse (AB) = adjacent/cosB = 20/cosB
[tex]= 20 \frac{2\sqrt{2} }{\sqrt{3} -1}\\\\= \frac{40\sqrt{2} }{\sqrt{3} -1}\\\\= 77.27[/tex]
⇒ AB = 77.27
By pythagoras theorem,
AB² = AC² + BC²
⇒ AC² = AB² - BC²
= 77.27² - 20²
AC² = 5570.65
⇒ AC = √5570.65
AC = 74.64
GEOMETRY 50POINTS
FIND x
Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have:
x + 37 > 15 (Sum of x and 37 is greater than 15)
x + 15 > 37 (Sum of x and 15 is greater than 37)
37 + 15 > x (Sum of 37 and 15 is greater than x)
From the first inequality, we can subtract 37 from both sides:
x > 15 - 37
x > -22
From the second inequality, we can subtract 15 from both sides:
x > 37 - 15
x > 22
From the third inequality, we can subtract 15 from both sides:
52 > x
Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
for similar questions on Triangle.
https://brainly.com/question/1058720
#SPJ8
There are 12 containers containing various amounts of water, as shown below. ←+ 0 H ½ X X X X X X 1 X 1½ X X X 2 Cups If all of the water were dumped into one container, how many cups would be in the container?
Answer: it contains 12 containers
Step-by-step explanation: i dont know what the answer is but i know what i can help you with all you have to do is round the answer.
Which expression is equivalent to 10f - 5f + 8 +6g +4?
The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.
To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:
10f - 5f + 8 + 6g + 4
Combining the terms with 'f', we have:
(10f - 5f) + 8 + 6g + 4
This simplifies to:
5f + 8 + 6g + 4
Next, we can combine the constant terms:
8 + 4 = 12
Thus, the simplified expression is:
5f + 12 + 6g
This expression is equivalent to 10f - 5f + 8 + 6g + 4.
In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.
For more question on expression visit:
https://brainly.com/question/1859113
#SPJ8
omari's monthly taxable income is ksh 24200. calculate the tax charged on omari's monthly earning
The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.
To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.
Assuming we have a simplified progressive tax system with three tax brackets:
For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.
For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.
For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.
To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:
Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.
Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.
The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.
Now, we can sum up the taxes for each bracket:
Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket
Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840
Total Tax = Ksh 3,340
For more such questions on tax charged visit:
https://brainly.com/question/1592982
#SPJ8