In geometry, a line segment is bordered by two distinct points on a line. Or we can say a line segment is a portion of the line that connects two points.
The length of the line segment does not differ and the distance between them does not change. The units in which a line can be estimated are centimetres, millimetres, meters, inches, or feet.
A closed-line segment has both endpoints, whereas an open-line segment has two endpoints. A line segment that has only one endpoint is known as a half-open line segment.
A line segment with two endpoints P and Q and is denoted by the bar symbol (—).
To know more about endpoints, here
https://brainly.com/question/29164764
#SPJ4
FIND THE SUM OF ALL NATURAL NUMBERS FROM 1 TO 100 (ARITHMETIC PROGRESSION)
Answer:
According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.
Misha says that if a line crosses the x-axis before it crosses the y-axis, the
values of m and b in its equation will both be positive. Is she correct?
No, Misha is not correct in her statement that the equation will be positive.
Define Slope.A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
What are coordinate pairs?An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.
No, Misha is not correct. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. A line can cross the x-axis before it crosses the y-axis, and the values of m and b in its equation can still be either positive, negative or zero.
For example, a line with the equation y = -2x + 1 will cross the x-axis at x = 1/2 and y-axis at (0,1) , so it crosses x-axis first but both m and b have negative values (-2 and 1 respectively).
Know more about slope by visiting:
https://brainly.com/question/3605446
#SPJ1
The start of an arithmetic sequence is shown below.
Work out the nth term
Work out the 30th term in this sequence.
4 - 13 - 22 - 31
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
Define arithmetic mean.When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.
Here,
Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.
Alternatively put,
=> an=a1+d(n−1)
.Arithmetic Sequence:
d=9
This is the formula of an arithmetic sequence.
=>an=a1+d(n−1)
Substitute in the values of
=> a1 =4 and
d=9
.=>an=4+9(n−1)
Simplify each term.
Tap for more steps...
an=4+9n−9
Subtract 9 from 4
an=9n−5
Thus 30th term :
=> a(30)=9(30)−5
=> a(30) = 265
Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.
To know more about arithmetic mean , visit
https://brainly.com/question/13000783
#SPJ1
what are the coordinates of the center of the center and the length of the radius of the circle whose equation is x^2 y^2
The coordinates of the center of the circle and the radius length of the specified circle are (-3,2) and 6 units, respectively.
What is circle?A circle is a shape formed by all points in a plane that are at a particular distance from the center. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant. A circle is a closed two-dimensional object in which the set of all the points in the plane is equidistant from a particular point called "centre". The line of reflection symmetry is formed by every line that travels through the circle. It also features rotational symmetry around the center for all angles.
Here,
x²+6x+9-9+y²-4y+4-4=23
(x+3)²-9+(y-2)²-4=23
(x+3)²+(y-2)²=36
(x+3)²+(y-2)²=6²
center=(-3,2)
radius=6
The coordinates of the center of the center and the length of the radius of the given circle is (-3,2) and 6 units.
To know more about circle,
https://brainly.com/question/26533660
#SPJ4
Math
A 6. 0 kg bowling ball traveling at 2 m/s strikes a 1. 5 kg bowling pin. Describe and compare the forces that act on the bowling ball and the bowling pin
during the collision.
By using formula and solving, Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t
What is collision?A collision is an event in which two or more objects come into contact with each other. In physics, a collision is defined as a rapid and forceful interaction between two or more objects that causes a transfer of energy. Collisions can be elastic or inelastic, depending on whether or not the total kinetic energy of the objects is conserved.
What is force?Force is a physical quantity that describes the interaction between two or more objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause an object to accelerate, change its shape, or change its direction of motion. Forces can be categorized into different types, such as contact forces, which act when two objects are in contact, and non-contact forces, which act at a distance. Some examples of non-contact forces are gravitational force, electric force, and magnetic force.
To calculate the force of impact on the bowling ball and bowling pin during the collision, you can use the formula:
Force of Impact = Change in momentum / Time of collision
The change in momentum is given by the formula:
Change in momentum = Final momentum - Initial momentum
The initial momentum of the 6 kg bowling ball traveling at 2 m/s is:
Initial momentum (ball) = 6 kg * 2 m/s = 12 kg*m/s
The final momentum of the bowling ball can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision. In this case, since the bowling pin is moving after the collision and the bowling ball is not, the final momentum of the bowling ball is zero.
Final momentum (ball) = 0
Change in momentum (ball) = Final momentum (ball) - Initial momentum (ball) = 0 - 12 kgm/s = -12 kgm/s
The force of impact on the bowling ball is:Force of impact (ball) = Change in momentum (ball) / Time of collision = -12 kg*m/s / t (t is the time of collision, assuming it's a short time)
Similarly, the initial momentum of the 1.5 kg bowling pin at rest is:
Initial momentum (pin) = 1.5 kg * 0 m/s = 0 kg*m/s
The final momentum of the bowling pin can be calculated using the conservation of momentum principle, which states that the total momentum of the system remains constant before and after the collision.
Final momentum (pin) = Initial momentum (ball) = 12 kg*m/s
Change in momentum (pin) = Final momentum (pin) - Initial momentum (pin) = 12 kgm/s - 0 kgm/s = 12 kg*m/s
The force of impact on the bowling pin is:
Force of impact (pin) = Change in momentum (pin) / Time of collision = 12 kg*m/s / t
To know more about force visit:
https://brainly.com/question/13191643
#SPJ4
The pitchers for the home team had 12 strikeouts for 32 batters, while the pitchers for the visiting team had 15 strikeouts for 35 batters. Which pitching team had a greater fraction of strikeouts.(Hint: Just make the 12 for 32 and 15 for 35 into fractions and see which is greater or less than.)
Answer:
2958843/5 5/1000775747373838388484737372737375823What should be added to 7x^2 5x 1 to get 3x^2 4x 7?
The value should be added will be [tex]y = -4x^{2} +9x+6[/tex]
Now, According to the question:
Let the value y be added to [tex]7x^2-5x+1[/tex] to give [tex]3x^2+4x+7[/tex]
y = [tex]3x^2+4x+7[/tex] - ( [tex]7x^2-5x+1[/tex])
y = [tex]3x^{2} +4x+7-7x^{2} +5x-1[/tex]
Combine like terms:
y = [tex]3x^{2} -7x^{2} +4x+5x+7-1[/tex]
Calculate the subtraction and addition.
[tex]y = -4x^{2} +9x+6[/tex]
Hence, The value should be added will be [tex]y = -4x^{2} +9x+6[/tex].
Learn more about Addition at:
https://brainly.com/question/24289893
#SPJ4
The complete question is this:
What should be added to [tex]7x^2-5x+1[/tex] to get [tex]3x^2+4x+7[/tex] ?
2x-(x+5)=-1
Solve for x.
Answer:
x=4
Step-by-step explanation:
2x-(x+5)=-1
Solve for x
Distribute the minus sign
2x-x-5=-1
Combine like terms
x -5 = -1
Add 5 to each side
x-5+5 = -1+5
x=4
[tex]2x-(x+5)=-1[/tex]
Distribute negative sign:
[tex]2x+-1(x+5)=-1[/tex]
[tex]2x+-x+-5=-1[/tex]
Combine Like Terms:
[tex](2x+-x)+(-5)=-11[/tex]
[tex]x-5=-1[/tex]
Add 5 to both sides:
[tex]x-5+5=-1+5[/tex]
[tex]\fbox{x = 4}[/tex]
Person A buys 10 granola bars and 6 cups of yogurt for $18. Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the cost of each item.
Answer:
granola bar: $1.50yogurt: $0.50Step-by-step explanation:
You want the cost of each item when person A buys 10 granola bars and 6 cups of yogurt for $18, and person B buys 5 granola bars and 4 cups of yogurt for $9.50.
EquationsThe equations describing the relations can be written ...
10g +6y = 18 . . . . . . . person A's purchase
5g +4y = 9.50 . . . . . . person B's purchase
SolutionSubtracting half of the first equation from the second, we find ...
(5g +4y) -1/2(10g +6y) = (9.50) -1/2(18)
y = 0.50 . . . . . . . . . . simplify
Substituting this into the first equation gives ...
10g +6(0.50) = 18
10g = 15 . . . . . . . . . . subtract 3
g = 1.50 . . . . . . . . . divide by 10
Each granola bar costs $1.50; each cup of yogurt costs $0.50.
__
Additional comment
The attachment shows the solution found using a calculator to find the reduced row-echelon form of the augmented coefficient matrix. The variable values are in the right column of the reduced matrix. This tells us granola bars are $1.50, and yogurt cups are $0.50, as we found above.
At an archeological site, the remains of two ancient step pyramids are congruent . If ABCD cong EFGH find each of the following . (Diagrams are to scale. )
The measurements are found using congruency.
What does congruency mean?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
It is given that ABCD ≅ EFGH :
According to congruency,
22. AD = EH, so AD = 335 ft.
23. GH= CD, so GH = 45ft.
24. m∠GHE = m∠CDA, so m∠GHE= 52°
25. m∠BAD= m∠FEH, so m∠BAD= 52°
26. EF= AB, so EF= 45ft
27. BC= FG, so BC= 280ft
28. m∠DCB= m∠HGF, so m∠DCB= 128°
29. m∠EFG= m∠ABC, so m∠EFG= 128°
To learn more about congruency, refer to the link below:
brainly.com/question/30094441
#SPJ1
What are the 15 types of angles?
There are various classifications of angles, some of which include: Acute angles, Right angles, Obtuse angles, Straight angles, Reflex angles, Complementary angles, Supplementary angles, Adjacent angles, Linear pair, Vertically opposite angles, Alternate interior angles, Alternate exterior angles, Corresponding angles, Conjugate angles, and Explementary angles.
It's important to note that this is not an exhaustive list and the classification may vary depending on the context.
Acute angles which measure less than 90 degrees, Right angles that measure exactly 90 degrees, Obtuse angles that measure more than 90 degrees but less than 180 degrees.
There is also Straight angles that measure exactly 180 degrees, Reflex angles that measure more than 180 degrees but less than 360 degrees, Complementary angles which add up to 90 degrees, Supplementary angles which add up to 180 degrees.
Then there is Adjacent angles that share a common vertex and a common side but no common interior points, Linear pair which add up to 180 degrees and share a common side, Vertically opposite angles that are formed by two intersecting lines and are opposite to each other, Alternate interior angles that are formed by two intersecting lines on opposite sides of a transversal and inside parallel lines, Alternate exterior angles that are formed by two intersecting lines on opposite sides of a transversal and outside parallel lines, Corresponding angles that are formed by two intersecting lines in the same relative position.
Conjugate angles are angles which are supplementary but non-adjacent, and Explementary angles are angles which add up to 90 degrees.
To know more on angles
https://brainly.com/question/19247815
#SPJ4
Geometry - Should be pretty easy
Answer:
DQR
Step-by-step explanation:
DEF is complentary to DQR
Answer:
∆DQR
Step-by-step explanation:
You want the similarity statement if the triangles shown are similar.
SimilarityTriangles will be similar if they have congruent corresponding angles, or proportional corresponding sides.
No angles are shown in the figure, but side lengths are given.
We expect that if the triangles are similar that the corresponding sides will be ...
DE ⇔ DQEF ⇔ QRFD ⇔ RDProportionThe attached calculator display shows the ratios of these side lengths are the same: 14/3. That means ...
∆DEF ~ ∆DQR
<95141404393>
1)
2)
Which relation is not a function?
1
-A
30
2
B
3.
: mo
C
A
4
36
3
3)
4)
2-
x
relations
246
6:
8-
Co
8
-10
12
₹10
12
Answer:
2, cause it shows a different function or pattern
For each linear relationship determine the y intercept write an ordered pair and explain its meaning
A: Ailee has a Gift card to a coffee shop worth $20 each drink she purchases using the gift card costs $4.25
B: Duncan begins to hike a trail that is an elevation of 1000 feet as he hikes his elevation increases 2000 feet each hour he hikes
Please help!!!
Answer: For the linear relationship in A, the y-intercept is the point where the line crosses the y-axis. This point represents the starting balance on Ailee's gift card before she makes any purchases.
The y-intercept of this linear relationship is the point (0, 20), which represents the fact that Ailee's gift card has a starting balance of $20 before she makes any purchases.
For the linear relationship in B, the y-intercept is the point where the line crosses the y-axis. This point represents Duncan's starting elevation before he begins to hike.
The y-intercept of this linear relationship is the point (0, 1000), which represents the fact that Duncan starts his hike at an elevation of 1000 feet.
Step-by-step explanation:
6) The area of a triangle is A = bh-2. If the base (b) is H untis and the
height (h) Is 7 units, what is the area of the triangle?
I
Answer:
The area of a triangle can be calculated using the formula A = 1/2 * b * h, where b is the base and h is the height of the triangle. In this case, if the base of the triangle is H units and the height is 7 units, the area of the triangle would be A = 1/2 * H * 7 = 3.5 * H.
Step-by-step explanation:
Write an equivalent expression by distributing the "-" sign outside the parentheses:
-(-10p - 0. 7q) – 4. 6
After distribution of the negative sing in the parenthesis, the equivalent expression is 10.7p - 4.6
The expression that is given to us is -(-10p - 0. 7q) – 4. 6.
Now, we know that the meaning of equivalent expression is the it has the same value as that of the original expression.
We have to use the "-" and distribute it over the expression to form an equivalent relation,
So, we know,
-(-10p - 0.7q) – 4.6
Here, p is a constant,
Multiplying the negative sign inside of the bracket,
= (-(-10p)-(-0.7p)-4.6
= 10p + 0.7p - 4.6
= 10.7p - 4.6
So, the equivalent expression is 10.7p - 4.6.
To know more about mathematical expressions, visit,
https://brainly.com/question/1859113
#SPJ4
Hi! I need Help With The Bottom Answers Someone Already Answered The Top So Just The Bottom Questions!
F:4+4=8
A:23+8+4=35
H:53+3+28=84
I:11+17+93=121
I:24+8+3=35
I think that is all correct
What are the 3 segments?
Business-to-Business (B2B): This segment involves transactions between two businesses, Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer and Consumer-to-Consumer (C2C): This segment involves transactions between two consumers.
1. Business-to-Business (B2B): This segment involves transactions between two businesses. Examples of B2B include sales of raw materials by a manufacturer to a wholesaler or the sale of supplies by an office supply company to a retailer.
2. Business-to-Consumer (B2C): This segment involves transactions between a business and a consumer. Examples of B2C include online retailers selling products directly to consumers, subscription services, and digital content providers.
3. Consumer-to-Consumer (C2C): This segment involves transactions between two consumers. Examples of C2C include online marketplaces, auctions, and classifieds where individuals can buy and sell items to other individuals.
the complete question is : What are the 3 segments of e-commerce ?
learn more about transaction here
https://brainly.com/question/2473679
#SPJ4
Which of the following would NOT cast doubt of the usefulness of sample? data? Choose the correct answer below.
a. Order of questions in a survey
b. Missing data
c. Nonresponse
d. An effective sampling method
An effective sampling method is not cast doubt on the usefulness of the sample
The effective sample is a calculation of the approximate sample size needed to obtain the same degree of accuracy as a simple random sample. It is denoted mathematically by the formula n/D, where n represents the sample size and D denotes the design effect. It is employed as a means of condensing the volume of data.
Effective sample size calculations are mostly used for qualitative analyses of the sample size. The sample size calculates the total number of measurements or observations made during an experiment or survey. The effective sample size—rather than the actual sample size—is utilized in this assessment since it is thought that a sample size of 30 is necessary for an analysis to be valid.
To know more samples at:
https://brainly.com/question/27829028
#SPJ4
Please help me with my HW
Answer:
24d^5
Step-by-step explanation:
How do you know if you add or subtract in elimination?
For m(x)=
-3/4x+6, find the value of x for which m(x) = 0.
The value of x when m(x) = 0 is 8.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.
The given function is,
m(x) = -3/4 x + 6
Here the value of m(x) depends on the value of x.
m(x) = 0
-3/4 x + 6 = 0
-3/4 x = -6
x = -6 ÷ -3/4
x = 6 × 4/3
x = 8
Hence when m(x) = 0, the value of x is 8.
To learn more about Linear Functions, click on the link :
https://brainly.com/question/29205018
#SPJ1
find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius 3
The Volume of largest Right Circular Cylinder that can be inscribed in Sphere of radius 3 cm is 65.3 cm³ .
Let the half height of of the cylinder be = h ;
we use h instead of [tex]\frac{h}{2}[/tex] for easier simplification ,
In order to find the Volume of cylinder , we multiply the area of top with the total height of cylinder .
So , Volume = [tex]\pi \times (Radius Of Cylinder)^{2}\times (Height Of Cylinder)[/tex]
Volume = [tex]\pi \times (\sqrt{r^{2} -h^{2} } )^{2}\times (2h)[/tex];
Volume [tex]= 2\pi h(r^{2} -h^{2} )[/tex]
Now , we need the derivative of volume function and equate to 0. If we move the h inside parenthesis, we only need to use power rule to get derivative.
So , we get , V = [tex]2\pi (r^{2} h-h^{3} )[/tex] ,
On simplifying further ,
we have ,
Volume of Largest Right Circular Cylinder ⇒ [tex]\frac{4\sqrt{3} \pi r^{3} }{9}[/tex] ;
it is given that radius of sphere is = 3 cm ,
Substituting value of radius in Volume formula ,
we get ,
V = [tex]\frac{4\sqrt{3} \times 3.14\times 3^{3} }{9}[/tex] ;
V = 65.2636 cm³
V ≈ 65.3 cm³.
Therefore , the volume of the largest right circular cylinder is 65.3 cm³.
Learn more about Volume here
https://brainly.com/question/29235668
#SPJ4
Your friend wants to mark her favorite campsite on the map. She knows that the campsite is 65 miles north of her town. What distance on the map (in inches) represents an actual distance of 65 miles?
inches
Answer:
Step-by-step explain
We know that the campsite is 65 miles north of her town.
There are 63,360 inches in a mile
so, if you multiply it would look like
63,360 x 65 = 4,118,400
so, your answer would be 4,118,400 inches
You need to put equation signs in between the 6. 1 gross = 144
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Place the arithmetic symbol between the 6 times 6 to become one. Then we have
⇒ 6 + 6 - 6 - 6 + 6 / 6
⇒ 1
The arithmetical symbols in between these numbers make the total 1 gross will be 6 + 6 - 6 - 6 + 6 / 6.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
a wall in marcus's bedroom is 8 2/25 feet high and 16 2/3 long. If he paints 1/2 the wall blue how many square feet will be blue
Answer: 66.70
Step-by-step explanation:
8 2/25 times 16 2/3 then divide by 2 and you get 66.70 will be blue
In Lewis County , there were 2 , 277 student athletes competing in spring sports in 2014 . That was 110% of the number from 2013, which was 90% of the number from the year before. How many student athletes signed up for a spring sport in 2012
In the spring of 2012, 2300 student athletes participated in a sport.
How do I calculate a percentage?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
In 2014, there were 2277 student athletes participating in spring sports.
Suppose there were x contestants in 2013.
The answer was 2277, which was 110 percent more pupils competing in 2014 than in 2013. So,
[tex]$110 \%$ of $\mathrm{x}=2277$$\frac{110}{100} \times \mathrm{x}=2277$$\mathrm{x}=\frac{2277 \times 100}{110}$$\mathrm{x}=2070$[/tex]
2070 pupils therefore competed in 2013.
Let y be the student who will be vying in 2012.
Now, the number of pupils competing in 2070 was 90% that of the year 2012's.
So,
[tex]$90 \%$ of $y=2070$$$\begin{aligned}& \frac{90}{100} \times y=2070 \\& y=\frac{2070 \times 100}{90} \\& y=2300\end{aligned}$$[/tex]
As a result, 2300 students competed in the 2012 competition.
Therefore, the answer is 2300.
To learn more about percentage refer to:
https://brainly.com/question/24877689
#SPJ4
You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2?
In scenerio 1, the money in the retirement account at 62 years old is $1,267,250.76
In scenerio 2, the money in the retirement account at 62 years old is $ 633,625.38.
How do we calculate future value of an ordinary annuity?Scenerio 1:
a) 6% of salary = Salary * 6% = $6,100 * 6% = $366
b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366
c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where:
FV = Future value = Money in the retirement account at 62 years old = ?
M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732
r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052
n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444
Substituting all the values into equation (1), we have:
FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $1,267,250.76
d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504
e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76
Scenario 2:
a) 3% of salary = Salary * 3% = $6,100 * 3% = $183
b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183
c) Using equation (1), we have:
M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366
Substituting all the values into equation (1), we have:
FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $633,625.38
d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00
e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38
The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38
Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183
Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183
Learn more about future value here: https://brainly.com/question/29380677.
#SPJ1
Charles and wilma have diffrent internet providers. Charles pays $0. 25 per gigabyte of data. Wilma pays a flat fee of $20 and $0. 05 per gigabyte How many gigabytes of data must each use for charles internet bill to be equal to wilma's interet bill
100 terabytes of data must be used in order for Charles' internet bill to equal Wilma's internet cost.
What is the Intercept of the equations?Assume that there are x gigabytes of data.
The equation for Charles is y = 0.25x since he pays $0.25 for each gigabyte of data.
The calculation for Wilma is y = 0.05x + 20 because she pays a flat rate of $20 and $0.05 per gigabyte.
Charles must pay the same amount for internet service as Wilma, so;
0.25x = 0.05x + 20
0.2x = 20
x = 20/0.2
x = 100
Hence, 100 terabytes of data must be used in order for Charles' internet bill to equal Wilma's internet cost.
learn more about equation intercepts at:
brainly.com/question/26249361
#SPJ4
If jimmy buys 5 apples and gets eaten alive by ___ How many apples does he have left?
The number of apples that he has left will be 2 apples.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If jimmy buys 5 apples and gets 3 apples eaten alive by him.
Then the number of apples that he has left will be given by subtracting 3 from 5. Then the expression is given as,
⇒ 5 - 3
⇒ 2
The number of apples that he has left will be 2 apples.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
The complete question is given below.
If jimmy buys 5 apples and gets 3 apples eaten alive by him. How many apples does he have left?