If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.
How the future value is computed?The future value for this investment is computed in two separate solutions.
We have used an online finance calculator to facilitate the process.
The future value denotes the present deposits compounded at an interest rate.
Initial Deposits:
N (# of periods) = 32 quarters (8 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $0
PMT (Periodic Deposit) = $1,000
Results:
FV = $43,489.87
Sum of all periodic payments = $32,000.00
Total Interest = $11,489.87
Subsequent Deposits:
N (# of periods) = 76 quarters (19 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $43,489.87
PMT (Periodic Payment) = $200
Results:
Future Value (FV) = $215,293.42
Sum of all periodic payments = $15,200 ($200 x 76 quarters)
Total Interest = $156,603.55
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Brain Builders
Use the graph for Exercises 24 and 25.
24. Before leaving the grocery store, Kenny wrote the
y-coordinate first and the x-coordinate second when telling
his sister where to meet him. To his surprise, she was at
the right location. If his sister did not make an error, where
did the siblings meet? Explain how you know.
The siblings met at the point (4,7). This can be determined by looking at the graph and seeing that the point (4,7) is the only point with an x-coordinate of 4 and a y-coordinate of 7.
What is coordinate?Coordinate refers to the pair of numbers used to identify the position of a particular point on a graph, map, or other two-dimensional plane. Each coordinate consists of an x-coordinate and a y-coordinate that indicate the horizontal and vertical position of the point, respectively. Coordinates can be used to plot points, draw shapes, and determine distances between points. For example, the coordinates (4, 7) would tell you that the point is located four units to the right and seven units up from the origin point. Coordinates can also be used to describe the location of a point in three-dimensional space, with the addition of a z-coordinate.
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Consider the line y = 8x-2.
Find the equation of the line that is parallel to this line and passes through the point (3, -2).
Find the equation of the line that is perpendicular to this line and passes through the point (3,-2).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Answer:
parallel line: y = 8x - 26
perpendicular line: y = -1/8 x - 13/8
Step-by-step explanation:
1.
Lines are parallel, so slopes are equal, and y-intercepts are different.
Given line:
y = 8x - 2
New line:
y = 8x + b
Use point (3, -2) and solve for b.
-2 = 8(3) + b
-2 = 24 + b
b = -26
Equation: y = 8x - 26
2.
Lines are perpendicular, so slopes are negative reciprocals.
Given line:
y = 8x - 2
New line:
m = -1/8
y = -1/8 x + b
Use point (3, -2) and solve for b.
-2 = -1/8 × 3 + b
-2 = -3/8 + b
b = -16/8 + 3/8
b = -13/8
Equation: y = -1/8 x - 13/8
Question
A scientist wants a 90 ounce acid solution with a concentration of 12%. She has concentrations of 8% and 18%. How
much of each solution must she use to get the desired concentration?
On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
12% of 90 = 12/100 X 90
= 0.12 X 90 = 10.8
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Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214? Explain.
There are 3,024 different ways 1,214 can be shown.
What is permutation?Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given 1,214
since there are 4 places in the digit,
so 4 values less than 10 can be solved by
9, 8, 7, and 6
so by permutation to find ⁹P₄ = 9!/(9 - 4)!
= (9 x 8 x 7 x 6 x5!)/5!
⁹P₄ = 3,024
Hence there are 3,024 different ways.
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Write the word sentence as an equation. Then solve the equation
84 is 99 fewer than a number c.
7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.
Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.
The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.
So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.
Step-by-step explanation:
let sets a and b defined as follows
A is c,d,e,f,g
b is the set of odd numbers greater than 5 and less than 13
Answer:
The set A is defined as the set containing the elements c, d, e, f, and g.
The set B is defined as the set of odd numbers greater than 5 and less than 13. This set includes the elements 7, 9, and 11.
Step-by-step explanation:
Write the product of 0.4*0.4*0.4 in exponential form
Answer:
It is 6.4*10^-2.
this is your answer
The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
200.96 square inches
175.84 square inches
100.48 square inches
25.12 square inches
Answer: D
Step-by-step explanation: 25.12
Answer: The actual answer is (175.84 square inches)
Step-by-step explanation:
First, find the area of the pizza.
You need to use the formula for area of a circle: A = πr^2
or in words, the area of a circle is equal to pi times radius to the second power.
So find the radius which is half the diameter.
The diameter is 16 inches, so the radius is 8 inches.
Now raise 8 to the second power, meaning that you need to times 8 by 8
(8 * 8 = 64) Now you times 64 by pi or 3.14. (64 * 3.14 = 200.96)
That is the area of the entire pizza.
But you still need to find how many square inches are left after 1/8 is eaten.
If 1/8 is eaten, then that means the pizza is divided into eighths.
Take 200.96 and divided that by 8 to find how much the individual pieces are.
200.96/8 = 25.12
But you need to find what is left is the pizza, so times 25.12 by 7 because that is how many pieces are left. 25.12 * 7 = 175.84
Sorry for the long explanation, but here is proof that the answer is correct. I took the same test and got the answer right
Here is a photo from my test:
Have a good day
Josephine wrote the numbers 1-100 and placed them in a bag.If she selects a number without looking what is the probability that the number is greater than 78
A gym membership is $28 to join and $10 paid monthly.
Create a table to represent this scenario, then create an equation.
Enter your answers in the boxes.
Months Purchased Total Cost ($)
0 28
1
38
2
48
3
58
4
68
The equation to represent this scenario is y =
x +
.
Answer:
sorry needed points so sorry
Step-by-step explanation:
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Match each expression on the left with an equivalent expression on the right. Not all of the options on the right will be used.
361,000
1,400
100 x 14
14(10)
361 - 1000
100(361)
36, 100
14,000
3,610
140
On solving the provided question, we can say that on matching the expressions are 100X 14 = 1400 and 14(10) = 140 and 361 . 100 = 36100 and 100(361) = 36100
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
so, on matching the expressions are
100X 14 = 1400
14(10) = 140
361 . 100 = 36100
100(361) = 36100
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What’s the answer pls?
Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
From the provided figure, it is clear that there are two triangles.
ABC and EFG are the triangles.
AB = EF
AC = FG
BC = EG
As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.
Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
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"describe the domain and range for f(x)=3^x-1"
Answer:
Domain: All real numbers
Range: All real numbers greater than or equal to -1
Fractions greather than 1/2
Answer:
[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] (in general, the numerator has to be greater than half the denominator)
Step-by-step explanation:
There are an infinite number of fractions greater than 1/2, but we can generally form a rule to figure out whether a fraction is greater than 1/2, which will help us find those fractions!
Forming a Rule:Let's first just express a fraction in the form: [tex]\frac{a}{b}[/tex], and we have to ask our self, what determines whether this is 1/2? Well we know if we have 1/2, and multiply it by two, then we have a whole, or one, but the only case where we have a whole, or one, in fraction form, is where the numerator and denominator are equal.
This means, multiplying the numerator "a" by 2, will result in it being equal to the denominator "b". From here, it can be determined that for the fraction: [tex]\frac{a}{b}[/tex], to be 1/2, then the numerator "a" has to be half the denominator "b". But this is just telling us what "a" and "b" need to be, for the fraction to be equal to 1/2, not greater than 1/2. This is still useful, since in general the following is true: [tex]\frac{a+1}{b}[/tex], if we add one to the numerator, the fraction becomes bigger. So if we want the fraction to be bigger than 1/2, the numerator "a" just needs to be bigger or larger than the half the denominator "b".
Examples:Let's select a denominator, and from there find numerators that make the fraction bigger than 1/2. For this example let's just select "9". In this case, for a fraction to be 1/2, the numerator just has to be larger than 9/2 or 4.5, but since we can't have decimals in fractions, or at least proper fractions, we just need the numerator to be greater than or equal to 5 (5 is included, since it's still bigger than 4.5)
[tex]\frac{4}{5}[/tex] is actually the only proper fraction, since 5/5 would just simplify to one.
Let's do another example, in this case let the denominator be 10. For the fraction to be considered greater than 1/2, the numerator, has to be greater than half the denominator, 10/2 = 5.
[tex]\frac{6}{10}, \frac{7}{10}, \frac{8}{10},\frac{9}{10}[/tex] would all be valid answers (although some do simplify further). But all of them represent fractions which have a greater value than 1/2
fatima flies her drone 5 feet above the ground diamond she rotates the drone to the right so far the drone has flown a total of 12 feet how far is the drone from the start point
Therefore , the solution of the given problem of triangle comes out to be the distance of the drone from the start point is 13feet.
What is the triangle?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
Here,
Given : Height of drone = 5 feet
and distance of drone covered is 12 feet
Thus ,
to calculate the distance of the drone from the start point
distance can be represented as H
Since it forms right triangle.
By using pythagoras theorem,
=> 5² + 12² = H²
=> H² = 169
=> H = √169
=> H = 13
Therefore , the solution of the given problem comes out to be the distance of the drone from the start point is 13feet.
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Find the slope of the line in which x=-24
Answer:
it is undefined
Step-by-step explanation:
Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.
Answer:
undefined slope
Step-by-step explanation:
When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.
a radio caller won the grand prize, where the caller gets to
spin a wheel with prizes of $500, $750, $1,250, $21500,
$5,000, $10,000, and $25,000 on a wheel. The probability
the wheel lands on $500 is }, landing on $750 is
crIN
landing on $1,250 is 25,
, landing on $2,500 is 25, landing
on $5,000 is 25, landing on $10,000 is 25, and landing on
$25,000 is
25 •
What is the expected amount of money
the radio caller should win if the caller gets to spin the
wheel once?
O $5,050
O $6,450
O $4,100
O $3,650
Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.
$500 * 1/8 = $62.50
$750 * 1/8 = $93.75
$1,250 * 1/8 = $156.25
$2,500 * 1/8 = $312.50
$5,000 * 1/8 = $625.00
$10,000 * 1/8 = $1250.00
$25,000 * 1/8 = $3,125.00
Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00
So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.
It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.
The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.
Step-by-step explanation:
The sum of any three different even numbers is odd.
find the value of r so the line that passes through each pair of points has the given slope (5, 3), (r, -5), m=4
Answer:
r=3
Step-by-step explanation:
use slope formula : y2-y1 / x2-x1
-5-3 / r-5
the numerator is -8 which means the denominator has to be -2 in order to have the slope be 4
so r-5 = -2
3-5 = -2
In the problem on the previous page, suppose Alex wanted to know how many weeks it would take him to work 51 hours. Alex works 3 hours a day and 4 days a week.
1. What are you asked to find?
2. What is a good plan for solving the problem?
3. Does your answer make sense? Explain.
1. you are asked to find how many weeks it would take Alex to work 51 hours.
2. Alex works [tex]3\frac{1}{7}[/tex] weeks.
3. It makes sense in fractional from.
What is fraction?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.
Alex works 3 hours a day and 4 days a week.
Alex works in a week = ( 3×4) hour = 12 hour
Alex works = 51 hours = 48 hours + 3 hours = (48/12) weeks + 1 day
= 3 weeks and 1 day.
= [tex]3\frac{1}{7}[/tex] weeks.
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h(0)=
evaluate the function please!!
Solve this inequality for x.
Answer:
A. x ≥ 21[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
81 - 1[tex]\frac{1}{5}[/tex] x ≤ 55
-1[tex]\frac{1}{5}[/tex] x ≤ 55-81
-[tex]\frac{6}{5 }[/tex] x ≤ -26
x ≥ -26(-[tex]\frac{5}{6}[/tex]) **flip the inequality when you divide by a negative number
x ≥ 21[tex]\frac{2}{3}[/tex]
Laura and Shelby ordered pizzas and chips. Lara ordered 5 pizzas and 2 bags of chips and paid $55. Shelby ordered 10 pizzas and 4 bags of chips and paid $95. How much would 1 pizza and 1 bag of chips cost?
Cannot be determined.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here 5 pizzas and 2 bags of chips cost $55 and 10 pizzas and 4 bags of chips cost $95
let the cost of one pizza be p and a bag of chips be c then we construct the following linear equations:
5p+2c=55
10p+4c=95
Clearly the equations are colinear but 10p+4c≠110=1(5p+2c0
and thus two lines don't have a unique solution.
Hence, the cost cannot be determined as the two equations have no solution in common.
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the quotient of x divided by 5 is greater than or equal to 6. Write an inequality and graph its solution
Lucas hosted a New Year's dinner for his employees.
The total bill was $1,011.50. He left the server a 20%
tip. How much money did Lucas tip the server?
Round your answer to the nearest hundredth.
Answer:
$202.30
Step-by-step explanation:
You want to know the value of a 20% tip on a bill of $1011.50.
TipThe tip amount can be found by multiplying the bill amount by the tip percentage:
20% · $1011.50 = $202.30
Lucas tipped the server $202.30.
__
Additional comment
You know that 10% of the amount can be found by moving the decimal point one place: $101.15.
20% of the amount will be double this value: $202.30. You can do this math mentally.
The cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick, how thick is the texturing on wall? A. 3/16, b. 6/12, C 1/4, D 6/16
When the cross-section of a wall is 7/16 of an inch thick and the drywall is 1/4 inches thick, the thickness of the texturing on wall is A. 3/16
How to calculate the Fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
From the information, the cross-section of a wall is 7/16 of an inch thick. If the drywall is 1/4 inches thick. The thickness of the texturing on the wall is the total thickness of the wall minus the thickness of the drywall. The total thickness of the wall is 7/16 inches, and the thickness of the drywall is 1/4 inches, so the thickness of the texturing is:
= 7/16 inches - 1/4 inches
= 3/16 inches.
Therefore, the answer is A. 3/16 inches.
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What is a b c d and e?
Answer:
Step-by-step explanation:
Helpp!! Solve the system by graphing.
The solution of the system of equations:
y = 3x - 4
y = (-1/2)*x + 3
Is (2, 2).
How to solve a system of equations graphically?Here we have the following system of equations:
y = 3x - 4
y = (-1/2)*x + 3
To solve this graphically, we just need to graph both equations on the same coordinate axis, and find a point where these two graphs intercept.
Below you can see the graph of the system, and there you can see that the lines intercept at the point (2, 2), so that is the solution of the system.
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