Answer:
2x2x2x7 is 56, 2^2x3x7 is 84, and 2x2x2x13 is 104.
Step-by-step explanation:
Your parents invest $10,000 in a college fund when you are born. They find a fund that will return 8% per year for 18 years.
When you are 18 you find a school that charges $12,000 tuition per year. Tuition increases at a rate of 11% per year (so the second year will have a tuition of $13,320) , will this money take care of four years of school? How many years of college will this take care of? Explain your answer fully.
The interest is compounded in the investment and the fees, the 4 years
school fees is however larger than the future value of the investment.
Response:
The money is less required to take care of four years of schoolTwo yearsHow can the future value of the amount invested be found?First part:
The future value, FV, of the investment after 18 years is given as follows;
[tex]FV = \mathbf{PV \cdot (1 + i)^n}[/tex]Where;
PV = The present value = $10,000
i = The interest rate = 8% = 0.08
n = The number of years = 18
Which gives;
[tex]FV = 10,000 \times (1 + 0.08)^{18} \approx \mathbf{39,960.195}[/tex]
The future value of the investment, FV = $39,960.195
The school fees each year is given as follows;
Fees = First year fees·(1 + r)ⁿ
Where;
First year fees = $12,000
r = Increase rate of the school fees = 11% = 0.11
n = The number of years
The school fees for four years is given as follows;
∑Fees = $12,000 + $12,000·(1 + 0.11) + $12,000·(1.011)² + $12,000·(1.011)³
Which gives;
∑Fees = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² +12,000·(1 + 0.11)³ = 56,516.772
The total tuition fees for four years = $56,516.772
The future value of the investment after 18 years, $39,960.195 is less
than the amount required as school fees for four years, therefore;
The money is less than the amount to take care of four years of schoolSecond part:
The fees for 3 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^3[/tex] = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² = 40,105.2 > 39,960.195
The fees for 2 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^2[/tex] = 12,000 + 12,000·(1 + 0.11) = 25,320 < 39,960.195
The number of years of college the value of the investment will take care of is therefore;
Two yearsLearn more about future value here:
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Help bell math math math
y = ax + b
The coefficient of x is the slope of the line in this form of the linear equations.
=====================================
The perpendicular line have negative and inverse slope which means the product of their slope must equals to - 1 .
Thus if we suppose that the line we want to find it's equation has a slope of m ; we have :
4 × m = - 1
Divide both sides by 4
4m ÷ 4 = - 1 ÷ 4
m = - 1/4
Thus we know the coefficient of x now :
y = - 1/4 x + b
======================================To find the value of b we need one of the point that the line passed through it which is the point ( 4 , - 11 ) .
All we have to is put the coordinates in the equation and find the value of b.
Let's gooo....
y = - 1/4 x + b
put the coordinates in the equation
- 11 = (- 1/4)×4 + b
- 11 = - 1 + b
Add both sides 1
- 11 + 1 = -1 + 1 + b
b = - 10
======================================
Thus :[tex]y = - \frac{1}{4} x + ( - 10) \\ [/tex]
[tex]y = - \frac{1}{4} x - 10 \\ [/tex]
Answer:
y = ax + b
Step-by-step explanation:
The value of q is:
A. 42.
B. 39.
C. 40.
Answer:
40
Step-by-step explanation:
Its pretty easy i did that on a test and got a 100
Add the fractions and whole numbers
21 13/16 +
5 3/32
Answer: 16 2/8
21 13/16+5 3/32=?
13/16 3/32 32 divided by 16 = 2 so you need to simplified 32/16 and 3/32= 16 so both 13/16 + 32/16= 48/16 then you need to simplified again to make it even and it will be 3 so you add the three with the wholes it will make 16 so know we simplified and divide the fraction 48/16 so once you divide it equals 8 because 8x2=16 and 8x6=48 so it will be 2/8 so the answer is 16 and 2/8
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have a nice day : )
13.333...% as a fraction
Answer:
[tex]13 \frac{333}{1000}[/tex]
Step-by-step explanation:
The amount of numbers after the decimal point tell you the amount of zeros to put after the 1 in the denominator.
Just rewrite the whole number infront of the decimal point into the fraction
Answer:
[tex]\frac{2}{15}[/tex]
Step-by-step explanation:
[tex]13.333...\%=\frac{13.333...}{100}=\frac{10+3.333...}{100}=\frac{10}{100}+\frac{3.333...}{100}[/tex]
[tex]=\frac{1}{10}+\frac{\frac{10}{3}}{100}=\frac{1}{10}+\frac{1}{30}=\frac{4}{30}=\frac{2}{15}[/tex]
You enter an online Esports tournament. The entry fee is $17, and the top 3 finishers win money. First place wins $325. Second place wins $276. Third place wins $106. You give yourself an X chance of finishing in the top 3, and if you finish top 3, then you have an equal chance of finishing first, second, or third. What is X such that entering this tournament is a fair gamble for you. A fair gamble is one where the expected value of entering the tournament is $0.
Using the expected value of a discrete distribution, it is found that X = 0.0673.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, we have that the distribution is:
P(X = -17) = 1 - X.
P(X = 325) = X/3.
P(X = 276) = X/3.
P(X = 106) = X/3.
Hence, since the expected value is 0:
[tex]-17(1 - X) + 325\frac{X}{3} + 276\frac{X}{3} + 106\frac{X}{3} = 0[/tex]
[tex]-17 + 17X + 235.67X = 0[/tex]
[tex]252.67X = 17[/tex]
[tex]X = \frac{17}{252.67}[/tex]
[tex]X = 0.0673[/tex]
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Brandon has a jar of quarters and dimes with a total value of $9.65. The number of quarters is 7 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
The supplement of a 60∘ angle is an angle that measures how many degrees?
Answer:
120 Degrees
Step-by-step explanation:
Supplementary means angles that add up to 180 Degrees, so 180 - 60
t is inversely proportional to the square of d , t= 0.2 when d =8 find t when d = 10
help needed brainliest will be given for attempt
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Answer:
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Step-by-step explanation:
Simplify the expression.
2.4 - 4.3n - 3n + 6
Answer:
-7.3n+8.4
Step-by-step explanation:
combine like terms
Hope this helps! Have a great day!!
Answer:
8.4 - 7.3n
Step-by-step explanation:
1. Rearrange
2.4 - 4.3n - 3n + 6 = 2.4 + 6 - 4.3n - 3n
2. Combine like terms
2.4 + 6 - 4.3n - 3n = 8.4 - 7.3n
The answer is 8.4 - 7.3n
Hope this helps :)
Have a great day!
Write the improper fraction as a mixed number or a whole number.
956
125
Answer:
956= 9/56
125= 1/25
Step-by-step explanation:
A car dealer purchases a car for $5,000 and sells for $6,600 what is his percentage profit? Round your answer to the nearest whole percent
Answer:
32%
Step-by-step explanation:
The percentage profit is the ratio of profit to original cost, expressed as a percentage. The profit is the difference between the selling price and the cost.
profit = selling price - cost
profit = $6600 -5000 = $1600
The ratio of that to cost is ...
$1600/$5000 = 0.32
As a percentage, that is ...
0.32 × 100% = 32%
The car dealer's profit was 32% of his cost.
The average size of a human cell is one-ten-thousandths (0.0001) of a meter. Write it in scientific notation. ( Follow this format without spaces: _.___x10^__ )
Answer:
The average size of a human cell is one-ten-thousandths (0.0001) of a meter. Write it in scientific notation. ( Follow this format without spaces: 1769 ma 20
Which of the following numbers is the smallest
The smallest number from the folowing option is A . 0.0082.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
The given numbers are;
0.0082
1/3
0.048
0.36
1/9
thus, The smallest number from the folowing option is A . 0.0082.
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What is the slope of the line?
Answer:
The slope of the line is -3
Step-by-step explanation:
I chose the points (-2,3) and (0,-3)
The slope formula: m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{-3-3}{0-(-2)}[/tex] ==> [tex]\frac{-3-3}{0+2}[/tex] ==> [tex]\frac{-6}{2}[/tex] = [tex]-3[/tex]
Our final answer is -3.
Hope that helps!
(2x-3)(3x+4) expand and simplify?
Answer:
6x2-x-12
Step-by-step explanation:
The given expression:
(
2
x
−
3
)
(
3
x
+
4
)
Simplify by using the FOIL method:
(
2
x
−
3
)
(
3
x
+
4
)
=
2
x
⋅
3
x
+
2
x
⋅
4
−
3
⋅
3
x
−
3
⋅
4
=
6
x
2
−
x
−
12
Therefore, the simplest form of the given expression is
6
x
2
−
x
−
12
.
A new movie theater opens at the local mall. During the first month, the owner collected information
on how many customers they had throughout each day. The owner concluded that the number of
customers the theater has at any given moment can be represented by C(x) = -x2 + 11x where x
represents the number of hours that the movie theater has been open on a given day. The theater
opens at 12:00 PM.
At what time does the theater have no customers?
a.
11:00 PM
b. 5:30 PM
c. 2:00 PM
d. 8:30 PM
The time at which the theatre does not have any customers is; Choice A: 11:00 PM
Functions and variableFrom the task content;
The function which represents the number of customers the theater has at each point in time is;C(x) = -x² + 11xHence, when C(x) = 0, the theater has no customers.
0 = -x² +11xDivide through by x;
0 = -x +11x = 11.
Read more on functions and variables;
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3. Over the next two days, Job.net Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 2. On the second day, the agency will interview clients in groups of 4. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?
Here is my answer. Good luck.
. A jeweler has 100 necklaces and bracelets to sell at a flea market. Bracelets are selling for $5.75 each, and necklaces are $8.50 each. If the jeweler makes $685.00 after selling all of the items, how many of each type of jewelry did the jeweler sell?
Answer:
there are total 60 bracelets and 40 necklaces.
Explanation:
let necklaces be x
let bracelets be y
make two equations from the given values:
x + y → 1005.75y + 8.50x → $685solving steps:
x + y → 100
x → 100 - y
using substitution method:
5.75y + 8.5x → 685
5.75y + 8.5(100 - y) → 685
5.75y - 8.5y + 850 → 685
-2.75y → 685 - 850
-2.75y → -165
y → 60
Find x:
x + y → 100
x → 100 - 60
x → 40
Answer:
60 bracelets
40 necklaces
Step-by-step explanation:
Let n = number of necklaces sold
Let b = number of bracelets sold
Given:
Total number of items sold = 100⇒ n + b = 100
Given:
Sale price of bracelet = $5.75Sale price of necklace = $8.50Total sales = $685⇒ 5.75b + 8.5n = 685
Rewrite n + b = 100 to make b the subject, substitute into 5.75b + 8.5n = 685 and solve for n:
⇒ b = 100 - n
⇒ 5.75(100 - n) + 8.5n = 685
⇒ 575 - 5.75n + 8.5n = 685
⇒ 575 + 2.75n = 685
⇒ 2.75n = 110
⇒ n = 40
Substitute found value for n into n + b = 100 and solve for b:
⇒ 40 + b = 100
⇒ b = 60
What is 4x – 5 = 16 ? I have to show my work
Answer: x = 21/4
First, you want to Add 5 to both sides of the equation:
4x - 5 + 5 = 16 + 5.
Then you want to simplify:
4x = 21.
Divide both sides of the equation by the same term:
4x/4 = 21/4.
Then you want to simplify:
x = 21/4.
The final solution is:
x = 21/4
Exact Form:
x = 21/4
Decimal Form:
x = 5.25
Mixed Number Form:
x = 5 1/4
Step-by-step explanation:
Hope this helps =)
What is the length of ONE side in a square if the perimeter is 4x + 25
Answer:
Hi, you already asked this question, the answer is 6...
Step-by-step explanation:
Fatima is painting this cardboard cut out for her class play. the cutout is a trapezoid 3 m tall. it has a square opening. what is the area that Fatima needs to paint?
PLS SHOW WORK.
Answer:
8 square meters
Step-by-step explanation:
Area of the trapezoid is (1/2)(3)(2+4)=9
Area of the trapezoid is (1)(1)=1
So the area she needs to paint is 9 - 1 = 8
Equations of the form cosθ=k where -1 ≤ k ≤ 1 has/have ______________ solution(s).
A. two
B. infinitely many
C. one
D. none
Please help - trig identity
Answer:
Step-by-step explanation:
[tex]LHS=cosec(x)-cosec(x)cos^{2} (x)\\\\LHS=cosec(x)-cosec(x)(1-sin^{2} (x))\\\\LHS=cosec(x)-cosec(x)+cosec(x)*sin^{2} (x)\\\\LHS=cosec(x)-cosec(x)+cosec(x)\frac{1}{cosec^{2}(x) } \\\\LHS=cosec(x)-cosec(x)+\frac{1}{cosec(x) }\\\\LHS=\frac{cosec^{2}(x)-cosec^{2}(x)+1 }{cosec(x)} \\\\LHS=\frac{1}{cosec(x)} \\\\LHS=sin(x)=RHS[/tex]
Hence,LHS=RHS proved
can I have help pls
i’ll give brainliest!
Answer:
-6
Step-by-step explanation:
just keep the same slope and just pretend to move the line up 8 which would decrease the x value by 14 equaling -6
Find the circumference of the circle below:
15.7 cm
31.4 cm
100 cm
314 cm
help me
Answer:
31.4 cm
Step-by-step explanation:
[tex]C=2\pi r[/tex]
[tex]=2*\pi *5[/tex]
[tex]\neq 31.41593[/tex]
≈ 31.4
Which of the following is true about the line that passes through the points (-5, 8) and (1,8
Answer: there is a horizontal line on the bottom side to each point.
Step-by-step explanation: -5 x 8y, 1x 8y so from each position they are on the bottom. negative on the right, positive on the left (x axis)
Rewrite the quadratic function below in standard form. y = 3(x+9)(x+1)
Answer:
y = 3x² + 30x + 27
Step-by-step explanation:
Formula: Ax + By = C
y = 3 (x + 9) (x + 1)
y = 3x + 27x + 3x + 7
y = 3x² + 30x + 27