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, $39,960.195 is less
than the amount required as school fees for four years, therefore;
The money is less than the amount to take care of four years of schoolSecond part:
The fees for 3 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^3[/tex] = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² = 40,105.2 > 39,960.195
The fees for 2 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^2[/tex] = 12,000 + 12,000·(1 + 0.11) = 25,320 < 39,960.195
The number of years of college the value of the investment will take care of is therefore;
Two yearsLearn more about future value here:
https://brainly.com/question/14545379
What is the slope of the line passing through the points (4, -2) and (-5, 4)?
Answer:
-2/3
Step-by-step explanation:
We can use the slope formula when we have two points
m = ( y2-y1)/(x2-x1)
= ( 4 - -2)/( -5 -4)
= ( 4+2)/( -5-4)
= 6/ -9
Simplifying
= -2/3
Slope:-
m=4-(-2)/-5-4m=4+2/-9m=-6/9m=-2/3paul was given 2760$ to buy toys for a group of children.A)what would be the greatest number of toys paul could buy if each toy cost $9?B)how much money would be left after buying the toys? (wright equation)(anser it understandble)
Step-by-step explanation:
Question A-
To find: Greatest number of toys that Paul can buy with $2760
We can simply divide the total money by the toy's price-
total money/toy's price
= 2760 / 9
= 306.6
= 306 (since we cannot buy .6 of a toy we round it off to the previous number)
Question B-
To find: Amount of money left after buying the toys
The remanider of 2760/9 will give us the money left with Paul
= $6
Find the exact value of sin 4pi/3 in simplest form with a rational denominator.
Answer:
Sin4π/3
It should be in degree from by using radian to degree formula.
simplify the radical expression 3√40
Answer:
Exact Form= 6√10
Decimal Form=18.97366596
I know i use the product rule but I keep getting the wrong answer
Answer:
dx/dt | (x=3) = 27/2
Explanation:
x*y = 2 ......... (a)
At x = 3, (3)*y = 2 => y = 2/3
Differentiate (a) wrt t,
x.dy/dt + y.dx/dt = 0 ........ (b)
Put x=3, dy/dt=-3 and y=2/3 in the differential equation (b),
3(-3) + (2/3)*dx/dt = 0
dx/dt = (9*3)/2 = 27/2
solve fast kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:
[tex]-\frac{9h}{5} + 0.7[/tex]
What number is 85% of 112?
Answer:
So 85 percent of 112
A percentage basically means “out of a hundred”
So 85 percent is 85/100
85/100 is 0.85
KEY word is “of”, we multiply when there’s of
0.85*112= 95.2
95.2 is 85 percent of 112
20 points!! Please look at the picture below
Answer:
I believe the answer is D.
Write the product of 6 x 6 x 6 x z x z in exponential form.
Answer:
[tex]6^3z^2[/tex]
Step-by-step explanation:
1. Count the number of 6's.
There are three 6's, thus making [tex]6^3[/tex].2. Multiply number of 6's by number of z's.
There are two z's, thus making [tex]z^2[/tex]. [tex]6^3 * z^2 = 6^3z^2[/tex].What is the equation of the line that passes through the point (6.-6) and has an undefined slope
Answer:
x=6
Step-by-step explanation:
If a line has an undefined slope, then it has to be a vertical line.
Since the line is vertical, there is only one x value for any given y value. This means we can use the x value in the given coordinate pair to find the equation...
x=6
14- 2.5f = 50
Please help
Answer:
f=-14.4
Step-by-step explanation:
[tex]14- 2.5f = 50\\\\14-50=2.5f\\\\-36=2.5f\\\\f=\frac{-36}{2.5}\\\\f=-14.4[/tex]
Hi!
14-2.5f=50
Move 14 to the right, using the opposite operation:
-2.5f=50-14
-2.5f=36
Divide both sides by -2.5 to isolate f:
f=-14.4
Note: If we divide a negative by a negative, we get a positive.If we divide a positive by a negative, we get a negative.Hope it helps!
Have a Great Day!
~Content Teen
[tex]\bf{-MistySparkles^**^*[/tex]
For a homework due tomorrow.
What is cos 45?
What is sin 45?
They are the same :)
0.7071
[tex] \cos(45) = \frac{ \sqrt{2} }{2} = 0.71(2d.p) \\ \\ \sin(45) = \frac{ \sqrt{2} }{2} = 0.71(2d.p)[/tex]
For what values of x is the expression below defined?
O A. x = 0
O B. x > 0
O c. x< 0
O D. x< 1
Answer:
x>0
Step-by-step explanation:
i took the quiz :))
Kevin spins a spinner like the one shown and flips a coin. The probability of landing on purple and heads is 1/8. How many sections of the spinner should be colored purple?
===============================================
Explanation:
Let x be the number of purple sections.
x/8 represents the probability of landing on purple since we have 8 equal sections total of this pizza.
Multiply this with the probability of landing on heads (1/2)
(1/2)*(x/8) = x/16
x/16 is the probability of getting a purple section and having the coin land on heads.
Set that equal to the 1/8 mentioned in the instructions and solve for x.
x/16 = 1/8
8x = 16
x = 16/8
x = 2
Or you can solve like this
x/16 = 1/8
x/16 = 2/16
x = 2
Kevin needs to shade 2 of the sections purple.
Side note: It's a bit unfortunate that the entire paper is purple overall. Though I'm probably being a bit nitpicky right now.
help I need an answer
Write the expression with fewer terms.
3(x−2)+4(x−2)−5(x−2)3(x−2)+4(x−2)−5(x−2)
Answer:
[tex]-15x^{2} +66x-72[/tex]
Step-by-step explanation:
Simplify or expand:
[tex]3(x-2)+4(x-2)-5(x-2)[/tex] × [tex]3(x-2)+4(x-2)-5(x-2)[/tex]
Multiply the monomials:
3(x-2)+4(x-2)-15(x-2)(x-2)+4(x-2)-5(x-2)
Apply the Distributive Property:
3x-3×2+4(x-2)-15(x-2)(x-2)+4(x-2)-5(x-2)
3x-3×2+4x-4×2-15(x-2)(x-2)+4(x-2)-5(x-2)
3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4(x-2)-5(x-2)
3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4x-4×2-5(x-2)
3x-3×2+4x-4×2+(-15x-15×(-2))(x-2)+4x-4×2-5x-5×(-2)
Determine the sign for multiplication or division:
3x-3×22+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x-5×(-2)
3x-3×2+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x+5×2
Calculate the product or quotient:
3x-6+4x-4×2+(-15x+15×2)(x-2)+4x-4×2-5x+5×2
3x-6+4x-8+(-15x+15×2)(x-2)+4x-4×2-5x+5×2
3x-6+4x-8+(-15x+30)(x-2)+4x-4×2-5x+5×2
3x-6+4x-8+(-15x+30)(x-2)+4x-8-5x+5×2
3x-6+4x-8+(-15x+30)(x-2)+4x-8-5x+10
Apply the Distributive Property
3x-6+4x-8-15x(x-2)+30(x-2)+4x-8-5x+10
3x-6+4x-8-15x×x-15x×(-2)+30(x-2)+4x-8
3x-6+4x-8-15x×x-15x×(-2)+30x-30×2+4x-8-5x+10
Determine the sign for multiplication or division:
3x-6+4x-8-15x×x+15x×2+30x-30×2+4x-8-5x+10
Multiply the monomials:
3x-6+4x-8-[tex]15x^{2}[/tex]+15x×2+30x-30×2+4x-8-5x+10
3x-6+4x-8-[tex]15x^{2}[/tex]+30x+30x-30×2+4x-8-5x+10
Calculate the product or quotient:
3x-6+4x-8-[tex]15x^{2}[/tex]+30x+30x-60+4x-8-5x+10
Reorder and gather like terms:
(3x+4x+30x+30x+4x-5x)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
Collect coefficients of like terms:
(3+4+30+30+4-5)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
Calculate the sum or difference:
(7+30+30+4-5)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
(37+30+4-5)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
(67+4-5)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
(71-5)×x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
66x+(-6-8-60-8+10)[tex]-15x^{2}[/tex]
66x+(-14-60-8+10)[tex]-15x^{2}[/tex]
66x+(-74-8+10)[tex]-15x^{2}[/tex]
66x+(-82+10)[tex]-15x^{2}[/tex]
66x-72[tex]-15x^{2}[/tex]
Rewrite the expression:
[tex]-15x^{2}[/tex]+66x-72
Need help really bad please and thank you!
Answer:
Step-by-step explanation:
The side opposite the given width of x is also x.
So you have to relate 3 facts.
The angle
The adjacent side
The hypotenuse.
Formula
Cos(28) = x / 35
Solution
Cos(28) = x / 35 Multiply both sides by 35
35 cos(28) = 35 * x / 35 Cancel
35 cos(28) = x Multiply
30.90 = x
Rounded, it is 30.9
Answer:30.9 cm
Step-by-step explanation: =X/35
X= 35 cos 28'
X= 30. 90cm
width 06
Rectangle = 30.9cm
how many acute angles dose a right triangle have?
Answer:
2 acute angles
Step-by-step explanation:
A right triangle HAS to have a right angle, which is 90 degrees. This means the other two angles must add up to:
180-90 = 90 degrees
Acute angles are LESS than 90 degrees. You cannot add two positive integers over 90 to get 90 (obtuse angles), and you can also not have two 90 degree angles since that forms a straight line, therefore meaning the other two angles must be acute.
Answer:
2
Step-by-step explanation:a normal right triangle has 3 angles in total and looking at the bend in each corner only two of them are acute so that makes it 2
50 Points!!!
(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation?
Step-by-step explanation:
(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain
For this case what we see is that we have a scatter diagram, which we can model using a linear trend defining the following variables:
x: number of hours studied.
y: test scores.
The linear relationship would be of the form:
y = mx + b
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
y = 8x + 40
For three hours of study we have that the note would be approximate:
y = 8 * (3) + 40
y = 64
(c) What does the number 40 in Part (b) mean in the context of the situation?
The number 40 means that if you do not devote any study time, then you expect the test score to be 40.
Simplify fully please
Answer:
Keep Change Flip. Then, multiply out.
You will get:
x^3 - 9x +2x^2 - 18 / 3x^3 - x^2 - 27x + 9
Now factorise top and bottom to get :
(x+2)(x+3)(x-3) / (3x-1)(x+3)(x-3)
The same bracket at the top and bottom cancels out to give the final answer of:
x+2 / 3x-1
Or
x+2 ÷ 3x-1
Hope this helps!
Use the difference of 2 squares to expand x^2-9 to (x+3)(x-3).
factorizing 3x^2 + 8x -3 gives (3x-1)(x+3). With all these, we can simplify as shown in the picture above
Which of the following functions has an inverse THAT IS NOT a function?
Answer:
your choice is correct
Step-by-step explanation:
f(x) = x^2 does not pass the horizontal line test (a horizontal line intersects its graph in two places), so its inverse does not pass the vertical line test. The inverse is not a function.
_____
Comment on the graph
The original function f(x)=x^2 is shown by the red curve. Its reflection across the orange dashed line y=x gives the inverse relation, in blue. The black horizontal and vertical lines show the multiple points of intersection with the curves, indicating the inverse relation is not a function.
Step-by-step explanation: hope this helps a little bit
*20.) When (3x - 2)^2 is subtracted from 4x², the result in simplest form is
Answer:
[tex]- 5 {x}^{2} + 12x - 4[/tex]
Step-by-step explanation:
[tex]4 {x}^{2} - (3x - 2)^{2} \\ \\ = 4 {x}^{2} - [ {(3x)}^{2} - 2(3x)(2) + {(2)}^{2} ]\\ \\ = 4 {x}^{2} - [ 9 {x}^{2} - 12x + 4]\\ \\ = 4 {x}^{2} - 9 {x}^{2} + 12x - 4\\ \\ = - 5 {x}^{2} + 12x - 4[/tex]
Answer:
-5x² + 12x - 4
Step-by-step explanation:
4x² - (3x - 2)²
4x² - (3x - 2) * (3x - 2)
4x² - (9x² - 6x - 6x + 4)
4x² -1 (9x² - 6x - 6x + 4)
(4x² - 9x²) + (6x + 6x) - 4
-5x² + 12x - 4
Hope this helps!
If one yard of material cost 2.00 how much do 5 1/2 yards cost?
Answer:
$11
Step-by-step explanation:
5*2=10 (for 5 yards) plus 1.00 for the 1/2 yard
Answer:
$ 11.00 or 11
Step-by-step explanation:
2.00 X 5 1/2 = 11
You would multiply the cost of $ 2.00 (one yard) with the total yard 5 1/2 and get 11 or $11
So your answer is for a total of 5 1/2 yards it would cost $11.
Use the inequality to answer the following question.
0.06g + 0.6< 6
Which set of values contains possible solutions for g?
( 45,50,60)
(45,50,59)
(45,60,70)
(35,45,65)
Answer:
45,50,60Step-by-step explanation:
pa correct nlng ty sa points.I need help on this
Answer:
(in order)
Size small shirts: 18, 36, 63, 1800
Size large shirts: 4, 8, 14, 200
Step-by-step explanation:
For every 9 small, there is 2 large, therefore if there is 18 small, then there is 4 large because there are two 9s in 18.
What is 2/3 with a denominator of 48
Answer:
32
Explanation:
We can multiply the numerator by the number and leave the denominator as: (2 x 48) / 3 = 96/3 = 32.
What is a necessary step for constructing parallel lines?
Draw a line that intersects the first line using a straightedge.
Draw a ray that intersects the first line at a right angle using a straightedge.
Draw arcs on either side of a given point on the line.
Draw arcs on either side of a given point off the line.
The necessary step for constructing parallel lines is to draw a line that intersects the first line using a straightedge.
What are parallel lines?Two lines are said to be parallel in a plane if they do not intersect each other even if extended till infinite in both the directions.
Steps to construct a parallel line using ruler and compass are:
Draw a line segment AB and mark any point P above the line ABDraw a line that intersects the first line using a straightedge and mark it as Point X. Now we get a line AB and a transverse PX.Open a compass more than half of the distance between PX. Using this, place the compass on Point X and scribe an arc MN on the transverse PX. Similarly, using the same distance, scribe an arc by keeping the compass on Point P and mark it as EF. The point where EF cuts PX is Q. Using this Q as a center, draw an arc marked R on EF.Join this R and P and extend the line segment and mark is as C and D.The resultant image is given below.To learn more about parallel lines, refer:
https://brainly.com/question/4954460
#SPJ2
find area and perimeter of the rectangle with vertices (2,6),(2,-3),(5,-3),and (5,6)
Answer:Find all times on the clock where the angle between the minute and the hour hand (backwards and forwards) equals 26°
Using our clock angle calculator for 5:32, we see that the angle between the hands equals 26°
Using our clock angle calculator for 6:28, we see that the angle between the hands equals 26°
Final Times that form an angle of 26°
Step-by-step explanation:
f(x)=2/3x−1 and g(x)=−4x+6.
Answer:
f(x)=2/3x−1 and g(x)=−4x+6.
answer-x=3/2
solving-x=1.1/2 , x=1.5
Step-by-step explanation:
Answer:
This is an impossible transformation as the types cannot change. They are from different types.
Step-by-step explanation:
Refer to the graph.
A student takes a 10-question, multiple-choice exam with three choices for each question and guesses on each question. Find the probability of guessing exactly 4 out of 10 correctly.
Answer:
unlikely bcz it didn't reach the half of rate (10)
i need help on this to bring my grade up
The Answer Is: "5x + 16"