To have $18,000 in 2 years with a 20% annual interest rate compounded continuously, you need to invest approximately $12,065.76.
Explanation:To determine the amount of money you need to invest to have $18,000 in 2 years with a 20% annual interest rate compounded continuously, we can use the formula:
A = P * e^(rt)
Where:
A is the future value (in this case $18,000)P is the principal amount we need to finde is the mathematical constant approximately equal to 2.71828r is the interest rate (20% = 0.20)t is the time in years (2 years)Substituting the values into the formula:
18,000 = P * e^(0.20*2)
Simplifying:
18,000 = P * e^(0.40)
P = 18,000 / e^(0.40)
Using a calculator to evaluate the exponential term:
P ≈ 12,065.76
Therefore, you need to invest approximately $12,065.76 to have $18,000 in 2 years.
What is the equation of the line that is parallel to the line 2x+3y=-8 and passes through the point (2,-2)?
Equation of line passing through (2, -2) and parallel to 2x+3y = -8 is [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Solution:Need to write equation of line parallel to 2x+3y=-8 and passes through the point (2, -2)
Generic slope intercept form of a line is given by y = mx + c
where "m" = slope of the line and "c" is the y - intercept
Let’s first find slope intercept form of 2x+3y=-8 to get slope of line
[tex]\begin{array}{l}{2 x+3 y=-8} \\\\ {=>y=\frac{-2 x-8}{3}} \\\\ {\Rightarrow y=-\frac{2}{3} x-\frac{8}{3}}\end{array}[/tex]
On comparing above slope intercept form of given equation with generic slope intercept form y = mx + c,
[tex]\text {for line } 2 x+3 y=-8, \text { slope } m=-\frac{2}{3}[/tex]
We know that slopes of parallel lines are always equal
So the slope of line passing through (2, -2) is also [tex]m=-\frac{2}{3}[/tex]
Equation of line passing through [tex](x_1 , y_1)[/tex] and having slope of m is given by
[tex]\left(y-y_{1}\right)=\mathrm{m}\left(x-x_{1}\right)[/tex]
[tex]\text { In our case } x_{1}=2 \text { and } y_{1}=-2[/tex]
Substituting the values in equation of line we get
[tex](y-(-2))=-\frac{2}{3}(x-2)[/tex]
[tex]\begin{array}{l}{\Rightarrow y+2=\frac{-2 x+4}{3}} \\\\ {=>3(y+2)=-2 x+4} \\\\ {=>3 y+6=-2 x+4} \\\\ {3 y=-2 x-2}\end{array}[/tex]
[tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
Hence equation of line passing through (2 , -2) and parallel to 2x + 3y = -8 is given as [tex]y=\frac{-2 x}{3}+\frac{-2}{3}[/tex]
what is 60 times one fourth as a whole number
Answer:
150
Step-by-step explanation:
60 x 1/4 = 150
Answer:
15
Step-by-step explanation:
" 60 times one fourth" can be written as 60/4, which in turn is 15.
57 first-year teachers and 19 experienced teachers attended a school staff meeting meeting. What percentage of the teachers in the meeting were first-year teachers?
Write your answer using a percent sign (%).
Answer:
75%
Step-by-step explanation:
57 / (57+19) = 0.75
Final answer:
About 75% of the teachers in the meeting were first-year teachers, as calculated by dividing the number of first-year teachers by the total number of teachers and then multiplying by 100.
Explanation:
To determine what percentage of the teachers in the meeting were first-year teachers, we use the formula 'part over total, times one hundred, equals percent'. In this scenario, the 'part' is the number of first-year teachers which is 57, and the 'total' is the sum of first-year and experienced teachers, which is 57 + 19 = 76. The calculation then becomes 57/76 times 100, to find that percentage.
Carrying out the calculation:
(57 / 76) times 100 = 0.75 times 100 = 75%
Therefore, approximately 75% of the teachers at the meeting were first-year teachers.
A book sold 34,100 copies in the first month the release suppose this represents 7.9% of the number of copies sold to date how many copies have you sold to date? Round to the nearest whole number
Answer:
431,646
Step-by-step explanation:
[tex]\frac{7.9}{100} = \frac{34,100}{x} \\[/tex]
Simply multiply 100x34,100 (3,410,000) and divide by 7.9 to get your answer= 431,645.57. Round to the nearest whole number and you get your finl outcome which is 431,646.
Answer:
Step-by-step explanation: Let the no. of copies sold to date be y
A.T.Q
7.9/100 * y = 34100
y = 34100*100/7.9
= 3410000/7.9
= 431645.56
Rounding it off to nearest no. it will be
Total 431646 copies have been sold to date.
Hope this helps u :)
If a person walks 2.4 miles in 1.5 hours, how far can he walk in 3 hours?
2.4 miles
6.2 miles
4.8 miles
Answer:
The answer is 4.8
Step-by-step explanation:
The answer is 4.8 because 1.5h is half of 3 hours so if he walks 3.0m (which is double the first amount he walked) the answer will double.
so 2.4+2.4 = 4.8
or 2.4x2 = 4.8
And there u go!
A gardener at a nursery is filling pots with soil to prepare to
transplant seedlings into these larger pots. Each new pot needs about 27 cubic inches
of soil. The amount of soil s (in cubic inches) it takes to fill p pots is given by the
function s = 27p
a.
The gardener is filling the pots from a bag of soil that contains 3456 cubic
inches of soil. How many pots can be filled from the bag?
b.
Suppose the gardener needs to fill at most 109 pots. How much soil (in cubic
inches) will the gardener need?
Answer:
a. 127 pots
b. 2,943 cubic inches
Step-by-step explanation:
To find the amount of pots of soil can be filled, you can use the equation given. s = 3456 in part a
a.
s = 27p
3456 = 27p
divide 3456 by 27 to isolate p
p = 127 pots
Instead of substituting for s like in part a, you can now substitute for p, since you know that you need to fill 109 pots.
b.
s = 27 * 109
s = 2943 cubic inches
The gardener can fill 128 pots with the 3456 cubic inches of soil available. If the gardener needs to fill at most 109 pots, they will require 2943 cubic inches of soil.
To solve both parts of the question, we will use the function s = 27p, where s represents the amount of soil (in cubic inches) and p represents the number of pots.
Part a: Calculating the Number of Pots
The gardener has a bag containing 3456 cubic inches of soil. To find out how many pots can be filled from the bag, we need to divide the total amount of soil by the amount needed per pot:
p = 3456 cubic inches / 27 cubic inches per pot = 128 pots
Part b: Soil Needed for a Maximum Number of Pots
If the gardener needs to fill at most 109 pots, the total amount of soil required can be calculated using the provided function:
s = 27 cubic inches per pot * 109 pots = 2943 cubic inches of soil
sin x= 1.5
value of x
Answer:
x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
Step-by-step explanation:
Solve for x:
sin(x) = 1.5
1.5 = 3/2:
sin(x) = 3/2
Take the inverse sine of both sides:
Answer: x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z
or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z
A piece of cloth costs 200$.if the piece was 5m longer, and the cost of each metre of clth was 2$ less, the cost of the piece would have remained unchanged. How long is the piece and what is its original number of persons.
Answer:
20 m long,
each piece of cloth for $10
Step-by-step explanation:
Let x m be the length of the piece of cloth.
Original cloth:
Length = x m
Cost = $200
Cost per meter [tex]\dfrac{\$200}{x}[/tex]
Changed cloth:
Length = x + 5 m (5 m longer)
Cost = $200
Cost per meter [tex]\dfrac{\$200}{x}-\$2[/tex] (each metre of cloth was $2 less)
Hence,
[tex]\left(\dfrac{200}{x}-2\right)\cdot (x+5)=200[/tex]
Multiply the equation by x:
[tex](200-2x)(x+5)=200x\\ \\200x+1,000-2x^2-10x=200x\\ \\-2x^2-10x+1,000=0\\ \\x^2+5x-500=0\\ \\D=5^2-4\cdot(-500)=25+2,000=2,025\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{2,025}}{2}=\dfrac{-5\pm 45}{2}=-25,\ 20[/tex]
The length cannot be negative, so x = 20 m, each metre for $10.
Answer:
The piece is 20 m long and costs $10 per meter
Step-by-step explanation:
The total cost of the cloth in $ can be expressed as
C = xu
Where x is the length of the cloth in m, and u is the unit cost in $/m
The problem states that if the length was 5 meters more and the unit cost was $2 less, the cost would not change, that is
C = (x+5)(u-2)
Operating:
C = xu-2x+5u-10
Since C = xu, then
-2x+5u=10 [1]
We also know that
xu=200 [2]
Isolating u in [1] we get
[tex]u=\frac{10+2x}{5}[/tex]
Replacing into [2]
[tex]x\frac{10+2x}{5}=200[/tex]
Simplifying
[tex]10x+2x^2=1000 \\=> x^2+5x-500=0[/tex]
Factoring
(x-20)(x+25)=0
Which gives x=20, x=-25. We can only use the positive value of x, so
x=20 m and therefore
u=200/20=10$
So the piece is 20 m long and costs $10 per meter
TO TRANSMIT INFORMATION ON THE INTERNET, LARGE FILES ARE BROKEN INTO PACKETS OF SMALLER SIZES. EACH PACKET HAS 1,500 BYTES OF INFORMATION. AN EQUATION RELATING PACKETS TO BYES OF INFORMATION IS GIVEN BY B=1,500P REPRESENTS THE NUMBER OF PACKETS AND B REPRESENT THE NUMBER OF BYTES OF INFORMATION.
A. HOW MANY PACKETS WOULD BE NEEDED TO TRANSMIT 30,000BYTES OF INFORMATION
B. HOW MUCH INFORMATION COULD BE TRANSMITTED IN 30,000 PACKETS
Answer:
A. It would be needed 20 packets to transmit 30,000 bytes of information and B. 45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
Step-by-step explanation:
1. Let's review the information provided to us for solving the question:
Size of each packet of information = 1,500 bytes
Number of packets = P
Number of bytes of information = B
2. Let's answer the questions:
A. How many packets would be needed to transmit 30,000 bytes of information?
P = 30,000 ÷ 1,500
P = 20
It would be needed 20 packets to transmit 30,000 bytes of information
B. How much information could be transmitted in 30,000 packets?
B = 30,000 * 1,500
B = 45'000,000
45'000,000 (45 million) of bytes could be transmitted in 30,000 packets.
Note: Same answer provided to question 14037480, answered by me.
Is -2/-5 equivalent to 2/5?
Answer:
yes
Step-by-step explanation:
Note that a [tex]\frac{-}{-}[/tex] results in a +, thus
[tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
Ắner:-2:-1=2
-5:-1=5
-2/-5=2/5
Step-by-step explanation:
solve this pls!!! I need to turn it into
-3
_____
(x+2)(x-5)
Step-by-step explanation:
[tex]\dfrac{-3}{(x+2)(x-5)}\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=\dfrac{-3}{(x)(x)+(x)(-5)+(2)(x)+(2)(-5)}\\\\=\dfrac{-3}{x^2-5x+2x-10}\qquad\text{combine like terms}\\\\=\dfrac{-3}{x^2-3x-10}[/tex]
[tex]\dfrac{64x-8x^2}{10x-80}=\dfrac{-8x(x-8)}{10(x-8)}\qquad\text{cancel}\ (x-18)\\\\=\dfrac{-8x}{10}=-\dfrac{8x:2}{10:2}=-\dfrac{4}{5}x[/tex]
The length of a rectangle is 6 units less than the width. The area of the rectangle is 27 units. What is the width, in units, of the rectangle?
The width of rectangle is 9 units.
Step-by-step explanation:
Given,
Width of rectangle = w
Length of rectangle = l = w - 6
Area of rectangle = A = 27 units
[tex]Area\ of\ rectangle=\l*w\\27=(w-6)(w)\\27=w^2-6w\\0=w^2-6w-27\\w^2-6w-27=0\\w^2+3w-9w-27=0\\w(w+3)-9(w+3)=0\\(w+3)(w-9)=0\\[/tex]
Either,
w+3=0 =>w= -3
Or,
w-9=0 =>w=9
As width cannot be negative, therefore,
Width = 9 units
The width of rectangle is 9 units.
Keywords: rectangle, area
Learn more about rectangles at:
brainly.com/question/3309261brainly.com/question/3333996#LearnwithBrainly
IM GIVING THE REST OF MY POINTS FOR THIS 45 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!
ANSWER QUICK THANK YOU
THERE ARE 5 QUESTIONS!!!!!!!!!!!
Answer:
1b 2d 3c 4d 5a
Step-by-step explanation:
sales tax in Philadelphia is 8.5%. what is the price of your items before taxes if your final price is $162.75
Answer:
177.87
Explanation:
162.75 * 100 = 177.87
91.5
177.87 * 0.915 = 162.75
Answer:
177.87 is the correct answer. Really hope that this helped :)
Step-by-step explanation:
In this figure, AB || CD and mZ6 = 75"
What is mZ3?
Enter your answer in the box.
Answer:
105
Step-by-step explanation:
Theorem:
If parallel lines are cut by a transversal, then same-side interior angles are supplementary.
Lines AB and CD are parallel, and angles 3 and 6 are same-side interior angles, so by the theorem above, angles 3 and 6 are supplementary. That means that the sum of their measures is 180 deg.
m<3 + m<6 = 180
m<3 + 75 = 180
Subtract 75 from both sides.
m<3 = 105
Answer: 105 degrees
4 MATH QUESTIONS AND YOU WILL GET 20 POINTS PLEASE PLEASE HELP I NEED THIS
Answer:
1. x=160 (here given as ques no. 5)
2. x=81 (here given as ques no.5)
4. No (here given as ques no. 8)
Step-by-step explanation:
1. Given ∠STR=∠SRT=20°
we know ∠STR+∠STU=180
x+20=180
x=160
2. By external angle property
x+24=105
x=81
3. By Angle Sum Property
∠ 1=∠2=∠3=∠4=90
and
∠5=∠6=∠7=∠8=90
Hence all angles are equal to 90
and we know only parallel lines have
∠4=∠5
∠3=∠6
hence line 'r' and line 't' are parallel.
4. For being parallel side pieces must not form a triangle(i.e. sum two interior angle must be equal to 180)
But here sum of interior angle 174
Hence a triangle is possible.
So , lines are not possible .
Paton knows she will make a selection from 36 total possible outcomes. Which statement might describe what Paton is doing? Check all that apply.
Answer: All but statement 1
Step-by-step explanation:
In order to get 36 as an outcome, the numbers need to multiply together in order to get 36. In other words, a*b*c*d*....= desired outcome number. In statement 1, 3*9=27, and therefore not 36 outcomes. The rest do multiply to 36.
Answer:
2,3,4,5
Step-by-step explanation:
Stay safe! Hope this helps!
What is 0.3 divided 0.24 doing long division
Answer:
1.25
Step-by-step explanation:
Change 0.3 and 0.24 into whole numbers. So this would be 30 and 24. You do 30/24 and simplify it to 5/4 (because you divide 6; both numerator and denominator) which gives you 1.25.
Final answer:
Detailed explanation on dividing 0.3 by 0.24 using long division.
Explanation:
Dividing 0.3 by 0.24 using long division:
First, insert a decimal point after 0.3 to make it 0.30.
Then, perform long division: 0.30 ÷ 0.24 = 1 remainder 0.06.
Bring down another zero to continue dividing: 0.06 ÷ 0.24 = 0.25.
what is the percent decrease from 5000 to 4000?
Answer:
20%
Step-by-step explanation:
5000 - 4000 = 1000
[tex]\frac{1000}{5000}[/tex] × 100
[tex]\frac{1}{5}[/tex] × 100
0.2 × 100 = 20%
Check:
5000 - 20% of 5000
5000 - 2/10 × 5000
5000 - 1000
= 4000
Answer:
20% decrement
Steps:
➥5000-x% of 5000=400
➥5000-x% × 5000=4000
➥5000-4000=x% × 5000
➥1000=x% × 5000
➥x%=1000/5000
➥x%=0.2
➥x%=20/100
➥x%=20%
Rebecca started with 30 pieces of candy and gave away x
pieces. Ana started with 45 pieces of candy and gave away
twice as many pieces as Rebecca did. How many pieces of
candy did Rebecca give away if they had the same number of
pieces of candy left?
Answer:
The correct answer would be 15.
Step-by-step explanation:
30-15=15
45-2(15)=15
What additional information is required for the 2 triangles to be congruent by SAS?
n is a positive integer.Explain why n(n-1) must be an even number.
Please can someone explain this algebraically.
Answer:
n and (n - 1) are consecutive integers.
Step-by-step explanation:
We are given 'n', a positive integer.
This 'n' can either be odd or even.
Case I:
When 'n' is odd
The n - 1 is even.
Note that the product of odd and even is always even. That is the product of n and (n - 1) is even.
Case II:
when 'n' is even
Then n - 1 is odd.
Again, using the similar logic we can say that the product of n and n - 1 should be even because here, 'n - 1' is even and 'n' is odd.
The sum of two numbers is 53 and the difference is 27. What are the numbers?
Final answer:
The two numbers are 40 and 13.
Explanation:
We are given that the sum of two numbers is 53, and their difference is 27. Let's denote the two unknown numbers as x and y, where x is the larger number.
The system of equations based on the given information is:
x + y = 53x - y = 27By adding the two equations, the y's cancel out:
(x + y) + (x - y) = 53 + 272x = 80x = 40Now, we can find the value of y by substituting x into the first equation:
40 + y = 53y = 53 - 40y = 13The two numbers are 40 and 13.
8 * 4 = (A * 7) – (A * 3)
Answer:
A=32
Step-by-step explanation:
Which describes the cross section of the square prism that passes through the vertices A, B, C, and D shown below?
a rectangle
a square
a kite
a trapezoid
Answer:
Trapezoid
Step-by-step explanation:
I need help with 25 and 26 plzz
Answer:
Step-by-step explanation:
25.
Combine like terms.
4t+7=-33
subtract 7 from both sides
4t=-40
divide both sides by 4
t=-10
26.
Subtract 2a from both sides
5=7a-16
add 16 to both sides
21=7a
divideby 7 on both sides
a = 3
I'd suggest getting the app photomath or using cymath to help you with these problems. they give you the answer and how to get it step by step
A line passes through the point (6,1) and has a slope of -3.
Write an equation in point-slope form for this line
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{1})~\hspace{10em} \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{6})[/tex]
Molly has walked 80% of the way to school.She has walked 16 blocks.How many blocks is her whole trip to school?
Answer:
20 blocks
Step-by-step explanation:
80% = 0.8
16 / 0.8 = 20
Your company takes orders over the phone. The company’s average time is 4.6 minutes.The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Answer:
0.4
Step-by-step explanation:
The mean difference between the call will be 0.4. Then the correct option is C.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Your company takes orders over the phone. The company’s average time is 4.6 minutes. The graph below shows 4 calls and the difference between the call time and the company’s average call time.
Then the mean difference between the call will be
Mean = (Sum of the observation) / (Number of the observation)
Mean = (-2.32 - 1.55 + 4.79 + 0.68) / 4
Mean = 1.6 / 4
Mean = 0.4
The mean difference between the call will be 0.4. Then the correct option is C.
Your question was incomplete, but the complete question is attached below.
More about the mean link is given below.
https://brainly.com/question/521501
#SPJ6
A hockey puck slides across an ice pond at a constant speed of 18 meters per second. Complete the table to determine the distance the hockey puck slides at different times.
Answer:
1 18
2 36
3 54
4 72
Step-by-step explanation:
18 m/s every second means you multiply the time by rate (to get the distance traveled in 2 seconds, multiply 18m/s by 2 to get 36)