Answer:
$3577.20
Step-by-step explanation:
You can save 11% of your income each month, so in 12 months, you can save ...
12×0.11×$2710 = $3577.20
Consider the two savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100 per month in an account with an APR of 5%, while Zach deposits $1200 at the end of each year in an account with an APR of 5%.
Step-by-step explanation:
It is not specified the compounding period, which in general is a month these days. So we will assume money is compounded each month, otherwise there is no point depositing monthly.
1. Yolanda:
APR=5% is equivalent to
Monthly interest = 5%/12 = 5/12% = 5/1200 = 1/240 = i
Monthly deposit = 100 = A
Future value after 14 years = 14*12 months = 168 months = n
FV1 = A((1+i)^n-1)/i
=100*((1+1/240)^168-1)/(1/240)
= $24259.83
2. Zach
He deposits 1200 at the end of the year. The last payment does not benefit from interest.
Since it is a yearly payment, each amount earns interest over a year, giving an annual interest of
(1+i)^12 -1 = 1.051161897881733 -1 =0.051161897881733 = j
Thus for 13 annual payments with annual interest j gives a compounded amount after 14 years, plus the last payment which does not earn interest
FV2 = A((1+j)^n-1)/j
= 1200((1.051161897881733)^13-1)/(0.051161897881733)+1200
= 22613.34
Summary
Total investments:
Yolanda = 12*100*14 = 16800
Zach = 1200 * 14 = 16800
So both investors have invested $16800 over the 14 year period.
Since Yolanda achieves a higher future value after 14 years ($24259.83) over that of Zach ($22613.34), financially Yolanda has a better strategy.
Note:
If zach had invested annually at the beginning of the year, he would have obtained:
A((1+j)^n-1)/j
= 1200((1.051161897881733)^14-1)/(0.051161897881733)
= 24908.88
which is superior over Yolanda's return.
(1 point) Standard automobile license plates in a country display 2 digits, followed by 3 letters, followed by 2 digits. How many different standard plates are possible in this system
Answer:
175,760,000 possible standard plates
Step-by-step explanation:
For digits, there are 10 possible values (0 to 9)
For letters, there are 26 possible alphabet (a - z)
Assuming the letter case is irrelevant.
Given that the license plate consists of;
2 digits, followed by 3 letters, followed by 2 digits
N1 = 2 digits = 10 × 10
N2 = 3 letters = 26× 26 × 26
N3 = 2 digits = 10×10
In the absence of any other conditions, the number of possible plates in this system is;
N = the product of N1, N2 and N3 above.
N = N1 × N2 × N3
N = 10×10×26×26×26×10×10
N = 175,760,000 possible standard plates
The density of salt is 80 pounds per cubic foot (lb/ft3). 1 pound (lb) is approximately 0.4536 kilogram (kg). 1 cubic foot (ft3) is approximately 0.0283 cubic meter (m3). What is the approximate density of salt in kilograms per cubic meter (kg/m3)?
Answer: Density = 1,282.26 kg/m^3
Step-by-step explanation:
Density = 80 lb/ft^3
We know that:
1lb = 0.4536 kg.
1ft^3 = 0.0283 m^3
then we can write:
1 = (0.4536kg)/(0.0283 m^3)*(1ft^3/lb)
we can multiply our equation by this, and it wont be affected, then we have:
Density = 80 lb/ft^3 = 80 lb/ft^3 (0.4536kg)/(0.0283 m^3)*(1ft^3/lb)
Density = 1,282.26 kg/m^3
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting three Democrats and three Republicans
Answer:
39.16% probability of selecting three Democrats and three Republicans
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the people are selected is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
3 Democrats, from a set of 8.
3 Republicans, from a set of 8.
[tex]D = C_{8,3}*C_{8,3} = (C_{8,3})^{2} = (\frac{8!}{3!5!})^{2} = 56^2 = 3136[/tex]
Total outcomes:
6 people from a set of 16.
[tex]T = \frac{16!}{6!10!} = 8008[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{3136}{8008} = 0.3916[/tex]
39.16% probability of selecting three Democrats and three Republicans
David and Tina share their profit in a ratio of 5:7. Tina gets £70 more than David. How much money did David receive?
Answer:
Amount of money David received = £ 175
Step-by-step explanation:
Both of them share their profit in a ratio of 5:7 . Tina got £70 more than David. Let
the amount David received = a
amount Tina received = 70 + a
the total profit = 70 + 2a
Amount David received = 5/12 × 70 + 2a = a
Therefore,
5/12 × 70 + 2a = a
350 + 10a/12 = a
cross multiply
350 + 10a = 12a
collect like terms
350 = 12a - 10a
350 = 2a
divide both sides by 2
a = 350/2
a = 175
Amount of money David received = £ 175
please answer my question
Answer:
B
Step-by-step explanation:
To find a perpindicular line, you want to find the reciprical slope, and have a point.
We already have the point which is (3,9)
All we have to do is find the new slope what is easy, get the orginal slope,
flip the sides and polarity of it. So from the slope -3/2, you get 2/3.
Now you just plug all the new values into slope point formula.
y - y1 = m(x - x1).
You do simple algebra and get B as your answer
Triangle L M N is shown. Angle L M N is a right angle. Angles N L M and L M N are 45 degrees. The length of L N is x. Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = LM = x StartRoot 2 EndRoot tan(45°) = StartFraction StartRoot 2 EndRoot Over 2 EndFraction tan(45°) = 1
Answer:
A.) NM= x
C.) LM = x√2
E.) tan (45°) = 1
Step-by-step explanation:
If the legs are both x, then the hypotenuse is equal to [tex]x\sqrt{2[/tex]
Therefore, LM= [tex]x\sqrt{2[/tex] is correct and MN= x
Disclaimer: The sum is done according to the picture attached as the question given is wrong.
The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.What are isosceles right triangles?An isosceles triangle is a triangle where two sides and their corresponding angles are equal.
A right triangle is a triangle with one angle = 90°.
An isosceles right triangle is a right-angled triangle with two legs including the right angle are equal. Their corresponding angles are equal and each of them = 45°. So, the three angles of an isosceles right triangle are 45°, 45°, and 90°, always.
How do we solve the given question?In the figure, we can see that we have a ΔLMN, with ∠L = 45°, ∠M = 45°, and ∠N = 90°. Also, we can see that LN = x.
The given angles of ΔLMN determine that it is an isosceles right triangle with a right angle at N.
Since, the two legs involving the right angle, that is N, are equal, we can say that, NM = LN = x.
The hypotenuse of the ΔLMN, that is the side opposite to ∠N, that is LM, can be found using the Pythagoras theorem, by which in a right-angled triangle,
Hypotenuse² = Base² + Perpendicular².
∴ LM² = LN² + NM² = x² + x² = 2x².
or, LM = √(2x²) = x√2.
The tangent of an angle ∅, that is, tan ∅ is computed using the formula,
tan ∅ = Perpendicular/Base.
To calculate tan 45°, that is, tangent to ∠L, we take Perpendicular = NM and Base = LN.
∴ tan 45° = NM/LN = x/x = 1.
Now, we check all the given options:
NM = x. TRUE (computed)NM = x√2. FALSE (∵ NM = x)LM = x√2. TRUE (computed)tan 45° = √2/2. FALSE (∵ tan 45° = 1)tan 45° = 1. TRUE (computed)∴ The true statements regarding the given isosceles right triangle ΔLMN are:
NM = xLM = x√2tan 45° = 1.Learn more about isosceles right triangle at
https://brainly.com/question/691225
#SPJ2
what is the value of x?
X = 30 degrees.
See the attached image
Chris placed $7,400 in a savings account which compounds interest annually at a rate of 5.7%. How much will he have in the account after 4 years?
Answer:$9237.02
Step-by-step explanation:
A = p(1+r/n)^nt
A = 7400 (1 + 0.057)^4
A = 7400(1.057)^4
A = 9237.02
Do not add the .02 at the end of this answer
PLEASE 36 POINTS!!! I WILL ALSO GIVE BRAINLIEST A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer: D: (2, 0)
Step-by-step explanation:right on Edge 2020
Answer:
yes its d
Step-by-step explanation:
did on edge
Help pls any kind soul pls help
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times as old, that means that Olly's age is 3 * x or 3x for short.
Answer:
3x
Step-by-step explanation:
If Dan is x years old and Olly is 3 times old as Dan, then the expression is 3x.
26.355 rounded to the nearest hundredth tell anser
Answer:
26.36
Step-by-step explanation:
Hundredths are the second decimal place from the decimal. You would round up to 26.36 because the number before that is up to 5. If it was below 5 you would round down to 26.35.
5 cards are drawn from a standard deck of 52 playing cards. How many different 5-card hands are possible if the drawing is done without replacement
Answer:
many different 5-card hands are possible if the drawing is done without replacement in 2598960 ways
Step by step Explanation:
This problem is on combination, which is a selection of items from a particular collection, but here the order of selection does not matter.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
50 POINTS PLEASE HELP will mark brainlest COMPRESSION BY A FACTOR OF 2 photos attached
Answer:
Point A'(-1,5) ........ corrected A' instead of A
Point B'(3,-3)
Step-by-step explanation:
The current function has vertex (2,-4), and passes through (6,0).
Using the standard formula
y = a(x-h)^2+k
we have
h = 2, k=-4
parabola passes through (6,0) =>
0 = a(6-2)^2 -4 = 16a -4
a = 1/4
so equation of given curve is
f(x) = (1/4)(x-2)^2-4
If the curve is compressed horizontally by a factor of 2, then the image is
g(x) = (1/4)(2(x-2))^2-4
=(x-2)^2 -4
Given A(-4,5), B(4,-3)
f(-4) = 5
f(4) = -4
With a compression factor of 2, coordinates of y do not change.
for point A'
5 = (x-2)^2 -4
5 = (x-2)^2 -4
(x-2)^2 = 9
(x-2) = +/- 3
x-2 = -3, x = -1 (to the left of vertex, ok)
x-2 = +3, x = 5 (to the right of vertex, alternate point x)
Point A'(-1,5) ........ corrected A' instead of A
For point B'
y = -3
-3 = (x-2)^2-4
(x-2)^2 =1
x-2 = +/- 1
x-2 = +1, x=3 (to the right of vertex, point required)
x-2 = -1, x= 1 (to the left of vertex, alternate point Y)
Point B'(3,-3)
Which function represents a parabola that opens downward and has a vertex at (3,-4)
Answer:
y = -(x-3)² -4
Step-by-step explanation:
Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $770. Find the lower rate of interest. _________ %
Answer:
10% interest.
Step-by-step explanation:
Interest I = PRT/100
If the rate R = x% we have
550 = P*x *1 / 100
and
770 = P*(x + 4) * 1 / 100
so From first equation
Px = 55000 and from the second
Px + 4P = 77000
So Px = 77000 - 4P
Therefore 77000 - 4P = 55000
4P = 22000
P = 5,500
So x = 55000/5500 = 10%.
And the rate for the other fund is 10 + 4 = 14%.
10x - 30 = 5y
2x = y + 6
Answer:
the equations are dependent; both describe the line y = 2x -6
Step-by-step explanation:
Remove the common factor of 5 from the first equation and you have ...
2x -6 = y
Subtract 6 from the second equation and you have ...
2x -6 = y
The two equations are the same, so describe the same line. The solution set is all points on that line. The equations are dependent, and have an infinite number of solutions.
A cable that weighs 6 lb/ft is used to lift 700 lb of coal up a mine shaft 600 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)
Answer:
15000000ft-Ib
Step-by-step explanation:
We were told to Show how to approximate the required work by a Riemann sum which is a certain kind of approximation of an integral by a finite sum.
. So we will need to divide the cable into 6 segments,
✓let us denote x as the distance between the top of the mine shaft and the segment.
✓Let us denote ∆x as the length of the segment
Then work done on a segment, work done on the coal and total work done can now be calculated.
CHECK THE ATTACHMENT FOR THE DETAILED EXPLANATION
Suppose that the weight of a cable is [tex]6 \ \frac{lb}{ft}[/tex] and used to lift [tex]700\ lb[/tex] of coal up a mining shaft [tex]600\ ft[/tex] deep.
Let the ith portion of a cable have a width of [tex]\Delta x[/tex], therefore the weight of the ith part of the cable is [tex]6\ \Delta x[/tex], and the distance of the ith part of the cable from the mineshaft is [tex]x_i^{*}[/tex].As a result, the effort done on the ith segment of the wire is [tex]6x_i^{*}, \Delta x[/tex]. The overall amount of work completed for the cable is as follows:[tex]\to W_{ca} = \lim_{n\to \infty} \Sigma^{n}_{i=1} 6x_i^{*} \Delta x \\\\[/tex]
[tex]=\int^{600}_{0} 6x \ dx\\\\= [6x^2]^{600}_{0} \\\\= 3 (360000)\\\\ = 1080000\ ft-lb\\\\[/tex]
Thus, the work done again for cable is [tex]W_{ca} = 1080000 \ ft-lb[/tex].
If the cable weighs 700 lbs and the distance is 600 feet, As a result, the effort expended in raising the coal to the top of the mineshaft is referred to as
[tex]\to W_{co} = 700 \times 600 = 420,000 \ ft-lb[/tex]
As a result, the total amount of work completed is as follows:
[tex]\to W =W_{ca}+W_{co} \\\\[/tex]
[tex]= 1080000+ 420000 \\\\= 1500000 \ ft-lb \\\\[/tex]
Hence, the total work done is [tex]\bold{W = 1500000\ ft- lb}[/tex].
Learn more about:
brainly.com/question/15412736
Simplify the square root of 2 times the cube root of 2.
two to the one sixth power
two to the two thirds power
two to the five sixths power
two to the seven sixths power
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
Answer:
2 to the 1/6 th power
Step-by-step explanation:
square root = 1/2
Cube root = 1/3
so 1/3 x 1/2= 1/6
can i please have brainlest
Any help would be greatly appreciated
Answer: (-3, -2)
Step-by-step explanation:
Plug in -2 for y to find x
x - 5(-2) = 7
Multiply -5 and -2
x + 10 = 7
Subtract 10 from both sides
x = -3
The first ordered pair is (-3, -2)
Which expression is not requivalent to
3x - 2?
Answer:
anything that is not -2+3x or x=2/3 is wrong
Step-by-step explanation:
3) The fastest train on Earth, the TGV from France, can travel at faster speeds than trains in the
United States. During a speed test, the train traveled 8.0 x 10^2 miles in 2.5 hours. Compute the
speed of the train. (Try solving this problem using scientific notation.)
Answer:
[tex]3.2*10^2=320[/tex] mph
Step-by-step explanation:
hello,
it travels [tex]8.0*10^2[/tex] miles in 2.5 hours
So in 1 hours it travels
[tex]\dfrac{8.0*10^2}{2.5}=3.2*10^2[/tex]
miles
hope this helps
Can you please help me solve thanks step by step
Answer:
40 degrees
Step-by-step explanation:
We know the entire angle of ABD is 70 and CBD and ABC are in it.
Since we know one of them (CBD) is 30, we can subtract 30 from 70 to find ABC. This is because the angle of ABC and CBD equal ABD.
30 + x = 70
-30 from both sides
x = 40
John is going for a walk. He walks for 6.4 miles at a speed of 2 miles per hour. For how many hours does he walk?
Answer:
t = d/s
t = 6.4 / 2 miles
t = 3.2 miles
Step-by-step explanation:
follow me plzzz
Which expression is equivalent to x + y + x + y + 3(y + 5)?
Answer:
2x + 5y + 15
Step-by-step explanation:
Step 1: Combine like terms
2x + 2y + 3(y + 5)
Step 2: Distribute
2x + 2y + 3y + 15
Step 3: Combine like terms
2x + 5y + 15
Answer: 2x + 5y + 15
Step-by-step explanation:
Which expression is equivalent to x + y + x + y + 3(y + 5)?
PLEASE HELP ME!!!!!!!!!! What polygon is tesellated to form this image?
Answer:
Pentagon
Step-by-step explanation:
the head is the closest I see
Convert 58% to a decimal
Answer: 0.58
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 58% as the ratio 58 to 100 or 58/100.
Dividing by 100 moves the decimal point 2 places to the left so 58/100 would move the decimal point 2 places to the left which would give us .58 or 0.58. So 58% can be written as the decimal 0.58.
I NEED HELP PLEASE, THANKS! :) Write the augmented matrix for the system of linear equations. –9w + x + 8y + 2z = –6 –5x + 9y – 7z = 6 –3w – 6x + 4y + 9z = 4 –3w – 8x + y = –2
Answer:
3rd Matrix
Step-by-step explanation:
When you start putting the coefficients in as the matrix, you see that -9 has to be the 1st number, so that eliminates choice B and choice D as answers. You are left with choices A and C. C is the correct choice because when you plug in the second equation, your coefficient is -5, not 0.
Answer:
First Matrix
Step-by-step explanation:
Looking at the first equation, we see that the leading coefficient is -9. This gets rid of choice B and D because the first number in these matrices are not -9. You are left with choices A and C. Looking at the second equation, we see that there is no "w" variable, so we need to add one. The coefficient of this "w" is going to be 0. This means that A is the correct choice. Just to be sure though, evaluate all other coefficients to see if they line up with the matrix. Hope this helps.
the area of a right triangle is 77 m^2. the hypotenuse has a length of √317 m. what is the length of the legs?
Answer:
11 m and 14 m
Step-by-step explanation:
Legs: x and y
---
1/2xy= 77 ⇒ xy= 154
√x²+y²= √317 ⇒ x²+y²=317
x²+y²+2xy= (x+y)²= 2*154+317= 625 ⇒ x+y= √625= 25
x= 25-y
xy=154 ⇒ y(25-y)= 154 ⇒ 25y- y²=154 ⇒ y²- 25y +154=0 ⇒ y=11 and y=14
x= 25-y= 14 and 11
Find the value of X.
Answer:
x = 4√5
Step-by-step explanation:
The triangles are all similar, so corresponding lengths are proportional.
hypotenuse/short side = x/5 = (11+5)/x
x^2 = 80 . . . . cross multiply
x = 4√5 ≈ 8.94427