simon will deposit $250 into two savings accounts. account 1 earns 1.6% interest compounded annually. account 2 earns 1.6% simple annual interest. if simon makes no additional deposit or withdrawals, which account is closest to the difference in the interest that the account will have earned at the end of 10 years. A. $253.01 B.$43.01 C.$83.01 D.$3.01
Answers
The difference in the interest that the account will have earned at the end of 10 years is of:
D. $3.01.
What is the account 1 interest earned?The amount of interest earned, in compound interest, after t years, is given by:
\(I(t) = P\left(1 + \frac{r}{n}\right)^{nt} - P\)
In which the variables are listed as follows:
P is the principal.r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.In the context of this problem, these parameters are given as follows:
P = 250, r = 0.016, n = 12, t = 10.
Hence the interest earned by account 1 is:
\(I(10) = 250\left(1 + \frac{0.016}{12}\right)^{12 \times 10} - 250 = 43.35\)
What is the account 2 interest earned?For simple interest, the amount of interest earned is:
I(t) = Prt.
Hence:
I(10) = 250 x 0.016 x 10 = 40.
Hence the difference is:
43.35 - 40 = $3.35.
Which is closest to option D.
More can be learned about simple interest at https://brainly.com/question/25793394
#SPJ1
Related Questions
a coin is flipped 6 times. if more heads are flipped than tails, the probability that all 6 are heads is , what is the value of ?
Answers
The probability that all 6 flips result in heads is 1/64
The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0
For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64
P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)
P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64
Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.
Learn more about probability and coin flipping:https://brainly.com/question/30544804
#SPJ11
A fire department needs to raise its
ladder to the 5th story window which is
approximately 55 feet off of the ground. The ladder
can extend to a length of 60 feet. This ladder is
already 8 feet off of the ground because it is on top
of the truck. If the ladder is fully extended when
reaching the window, how far away should the base
of the ladder be from the building? Round the
answer to the nearest foot.
A. 5 feet
B. 24 feet
C. 37 feet
D. 81 feet
Answers
Answer:
b, 24
Step-by-step explanation:
same side interior angles are _____ congruent
A.always
B.never
C.sometimes
Answers
Answer:
B. Never
Step-by-step explanation:
that's just what my math teacher told us...
What is the range
of 98, 99, 100,
90, 98, 100?
Answers
Answer:
10
Step-by-step explanation:
Increasing order:-
90,98,98,99,100,100Range = Highest term - Lowest term
Range = 100 - 90
Range = 10
Hence,
Range of the given term is 10
Answer:
10Step-by-step explanation:
The data set in ascending order:
90, 98, 98, 99, 100It has min = 90, max = 100
The range is the difference between min and max:
100 - 90 = 10find a function whose square plus the square of its derivative is 1.
Answers
A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).
The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).
This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.
The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.
Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.
Learn more about sine function here:
https://brainly.com/question/29277391
#SPJ11
What is 2,367 x 578 =
Answers
Answer:
Step-by-step explanation:
1368126
Answer: your answer is 1,368,126
Step-by-step explanation:
18 x 1/6 simplify if can thank u
Answers
Answer:
3
Step-by-step explanation:
\(18*\frac{1}{6} \\\\3\)
Answer:
=3x
Step-by-step explanation:
18x^1 / 6
=3x
A kinesiologist measures 10 volleyball players heights (in cm), with the following results: 185, 182, 165, 189, 170, 150, 174, 151, 180, 158 What is their average height?
Answers
Their average height is 159.4
In this case, the kinesiologist measured the heights of 10 volleyball players in centimeters. One common way to describe a set of data like this is to calculate the average, or mean, height of the players.
To calculate the average height, we add up all of the heights and divide by the total number of players. In this case, we have:
185 + 182 + 165 + 189 + 170 + 150 + 174 + 151 + 180 + 158 = 1594
We have 10 players in total, so we divide the sum of the heights by 10:
1594 / 10 = 159.4
Therefore, the average height of the 10 volleyball players is 159.4 centimeters.
To know more about average here
https://brainly.com/question/16956746
#SPJ4
Write the equations of the parallel or perpendicular lines.
Answers
Answer:
ikl;'
Step-by-step explanation:
Find the rectangular coordinates of the point(s) of intersection of the polar curves r = 5 sin(theta) and r = 5 cos(theta)|. a) (0, 0)| and (5, 5)| b) (0, 0)| and (5/2, 5/2)| c) (0, 0)| and (5/4, 5/4)| d) (1, 1)| and (5/4, 5/4)| e) (0, 0)| and (-5/2, -5/2)|
Answers
The coordinates of the first point of intersection in rectangular form are (x, y) = ((5/2), (5/2)).
To find the points of intersection between the polar curves r = 5 sin(θ) and r = 5 cos(θ), we need to equate the two equations and solve for θ. Let's start by setting the two equations equal to each other:
5 sin(θ) = 5 cos(θ)
Dividing both sides by 5 gives:
sin(θ) = cos(θ)
Now, we can use the trigonometric identity sin(θ) = cos(90° - θ). Replacing cos(θ) with sin(90° - θ), the equation becomes:
sin(θ) = sin(90° - θ)
Since the sine function is equal to itself for any angle plus multiples of 360°, we can write:
θ = 90° - θ + 360° x n
Here, n represents any integer value. Solving for θ, we get:
2θ = 90° + 360° x n
Dividing both sides by 2, we have:
θ = 45° + 180° x n
Now, let's substitute this value of θ back into the original equation r = 5 sin(θ) (or r = 5 cos(θ)) to find the corresponding r-values.
For θ = 45°:
r = 5 sin(45°) = 5 cos(45°)
Using the values of sine and cosine for 45°, we get:
r = 5 x √(2)/2 = 5 x √(2)/2
Simplifying further, we have:
r = (5/2) x √(2)
Therefore, the coordinates of the first point of intersection are (r, θ) = ((5/2) x √(2), 45°).
Now, let's consider the value of θ for n = 1:
θ = 45° + 180° x 1 = 45° + 180° = 225°
For θ = 225°:
r = 5 sin(225°) = 5 cos(225°)
Using the values of sine and cosine for 225°, we get:
r = 5 x (-√(2)/2) = -5 x √(2)/2
Simplifying further, we have:
r = (-5/2) x √(2)
Therefore, the coordinates of the second point of intersection are (r, θ) = ((-5/2) x √(2), 225°).
To convert these polar coordinates into rectangular coordinates, we can use the formulas:
x = r x cos(θ) y = r x sin(θ)
For the first point of intersection, (r, θ) = ((5/2) x √(2), 45°):
x = ((5/2) x √(2)) x cos(45°) = (5/2) x √(2) x √(2)/2 = (5/2) y = ((5/2) x √(2)) x sin(45°) = (5/2) x √(2) x √(2)/2 = (5/2)
Hence the correct option is (b).
To know more about rectangular coordinates here
https://brainly.com/question/31904915
#SPJ4
If DA = 6 and MD = 4, what is the length of DK?
Answers
Answer:
DK = 9
Step-by-step explanation:
In triangle AMD,
h² = p² + b²
or, h² = 6² + 4²
or, h²= 36 + 16
so, h² = 52
so, AM² = 52
Take x as reference angle,
cos²x = 16/52
Now,
In triangle, AMK,
Taking x as reference angle,
cos²x = b²/h²
cos²x = AM²/MK²
or, cos²x = 52/MK²
Now,
cos²x = 16/52 = 52/MK²
or,
16/52 = 52/MK²
or, 16MK² = 2704
or, MK² = 2704/16
or, MK² = 169
so, MK = 13
Now,
DK = MK - MD
or, DK = 13 - 4
so, DK = 9
Answer:
DK= 9
Step-by-step explanation:
I guessed and got it right :)
Calculate X you must include the steps in your solution and the definitions and/or conjuncture that you use
Answers
Answer: x = 8
because The upper triangle is an isosceles triangle (the two sides are equal)
=> 5x + 5 = 45°
<=> x = (45 - 5) : 5
<=> x = 40:5 = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
5x + 5 + 5x + 5 + 90 = 180, that is
10x + 100 = 180 ( subtract 100 from both sides )
10x = 80 ( divide both sides by 10 )
x = 8
Two spheres are similar. The radius of the first sphere is 10 feet. The volume of the other sphere is 0.9 cubic meters. Use 2.54cm=1 in. to determine the scale factor from the first sphere to the second.
Answers
The scale factor from the first sphere to the second is approximately 0.004999.
To determine the scale factor from the first sphere to the second, we can use the relationship between volume and radius for similar spheres.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.
Given that the radius of the first sphere is 10 feet, we can calculate its volume:
V1 = (4/3)π(10^3)
V1 = (4/3)π(1000)
V1 ≈ 4188.79 cubic feet
Now, let's convert the volume of the second sphere from cubic meters to cubic feet using the conversion factor provided:
0.9 cubic meters ≈ 0.9 * (100^3) cubic centimeters
≈ 900000 cubic centimeters
≈ 900000 / (2.54^3) cubic inches
≈ 34965.7356 cubic inches
≈ 34965.7356 / 12^3 cubic feet
≈ 20.93521 cubic feet
So, the volume of the second sphere is approximately 20.93521 cubic feet.
Next, we can find the scale factor by comparing the volumes of the two spheres:
Scale factor = V2 / V1
= 20.93521 / 4188.79
≈ 0.004999
Therefore, the scale factor from the first sphere to the second is approximately 0.004999. This means that the second sphere is about 0.4999% the size of the first sphere in terms of volume.
learn more about scale factor here
https://brainly.com/question/29464385
#SPJ11
A jar of peaches weigh 13 ounces .There are 16 jar in a crate How many ounces does crate weight?
Answers
Answer:
208 ounces
Step-by-step explanation:
Multiply 13 by 16
Answer:
Step-by-step explanation:
13*16= 208 ounces
16 ounces is one pound. So the crate is 13 pounds.
you should use a ____ chart to compare values side by side, broken down by category.
Answers
A column chart is an excellent tool for comparing values side by side, broken down by category. With its clear and concise display of data, it is an invaluable asset for businesses, researchers, and anyone looking to understand complex information quickly and easily.
To compare values side by side, broken down by category, a column chart is an effective tool. Column charts are ideal for comparing data across different categories or groups, as they clearly display the differences between values. When creating a column chart, the categories are listed on the horizontal axis, and the values are listed on the vertical axis. Each column represents a different category, and the height of the column corresponds to the value of that category. Column charts can be customized to fit specific needs, such as adding colors or labels to each category. They are also versatile and can be used to display a wide range of data, from sales figures to survey results. You should use a bar chart to compare values side by side, broken down by category. Bar charts are a helpful visualization tool that allows you to compare data across different categories in an easy-to-read format.
Learn more about column chart here
https://brainly.com/question/29904972
#SPJ11
A certain loan program offers an interest rate of 3%, compounded continuously. Assuming no payments are made, how much would be owed after seven years on a loan of $3100?Round your answer to the nearest cent.
Answers
The amount that would be owed after seven years is $3824.40
EXPLANATION
Given:
Principal(P)= 3100
rate (r) =0.03
Time (t) = 7
Using the formula below (since it is continuously compounded):
\(A=Pe^{rt}\)Substitute the values into the formula and evaluate.
\(=3100\times e^{0.03\times7}\)\(=3100\times e^{0.21}\)\(\approx3824.40\)Hence, the amount that will be owed is $3824.40
Mr. Smith is ordering steaks to serve at a poker game with his friends. The first company charges a delivery fee of $10 plus $15 per steak. The second company charges a delivery fee of $25 and charges $10 per steak. How many steaks would Mr. Smith have to order so that both companies cost the same amount?
Answers
Answer:
3
Step-by-step explanation:
1. One= $25 Two= $40 Three= $55
2. One= $35 Two= $45 Three= $55
The scatter plot shows the number of minutes people had to wait for service at a restaurant and the number of staff available at the time.
A line that models the data is given by the equation $$, where $$ represents the wait time, and represents the number of staff available.
The slope of the line is -1.62. What does this mean in this situation?
it means that the scatter plots are off the chart
Is a slope of 1.62 realistic in this context?
no because it is not a coordinate and there isn't any decimals in the wait time
The $$-intercept is $$. What does this mean in this situation?
it means there's more waiting time
Is a $$-intercept of $$ realistic in this context?
no because when you try to find it it goes off the graph and isnt calculable.
Edit my response f
Answers
The slope of a linear regression is the rate of change of the line of the best fit
The interpretation of the slope is that the wait time per staff is 1.62 minutesThe slope value is realisticHow to interpret the slopeThe linear regression is given as:
\(y = -1.62x + 18\)
Where
y represents the wait timex represents the number of staffUsing the above representations, the slope means that the wait time per staff is 1.62 minutes
Also, the slope value is realistic because time can be measured in decimals
Read more about linear regressions at:
https://brainly.com/question/25987747
What would be the angle between the two perpendicular lines.
Answers
Answer:
90 degrees
90 degreesPerpendicular lines are lines that intersect at a right (90 degrees) angle.
Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the vertices are integers.
Which statement is true about the slope of HK and the slope of PK?
Answers
Answer:
Step-by-step explanation:
b
how can i solve these simultaneous equation 11x+11y=1001 and 10x+y=10
Answers
Answer:
\(10x + y = 10 (1)\\ 11x + 11y = 1001(2) \\ from \: equation \:(1) \: y = 10 - 10x \\ 11x + 11(10 - 10x) = 1001 \\ 11x + 110 - 110x = 1001 \\ 11x - 110x = 1001 - 110 \\ - 99x = 891 \\ \frac{ - 99x}{ - 99} = \frac{891}{ - 99} \\ x = - 9 \\ y = 10 - 10x \\ y = 10 - 10( - 9) \\ y= 10 + 90 \\ y = 100\)
Step-by-step explanation:
Hope that this is helpful.
Have a great day.
look at the picture.
Answers
Answer:
66
Step-by-step explanation:
66 square root is 8.12403840464
Answer:
i got 66
Step-by-step explanation:
REEEEEEEEEEEEEEEEE
Show that if (an) is a convergent sequence then for, any fixed index p, the sequence (an+p) is also convergent.
Answers
If (an) is a convergent sequence, then for any fixed index p, the sequence (an+p) is also convergent.
To show that if (an) is a convergent sequence, then for any fixed index p, the sequence (an+p) is also convergent, we need to prove that (an+p) has the same limit as (an).
Let's assume that (an) converges to a limit L as n approaches infinity. This can be represented as:
lim (n→∞) an = L
Now, let's consider the sequence (an+p) and examine its behavior as n approaches infinity:
lim (n→∞) (an+p)
Since p is a fixed index, we can substitute k = n + p, which implies n = k - p. As n approaches infinity, k also approaches infinity. Therefore, we can rewrite the above expression as:
lim (k→∞) ak
This represents the limit of the original sequence (an) as k approaches infinity. Since (an) converges to L, we can write:
lim (k→∞) ak = L
Hence, we have shown that if (an) is a convergent sequence, then for any fixed index p, the sequence (an+p) also converges to the same limit L.
This result holds true because shifting the index of a convergent sequence does not affect its convergence behavior. The terms in the sequence (an+p) are simply the terms of (an) shifted by a fixed number of positions.
Learn more about convergent sequence
brainly.com/question/32549533
#SPJ11
This recipe makes 4 portions of porridge.
Complete the amount of each ingredient that is needed to make just 3 portions.
Recipe: Serves 4
240 g oats
1.2 L milk
60 g sugar
Can someone help
Answers
Answer:
180 g oats
0.9 L milk
45 g sugar
Step-by-step explanation:
those are all divided by 3/4 making just 3 portions :D
Annapolis Company purchased a $4,000, 6%, 5-year bond at 101 and held it to maturity. The straight line method of amortization is used for both premiums & discounts. What is the net cash received over the life of the bond investment? (all money received minus all money paid, round to nearest whole dollar)
Answers
Answer:
The answer is "\(\bold{\$1160}\)"
Step-by-step explanation:
Calculating total paid money:
\(= \$4000 \times 101\% \\\\= \$4000 \times \frac{101}{100} \\\\=\$40 \times 101\\\\=\$4040\)
\(\text{Total received money = Principle on Maturity + Interest for 5 years}\)
\(= \$4000 + \$4000\times 6\% \times 5 \\\\= \$4000 + \$4000\times \frac{6}{100} \times 5 \\\\= \$4000 + \$40 \times 6 \times 5 \\\\= \$4000 + \$40 \times 30 \\\\= \$4000 + \$1200 \\\\= \$5200 \\\\\)
Total earnings over the life of the corporate bond
\(= \$5200 - \$4040 \\\\=\$1160\)
The mass of An African penguin is 3.599 kilograms write three expressions that describe the mass of the penguin.
Answers
The expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms
How to determine the expressions that describe the mass?The mass of the penguin is given as
Mass = 3.599 kilograms
Convert the mass from kilograms to grams.
So, we have:
Mass = 3.599 * 1000 grams
Evaluate the product
Mass = 3599 grams
Next, convert the mass from grams to ounce
So, we have:
Mass = 3599/28.35 ounce
Evaluate the quotient
Mass = 126.95 ounces
Hence, the expressions that describe the mass are Mass = 3599 grams, Mass = 126.95 ounces and Mass = 3.599 kilograms
Read more about metric units at:
https://brainly.com/question/2004114
#SPJ1
Help with this question and i will do brainliest (if there are multiple answers)
Answers
Answer:
a=2/5
Step-by-step explanation:
1.7((2)/(5))+0.3((2)/(5)) = 0.8=80/100=4/5
Answer:
the answer is a=2/5
Step-by-step explanation:
combine like terms 1.7+0.3=2
get the varliable alone 2/4/5
answer 2/5
I have a shuffled deck of 52 playing cards. A deck of cards has four different suits, with an even number of cards in each. I pick a card at random. What is the probability of me picking any card which is in the spades suit, as a decimal?
Answers
Answer:
The probability is 0.25
Step-by-step explanation:
Here is a probability question.
We want to know the probability of picking a card which is in the spades suit.
Now, what we know is that there are a total of 52 cards and we have 4 suites.
Each suite have equal number of cards. So definitely the number of cards in the spades suit will be 52/4 = 13 cards
Thus, the probability of picking any card in the spades suit = number of cards in the spades suit/ Total number of cards in the deck
Mathematically that would be 13/52 = 1/4 = 0.25
according to ada guidelines, a ramp with a two-foot vertical rise should be at least:
Answers
According to ADA guidelines, a ramp with a two-foot vertical rise should be at least 20 feet long.
This length allows for a gentle slope that is safe and accessible for individuals with mobility impairments, including those using wheelchairs or other mobility aids. The slope of the ramp should not exceed 1:12, which means that for every inch of vertical rise, the ramp should extend 12 inches horizontally.
The ADA guidelines are designed to ensure that individuals with disabilities have safe and accessible routes of travel in public spaces. Ramps with proper dimensions and slope ratios are critical for individuals with mobility impairments to access buildings and spaces that may not be accessible via stairs. Ramps should also be designed with non-slip surfaces, handrails, and other safety features to prevent accidents and ensure that all individuals can use them safely and comfortably.
To learn about ADA Guidelines : brainly.com/question/24002008
#SPJ11
help pls! this is khan academy and i need to pass this class
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: Scale factor is 4
Explanation:
56 / 14 = 4
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
The scale factor from Figure A to Figure B is 4
Step-by-step explanation:
As the sides of these triangles do not have angles for use to calculate the exact areas, allowing us to divide the larger triangle by the smaller to find the scale factor, we must look at the lengths of the sides within these two triangles. After inspection, we can see that corresponding sides may instead be divided into one another. For example,
56/14
64/16
28/7
These pairs of corresponding sides may be divided as so and all reach the conclusion of a value of 4. This means that the larger triangle has sides that are a multiple of 4 to the smaller triangle.
Thus the scale factor from Figure A to Figure B is 4!