Compounding interest monthly on a bank's savings account results in the annual interest being divided into 12 parts and applied each month, leading to a greater amount of compound interest as interest is earned on previously accumulated interest more frequently.
When a bank's savings account pays a certain percentage of interest per year and compounds monthly instead of yearly, two things happen:
The interest gets divided into 12 parts, since there are 12 months in a year. For a 3% annual rate, the monthly rate becomes 0.25% (3% divided by 12).
The smaller monthly interest rate is applied more frequently (12 times a year), which results in compound interest. This means interest is earned not only on the initial deposit (the principal) but also on the interest accumulated from previous months. The end result is that your balance grows at a faster rate compared to yearly compounding because you're earning interest on top of interest more frequently.
The given expression for the amount after t years is P(1 + I/n)¹nt. If n increases, the value inside the parentheses becomes closer to 1, but since it's raised to the power of nt, the overall effect is that the compound interest increases the total amount more quickly than if it were compounded annually (yearly compounding).
What is the theoretical probability of the spinner landing on Elisondra’s section?
Answer:
1/4
Step-by-step explanation:
Just did this.
For his craft project, James bought 1010 10 10 pieces of ribbon that were each 2.1 feet2.1\text{ feet} 2.1 feet 2, point, 1, start text, space, f, e, e, t, end text long. How many total yards of ribbon did James buy?
To find the total yards of ribbon, convert the length of each piece of ribbon from feet to yards and multiply it by the total number of pieces. James bought 707 yards of ribbon.
Explanation:To find the total yards of ribbon, we need to convert the length of each piece of ribbon from feet to yards and then multiply it by the total number of pieces.
Since 1 yard is equal to 3 feet, we can use the conversion factor of 1 yard/3 feet to convert each piece of ribbon from feet to yards.
2.1 feet x (1 yard/3 feet) = 0.7 yards
Now, we can multiply the converted length of each piece of ribbon (0.7 yards) by the total number of pieces (1010) to find the total yards of ribbon:
0.7 yards x 1010 = 707 yards
Therefore, James bought a total of 707 yards of ribbon.
A house was bought for £100,000
Its value appreciates by 7.5% each year for the Nirst three years. What was its value at the end of the three years?
Answer:
122500
Step-by-step explanation:
The formula
A=p(1+rt)
A ?
P 100000
R 0.075
T 3 years
A=100,000×(1+0.075×3)
A=122500
Final answer:
The value of the house at the end of three years would be approximately £123,696.47.
Explanation:
To find the value of the house at the end of three years, we need to calculate the appreciation for each year and add it to the original value. Since the value of the house appreciates by 7.5% each year, we can calculate the value after three years using the formula:
New Value = (1 + Rate of Appreciation) * Original Value
Let's calculate:
New Value after first year = (1 + 0.075) * £100,000 = £107,500New Value after second year = (1 + 0.075) * £107,500 = £115,062.50New Value after third year = (1 + 0.075) * £115,062.50 = £123,696.47The value of the house at the end of the three years would be approximately £123,696.47.
if a scientist is able to use 4 kilograms of fertilizer for 5 weeks how much fertilizer did they use each week
Answer:
0.8 kilograms of fertilizer
Step-by-step explanation:
Looking at the data given to us in a fraction form, we can imagine:
4 kilograms / 5 weeks
To find out how many kilograms of fertilizer was used each week, we're going to divide that fraction out, so we're going to do 4 divided by 5. Dividing this will give you:
0.8 kilograms
Therefore your answer is that they use .8 kilograms of fertilizer each week.
Answer:
6
Step-by-step explanation:
Two 10 pound forces act on the same object at the same time. Find the
magnitude of their resultant if 135° is between the two forces.
Final Answer:
The magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
Explanation:
To find the magnitude of the resultant force when two forces are acting at an angle to each other, we can use the law of cosines. In this scenario, we have two forces each of 10 pounds acting on an object with an angle of 135° between them. Let's denote the forces as F1 and F2, both of which have magnitudes of 10 pounds. The angle between them is θ = 135°.
The formula for the resultant force R when two forces act at an angle θ is:
[tex]\[ R = \sqrt{F1^2 + F2^2 + 2 \cdot F1 \cdot F2 \cdot \cos(θ)} \][/tex]
In our case:
[tex]\[ F1 = F2 = 10 \, \text{pounds} \][/tex]
[tex]\[ θ = 135° \][/tex]
Plugging these values into the formula, we get:
[tex]\[ R = \sqrt{10^2 + 10^2 + 2 \cdot 10 \cdot 10 \cdot \cos(135°)} \][/tex]
[tex]\[ R = \sqrt{100 + 100 + 200 \cdot \cos(135°)} \][/tex]
The cosine of 135° is -√2/2 (since 135° is in the second quadrant where the cosine is negative):
[tex]\[ R = \sqrt{200 - 200 \cdot \frac{-\sqrt{2}}{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100\sqrt{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100 \cdot 1.414} \] (Since √2 is approximately 1.414)[/tex]
[tex]\[ R = \sqrt{200 + 141.4} \][/tex]
[tex]\[ R = \sqrt{341.4} \][/tex]
[tex]\[ R \approx 18.47 \text{ pounds} \][/tex]
Therefore, the magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
which trend is the plot
Answer:
positive trend
Step-by-step explanation:
the points are all positive
Answer: it shows no trend they’re all scattered and there is no straight line
Step-by-step explanation:
The graph shows the function g(x) for a restricted domain.
On a coordinate plane, a function starts at (negative 4, 0) and then curves through the y-axis at (0, 1.5) and then goes through point (4, 2).
Which is the function g(x) for a restricted domain?
g(x) = Negative RootIndex 3 StartRoot x minus 4 EndRoot; x greater-than-or-equal-to –4
g(x) = Negative RootIndex 3 StartRoot x 4 EndRoot + 4; x greater-than-or-equal-to 0
g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4
g(x) = Negative RootIndex 3 StartRoot x EndRoot minus 4; x greater-than-or-equal-to 0
Answer:
Option 3
g(x) = Negative RootIndex 3 StartRoot x + 4 EndRoot; x greater-than-or-equal-to –4
Step-by-step explanation:
Since the graph starts at x = -4 and towards the right, domain is x 》-4
g(x) = -(x + 4)^⅓
Because,
0 = -(-4 + 4)^⅓
0 = 0
The function g(x) for the restricted domain is g(x) = -∛(x-4); x ≥ -4.
Explanation:The function g(x) for the restricted domain can be determined by analyzing the given information. The function starts at (-4, 0) and curves through the y-axis at (0, 1.5) before passing through point (4, 2). Based on this, the correct function is g(x) = -∛(x-4); x ≥ -4.
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If Casey places $890 in a savings account,
how much interest will he earn in 12 years at a
5% simple interest rate?
Answer:
$534
Step-by-step explanation:
Simple Interest formula: I = Prt
I = $890 * (0.05)* 12
I = $534
Answer:
Step-by-step explanation:
534
The paper cup is 9 cm tall and the circular opening has a radius of 2.5 cm.
What is the minimum amount of paper needed to make the paper cup to the nearest whole cm² assuming no overlap in the paper?
Final answer:
The minimum amount of paper needed to make the paper cup to the nearest whole cm² is approximately 283 cm².
Explanation:
To find the minimum amount of paper needed to make the paper cup, we need to calculate the surface area of the cup. The formula for the surface area of a cylinder is:
A = 2πrh + π[tex]r^2[/tex]
Given that the height (h) of the cup is 9 cm and the radius (r) of the circular opening is 2.5 cm, we can plug in the values to calculate the surface area:
A = 2 × 3.14159 × 2.5 × 9 + 3.14159 × [tex]2.5^2[/tex]
Simplifying the equation, we get:
A ≈ 282.74 [tex]cm^2[/tex]
Rounding to the nearest whole , the minimum amount of paper needed is approximately 283 [tex]cm^2.[/tex]
What is the length of side XY as shown on the coordinate plane?
O units
1 units
3 units
4 units
after a long and intense thinking of 2 seconds it's 4 units
whats is 224 + 253 add and ill mark you brainleist for the fast quick right answer
Answer:
I dont like math no fair
Answer:
477 :)
Step-by-step explanation:
For math definetly reccommened photo math it is a app that only works on apple but will be the greatest help and always has right answer cause it is high quality app but if you have a apple product then it will be free
look at the graph and tell me why it is proportional or nonproportional and why?
IF YOU ANSWER I WILL MARK U BRANLYEST
Answer:
I think it is not proportional because the line is supposed to go thro the middle of each dot, and some of the dots don't have a line thro the middle only on the side or not even on the dot.
Hope this helps!
Step-by-step explanation:
please mark me brainliest...
PLEASE HELP ME 30POINTS +BRAINLY
1) If a die is rolled once, determine the probability of rolling a 4: Rolling a 4 is an event with 1 favorable outcome (a roll of 4) and the total number of possible outcomes is 6 (a roll of 1, 2, 3, 4, 5, or 6). Thus, the probability of rolling a 4 is [tex]\frac{1}{6}[/tex].
If a die is rolled once, determine the probability of rolling at least a 4: Rolling at least 4 is an event with 3 favorable outcomes (a roll of 4, 5, or 6) and the total number of possible outcomes is again 6. Thus, the probability of rolling at least a 4 is [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex].
Here are two more examples:If a coin is flipped twice, determine the probability that it will land heads both times:
Favorable outcomes: 1 -- HH
Possible outcomes: 4 -- HH, HT, TH, TT
Thus, the probability that the coin will land heads both times is [tex]\frac{1}{4}[/tex].
If Dan grabs one sock from a drawer containing 3 white socks, 4 blue socks, and 5 yellow socks, what is the probability that he will grab a white sock?
Favorable outcomes: 3 (3 white socks)
Possible outcomes: 12 (3 white socks + 4 blue socks + 5 yellow socks)
Thus, the probability that Dan will grab a white sock is [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex].
Evaluate ab + 5c - d. If a =3, b=2, c=7, and d=4Immersive Reader
(1 Point)
Answer:
46
Step-by-step explanation:
a:3, b:2 , c: 7 and d:4
ab + 5c - d
(3*5) + 5(7) - 4
(15 + 35) -4
50- 4 :46
Answer:
37.
Step-by-step explanation:
ab + 5c - d
= 3*2 + 5*7 - 4
= 6 + 35 - 4
= 37.
Can someone please help me with 10,11,and 12 I WILL MARK BRAINLIEST!!!
Answer:
10 is acute
11 is a right
12 obtuse
Step-by-step explanation:
X^2-x-20 how do I write that in factored form
Answer:
(x+4)(x-5)
Step-by-step explanation:
You need to find two numbers that multiply to be -20 but add up to be -1.
Answer:
( x - 5 ) ( x + 4 )
Step-by-step explanation:
When solving quadratic equations it's important to remember that they have 2 solution. We need to work out the factors, sum and the products to successfully factorise the quadratic and solve it. So,
x² - x - 20 = 0
Sum = -1
Product = -20
So we need two numbers that sum to -1 and multiply together to make -20
Factors = -5 and 4
x² - 5x + 4x - 20
Factor x² - 5x and 4x -20 separately
x² - 5x = x ( x - 5 )
4x - 20 = 4 ( x - 5 ) So
x ( x - 5 ) + 4 ( x - 5 )
We can see a common factor of ( x - 5 ) and the other bracket would be ( x + 4)
( x - 5 ) ( x + 4 )
find the 11th term for : 64, -32, 16, -8
A . -.625
B. 0.625
C. .03125
D. -.03125
Answer:
0.0625 is what i got
Step-by-step explanation:
64, -32, 16, --8, 4, -2, 1, -.5, .25, -.125, 0.0625
Which is the simplified form of the expression?
Please help!
Answer:
A
Step-by-step explanation:
A number cube has faces numbered 1 through 6, and a coin has two sides, "heads" and "tails". The
number cube will be rolled once, and the coin will be flipped once. Find the probability that the
number cube shows a 6 or the coin shows "heads." (Express your answers as fractions in lowest
terms.)
Answer:
The required probability is [tex]\dfrac{1}{12}[/tex].
Step-by-step explanation:
Let A be the event of rolling the number cube.
Let B be the event of tossing the coin.
Total number of possibilities of rolling the number cube and tossing the coin are 12 here.
[tex]\{(1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)\}[/tex]
where H means Head on toss of coin and T means Tails on toss of coin.
Formula for probability of an event E is:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, we have to find the probability of event 'E' i.e. getting a 6 on number cube and heads on coin.
Number of favorable cases are 1 and total cases are 12.
[tex]\Rightarrow P(E) = \dfrac{1}{12}[/tex]
On a coordinate plane, a parabola opens up with solid circles along the parabola at (negative 6, 5), (negative 5, 0), (negative 4, negative 3), (negative 3, negative 4), (negative 2, negative 3), (negative 1, 0), (0, 5).
What is the vertex of the parabola in the graph?
(
,
)
Answer:
the answer is (-3,-4)
Step-by-step explanation: -3, -4
The vertex of the parabola is (-3, -4)
what is parabola?A parabola is defined as a set of points in a plane which are equidistant from a straight line or directrix and focus.
Given:
The solid circles along the parabola are:
(-6, 5), (-5, 0), (-4, -3), (-3, -4), (-2, -3), (-1, 0), (0, 5).
As, the minimum point of y occurs at (-3, -4).
So, the x-intercept of the parabola is
x=-5 or x=-1
x+5=0 or x+1=0
(x+5)(x+1)=0
x² + 6x+ 5 =0
Now, vertex of equation at axis of symmetry x= -b/2a
x= -6/2 = -3
and, f(-3)= -3 * (-3) + 6(-3) + 5
f(-3)= -4
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find, to the nearest inch, the volume of a circular cone with a radius of 12 inches and a slant height of 20 inches. include step by step process. HELP PLEASE ASAP
We have been given that a cone has a radius of 12 inches and slant height of 20 inches. We are asked to find the volume of the cone.
We will use volume of cone formula to solve our given problem.
[tex]V=\frac{1}{3}\pi r^2\sqrt{l^2-r^2}[/tex], where
V = Volume of cone,
r = Radius,
l = Slant height.
Upon substituting our given values in volume formula, we will get:
[tex]V=\frac{1}{3}\pi\cdot 12^2\cdot \sqrt{20^2-12^2}[/tex]
[tex]V=\frac{1}{3}\pi\cdot 144\cdot \sqrt{400-144}[/tex]
[tex]V=48\pi\cdot\sqrt{256}[/tex]
[tex]V=48\pi\cdot16[/tex]
[tex]V=2412.743157[/tex]
[tex]V\approx 2412.74[/tex]
Therefore, the volume of the cone is approximately 2412.74 cubic inches.
I need help with everything.
Step-by-step explanation:
5. 102 = 6( 1 + 4p)
102 = 6 + 24p
102 - 6 = 24p
96 = 24p
96/ 24 = p
4 = p
2x3 to the second power plus 5 to the second power
Answer: 43
Multiply
3×3=9
New Problem: (2)(9)+5²
Multiply
2×9=18
New Problem: 18+5²
Multiply
5×5=25
New Problem: 18+25
Add
18+25=43
Answer:
it would be 43 :)
Step-by-step explanation:
first you have to do 3 squared which is 9 then you multiply it by 2. Then square 5 which is 25 and add 25 +18+ 43
James spends 45 minutes taking caring of Mr Silva's dog .Then,he spends 25 minutes folding laundry. Next ,he spends 20 minutes cleaning his room.How long does it take James to do all of his chares?
Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below.
A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Shaded plants (inches). There are 0 dots above 1.5, 4 above 2, 3 above 2.5, 2 above 3, 0 above 3.5 and 4, and 1 above 4.5.
A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Full Sun plants (inches). There are 0 dots above 1.5, 1 above 2, 0 above 2.5, 2 above 3, 0 above 3.5, 4 above 4, and 3 above 4.5.
Which best explains the variability of the sets?
The shaded plants set has greater variability because more data is clustered around the median.
The sets are equally variable because the ranges of the data sets are equal.
The full sun plants set has greater variability because the IQR for full sun plants is greater.
Question;
1) The shaded plants set has greater variability because more data is clustered around the median.
2) The sets are equally variable because the ranges of the data sets are equal.
3) The full sun plants set has greater variability because the IQR for full sun plants is greater.
Answer:
The correct option is;
3) The full sun plants set has greater variability because the IQR for full sun plants is greater
Step-by-step explanation:
To answer the question, we present the dot plot as follows;
Heights of Shaded plants (inches)
0 4 3 2 0 0 1
0 1.5 2 2.5 3 3.5 4 4.5
We calculate the five numbers as follows;
Max = 4.5
Min = 2
1st quartile = (10+1)/4 th term = 2
2nd quartile (Median) = (10+1)/2 th term = 2.5
3rd quartile = 3×(10+1)/4 th term = 3
Interquatile range (IQR) = Q₃ - Q₁ = 3 - 2 = 1
Where:
Q₁ = 1st quartile
Q₃ = 3rd quartile
Heights of Full Sun plants
0 1 0 2 0 4 3
1.5 2 2.5 3 3.5 4 4.5
We calculate the five numbers as follows;
Max = 4.5
Min = 2
1st quartile = (10+1)/4 th term = 3
2nd quartile (Median) = (10+1)/2 th term = 4
3rd quartile = 3×(10+1)/4 th term = 4.5
Interquatile range (IQR) = Q₃ - Q₁ = 4.5 - 3 = 1.5
The interquartile range, IQR, is a measure of variability
Therefore, the full sun plants set has greater variability because the IQR for full sun plants is greater.
In a game, four cards are labeled N, S, E, and W. Two tiles are numbered 1 and 2. Two discs are red and blue. A player randomly selects one card, one tile, and one disc.
Find the probability the player selects a card with S or E, a tile with 2, and a red disc.
Answer:
The probability is 1/8.Step-by-step explanation:
Two find the final probability asked, first we need to find each probability.
Probability of a card with S or E.This probability is defined by the sum of the probability of getting a card with S, and a probability of getting a card with E. Remeber, when the probability involves "or", that means sum.
[tex]P_{S \ or \ E} =\frac{1+1}{4}=\frac{2}{4} =\frac{1}{2}[/tex]
Probability of a tile with 2.There are two tiles only, and one of them is numbered 2. So, its probability is
[tex]P_{2}=\frac{1}{2}[/tex]
Probability of a red disc.There are two discs only. So, the probability of getting a red disc is
[tex]P_{red}=\frac{1}{2}[/tex]
Now, the combined probabilty of all these events can be found by multiplying, because we want to now the chances of getting all these results which are independent.
[tex]P_{total}=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} =\frac{1}{8}[/tex]
Therefore, the probability is 1/8.
Finding Surface Area
Find the total surface area of the prism. Round to the nearest tenth.
Answer:
672 squared in.
Step-by-step explanation:
first, we're going to find the height of the prism (it's not provided to us)
im using the Pythagorean Therm .
height: 8 in.
(i got lazy)
44 cm
Find the surface area of the triangular prism. The base of the
prism is an isosceles triangle.
25 cm
24 cm
14 cm
can you help me?
Answer:
Step-by-step explanation:
120 and 56
Explain why a polar curve is not always bounded
Answer:
vvvvvvvvvv
Step-by-step explanation:
there are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. a polar curve is required to have an unbounded function (right side of r = f(θ)) to be an unbounded polar.
Answer:
There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(θ)) to be an unbounded polar.
be safe and have a day
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Tickets numbered 1 to 20 are placed in a hat. Two tickets are drawn out at random, without
replacement. Find the probability that:
a: the first number drawn is even and the second number is odd
b: both of the numbers are prime.
-please help include explanation too, it would be really helpful if u can!-
Answer: 5/19
Step-by-step explanation:
There is a total of 20 tickets numbered from 1 to 20.
10 of the tickets has even number and 10 of the tickets have odd numbers.
probability of drawing a ticket that has even number =10/20 which is equal to 1/2
there are total 19 tickets and 10 odd tickets are available.
Probability of drawing a ticket that has odd number =1019
probability =1/2∗10/19=5/19
Answer:
a. 5/19, b. 14/95
Step-by-step explanation:
a. since the first number drawn has 10/20 chance of being even and it's not put back (you assume that you pull an even #), so the second number pulled has a 10/19 chance of being odd.
10/20*10/19 = 5/19
b. 2, 3, 5, 7, 11, 13, 17, 19 are the prime numbers, so 8/20 for the first pull and then 7/19 for the second pull
8/20*7/19 = 14/95