The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46
How to calculate compound interest and simple interest?Principal, p = $2,000Interest rate, r = 4% = 0.04Time, t = 6 yearsNumber of periods, n = 365 daysCompound interest:
A = P(1 + r/n)^nt
= 2,000(1 + 0.04/365)^(365×6)
= 2,000.00(1 + 0.000109589041095)^(2190)
= 2000(1.0.000109589041095)^2190
= 2000 (0.00010958904109589)
= $2,542.46 to the nearest cent
Simple interest:
S.I = principal × rate × time
= 2,000 × 0.04 × 6
= $480
Total = Principal + simple interest
= $2,000 + $480
= $2,480
To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest
= Compound interest - Simple interest
= $2,542.46 - $2,480
= $62.46
In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.
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Use what you know about domain to select all of the following functions that could be the one graphed.
Using transformations, the functions that could represent the one graphed are given as follows:
y = sqrt(x) - 3.y = sqrt(x) - 1.What is a transformation?A transformation is when a function undergoes a change in it's definition. Depending on the type of the transformation, the function can keep the same orientation, same side lengths, and so on.
In the context of this problem, the function kept the same orientation, it just changed it's position, hence the type of transformation that the function underwent was a translation.
The possible translations are given as follows:
Translation down, changing the range.Translation up, changing the range.Translation left, changing the domain.Translation right, changing the domain.The domain of the graphed function is given by:
x ≥ 0.
Which is the same domain as the parent square root function, given as follows:
y = sqrt(x).
From the graph, the function was translated down a units, changing it's range, hence the function has the following format:
y = sqrt(x) - a.
Hence the first two options can be correct, either with a = 1 or with a = 3. The last two options change the range but not the domain, hence they are incorrect.
What is the missing information?The image at the end of the answer gives the complete problem.
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A rectangle garden is 9ft longer than wide. It’s area is 580ft2. What are it’d dimensions?
The dimensions of the rectangular garden are 20 feet and 29 feet respectively.
How to determine the dimensions of the rectangleIt is vital to note that the formula for the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of a rectanglew is the measure of the width of a rectangleFrom the information given, we have that;
Area = 580ft²
Length = 9 + width
L = 9 + w
Substitute the values into the formula, we have;
580 = (9 +w)(w)
expand the bracket
580 = 9w + w²
Make into quadratic equation
w² + 9w - 580 = 0
Factorize the equation
w² + 29w - 20w - 580 = 0
Factor the common terms
w( w + 29) - 20(w + 29) = 0
Then,
w + 29 = 0
w = -29
and w - 20 = 20 feet
We have the expression of length as l = 9 + w
Length, l = 9 + 20
Length, l = 29 feet
Thus, the values are 20 feet and 29 feet
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write an equation to describe the relationship between w and z w: | 18 | 45 | 81z: | 2 | 5 | 9
Notice that the values for w are multiples of 9, and their respective factor is expressed on the values of z. Therefore, the equation to describe the relationship between w and z is w=9z
The coordinates of point A are (-2,5). The coordinates of point B are (3,5). Which expression represents the distance, in units, between A and B?
The distance expression of the number of units between points A and B is √[(-2 - 3)^2 + (5 - 5)^2]
How to determine the expression of the distance between A and B?From the question, we have the following parameters:
The coordinates of point A are (-2,5). The coordinates of point B are (3,5).This means that
A = (-2, 5)
B = (3, 5)
The distance between the points is calculated as
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Where
A = (x1, y1) = (-2, 5)
B = (x2, y2) = (3, 5)
Substitute the known values in the above equation
So, we have
Distance = √[(-2 - 3)^2 + (5 - 5)^2]
The question does not imply that the we simplify the above expression
So, we leave the expression unsimplified
Hence, the expression of the distance between A and B is √[(-2 - 3)^2 + (5 - 5)^2]
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Mr smith wants to put fence around his yard the dimensions of the yard are 61ft by 39ft the fencing is sold in whole meters how much fencing should he buy
The most appropriate choice for perimeter of rectangle will be given by-
Mr Smith must buy 61 m of fencing.
What is perimeter of rectangle?
It is equal to the total distance of the boundary of the rectangle.
If length of rectangle is l m and breadth of rectangle is b m, perimeter of rectangle is 2 x (l + b) [tex]m^2[/tex]
Here,
Length of yard = 61 ft
Breadth of yard = 39 ft
Perimeter of yard = 2 x (61 + 39)
= 2 x 100
= 200 ft
1 ft = 0.305 m
200 ft = 0.305 x 200 m
= 61 m
Mr Smith must buy 61 m of fencing.
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11. The perimeter of rectangle DOGS is 408 cm. The ratio of the length to width is 5:7. What is thewidth of the rectangle?
The width of the rectangle DOGS is 119cm
To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.
This means that if 12 of 12 parts add to the perimeter (408cm):
[tex]\frac{5}{12}+\frac{7}{12}=\frac{12}{12}[/tex]12/12 represents the perimeter 408cm.
The, we can divide the perimeter by 12 and get:
[tex]\frac{408}{12}=34[/tex]Since the width is 7/12 of the perimeter:
[tex]34\cdot7=238[/tex]But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:
[tex]\frac{238}{2}=119[/tex]And we get the final answer of 119cm
Simplify (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² - 5x + 3y).
The simplified form for (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y) is (5x² + 0y² - 10x + 4y - 2xy).
At least one squared term must be present because a quadratic is a second-degree polynomial equation. It is also known as quadratic equations. The answers to the issue are the values of the x that satisfy the quadratic equation. These solutions are called the roots or zeros of the quadratic equations. The solutions to the given equation are any polynomial's roots. A polynomial equation with a maximum degree of two is known as a quadratic equation, or simply quadratics.
How is an equation made simpler?The equation can be made simpler by adding up all of the coefficients for the specified correspondent term through constructive addition or subtraction of terms, as suggested in the question.
Given, the equation is (3x² + 2y² - 5x + y) + (2x² - 2xy - 2y² -5x + 3y)
Removing brackets and the adding we get,
3x² + 2x² + 2y² - 2y² + (- 5x) + (- 5x) + y + 3y + (- 2xy) = (5x² + 0y² - 10x + 4y - 2xy)
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John pizza sells one 18-inch or two 12 inch pizza for $10.99. Determine which size gives more pizza
Using the formula for the area of a circle calculate the area for both deals.
for the 18-inch pizza
[tex]\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot18in^2 \\ A=324\pi\approx1017.88in^2 \end{gathered}[/tex]for the two 12-inch pizza
[tex]\begin{gathered} A=2\cdot\pi\cdot r^2 \\ A=2\cdot\pi\cdot12^2 \\ A=288\pi\approx904.78in^2 \end{gathered}[/tex]Nolan is dividing 2 by 11. If he continues the process, what will keep repeating in the quotient?\
If Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...
Here Nolan is dividing 2 by 11.
Division is one of the basic arithmetic operation. Division is operation of splitting a specific number into equal parts
The quotient is the result from dividing a number from another number.
Divide the given terms and the result will be
2/11 = 0.1818...
The result will be a repeating quotient . Here the pattern is repeating endlessly
Hence, if Nolan is dividing 2 by 11 and he continues the process, the the result will be repeating quotient 0.181818...
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Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is V = 3/4pi r^3 and its surface
area is 4pi r². Determine the rate at which the surface area is changing with respect to time when r = 40 cm.
(Use symbolic notation and fractions where needed.)
Answer:
The rate at which the surface area is changing with respect to time when r = 40 cm is 22400π cm²/min
Not sure if you want it in absolute values since the question says use symbolic notation but if so, multiplying by π gives 70371.675 cm²/min
Step-by-step explanation:
[tex]\text {Volume of a sphere of radius r is given by }\\\\ \text {$V = \dfrac{3}{4}\pi r^3$}[/tex]
The surface area of a sphere of radius r is given by:
[tex]\\S = 4\pi r^2\\[/tex]
The rate of change of surface area is given by
[tex]\dfrac{dS}{dt} = \dfrac{d}{dt}\left(4\pi r^2\right)}\\\\\dfrac{dS}{dt} = 4 \pi \dfrac{d}{dt}\left( r^2\right)}\\\\\\\dfrac{d}{dt}(r^2) = 2r\dfrac{dr}{dt}\\\\\\[/tex]
[tex]\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}[/tex]
We are given that [tex]\text{$\dfrac{dr}{dt}$}[/tex] = 70 cm/min and asked to find rate of change of S when r = 40 cm
Substituting these values into the equation for [tex]\dfrac{dS}{dt}[/tex]
[tex]\dfrac{dS}{dt} = 8 \pi \cdot 40 \cdot 70\\\\\\\\\dfrac{dS}{dt} = 22400 \pi \;cm^2/min[/tex]
In absolute values
To rent a car for a trip, 4 friends are combining their money. The
table shows the amount of money that each puts in. One expression for their
total amount of money is 137+b+212 +c. Use a Commutative Property to
find equivalent expressions.
Use pencil and paper. If they need $700 to rent a car, find at least two
different pairs of numbers that friends B and D must put in.
Friend
A
B
C
D
Travel Fund
Amount (dollars
137
212
с
Which expressions below are equivalent to 137 +b +212 + c by a Commutative Property? Select all that apply.
Answer: 1049
Step-by-step explanation:
please please help me out
.
[tex]Pr(x)=\sum_{x\mathop{=}0}^nnC_x\times p^x\times q^{n-x}[/tex][tex]x=0,\text{ n=43, p=}\frac{1}{124},\text{ q=1-}\frac{1}{124}=\frac{123}{124}[/tex][tex]Pr(x=0)=43C_0\frac{}{}\times(\frac{1}{124})^0\times(\frac{123}{124})^{43}=0.71[/tex]Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of
(fx)=1 / 1/2
and the x axis between x=2 and x=5.
Volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.
As given,
Volume of solid of revolution formed by rotating about the x-axis region between the graph of f(x)= x /2:
Volume = π∫[f(x)]²dx
⇒Volume =π∫(x/2)²dx
⇒Volume =(π/4)∫x²dx
⇒Volume =(π/4) (x³/3)
=(π/12)(x³)
x axis between x=2 and x=5
Volume =(π/12)(125-8)
=117π/12 unit³
Therefore, volume of solid of revolution formed by rotating about the x axis the region between the graph of f(x)= x /2 and the x axis between x=2 and x=5 is 117π /12unit³.
The complete question is:
Find the volume of the solid of revolution formed by rotating about the x axis the region between the graph of
f(x)= x /2
and the x axis between x=2 and x=5.
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Factor 16cd − 56c2d.
--------------------------------
Show your work.
The factorised form of the algebraic expression 16cd − 56c²d as given in the task content is; 8cd (2 - 7c).
What is the factorised form of the expression 16cd − 56c²d?It follows from the task content that the factorised form of the expression; 16cd − 56c²d as given is to be determined.
Since the given expression is;
16cd − 56c²d
First, each of the terms can be factored as follows;
16cd = 2 × 2 × 2 × 2 × c × d
56c²d = 2 × 2 × 2 × 2 × 7 × c × c × d
Therefore, since the factors which are common to both terms as follows; 2 × 2 × 2 × c × d = 8cd.
Therefore the factorised form of the expression is;
8cd (2 - 7c).
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Please help me with this question thank you
As given by the question
There are given that the expression
[tex]22=\frac{a}{5}[/tex]Now,
Multiply by 5 on both side of the equation
So,
[tex]\begin{gathered} 22=\frac{a}{5} \\ 22\times5=\frac{a}{5}\times5 \\ 22\times5=a \\ 110=a \end{gathered}[/tex]Hence, the value of a is 110.
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%.
What is a possible reading on the scale if you put 500 kilograms of iron ore on it?
(Would enjoy an explanation!)
If An industrial scale is guaranteed by the manufacturer to have a percent error of no more than 1%. Its possible reading on the scale if you put 500 kilograms of iron ore on it is :495, 505.
Percent errorPercent error = 1%
Kilogram of iron ore = 500 kilograms
First step is to find the 1% of 500 kilograms
= .01 × 500 kilograms
= 5
Second step is to find the possible reading
Possible reading :
500 - 5
=495
500 + 5
= 505
Therefore we can conclude that based on the above analysis the possible reading can be between 495 and 505.
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In your book copy and complete the image below work out the what number replaces then ? to simpfly the ratio 8:12
Answer:
2:3
Step-by-step explanation:
solve thw variable 6/18=×/36
6/18=×/36
solve for x
x=(6/18)36
x=6(36/18)
x=6(2)
x=12
Calculate the pay for the following day of a weekly time card given a wage of $14.50/hr. Name Week of: SI Morning lo Out Monday | 08:15 12:15 Afternoon In Out 13:00 17:30 pay = $[?] Round your answer to the nearest hundredth. Can you please just give me the direct answer for the pay cause I don't have mutch time to answer this problem.
As we can see in the card, on Monday the worker clocked in at 08:15 and clocked out at 12:15. This means they worked 4 hours.
They then clocked in at 13:00 and clocked out at 17:30. This means they worked for 4 and a half hours.
Since they earn a wage of $14.50/h, they earned:
[tex](4+4.5)\cdot14.50=8.5\cdot14.50=123.25.[/tex]So that day they earned $123.25
Who knows answer to this?
Complete the table and find the value of each vehicle at the end of the indicated year.Car ACar BCar Value at the Endof the Indicated Year1st2nd3rd4th 5th
Let's look at car A first.
As already solved, just after it is purchased its value decreases 20%.
Purchased at $30000, its value inmediatly decreases to $24000 ($30000 -
0.2*$30000 = $24000).
We know the yearly depreciation for car A os $2000.
Then, at the end of the first year, its value will decrease from $24000 to $24000 - $2000 = $22000.
Every year its value decreases $2000. Followint the same logic, at the end of the second year its value will decrease from $22000 to $22000 - $2000 = $20000 and so on. Now, we can build the table:
End of first year: $24000 - $2000 = $22000
End of second year: $22000 - $2000 = $20000
End of third year: $20000 - $2000 = $18000
End of fourth year: $18000 - $2000 = $16000
End of fifth year: $16000 - $2000 = $14000
an airplane covers 1259km in an hour find the distance it will cover 23/6 hours
Answer:
4826.166666km
Step-by-step explanation:
d=distance
[tex]\frac{1259km}{1h} =\frac{d}{23/6h}[/tex]
= [tex]\frac{1259km}{1h}= \frac{6d}{23}[/tex]
= [tex]1259=\frac{6d}{23}[/tex]
= [tex]1259*23=6d[/tex]
= [tex]28,957=6d[/tex]
= [tex]\frac{28,957}{6}=d[/tex] ≈4826.166666
Please see no 17 attached.
To convert the number given in base 7 to a bse 10 number we follow the procedure shown, that is, we need to multiply each number by the appropiate power of seven (given by their position) and then add them, then we have that:
[tex]\begin{gathered} 21603_{\text{seven}}=(2\times7^4)+(1\times7^3)+(6\times7^2)+(0\times7^1)+(3\times7^0) \\ 21603_{\text{seven}}=5442_{\text{ ten}} \end{gathered}[/tex]Therefore:
[tex]21603_{\text{seven}}=5442_{\text{ ten}}[/tex]2 5/8 divided by 2 1/4
Answer:
Step-by-step explanation:
[tex]2\frac{5}{8} =\frac{2 \times 8+5}{8} =\frac{21}{8} \\2\frac{1}{4} =\frac{2 \times 4+1}{4} =\frac{9}{4} \\2\frac{5}{8} / 2\frac{1}{4} \\=\frac{21}{8} /\frac{9}{4} \\=\frac{21}{8} \times \frac{4}{9} \\=\frac{7}{6} \\=1\frac{1}{6}[/tex]
Part 1Simplifyeach fraction. Some fractions can be simplified more than once A 110/390
Given the fraction below
[tex]\frac{110}{390}[/tex]To simplify the above fraction, we will divide both the numerato
Calculate the expected value of the scenario.
Expected value:
[tex]E(x)=\Sigma(x_i*p(x_i))[/tex]For the given scenario:
[tex]E(x)=(1*0.25)+(2*0.38)+(3*0.03)+(4*0.16)+(5*0.18)[/tex][tex]E(x)=0.25+0.76+0.09+0.64+0.9[/tex][tex]E(x)=2.64[/tex]Then, the expected value is 2.64MODELING REAL LIFE A football player punts a football from a height of 2 feet. The ball reaches a maximum height of
50 feet after traveling 56 feet horizontally, and is caught 111 feet from where the ball was kicked. The path of the ball can
be modeled by a parabola, where y is the height (in feet) and x is the horizontal distance traveled (in feet). At what height
is the ball caught? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
Shape A and B are mathematically similar.
The area of shape A is 210 cm².
A
21 cm
B
Area =
42 cm
Work out the area of shape B.
Answer:
6 is the awnswer
Step-by-step explanation:
The undergraduate library at State U tends to have 33.4 students enter every hour during normal operation. Over the next two hours, what is the probability at least 75 students arrive at the library?
The probability that at least 75 students arrive at the library is 0.1440.
How to calculate the probability?From the information, the undergraduate library at State U tends to have 33.4 students enter every hour during normal operation.
The expected number of students for the two hours will be:
= 2 × 33.4
= 66.8
The probability that at least 75 students arrive at the library will be:
P(x >= 75) = 1 - P(x <= 74)
This will be looked at in the distribution table
= 1 - 0.8560
= 1.440
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