Answer: (a) 3270 (b) 6270
Step-by-step explanation:
Formula for compound interest: P (1 + r/100 ) ^n,
where P = principal, r = interest rate, n = number of years
------------------------------------------------------------------------------------------------------------
In question (a),
P = $3000
r = 9%
n = 1
3000 ( 1 + 9/100) ^1 = $3270
------------------------------------------------------------------------------------------------------------
In question (b),
P = $3000
r = 9%
n = 2
3000 ( 1 + 9/100) ^2 = $6270
Mike took a loan of $20,000 from a bank on 4 February 2009 at the rate of 8% p.a and paid back the same on 6th July 2009. Find the total amount paid by Mike
A. N20,666.30
B. N21,777.40
C. N22,888.50
D. N24,999.60
For positive integer n, defined
[tex] \rm f(n) = n + \frac{16 + 5n - 3 {n}^{2} }{4n + 3 {n}^{2} } + \frac{32 + n - 3 {n}^{2} }{8n + {3n}^{2} } + \frac{48 - 3n - 3 {n}^{2} }{1 2n+3 {n}^{2} } + \cdots + \frac{25 {n} - 7n^{2} }{7 {n}^{2} } [/tex]
Then, the value of [tex] \displaystyle\rm\lim_{n \to \infty } [/tex] is equal to
Following the first term [tex]n[/tex], the [tex]k[/tex]-th term [tex]\left(k\in\{1,2,3,\ldots,n\}\right)[/tex] in [tex]f(n)[/tex] is given by
[tex]\dfrac{16k + (9-4k)n - 3n^2}{4kn + 3n^2}[/tex]
That is,
[tex]k=1 \implies \dfrac{16 + (9-4)n - 3n^2}{4n + 3n^2} = \dfrac{16 + 5n - 3n^2}{4n + 3n^2}[/tex]
[tex]k=2 \implies \dfrac{16\cdot2 + (9-8)n - 3n^2}{4\cdot2n + 3n^2} = \dfrac{32 + n - 3n^2}{8n + 3n^2}[/tex]
and so on, up to
[tex]k=n \implies \dfrac{16n + (9-4n)n - 3n^2}{4n^2 + 3n^2} = \dfrac{25n - 7n^2}{7n^2}[/tex]
We then have
[tex]\displaystyle f(n) = n + \sum_{k=1}^n \frac{16k + (9-4k)n - 3n^2}{4kn + 3n^2} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} - \frac1n \sum_{k=1}^n \frac{4kn + 3n^2}{4k + 3n} \\\\ ~~~~~~~ = n + \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}- \frac1n \sum_{k=1}^n n \\\\ ~~~~~~~ = \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3}[/tex]
Now as [tex]n\to\infty[/tex], the right side converges to a definite integral.
[tex]\displaystyle \lim_{n\to\infty} f(n) = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \frac{16\frac kn + 9}{4\frac kn + 3} \\\\ ~~~~~~~~~~~~~ \,= \int_0^1 \frac{16x + 9}{4x + 3} \, dx[/tex]
Wrap up by substituting [tex]x\mapsto\frac{x-3}4[/tex].
[tex]\displaystyle \lim_{n\to\infty} f(n) = \frac14 \int_0^1 \frac{16x + 9}{4x + 3} \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \frac{4x - 3}x \, dx \\\\ ~~~~~~~~~~~~~\, = \frac14 \int_3^7 \left(4 - \frac3x\right) \, dx \\\\ ~~~~~~~~~~~~~\, = \left. \frac14 (4x - 3\ln|x|) \right\vert_3^7\\\\ ~~~~~~~~~~~~~\, = \boxed{4 + \frac34 \ln\left(\frac37\right)}[/tex]
A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 16t² + 128t
For what time period is the projectile at least 192 feet above the ground?
Select the correct choice below and fill in the answer boxes to complete your choice.
OA. For the time period between (and inclusive of)
(Simplify your answers.)
OB. For the time period between (and not inclusive of)
(Simplify your answers.)
seconds and
seconds and
seconds the projectile will be at least 192 ft above the ground.
seconds the projectile will be at least 192 ft above the ground.
For the time period of the projectile at least 192 feet above the ground is between 2 second and 6 second
Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:
16t2-128t+192=0 or, simplified, 8t2-64t+96=0
or t2-8t+12=0
since it is now in quadratic form, we can solve using the quadratic formula:
t = 2 and 6
So the time period from approximately 2 second and 6 second has the projectile above 192 feet.
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Can someone PLEASEE help me
how many zeros will be in the product of 5 x 105 the 105 is the 10 of the power of 5
Answer: this equation has 5 zeroes.
Step-by-step explanation:
The number of zeroes in any number can be found by,
we have expression as
[tex]5*10^{5}[/tex]
now ;
10*10 has 2 zeroes;
10*10*10 has 3 zeroes;
similarly ;
this equation has 5 zeroes.
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Answer:
none
Step-by-step explanation: 105×5=525
What's the current temperature? 5 + (-12) = ?
Answer:
-7
Step-by-step explanation:
To add a positive number, 5, and a negative number, -12, take the absolute value of both numbers.
You get 5 and 12.
Subtract the smaller absolute value from the larger absolute value.
12 - 5 = 7
The sign of the answer is the same sign as the number that has the larger absolute value. The absolute of 5 is 5. The absolute value of -12 is 12. -12 has the larger absolute value, and -12 is negative, so the answer is negative.
5 + (-12) = -7
A toy ball in the shape of a sphere expands and contracts. When it is completely closed, it has a diameter of 20.5 inches. Find the volume of the sphere when it is completely closed. Use 3.14 for π.
The volume of the sphere when it is completely closed is 4508.58 cubic inches
Volume of a sphereThe formula for calculating the volume of a sphere is expressed as:
V = 4/3πr³
where
r is the radius = 20.5/2
radius = 10.25 in
Substitute
V = 4/3 (3.14)*10.25³
V = 4/3(3.14)
V =4508.58 cubic inches
Hence the volume of the sphere when it is completely closed is 4508.58 cubic inches
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6 mm
4 mm
h
12 mm
8.5 mm
A produce store sold 63 apples If the ratio of red apples to green apples sold was 7:2 What is the combinded amount of red and green apples sold?
Answer:
The total amount of apples sold is 63. There were 49 red apples and 14 green apples
Step-by-step explanation:
red: green : total
7 2 7+2
7 2 9
When we use the ratios, the total is 9
We are given the total is 63
63 divided by 9 is 7
We need to multiply each number by 7
red: green : total
7*7 2*7 9*7
49 14 63
The total amount of apples sold is 63. There were 49 red apples and 14 green apples
Answer:
the answer is red apples 49 and green apples 14.
Esteban bought a desk lamp at a sale price of $20.25. The original price of the lamp was $45. What was the discount rate of the desk lamp?
Answer:
55%
Step-by-step explanation:
Ans
65.25 Step-by-step explanation:
There are five questions listed below. Each question includes the quantity 43. Match the 43 in each question on
the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer
options on the right will be used more than once.
What number is 15% of 43?
43% of 300 is what number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
percent
base
amount
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
What number is 15% of 43?
43 here is the base43% of 300 is what number?
Here 43 is the percent12% of what number is 43?
43 is used here as amount43 is what percent of 106?
43 is used here as amountWhat percent of 43 is 6?
43 here is the baseWhat is base?The base as used in the question refers to the main number that is a=to say the number on which other calculation are focused on.
What is percent?Percent is a term used in mathematics to refer to a fraction with a denominator of one hundred. Numbers in percent is accompanied with the percent symbol which is %. Any number having that symbol means that the number is a fraction with a denominator of one hundred.
What is amount?The term amount as used refers to the result gotten when some mathematical operation is being done on the base.
The calculations to the questions asked are below:
What number is 15% of 43?
= 15/100 x 43
= 6.45
43% of 300 is what number?
= 43/100 x 300
= 129
12% of what number is 43?
= 12/100 x 43
= 5.16
43 is what percent of 106
= 43/106 * 100
= 40.56%
What percent of 43 is 6
= 6/43 x 100
= 13.95%
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Any help would be appreciated.
What is that for?
??????????????????????????????????????????????????????????????????????
Help, I don’t know how to solve this
Answer:
a=A/8
Step-by-step explanation:
This MIGHT be the answer, I am 99% sure!
Triangle ABC has coordinates A(0, 6), B(3, 0), and C(4, 3). Triangle ABC is reflected across the x-axis. What are the coordinates of C’?
Answer:
Step-by-step explanation:
create the cartesian system, sign the points, because the new triangle is reflected, so we need to use the straight lines which points on its ends, perpendicular to the x-axis, then we get A(0,-6), B(3,0), C(4,-3)
Select the correct answer.
Will is at a shirt sale where he can buy one and get a second one for 40 percent off. He wants to buy two shirts priced at $29 each. How much
will he pay?
cost after discount = (2x list price) - (list price x discount percentage)
OA
$24.90
The amount he would pay is $46.40.
How much will he pay?
Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.
The amount paid = list price of the first shirt + [list price of the second shirt x ( 1 - percentage discount)]
$29 + [$29 x (1 - 0.4)]
$29 + ($29 x 0.6) = $46.40
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12. Determine if the following equation has one solution, no solution, or infinite
solutions: 3(4x + 6) = 2(6x + 9).
Answer:
Infinite Solutions
Step-by-step explanation:
3(4x + 6) = 2(6x + 9)
Distribute coefficients
12x + 18 = 12x +18
Same equations which means infinite solutions
for each table, find the constant of proportionality. use decimal notation if neccescry
Step-by-step explanation:
the constant k of proportionality is defined by
y = kx
or in our case
b = ka
so, let's see
14 = k×2
k = 14/2 = 7
this also works for the other data pairs :
7×5 = 35
7×9 = 63
7 × 1/3 = 7/3
perfect.
so, the constant of proportionality is 7.
PLEASE SOLVE THIS FOR ME. I ONLY KNOW THAT THE ANSWER WILL HAVE AN X IN IT
Answer: [tex]\boxed{\sqrt{12x-1}}[/tex]
Step-by-step explanation:
[tex]\sqrt{2(6x-3)+5}\\ \\\sqrt{(12x-6)+5} \\\\\boxed{\sqrt{12x-1}} \\\\This\ is\ as\ far\ as\ you\ can\ simplify\ this[/tex]
name a fraction between 6/7 and 1
Answer:7/8, 8/9, 9/10, 10/11, etc.
15% of the students in the 6th grade wear glasses. If 12 students wear glasses, how can you determine the number of students in the 6th grade? Explain your reasoning.
Answer: There are 80 people in the 6th grade
Step-by-step explanation:
What is the answer to -5 - 7.
Answer:
it is negative 12
Step-by-step explanation:
-12
Answer:
-12
Step-by-step explanation:
TOOIS
Question 3
A pipe is leaking at a rate of 8 fluid ounces per minute. How many gallons per hour will leak from the pipe?
0.02 gal/hr
A
B
C
D
3.75 gal/hr
17.07 gal/hr
3,840 gal/hr
If a pipe is leaking at a rate of 8 US fluid ounces per minute, then 3.75 US liquid gallons of the fluid will leak from the pipe in an hour.
As per the question statement, a pipe is leaking at a rate of 8 US fluid ounces per minute and we are required to calculate the amount of leak that will occur at the same rate of leakage, in an hour, in the units of US liquid gallons.
To solve this question, we need to know to know about two basic mathematical conversions, i.e.,
1 US Liquid Ounce = 0.00781 US Liquid Gallons, and
1 hour = 60 minutes.
Therefore, amount of leak that will occur at the rate of 8 US fluid ounces per minute, in an hour = [tex](8 * 60)=480[/tex] US fluid ounces.
And 480 US fluid ounces = [tex](0.00781 * 480)=3.75[/tex] US Liquid Gallons.
Hence, 3.75 US Liquid Gallons of fluid will leak from the pipe in an hour.
Fluid Ounce: It is an unit of volume, used for measuring liquids. "The British Imperial" and the "United States customary" fluid ounce are the only two that are still in use. The US Fluid ounce is an unit of capacity equal to one-sixteenth of a US pint (approximately 0.03 liter), while the British Imperial fluid ounce a unit of capacity equal to one twentieth of a pint (approximately 0.028 liter).Liquid Gallons: In the United States, Liquid Gallon is an unit of liquid capacity equal to four quarts or 231 cubic inches or 3.785 liters, while in the Great Britain, also known as the "Imperial Gallon", it is an unit of liquid and dry capacity equal to four quarts or 277.42 cubic inches or 4.544 liters.To learn more about Fluid Ounces and Liquid gallons, click on the klink below.
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Kiyana's grandmother has a collection of hats for special occasions. Each hat is in a cube-shaped box with edges 1 ft long. She stores the boxes in a rectangular closet with the dimensions shown. Length = 6 ft N Height = 9 ft Width= 5 ft 3 4 5 > 2 of 5 Completed What is the maximum number of boxes that Kiyana's grandmother can fit inside the closet? Choose one option from each drop-down menu to answe the question. Kiyana's grandmother can fit a maximum of [ ] boxes along the length,[. ] boxes along the wide and [ ]boxes along the height of the closet. This means she can fit a maximum of [ ]boxes inside the closet
The maximum number of cubical boxes of side 1 feet that can be placed in a rectangular closet of length 6 feet, height 9 feet and breadth 5 feet is 270 boxes. Maximum number of boxes that can be placed along the length, height and breadth will be 168 boxes, 198 boxes and 150 boxes respectively.
Since the cube shaped boxes of length 1 feet are to be placed in the rectangular closet, the maximum number of boxes that will fit completely would be given as a comparison of volume of rectangular closet being equal to product of number of boxes and volume of 1 cubical box.
Volume of rectangular closet = Number of boxes * Volume of 1 cubical box
6 * 9 * 5 = n * (1*1*1)
Therefore, n = 270 boxes.
To calculate maximum number of boxes that will fit along the length would be calculated as product of length and breadth along 2 faces of closet and length and height along another 2 faces of closet.
Thus, [(9*6) + (9*6) + (6*5) + (6*5)] = 168 boxes along the length.
Similarly, to calculate maximum number of boxes that will fit along the height would be calculated as product of height and breadth along 2 faces of closet and length and height along another 2 faces of closet.
Thus, [(9*6) + (9*6) + (9*5) + (9*5)] = 198 boxes along the height
Similarly, to calculate maximum number of boxes that will fit along the breadth would be calculated as product of height and breadth along 2 faces of closet and length and breadth along another 2 faces of closet.
Thus, [(5*6) + (5*6) + (9*5) + (9*5)] = 150 boxes along the breadth.
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Under her cell phone plan, Morgan pays a flat cost of $54 per month and $5 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $70 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
Answer: She can use 4 gigabyte while remaining in her budget.
Step-by-step explanation:
You would first subtract 54 from 70 which leaves you with 16,
Then you would divide 16 by 4 to find how many gigabytes she could use which gives you 4
So she can use 4 gigabyte while remaining in her budget.
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Answer: Answer is 3
Step-by-step explanation:
let the maximum number of gigabytes of data is x
total budget is $70
then, flat cost is $54 and $5per gigabyte
we get:
54 +5 × x= 70
5x =70 - 54
x = [tex]\frac{16}{5}[/tex] = 3.2 ≈ 3
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reflection across y = -1
Please I need help ASP I will mark you brainless please
Answer:
See picture below.
Step-by-step explanation:
Which expression is equivalent to 4−3(x+2)+2(3−2x)? −7x+16 −7x+4 −x+16 −x+4
The equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4
How to determine the equivalent expression?The expression is given as:
4 − 3(x + 2) + 2(3 − 2x)
Open the brackets
4 − 3(x + 2) + 2(3 − 2x) = 4 - 3x - 6 + 6 - 4x
Collect the like terms
4 − 3(x + 2) + 2(3 − 2x) = - 3x - 4x + 4 - 6 + 6
Evaluate the like terms
4 − 3(x + 2) + 2(3 − 2x) = -7x + 4
Hence, the equivalent expression of 4 − 3(x + 2) + 2(3 − 2x) is -7x + 4
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PLEASE HELP 4/z>3; z=2
answer and steps to get it in the picture
8. How much energy does a 12 V battery in your car use to move 2.5 C through the electrical
circuit?
The energy required is 30 watts second.
In order to accomplish work and to produce heat and light, energy must be transferred to a body or to a physical system. Energy is the quantitative attribute that does this. Energy is a preserved resource; according to the rule of conservation of energy, energy can only be transformed from one form to another and cannot be created or eliminated.
The voltage of a battery is 12 V and;
The charge is 2.5C.
Now, energy can be defined as the product of voltage and charge.
Therefore,
E = V × C
E = 12 × 2.5
E = 30 watt second
Hence, the energy needed by the 12 V battery to move 2.5 C through the electrical circuit is 30 watts second.
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writing linear equations: two points or graph worksheet, please help
Answer:
Q3
Slope = 5
Standard= y=5X+15
Q5
Slop =-4
Standard= y=-4x+4
Step-by-step explanation:
m=-5-5/-4+2=-10/-2= 5
y-5=5(x+2)
y-5=5x+10
y=5x+15
simple example of a literal equation
Answer:
E = mc²
Step-by-step explanation:
You want an example of a literal equation.
Literal equationA literal equation is one that uses variable names to represent numerical values.
Any equation that has no numbers is a literal equation.
One of the more famous literal equations in the world is Einstein's relation between mass and energy:
E = mc²
We use literal equations as formulas for length, area, volume, and relations between chemical and engineering properties.
P = 2(L+W) . . . . perimeter of a rectangle with length L and width W
V = I·R . . . . voltage in a circuit with current I and resistance R
PV = nRT . . . . ideal gas law relating pressure, volume, temperature, and quantity of gas