money would she have at the end of vacation = 377,789,318,629,571,617,095.67 dollars.
What does "compounding" mean?When interest is applied to a principal amount together with the interest that has already been paid, this process is known as compounding. This means that compounding, sometimes known as the "wonder of compounding," can be thought of as interest on the compound, which has the effect of increasing returns from interest over time.
What is an appropriate compounding procedure?Current good compounding practices refer to the minimal requirements for the procedures, facilities, and controls used to compound medicine to ensure that it has the identity, and strength, and satisfies the quality and purity requirements it is claimed to have.
According to the given information:She puts in one penny the first day, 2 pennies the second, 4 pennies the third...and so on.
The total sum is thus,
(1, 3, 7, 15, 31, 63, 127)
Which translate to
(2^1-1, 2^2-1, 2^3-1, 2^4-1, 2^5-1, 2^6-1, 2^7-1,..)
So at the end of the 75th day, the total amount is 2^75-1
or
37778931862957161709567 pennies
or
377,789,318,629,571,617,095.67 dollars.
money would she have at the end of vacation = 377,789,318,629,571,617,095.67 dollars.
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I understand that the question you are looking for is:
Your friend is saving pennies. She puts one penny into her piggy bank the first day, two pennies the second day, four the third day, and so on, doubling the number of pennies added. How many much money would she have at the end of vacation, if she could keep saving at this rate? Vacation lasts 75 days.
Can someone solve it please?
Juanita recorded 1 1/2 hours of a school musical concert. during editing, she deleted 1/3 of the recording. what was the length of the recording after editing was completed?
The final length of Juanita recording after editing was completed was 7/6
To solve this exercise, we have to state the equation using the information of the problem:
Information about the problem:
Recorded= 1 1/2 hDeleted= 1/3Final length= ?Transforming the mixed number to fraction, we get:
1 1/2 =
[(2*1) +1] /2
(2+1)/2
3/2
Calculating the final length of the recording, we have:
Final length = Recorded - deleted
Final length = 3/2 - 1/3
Final length = (9-2) / 6
Final length = 7/6
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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2x - 1 = 3x + 8
i ended up getting -7 but i know it’s wrong i just don’t know what i did wrong
Answer:
2x-1=3×+8
Step-by-step explanation:
2×-3x=8+1
-x=9
x=-9
Find an equation of the sphere that passes through point (1,8,1) and has center (3,5,-1)
The sphere's equation that passes through the given point is:
(x - 3)² + (y - 8)² + (z - 1)² = 30What is the standard equation of a sphere?A sphere's standard equation is defined by its center and radius. Remember that the radius is the distance between any two points on the sphere. The standard formula is: [tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2[/tex]To find the equation of the sphere:
The radius of a sphere is equally distant between any two points on the sphere. The sphere's center is: (3, 8, 1)So,
P = (4, 3,−1)C = (3, 8, 1)r = d(C, p)Now,
[tex]\begin{aligned}&=\sqrt{\left(x_c-x_p\right)^2+\left(y_c-y_p\right)^2+\left(z_c-z_p\right)^2} \\&=\sqrt{(3-4)^2+(8-3)^2+(1-(-1))^2} \\&=\sqrt{(-1)^2+(5)^2+(2)^2} \\&=\sqrt{1+25+4} \\\therefore r &=\sqrt{30}\end{aligned}[/tex]
Supplement the center point and radius into the standard sphere equation:
[tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2\\(x-3)^2+(y-8)^2+(z-1)^2=(\sqrt{30})^2\\(x-3)^2+(y-8)^2+(z-1)^2=30[/tex]
Therefore, the sphere's equation that passes through the given point is:
(x - 3)² + (y - 8)² + (z - 1)² = 30Know more about the standard equation of a sphere here:
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The correct question is given below;
Find an equation of the sphere that passes through the point (4, 3,−1) and has to center (3, 8, 1).
Given m|n, find the value of x.
Water flows through a cylindrical pipe of radius 0.74 cm.
It fills a 12 l bucket in 4 minutes. When the 12 l bucket is emptied in to a circular pool, the water level rises by 5 mm. Calculate the radius of the pool.
The radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.
We have that:
Radius of the water pipe = 0.74 cm
r = 0.74 cm
It fills a 12 L bucket in 4 minutes
1 L = 1000 cm³
12 L = 12,000 cm³
Volume of water put in the pool = 12,000 cm³
Height of the pool that rise = 5 mm = 0.5 cm.
H = 0.5 cm
Let the radius of the pool be R.
Volume = π r² h
Substituting the values, we get that:
12,000 = ( 22 / 7 ) R² ( 0.5 )
R² = 7636.36
R = 87.39 cm
Therefore, we get that, the radius of the pool with height as 0.5 cm and volume as 12,000 cm³ is 87.39 cm.
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(Type exponential notation with positive exponents.)
The correct answer to the exponential expression which is as given in the task content is; 8³.
Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.
Exponential notationThe bases of exponential expression, if same, should be taken as one.If the bases of exponential notation are entirely different, then it should be simplified.In indices, Division between two different expressions simply means Subtraction of powers.Multiplication means addition of powersGina's working:
8^12 / 8^9
= 0^12 / 0^9
The Correct workings:
8^12 / 8^9
= 8^(12-9)
= 8³
So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.
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x^2+11x+15=30
find x
After simplifying the equation we acquire the value of x as:
x = 1.225 or x = ₋12.225
Given the equation is x² ₊ 11x ₊ 15 = 30
arrange the constants on one side.
x² ₊ 11x = 30 ₋ 15
x² ₊ 11x = 15
x² ₊ 11x ₋ 15 = 0
now simplify the equation using the formula: -b±√b²₋4ac / 2a
in the equation we have the values for a = 1 , b = 11 and c = ₋15
substitute the values and get the value of x.
= ₋11 ± √(11)² ₋ 4(1)(₋15) / 2(1)
= ₋11 ± √121 ₊ 60 / 2
= ₋11 ± √181 / 2
= ₋11 ± 13.45 / 2
= ₋11 ₊ 13.45 / 2 or ₋11 ₋ 13.45 / 2
= 2.45/2 or ₋24.45/2
= 1.225 or ₋12.225
Therefore x value is 1.225 or ₋12.225
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Mercury has a freezing point of -38. Water has a freezing point of 32. What is the difference
The position of a car is given, for positive t, by x = 9t - 3t3. x is in meters and t is in seconds. when (in seconds) it its velocity zero?
When the velocity of the car is zero. Then the time will be 1 second.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The position of a car is given, for positive t, by x = 9t - 3t³. x is in meters and t is in seconds.
We know that velocity is the rate of change of displacement. Then we have
v = dx / dt
v = 9 - 9t²
When the velocity of the car is zero. Then the time will be
v = 0
9 - 9t² = 0
1 - t² = 0
(1 - t)(1 + t) = 0
t = 1, -1
When the velocity of the car is zero. Then the time will be 1 second.
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Let A be the points (a,2a-1)and B be point (2a+4,3a+9) where "a" is a constant , given that the distance AB is √(260) .find the possible values of "a".note a is an integer .
Given that the distance AB is (260), let A be the points (a,2a-1) and B be the places (2a+4,3a+9) where "a" is a constant.
discover the several meanings of "a." noting that an is an integer An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing. Fractions are represented in the form of p/q. For example, ¼, ½, ¾, and so on.
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Group Activity let U= { 2, 4, 6, 8, 10, 12, 14, 16, 18} A = {4, 10, 12, 14,18} B = { 2,4,6,8,10,14,16} Drow the Venn diagram and Find 1.A' 2.B' 3.(AUB)' 4.A'UB'
We get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
We are given the sets as:
U= { 2, 4, 6, 8, 10, 12, 14, 16, 18}
A = {4, 10, 12, 14, 18}
B = { 2, 4, 6, 8, 10, 14, 16}
We first will find out A':
A' = U - A
A' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - {4, 10, 12, 14, 18}
A' = { 2, 6, 8, 16}
Now, we will find B':
B' = U - B
B' = { 2, 4, 6, 8, 10, 12, 14, 16, 18} - { 2, 4, 6, 8, 10, 14, 16}
B' = { 12, 18}
Now, we have to find:
(AUB)' = U - (AUB)
AUB = {4, 10, 12, 14, 18} U { 2, 4, 6, 8, 10, 14, 16}
AUB = { 2, 4, 6, 8, 10, 12, 14, 16, 18} = U
(AUB)' = U - U = ∅.
Now, we will find A' U B':
A' U B' = { 2, 6, 8, 16} U { 12, 18}
A' U B' = {2, 6, 8, 12, 16, 18}
Therefore, we get A' as { 2, 6, 8, 16}. B' as {12, 18}, (AUB)' as ∅ and A' U B' as {2, 6, 8, 12, 16, 18}.
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I will give brainliest if you explain
Answer:
See below
Step-by-step explanation:
The first one scales UP from 4 to 6 F'G'/FG = factor is 6/4 = 1.5
second one scales DOWN from 4 to 3
F'G' / FG = scale factor is 3/4
Third one is scaled DOWN
F'G' / FG = 2/4 = 1/2
Note when scale is DOWN the factor is less than one
when scale is UP , factor is more than one
i am equivalent to 5/6 the sum of my numerator and my denominator is 44 the sum of the digits in my denominator is 6 what fraction am i
Step-by-step explanation:
a/b = 5/6
a + b = 44
a = 44 - b
so, the first equation is
(44 - b)/b = 5/6
44 - b = 5b/6
264 - 6b = 5b
264 = 11b
b = 24
a = 44 - b = 44 - 24 = 20
the fraction is a/b = 20/24.
Also 2+4 as sum of the digits of the denominator = 6 is correct.
If point A is located at (5, –3) and point B is located at (–4, –6). Find AB A B rounded to the nearest tenth.
The distance between the point A and point B is 9.5 units
Distance between two pointsThe formula for calculating the distance between two points is expressed according to the formula shown below;
AB = √(x₂-x₁)²+(y₂-y₁)²
Using the given coordinates points A(5, -3) and B (-4, -6)
Substitute to have:
AB = √(5-(-4))²+(-3-(-6))²
AB = √(5+4)²+(-3+6))²
AB = √81+9
AB = √90
AB = 9.5 units
Hence the distance between the point A and point B is 9.5 units
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HELP ME PLEASE SUPER EASY
6.8x10^6, 6.6x10^6, 6.1x10^6, 6x10^
Answer:
6 x 10^6, 6.1 x 10^6, 6.6 x 10^6, 6.8 x 10^6
Step-by-step explanation:
Jill sold half of her comic books
and then bought seventeen
more. She now has 31. With how
many did she begin?
well, she really began with "x" total.
then she sold half of that, so hmmm 1/2 of "x" is just x/2 and she's left with half, so she sold x/2 and she was left only with x/2, and then she bought 17 more, we also know that she has 31 now, so
[tex]\stackrel{\textit{leftover}}{\cfrac{1}{2}x}~~ + ~~\stackrel{\textit{more bought}}{17}~~ = ~~\stackrel{\textit{now she has}}{31}\implies \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left(\cfrac{x}{2}~~ + ~~17 \right)~~ = ~~2(31)}\implies x+34=62\implies \LARGE \begin{array}{llll} x=28 \end{array}[/tex]
Evaluate the function.
ƒ(x) = −3x² − x – 15
Find f(−8)
Given ~
[tex] \: [/tex]
[tex] \tt \: f(x) = −3x² − x – 15[/tex]
[tex] \: [/tex]
now , put x= -8 in the function ~
[tex] \: [/tex]
[tex] \tt \: f( - 8) = −3( - 8)² − ( - 8) – 15[/tex]
[tex] \: [/tex]
[tex] \tt f(-8) = −3(64) − (-8) – 15[/tex]
[tex] \: [/tex]
[tex]\tt f(-8) = −192 − (-8) – 15[/tex]
[tex] \: [/tex]
[tex] \tt f(-8) = −192 − (-8) – 15[/tex]
[tex] \: [/tex]
[tex]\tt f(-8) = −184 – 15 [/tex]
[tex] \: [/tex]
[tex] \underline{\boxed{\red {\tt f(-8) = - 199}}}{\green ✓} [/tex]
[tex] \: [/tex]
hope helps ~
Kenzie runs at an average speed of 6.25mi/h. The length of her typical run is within one mile of 6 miles long.
Write an absolute value equation to represent the situation. Find the shortest or longest amount of time for Kenzie’s run. Round to the nearest minute.
Answer: 13512
100332
Step-by-step explanation:
The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.
To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.
The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.
To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.
The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,
which is approximately 0.6 hours or 36 minutes.
The maximum time would be (6 + 1)/6.25 hours,
which is approximately 1.12 hours or 67 minutes.
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Will give brainliest.
Answer:
Option 3
Step-by-step explanation:
First tke lcm i.e. 6 then multiply the dinominator to make six.
Multiply tje above no. With the same digit the sub. The numerators
Answer:
c) 7/6
Step-by-step explanation:
The difference will be,
→ (5/3) - (1/2)
→ (10/6) - (3/6)
→ (10 - 3)/6
→ 7/6
So, the answer is 7/6.
is the value of the 1 in 1,440,000 10 times as great as the value of 4 in the hundred thousands place explain
Answer:
Yes because first ( right to left) 4 is 400,000 while the other 4 is 40,000
Step-by-step explanation:
40,000x 10= 400,000
thanks
Find the distance between the two points in simplest radical form
(-4,-1) and (1,-9)
The difference between the two points ; (-3,10 )
given
(-4,-1) and (1,-9)
here we have to find the difference between -4 and -1
which is -3 so u go -3 spaces left so it would be -3
then , find the difference between 1 and -9 which is 10 so u go 10 spaces down so the difference between is;
(-3,10).
therefore the distance between two point are (-3,10)
Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.to know more about distance.
We will use the distance formula in order to find the distance between points a and b. By substituting the points A(3, 4) and B(1, 2) in the above formula we get our required distance d. Hence, distance d = 2√2 units
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what is the diameter of a 5.23 cubic yard ball
Answer:
It is the size of a cube that is 1 yard on a side. It is about 202 gallons or about 765 liters. A cubic foot is a unit of volume. It is the size of a cube that is 1 foot on a side. It is about 7.5 gallons or about 28.3 liters. Cubic Yards to Cubic Feet Conversions (some results rounded)
Step-by-step explanation:
I am a two-dimensional shape.
I have two pairs of parallel sides.
I have no axis of symmetry.
What am I?
Answer: Non-rectangular Parallelogram
The opposite sides are parallel, but the figure is not a rectangle. It's also not a square either since those figures have an axis of symmetry.
is anybody good at maths
15times15 divide by 20 takeway 5 add100
[tex]111.2[/tex]
Step-by-step explanation:
As per the question, 15 times 15 i.e. 225
[tex]15 \times 15 = 225[/tex]
225 divide by 20 i.e. 11.25
[tex] \frac{225}{20} = 11.25[/tex]
take away five from the 11.25 then it will be 11.2
Add 100 to 11.2 i.e
[tex]11.2 + 100 = 111.2[/tex]
Answer: 115
Step-by-step explanation:
[tex]\displaystyle\\\frac{15*15}{20-5} +100=\\\\\frac{15*15}{15} +100=\\\\15+100=\\\\115[/tex]
Chloe and tino have a combined age of 48. three years ago chloe was double the age tino is now. find tinos age
(solve using simultaneous equations)
As given Chole and Tinos age , the present age of Tino is equal to 15 years.
As given,
Let x and y be the present age of Chole and Tino. respectively.
Combined age = 48
Given condition,
x + y = 48 _______(1)
Three years ago
x - 3 = 2y
⇒x =2y +3 _______(2)
Substitute the value of x in (1),
2y+3 +y =48
⇒ 3y = 45
⇒ y = 15years
Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.
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Find the first four multiples of 15.
Answer:
15, 30, 45, 60
Step-by-step explanation:
ALL OF THE MULTIPLES OF 15
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735
All numbers can be divided or the product of 15 is a multiple of 15.
pls help. stuck on problem
Answer: x = 7 ft, DO = 25 ft, OG = 35 ft
Step-by-step explanation:
We will write an equation using the segment addition postulate.
Given by segment addition postulate:
DO + OG = DG
Substitute known values:
(4x - 3) ft + (2x + 21) ft = 60 ft
Combine like terms and simplify:
6x + 18 ft = 60 ft
Subtract 18 ft from both sides of the equation:
6x = 42 ft
Divide both sides of the equation by 6:
x = 7 ft
Now, we will "plug" this value in and solve for the segments.
DO ➜ (4x - 3)ft ➜ (4(7) - 3) ft ➜ 28 - 3ft = 25 ft
OG ➜ (2x + 21) ➜ (2(7) + 21) ft ➜ 14 + 21 = 35 ft
22) Larry earns a yearly salary of $35,000 plus 5% commission on his sales. If his total sales for the
aro $260.000 what will be his total earnings ( salary and commission) for the year?
Answer:
48000
Step-by-step explanation:
260000*5%=13000
35000+13000=48000
the cost C (in dollars) of making n watches is represented by C=15n+85. how many watches are made when the cost is $385
