The situation can be represented by a geometric sequence with a(1) = 5000 and ratio or r = 3/4. At the start of the 10th day, the remaining helium volume is 375.42 cm³
Let a(n) be the volume of helium left in the balloon at the nth day.
Day 1: The balloon is filled with 5000 cm³ of helium. We can conclude the volume of helium in day 1 is:
a(1) = 5000.
Day 2: The volume of helium loses 1/4 from its initial volume. Hence,
a(2) = (1 - 1/4) . a(1)
= 3/4 . 5000 = 3/4 . 5000 = 3750
Day 3: The volume of helium loses 1/4 from its volume in day 2. Hence,
a(3) = (1 - 1/4) . a(2)
= 3/4 . 3750 = 2812.5
Continue the process, it will form a geometric sequence with a(1) = 5000 and ratio or r = 3/4.
To find the 10th term, use the nth term formula:
a(n) = a(1) . r^(n-1)
a(10) = 5000. (3/4)¹⁰⁻¹
= 5000. (3/4)⁹ ≈ 375.42
Hence, at the start of the 10th day, the remaining helium volume is 375.42 cm³
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Compare the two numbers. Use > or < .
16, √16
The value of Square root √16 is equals to 4, and the number 16 is larger than the number 4 then 16 > √16.
What is a Square root?In arithmetic, a number y whose square (the outcome of multiplying the number by itself, or y y), equals x is known as the square root of a number x.The phrase (or quantity) whose square root is under consideration is referred to as the radicand.In this situation, the expression or number under the radical sign is called the radicand and it is 9.Within the context of complex numbers, one can talk about square roots of negative numbers.Square roots can be taken into account more broadly in any situation where the concept of an object's "square" is specified.Among other mathematical structures, these include function spaces and square matrices.Let the value of √16 be 4 then 16 > √16.
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What are the cooridinates of the point that partitions segment HE in the ratio of 2:3?
Using proportions, the coordinates of the point C that partitions segment HE in the ratio of 2:3 are found according to the following equation:
C - H = 2/5(E - H).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, we have point C that partitions segment HE in the ratio of 2:3, hence it is 2/5 of the way from H to E, and the rule is given by:
C - H = 2/5(E - H).
Then:
Replacing the x-coordinates of H and E, we find the x-coordinate of C.Replacing the y-coordinates of H and E, we find the y-coordinate of C.More can be learned about proportions at https://brainly.com/question/24372153
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Write and solve an equation to answer the question.
The area of the postcard is 24 square inches. What is the width b of the message (in inches)?
Equation: __ =24
The width of the message as shown in the image attached is 3 inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let b represent the width of the message. The area of the postcard is 24 square inches, hence:
(b + 3)4 = 24
4b + 12 = 24
b = 3
The width of the message as shown in the image attached is 3 inches.
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At its peak, an online shopping site was selling about 420 items per second. At this rate, how many items would it sell in 30 minutes (1,800 seconds)?
The online site would sell
items in 30 minutes.
Step-by-step explanation:
420x1800=756000
so 756k items in 30 minutes
me nu elin.
Joan had 174 dollars to spend on 7 books. After
buying them she had 13 dollars. How much did
pas
each book cost?
vab 199
Weit
ration
angiario
new
for this situation
Answer:
23 dollars.
Step-by-step explanation:
She spent a total of 174 - 13 = 161 dollars.
So, the cost of each book = 161/7
= 23 dollars.
x decreased by 13 is at least 15
Answer:
x [tex]\leq[/tex] 28
Step-by-step explanation:
lets say you chose 27 . 27 - 13 = 14 . thats not enough . but everything 28 and above would work for x . so x would be equal to or greater than 28 . hope this helps :)
Solve |x-5| + 7 = 13.
A. x= -11 and x = 1
B. x= -11 and x = -1
C. x 11 and x = -1
D. x= 11 and x = -11
|x-5| + 7 = 13 is equal to x= -11 and x = 1.
[tex]|x-5|+7=13[/tex]
Subtract 7 from both sides
[tex]|x-5|+7-7=13-7[/tex]
Simplify
[tex]|x-5|=6[/tex]
Apply absolute rule: If [tex]$|u|=a, a > 0$[/tex] then [tex]$u=a$[/tex] or [tex]$u=-a$[/tex] [tex]$x-5=-6$[/tex] or [tex]$x-5=6$[/tex]
[tex]$$x-5=-6 \text { or } x-5=6$$[/tex]
[tex]$$x=-1 \text { or } x=11$$[/tex]
Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.
Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.
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A standard 1 kilogram weight is a cylinder 54.5 mm in height and 53.0 mm in diameter. what is the density of the material?
The density of the material is 0.4 kg/cubic cm.
Given that:-
Height of the cylinder = 54.5 mm
Diameter of the cylinder = 53.0 mm
Weight of the cylinder = 1 kg
We have to find the density of the cylinder.
We know that,
Density = mass/volume
Here, mass = 1 kg
We know that,
Volume of a cylinder = [tex]\frac{1}{3} \pi r^2 h[/tex]
Where,
r is the radius of the cylinder, and
h is the height of the cylinder
Here, h = 54.5 mm, and
r = 53/2 = 26.5 mm
Hence,
Volume of cylinder = (1/3)*(22/7)*(26.5)(26.5)*54.5 ≈ 2566.088 ≈ 2566 cubic mm. = 2566/(10*10*10) cubic cm = 2.566 cubic cm
Density of cylinder = 1kg/2.566 cubic cm ≈ 0.3897 ≈ 0.4 kg/cubic cm.
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Which is the graph of the solution set of −2x + 5y > 15?
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (5, 1). Everything below and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 5) and (10, 9). Everything above and to the left of the line is shaded.
Answer:
it is the first option
Step-by-step explanation:
First step. Switch the greater than sign and turn the linear inequality to slope formula. after that graph the line. it is a dashed line due to not being greater than EQUAL to. if not equaled to then it is dotted. then you need a point as your testing point to see if it is shaded in that area. I chose to(0,0) but you could have chose any point. Once you plug in the zeros you will notice you get the false statement of 0 greater than 15. so obviously that is a no so you shade the opposite side of your testing point. phew
Answer:
A. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
Step-by-step explanation:
what is the value of the expression below when A=-3, B=2, and C=-4
2
a -2ac+5c
Answer: -50
Step-by-step explanation:
2a-2a+5c
2(-3)-2(-3)(-4)+5(-4)=
-6-24-20=-50
simplify with the steps
By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.
How to simplify an algebraic expression
In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:
[(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] Given[(3 · a · b²) / (5 · b²)] ÷ [√(9 · a²) / √(100 · b²)] Square root of a division[(3 · a · b²) / (5 · b²)] ÷ [(√9 · √a²) / (√100 · √b²)] Square root of a product[(3 · a · b²) / (5 · b²)] ÷ [(3 · a) / (10 · b)] Definition of square root[(3 · a · b²) · (10 · b)] / [(5 · b²) · (3 · a)] Division of fractions(30 · a · b³) / (15 · a · b²) Associative and commutative properties / Definition of multiplication / Multiplication of powers of equal base2 · b Associative and commutative properties / Definition of division / ResultThe expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.
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positive & negative functions & the end behavior
Step-by-step explanation:
f(x) = 5|x - 1| - 5
f(x) will be positive that means >= 0, if
5|x - 1| - 5 >= 0
5|x - 1| >= 5
|x - 1| >= 1
that will be true for x <= 0 or x >= 2
f(x) will be negative for the other cases.
so, 0 < x < 2
f(x) is increasing in
[1, infinity)
the value "1" is for sure included, as it starts the increasing part.
f(x) is decreasing in
(-infinity, 1]
"1" is again included, because it ends the decreasing part.
end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
A farmer needs to make a 1000 -square-foot rectangular enclosure for her cows. She wants to save money by purchasing the least amount of fencing possible to enclose the area. What whole-number dimensions will require the least amount of fencing?
F. 8ft by 125ft
G. 10ft by 100 ft
H. 20ft by 50 ft
J. 25ft by 40 ft
The dimensions of the 1000-square-foot rectangular enclosure with the least amount of fencing should be 25ft by 40ft.
The amount of fencing needed can be calculated by getting the perimeter of each choice of dimensions.
Perimeter is defined as the distance that surround any two-dimensional shape. For a rectangle, the perimeter is given by the formula
P = 2l + 2w
Solving for the perimeter of each of the following choices:
F. 8ft by 125ft
P = 2l + 2w
P = 2(8) + 2(125)
P = 16 + 250
P = 266ft
G. 10ft by 100ft
P = 2l + 2w
P = 2(10) + 2(100)
P = 20 + 200
P = 220ft
H. 20ft by 50ft
P = 2l + 2w
P = 2(20) + 2(50)
P = 40 + 100
P = 140ft
J. 25ft by 40ft
P = 2l + 2w
P = 2(25) + 2(40)
P = 50 + 80
P = 130ft
The dimensions with the least perimeter will require the least amount of fencing.
Hence, a 1000 -square-foot rectangular enclosure, with dimensions 25ft by 40ft, will require the least amount of fencing.
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5/8 divided by 5/16?
Answer:
2
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \large{\frac{5}{8}} \: \div \large{\frac{5}{16}} \\ \\ = \frac{5}{8} \times \frac{16}{5} \\ \\ = \green 2 \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Answer:
2
Step-by-step explanation:
(5/8) ÷ (5/16)
= (5*16) ÷ (8*5)
= 80 ÷ 40
= 2
Can someone help me find the value of x
Answer:
25
Step-by-step explanation:
180 - 25 = 155
180 - 155 = 25
A regulation volleyball has a circumference of about 66 centimeters. The ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6: 1 . What is the circumference of the children's ball? Round to the nearest centimeter.
The circumference of the children's ball to the nearest centimeter is 52 centimeters.
If a regulation volleyball has a circumference of about 66 centimeters, solve for its radius using the formula for the circumference of a circle given by:
C = 2πr
66 centimeters = 2πr
r = 33/π centimeters
Then, solve for the surface area of this regulation volleyball using the formula given by:
A = 4πr^2
A = 4π(33/π centimeters)^2
A = 4356/π square centimeters
If the ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6 : 1, then
surface area of regulation volleyball : surface area of a children's ball = 1.6 : 1
surface area of a children's ball = 4356/π square centimeters/1.6
surface area of a children's ball = 2722.5/π square centimeters
If the children's ball has a surface area of 2722.5/π square centimeters, solve for its radius using the formula for the surface area given by:
A = 4πr^2
2722.5/π square centimeters = 4πr^2
r = 26.0887907/π centimeters
Solving for the circumference:
C = 2πr
C = 2π(26.0887907/π centimeters)
C = 52.17758139 centimeters
Rounding off to the nearest centimeter.
C = 52 centimeters
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If (44)x = 432, what is the value of x?
4
7
8
28
Answer:
9.81....
Step-by-step explanation:
x = 432/44
x = 9.81...
Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually. She makes no additional deposits or withdrawals. Which amount is closest to the interest Mrs. Chavez will have earned at the end of 4 years?
If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years
Total invested amount = $8000
Interest rate = 8.62%
The interest is compounded annually
Time period = 4 years
We know
[tex]A=P(1+\frac{r}{100})^{t}[/tex]
Where,
A = Final amount
P = Principal
r = Interest rate
t = Time period
Substitute the values in the equation
A= [tex]8000(1+\frac{8.62}{100})^{4}[/tex]
A= $11136
Compounded interest = 11136-8000
=$3136
Hence, If Mrs. Chavez put $8,000.00 in her IRA savings account that offers 8.62% interest compounded annually, then she will earn $3136 interest at the end of the 4 years
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How many atoms of carbon (C) are present in the reactants of the following chemical equation?
C7H16+O2
CO₂ + H₂O
(1 point)
7 atoms
16 atoms
1 atom
23 atoms
The reactants in the chemical equation C7H16 + O2 = CO2 + H2O have a total of 7 atoms in them.
How to count the number of atoms?The chemical formula of a compound indicates how many atoms are present in the substance.
The number of atoms of each element present in a molecule is noted in a chemical formula.
The answer to this query provides the following description of the chemical interaction between heptane and oxygen:
O2 + C7H16 = CO2 + H2O
Hexane's chemical composition reveals that the reactant side of the reaction has 7 carbon atoms.
Therefore, there are 7 atoms total in the reactants of the chemical equation C7H16 + O2 = CO2 + H2O.
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Can you guys help me please
The shortest length of fabric, in inches, that Kirk could use to make the tablecloth without putting any separate pieces of fabric together is 30 inches
How to solve for the shortest length of fabric required to make the table clothGiven data
diameter of the table = 3 feet
hang down dimension = 5 inches
sew down dimension = 1 inch
width of rectangular fabric = 60 inches
The question seeks for area of the table cloth, for a circular table area of a circle = pi * r^2
required radius of cloth
= radius of the table + hang down dimension + sew down dimension
= 3 feet / 2 + 5 inches + 1 inch
= 1.5 * 12 inches + 5 inches + 1 inch
= 18 + 5 + 1
= 24 inches
Area of required cloth
= pi * 24^2
= 1809.557 square inches
Area of fabric = Area of required cloth
length * wide = 1809.557 square inches
length * 60 = 1809.557 square inches
length = 1809.557 / 60 square inches
length = 30.159 inches ≈ 30 inches
Therefore option H which is 30 inches is the answer
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Coventry Estates sells houses.
In February they sold twice as many houses as in January.
In March they sold 10 more houses than in February.
In April they sold half as many houses as in March.
Coventry Estates sold a minimum of 123 houses from 1st January to 30th April.
Find the least number of houses sold in January.
The total number of houses sold in January by Coventry Estates are 18.
How to do the twice of number? This suggests that the amount of A is twice as large as the quantity of anything else, which in this case is B. So, if you have a dozen B items, you have twice a certain number for A, which is 24.As per the given question;
Let the total sales of the houses in January be 'x'.
In February they sold twice as many houses as in January.
February = 2x.
In March they sold 10 more houses than in February.
March = February + 10
March = 2x + 10
In April they sold half as many houses as in March.
April = March/2
April = (2x + 10)/2 = x + 5
The total sold houses = 123.
Add all the sold houses;
x + 2x + 2x + 10 + x + 5 = 123
6x + 15 = 123
On simplification;
x = 18
Thus, the total number of houses sold in January by Coventry Estates are 18.
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PLS HELP ME WITH THIS
How do you find equivalent expressions?
Image result for what is equivalent to (5x/6)
Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.
A rectangular field is 250m by 190m. How far is it across diagonally?
Answer:
314.0063694
Step-by-step explanation:
You will have to use the pythogoras. triple to solve the equation
Answer:
314 mStep-by-step explanation:
the diagonal is the hypotenuse of the two triangles that form the rectangle (see figure) we solve with Pythagoras
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
a² = b²+ c²
a² = 250² + 190²
a² = 62500 + 36100
a² = 98600
a = √98600
a = 314 m
9+4y=-5x+7y solve for x
Answer:
x=3/5y-9/5
Step-by-step explanation:
Answer:
5x=7y-4y-9
5x=9-3y
[tex]\frac{5x}{5}[/tex]=[tex]\frac{9-3y}{5}[/tex]
[tex]x=\frac{9-3y}{5}[/tex]
here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB
Making a perpendicular bisector on the segment that gives the half length of AB
Given that,
here are 2 points in the plane. Explain how to construct a line segment that is half the length of AB is to explain.
A line can be defined by the shortest distance between two points is called as a line.
Here,
Two points are given on the plane,
Draw line segment joining these two points on the plane,
Now with help of a compass draw a perpendicular bisector on the line, that bisects the segment into two equal halfs.
Thus, making a perpendicular bisector on the segment that gives the half length of AB
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My little sister, Savannah, is three years old and has a piggy bank that she wants to fill. She
started with five pennies and each day when I come home from school, she is excited when I give her three pennies that are left over from my lunch money. How much money will Savannah have after 10 days? How many days will it take for her to have at least $1.50? Justify your answer with a mathematical model of the problem situation.
Answer:
after 10days savannah will have 31 pennies
Step-by-step explanation:
arithmetic progression (AP)
(a1) started with, 5 pennies
common difference (d), 3 pennies
formula: Tn = a + (n-1)d
after 10 days, T10 = 5 + (10- 1)(3)
T10 =5 + 27
T10= 31
therefore after ten days savannah has 31 pennies
if h(t)=1248-160t+16t
Answer: 816
Step-by-step explanation:
h(3) = 1248 - 160(3) + 16(3)
h(3)= 1248 - 480 + 48
h(3)= 816
80 students visited the library
over three days. The two-way
table shows some information
about these students.
Monday
Year 7
Year 8
Total
14
Tuesday Wednesday Total
13.
38
33
26
80
The missing values of the table are a=7, b=18, c=15, d=13, e=42 and f= 21
We can easily complete the give table using simple addition and subtraction
Monday Tuesday Wednesday Total
Year 7 7 18 13. 38
Year 8 14 15 13 42
Total 21 33 26 80
The correct question is 80 students visited the library
over three days. The two-way
table shows some information
about these students.
Monday Tuesday Wednesday Total
Year 7 a b 13. 38
Year 8 14 c d e
Total f 33 26 80
Complete the table.
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convert the following to base 10
a:325.6eight b:11101.011two
Solve the differential equation dpdt=5p a. assume a is a non-zero constant, and use c for any constant of integration that you may have in your answer. p=
The solution of the differential equation as given in the task content is; ln(5p +a)/5 + C = t
What is the solution of the differential equation as in the task content?It follows from the task content that the solution of the differential equation is required.
Given;
dp/dt=5p +a
To find; solution to the differential equation;
By variable separation; the resulting equation is;
dp/(5p +a) = dt
By integrating both sides of the equation; we have;
ln(5p +a)/5 + C = t
Ultimately, although both sides of the equation integrated yield a constant of integration as the integral is indefinite, the two constants have been combined into constant, C as in the equation above.
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