Answer:
Step-by-step explanation:
a) The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b) We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
a.
To find the area covered by algae 10 days after it was first spotted, we need to convert 10 days into weeks, since the growth rate is given in terms of weekly doubling.
There are 7 days in a week,
So 10 days are approximately 1.43 weeks (10/7).
Let A be the area covered by algae in square meters after n weeks.
Then we can use the formula for exponential growth:
A = 12.5 x [tex]2^n[/tex]
Substituting n = 1.43, we get:
A = 12.5 x [tex]26^{1.43}[/tex]
A ≈ 32.64
Therefore,
The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.
b.
We know that the area covered by algae doubles each week.
One week is equivalent to 7 days, so after one week, the area covered by algae will be twice the initial area of 12.5 square meters, or 25 square meters.
We can represent this mathematically as:
A = 12.5 x [tex]2^1[/tex]
Now, let's consider what happens after two weeks, or 14 days.
The area covered by algae will double again, so it will be four times the initial area of 12.5 square meters or 50 square meters.
We can represent this mathematically as:
A = 12.5 x 2²
Using the same reasoning, we can find that after three weeks (21 days), the area covered by algae will be eight times the initial area or 100 square meters:
A = 12.5 * 2³
In general, we can see that after n weeks, the area covered by algae will be 2^n times the initial area of 12.5 square meters. This can be written as:
A = 12.5 x [tex]2^n[/tex]
If we want to find the area covered by algae after one day, we can use the fact that one day is equivalent to 1/7 of a week.
So, after one day, the area covered by algae will be:
A = 12.5 x [tex]2^{1/7}[/tex]
Simplifying this expression using the laws of exponents, we get:
A = [tex]12.5^{1/7}\times2[/tex]
Therefore,
We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.
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Word problem with multiple decimal operations
Maria sells beaded necklaces. Each large necklace sells for $4.50 and each small necklace sells for $3.90. How much will she
earn from selling 1 large necklace and 4 small necklaces?
Answer: $20.10
Step-by-step explanation: If you multiply 3.90 by 4 and add 4.50 you get 20.10
Answer:
!20.1
Step-by-step explanation:
I got here by multiplying $3.90 by four and adding $4.50. This equals $20.1
Hence the answer is: She will earn $20.1
Brainliest Please
1)
4 ft
5.4 ft
What is the area
Answer: 21.6
Step-by-step explanation:
length X height
4(5.4)=21.6
Preview
-116. Solve the following systems of equations using any method (graphing, elimination, substitution). Check each
solution, if possible.
a. - 2x + 3y = 1
2x+6y= 2
c. 3x - y = 7
y = 3x - 2
b. y = x + 4
x = -3y
d. x + 2y = 1
3x + 5y = 8
The equations are solved using graphing, elimination, substitution methods.
What is system of equation?A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.
The systems of equations are given below are given below,
(a) -2x + 3y = 1(using elimination method)
2x+6y= 2
eliminating x term we get,
9y = 3
⇒y=3.
(b) y = x + 4 ---(1)(using substitution method)
x = -3y---(2)
Substitute (2) in (1) we get,
y = -3y+4
⇒4y=4 ⇒y=1
(c) 3x - y = 7 (using graphing method)
y = 3x - 2
This system has no intersection point
So this system has no solution.
( The graph is attached below.)
(d) x + 2y = 1-----(1) (using elimination method)
3x + 5y = 8-----(2)
For eliminating x we have to the multiply equation(1) by 3,
we get 3x+6y=3
eliminating 3x we get, y=-5/3 substitute y in (1) we get x=49 /3
Hence, the equations are solved using graphing, elimination, substitution methods.
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How does a number line help to show that 3 divided by 1/4 is equal to 3x4
Answer:
To show that 3 divided by 1/4 is equal to 3x4 on a number line:
1. Draw a number line starting from 0 and mark every 1/4 division.
2. Label 3 divisions with the corresponding value '3'.
3. Move 4 divisions in the same direction as that of 3 divisions.
4. Mark the point at 4 divisions and label it as ’12’.
5. From the starting point to the point labelled ‘12’, there are 7 divisions.
6. Since each division represents a quantity of 1/4, dividing 3 by 1/4 (or multiplying by 4) will result in a total of 12, or 3x4.
Gina is making a square tablecloth. How much fabric does she need?
Answer:
Step-by-step explanation:
You need the area.
If this is a square - it is 54 × 54 = 2916 inches squared
Choose the situation that best fits the equation:
x - 6
Choose the situation that best fits the equation:
x - 6
a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.
b. Elena has more roses than Lin. Lin has 6 roses and Elena has x roses.
c. Elena has half the roses Lin has. Lin has 6 roses and Elena has x roses.
d. Elena has twice as many roses as Lin. Lin has 6 roses and Elena has x roses.
Answer:
a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.
Step-by-step explanation:
What is the value of 45 out of 50 percent?
Answer:
22.5%
Step-by-step explanation:
45×50/100 gives you the answer using BODMAS
hi guys can u guys answer this question
Answer:
a= 77, b= 77, c= 103.
Step-by-step explanation:
a= 77 (vertically opposite)
b= a= 77 (corresponding angles)
c= 180-77
= 103 (angles on a straight line)
Use the distributive property to write an equivalent expresión for the perimeter of the triangle
The equivalent perimeter expression is 3 * 3
How to detemrine the perimeterFrom the question, we have the following parameters that can be used in our computation:
Side lengths = 3m, 3m and 3m
The perimeter of the triangle is the sum of the side lentths
So, we have
perimeter = 3 + 3 + 3
Using the distributive property, we have
Perimeter = 3 * 3
Hence, the perimeter expression is 3 * 3
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Complete question
The lengths of the sides of a triangle are represented by 3m, 3m and 3m.
2) The school that Imani goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252.
The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket.
What is the price each of one senior citizen ticket and one student ticket?
The price of each ticket is given as follows:
Senior: $14.Student: $14.How to obtain the prices?The prices for each type of ticket are obtained via a system of equations, for which the variables are given as follows:
Variable x: price of a senior ticket.Variable y: price of a student ticket.On the first day of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252, hence:
12x + 6y = 252
2x + y = 42 (simplifying by 6).
y = 42 - 2x.
The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket, hence:
6x + y = 98
y = 98 - 6x.
Equaling the two equations, the value of x is obtained as follows:
42 - 2x = 98 - 6x
4x = 56
x = 56/4
x = 14.
Then the value of y is of:
y = 98 - 6(14)
y = 14.
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what is 18% of 45 help please
Answer:
8.1
Step-by-step explanation:
100%= 45
1%= 45÷100
= 0.45
18%= 0.45×18
= 8.1
Which equation represents the graph?(picture below)
1. Y= - 3/2 x + 5
2. Y= - 2/3 x + 3
3. Y= 2/3 x - 3
4. Y= 3/2 x - 5
sams monthly gross income is 6000$ if sams federal tax rate is 10.5% and his state tax rate is 4.25%
A)how much money does sam bring home annually
B)How much social security tax does Sam pay monthly
C)How much Medicare tax does Sam pay annually
I need an answer quickkkk i am timed
The vertical asymptote is at x = -2
The horizontal asymptotes are at y =0.
How to get the asymptotes?First, the vertical asymptote, it happens when the denominator becomes zero, then we need to solve:
-x - 2 = 0
x = -2
The vertical asymptote is at x = -2
For the horyzontal asymptotes we need to check the limit as x tends to ±∞, in both cases because x is only in the denominator, the function will tend to zero.
So we have two horizontal asymptotes at y = 0.
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what is the value of 10 ml in teaspoon?
10 ml is equal to 2 teaspoons. This is because 1 teaspoon is equal to 5 ml. To calculate the number of teaspoons in 10 ml, you must divide 10 ml by 5 ml. 10 ml divided by 5 ml equals 2 teaspoons.
To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. This means that for every 1 teaspoon, there are 5 milliliters. To figure out the number of teaspoons in 10 ml, you must take 10 ml and divide it by 5 ml. This will give you the number of teaspoons in 10 ml.When converting from milliliters to teaspoons, it is important to use the correct conversion factor. If you use the wrong conversion factor, you will end up with incorrect results. For example, if you use 1 teaspoon = 4 ml instead of 1 teaspoon = 5 ml, you will end up with an incorrect result.In addition to using the conversion factor, it is also important to keep in mind that a teaspoon is a measure of volume, not weight. This means that the amount of liquid in a teaspoon may vary depending on the density of the liquid. For example, a teaspoon of water will contain more liquid than a teaspoon of honey.
In conclusion, 10 ml is equal to 2 teaspoons. To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. It is important to remember that a teaspoon is a measure of volume, not weight, and the amount of liquid in a teaspoon may vary depending on the density of the liquid.
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What is 1 Litre equal to in cm3?
There are 1000 cubic centimetres in a litre (cm3). This is so because one cubic centimetre (cc) equals one millilitre (ml), and one litre (l) equals 1000 ml.
1000 ml make up 1 litre (L).
ml (millilitres) = cm3
1000 ml = 1000 cm3
1 L = 1000 cm3
One litre is equal to one thousand cubic centimetres (cm3). This is because one cubic centimetre is equivalent to one millilitre (ml), and one litre is equal to 1000 millilitres (ml). The subsequent actions can be conducted in order to calculate this. Initially, one litre (L) equals one thousand millilitres (ml). Second, one cubic centimetre is equivalent to one millilitre (cm3). Thus, one millilitre is equivalent to one hundred cubic centimetres. Last but not least, one litre equals one thousand cubic centimetres, or 1 L = 1000 cm3. Anybody wishing to translate between the two different volume measures will find this information valuable. For instance, if a recipe calls for a certain amount of an ingredient in litres, it is simple to convert that amount to cubic centimetres if necessary.
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|
(3v 8w+19)+ (6w-6)
Answer:
3v + 14w + 13
Step-by-step explanation:
The expression can be simplified as follows:
(3v + 8w + 19) + (6w - 6)
Combining like terms, we have:
(8w + 6w) and (19 - 6)
3v + 14w + 13
So the simplified expression is equal to 3v + 14w + 13.
Evaluate m³ +n if m= 1.2 and n = 13
Answer:
14.728
Step-by-step explanation:
m³ + n if m = 1.2 and n = 13
= (1.2)³ + 13
= 1.728 + 13
= 14.728
please fill out the steps
The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).
How to simplify a rational equation
In this problem we need to determine the simplified form of a rational equation, whose form is:
R(x) = P(x) / Q(x)
Where:
P(x) - Polynomic numerator.Q(x) - Polynomic denominator.
The simplification process can be done by means of algebra properties. First, write the rational equation:
[x + 1 / (x - 2)] / [x² / (x - 2) + 1]
Second, expand the numerator and the denominator:
[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]
Third, simplify the fraction by algebra properties:
[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]
(x - 1)² / [(x + 2) · (x - 1)]
(x - 1) / (x + 2)
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Pythagorean Theorem. I have to turn this in by Friday
Answer:
1. b = [tex]\sqrt{20}[/tex]
2. c = [tex]\sqrt{2[/tex]
3. b = [tex]\sqrt{105}[/tex]
4. c = [tex]\sqrt{113}[/tex]
5. c = [tex]\sqrt{52}[/tex]
6. b = [tex]\sqrt{80}[/tex]
7. b = [tex]\sqrt{130}[/tex]
8. a = [tex]\sqrt{48}[/tex]
9. c = [tex]\sqrt{149[/tex]
10. c = [tex]\sqrt{5}[/tex]
Example:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]8^{2}[/tex] + [tex]b^{2}[/tex] = [tex]12^{2}[/tex]
64 + [tex]b^{2}[/tex] = 144
64 + [tex]b^{2}[/tex] = 144 - 64
[tex]b^{2}[/tex] = 80
[tex]\sqrt{b}[/tex] = [tex]\sqrt{80}[/tex]
Write an equation for the table.
Pls help!
Answer:
Step-by-step explanation:
its 3.02
Select "Rational" or "Irrational" to classify each number.
2/3
π
400−−−
√36/2
The answer is:
2/3 - Rationalπ - Irrational400−−− - Rational√36/2 - RationalBecause it can be written as the ratio of two integers, 2/3 is a rational number (2 and 3).Since it has an unlimited number of non-repeating decimals after the decimal point and cannot be written as a finite or repeating decimal, is an irrational number.400 can be written as a ratio of two integers, making it a rational number (400 and 1).Because it reduces to 3, which is a ratio of two integers, 36/2 is a rational number (3 and 1). So, 36/2 makes sense.To know more about Rational and Irrational visit:
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Please somebody help me
Using mathematical operators, the value of the expression is 23
What is simplification of expressionSimplification of an expression is the process of reducing a mathematical expression to its simplest form while retaining the same value. This is done by using various rules and techniques, such as combining like terms, using the distributive property, and applying the order of operations.
The goal of simplification is to make the expression easier to work with and understand. It also helps to avoid errors when solving problems or simplifying more complex expressions.
In this expression given;
3(x + 2y) - 2x + 10 = ?
x = 1, y = 2
3(1 + 2(2)) - 2(1) + 10 = 23
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A rectangular prism is 8.8 centimeters long and 4.4 centimeters high. Its volume is 271.04 cubic centimeters. What is the width of the rectangular prism?
The height of the cylindrical concrete pillar is approximately 153.2 centimeters.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
[tex]V = a\times b \times c \: \: unit^3[/tex]
We are given that;
Length of prism=8.8cm
Height=4.4cm
Volume=271.04 cubic centimeters.
Now,
We can use the formula for the volume of a cylinder to find the height of the pillar. The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:
r = 10/2 = 5 centimeters
Now we can substitute the given volume and radius into the formula and solve for the height:
12,042 = π(5)^2h
Divide both sides by π(5)^2:
h = 12,042 / (π(5)^2)
h ≈ 153.2 centimeters (rounded to one decimal place)
Therefore, by the given volume the answer will be 153.2 centimeters.
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Find the coordinates of the centroid of the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0).
The centroid of this triangle is located at the point (6, 3).
The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.
The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.
To find the coordinates of the centroid of a triangle, we will use the following formula:
G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3
Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.
So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:
G = (2 + 6 + 10)/3, (5 + 5 + 0)/3
G = (18/3, 10/3)
G = (6, 3.333...), which we can round to (6, 3)
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I need help with this please and thank you.
Answer: 6x^2-x-1
Step-by-step explanation:
(3x+1)(2x-1) = 6x^2 - 3x + 2x -1
6x^2-x-1
an object has a mass of 8.1kg what is its weight
The weight of the object is 79.461 newtons.
How to determine the weightThe standard value for the acceleration due to gravity is approximately 9.81 m/s^2 near the Earth's surface.
To find the weight of an object with a mass of 8.1 kg, we can use the formula:
Weight = mass x acceleration due to gravity
So, the weight of the object is:
Weight = 8.1 kg x 9.81 m/s^2
Weight = 79.461 N (newtons)
Hence, the weight is 79.461 newtons.
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What is 25 mcg to mg ?
25 mcg is equal to 0.025 mg. both are unit of measurement of weight.
The prefix "mcg" stands for microgram, which is a unit of measurement in the metric system that is one millionth of a gram (10⁻⁶ g). On the other hand, "mg" stands for milligram, which is one thousandth of a gram (10⁻³ g). Therefore, to convert from mcg to mg, you need to divide the value in mcg by 1000.
In this case, 25 mcg divided by 1000 equals 0.025 mg. It's important to be mindful of the units when dealing with measurements, as confusion between different units of measurement can lead to incorrect calculations and dosing errors.
Overall, when converting from mcg to mg, you can easily make the conversion by dividing the value in mcg by 1000, as the prefix "milli" represents a factor of 1000 in the metric system.
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Calculate the value of each expression. (-8) x 2/3. (-8) x (-2/3). -18/3. 18/(-3). (-18)/(-3)
The values of the given expressions are respectively, -5.33, 5.33, -6, -6, 6
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Here are the calculations for each expression:
1. (-8) x 2/3
= (-8) x 2/3
= -16/3
= -5.33
2. (-8) x (-2/3)
= (-8) x (-2/3)
= 16/3
= 5.33
3. -18/3 = -6
4. 18/(-3) = -6
5. (-18)/(-3) = 18/3
= 6
So, the values of each expression are -5.33..., 5.33..., -6, -6, and 6, respectively.
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the point (3,W) is on the graph of y= 2x +7. What is the value of W
Answer:13
Step-by-step explanation:
y=2x+7
x=3
2*3+7=13?
The solution is, the value of w is 13.
Here, we have,
We are given that the point (3,w) lies on the line y = 2x + 7.
This means that if we substitute x = 3 into the equation y = 2x + 7,
we will get the value of y at x = 3, which is equal to w.
so, we get,
Substituting x = 3 into the equation y = 2x + 7, we have:
y = 2(3) + 7
y = 6 + 7
y = 13
So, after simplification we get, w = 13
Therefore, the value of w is 13.
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