The amount of mold after n days is 3 × (1.5)ⁿ⁻¹.
What is Geometric Progression?Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.
This ratio is common ratio.
At first, mold was 3 cm², then 4.5 cm², and it was increasing each day by 50%.
a₁ = 3
a₂ = 4.5
a₃ = 4.5 + (4.5 × 50%) = 6.75
.............
Here the common ratio, r = a₂/a₁ = a₃/a₂ = ..... = 1.5
n th term of a GP = a rⁿ⁻¹, where a is the first term and r is the common ratio.
Area of mold after n days = 3 × (1.5)ⁿ⁻¹
Hence the mold at any time can be calculated by the formula 3 × (1.5)ⁿ⁻¹.
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Fraction is equivalent
3
_
21
[tex]\huge\text{Hey there!}\\\\\\\mathsf{\dfrac{3}{21}}\\\\\mathsf{= \dfrac{3\div3}{21\div3}}\\\\\mathsf{= \dfrac{1}{7}}\\\\\huge\text{Therefore, your\ answer\ should\ be: \huge\boxed{\mathsf{\dfrac{1}{7}}}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
2 2/5 times 1/4 simplest form
Answer:
37/56
Step-by-step explanation:
Answer: 3/5 = 0.6
Step-by-step explanation:
1. 2 2/5 x 1/4 = 12/20
2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5
3. 12/5 times 1/4 = 12/20
4. 12/20=3/5
-1=1/3v
show work
∨=
⇄
Answer:
v = 1/-3
Step-by-step explanation:
cross multiply
-3v = 1
then:
divide through by the coefficient of v which is -3
-3v/-3 = 1/-3
[tex]-1=\dfrac{1}{3} v[/tex]
Flip:
[tex]\dfrac{1}{3} v=-1[/tex]
Multiply both sides by 3:
[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]
[tex]\fbox{v = -3}[/tex]
Evaluate the expression 2a+3d
Answer:
Step-by-step explanation:
Nothing further can be done with this topic
So, your answer would have to be 2a+3d
The weekly sales of an album have increased since it was first sold at a music store 6 weeks ago. The linear regression equation describing the change is y=1.9x+13.3 , where x represents the week and y represents the number of albums sold per week. Round the residual value to the nearest integer and then construct a residual plot of the data.
The residual value to the nearest integer and then construct the residual plot of the data will be 25.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Since an album went on sale for the first time at a music retailer six weeks ago, its weekly sales have climbed. The change is described by the linear regression equation y=1.9x+13.3, where x is the week and y is the number of albums sold each week.
The residual value is given as,
y = 1.9(6) + 13.3
y = 11.4 + 13.3
y = 24.7
y ≅ 25
The residual value to the nearest integer and then construct the residual plot of the data will be 25.
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Tank 1: 36 inches long, 18 inches wide, and 12 inches tall. How many gallons of water is in the tank?
I need a step-by-step explanation please
In a tank that is 36 inches long, 18 inches wide, and 12 inches tall have approximately 33 gallons of water.
How to calculate volume of a tank?The rectangular tank's volume may be calculated using the formula V = l*b* h, where "l" stands for the tank's length, "b" for its width, "h" for its height, and "V" for its volume.
Define volume.The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume = length*width*height
V=36*18*12
V=7776 inches^3
which is approximately 33 gallons.
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The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/7x+200. A) Find a model that expresses the revenue R as a function of x. (Remember, R= xp). R(x)=____ B) What is the domain of R? C) What is the revenue if 200 units are sold? D) What quantity maximizes revenue? What is maximum revenue? E) What price should the company charge to maximize revenue?
A) The model that expresses the revenue R as a function of x is R(X) = -1/7x + 200
B) The domain of R is (-∞, +∞)
C) If 200 units are sold, then the revenue is $228.57
D) The quantity that maximizes revenue is 200 and the maximum revenue is $228.57
E) The price should the company charge to maximize revenue $228.57
Here we have given the function that can be model that expresses the revenue R as a function of x is written as,
=> R(X) = -1/7x + 200
Here the domain value of R has take the value from negative infinity to positive infinity.
When we take the value of x as 200, then the revenues of the sold goods is calculated as,
=> R(200) = -1/7 (200) + 200
When we simplify this one then we get the value of R as
=> R = 28.57 + 200
=> R = 228.57
As per the given function the maximum number of units sold is written as 200, and the maximum revenue is written as 228.57
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Choose three true statements about the angles of the figure
1: Z1 and the 55* angle are adjacent
2: mZ1=55* because Z1 and the 55* angle are vertical angles
3: mZ2=125* because Z2 and the 55* angle are supplementary
4: mZ2 cannot be determined from the information
5: mZ1=180*-55*
6: mZ2=180*-55*-45*
Answer:
2,5,6
Step-by-step explanation:
-Z1 and 55*are vertical angles
-Z1 and 55*are angles on a straight line=180*
this means 180*=55*+Z1
make Z1 subject of the formula- Z1=180*-55*
- mZ2,55*,45* are all angles in the given triangle
since the sum of angles in a triangLe =180*
therefore-180*=Z2+55*+45*
make Z2 the subject of the formulary
Z2=180*-55*-45*
Consider the following 8 numbers, where one labelled x is unknown. 28, 39, 21, x , 33, 38, 2, 45 Given that the range of the numbers is 57, work out 2 values of x
The needed two values of x are: 59 and -12.
The difference between a sequence's maximum value and minimum value is referred to as the sequence's range.
A sequence's range is just a set that identifies the sequence. The set x1, x2, x3, and so forth is typically used to describe the range; it is also written as xn; n = 1, 2, 3,...
Given sequence of 8 numbers as: 28, 39, 21, x , 33, 38, 2, 45
Given range of above sequence: 57
Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that the range remains at 57.
Case 1: x as minimum value of given sequence:
If so, then the maximum value is 45. Then-
range = maximum value - minimum value
57 = 45 - x
x = -12
Case 2: x as maximum value of the given sequence:
If so, then the minimum value of the sequence is 2. Then-
range = maximum value - minimum value
57 = x - 2
x = 59
Thus, the needed two values of x are: 59 and -12.
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−4 1 + 2/3 × 3/5 ÷(−2/5 )
the answer to −41 + 2/3 × 3/5 ÷(−2/5 ) is -42
(#7) A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
The ratio of surface area to volume is 6:s
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, A cube has an edge length given by the variable “s”. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s² volume= s³
The ratio = 6s² / s³
= 6 / s
Hence, the required ratio is 6:s
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A community hall is in the shape of a cuboid.
Total cost of Painting and tileing is for the cuboidical community hall is $2172.
What is a Cuboid ?A three-dimensional form called a cuboid contains six faces, twelve edges, and eight vertices. It differs from a cube in that a cuboid's faces are entirely rectangular in shape whereas a cube's faces are square. A cuboid has three dimensions: length, breadth, and height.
Properties of a Cuboid are :
There are 6 faces, 12 edges, and 8 vertices on a cuboid.
All of the cuboid's faces have rectangular shapes.
The cuboid's opposing edges are parallel to one another.
The dimensions of a cube are length, breadth, and height.
All of the angles created at the cuboid's vertices are 90 degrees.
Surface area of 4 walls and Ceiling is = 40*3*2 + 15*3*2 + 40*15 = 930
Surface area of the floor is 40 *15 = 600
10 lt of tin covers 25
1 can be covered by 10/25 lt
930 can be covered by (10/25) * 930 = 372 lt.
Total cost of Painting is $372.
1 of floor tiles cost $3
600 of floor tiles will cost 3*600 = $ 1800
Total cost of Painting and tileing is for the cuboidical community hall is $ 372 + 1800 = $2172.
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How do you solve a 3 system of equations with 3 variables?
One way to solve a system of 3 equations with 3 variables is to use Gaussian elimination or Gauss-Jordan elimination method.
Gaussian elimination method:
Write the augmented matrix of the system of equations.Use row operations to transform the matrix into an upper triangular matrix.Use back substitution to find the values of the variables.The steps for Gaussian elimination are as follows:
Write the system of equations in matrix form, where the coefficients of the variables are in the matrix and the constants are in the column vector on the right side.Use row operations to transform the matrix into an upper triangular matrix. These operations include adding or subtracting multiples of one row to another, and multiplying or dividing a row by a non-zero scalar.Use back substitution to find the values of the variables. Starting with the last equation, substitute the known values of the variables into the other equations to find the value of the next variable. Repeat until all variables are known.Gauss-Jordan elimination method is similar to Gaussian elimination, however in the final step, it converts the matrix into a Reduced Row Echelon Form (RREF) which leads to more easily solving the system of equations.
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Please help fast
a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second. The height h, in feet, of the rock t seconds after it was thrown can be modeled by the function h(t)=-16t^2 +96t+40. Find the height of rock 4 seconds after it was thrown.
The height of rock 4 seconds after it was thrown is 168 ft.
What is speed?Speed is measured as distance moved over time.
Speed = Distance/ Time.
Here, given that,
we have
a rock is thrown off a bridge 40 feet above a river at an initial velocity of 96 feet per second.
The height h, in feet, of the rock
t seconds after it was thrown can be modeled by the function
h(t)=-16t^2 +96t+40.
where
h -----> is the height in feet of the rock
t -----> the time in seconds
For , t=4, we get,
substitute the value of t in the function and find the value of h
h(4)=-16×4^2 +96×4+40.
So, h= 168
Hence, the height of rock 4 seconds after it was thrown is 168 ft.
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Which function best represents the sequence 10, 13, 16, 19, 22..., where n is a positive whole number?
a(n) = 7+3n
Ob(n) = 10 + 3n
Oc(n) = 7+3
Od(n) = 10 +3"
Answer:
first function
Step-by-step explanation:
there is a common difference between consecutive terms , that is
13 - 10 = 16 - 13 = 19 - 16 = 22 - 19 = 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 10 and d = 3 , then
[tex]a_{n}[/tex] = 10 + 3(n - 1) = 10 + 3n - 3 = 7 + 3n
-16x-32y=52 solve for y
Answer: I think 7/2?
Step-by-step explanation:
The minimum hours of daylight occur mid-year with the maximum hours of daylight occuring in December.b.The maximum hours of daylight occur in January. The amount of daylight decreases each month until the minimum is reached in December.c.The minimum hours of daylight occur in December. The amount of daylight decreases each month until the minimum is reached.d.The minimum hours of daylight occur in January and December. The amount of daylight increases each month until it reaches a maximum mid-year.
The minimum hours of daylight occur in January and December is the correct answer . The amount of daylight increases each month until it reaches a maximum mid-year. Therefore, option D is correct.
The reason behind this is the rotation and revolution of Earth around the sun. The more the sun is towards the North Pole the shorter the day will be. On the equator, daylight will last generally for 12 hours as because sunlight falls directly on the equator
Therefore the shortest duration of daylight occurs in the month of December solstice when the North Pole is at its maximum distance from the Sun .
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If you are doing a linear regression, what is the slope of the line predicted by the null hypothesis?
Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
Define slope.
The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in
the formula y = 3x - 7.
Here,
The slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
:
: B not equal to 0
The slope is equal to zero according to the null hypothesis, however the slope is not equal to zero according to the alternative hypothesis.
The alternative hypothesis therefore asserts that the slope is not equal to zero, whereas the null hypothesis asserts that the slope is equal to zero.
Therefore , the solution of the given problem of slope comes out to be the slope won't be equal to zero if the independent variable X and the dependent variable Y have a substantial linear connection.
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PLEASE HELP ASAP
Chris stopped for gas twice on a long car trip The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon. On the trip, Chris bought a total of 20 gallons of gas and spent $29.80. If x = the number of gallons that Chris bought at the first station, and y = the number of gallons Chris bought at the second station, which system of equations could be used to find the number of gallons of gas Chris bought at each station.
A.1.45x + 1.55y = 20 and x + y = 29.80
B. x + y = 20 and 1.45x + 1.55y = 29.80
C. x + y = 20 and 1.45x - 1.55y = 29.80
D. xy = 20 and 1.45x + 1.55y = 29.80
The system of equations could be used to find the number of gallons of gas Chris bought at each station is,
B. x + y = 20 and 1.45x + 1.55y = 29.80.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, Chris stopped for gas twice on a long car trip.
The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon and filled a total of 20 gallons of gas and cost him a total of $29.80.
Therefore the system of linear equations that represents the context is,
x + y = 20 and 1.45x + 1.55y = 29.80.
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2. Ask one of your teachers how tall they are in feet/in. Write it here:
Now, covert their height into centimeters (cm).
feet
in.
1 ft = 12 in
1 in = 2.54 cm
My teacher:
- 5'3
- 5.25 ft
- 63 in
- 160 cm
can someone help me?
Answer:
Step-by-step explanation:
The solution is the point where the 2 lines intersect.
If they intersect where x = 1 and y = 2 the solution is (1, 2).
Please help, it's much appreciated! <3333 It's midterms studying. 20 points!
A manufacturer makes trusses, or triangular supports, for the roofs of houses. Each truss is the shape of an isosceles triangle in which the sides are congruent. The length of the base is 4/3 the length of the congruent sides.
The perimeter of each truss is 60ft. Find each side length
Answer: The length of each side of the triangle is;
Equal sides, x = 21.02 = PQ = PR
QR = 28.03
Step-by-step explanation: The trusses made by the manufacturer have the shape of an isoscellestriangle and as such two congruent sides PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.
The perimeter of each truss is 70ft.
Let the length of each congruent side be x ft.
Therefore,
Perimeter = x + x + (4/3)x
Perimeter, p = 70 = 3.33x
x = 70/3.33
x = 21.02
Therefore, Length of QR is; QR = (4/3) x
QR = (4/3) × 21.02
QR = 28.03
What are the 4 ways to solve a quadratic equation?
The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula and 4) Graphing
1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.
2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.
3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.
4. Graphing : is another method useful for solving quadratic equation.
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Give your answer in the form y=ma + c, where m and c are integers or
fractions in their simplest forms.
Bookwork code, $79
Canalda
allowst
What is the equation of line H?
33
Line
Watch video
Answer? Helllppo
Erin combined 1 17/18 pounds of peanuts with 1 5/6 pounds of M&M's to create trail mix, then evenly distributed the mix in 8 bags. how many pounds of trail mix are in each bag?
There are 17/36 pounds of trail mix in each bag.
Finding out how much pounds of trail mix are in each bagTo find out how many pounds of trail mix are in each bag,you need to first add the weight of the peanuts and M&M's together.
1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) = [tex]\frac{35+33}{18}[/tex] =[tex]\frac{68}{18}[/tex]
which can be simplified to 3 [tex]\frac{14}{18}[/tex]
So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.
To find out how many pounds of trail mix are in each bag, you will divide the total weight of the trail mix by the number of bags.3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =
[tex]\frac{68}{18}[/tex] ÷ [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]
which can be simplified to [tex]\frac{17}{36}[/tex]
So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.
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Which table shows the function y = -2x + 4?
Answer:
Slope = -2 Y intercept is (0,4)
Step-by-step explanation:
What is numerical coefficient in 3xy?
The numerical coefficient in 3xy is 3.
In algebraic expressions, terms are made up of coefficients and variables. A coefficient is a numerical value that multiplies a variable or a set of variables. In the term 3xy, the numerical coefficient is the number that appears in front of the variable (x and y) and it's 3 in this case.
It is used to indicate the degree of the term or the number of times the variable is present in the term. In this case, it is indicating that the variable x and y are present three times in the term.
It's important to note that if there is no coefficient before the variable, it is assumed to be 1. It's also noteworthy that the coefficient can be a whole number, a fraction, or even a variable, but in this case it is a whole number. Understanding the concept of coefficient is very important in understanding algebraic equations and expressions.
The numerical coefficient in 3xy is 3.
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Regular hexagon $ABCDEF$ is the base of right pyramid $\allowbreak PABCDEF$. If $PAD$ is an equilateral triangle with side length 8, then what is the volume of the pyramid
The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .
The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.
so the height becomes,
√3a/2 = 4√3
The area of the hexagon is calculated using the formula ,
=3√3/2 x a²
=3√3/2 x 64
= 963√3
=332.553 square units.
Volume of a pyramid is calculated as ,
1/3 x base x height
= 1/ 3 x 8 x 8
= 1/3 x 64
=21.33 cubic units answer.
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Mrs. Katz’s science class has spherical beakers that measure 14 centimeters in diameter. If Mrs. Katz wants to fill the sphere, what is the volume in cubic centimeters that she can fit into the beaker? round your answer to the nearest hundredth.
The volume of the spherical beaker is 1436.76 cubic centimeters
How to determine volume a spherical beaker?
In order to determine the volume the spherical beaker, you need the formula for the volume of a sphere.
The volume of sphere is given by the formula:
Volume of sphere = 4/3 πr³
where r is the radius of the sphere
Since the spherical beaker that measure 14 centimeters in diameter. The radius of the beaker will be:
radius = 14/2 = 7 cm
Volume of the spherical beaker = 4/3 × π × 7³
Volume of the spherical beaker = 1436.76 cubic centimeters
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MATH HELP CALC
LOOK AT IMAGE
The right Riemann sum for the given function is 2.5.
Firstly, we must find the width of each of the subintervals Δx,
We know n = 4, a = 0, b = 2
∴ Δx = b - a / n
Δx = 2 - 0 / 4
Δx = 1/2
The width of each rectangle is 0.5
Next, we must find the locations of the right endpoints of the rectangles -
x1 = a + Δx(1) = 0.5
x2 = a + Δx(2) = 1
x3 = a + Δx(3) = 1.5
x4 = a + Δx(4) = 2
Now that we have the width of each rectangle, Δx = 0.5, and the right endpoints for the rectangles, x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2.
we can compute the right Riemann sum.
Computing the sum of the areas of the rectangles:
∑Δx f(x) = ∑ 0.5f(xi)
= 0.5 f(x1) + 0.5 f(x2) + 0.5 f(x3) + 0.5 f(x4)
= 0.5 (0.5) + 0.5 (1) + 0.5 (1.5) + 0.5 (2)
= 2.5
[tex]\int\limits^2_0 {x^{3} } \, dx[/tex] ≈ 2.5
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