The inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(a). G(s)= 1 / s(s+2)(s+3)
Using partial fraction expansion, we can write G(s) as 1/s + 2/s+2 + 3/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 1/s is 1, the inverse Laplace transform of 2/s+2 is 2e^(-2t) and the inverse Laplace transform of 3/s+3 is 3e^(-3t). Therefore, the inverse Laplace transform of G(s) is 1 + 2e^(-2t) + 3e^(-3t).
(b). G(s)= 10 / (s +1)^2(s+3)
Using partial fraction expansion, we can write G(s) as 5/s+1 + 5/s+3. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 5/s+1 is 5e^(-t) and the inverse Laplace transform of 5/s+3 is 5e^(-3t). Therefore, the inverse Laplace transform of G(s) is 5e^(-t) + 5e^(-3t).
(c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x
Using partial fraction expansion, we can write G(s) as 50/s + 50/s+1 + 50/s+2 + 50/s+4. Then, using the Laplace transform table, we can find the inverse Laplace transform of each of these fractions. The inverse Laplace transform of 50/s is 50, the inverse Laplace transform of 50/s+1 is 50e^(-t), the inverse Laplace transform of 50/s+2 is 50e^(-2t) and the inverse Laplace transform of 50/s+4 is 50e^(-4t). Therefore, the inverse Laplace transform of G(s) is 50 + 50e^(-t) + 50e^(-2t) + 50e^(-4t)e^-x.
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the sum of 6 and the square of 12
the quotient of 30 and the sum of 5 and 7
the difference of 4 cubed and 25
5 more than the product of 12 and 8
The solutions are 150, 2.5, 39 and 101. The solutions have been obtained using the arithmetic operations.
What are arithmetic operations?
In all, there are four basic mathematical operations which are applicable for all the real number. The operations are as follows:
1.Addition(‘+’) operation which gives the sum of the numbers.
2.Subtraction(‘-’) operation which gives the difference of the numbers.
3.Multiplication(‘×’) operation which gives the product of the numbers.
4.Division(‘÷’) operation which gives the quotient of the numbers.
1. The sum of 6 and the square of 12
The square of 12 = 12*12 = 144
Sum of 6 and 144 = 6 + 144 = 150
2. The quotient of 30 and the sum of 5 and 7
The sum of 5 and 7 = 5 + 7 = 12
The quotient of 30 and 12 = 30 ÷ 12 = 2.5
3. The difference of 4 cubed and 25
The cube of 4 = 4*4*4 = 64
The difference of 64 and 25 = 64 - 25 = 39
4. 5 more than the product of 12 and 8
The product of 12 and 8 = 12*8 = 96
5 more than 96 = 5 + 96 = 101
Hence, the solutions are 150, 2.5, 39 and 101.
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I need help with this equation nowww
The new coordinate of Q after a rotation of 90° is (10, -5)
How to determine the new coordinate of Q after a rotation of 90°?Rotation simply means turning
In order to answer this question, you need to know the rotation rule for 90° about the origin.
If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x).
From the graph, the initial coordinate of Q is (-5, -10).
Thus, the new coordinate of Q will be (10, -5)
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The mean is calculated for for 551 respondents and the result is 1.5
The level of measurement of the data can be given as follows:
Interval or ratio.
How to obtain the levels of measurement of the data?There are four levels of measurement for the data, given as follows:
Nominal.Ordinal.Interval.Ratios.The measures of central tendency for each level are given as follows:
Nominal: ModeOrdinal: Mode and median.Interval: Arithmetic mean, mode and median.Ratios: Arithmetic mean, geometric mean, mode and median.For this problem, we have the arithmetic mean, meaning that the level of measurement can be either interval or ratio.
Missing InformationThe problem asks for the level of measurement of the data.
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A restaurant server believes the distribution of their tips has a model that is slightly skewed to the left, with a mean of $10.70 and a standard deviation of $6.70. They
usually wait on about 60 parties over a weekend of work.
a) Estimate the probability that they will earn at least $800 in tips.
b) How much do they earn on the best 10% of such weekends?
Answer:
a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))
We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.
P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)
b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)
We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.
Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)
Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.
Anything would be awesome!
The composition with rotation to map ΔABC to ΔA'B'C' is;
Reflection across the y-axis and 270 degrees counterclockise rotation about the origin
How to interpret Rotation transformation?
A rotation is defined as a type of transformation that takes each point in a figure and rotates it to a specific number of degrees around a given point.
Now, the coordinates of triangle ABC from the graph are;
A(-8, -2)
B(-6, 3)
C(-5, -1)
The coordinates of triangle A'B'C' from the graph are;
A(-2, -8)
B(3, -6)
C(-1, -5)
Now, the transformation rule for reflection across the y -axis is (x, y) → (-x, y) .
Finally rotation 270 degrees counterclockwise will produce;
(-x, y) → (y, x)
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Three partners share a business. Max owns 3 8 , Sherry owns 2 5 , and Duane owns the rest. If the profits this year are $350,000, how much does each partner receive (in $)?
answer:
Max =$131,250
Sherry=$140,000
Duane=$78,750
Step-by-step explanation:
Max will receive 3/8 ×$350,000=$131,250
Sherry will receive 2/5 × $350,000=$140,000
Duane will receive $350,000-$(131,250+140,000)
$350,000-$271,250=$78,750.
Oil is leaking from an oil tanker at the rate of 3000 liters per hour. 8 liters of oil spread out over 10 square meters of ocean surface.
a) The radius of the area of the oil leakage is described by R = √(112.345 · t).
b) The time related to a radius 1 kilometers is approximately 8901.153 hours.
How to analyze an oil leakage from oil tanker
In this problem an oil tanker has a leakage on ocean surface, the consequence of such event is a contaminated area of circular form, whose formula is described below:
A = π · R²
Where:
A - Area, in square meters. R - Radius, in meters.And the area density (σ), in liters per square meter, is defined by following formula:
V = σ · A
Where V is the volume leaked, in liters, whose formula is described:
V = V' · t
Where:
V' - Leaking rate, in liters per hour.t - Time, in hour.Part A - The resulting expression in terms of time is shown below:
V = σ · A
V' · t = σ · π · R²
R = √[(V' · t) / (σ · π)]
(V' = 3000 L / h, σ = 4 / 5 L / m²)
R = √[(3000 · t) / (8.5π)]
R = √(112.345 · t)
Part B - If we know that R = 1000 m, then the time needed is:
1000 = √(112.345 · t)
t = 8901.153 h
Remark
Statement is incomplete. Complete form is shown below:
Oil is leaking from an oil tanker at the tanker of 3000 liters per hour. 8 liters of oil spread out over 10 square meter of ocean surface. A circular oil slick forms.
a) Express the radius R of the oil slick as a function of the time t (in hours) the tank has been leaking.
b) After how many hours will the oil slick have radius 1 kilometer?
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The picture shows six equal squares. The total is 54ft2. What is the perimeter?
Answer:
72ft
Step-by-step explanation:
Area of one square = 54ft^2/6 = 9ft^2
The side of the square is the square root of the area, so the side length of one square is
√9ft^2 = 3ft.
each square has a perimeter of
4*3ft = 12ft.
So the perimeter of all six squares is
12ft * 6 = 72ft
Which of the following is most likely the next step in the series?
Answer:
Choice C. is the answer
Step-by-step explanation:
greetings !!
just following the series the
First starts with simple square which have four sides.The second have five sides which is a Pentagon.The third one will have a hexagon or six side shape.Then, finally it will be preceded by a heptagon which is a seven sided have in regard to the series.If any questions and unclear ideas tag on comment box.
Hope it helps!!!
What is the Product?
The product meaning in maths is a number that we get to by multiplying two or more other numbers together.
What is Product?
In mathematics, a product is the outcome of multiplying two or more numbers together.
Let us consider the scenario. A person had to buy 4 cupcakes. Each cupcake costs $5.
To calculate the total amount he needs to pay at the checkout counter, add the cost of each cupcake 4 times (as he needs to buy 4 cupcakes).
So, the answer will be -
5 + 5 + 5 + 5 = 20
If he needed 10 cupcakes, he would have to add the cost 10 times.
This is where the concept of multiplication and product can help him.
He can find the cost as -
4 times 5 or 4 × 5,
He can skip count by 5, four times and get the answer as 20.
Therefore, product is repetition for the sum of numbers.
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help me slove this math please
By Linear Function f(x) = -4 + 2 and g(x) = x - 3 this we get the Value -2.
How to Find a Linear Function?The slope-intercept form or the point-slope form are used to find a linear function.
With the aid of an example, the procedure for determining a linear function is the same as determining a line's equation.
When "m" and "b" are real numbers, then a function has the form f(x) = mx + b.
Examples :
f(x) = -4 + 2,g(x) = x - 3: -2
Steps
Find f ° g given f(x) = -4 + 2, g(x) = x - 3
f ° g = f(g (x))
Constant function results in a constant
f (x ) = -4 + 2
-4 + 2 = -2
Answer = -2.
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Select all ratios equivalent to 12:6.
10:5 18:9 11:2
The ratios that are equivalent to 12:6 are (a) 10 : 5 and (b) 18 : 9
How to determine the equivalent ratioFrom the question, we have the following parameters that can be used in our computation:
Ratio = 12 : 6
Divide both sides of this ratio by 6
So, we have the following representation
Ratio = 2 : 1
Multiply the ratio by 9
Ratio = 18 : 9
Multiply the ratio by 5
Ratio = 10 : 5
Hence, the equivalent ratios are 10:5 and 18:9
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What is the arc of WY
The angle ∠G will be 140° for the given curve.
What is the arc of the circle?An arc is a section of a circle's or curve's boundary in mathematics. It is additionally known as an open curve. The circumference also referred to as the perimeter, is the measurement around a circle that defines its edge.
Given that the angle ∠I is equal to 70°. The value of angle G will be calculated by the angle of the arc theorem.
One-half the size of the central angle is the size of an angle that is inscribed in a circle. Congruent inscribed angles are those that intersect the same arc.
∠I = ( 1 / 2 ) x ∠G
∠G = 2 x ∠I
∠G = 2 x 70
∠G = 140
Hence, the angle ∠G will be 140.
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How do I do this problem I do not get it do I add when I found the volume of both
Answer: 149 cm^3
To find the volume for a cube, the formula is V = a^3, where a = length of one side.
Smaller cube:
a = 3
(3)^3, or 3 x 3 x 3
= 27 cm^3
Larger cube:
a = 5
(5)^3, or 5 x 5 x 5
= 125 cm^3
To find the volume of the entire sculpture, add the volumes of each of the cubes.
27 + 125
= 149 cm^3
What number after being increased by 22% results in a value of 305 round your answer to the nearest hundredth if necessary
According to the given information in the question answer is 250.
What does "rounding to the nearest hundredth" actually mean?Any decimal number is rounded down to the closest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, increasing 2.167 to the closest tenth yields 2.17.
To the closest hundredth, what is 10.2719?In this exercise, we must round the supplied number up to the nearest hundred, making it 10.2719. We must add two more decimal places to this number in order to round it to the nearest hundreds. Additionally, we saw that all of the numbers following the second decimal place are fewer than five, therefore they can be ignored and the result is 10.27.
Using the following formula, you can determine this:
x = (100 * 305) / 122
Where x is the original number and 122 is 100 + 22 (the 100 representing the original value and 22 representing the increase of 22%).
x = (100 * 305) / 122 = 250
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 5 3√x , y = 0, x = 1
The volume of the cylinder is
V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
See the image as the answer is given in the image down below.
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The volume of the cylinder is V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
See the image as the answer is given in the image down below.
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the distance around a standard tennis court is 228 feet. if the length of the court is 30 feet more than twice the width, find the dimensions of the tennis court
The dimensions of the tennis court are 42 feet by 114 feet.
Let the width of the tennis court be x feet.
We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.
2(2x + 30) + 2x = 228
4x + 60 = 228
4x = 168
x = 42
The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.
The dimensions of the tennis court are 42 feet by 114 feet.
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Determine the number of classes in the frequency table below.
Class | Frequency
23-24 , 7
25-26 , 2
27-28 , 6
29-30 , 4
31-32 , 1
The number of classes in the frequency table given below is; 5 classes
How to Interpret a Frequency Table?We are given the classes of the frequency table as;
23 - 24
25 - 26
27 - 28
29 - 30
31 - 32
Now, we see from the class intervals that there are a total of five classes because each class interval has a frequency of occurrence as seen in the given frequency table.
The frequencies for each class interval is as follows;
7, 2, 6, 4, 1
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Please solve ASAP.
Will give brainliest!!
Thank you!
Answer:
Step-by-step explanation:
5
On the curve y=x/3 , point P has coordinates (2, 0.667). What is the slope of the curve at point P?
A. 0.033
B. 0.067
C. 0.333
D. 0.667
The correct option regarding the slope of the linear function at point P is given as follows:
C. 0.333.
How to obtain the slope of the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The line in this problem is defined as follows:
y = x/3.
Meaning that:
The slope is of 1/3.The intercept is of 0.The slope is the same for each point on the curve, hence the correct option is given by option C.
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Principal 1,565.89 1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
The annual percentage rate for this credit card account is 15.75%.
How is the annual percentage rate determined?The annual percentage rate (APR) is the actual annual cost of borrowing money.
Before applying the APR on the account balance, we determine the monthly percentage rate (MPR) by dividing the APR by 12.
Given the interest in dollars and the principal or account balance, the APR can be computed by dividing the interest by the account balance and multiplying it by 12.
Principal $1,565.89 $1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
Interest rate (MPR) = 1.31235% ($20.55/$1,565.89 x 100)
Annual percentage rate = 15.75% (1.31235% x 12)
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Question Completion:What is the annual percentage rate?
You are standing 143 feet away from the base of a building and your clinometer measures 17° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.
Answer:
43.7 ft
Step-by-step explanation:
h= height of the building
tan(17) = h/143
h = tan(17) x 143 = 43.7 ft
1. If SW = 25 and ST = 24, find the area of rectangle RSTW.
2. If SZ = 25 and WT = 14, what is ST?
1. Using the Pythagoras theorem, the area of the rectangle RSTW is 168 units².
2. Using the Pythagoras theorem, the measure of line segment ST is 48 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagonal SW measures = 25 units
The breadth ST measures = 24 units.
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(25)² = (24)² + (WT)²
(WT)² = (25)² - (24)²
(WT)² = 625 - 576
(WT)² = 49
WT = √49
WT = 7 units
The length WT measures = 7 units
The formula for the area of the rectangle is -
Area = Length × Breadth
Area = WT × ST
Area = 7 × 24
Area = 168 units²
Therefore, the area of the rectangle is obtained as 168 units².
The line segment SZ measures = 25 units
According to the properties of rectangle the diagonals bisect each other.
So, the measure of SW = 2(SZ) = 50 units
The length WT measures = 14 units
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(50)² = (ST)² + (14)²
(ST)² = (50)² - (14)²
(ST)² = 2500 - 196
(ST)² = 2304
ST = √2304
ST = 48 units
Therefore, the breadth ST measures = 48 units.
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The function f(x)=x is translated 4 units left and 3 units up. Which function represents the transformation?
A function that represents the transformation include the following: B. g(x) = (x + 4) + 3.
What is a translation?In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.
Conversely, the translation a geometric figure or graph upward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.
By translating the pre-image vertically upward by 3 units and horizontally left by 4 units, the function becomes;
f(x) = x
f(x) → g(x) = (x + 4) + 3.
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square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. the sides are then folded to form an open box. the surface area, in square units, of the interior of the box is
The surface area of the interior of the box is the total area of the interior walls of the box.
This can be calculated by subtracting the area of the 5 unit square removed from the total area of the original 20 by 30 unit rectangular sheet of cardboard. This gives us an area of 450 units. To calculate the area of the interior walls, we need to multiply the length and width of the remaining rectangle. This gives us a length of 15 units and a width of 25 units, which gives us a total area of 375 units. Therefore, the surface area of the interior of the box is 375 square units. We can calculate this using the formula A = L x W, where A represents the area, L represents the length and W represents the width.
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Plot the image of point QQQ under the translation (x,y)\to(x+1,y+2)(x,y)→(x+1,y+2)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 1, comma, y, plus, 2, right parenthesis.
The coordinates of the image of the point Q is Q'(3, 6).
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
From the given graph, we have point Q(-4, 4).
Here the point is translated.
After translation, the original figure is shifted from a place to another place without affecting it's size.
The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).
So the given point is (-4, 4).
(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).
So the required point is (-3, 6).
Hence the image of point Q is (-3, 6).
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Your question is incomplete, Probably, the correct graph for the question is given below.
What is the answer to the equation
Z - 2/5=1/3
Answer:
To solve the equation Z - 2/5=1/3, we need to get Z alone on one side of the equation.
First we add 2/5 to both sides of the equation to get
Z - 2/5 + 2/5 = 1/3 + 2/5
Z = 1/3 + 2/5
To combine the fractions on the right side of the equation, we need to find a common denominator.
The common denominator of 1/3 and 2/5 is 15
So we can convert 2/5 to 9/15
Z = 1/3 + 9/15
Now we can add the fractions
Z = 12/15 + 9/15
Z = 21/15
So the solution to the equation is Z = 21/15
Step-by-step explanation:
The angle of depression from the top of a cliff to a nearby town is 10 degrees.
If the top of the cliff is 354 feet above the town, how far is the town from the base of the cliff?
The distance of the town from the base of the cliff is; 62.42 ft
How to use trigonometric ratios?The 6 trigonometric ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/ adjacent
sec θ = 1/cos θ
cosec θ = 1/sin θ
cot θ = 1/cot θ
We are given the angle of depression as 10 degrees. By definition of alternate angles, the angle the hypotenuse formed will make with the base of the town is 10 degrees.
Since the height from the cliff to the town is 354 ft, then we can use trigonometric ratio to find the distance of the town from the base of the cliff as;
354/adjacent = tan 10
adjacent = 354 * tan 10
adjacent = 62.42 ft
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What is the ratio of red apples to all apples in the basket?
What is the ratio of red apples to green apples?
Answer: a) 8:6
b) 8:14
Step-by-step explanation:
You got the answer correct for a but you have to switch the numbers around because the ratio of red apple to green apples is 8:6
What is the percent of decrease from 100 to 60?
Answer:
40% decrease
Step-by-step explanation:
since it is 100 it is easy to convert to a percentage. 100-60=40 so you have a 40% decrease