Answer:
$2.50
Step-by-step explanation:
13. R(x) (2x+6)(x-1) (4-x)(x+2) Find any vertical asymptote(s) and any horizontal asymptote(s)
The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.
To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.
The factors are (2x+6), (x-1), (4-x), and (x+2).
So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.
To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.
Since the highest exponent is 1 and there is no coefficient, the answer is y=0.
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an investment of $12,000 earns an interest of 2.5% per year
compounded monthly, for 6 years. calculate the Future value and
effective annual interest rate
The future value of the investment after 6 years is $14,370.88; while the effective annual interest rate is 2.56%.
To calculate the future value of the investment, we can use the formula: FV = PV (1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, PV = $12,000, r = 0.025, n = 12 (compounded monthly), and t = 6.
Plugging these values into the formula, we get:
FV = $12,000 (1 + 0.025/12)^(12*6)
FV = $12,000 (1.002083333)^72
FV = $14,370.88
Therefore, the future value of the investment after 6 years is $14,370.88.
To calculate the effective annual interest rate, we can use the formula: EAR = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year.
In this case, r = 0.025 and n = 12 (compounded monthly).
Plugging these values into the formula, we get:
EAR = (1 + 0.025/12)^(12) - 1
EAR = (1.002083333)^12 - 1
EAR = 0.02568245
Therefore, the effective annual interest rate is 2.568245%.
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Select the two real roots of the polynomial fun S(r)=r^(5)+5r^(4)-7r^(3)-43r^(2)-8r-48
The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 are r = -8 and r = 3.
The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 can be found by factoring the polynomial and finding the values of r that make the function equal to zero.
First, we can factor the polynomial using the Rational Root Theorem, which states that if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is -48 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.
We can use synthetic division to test these possible roots and find the ones that make the function equal to zero. After testing the possible roots, we find that the two real roots are r = -8 and r = 3.
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0 A community center offers classes for students.
. The range of the number of students in each class is 13.
. The median number of students in each class is 9.
Which of the following box-and-whisker plots could represent the numbers of students in the classes?
Numbers of Students
Numbers of Students
in Classes
in Classes
C₂
+++
2 4 6 8 10 12 14 16 18 20 22 24
Numbers of Students
in Classes
+++
2 4 6 8 10 12 14 16 18 20 22 24
B.
D.
++
2 4 6 8 10 12 14 16 18 20 22 24
Numbers of Students
in Classes
+111*
2 4 6 8 10 12 14 16 18 20 22 24
T
The response is A.
Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.
what is the range?The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.
As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
from the question:
According to the information provided, the number of pupils in each class might range from 9+6 = 15 to 9+6 = 3. Because the maximum value exceeds 15, options C and D cannot accurately represent the number of students in the classes.
Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.
Option B's median value is 9, but its range (from 9-5 = 4 to 9+5 = 14) is only 11, which is less than the range that could be achieved by the number of students. As a result, option B cannot accurately reflect the number of students enrolled in each class.
Thus, the response is A.
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How can you use the factored form of the polynomial x^4 - 2x^3 - 9x^2 + 18x = x(x-3)(x+3)(x-2) to find the x intercepts of the graph of the function?
Answer:
see explanation
Step-by-step explanation:
the x- intercepts are the values of x on the x- axis where the graph crosses the x- axis.
On the x- axis the y- coordinate of any point is zero.
Set the factored form of the polynomial to zero and solve for x
x(x - 3)(x + 3)(x - 2) = 0
equate each factor to zero and solve for x
x = 0
x - 3 = 0 ⇒ x = 3
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
the x-intercepts are then x = - 3, x = 0, x = 2, x = 3
these can be confirmed from the graph of the polynomial
15 oz to lbs fraction form
The number of lbs in 15. oz is 9 3/8 lb
What is conversion?A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
lb and oz are both units of weight of a substance.
1 oz = 0.0625 lb
therefore 1 oz = 625/1000
= 25/40 lb
15 oz = 25/40 × 15
= 75/8 lb
= 9 3/8 lb
therefore the number of lbs in 15 oz is 9 3/8 lb
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how do i answer this
The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.
What is a Cuboid?A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.
How to Calculate Mass of a Cuboid?To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:
Mass = Density x Volume
where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.
In the given question,
Using the given values, we can now calculate the mass of the solid copper cuboid in kg.
The volume of the copper cuboid is:
Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³
The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:
Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g
To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:
Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg
Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.
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Four different forecasts and have calculated the following MSE levels:
2 Month moving average = 4.5
3 Month moving average = 2.1
Exponential smoothing = 3.7
Exponential Smoothing with Trend = 2.45
Which forecast is best?
A. 2 Month Moving Average
B. 3 Month Moving Average
C. Exponential Smoothing
D. Exponential Smoothing with Trend
The best forecast is the one with the lowest MSE level. In this case, the "3 Month Moving Average" has the lowest MSE level of 2.1, making it the best forecast. Therefore, the correct answer is B. 3 Month Moving Average.
One common metric used to compare forecasting methods is the Mean Squared Error (MSE). The MSE measures the average squared difference between the actual values and the forecasted values, so a lower MSE indicates a better fit.
In this case, we have four different forecasting methods and their respective MSE values. The 3 Month Moving Average has the lowest MSE of 2.1, which suggests it is the best forecasting method among the four options.
Thus, the answer is B. 3 Month Moving Average.
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TB The number is 27% of the pupils in a school are in Primary Six. There are 540 Primary Six pupils How many pupils are there in the school? % % There are 20 pupils in the school. 27%-> 1% →>> 100%->
In linear equation, 2000 pupils are there in the school.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.
= 540/27%
= 54000/27
= 2000
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Liz and Sara each ride their bikes every day. The table shows the number of miles Liz and Sara rode their bikes during five randomly selected days. Based on the data in the table, who has a greater mean and how much is it greater?
Answer:
To determine who has a greater mean, we need to calculate the mean (average) number of miles ridden by Liz and Sara and compare them.
Day Liz Sara
1 7 6
2 12 8
3 10 5
4 8 10
5 5 7
To find the mean for Liz, we add up the miles she rode and divide by the number of days:
Mean for Liz = (7 + 12 + 10 + 8 + 5) / 5 = 8.4 miles per day
To find the mean for Sara, we add up the miles she rode and divide by the number of days:
Mean for Sara = (6 + 8 + 5 + 10 + 7) / 5 = 7.2 miles per day
Therefore, Liz has a greater mean than Sara by 1.2 miles per day (8.4 - 7.2 = 1.2).
Please show your work.
Question 13 Determine whether the given ordered pair is a solution to the system. (9,2) 8x-4y=64 3y=6x-47 No Yes
NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.
The given ordered pair is (9,2) and the system of equations is:
8x-4y=64
3y=6x-47
To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.
For the first equation:
8(9)-4(2)=64
72-8=64
64=64
For the second equation:
3(2)=6(9)-47
6=54-47
6=7
The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.
The final answer is: No, the given ordered pair is not a solution to the system.
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Find the surface area of the square pyramid using the net. Use the
template included if needed. Your response MUST include correct area
labeling.
8 in.
8 in.
5 in...
8 in.
5 in.
8 in.
1 point
Based on the information, we can infer that the surface area of the pyramid is: 105 inches²
How to find the surface area of the pyramids?To find the surface area of the pyramids we must perform the following procedure:
We must find the surface of each of the faces and the base.
height of the triangle faces = 8 inches.Base side length = 5 inches.8 * 5 / 2 = 20 inches²According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).
20 inches² * 4 = 80 inches²Base area = b * hBase area = 5 * 5Base area = 25 inches ²We must add the surfaces of the faces and the base.
25 inches² + 80 inches² = 105 inches²According to the above, the surface area of the pyramid would be 105 inches².
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"For each of the following, two sides and an angle of a triangle
are given. Determine whether the given information results in two
triangles, one triangle, or no triangles. Show your thinking using
the"
For each of the given , we need to use the Law of Sines to determine whether the given information results in two triangles, one triangle, or no triangles. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of the opposite angle is the same for all three sides:
a/sin A = b/sin B = c/sin C
Let's look at each scenario and apply the Law of Sines:
Scenario 1: a = 7, b = 10, A = 50°
Using the Law of Sines, we can find the value of angle B:
7/sin 50° = 10/sin B
sin B = 10*sin 50°/7
sin B = 0.918
B = sin^-1(0.918) = 66.4°
Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:
C = 180° - 50° - 66.4° = 63.6°
Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.
Scenario 2: a = 5, b = 7, A = 120°
Using the Law of Sines, we can find the value of angle B:
5/sin 120° = 7/sin B
sin B = 7*sin 120°/5
sin B = 1.209
Since the sine of an angle cannot be greater than 1, this scenario does not result in a triangle.
Scenario 3: a = 9, b = 12, A = 30°
Using the Law of Sines, we can find the value of angle B:
9/sin 30° = 12/sin B
sin B = 12*sin 30°/9
sin B = 0.667
B = sin^-1(0.667) = 41.8°
Since the sum of the angles in a triangle must equal 180°, we can find the value of angle C:
C = 180° - 30° - 41.8° = 108.2°
Since all three angles add up to 180° and are positive, we can conclude that this scenario results in one triangle.
In conclusion, scenario 1 and scenario 3 result in one triangle, while scenario 2 does not result in a triangle. We can determine this by using the Law of Sines and checking whether the values of the angles are valid and add up to 180°.
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there are 14 kiwis 12 strawberries and 18 bananas in a basket. wha is the ratio of strawberries to bananas
The ratio of strawberries to bananas in the basket is 12:18 or 2:3. To find this ratio, you simply take the number of strawberries and place it over the number of bananas. In this case, there are 12 strawberries and 18 bananas, so the ratio is 12:18.
However, this ratio can be simplified by dividing both numbers by their greatest common factor, which is 6. So, the simplified ratio of strawberries to bananas is 2:3. This means that for every 2 strawberries, there are 3 bananas in the basket.
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a rectangle has a perimeter of 16 centimeters. what is the greatest area the rectangle can have
Step-by-step explanation:
Let L and W be the length and width of the rectangle, respectively.
We know that the perimeter, P, of a rectangle is given by:
P = 2L + 2W
In this case, P = 16 cm, so we have:
16 = 2L + 2W
Simplifying, we get:
8 = L + W
To find the greatest area of the rectangle, we need to maximize the product of L and W, which is the formula for the area, A:
A = L * W
We can solve for one variable in terms of the other using the equation we found earlier:
L = 8 - W
Substituting this into the formula for the area, we get:
A = (8 - W) * W
Expanding and simplifying, we get:
A = 8W - W^2
To find the maximum value of A, we can use calculus or complete the square. Completing the square, we get:
A = -(W - 4)^2 + 16
Since the square of a real number is always nonnegative, the maximum value of A occurs when (W - 4)^2 = 0, which is when W = 4.
Substituting this value back into the equation for the perimeter, we get:
8 = L + 4
L = 4
Therefore, the rectangle with a perimeter of 16 cm and the greatest area is a square with sides of length 4 cm, and its area is:
A = L * W = 4 * 4 = 16 square centimeters.
what is this? linear , non linear function , not a function
Answer:
not a function
Step-by-step explanation:
Answer:
not a function
Step-by-step explanation:
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $5, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 5 + 2x, where x represents the number of pounds of the package. Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A. A package that weighs 15 pounds will cost $35 for both options.
B. A package that weighs 15 pounds will cost $25 for both options.
C. A package that weighs 10 pounds will cost $15 for both options.
D. A package that weighs 5 pounds will cost $15 for both options.
A package that weighs 5 pounds will cost $15 for both options.
How to solve the cost of two shipping options to be same?The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.
Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.
We'll compare the equation as a whole.
In this case,
5 + 2x = 15
Compile similar terms,
2x = 15 - 5
2x = 10
x = 10 / 2
x = 5
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Suppose you have deposited $1000 into a bank and assume the
account is compounded continuously. If you hope that your balance
will reach to $2000 in 10 years, what is the annual interest rate r
should
The annual interest rate.
To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.
We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:
$2000 = $1000e10r
Dividing both sides by $1000, we get:
2 = e10r
Taking the natural logarithm of both sides, we get:
ln(2) = 10r
Dividing both sides by 10, we get:
r = ln(2)/10 ≈ 0.0693
Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.
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Can someone please answer and explain a & b please, thank you.
A roll of ribbon was 12 meters long. Diego cut 9 pieces of ribbon that were 0.4 meter
each to tie some presents. He then used the remaining ribbon to make some
wreaths. Each wreath required 0.6 meter. For each question, explain your reasoning.
a. How many meters of ribbon were available for making wreaths?
b.
How many wreaths could Diego make with the available ribbon?
Answer: a. 8.4 meters b. 14 wreaths
Step-by-step explanation:
The following equation shows the problem, with x representing the number of wreaths made:
12 = 9(0.4) + 0.6x
To answer a, get 0.6x alone:
12 = 9(0.4) + 0.6x
12 = 3.6 + 0.6x
8.4 = 0.6x
There were 8.4 meters available to make wreaths
To answer b, get x alone
8.4 = 0.6x
14 = x
Diego could make 14 wreaths with the available ribbon
Hope this helps!
Given f(x) = 3VX and g(x) = 2x, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0) (a) (fog)(4) = _____ (Type an exact answer, using radicals as needed. Simplify your answer.)
The answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.
The given expressions are f(x) = 3√x and g(x) = 2x. We need to find the following expressions: (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0)
(a) (fog)(4) = f(g(4)) = f(2(4)) = f(8) = 3√8 = 3√(4*2) = 3√4 * √2 = 3*2*√2 = 6√2
(b) (gof)(2) = g(f(2)) = g(3√2) = 2(3√2) = 6√2
(c) (f of)(1) = f(f(1)) = f(3√1) = f(3) = 3√3
(d) (gog)(0) = g(g(0)) = g(2(0)) = g(0) = 2(0) = 0
Therefore, the answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.
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For the following polynomial one zero is given. f(x)=x^(4)+16x^(2)-225,-5i is a zero.
The zeros of the polynomial are -5i, √5i, -√5i.
The given polynomial is: f(x)=x⁴+16x²-225.
What is Zeros of a polynomial?Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.
The given zero is: -5i
To find the remaining zeros of the polynomial, we need to factor the polynomial.
We can factorize the polynomial as:
f(x) = (x² + 5i)(x² - 5i)
Finding Zeros:
Therefore, the remaining zeros of the polynomial are:
x = ±√5i
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Dilate Triangle XYZ: X (1,1) Y (2,2), and Z (3,0), (xy)-= (2x, 2y) centered at point X.
X’(. )
Y’(. )
Z’(. )
Using dilation, the scale factor here is 2,
X' = (2,2)
Y' = (4,4)
Z' = (6,0)
What do you mean by dilation?A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. The pre-image is the original figure, while the image is the new figure that emerges via dilatation. Two types of dilation exist:
Expansion describes an increase in an object's size.
Reduction in size is referred to as contraction.
In the given question,
The scale factor here is 2.
So, the new dilated triangle will be:
X' = (2,2)
Y' = (4,4)
Z' = (6,0)
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35+=7(_+_) i need help asp
Answer:
dddiejehehegeheheheh
suppose a house painter rests a 20-foot ladder against a building, then decides the ladder needs to rest 1 foot higher against the building.Will moving the ladder 1 foot towards the building do the job?If it needs to be 2 feet lower, will moving the ladder 2 feet away from the building do the trick? Let's investigate
Moving the ladder 1 foot towards the building will not be enough to raise it by 1 foot, and moving it 2 feet away from the building will not be enough to lower it by 2 feet.
The relationship between the distance the ladder is moved along the ground (run) and the resulting change in height (rise) is determined by the ladder's angle of inclination, which is constant. This angle can be calculated using trigonometry, specifically the tangent function:
[tex]angle = arctan(rise/run)[/tex]
For a 20-foot ladder, the angle of inclination is approximately 75.96 degrees. If the painter moves the ladder 1 foot towards the building, the run will decrease from 20 feet to 19 feet, which means the rise will decrease proportionally according to the tangent function:
[tex]new rise = tan(angle) * new run[/tex]
[tex]new rise = tan(75.96) * 19[/tex]
new rise ≈ 18.7 feet
So, moving the ladder 1 foot towards the building will only raise it by about 0.3 feet, not enough to achieve the desired 1-foot increase. Similarly, moving the ladder 2 feet away from the building will increase the run from 20 feet to 22 feet, causing the rise to increase proportionally according to the tangent function:
new rise = tan(angle) x new run
new rise = tan(75.96) x 22
new rise ≈ 21.3 feet
Therefore, moving the ladder 2 feet away from the building will only lower it by about 1.3 feet, not enough to achieve the desired 2-foot decrease.
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4. What is the simplest form of the expression?
√20+√45-√5
04√5
13 √5
5√5
Answer:
4√5
Step-by-step explanation:
To simplify √20+√45-√5, we need to look for factors that can be simplified under the square root. We can simplify 20 and 45 by factoring out perfect squares:
√20 + √45 - √5 = √(4×5) + √(9×5) - √5
= 2√5 + 3√5 - √5
= 4√5
Therefore, the simplest form of the expression is 4√5
Which two variables vary the most across these countries?
Which variable varies the least?
What does the profile plot tell us about sources of protein in
Denmark, Norway and Sweden?
The two variables that vary the most across these countries are "Animal Protein" and "Vegetable Protein."
The variable that varies the least is "Total Protein." The profile plot tells us that Denmark has the highest amount of animal protein, followed by Norway and then Sweden. However, Sweden has the highest amount of vegetable protein, followed by Denmark and then Norway. Overall, Denmark has the highest total protein, followed by Norway and then Sweden.
This suggests that Denmark relies more heavily on animal protein sources, while Sweden relies more heavily on vegetable protein sources. Norway falls somewhere in the middle, with a more balanced mix of animal and vegetable protein sources.
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Question 3 Which equation illustrates the commutative property of addition? (2+1)+3=(1+2)+3 (1+2)+3=1+(2+3) 2(1)+2(3)=2(1+3) 1+0=1 Moving to another question will save this response.
The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)
The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).
The commutative property of addition states that the order of the numbers does not matter when adding them together.
In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.
Here is the step-by-step explanation:
Identify the commutative property of addition, which states that a+b=b+a.
Look at the given equations and see which one follows the commutative property of addition.
The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.
Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).
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If tan t = 5/3 and 0
Cos t = ___
Csc t = ____
sec t = ____
cot t = ____
cost = 3/√34, csct = √34/5, sect =√34/3 , and cott = 3/5
explanation:-
The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t
we know sec² t - tan² t = 1
or, sec²t= 1 + tan²t = 1+(25/9) = 34/9
or, sect = √(34/9) = √34/3
or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t
now, also, csc²t - cot²t = 1
or, csc²t = 1+cot²t = 1+ 9/25 = 34/25
or, csc t= √34/5
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Simplify the expression (2x^(2)+5x+2)/(x^(2)+1x-6)-:(x^(2)+6x+8)/(2x^(2)-5x+2) and give your answer in the form of (f(x))/(g(x))
The simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).
To simplify the expression (2x^(2)+5x+2)/(x^(2)+1x-6)-:(x^(2)+6x+8)/(2x^(2)-5x+2), we need to find a common denominator and then subtract the numerators. The common denominator in this case is (x^(2)+1x-6)*(2x^(2)-5x+2).
So, the expression becomes:
((2x^(2)+5x+2)*(2x^(2)-5x+2)-(x^(2)+6x+8)*(x^(2)+1x-6))/((x^(2)+1x-6)*(2x^(2)-5x+2))
Simplifying the numerator, we get:
(4x^(4)-5x^(3)-4x^(2)+27x+4-1x^(4)-7x^(3)-14x^(2)-6x-8x^(2)-48x-48)/((x^(2)+1x-6)*(2x^(2)-5x+2))
Combining like terms, we get:
(3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2))
So, the simplified expression is (3x^(4)-12x^(3)-26x^(2)+21x-44)/((x^(2)+1x-6)*(2x^(2)-5x+2)), or (f(x))/(g(x)), where f(x)=3x^(4)-12x^(3)-26x^(2)+21x-44 and g(x)=(x^(2)+1x-6)*(2x^(2)-5x+2).
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