A small country emits 120,000 kilotons of carbon dioxide per year. In a recent global
agreement, the country agreed to cut its carbon emissions by 3.4% per year for the
next 6 years. In the first year of the agreement, the country will keep its emissions at
120,000 kilotons and the emissions will decrease 3.4% in each successive year. How
many total kilotons of carbon dioxide would the country emit over the course of the 6
year period, to the nearest whole number?
The total carbon dioxide that the country would emit over the course of the 6 year period is 661,505 kilotons.
What is the total carbon dioxide that would be emitted?The formula that can be used to determine the emission each year is:
Emission in the first year x(1 - rate of decrease)^number of years
Emission in the first year = 120,000
Emission in the second year = 120,000 x (1 - 0.034)^1 = 115,920
Emission in the third year = 120,000 x (1 - 0.034)^2 = 111,978.72
Emission in the fourth year = 120,000 x (1 - 0.034)^3 = 108,171.44
Emission in the fifth year = 120,000 x (1 - 0.034)^4 = 104,493.61
Emission in the sixth year = 120,000 x (1 - 0.034)^5 = 100,940.83
Sum of emissions from the first year to the sixth year = 661,505
This illustrates the concept of exponential decrease.
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Polynomial using Remainder Theorem and Factor Theorem checking using synthetic division.
x^4 - x^3 - 3x^2+ 4x + 2 ÷ (x + 2)
Answer: 2 / (x + 2)
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How many three-digit natural numbers have digits that sum to 13 and leave a remainder of 1 when divided by 4?
Radayna’s family put a new ladder on the side of their swimming pool. As shown below, the pool is 4 feet tall and the distance on the ground between the pool and where the ladder touches the ground is 3 feet.
What is the length, in feet, of the new ladder that Radayna’s family put on the side of their swimming pool?
A
25
B
12
C
7
D
5
The required length of the ladder using the Pythagorean theorem is (D) 5 ft.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c² = a² + b², where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.
So, the length of the ladder will be:
Pythagorean theorem: c² = a² + b²
Now, substitute the values and calculate as follows:
c² = a² + b²
c² = 4² + 3²
c² = 16 + 9
c² = 25
c = √25
c = 5ft
Therefore, the required length of the ladder using the Pythagorean theorem is (D) 5 ft.
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What expression is equivalent to -2/5
Answer:
2/-5
Step-by-step explanation:
Part A
ANALYZE Reece says that if you solve a system of equations using elimination by addition and the result is 0=2, then the solution of the system is (0,2). Select a counterexample to show that her statement is false.
A)
x+y = 1
-x-y = -1
B)
x+y=1
x-y=1
C)
x+y=1
-x-y=1
D)
x+y=-1
-x-y=-1
Part B
Justify your argument.
This system of equations has Select Choice
The counter example for the system of equation is given by x + y = 1 ,
-x - y = 1 has the result 0 = 2 but ( 0, 2 ) is not the solution of the equation. It proves statement is false.
As given in the question,
Form the given system of equations , using elimination method to get the solution of the equation which shows the result 0 = 2 is as follow:
a. x + y = 1
- x - y = -1
0 = 0
Not the required result.
b. x + y = 1
x - y = 1
2x = 2
Not a required result.
c. x + y = 1
- x - y = 1
0 = 2
Required result.
Analyze : substitute x = 0 and y = 2 in any one equation
0 + 2 = 1
or -0 -2 = 1
Both the equations proves that statement is false.
d. x + y = -1
-x -y = -1
0 = -2
Not a required result.
Therefore, the system of equation of option c. x + y = 1 , -x - y = 1 has the result 0 = 2 and proves it is the false statement.
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1. what is an equation for the line shown?
2. graph the line with equation y=1/3x-5
Answer:
y= -1/2x+2
Start at -5 then go up 1 then right 3
Step-by-step explanation:
Graph the line y=-2/3 x+8 with appropriate labels and scale. Plot the point on the line that represents the solution to the question in part D.
The graph of the line y = (-2/3)x + 8 with appropriate labels and scale has been plotted
The equation of the line is given that
y = (-2/3)x + 8
The given equation is in slope intercept form of the line
y = mx + b
Where m is the slope of the line
b is the y intercept
y is the y coordinate value
x is the x coordinate value
The slope of the line = -2/3
The slope of the line is the change in y coordinates with respect to the change is x coordinates of the line
y intercept is 8
Substitute the value of x in the equation and find the value of y
Plot the graph using the equation
Therefore the graph of the line has been plotted
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Find 4C – 3D. gradpoint help algebra 2
Answer:
-11 in top left, 5 in top right, -12 in bottom left, and -2 in bottom right.
Step-by-step explanation:
4C is the matrix C with all its elements multiplied by 4. Same logic applies for 3D. Then subtract each element of 3D from its counterpart of 4C which gives you the final answer. A big shortcut however if you have a TI-84 Plus Graphing Calculator is to use second x^-1 for matrices to edit the matrices and do matrix operations.
Solve a system by elimination.
8x-2y=2
4x-y=2
Answer:
No solution.
Step-by-step explanation:
You would multiply -2 to the 2nd equation and you would get -8x+2y=-2 and you would add that to 8x-2y=2 and when you would add all of them would eliminate or cross each other out, showing no solution.
At the district competition for 5th grade jump-roper of the year, the following number of jumps were recorded per student:
203, 245, 237, 233, 90, 100, 100, 277, 265, 264, 265, 285, 288, 291, 291, 290, 300, 224, 200, 257, 290, 279, 266, 288
What is the mean number of jumps, rounded to the nearest hundredth?
What is the median number of jumps?
At the district competition for 5th grade jump-roper of the year, the mean number of jumps, rounded to the nearest hundredth is 242.83 and the median number of jumps is 265
The mean can be calculated as follows:
Observations (the number of jumps each student without pausing was counted); There were 24 observations
Mean is calculated by adding all of the observations together.
Mean = (203 + 245 + 237 + 233 + 90 + 100 + 100 + 277 + 265 + 264 + 265 + 285 + 288 + 291 + 291 + 290 + 300 + 224 + 200 + 257 + 290 + 279 + 266 + 288)/24
Mean = 5828/24
Mean = 242.83
to figure out the median;
The observations must first be put into either ascending or descending order.
Ordered in descending order
90, 100, 100, 200, 203, 224, 233, 237, 245, 257, 265, 265, 265, 266, 277, 279, 285, 288, 288, 290, 290, 291, 291, 300
Given that there have been 24 observations (an even number).
The middle number, 265 and 265 at the midway of items 12 and 13, is used to calculate the median.
The average of these figures is then determined.
Median = 1/2 (265 + 265)
Median = 265
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Which of the following proves these triangles are congruent
A. ASA
B. Not enough information
C. AAS
Answer:
not enough information
What is the product of -2/7 and -3/7 ?
Answer:
6/49
Step-by-step explanation:
-2/7 * -3/7 = (-2 * -3) / (7*7) = 6/49
write an equation for the line, in point-slope form, that passes through the following points (5,-5) (-1,-1)
Answer:
[tex]y+5=-\frac{2}{3}(x-5)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{-1-(-5)}{-1-5}=-\frac{2}{3}[/tex].
Using the point [tex](5,-5)[/tex], the equation is [tex]y+5=-\frac{2}{3}(x-5)[/tex].
help please! I dont understand! :(
brainliest
Can someone pls help I’ll give brainliest and tons of points
Answer:12,-8
Step-by-step explanation:
3 to the right 1 down
Using the information in the Box-and-Whisker plot below, what is the 2nd Quartile?
A. 5
B. 12.5
C. 20
D. 27.5
The answer would be (C) 20.
Answer:
The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.
In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.
Option B, 12.5, is the correct answer.
Step-by-step explanation:
two students found the slope of the line shown. tavion used the points (-1,-3) and (0,-1) while jess used the points (3,5) and (0,-1). which of the following is a true statment
All the statements are true.
What is meant by slope of a line?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Why is the formula for slope?Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilizing the equation of a line.
A. The triangles drawn between each pair of points are similar.
B. The ratio of y2-y1/x2-x1 will be the same for Tavion and Jess.
C. Both students should find a slope of .
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A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length at a rate of 3 cm/s. At what rate is the area of the rectangle increasing after 23 s?
Answer:
The area of the rectangle is increasing at a rate of 54 cm2/s.
Step-by-step explanation:
The speed of sound in ocean water is 1,500 m/sec. If scientist use
sonar to determine the depth of the ocean and find it takes 20 seconds
for the sound wave to return to the ship, how deep is the ocean at that
point?
O15,000 meters
O 3,000 meters
O 30,000 meters
O 1,500 meters
Speed
1500 m/sec
Time 20 seconds
Given speed and time, you can calculate distance.
Distance = Time * Speed
Distance = 1500 * 20
Distance = 15000 * 2
Distance travelled by the sonar = 30,000 meters
Since its bouncing off the ocean floor and returning, divide by 2 to find one way distance.
Depth 15,000 meters
Hope this helps :)
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- Jeron
What is this as an algebraic expression for this:
12¾ less than the product of 7 and a number x
In the picture, I need help with #14.
Answer:
7x -(12¾)
Step-by-step explanation:
You want the algebraic expression for "12¾ less than the product of 7 and a number x".
TranslationThe product of 7 and x is represented as ...
7x
If you want 12¾ less than that, then you subtract 12¾.
7x -12¾ . . . . . . . the desired expression
__
Additional comment
A "product" is what we call the result of multiplication. The operation of multiplication can be indicated several ways. If there is no ambiguity, the most common way to show multiplication is to write the values next to each other without any symbol.
7x . . . . 7 times x
Sometimes, it is helpful to put the values in parentheses:
(7)(x)
A multiplication symbol can be used, if desired.
7·x
(7)×(x)
When showing multiplication using the symbol ×, care must be taken to differentiate it from the symbol x, especially if confusing these symbols will give a different result than desired. (Sometimes, when the symbol × is unavailable, an 'x' is used instead.)
Occasionally, you will see a dot on the baseline used as a multiplication symbol. Likewise, you may see a centered dot intended as a decimal point.
7.x . . . . . 7 times x
7·3x . . . . 7 and 3 tenths times x (maybe)
When different numbers are involved, the use of a baseline dot for multiplication, and a centered dot for a decimal point can be confusing.
7.3.x . . . . could be (7)(3)(x) or (7.3)(x)
7·3.x . . . . could be (7)(3)(x) or (7.3)(x)
In general, a notation should be chosen so as to reduce any ambiguity to a minimum and communicate in a way that the audience understands.
When a mixed number is involved, as above, it can be useful to enclose it in parentheses, so it is not confused with the product of an integer and a fraction. The font used to express the fraction can be chosen to help reduce the ambiguity.
If I don’t get this answer I will fail my math class and get my phone taken so someone pls help me with this
2
x² + yz use x = 4, y = 6 and z= 3.
Answer: 50
Step-by-step explanation:
Assuming your expression is 2x^2+yz, just plug the numbers in: 2*4*4+6*3 = 32 +18 = 50
Plugging in just means looking at the values the probme give syou for variables (x=4 for example) and replacing the variable with that number in the expression you want to find the value of.
Type an equation for the following pattern.
y=-2 x+[?]
The equation that satisfies the given pattern is y = -2x
Given,
x ; 1, 2, 3, 4, 5
y ; -2, -4, -6, -8, -10
The pattern; y = -2x + ?
We have to find an equation that satisfies the given pattern;
Here,
Take k as ?
Then,
y = -2x + k
Where,
x = 1 and y = -2
Now,
-2 = -2 × 1 + k
-2 = -2 + k
k = -2 + 2 = 0
k = 0
That is,
The equation will be like, y = -2x
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22 divided by (7.8-|-3 2/5|)x(-3) to the power of 2 - 9 1/5
Answer:
35.8
Step-by-step explanation:
It looks like you want the value of ...
[tex]\dfrac{22}{7.8-\left|-3\dfrac{2}{5}\right|}\times(-3)^2-9\dfrac{1}{5}[/tex]
EvaluationSimplifying and writing the numbers as decimal values, we have ...
[tex]\dfrac{22}{7.8 -3.4}\times9-9.2=\dfrac{22}{4.4}\times9-9.2=5\times9-9.2\\\\=45-9.2=\boxed{35.8}[/tex]
Determine the measure of angles #1-#20 in the following figure.
Line AB is parallel to Line CD.
Line EF is parallel to Line GH.
Angle #5 = 63⁰
Angle #8 = 80⁰
The measure of all the angles from 1 to 20 is obtained from the concepts related to transversal lines.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
Given, AB || CD and EF || GH.
m∠5 = 63° and m∠8 = 80°.
Now from all the concepts of vertically opposite angles are equal,
pair of alternate angles are equal, the sum of all the sides of interior angles in a triangle is 180°, pair of linear angles is 180°, measure of an exterior angle in a triangle is the sum of two opposite interior angles we obtain that,
m∠1 = 37°, m∠2 = 63°, m∠3 = 80°, m∠4 = 37°, m∠5 = 63°, m∠6 = 80°,
m∠7 = 100°, m∠11, = 63°, m∠12 = 80°, m∠13 = 47°. m∠14 = 63°, m∠15 = 80°,
m∠16 = 47°, m∠17 = 110°, m∠18 = 70°, m∠19 = 110°, m∠20 = 70°.
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a.) consider an n x n matrix A with the property that the row sums all equal the same number s. show that s is an eigenvalue of A. (hint: find an eigenvector)
b.) consider n x n matrix A with the property that the columns sums all equal th same number s. show that s is an eigenvalue of A.
s is an eigenvalue of A.
What is eigenvalue?Eigenvalues are a unique collection of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar component.
A =[tex]\left[\begin{array}{ccc}a_{11} &a_{12} &\\a_{21} &a_{22} &\\&\end{array}\right][/tex][tex]\left[\begin{array}{ccc}f1\\f2&\\\end{array}\right][/tex]
[tex]f_{1} = a_{11} + a_{12}[/tex]
[tex]f_{2} = a_{21} + a_{22}[/tex]
We see that if (A - sI) is unique, then s is an eigenvalue of A. ( I is the identity matrix). Keep in mind that if every column in A adds up to s, then the total of the resultant vector is zero when s is subtracted from one item.
We know that the image of a matrix is the span of its column vectors. Since all the column vectors are members of the above-mentioned subspace, the image of the transformation is contained in this subspace. Thus, the rank of our n x n matrix is less than n. Thus, (A - sI) is singular.
Thus, s is an eigenvalue of A.
Transposition preserves eigenvalues (this is actually a profound statement, in a way). If A has columns adding to s, then A^T has rows adding to s. Let v be the column vector of 1's.
A^T * v = s * v.
Thus, s is an eigenvalue of A^T
Thus, s is an eigenvalue of A.
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(18 - 4) to the power of 2
Answer:
196
Step-by-step explanation:
(18-4)^2
14^2 or 14x14
14x14=196
an order calls for 500 ml of heparin is to be administered over 18 hours. the tubing size delivers 15 drops per gtt/ml. what is the drip rate?
If the tubing size delivers 15 drops per gtt/ml, then the drip rate is 7 gtt/min.
What is the Drip rate and How can u calculate it?
This easy calculation can be used to determine the IV drip rate: Total Volume (mL)/Time (min) x Drop Factor (gtt/mL) equals IV Drip Rate (gtt/min) When given the volume to be injected, the drip rate, and the drop factor, this equation can also be rearranged to determine the amount of time needed for an infusion.
Based on how many drops (gtt) are given to the patient each minute, the rate of an intravenous infusion is described as having an IV drip rate. The amount that needs to be infused in total, the type of tubing used (microdrip vs. macrodrip), and the length of time the infusion is scheduled to run all have an impact on this.
We will use the drip rate formula
Total Volume(mL)/Time (min) x Drop Factor(gtt/mL) = IV Drip Rate (gtt/min)
18 hours = 18 × 60min
= 1080 mins
IV Drip Rate = 500/1080 × 15
= 7 gtt/ min
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A 4-sided polygon is classified as a quadrilateral.
True
False
Answer:
TRUEEEEEEEEEEEEEEEEEE
Step-by-step explanation:
Write and solve the inequality: Sixty-three is at most triple the difference of double a number and three
Answer: n=30
Step-by-step explanation:
first, you subtract 3, as 'and' refers to addition and the opposite is subtraction. this gives you 60.
then you divide by 2, which gives you 30.
if you want, you can input 30 into the equation the situation creates, which is 63 = 2n + 3. input 20 makes 2(30) + 3, which is 60 + 3, which is 63.