From the image
\(\begin{gathered} y_2=7 \\ y_1=-8 \\ x_1=2 \\ x_2=-1 \end{gathered}\)\(\begin{gathered} \text{The slope is given as } \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{7-(-8)}{-1-2} \end{gathered}\)\(m\text{ =}\frac{15}{-3}=\text{ -5}\)A media personality argues that global temperatures are not rising because every year an increase is reported such as 0.09 degrees Celsius. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:
1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.
2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.
3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.
In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.
Write the equation in slope-intercept form
through (-2, 1) parallel to y = -3x+1
Answer:
A parallel line has the same slope, but is translated away from the line it is parallel to. Let's create an equation using what we have:
−
1
=
−
3
(
−
2
)
+
b
−
1
=
6
+
b
−
7
=
b
y
=
−
3
x
−
7
Hope this helped!!
Find the value of X.
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
-2x - 6 = 40
Add 6 to both sides
-2x = 40 + 6
-2x = 46
Divde both sides by (-2)
x = 46/(-2)
x = -23
PLEASE WRITE THE EQUATION THAT IS WHAT IT IS ASKING!! THE EQUATION IS IN SLOPE INTERCEPT FORM!!
Answer:
y = -3x-5
Step-by-step explanation:
11. Martin's suitcase has a volume of 1,080 cubic inches. Lily's suitcase measures 9 inches wide, 13 inches long, and 21 inches high. What is the combined volume of the two suitcases?
Answer: 3,348 cubic inches
Step-by-step explanation:
1. Since we know that volume= length x width x height, then we can plug our values into this equation.
2. So, we would do volume= 9 x 12 x 21.
3. 9 x 12 = 108, and 108 x 21 =2,268.
4. Now that we have both of the volumes, we have to add them together.
5. 1,080 + 2,268 = 3,348
6. The combined volume is 3,348 cubic inches.
Jasenio is shooting target practice with a bow and arrow. His target is a paper rabbit that runs along a track. The track is 50 meters away from Jasenio and he estimates that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him. At what true bearing should Jasenio aim his bow and arrow?
a) 3.49°
b) 11.31°
c) 78.46°
d) 78.69°
The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°
How to apply Trigonometric Ratios?
We have different trigonometric ratios such as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.
This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;
tan θ = 10/50
where θ is the true bearing angle. Thus;
tan θ = 0.2
θ = tan⁻¹0.2
θ = 11.31°
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!
A washer and dryer cost a total of 928$. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer:
Cost of Washer = $696
Cost of Dryer = $232
Step-by-step explanation:
Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.
Put the equation together, so we can add the x variables together.
3x + x = 4x
The total cost will be what the '4x' is equal to.
4x = 928
Going back to algebra, we solve the equation by dividing both sides by 4.
x = 232
Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.
3x
3(232) = 696.
To check the answer, we can add them together to make sure we get the total cost.
696 + 232 = 928
I'm not good ar graphs requesting assistance...
Answer:
Seven erasers cost $3.50
Hope this helps :)
Answer:
7 erasers cost 3.50
Step-by-step explanation:
I need help with this please
Point located at each location: 1) A 2) I 3) W 4) H 5) X 6) G 7) J 8) N 9) U 10) M 11). Ordered pairs are: B(2,8) 12) E(0,0) 13) T(3,3) 14) Q(8,7) 15) Y(7,6) 16) R( 9,8) 17) F(9,0) 18) S(3,6) 19) C(6,7)
Describe Ordered pair?
An ordered pair is a pair of mathematical object elements, such as numbers or other mathematical elements, where the order in which the object elements are listed is important. The ordered pair is usually written in the form (a, b), where 'a' represents the first element or coordinate, and 'b' represents the second element or coordinate.
In the context of the Cartesian coordinate system, an ordered pair represents a point in two-dimensional space, where the first element or coordinate represents the horizontal position on the x-axis and the second element or coordinate represents the vertical position on the y-axis. The order of the elements in an ordered pair is crucial because (a, b) is different from (b, a) and represents a different point in two-dimensional space.
Point located at each location is:
1) A
2) I
3) W
4) H
5) X
6) G
7) J
8) N
9) U
10) M
The ordered pair for given points is:
11) B(2,8)
12) E(0,0)
13) T(3,3)
14) Q(8,7)
15) Y(7,6)
16) R( 9,8)
17) F(9,0)
18) S(3,6)
19) C(6,7)
The graph for remaining is questions is attached below.
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which point from the equation would you use? y-7=3(x+9)
Another point on the line is (-9, 7). Ultimately, the choice of which point to use depends on the context or specific requirements of the problem you are solving.
To determine which point to use from the equation y - 7 = 3(x + 9), we need more information.
The equation provided represents a linear equation in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Without additional context or specific instructions, we can choose any point that satisfies the equation to use as a reference.
For example, if we let x = 0, we can solve the equation for y:
y - 7 = 3(0 + 9)
y - 7 = 3(9)
y - 7 = 27
y = 27 + 7
y = 34
So, one point on the line is (0, 34).
Alternatively, if we let x = -9, we can solve the equation for y:
y - 7 = 3(-9 + 9)
y - 7 = 3(0)
y - 7 = 0
y = 7
So, another point on the line is (-9, 7).
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The model y=1.8x−76.9 represents the relationship between the temperature (°F) and the number of ice cream cones sold. Using the linear regression model, approximate the number of ice cream cones sold when it is 85°F. Round your answer to the nearest whole number.
When it is 85°F, they will sell approximately _ ice cream cones.
Graph of linear equation will be always straight line.
Number of ice cream cones sold be 76.
The relationship between the temperature (°F) and the number of ice cream cones sold is given by model,
\(y=1.8x-76.9\)
Where x represent temperature and y represent number of ice cream cone sold.
When temperature is 85°F , it means that , x = 85°F
So, \(y=1.8*85-76.9\\\\y= 76.1\)
Thus, number of ice cream cone sold is to be 76.
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BE is a diameter of the circle, ABC is a tangent to the circle. Find the size of angle ABD. Find the size of angle DEB
Answer: both 66
Step-by-step explanation:
A) 66
B) 66
report mean explanation with an example please please someone answer me please i want someoone to help me please please i will put brainliest answer and thank him and vote 5 stars please answer me please
please help!! need it fast, will give brainliest!! and pls show work !!
Find the measure of angle AEB
Answer:
An acute angle
Step-by-step explanation:
An acute angle is smaller than an obtuse ad right angle.
hope this helps and hope it was right 'cause I really don't know what you meant. :)
Which phrase matches the algebraic expression below?
2(x - 7) + 10
Answer:
Combining like terms
Step-by-step explanation:
Use the scenario to choose the correct answers. Complete Steps 1-2 in order.
A company records its sales for each year.
9. Step 1: Find the equation of the line of regression
y=ax+b
y=3.7 x+8.5
y=8.5 x+3.7
y=-8.5 x+3.7
y=-3.7 x+8.5
10. Step 2: Use the regression line as a model to estimate the sales of the company in 2022.
71.7 million dollars
64.3 million dollars
85 million dollars
38.1 million dollars
9. The regression line is given as follows: y = 8.5x + 3.7.
10. The estimate for 2022 is given as follows: 71.7 million dollars.
How to obtain the regression line?The regression line is obtained inserting the points of the table into a linear regression calculator.
From the table, the points are given as follows:
(1, 13), (2, 19), (3, 31), (4, 36), (5, 47).
(considering x as the number of years since 2014).
Inserting these points into a calculator, the equation is given as follows:
y = 8.5x + 3.7.
2022 is 8 years after 2014, hence the estimate is given as follows:
y = 8.5(8) + 3.7 = 71.7 million dollars.
(numeric value at x = 8, replace the lone instance of x by 8).
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6.3.67 x 10-3 is equivalent to:
A. 0.03267
B. 3.35.7
C. 0.003267
D. 3267
Select all the correct locations on the table.Which expressions are accurately described?3(7x² - 4)25y2-16(4x + 5)²(2y + 1)(y + 6)the product of 3 and the difference of 7times x squared and 4the square of the difference of 25 timesy and 16the sum of 4 times x squared and 5the product of the sum of 2 times y and1 and the sum of y and 6
We have:
- the product of 3 and the difference of 7 times x squared and 4 is:
\(3(7x^2-4)\)Correct.
- the square of the difference of 25 times y and 16 is:
\((25y-16)^2\)So, not correct.
- the sum of 4 times x squared and 5 is:
\(4x^2+5\)So, not correct.
- the product of the sum of 2 times y and 1 and the sum of y and 6 is:
\((2y+1)(y+6)\)Correct.
Answer:
The first one and the fourth one
What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed
The number of pavers required is 961.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
Given data
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.
We have to determine how many pavers are needed
We know that area of a regular hexagon
A = (3√3)/2 a^2
= (3√3)/2 〖(6)〗^2
= (3 x 1.732)/2 x 36
= 93.528 sq.inches
Now area of rectangle
= l x w
= 24 x 26 x (12)2 (1feet = 12 inches)
= 89856 sq.inches
Now pavers required
= 89856/93.528
= 960.73
= 961
Therefore the number of pavers required is 961.
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The first term of an arithmetic sequence is equal to 5 and the common difference is 10. Find the formula for the value of the nth term.
The formula for the nth term of the arithmetic sequence as in the task content is; a(n) = 5 + (n - 1)10.
Arithmetic SequenceIt follows from the task content that the nth term of the arithmetic sequence in which case, the first term is 5 and the commonwealth difference is 10 is to be determined.
Recall; The nth term of an arithmetic sequence is given by;
a(n) = a(1) + (n - 1)d
where, a(1) = First term = 5.
and, d = Common difference = 10.
Hence, the nth term of the arithmetic sequence can be determined by the formula;
a(n) = 5 + (n - 1)10.
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The height of a rectangular box is 7 ft. The length is 1 ft longer than thrice the width x. The volume is 798 ft³.
(a) Write an equation in terms of x that represents the given relationship.
The equation is
The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)
Let's break down the information given:
Height of the rectangular box = 7 ft
Length of the rectangular box = 1 ft longer than thrice the width (x)
Volume of the rectangular box = 798 ft³
To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.
The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.
Given that the height is 7 ft, we can substitute this value into the equation.
Volume = (Length) * (Width) * (7)
Now, let's focus on the length. It is described as 1 ft longer than thrice the width.
Length = 1 + (3x)
Substituting this value into the equation, we have:
Volume = (1 + (3x)) * (Width) * (7)
Since the volume is given as 798 ft³, we can set up the equation as follows:
798 = (1 + (3x)) * (Width) * 7
Simplifying further, we get:
798 = 7 * (1 + 3x) * (Width)
Dividing both sides of the equation by 7, we have:
114 = (1 + 3x) * (Width)
Therefore, the equation in terms of x that represents the given relationship is:
114 = (1 + 3x) * (Width)
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Maria has 8 more scarves than Lucy Lucy has 8 scarves. How many scarves does Maria have, write an equation?
The equation M = 8 + 8 represents the given information. Maria has 16 scarves.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's let "M" represent the number of scarves that Maria has.
According to the problem, "Maria has 8 more scarves than Lucy." We know that Lucy has 8 scarves. So, Maria has 8 more than that.
We can represent this information in an equation:
M = 8 + 8
We add 8 to Lucy's 8 scarves to get the total number of scarves that Maria has, which is 16.
So, Maria has 16 scarves.
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The required Maria has 16 scarves, and the expression models the situation is given as M = 8 + L.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's use the variable "M" to represent the number of scarves that Maria has. Since Maria has 8 more scarves than Lucy, and Lucy has 8 scarves, we can write an equation as,
M = 8 + L
where L is the number of scarves that Lucy has. Substituting L = 8 into this equation, we get:
M = 8 + 8
M = 16
Therefore, Maria has 16 scarves.
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A number, one-fourth of that number, and one-third of that number are added. The result is 38. What is the original number?
Answer:
24
Step-by-step explanation:
Let 12x represent the original number.
One fourth of that number can be represented by 3x, and one third of the number can be represented by 4x.
Create an equation that sets this equal to 38, and solve for x:
12x + 3x + 4x = 38
19x = 38
x = 2
The original number is represented by 12x, so plug in 2 as x:
12(2)
= 24
So, the original number is 24.
plllzzz help!! 20 points
Planes A and B are shown.
m
n
B
MA
If a new line, p, is drawn parallel to line /, which
statement is true?
O
Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line /
O Line p must be drawn in the same plane as line n.
The line which is on the same plane can be parallel, two lines are never parallel when they are in different planes, so option C is correct.
What is a line?An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
The given planes are A and B,
A new line, p, is drawn parallel to line l,
Line l in the diagram is located on plane A. Line p must be drawn on plane A in order to be parallel to line l. As a result, line p, which is located on plane B, will be perpendicular to line n and parallel to lines l and n.
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The image of the remaining question is attached below.
What is -20/2(7 2/3)
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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Select all of the true statements about the standard deviation of a quantitative variable. 1. Standard deviation is resistive to unusual values. 2.The standard deviation of a set of values is equal to 0 if and only if all of the values are the same. 3. Standard deviation is never negative. 4.Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. 5.If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation. 6.Standard deviation represents how far a group of values are from the mean of those values, on average.
Answer:
Considering the first statement
Standard deviation is resistive to unusual values
This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean
Considering the second statement
The standard deviation of a set of values is equal to 0 if and only if all of the values are the same.
This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.
Considering the third statement
Standard deviation is never negative.
This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.
Considering the fourth statement
Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation
This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean
Considering the fifth statement
If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation.
This statement is false because , let take an example
x -4 - 3 0 3 4
Generally the mean is mathematically evaluated as
\(\= x = \frac{\sum x_i }{n}\)
=> \(\= x = \frac{-4+ (- 3)+ 0 + 3 + 4 }{5}\)
=> \(\= x = 0 \)
Generally the standard deviation is mathematically evaluated as
\(\sigma = \sqrt{\frac{\sum (x_ i - \= x )^2}{y} }\)
\(\sigma = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (0 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{5} }\)
=> \(\sigma = 3.16 \)
Now when zero is removed the standard deviation is
\(\sigma_1 = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{4} }\)
=> \(\sigma_1 = 3.54 \)
Since \(\sigma \ne \sigma _1\) the above statement is false
Considering the sixth statement
Standard deviation represents how far a group of values are from the mean of those values, on average.
This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.
Step-by-step explanation:
Find the slope of the tangent line to the curve defined by 4x2+5xy+y4=370
at the point (−9,−1)
Answer:
The slope of the tangent line to the curve at the given point is -11/7.
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient (slope) of a curve. At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
Given function:
\(4x^2+5xy+y^4=370\)
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
Begin by placing d/dx in front of each term of the equation:
\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)
Differentiate the terms in x only (and constant terms):
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)
Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:
\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Use the product rule to differentiate terms in both x and y.
\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)
\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)
Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:
\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)
To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)
\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)
Therefore, slope of the tangent line to the curve at the given point is -11/7.
Find the product of 21 and the difference between one whole number 1/2 and -1/2
The product of 21 and the difference between one whole number 1/2 and -1/2 is; 42
What is the product of the two numbers?We want to find the product of 21 and the difference between one whole number 1/2 and -1/2. This can be expressed as;
21 * (1¹/₂ - (-¹/₂))
Let us first solve the bracket out using the order of operations rule named PEMDAS which stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction to get;
1¹/₂ - (-¹/₂)
= 1¹/₂ + ¹/₂
= 2
Thus;
21 * (1¹/₂ - (-¹/₂)) = 21 * 2
= 42
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