The total area is 0.0102.
The area to the left of z1=−2.575 is given by the standard normal cumulative distribution function as:
P(Z < -2.575) = 0.0051 (rounded to four decimal places)
The area to the right of z2=2.575 is the same as the area to the left of -2.575, since the standard normal curve is symmetric about the mean:
P(Z > 2.575) = P(Z < -2.575) = 0.0051
The total of the areas under the standard normal curve to the left of z1=−2.575 and to the right of z2=2.575 is:
0.0051 + 0.0051 = 0.0102
Therefore, the total area is 0.0102.
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How do you dilate a triangle by 2 3?
A dilation is a transformation that changes the size of an object by a scale factor. To dilate a triangle by a scale factor of 2/3, you will need to follow these steps:
Identify the center of dilation: The center of dilation is a fixed point around which the dilation takes place. This point is usually denoted by the letter "C".Identify the vertices of the triangle: The vertices of the triangle are the points that determine the shape and position of the triangle.Calculate the new coordinates of the vertices: To dilate a triangle by a scale factor of 2/3, you need to multiply the coordinates of each vertex by the scale factor. For example, if the coordinates of a vertex are (x, y), the new coordinates will be (2/3x, 2/3y).Plot the new coordinates: Once you have calculated the new coordinates of the vertices, you can plot them on the coordinate plane to create the dilated triangle.Connect the new points to form the new triangle: Connect the new points with lines to form the new triangleNote that the center of dilation C and the dilation factor are the same for all points on the triangle, also if the dilation factor is less than 1, the image is smaller than the original and if the dilation factor is greater than 1, the image is larger than the original.
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The complete question is -
How do you dilate a triangle by a scale factor of 2/3?
Two Places P and q have thesame Longitude. Their Latitude are 15°N and 36°s, Draw diagrams and calculate the great circle distance q
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is axis of rotation equal about the center at every angle. Every set of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetrical about the center at every angle.
Here,
The distance between Sydney and Cape Town's longitudes is 151.13° and 18.22°, respectively, for the little circle, which equals 533.669 km. Sydney to Capetown distance in a straight line is
151.13∘−18.22∘=132.91∘
Straight line distance from Sydney to Capetown
d= √53372+53372−2×5337×5337× cos132.91∘
= 9785 km
θ=cos⁻¹ (6400²+6400²−9785² / 2 x 6400×6400)=99.72∘
Great Circle route from Sydney to Cape Town
=>πR / 180∘ ×θ
=> 6400π180∘×99.72∘
=> 11138.831…≈11139 km
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
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a bag contains 3 red marbles and 4 blue marbles. a marbleis taken at random from the bag and replaced. another marble is taken rom the bag. work out the probability that the 2 marbles taken from the bag are the same colour
The probability that the 2 marbles taken from the bag are the same color is 25/49.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of red marbles = 3
Number of blue marbles = 4
Total marbles = 7
Now,
The probability of taking two blue marbles consecutively with replacement.
= 4/7 x 4/7
= 16/49
The probability of taking two red marbles consecutively with replacement.
= 3/7 x 3/7
= 9/49
Since the two marbles of the same color can be blue or red.
The probability that the 2 marbles taken from the bag are the same color.
= 16/49 + 9/49
= 25/49
Thus,
The probability that the 2 marbles taken are the same color is 25/49.
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Which equation represents a line perpendicular to the line with equation 2x + 3y = 12?.
The equation of the line perpendicular to 2x + 3y = 12 will be y = 3x/2 + c where c ∈ R.
The equation of the line given here is 2x + 3y = 12
Now rearranging it to the slope-intercept form we get
3y = -2x + 12
or, y = -2x/3 + 4
Now any 2 lines are perpendicular when the product of their slopes results in -1.
Hence, let the equation of the line perpendicular to the given line be
y = mx + c, where m is the slope of the line and c is the intercept.
Hence,
-2m/3 = -1
or, m = 3/2
Hence the equation of the line will be
y = 3x/2 + c where c ∈ R
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(a) The area of a rectangular parking lot is 8428 m²
If the width of the parking lot is 86 m, what is its length?
Length of the parking lot: _ m
(b) The perimeter of a rectangular pool is 376 m.
If the length of the pool is 99 m, what is its width?
Width of the pool: _m
Answer:
a) Length of the parking lot: 98 m
b) Width of the pool: 89 m
Step-by-step explanation:
a) The formula for the area of a rectangle is [tex]A=lw[/tex].
We need to evaluate the length. Lets solve for [tex]l.[/tex]
[tex]A=lw[/tex]
Divide both sides of the equation by [tex]w[/tex].
[tex]\frac{A}{w} =l[/tex]
We are given
[tex]A=8428\\w=86[/tex]
Lets evaluate [tex]l[/tex].
[tex]\frac{8428}{86}=l[/tex]
[tex]l=98[/tex]
b) The formula for the perimeter of a rectangle is [tex]P=2l+2w[/tex].
We need to evaluate the width. Lets solve for [tex]w[/tex].
[tex]P=2l+2w[/tex]
Subtract [tex]2l[/tex] from both sides of the equation.
[tex]P-2l=2w[/tex]
Divide each term by 2.
[tex]\frac{P}{2} -\frac{2l}{2} =\frac{2w}{2}[/tex]
Simplify.
[tex]w=\frac{P}{2}-l[/tex]
We are given
[tex]P=376\\l=99[/tex]
Lets evaluate [tex]w[/tex].
[tex]w=\frac{376}{2}-99[/tex]
[tex]w=188-99[/tex]
[tex]w=89[/tex]
Answer:
a) 98m , b) 89m
Step-by-step explanation:
(a) Given,
The area of a rectangular parking lot is 8428 m²width of the parking lot is 86 mTo Find : Length of the Parking lot
Length of a rectangle shape can be derived by the formula,
[tex]l = \frac{A}{w}[/tex]
[tex]l = \frac{8428}{86}[/tex]
[tex]l = 98m[/tex]
Hence , the length of a rectangular parking lot is 98m
(b) Given ,
The perimeter of a rectangular pool is 376 mlength of the pool is 99 mTo Find : The width of the rectangular pool
We take the width as variable 'x'
Now we plug it into the perimeter of a rectangle equation
[tex]376 = 2(99 + x)[/tex]
Using distributive property we,
[tex]376 = 198 + 2x[/tex]
We now flip the equation
[tex]2x + 198 = 376[/tex]
[tex]2x = 376 - 198[/tex] ( Transposing into the right hand side)
[tex]2x = 178[/tex]
[tex]x = \frac{178}{2}[/tex]
[tex]x = 89[/tex][tex]m[/tex]
Hence , the width of the rectangular swimming pool is 89m
In the triangle below, what is the side adjacent?? HELP
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
The following equations are equivalent:
2 + x = 5
x + (negative 4) = 7
Negative 5 + x = negative 2
All of these three equations are equivalent because they all represent the same mathematical relationship between x and other numbers. The variable x is the same in each equation. We can see this by applying the same operation on both sides of the equations, and the variable x will cancel out and the two sides will be equal.
What is midpoint formula Class 11?
The midpoint formula helps us to find the midpoint of a line given to us on a coordinate system.
The coordinate system in geometry is a plane space in which points are located using paired numerical values called coordinates. It is of two types Cartesian coordinate system and polar coordinate system
The cartesian coordinate system is further divided into majorly two parts i.e., 2-Dimensional and 3- dimensional systems. A 2-D system has 2 axis X and Y whereas a 3-D system has X, Y, and Z axes. The plane is divided into 4 quadrants
The midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in a 1:1 ratio.
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-3(2x-1)≤x-18 pls solve w/ explanation and steps
Is y 10 a linear function?
A function y = 10 a not linear function
We know that the general form of linear function is f(x) = a + bx
A linear function has one independent variable (for above function x) and one dependent variable(here, f(x)).
The graph of linear function is always a straight line.
Let y = f(x)
So, y = a + bx
where b is the slope of line
and a is the y-intercept
here, the independent variable is x and the dependent variable is y.
We have been given a function y = 10
The graph of y = 10 is a horizontal line parallel to x -axis and intersects y-axis at (0, 10)
There is no y-intercept and the slope is undefined.
Therefore, given function is not a linear function
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Translate this sentence into a equation
38 is the product of Dellas score and 2.
Use the variable d to represent Della’s score
The required translation of the given statement into an equation is given as 38 = 2d.
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,
38 is the product of Della's score and 2.
Let the variable d to represent Della’s score,
2 × d = 38
2d = 38
Thus, the required translation of the given statement into an equation is given as 38 = 2d.
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What is the full table of 5?
A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.
Write the complete table of 5.Here is an example of a full table of 5:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
5 x 6 = 30
5 x 7 = 35
5 x 8 = 40
5 x 9 = 45
5 x 10 = 50
In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.
It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.
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The sum of all interior angles in a polygon is 9 degrees. How many sides does the polygon have? Please show your working.
3. Choose any two complex numbers z, and z2 and show that the following statements are true for
those numbers. Then prove that the statements are true for any z₁ = a + bi and z₂ = c + di.
a. Z₁ + Z₁ and Z₂ + Z₂ are both real numbers.
b. Z₁-Z₁ and 22-Z₂ are both pure imaginary numbers.
c. Z₁ + Z₂ = Z₁ + Z₂
d. Z₁ Z₂ = Z₁ Z2
4. For what complex number z does z=z? Justify your conclusion.
The following statements are true for all the numbers. The proof is shown as follows.
What is an imaginary number?A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.
We know z₁ = a + bi and zbar= a-bi
z1+z1bar=2a that is purely real. Similarly with z2 +z2bar
z1-z1bar=-2bi that is purely imaginary. Similarly with z2-z2bar
Again
z1bar+z2bar= a-bi+c-di
z1+z2(whole bar)=a+c-(b+d)i
Hence Z₁ + Z₂ = Z₁ + Z₂
Similarly
z1bar.z2bar=z1.z2(whole bar)
Hence proved
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A geometry student named Mary claims that the two triangles in the diagram below are not similar to one another. She asserts that the ΔABC is not similar to ΔXYZ because triangle XYZ is bigger. Explain why Mary is mistaken in her conclusions about ΔABC and ΔXYZ. In writing your response, be sure to explain the difference between similarity and congruence. Also be sure to include important math concepts such as similarity, proportionality, and corresponding sides.
Mary is mistaken in her conclusion that the two triangles are not similar because size does not determine similarity. Similarity is determined by the proportionality of corresponding sides and the congruence of corresponding angles. Congruence is the equality of all the measures of the corresponding parts of two figures.
In order to determine if two triangles are similar, we must compare the ratios of corresponding sides. If the ratios of corresponding sides are equal, then the triangles are similar. In the diagram, it is not specified what the measures of the sides of the triangles are, so it is not possible to determine if the triangles are similar based on the information given. However, if the ratio of corresponding sides are same, then the triangles are similar.
It is important to note that similarity and congruence are different concepts. Congruence refers to the equality of all measures of corresponding parts of two figures, including side lengths and angles. Similarity refers to the proportionality of corresponding parts, including side lengths and angles. A triangle can be similar to another triangle without being congruent, and congruent triangles are always similar.
In summary, Mary is mistaken because the size of the triangle does not determine similarity, it is determined by the proportionality of corresponding sides and congruence of corresponding angles. Without knowing the measures of the sides of the triangles, it is impossible to determine if the triangles are similar based on the information given.
Select the point which lies in the fourth quadrant?
(1,−2)
(1,8)
(-5,-4)
(-5,2)
The point that lies in the fourth quadrant is (1, -2).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates are:
(1,−2), (1, 8), (-5, -4), and (-5, 2).
(1, -2) is in the fourth quadrant.
(1, 8) is in the first quadrant.
(-5, -4) is in the third quadrant.
(-5, 2) is in the second quadrant.
Thus,
(1, -2) lies in the fourth quadrant.
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Answer: (5,−2) is the only point in the fourth quadrant.
Step-by-step explanation:
Write a quadratic equation in standard form that has an axis of symmetry of x=-2and y intercept of 0,6
The quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.
A quadratic equation in standard form is of the form ax² + bx + c, where a, b, and c are constants.
The axis of symmetry of a quadratic equation is given by the line x = -b/2a, so if the axis of symmetry is x=-2, we can set -b/2a = -2, which gives b = 4a.
To find the y-intercept of the quadratic equation, we can set x = 0 and substitute that into the equation: y = a(0)² + b(0) + c = c
So, if the y-intercept is (0,6) then c = 6.
By using above two information, we can write the quadratic equation in standard form as:
a(x+2)² + 4a(x+2) + 6 =0
=> a(x²+4x+4) + 6 = 0
=> a(x²+4x+4) = -6
=> a(x²+4x+4) = -6
=> x² + 4x + 4 = -6/a
=> x² + 4x + 4 = -6/a +10
=> x² + 4x - 6 = 0
So, the quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.
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What is the equation for the line in slope-intercept form?
Answer: y = 8x
Step-by-step explanation:
The line passes through points (1,8) and (2,16).
Using this, we can first find the slope.
Slope = Δy/Δx = 8/1 = 8
So the slope is 8.
The equation is now
y = 8x + b
Let's use the point (1,8) to find the value of b now.
8 = 8 +b
b = 0
Therefore, y = 8x is the answer.
(you can skip the last step by noticing that the graph passes through the origin)
Answer:
y = 8x
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
From inspection of the given graph, two points on the line are:
(0, 0)(2, 16)Substitute the points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{16-0}{2-0}=\dfrac{16}{2}=8[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value of the point where the line crosses the y-axis. From inspection of the given graph, the y-intercept is zero. So b=0.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
[tex]\implies y=8x+0[/tex]
[tex]\implies y=8x[/tex]
Therefore, the equation for the line in slope-intercept form is:
y = 8xWhat are the domain and range of this function?
The correct option regarding the domain and the range of the quadratic function y = (x + 3)² - 5 is given as follows:
B. Domain all real values, Range [-5, infinity.]
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
y = (x + 3)² - 5.
Which is a concave up quadratic function with vertex at (-3,-5).
The quadratic function has no restrictions regarding the input, hence the domain is composed by all real values.
The minimum value of the function is of -5 at the vertex, hence the range is all values that are -5 or greater.
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A farmer decides to start selling his goats at a constant rate per month. After seven months, he has 280 goats left. After eleven months, he has 224 goats left.
If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.
To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:
slope = (y2 - y1) / (x2 - x1)Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.
In this case:
y2 = 224 (goats left after 11 months)y1 = 280 (goats left after 7 months)x2 = 11 (months)x1 = 7 (months)So the slope of the line is:
slope = (224 - 280) / (11 - 7)slope = -56 / 4 slope = -14The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.
It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.
This question is incomplete and should be written as:
A farmer decides to start selling his goats at a constant rate per month. After seven months, he has 280 goats left. After eleven months, he has 224 goats left. If the farmer made a straight line graph representing how many goats he had left over time, what would be the slope of the line?Learn more about linear equation here: brainly.com/question/14323743
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How do you find the coordinates of a midpoint example?
To find the coordinates of the midpoint of two points in a plane, you can use the midpoint formula. The midpoint formula is:
(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.
For example, if you have two points (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x,y) = ((3 + 7) / 2, (4 + 10) / 2)
(x,y) = (5, 7)
The midpoint of points (3,4) and (7,10) is (5,7).
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Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript one-fourth x?
8 Superscript three-fourths x
RootIndex 7 StartRoot 8 EndRoot Superscript x
RootIndex 12 StartRoot 8 EndRoot Superscript x
8 Superscript StartFraction 3 Over 4 x EndFraction
The equivalent expression is RootIndex 12 StartRoot 8 EndRoot Superscript x. Option C
What is an equivalent expression?An equivalent expression can be described as an expression that has the same solution as the original expression.
The equivalent always have a different arrangement of variables, terms and factors but the solution is the same with the initial expression.
From the information given, we have that;
3Root 8 Superscript one-fourth x
This is represented as;
[tex]\sqrt[3]{8}^\frac{1}{4} ^x[/tex]
Now, take the cube root of 8, we have;
[tex]8^\frac{1}{3} * \frac{1}{4}^x[/tex]
Multiply the exponents, we get;
[tex]8^\frac{1}{12}^x[/tex]
Now, represent in root for, we have;
[tex]\sqrt[12]{8} ^x[/tex]
Hence, the correct option is C
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Answer:
C
Step-by-step explanation:
;)
How do I olve thi ytem of equation uing the elimination method. (I don't jut want the anwer, I want an explanation on how to get the anwer. )
y=3x13
2x=y-9
Answer:
-4
Step-by-step explanation:
y=3x13
2x=y-9
2x=3x+13-9
2x=3x+13-9
2x=3x+4
-3 -3
-x=4
-x/ -x/
x=-4
(You said "3x13" so i'm going to guess you meant to say "3x+13").
(If you meant "3x-13" I can also help you with that too)!
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
The vertices of the new polygon A'B'C'D' is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (optionB)
What are vertices of a polygon?A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.
The vertices of the polygons are given as B(−2, 2), C(4, −2), D(4, 4) . The polygon is reduced by using a scale factor one fourth. i.e 1/4.
This means that each coordinates of the vertices will be reduced by 4 to give the vertices of the new polygon.
A = (-4,6) , A' = ( -1, 1.5)
B = ( -2,2) B' = ( -0.5, 0.5)
C = ( 4, -2) C' = ( 1, -0.5)
D = ( 4,4) , D' = ( 1, 1)
Therefore the vertices of the new polygon is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
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Answer:
its not b i tried and it was wrong
Step-by-step explanation:
What is 0.55 hectometers expressed in decimeters?a.550 dmb.5.5 dmc.55 dmd.0.00055 dmwhat is 0.55 hectometers expressed in decimeters? a.550 dmb.5.5 dmc.55 dmd.0.00055 dm brainly
The value of 0.55 hectometers expressed in decimeters is 550 decimeters. The result is obtained by using the concept of unit ladder system.
How the unit ladder method works?The common length units are kilometers to milimeter. The conversion can be described in a unit ladder system as follows.
km (kilometers)
hm (hectometers)
dam (decameters)
m (meters)
dm (decimeters)
cm (centimeters)
mm (millimeters)
Every time the length unit goes down, it is multiplied by ten. Every time the length unit goes up, it is divided by ten.
We have 0.55 hectometers. Express that value in decimeters!
From hectometers to decimeters, it goes down 3 times. So,
0.55 hectometers = 0.55 × 10 × 10 × 10 decimeters
0.55 hectometers = 0.55 × 1000 decimeters
0.55 hectometers = 550 decimeters
Hence, 0.55 hectometers is equal to 550 decimeters.
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Amelia ordered pancakes, a side of bacon, and orange juice. She also says that she will take care of the tax. How much does she owe?
Answer:
45 cents
Step-by-step explanation:
5. Principal = $ 6750, rate = 62/3 % p.a. and time = 3 years.
Answer:
Interest is $4185.00
Please give me brainliest
Step-by-step explanation:
[tex]i = \frac{p \: r \: t}{100} \\ i = \frac{6750 \times \frac{62}{3} \times 3 }{100} \\ i = \frac{418500}{100} \\ i = 4185[/tex]
Answer:
Step-by-step explanation:
Formula for simple interest =S= (P*R*T)/100
Here P=$6750,R=62/3% T=3Years
Simple interest for given is S= 41.85
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where × represents the number of years since 2012, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1171.
Regression equation:
Final answer:
The linear regression equation is y = 22.086x + 898.620 and the year for 1171 cases is 2024
How to determine the linear regression equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
Using a graphing calculator, we have the following summary
Sum of X = 15Sum of Y = 5723Mean X = 2.5Mean Y = 953.8333Sum of squares (SSX) = 17.5Sum of products (SP) = 386.5The regression equation is represented as
Regression Equation = ŷ = bX + a
Where
b = SP/SSX = 386.5/17.5 = 22.08571
a = MY - bMX = 953.83 - (22.09*2.5) = 898.61905
So, we have
ŷ = 22.08571X + 898.61905
Approximate
y = 22.086x + 898.620
When the new cases is 1171, we have
22.086x + 898.620 = 1171
This gives
x = 12
i.e. year = 2012 + 12 = 2024
Hence, the year is 2024
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Perform the following composition of transformation for point P (6, -4.)
T (-1,2) o R (180)
So, on solving the provided question we can say that coordinates are -
(6, -4.) and T (-1,2) y-y1 = m(x - x1) => 2x - y -16 =0
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
here,
coordinates are -
(6, -4.) and T (-1,2)
y-y1 = m(x - x1)
y +4 = 2(x -6)
y+ 4 = 2x - 12
2x - y -16 =0
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Look at the image down below
Using the concept of ratios, the constant of proportion between middle school and high school is 3/4
What is ProportionalityProportionality is a fundamental concept in mathematics and physics. It is a relationship between two or more variables where a change in one causes a proportional change in the other. In other words, the ratio between the two remains constant. Proportionality is an important concept in mathematics because it is used to make predictions and solve problems. The constant of proportionality is the ratio between the two variables that remain constant in a proportional relationship.
To determine the constant of proportionality in this relationship, we can write an equation in the form
y = kx
k = constant of proportionOr we can easily use ratio to find the constant of proportion
Number of girls in middle school = 6
Number of girls in high school = 8
The ratio = 6/8 = 3 / 4 = Option B
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