Answer:
Step-by-step explanation:
Calculating Average Weekly Pay for Uneven Work Hours Some professions like nurses & doctors in the healthcare industry might work longer shifts where they are on for 12 hours
SOMEONE PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
y=-2/3x+4
Step-by-step explanation:
Rise/run (from the y-intercept to the next point you go down 2 and then to the right 3)
Y-intercept (where the line touches the y-axis) 4
I need to know the question to a problem 10”=14,521
Answer:
The value of n in this equation is 5.
Step-by-step explanation:
This can be determined by using the property of exponents that states that x^n * x^m = x^(n+m). In this case, 10^n * 10^5 = 14,521, so 10^(n+5) = 14,521. Solving for n, we get n = 5.
Helen draws a random circle.
She then measures its diameter and circumference.
She gets a circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm correct to 2 significant figures.
Helen wants to find the value of T using the formula TC
C
Calculate the lower bound and
upper bound for Helen's value of T.
Give your answers correct to 3 decimal places.
The value that Helen wants to use is Pi = C/D. The lower bound value is 3.065, and the upper bound for Helen's value is 3.165.
What is circumference?
The circumference is the perimeter of the circle.
Given, the circumference, C, at 405 mm to three significant numbers.
She correctly estimates the diameter, d, to be 130 mm to two significant numbers.
Helen wants to find the value of Pi using the formula pi=C/D
We have, the circumference of the circle = C = 405 mm
The diameter of the circle = d = 130 mm
Pi = C/D
= 405 mm / 130 mm
= 405 / 130
= 3.115
3.115, measured to the nearest 0.1.
The degree of accuracy is nearest 0.1.
0.1/2 = 0.05
Upper bound = 3.115 + 0.05 = 3.165
Lower bound = 3.115 - 0.05 = 3.065
Therefore, the lower bound and upper bound for Helen's value are 3.165, and 3.065.
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The basketball team scored a total of 109 points last game. They made a total of 47 shots, including 2-point shots and 3-point shots. how many 2-point shots did they make? How many 3-points did they make?
[please include steps]
Based on the above, the number of 3-points that they make is 25.
What is the Simultaneous equation about?Simultaneous equation is a form of two equations that have to be solved at the same time. Thus, the number of 2 points made is 17, while that of 3 points is 25.
A set of equations that has to be solved simultaneously so as to determine the values of the unknown variables is termed simultaneous equation.
The given question would result to a simultaneous equation as follows;
let the number of 2 points made by represented by m, and that of 3 points by n.So that;
m + n = 42 ..................
i2m + 3n = 109 ...............
ii multiply equation 1 by 3 and equation 2 by 1 to have;3m + 3n = 126 ............
iii 2m + 3n = 109 .............
iv subtract eqaution iv from iii
m = 17
substitute the value of m in equation 1 to have:
m + n = 4217 + n = 42n = 42 - 17 = 25m = 17, n = 25
Thus the number of 2 points made was 17, while that of 3 points made was 25.
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include working out please
Answer:
y = 3x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (- 2, - 2) ← 2 points on the line
m = [tex]\frac{-2-4}{-2-0}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
Answer:
y=3x+4
Step-by-step explanation:
The formula used is point slope, or y=mx+b
here, the m is the slope, and the b is the y-intercept
The y-intercept is where the graph crosses the y-axis, also known as when x=0
In this case, the y intercept is at the point (0,4) so you'd plug in 4 for the 'b' in the equation
To find the slope, use the rise over the run of the graph.
To do this, pick two points along the graph, and count how many units up/down, and to the left/right between the two points
The units up/down goes on top, being positive if they're up, and negative if they're down
The units left/right go on bottom, being positive if they're right, and negative if they're left
In this case you go 3 units up, and 1 unit right, so the slope would be 3/1 or 3
Recreating the Original Triangle
You will be using the following original triangle in the following activity.
With a ruler, measure the sides of the original triangle to the nearest millimeter. Write down the length of each side in your math journal.
With a protractor, measure the angles of the original triangle to the nearest degree. Write down the measure of each angle in your math journal.
SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures?
SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure the angle between the sides that you chose and draw an angle of that measure on a separate sheet of paper. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length?
ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure the angles on either side of the side that you chose, and draw angle of those measures on either side of the line you traced on the paper. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them.
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?
The original triangle⬇️
The properties of the triangles created from the original triangle based on triangle congruency rules are as follows;
SSS: The triangle created using the lengths of the three sides of the original should have the same length and angles as the original
The triangle formed using SSS is a unique triangle and no other triangle has similar dimensions
SAS: The lengths of the sides and the measure of the angles should be the same
The triangle created using SAS is a unique triangle and there is not a way to have a third side that has a different length
ASA; The triangle formed using the ASA of the original triangle should have the same length as the same lengths and angles as the original triangle
The triangle formed using ASA is a unique triangle and there is not a way to create a triangle that has a different side length.
What are congruent triangles?Two triangles are congruent if the lengths of the three sides of one triangle are congruent to the three sides of the other triangle or if they meet the other conditions of triangle congruency.
Length of first measured side of the triangle = 52 units
Angle made by the first measured side with the horizontal = 41°
Length of the second measured side of the triangle = 87 units
Angle the second measured side makes with the horizontal = 33°
Length of the third measured side of the triangle = 113 units
Angle the third side makes with the horizontal ≈ 6.5°
Let the vertices of the first side be A and B, we get;
∠A = 180° - (41° + 33°) = 106°
∠C = 33° - 6.5° = 26.5°
∠B = 41° + 6.5° = 47.5°
SSS: The SSS (Side-Side-Side) congruency postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Therefore, the lengths of the sides and the measures of the angles of the triangle created using the lengths of the three sides of the original triangle will be the same as the original triangle.
The SSS congruency postulate indicates that the triangle created using the same lengths of the three sides of the original triangle is a unique triangle and there are no other triangles having the same side lengths but different angles
SAS: The Side-Angle-Side, SAS, congruency postulate states that if the adjacent sides and an included angle of a triangle are congruent to two adjacent sides and an included angle of another triangle, then the two triangles are congruent.
Therefore, the triangle formed using two sides of the original triangle and the included angle between them will have the same length as the sides of the original triangle, and the triangle formed using the SAS of the original triangle is unique
The length of the third side of the triangle created using the SAS measurement is always the same as the length on the original triangle
ASA: The Angle-Side-Angle, ASA, congruency postulate states that if two angles and the included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.
The triangle formed using the ASA is a unique triangles and therefore and there is no way to create a triangle that has a different side length
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Seth is comparing scenarios to determine which starting point he should get dropped off at to get him to school faster. Seth's house is 17 miles from school. In which scenario does seth start closer to school? in which scenario does seth travel at a greater speed, and what was the rate?.
In linear equation, He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Using linear function concepts, it is found that:
Seth starts closer to the school in the bus.
He travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
From the graph of the bus, when he takes the bus, he is 13 miles from the school, as he starts at position 4 and ends at 17.
At his friend house, he is 13 miles from the school only after 3 minutes, which means that the bus will be closer.
The scenario with the greater speed is the one with the higher slope, that is, higher rate of change, which is the change in distance divided by the change in time.
In the bus, change of 13 miles in 24 minutes, thus
mᵇ = 13/24 = 0.5417
From the friend's house, change of 2 miles in 3 minutes, thus
mf = 2/3 = 0.6667
Thus, he travels at a greater speed from his friend's house, at a rate of 0.6667 miles per minute, that is, 2 miles in 3 minutes.
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The normal cost of a pair of boots is £120.
In a sale the cost of the boots is reduced by 45%.
Work out the sale price of the boots.
Answer:
£54
Step-by-step explanation:
Write 45% as
45
100
Since finding the fraction of a number is the same as multiplying the fraction with the number, we have
45
100
of 120 =
45
100
× 120
Therefore, the answer is 54
If you are using a calculator, simply enter 45÷100×120 which will give you 54 as the answer.
You need to determine where to place the beams so that the chains are fastened to the rollercoaster at a height of 25 feet. Write the equation you would need to solve to find the horizontal distance each beam is from the origin. (10 points).
Using the roller coaster as an example, draw a right triangle.
The equation used to find the horizontal distance: h² = 30² - 25².16.58 feet is the horizontal distance.What are ways to arrive at the equation?25 feet is listed as the height.The answer to the whole question is that the roller coaster measures 30 feet long.Use h to symbolize the horizontal distance.
The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.
30² = h² + 25².
Assemble similar phrases.
h² = 30² - 25².
horizontal separation
In (a), there is:
h² = 30² - 25².
This results:
h² = 275
Take both sides' roots.
h = 16.58
Consequently, 16.58 feet are the horizontal distance.
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The table shows the number of miles people in the U.S. traveled by car annually from 1975 to 2015.
The equation for the line of best fit is y=0.048x + 1.345, where x is the number of years since 1975
and y is the number of vehicle-miles traveled in trillions. What do the slope and y-intercept
represent? Estimate the number of miles people in the U.S. traveled in 2007. What is a reasonable
prediction for the number of miles people in the U.S. will travel in 2022?
What the slope and the y-intercepts represent are;
Slope means that the rate at which the number of miles people in the U.S. traveled per year increased was 0.048
y-intercept means that the number of vehicle-miles traveled in 1975 is; 1.345 (in trillions)
A reasonable prediction for the number of miles people in the U.S. will travel in 2022 is; 3.601 (in trillions)
How to interpret the equation of line of best fit?
The equation for the line of best fit is given as;
y = 0.048x + 1.345
where;
x is the number of years since 1975
y is the number of vehicle-miles traveled in trillions
The equation of a line in slope intercept form has the general form as;
y = mx + c
where;
m is slope
c is y-intercept
Thus;
Slope = 0.048 which is the rate at which the number of miles people in the U.S. traveled per year increases.
y-intercept = 1.345 (in trillions) which is the number of vehicle-miles traveled in 1975
The year 2022 will be 47 years since 1975 and so the prediction is;
y = 0.048(47) + 1.345
y = 3.601 (in trillions)
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the famous kate lynn horsefeed is building a box as part of her science project. it is to be built from a rectangular piece of cardboard measuring 25 cm by 40 cm bycutting out a square from each corner and then bending up the sides. find the size of the corner square which will produce a container that will hold the most.
The original cardboard measures 25 cm by 40 cm. By cutting out a 10 cm by 10 cm corner square, the new measurement of the cardboard will be 15 cm by 30 cm. The volume of the container will be 4500 cm^3.
The goal of this project is to build a container out of a rectangular piece of cardboard measuring 25 cm by 40 cm. To do this, a square must be cut out of each corner of the cardboard and the sides must then be bent up. In order to produce a container with the most internal volume, the corner square should be 10 cm by 10 cm. This will result in four equal sides and a larger internal volume. The larger internal volume will allow the container to hold more material, thus making it more efficient for the project.
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I need help in this please help me at it
Step-by-step explanation:
come on, use some common sense.
length to breadth = 3/2.
so, when the breadth is 24, what is the factor compared to the original 2 of 3/2 ? 12.
2 × 12 = 24 cm
and then, we need to multiply the other ratio part by the sand factor
3 × 12 = 36 cm
when the length = 60 cm, then the factor compared to the original 3 of 3/2 is 20.
3 × 20 = 60 cm
and multiplying the other ratio part by the same factor
2 × 20 = 40 cm
when the breadth is 52, the factor compared to the original 2 of 3/2 is 26.
2 × 26 = 52 cm
and multiplying the other ratio part by the same factor
3 × 26 = 78 cm
A printer takes seconds to print a lyer. It took 75 seconds to print a batch of lyers without stopping. How many lyers were in the batch?
If it takes a printer seconds to print a single lyer, and it took 75 seconds to print a batch of lyers without stopping, the number of lyers in the batch is 75 / . This is because if it takes seconds to print a lyer, and we have 75 seconds available to print lyers, we can divide the total time available by the time it takes to print each lyer to find out how many lyers we can print.
For example, if it takes 3 seconds to print a single lyer, the number of lyers in the batch is 75 / 3 = 25. If it takes 2 seconds to print a single lyer, the number of lyers in the batch is 75 / 2 = 37.5.
Therefore, the number of lyers in the batch depends on the time it takes to print a single lyer. To find the exact number of lyers in the batch, we need to know the time it takes to print a single lyer.
Anwered
Nakeiha' family took a road trip to Mount Ruhmore. Nakeiha fell aleep 18% of the way through the trip. If the total length of the trip wa 400 mile, how many mile had they travelled when Nakeiha fell aleep?
After solving the percentage the distance through which Nakeiha fell asleep along the trip is 72miles.
What is percentage?Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.
How to solve percentages?To solve this question, we will do 18% x 400.
= (18/100) x 400
= 72 miles
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Addilyn mow two lawn. The firt lawn i 6 meter long and 4 meter wide. The area of the econd lawn i 6 time big but ha the ame width a the firt. What i the length of the econd lawn?
The length of second lawn is found as the 36 sq. m.
Explain the term area of the rectangle?The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area.In essence, the area of a rectangle is equal to the sum of its length and breadth.For the stated question-
First lawn:
Length = 6 mWidth = 4 mArea = length x width
A = 6 x 4 = 24 sq. m.
Second lawn:
Length = LWidth = 4 mArea A2 = 6 x Area of first lawnA2 = length x width
6 x A = L x 4
6 x 24 = L x 4
L = 6 x 6
L = 36 sq. m
Thus, the length of the second lawn is found as the 36 sq. m.
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Answer:
Step-by-step explanation:
36 is the answer
what is an equation of the line that passes through the points (8,-3) and (4,2)
Answer:
y = –5x/4 + 7
Step-by-step explanation:
x1 = 8 ,x2 = 4, y1 = –3 , y2 = 2
lets find the slope(m)
m = y2–y1/x2–x1
m = 2 – (–3)/ 4 – 8
m = 5/ –4
m= –5/4
to find the equation of a line using this as our guider y = mx + b
we will make use of one coordinate
(8,–3)
using the formula for one point
y – y1 = m(x – x1)
y – (–3) = –5/4(x – 8)
y + 3 = –5x/4 + 10
y = –5x/4 + 10 –3
y = –5x/4 + 7
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I am desperate for help with this - 100 pts for this question
A group of 3 friends went to a sporting event. It cost 30 for each of them to get in. What was the total cost for all of them to get in?
Answer:
£90
Step-by-step explanation:
1 friend = £30
all together there are 3 friends
30 x 3 = 90
or you can simplify and do 3x3 which is 9
and add the 0 at end (90)
each person = 30($)
people = 3
cost($) * number of people
[tex]30\times3[/tex]
[tex]=\fbox{90}[/tex]
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc?
Answer: The circumference itself can be considered a full circle arc length. Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc. Arc Length: In a circle, the length of an arc is a portion of the circumference.
An arc length is a portion of the circumference of a circle. You can use the measure of the arc (in degrees) to find its length (in linear units). In a circle, the ratio of the length of a given arc of the circumference is equal to the ratio of the measure of the arc to 360°.
It will help you.
Step-by-step explanation:
And bottom says solve for X someone help me
Answer:
2(x+8)=126
Step-by-step explanation:
GD is the bisector of CGE and 126 and the angle CGE are equal
Katelyn want to build a dek for her doll. Her actual dek i 3 feet tall. The clae i 10 in = 1ft. How tall will the doll dek be?
The height of the desk for the doll according to conversion scale given is 1.5in.
Based on the information provided, the height of Katelyn’s actual desk is 3 feet. She wants to build a desk for her doll and she wants to use a scale of 0.5 in: 1feet to convert the measurements. A conversion scale refers to a scale which indicates the relationship between two different units of measurement.
According to the given conversion scale,
1 feet = 0.5in
If the height is 3 feet, the measurement in inches would be:
3 feet = 3 feet * 0.5 in/ 1 feet = 1.5 in
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A water coller filll 150 glae in 30 minute how many glae of water can the coller filll in one minute
Five water glasses each minute, one minute to fill the cooler.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. what kinds of values and units
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
divide 150 by 30 equal 5
= 5
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Question 4
The weights for 12-month-old baby boys are normally distributed with a mean of 22.5 pounds and a standard deviation of 2.2 pounds.
Find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds.
ANSWER -
Answer:
70.5%
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
Mean μ = 22.5Standard deviation σ = 2.2Therefore, if the weights of the 12-month-old baby boys are normally distributed:
[tex]\boxed{X \sim\text{N} \left(22.5,2.2^2 \right)}[/tex]
where X is the weight of the baby boy.
To find the percentage to the nearest tenth of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds find P(19.7 ≤ X ≤ 24.4).
Calculator input for "normal cumulative distribution function (cdf)":
Upper bound: x = 19.7Lower bound: x = 24.4σ = 2.2μ = 22.5[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=0.704548741[/tex]
[tex]\implies \text{P}(19.7 \leq X \leq 24.4)=70.5\%[/tex]
Therefore, the percentage of 12-month-old baby boys who weigh between 19.7 and 24.4 pounds is 70.5% (nearest tenth).
Line a passes through the points (0, 4)
and (4, 0). Line b passes through the
points (0, 7) and (7, 0). Are the lines
parallel? Explain.
Answer:
Yes, the lines are parallel. This is because the lines have the same slope. The slope of a line is a measure of how steep the line is, and it is calculated by taking the difference of the y-coordinates of two points on the line and dividing it by the difference of the x-coordinates of the same two points. In this case, the slope of line a is -1, and the slope of line b is also -1. Because the lines have the same slope, they are parallel to each other.
The median of a boulevard i 8 feet wide and 300 feet long. What i the area of the median?
By using the formula for area of rectangle, it can be calculated that Area of the median is 2400 sq. feet
What is area of rectangle?
The area of a rectangle is calculated by multiplying the length by the width. For example, if a rectangle has a length of 10 feet and a width of 6 feet, the area would be 10 x 6 = 60 square feet. The area of a rectangle is a two-dimensional measurement and is typically expressed in units squared, such as square feet or meters squared. Other shapes, such as a triangle or a circle, also have areas and are calculated differently.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is calculated by the formula
Area = [tex]l \times b[/tex]
Length of the median = 300 feet
Width of the median = 8 feet
Area of the median = 300 [tex]\times[/tex] 8 = 2400 sq. feet
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In the diagram below, angle f is congruent to angle i. Enter segments in the blanks provided that would result in a true equation.
The segments in the blank provided is GH/FH=IH/JH so that the equation is true
What are the 4 characteristics of similar triangles?Similar triangles differ in size but have the same form. Corresponding angles are identical in comparable triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of the square of any two of their corresponding sides to any identical triangle's area is the same.
What are the 3 types of triangle similarity?The triangle similarity criteria are:
AA (Angle-Angle)
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
In the given question
<GHP=<IHJ (vertically opposite angles)
<JIH=<HPG (alternate angles)
From AA similarity critera
triangles JHI ~ triangle GHP
Hence
GH/FH=IH/JH
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Identify the line(s) of symmetry for the quadratic function below.
Answer:
y=-3
Step-by-step explanation:
A line of symmetry is the line where a function can be folded in half evenly. Here it occurs at y=-3
line of symmetry, the line at which point the graph begins to mirror itself, Check the picture below.
Suppose that 6 < x < 7 and 10 < y < 12. Find all possible values of each expression.
y - x
The set of all possible y-x values is between 3 and 6, excluding both endpoints.
===================================================
Explanation:
The y-x value is smallest when:
The y value is as small as possibleThe x value is as large as possibleI recommend to draw out a number line. The idea is to place x and y as close as possible to each other.
Based on those two conditions, we use y = 10 and x = 7 respectively. That gives y-x = 10-7 = 3 as the smallest possible difference. Keep in mind we can't actually reach this value so we would write y-x > 3 which is the same as 3 < y-x.
--------------------
Similarly, y-x is largest when:
The y value is largestThe x value is smallestLike earlier, use a number line to see why this would be the case. We're trying to space x and y out as far as possible.
The largest y value and smallest x value are y = 12 and x = 6 in that order. So the upper bound is y-x = 12-6 = 6. Like before, we can't actually reach this number which means we write y-x < 6.
--------------------
Recap:
In the 1st section, we found that 3 < y-xIn the 2nd section, we found that y-x < 6Put those two results together in a tidy compound inequality to get the final answer 3 < y-x < 6
It says: The expression y-x is between 3 and 6, excluding both endpoints.
Question 6 of 7
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22-23 Geometry Unit 3 EUA
Tyler was trying to prove that all rhombuses are similar. He thought, "If I draw 2 rhombuses. I can find dilations that will take one rhombus exactly onto the other." Then he wrote a proof.
All rhombuses are not similar. Which steps in Tyler's proof have flaws? Explain what is wrong with each step that is wrong.
Step 1: Let A BCD and W XYZ be rhombuses. By the definition of a rhombus, AB = BOECDE DA and WXEXY AYZEZW.
Step 2: Dilate rhombus ABC D by the scale factor given by
WX
4B Side A'B' will be the same length as W X because of how I chose the scale factor. Because all sides ofa
thombus are congruent, B'C' will be the same length as W X and therefore the same length as XY, C'D' will be the same length as Y Z, and A'D' will be the same length as W Z. That means all the corresponding sides of A' B'C'D and W XY Z will be the same length.
Step 3: If all the sides in 2 figures are proportional, then those 2 figures are similar, so there must be a sequence of transformations that take ABC D onto W XYZ using dilations and rigid motions.
Step 4: Translate A' B'C'D' by the directed line segment A'W so that A" and W coincide.
Step 5: Rotate A" B"C" D" by angle B"W X so that B/' and X coincide. Now segments A' B'' and WX coincide.
Step 6: If needed, reflect A" B''O' D'' over segment W X so that D'' and Z are on the same side of WIX. Now segments A"' D' and WZ coincide.
Answer:
Step-by-step explanation: Step 1: Tyler correctly states that rhombuses have all sides congruent.
Step 2: Tyler correctly states that dilating a rhombus by a scale factor will result in sides of the same length, but he does not provide a justification for why he chose the scale factor of WX/AB.
Step 3: Tyler correctly states that if all sides in two figures are proportional, then the figures are similar, but he does not provide a justification for why this is true.
Step 4: Tyler correctly states that he will translate A'B'C'D' by the directed line segment A'W, but he does not provide a justification for why this will result in A'' and W coinciding.
Step 5: Tyler correctly states that he will rotate A"B"C"D" by the angle B"WX, but he does not provide a justification for why this will result in B'' and X coinciding.
Step 6: Tyler correctly states that he will reflect A"B''C''D'' over segment WX if needed, but he does not provide a justification for why this will result in D'' and Z coinciding.
The table shows the number of cases of foodborne botulism in the United States for the years 2001 to 2005. Let x represent the
number of years since 2000. Find a linear model for the data. List the correlation coefficient.
U.S. Foodborne Botulism Cases
Year
Cases 39 28 20 16
2001 2002 2003 2004 2005
18
Source: Centers for Disease Control
Linear model:
Correlation coefficient: r =
Predict the number of foodborne botulism cases in the United States in 2007.
We require a more accurate and objective measure to determine the association between the two variables because visual exams are primarily subjective. We employ the linear correlation coefficient to express the degree and direction of the association between two variables:
[tex]r=\frac{\sum \frac{\left(x_i-\bar{x}\right)}{s_x} \frac{\left(y_i-\bar{y}\right)}{s_y}}{n-1}[/tex]
where the sample means and standard deviations of the x's are x and sx, respectively, and the y's are y and sy, respectively. n is the sample size. .
A different method of calculating the correlation coefficient is:
[tex]r=\frac{S_{x y}}{\sqrt{S_{x x} S_{y y}}}[/tex]
[tex]\begin{aligned}& \text { where } S_{x x}=\sum x^2-\frac{\left(\sum x\right)^2}{n} \\& S_{x y}=\sum x y-\frac{\left(\sum x\right)\left(\sum y\right)}{n} \\& S_{y y}=\sum y^2-\frac{\left(\sum y\right)^2}{n}\end{aligned}[/tex]
In honor of Karl Pearson, who created the linear correlation coefficient in the first place, it is also known as Pearson's product moment correlation coefficient. This metric quantifies the strength of the linear, or straight-line, relationship between the two variables as well as its positive or negative direction.
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