True or False: the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
It is false that the probability of the union of two events can be more than the probability of the intersection of the two events occurring.
This is because when two events intersect, the intersection of the two events refers to the occurrence of both events at the same time, while the union of the two events refers to the occurrence of either event or both events at the same time. therefore, the union of two events can have a higher probability of occurring than the intersection of two events since the union includes the possibility of both events occurring, while the intersection does not.
For example, let us consider two events, A and B. Event A has a probability of 0.3, and event B has a probability of 0.4. The probability of the intersection of these two events is 0.12(0.3 X 0.4) while the probability of the union of these two events is 0.7(0.3+0.4-0.12). As seen in this example, the probability of the union of two events (0.7) is greater than the probability of the interaction of two events(0.12)
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A scientist conducts an experiment on the growth of a certain bacteria culture.
The variable t represents the number of hours since the beginning of the experiment.
When t=0 (that is, at the beginning of the experiment), there were 50 bacteria in the culture.
Every 1 hour, the number of bacteria in the culture increases by a factor of 2.
The number of bacteria in the culture, N, can be modeled as a function of t by an exponential growth function N (t).
(Recall that an exponential growth function N (t) is a function of the form N(t)= ab', where a and b are positive constants.)
The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the number of bacteria in the culture at a given time be N ( t )
The culture increases by a factor of 2
So , the value of r = 200 % , r = 2
Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50
So , the exponential equation is
N ( t ) = N ( 0 ) ( 1 + r )^t
Substituting the values in the equation , we get
N ( t ) = 50 ( 1 + 2 )^t
N ( t ) = 50 ( 3 )^t
On simplifying the equation , we get
N ( t ) = a ( b )^t , where a = 50 and b = 3
Hence , the exponential equation is N ( t ) = 50 ( 3 )^t
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Shopping Preferences Visitors to a shopping mall in Atlanta, Georgia, were surveyed to determine their preference for shopping in wholesale warehouse stores. The following information was determined.
58 shopped in BJ’s Wholesale Club.
49 shopped in Sam’s Club.
45 shopped in Costco.
15 shopped in BJ’s Wholesale Club and Sam’s Club.
16 shopped in BJ’s Wholesale Club and Costco.
12 Shopped in Sam’s Club and Costco.
5 shopped in all three stores.
17 did not shop in any of the three stores.
How many participants shopped in ….
BJ’s Wholesale Club only
Costco only
Sam’s Club only
Exactly one of these warehouse stores.
Exactly one of these warehouse stores.
BJ’s Wholesale Club and Costco.
BJ’s Wholesale Club and Sam’s Club.
Sam’s Club and Costco.
None of these warehouse stores.
The number of participants that shopped in:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17
To answer this question, we can use a Venn diagram to visualize the data and find the number of participants that shopped in each category.
First, we'll create a venn diagram with three circles, one for each store (BJ's Wholesale Club, Sam's Club, and Costco). Then, we'll fill in the data from the question.
1. Start with the center of the venn diagram, where all three circles overlap. This represents the 5 participants who shopped in all three stores.
2. Next, fill in the overlapping sections between two circles. These represent the participants who shopped in two of the stores, but not the third.
- BJ's Wholesale Club and Sam's Club: 15 - 5 = 10
- BJ's Wholesale Club and Costco: 16 - 5 = 11
- Sam's Club and Costco: 12 - 5 = 7
3. Finally, fill in the sections that do not overlap with any other circles. These represent the participants who shopped in only one of the stores.
- BJ's Wholesale Club only: 58 - 10 - 11 - 5 = 32
- Sam's Club only: 49 - 10 - 7 - 5 = 27
- Costco only: 45 - 11 - 7 - 5 = 22
Now, we can use the venn diagram to answer the questions:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 32 + 22 + 27 = 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17
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Hans can choose Plan A or Plan B for his long distance charges.
The plan that costs less if Hans makes 300 minutes of long distance calls is Plan A by $ 4.
The number of long distance minutes till the plans cost the same is 350 minutes.
If the time spent on long distance calls is more than this amount, the plan that costs less is Plan B.
How to find the plan cost ?The cost per plan can be seen on the graph. At 300 minutes of long distance calls, Plan A costs $ 24 and plan B costs $ 28 so the cheaper plan is Plan A by :
= 28 - 24
= $ 4
The number of minutes till they cost the same is 350 minutes which is where they intercept and after this, Plan B will cost less.
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a number close to an exact value
Answer:
approximate number
Step-by-step explanation:
Hi this a great question. A number close to an exact value is an approximate number. That is a number that is close but not exactly equal to another number. It is the counterpart to exact numbers. There is no uncertainty in an exact number, while the definition of an approximate number is one in which uncertainty exists.
A store sells 8 bags of chips for $10 store B sells 10 bags of chip for $12 what is the unit rate for store a
Answer:
1 bag is 1.25 for store a
Step-by-step explanation:
10/8 = 1.25
PHYSICS A proton in a magnetic field follows a path on a coordinate grid modeled by the function f(x) = x^4 - 2x^2 "-15." What are the x-coordinates of the points on the grid where the proton crosses the x-axis
So the x-coordinates of the points where the proton crosses the x-axis are x = ±√(5).
What is function?In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain or range) with the property that each input is related to exactly one output. In other words, a function is a rule or a mapping that assigns a unique output value to each input value. Functions can be represented in various ways, such as equations, tables, graphs, or diagrams. They are used to describe and model a wide range of phenomena in mathematics and other fields, such as physics, engineering, economics, and social sciences. Functions are often denoted by symbols such as "f(x)", "g(x)", or "h(t)" and can be composed or combined to form new functions. They can also be classified according to various properties, such as whether they are continuous, differentiable, invertible, or periodic. In summary, in mathematics, a function is a relation between a set of inputs and a set of possible outputs that assigns a unique output value to each input value.
Here,
To find the x-coordinates of the points where the proton crosses the x-axis, we need to find the roots of the function f(x) = x⁴ - 2x² - 15. These are the values of x that make the function equal to zero, which correspond to the points where the proton crosses the x-axis.
To find the roots, we can use the factoring method or the quadratic formula. In this case, we can factor the function as follows:
f(x) = x⁴ - 2x² - 15
= (x² - 5)(x² + 3)
Setting each factor equal to zero and solving for x, we get:
x² - 5 = 0 or x² + 3 = 0
Solving for x in each equation, we get:
x = ±√(5) or x = ±i*√(3)
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What is the image of (3, -3) after a dilation by a scale factor of centered at the
origin?
What is the image of (-4, 7) after a dilation by a scale factor of 3 centered at the
origin?
What is the image of (3, 3) after a dilation by a scale factor of 5 centered at the
origin?
What is the image of (-8,-8) after a dilation by a scale factor of centered at the
origin?
The image of (3, -3) is (1, -1).
The image of (-4, 7) is (-12, 21).
The image of (3, 3) after a dilation by a scale factor of 5 is (15, 15).
The image of (-8,-8) is (-2, -2).
How to find image using a scale factor?The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.
To find the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin, multiply the coordinate by 1/3. That is:
image = (1, -1)
For image of (-4, 7) after a dilation by a scale factor of 3, multiply the coordinate by 3:
image = (-12, 21)
For the image of (3, 3) after a dilation by a scale factor of 5, multiply the coordinate by 5:
image = (15, 15)
For the image of (-8,-8) after a dilation by a scale factor of 1/4, multiply the coordinate by 1/4:
image = (-2, -2)
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Complete Question
What is the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin?
What is the image of (-8,-8) after a dilation by a scale factor of 1/4 centered at the origin?
where did Goku die nnnnnnnnnnnnnnnnnnnnnnnn
Answer:
Goku died you I just started watching
4. The Waskabaska Peaked Tent site has six
permanent tents shaped like pyramids. Each
pyramid has a rectangular base of ninety six
square feet. There is a table 2 feet by 6 feet
inside the tent. The height of the tent is ten feet
What is the total volume of all the tents.
The total volume of all the tents is 1920 cubic feet
What is the total volume of all the tents.From the question, we have the following parameters that can be used in our computation:
Number of tents = 6
Base area of the tents = 96 square ft
Height of the tent = 10 ft
The total volume of all the tents is calculated as
Volume = Number of tents * Base area of the tents * Height of the tent/3
Substitute the known values in the above equation, so, we have the following representation
Volume = 6 * 96 * 10/3
Evaluate
Volume = 1920
Hence, the volume is 1920 cubic feet
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Rectangle jklm is congruent to a 4 inch by 7 inch rectangle. How many different values are possible for the length of ?.
Two different values are possible for the length of Rectangle jklm.
When we say that two rectangles are congruent, we indicate that their sides are equal. The rectangles' lengths and widths have to be comparable. It's feasible that jm will be 4 or 7 inches long given that one rectangle has dimensions of 4 and 7. Two lengths are conceivable as the solution. The length and breadth make up the rectangle shape. A rectangle has four sides, and its opposing sides are all the same length. You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle.
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Fifteen friends are playing Duck, Duck, Goose. The friends sit equally spaced in a circle. There are three people between Stanley and Frank.
What is the measure of the major arc along the perimeter of the circle between Stanley and Frank?
Enter your answer in the box.
The measure of the major arc along the perimeter of the circle between Stanley and Frank is 264°.
What is an arc measure?A circle's arc, or circumference, is a section of the circle. The difference between an arc length and an arc measure is the angle the arc creates with the circle's center. It is possible to measure this arc in radians or degrees.
Given:
Fifteen friends are playing Duck, Duck, and Goose.
The friends sit equally spaced in a circle.
So, 360/15 = 24° is the angle measure of an arc.
There are three people between Stanley and Frank.
That means there are 11 people between Stanley and Frank.
So, 11 x 24 = 264° is the measure of the major arc.
And the perimeter of the major arc is 264°
Therefore, the perimeter of the major arc is 264°
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Question 3(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following graphs represents a linear function?
coordinate plane with a graph that passes through the points negative 3 comma 0 and negative 1 comma negative 4 and 1 comma 0
coordinate plane with a graph drawn that passes through the points negative 4 comma 0 and 0 comma negative 4 and 4 comma 0 and 0 comma 4
coordinate plane with a graph drawn that passes through the points negative 4 comma negative 2 and negative 4 comma negative 1 and negative 4 comma 0
coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2
The second and fourth graphs represent linear functions.
What is a linear function?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
To determine which of the given graphs represents a linear function, we need to check whether the graph is a straight line.
The first graph passes through the points (-3, 0), (-1, -4), and (1, 0). We can plot these points and see that they do not lie in a straight line. Therefore, the first graph does not represent a linear function.
The second graph passes through the points (-4, 0), (0, -4), (4, 0), and (0, 4). We can plot these points and see that they do lie on a straight line. Therefore, the second graph represents a linear function.
The third graph passes through the points (-4, -2), (-4, -1), and (-4, 0). We can plot these points and see that they lie on a vertical line. Therefore, the third graph does not represent a linear function.
The fourth graph passes through the points (-4, 0), (-2, -1), and (0, -2). We can plot these points and see that they do lie on a straight line. Therefore, the fourth graph represents a linear function.
Therefore, the second and fourth graphs represent linear functions.
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Answer: It is the second one
Step-by-step explanation:
Because It makes the most sense
4. If lines AB and XY are parallel, how many times do they intersect?
Answer:
Zero
Step-by-step explanation:
Which hill is the steepest
Answer:
Liberty Hill
Step-by-step explanation:
To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:
|m|= |Slope (or gradient)|
= |[tex]\frac{VerticalDistance}{HotizontalDistance}[/tex]|
The hill with the greatest absolute value of m is the steepest:
|[tex]m_{Dixie} = |\frac{40}{80}|[/tex]
= 0.5
[tex]|m_{Bell}| =|\frac{20}{80}|[/tex]
= 0.25
[tex]|m_{Liberty}| = |\frac{60}{80}|[/tex]
= 0.75
Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest
Mina is trapped at the top
of a 389 foot tall tower.
If Jonathan is standing
412 feet from the base of
the tower, what is the
angle of elevation from
him to Mina?
Answer:
We will use the trig ratio tan for this
Tan x°=opposite/adjacent
=>tan^-1(398/412)=x
=>x=44(approximately)
So the angle of elevation is 44°
Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.
Answer:
There is exactly one solution: (1, 2).
Step-by-step explanation:
For this, it's already in slope intercept form so all you have to do is graph the two and see at what point do these two lines cross, which is (1, 2).
Hope this helps!
I really need help with this question
Answer: Can't help I tried to figure it out, but it was wrong.
Step-by-step explanation: I'm sorry.
In excerise 13-16 find the measures of the numbered angles in rhombus DEFG image it’s only one question I would appreciate if you guys helped
The measure of the angles given in the rhombus are given as follows:
m∠GEF = 27°m∠2 = 27° m∠1 = 27° m∠4= 27°m∠5 = 63°m∠6 = 63°m∠3 = 90°What are the properties of a rhombus?A rhombus is a type of parallelogram with the following properties:
Opposite sides are parallel: The opposite sides of a rhombus are equal in length and parallel to each other.Opposite angles are equal: The opposite angles of a rhombus are equal in measure.Consecutive angles are supplementary: The sum of the measures of the consecutive angles in a rhombus is equal to 180 degrees.Diagonals bisect each other: The diagonals of a rhombus bisect each other and are equal in length.All sides are equal: In a rhombus, all sides are equal in length.To obtain the following, therefore, here is the premise behind each assertion:
m∠GEF = 27° - Givenm∠ 2 = 27° - Alternate anglesm∠ 1 = 27° - Corresponding angles in congruent triangles (CPCTC) m∠ 4 = 27° - Corresponding angles in congruent triangles (CPCTC) m∠ 5 = 63° - Bisected Supplementary angles (∠FGD and ∠GDE are supplementary)m∠6 = 63° - Bisected Supplementary anglesm∠3 = 90° - Sum of Angles in a triangleLearn more about rhombus:
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I need help with number 11
The values for x used in diagonal length is 2.
What is Rectangle?A quadrilateral is a rectangle.The opposing sides are level and parallel to one another.90 degrees is the angle of each interior.360 degrees is the total of all interior angles.The diagonals cut each other in half.The length of both diagonals is the same.Given:
We have LN= 7x+ 6 and MP = 9x- 2
As, the diagonals of a rectangle are equal then
LN= MP
7x+6= 9x - 2
-2x = -4
x= 2
Thus, the value is 2.
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passes through the point (4, 5);
slope = -1/4
The equation of line is y= -1/4x+ 6.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
passes through the point (4, 5);
slope = -1/4
Using the slope intercept form
y = mx + b
y= -1/4x + b
As the point passes through (4, 5) then
5 = -1/4 (4) + b
5 + 1 = b
b= 6
So, the equation of line is y= -1/4x+ 6.
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Hello I need help on this question
Answer:
Step-by-step explanation:
The triangles are similar so the sides are proportional.
It is important to match the sides correctly.
Triangle PQR is similar to Triangle STU
So the sides PQ similar to ST
QR similar to TU
PR similar to SU.
We are given one side in the smaller triangle SU which is 6.
SU matches to PR - if you divide PR by SU - 21 ÷ 6 = 3.5
So the sides of the smaller triangle are 3.5 times smaller
PQ = 14 then divide by 3.5 to get ST = 4
QR = 28 then divide by 3.5 to get TU = 8
The angles are much easier.
Similar triangles have the same angle measurement.
Find the corresponding angles.
To find ∠Q - add angles P and R and subtract from 180°.
All triangles interior angles add to 180°.
180 - (70 + 46) = 180 - 116 = 64°
Match up the corresponding angles:
∠S = 70°, ∠T = 64°, ∠U = 46°
SU = 6 ST = 4 TU = 8
Bobby has $27 to spend on ice cream for the month. The ice cream he likes is two dollars each how many ice cream‘s can he buy this month
?
Convert 16 kilometers into feet. Round your answer to the nearest whole number.
16 kilometers = 52493.4 feet
Formula: multiply the value in kilometers by the conversion factor '3280.8398950125'.
So, 16 kilometers = 16 × 3280.8398950125 = 52493.4383202 feet.
what is 23.5 cm to inches ?
1 cm is defined as 1/100 of a meter. One foot is defined as 1/3 of a yard or 12 inches in length. We know that, 1 inch = 2.54 cm and therefore, 23.5 centimeter = 9.252 inches
Centimeters :
The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and equals approximately 39.37 inches. It is defined as 1/100 of a meter.
The centimeter is based on the SI unit of measurement and is equal to one hundredth of a meter as indicated by the prefix "centi". The metric prefix ranges from 10-18 to 1018 in decimal, and the base (metric in this case) has no prefix and a modulus of 1. Exploring the most commonly used metric prefixes such as kilogram, mega, giga, tera, centi, milli, micro, and nano can be useful for quickly navigating metric units.
Inch:
Inches is a unit of length or distance in several systems of measurement, including traditional American units and British Imperial units. An inch is defined as 1/12 of a foot, so 1/36 of a yard. By modern definition, 1 inch equals 25 exactly 4 mm.
The term "inch" comes from the Latin unit "uncial", equivalent to "1/12" in Roman terms. There were several standards for inches in the past and the current definition is based on international yards. One of the earliest definitions of an inch was based on a barley grain, where an inch equals the length of three dry round grains of barley laid end to end. Another version of the inch is believed to be derived from the width of a person's thumb, where length was obtained by averaging the widths of three thumbs (small, medium, and thumb).
By multiplying the value in centimeters by the conversion factor 0.3937007874021.
So, 23.5 centimeters = 23.5 × 0.39370078740213
= 9.25196850395 inches.
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Suppose a population of cells starts at 200 and triples every day. Let p equal the cells and d equal the number of days since the 200 cells were observed. True or False: You could use the equation the equation below to model this situation.
p = 200 · 3d
True
False
The model [tex]p = 200.3^d[/tex] satisfies the statement, A population of cells starts at 200 and triples every day.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex]
Given, A population of cells starts at 200 and triples every day.
Where 'p' is the number of cells and 'd' is the number of days.
The situation is represented by [tex]p = 200.3^d[/tex].
Now, Three times 200 is 600 and Nine times 200 is 1800.
At d = 1.
[tex]p = 200.3^1[/tex].
[tex]p = 600[/tex].
And,
At, d = 2.
[tex]p = 200.3^2[/tex].
[tex]p = 1800[/tex].
So, The model satisfies the statement and it is true.
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what is 1.5inch to cm ?
Using the conversion formula of converting inches to centimeters, we get 1.5 inch is 3.81 centimeters.
To convert 1.5 inches to centimeters, we can use the formula:
1 inch = 2.54 centimeters
So, 1.5 inches = 1.5 x 2.54 = 3.81 centimeters
Therefore, 1.5 inches is equal to 3.81 centimeters.
The conversion factor between inches and centimeters is based on the definition of the inch and centimeter units. The inch is a unit of length in the imperial system of measurement, while the centimeter is a unit of length in the metric system. The conversion factor between the two systems is based on the definition of the meter, which is the primary unit of length in the metric system. In summary, 1.5 inches is equal to 3.81 centimeters, and this conversion is based on the relationship between the inch and centimeter units, as well as the definition of the meter as the primary unit of length in the metric system.
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need help with this, problem shown below show work
Answer:
Step-by-step explanation:i cant see words need closer view
Match the vocabulary word to the definition. Make sure to only enter CAPITAL letters with no spaces or numbers. (Your answer should look something like this WTYUSR)
The required matches are E1, B2, D3, A4,C5.
What is ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).
According to question:Correct matches for the given matching are
Ratio - A comparison of two or more items
So, E1
Rate - A comparison of two DIFFERENT units
So, B2
Unit Rate - A rate where the second number, item, or quantity equals one
So, D3
Ratio Table - A tool we use to find equivalent ratios
So, A4
Equivalent Ratio - Two or more ratios that have the same value
So, C5
Thus, required matches are E1, B2, D3, A4,C5.
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Data about the outside temperature and gas used for heating a building are given in the table.
Use a graphing calculator to create the line of best fit for the data.
temperature
(deg F) gas usage
(therms)
58 5,686
62 7,373
64 5,805
67 5,636
70 3,782
73 3,976
74 3,351
74 3,396
75 2,936
73 3,078
65 4,549
59 7,022
58 6,106
62 4,566
64 4,608
67 5,790
70 6,501
73 3,843
What is the equation of the line of best fit for this data? Round numbers to the nearest whole number.
What is the slope of the line of best fit? What does it mean in this situation?
What does the line of best fit estimate for gas usage when the outside temperature is 59 degrees Fahrenheit?
How does the actual gas usage compare to the estimated gas usage when the outside temperature is 59 degrees Fahrenheit?
Answer:
The equation of the line of best fit for this data is y = -106x + 6178.
The slope of the line of best fit is -106. This means that for every degree increase in temperature, the gas usage decreases by 106 therms.
The line of best fit estimates that when the outside temperature is 59 degrees Fahrenheit, the gas usage will be 7,022 therms.
The actual gas usage when the outside temperature is 59 degrees Fahrenheit is 6,106 therms. This means that the estimated gas usage is slightly higher than the actual gas usage.
Answer:
Step-by-step explanation:
A) y = -180x + 16938
B) The slope is -180. This means that for every increase in temperature/degrees the gas usage will decrease by 180.
C) -180x + 16938 = 6318 When the temperature is 59 degrees Fahrenheit the line of best fit estimates 6318 gas usage.
D) The gas usage when the temperature is 59 degrees is 7022 on the table, but the gas usage estimated is 6318. The difference is 704
-Hope this helps.