The points are not at a distance of 6 units from each other.
Given that the distance between point (2, 2) and point (8, 2) is 6 units a coordinate plane.
We need to find which other pairs of points are also 6 units apart.
The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either
( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).
If either of the conditions is satisfied, then only we can say that the two points has distance of 6 units between them.
Now, As given
Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)
Check whether the conditions are satisfied or not .
Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2
Now,
x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0
∴ we get
1st condition is satisfied, So the points have a distance of 6 units between them.
Now,
Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)
Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3
Now,
x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0
Here neither of the conditions are satisfied.
So, the points are not at a distance of 6 units from each other.
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Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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A flashlight can light a circular area of up to 6 feet in diameter. What is the maximum area that can be lit? Round to the nearest tenth if needed!
Answer: 28.3
Step-by-step explanation:
The question is just asking for the area of a circle with a diameter of 6. The equation for that is [tex]A = \pi r^{2[/tex].
Since the Radius (r) is half the diameter, your equation will look like this: [tex]A=\pi 3^2[/tex].
When plugged into a calculator, 28.27443 is the answer. Rounded to the nearest tenth would be 28.3. Hope this helps!
What is the measure of EACH interior angle of a
regular 16-sided polygon?
The measure of each interior angle of a regular 16-sided polygon is 157.5 degrees
How to determine the valueTo determine the value of the interior angle, we need to note that;
The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;
(n -2)180
Such that the variable n in the expression represents the number of sides of the polygon
From the information given, we have that;
(16- 2)180
expand the bracket
14(180)
multiply the values
2520 degrees
Then, we have;
16x = 2520
Make 'x' the subject
x= 157. 5 degrees
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In 2012, the population of a city was 6.53 million. The exponential growth rate was 2.79% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.
a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.
b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.
c) The population of the city will be 10 million in 2028.
d) The doubling time for the population is 25 years.
What is an exponential growth function?An exponential growth function is one of the two exponential functions, including an exponential decay function.
An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.
Population of the city in 2012 = 6.53million
Exponential growth rate = 2.79% per year
Let the number of growth years = t
Exponential growth function:a) y = 6.53(1.0279)^t
b) From 2012 to 2018, the number of years = 6 years
Population in 2018, y = 6.53(1.0279)^6
= 7.7 million
c) When the population will be 10 million = 15.5 years
10 = 6.53(1.0279)t
t = 15.5 years
= 16 years
= 2028
d) 13.06 = 6.53(1.0279)t
t = 25.189 years
= 25 years
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(+25)-5x5:2+2²
27-5×5=2+2²
Answer:
16.5 = 6
Step-by-step explanation:
The equation given is (+25)-5x5:2+2² = 27-5×5=2+2². When calculating, we first simplify the division to get (+25)-12.5+4 = 27-25+4. Then we add and subtract the values on either side to get 16.5 = 6. Finally, as the equation is incorrect, we can conclude that the initial assertion is false. It is important to carefully follow the order of operations and simplify expressions correctly to avoid errors in equations.
. Find the exact circumference in terms of pi of the circles. (5 points each)
Step-by-step explanation:
The hypotenuse of each of these right triangles can be found using Pythagorean theorem....the hypotenuse is also the DIAMETER of the circle
diamter * pi = circumference
First one:
Hypot^2 = 13^2 + 13^2
hypot ^2 = 338
hypot = diameter = sqrt (338)
circumference = diamter * pi = sqrt 338 pi ft ( or 13 sqrt(2) pi ft )
The second one is the same with slightly different numbers...you try it ...
Answer:[tex]\sqrt{338}\pi[/tex], [tex]25\pi[/tex]
Step-by-step explanation:
I will start with the second one, since it will be easier. Because this is a right triangle, you can use the given side lengths of the triangle to find the hypotenuse, which is also equal to the diameter of the triangle. Since the pythagorean theorem states that a^2(the shorter leg, squared) + b^2 (the longer leg, squared) = c^2 (the hypotenuse, squared) we can turn it into an equation like this:
[tex]7^{2\ }+\ 24^{2}\ =\ c^{2}[/tex]
(lets use x in place of c in the next few equations, for algebraic simplicity)
Simplify
[tex]49+\ 576\ =x^{2}[/tex]
[tex]625=x^{2}[/tex]
Get the square roots
[tex]\sqrt{625}=\sqrt{x^{2}}[/tex]
[tex]x=25[/tex]
Since x is equal to the hypotenuse, we know that the hypotenuse is also 25. This means the diameter of the second circle is 25, and we can now find the circumference. The EXACT circumference of the second circle is 25π, but a simplified version can be created by calculating it as if it were an equation. This comes out to around 78.5398163397, which would trail for infinity. which is why to get an exact measurement of the diameter, the most simplified exact version is displayed by multiplying the diameter by the pi symbol, because it is impossible to fit an infinite number in a finite space.
Now for the first circle, which I am now realising is no more difficult than the last one. We can do the same thing in this case, using pythagorean theorem, because there are two dash lines marking two of the lines on the circle to be equal to one another, we know that the two marked lines are equal to 13, despite not appearing to be.
We can use the same equation as we did before, but slightly modified.
[tex]13^{2}+13^{2}=x^{2}[/tex]
Simplify:
[tex]169+169=x^{2}[/tex]
[tex]338=x^{2}[/tex]
Now we can take the square roots of both sides of the equation.
[tex]\sqrt{338}=\sqrt{x^{2}}[/tex]
This is where we come to a bit of a pause. Because the square root of 338 is an irrational constant number, we have to use the unsimplified square root in our answer for the circumference, otherwise, our answer would not be exact.
The diameter of our circle is [tex]\sqrt{338}[/tex], which means that we can use an equation like this to find the circumference:
[tex]\sqrt{338}\pi[/tex]
But since we cannot simplify this any further without it not being exact, we must leave it as is.
Select the correct answer.
Which of these statements defines the term resources?
O A. materials that help you achieve your goals
OB. all the goods and services provided to people
OC. the government's ability to deal with economic problems
Reset
Next
The statements that defines the term resources is A. materials that help you achieve your goals.
What is resources?Resource can be described as all the materials available that is available in individual environment and can be seen as one that is technologically accessible.
It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible as welll as culturally sustainable and they serves as things that can help us and thjat can satisfy our needs and wants which is needed on daily basis.
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please help me thank you!!
Answer: 75%
Step-by-step explanation:
We will divide the wanted outcome by the total number of possible outcomes. Note that a decimal times 100 becomes a percentage.
[tex]\displaystyle \frac{\text{not picking a diamond card}}{\text{cards in the deck}} =\frac{39}{\text{52}} =0.75\;\;\;0.75*100=75\%[/tex]
I need help to solve this...
Answer:
2.38888
Step-by-step explanation:
That's what is says hope this helps
What is an angle that is adjacent to
Answer:
<HAG
Step-by-step explanation:
Two angles are adjacent when they have a common side and common vertex, and they do not overlap one another. In this case, <EAG, A is the vertex. <HAG has the same vertex, A, and it shares side AG.
PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
V = (1/2)(4/3)π(6.5^3) = 575.17 cubic inches
V = (1/2)(4/3)(3.14)(6.5^3) =
574.88 cubic inches
The correct answer is 574.9 cubic inches.
A researcher is interested in how client expectations of success before therapy relate to satisfaction with the sessions afterward. Ratings (on a 1-10 scale) for 10 participants are presented in the table below. This dataset will be used for Questions 1-4. Compute the Pearson r correlation coefficient for these data. Note: Show your work on a separate sheet of paper. You will be asked to upload a scan/picture of your work at the end of the test.
Client Expectations (x) Satisfaction (y)
1 3
1 1
2 3
3 7
3 9
4 5
6 8
6 7
7 10
7 7
Questions:
1.) What is the value of the Pearson correlation coefficient (r)? Please round your answer to 3 decimal places.
2.) What would the critical value (rcrit) be for a 2-tailed test with a .05 alpha level using the Client Expectation-Satisfaction dataset shown in Question 1? (Express your answer to 3 decimal places)
3.) Based on the correlation you calculated in Question 1 and the critical value you identified in Question 2, was the correlation statistically significant (i.e., would you reject the null hypothesis)?
1. Using the formula for Pearson correlation coefficient, we have:
x y xy x^2 y^2
1 3 3 1 9
1 1 1 1 1
2 3 6 4 9
3 7 21 9 49
3 9 27 9 81
4 5 20 16 25
6 8 48 36 64
6 7 42 36 49
7 10 70 49 100
7 7 49 49 49
n = 10
sum(x) = 40, sum(y) = 53, sum(xy) = 286, sum(x^2) = 214, sum(y^2) = 506
r = [n(sum(xy)) - sum(x)sum(y)] / sqrt{ [n(sum(x^2)) - sum(x)^2][n(sum(y^2)) - sum(y)^2] }
r = [10(286) - (40)(53)] / sqrt{ [10(214) - (40)^2][10(506) - (53)^2] }
r = 0.832 (rounded to 3 decimal places)
2. The critical value (rcrit) for a 2-tailed test with a 0.05 alpha level and 8 degrees of freedom is 0.632 (using a t-distribution table or calculator).
3. The calculated correlation coefficient (r = 0.832) is greater than the critical value (rcrit = 0.632), which means that the correlation is statistically significant. We would reject the null hypothesis and conclude that there is a significant positive correlation between client expectations and satisfaction with therapy sessions.
Find the surface area of the composite solid. Round your answer to the nearest hundredth.
The surface area is about square centimeters.
WILL GIVE BRAINLIEST
The surface area of the composite figure is about 98.56 sq.cm
What is the surface area of the composite figure?The composite figure is made up of a cylinder and a cuboid.
The formula for surface area of a cylinder is:
A = 2πr² + 2πrh
In this case, we only have top and not bottom. Thus:
A = πr² + 2πrh
A = π(1)² + 2π(1 * 6)
A = 37.7 sq.cm
Surface area of cuboid is:
A = 2(4 * 4) + 4(2 * 4) - π(1)²
A = 32 + 32 - π
A = 60.86 sq.cm
Total surface area = 37.7 sq.cm + 60.86 sq.cm
= 98.56 sq.cm
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5. Which graph represents 4x - 2y = 8?
Answer:
A
Step-by-step explanation:
4x - 2y = 8
x - int y = 0
4x = 8
x = 2
(2, 0)
y-int, x = 0
-2y = 8
y = -4
HELP ASAP I NEED THIS Use the image to determine the direction and angle of rotation.
90° clockwise rotation
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
Answer:
90 degrees counterclockwise
What meaning of the statement this?
This statement defines the concept of left and right sets of elements x of G with respect to the subgroup H of G.
How does the statement express it's meaning?The left set of x in G, denoted by xH, is the set of all elements of G obtained by multiplying x to the left by all elements of H. Formally xH = {xh: h ∈ H}, where "xh" denotes the product of x and h in G.
Similarly, the right-hand set of x in G, denoted Hx, is the set of all elements of G obtained by multiplying x on the right by all elements of H. Formally Hx = {hx: h ∈ H}, where "hx" denotes the product of h and x in G.
Generally, left and right sets are different sets and may contain different numbers of elements. However, if the group G is commutative (ie the order of multiplication does not matter), then the left and right sets are equal.
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Jason is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 1 point. What would be Jason's test score (out of o) if he got 9 questions wrong? What would be his score if he got a questions wrong?
Score with 9 questions wrong:
Score with x questions wrong:
The test score for Jason will be 55% for answering 11 questions right.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.
The test score will be calculated as,
[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]
[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]
[tex]\text{Test Score}=0.55\times100[/tex]
[tex]\text{Test Score}=0.55\%[/tex]
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What are the values of the trigonometric ratios for this triangle?
Drag the answers into the boxes.
The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.
We know that, sinθ = Opposite/Hypotenuse
sinθ = 8/17
We know that, cosθ = Adjacent/Hypotenuse
cosθ = 15/17
We know that, tanθ = Opposite/Adjacent
tanθ = 8/15
Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
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Hurry pls
50pts
Time limit
Tell me the domain and range
Tell me whether the graph is a function or not.
The answer choices are below
Examining the graph, it can be deduced that the graph is not a function.
the domain is x ≥ -3the range is all real numbersWhat is domain and range?Domain and range are mathematical notation utilized to define the spectrum of possible accepted input values (domain) as well as the corresponding output values (range) in a given function or relation.
A definitive domain correspondingly denotes the compilations of all plausible inputs that generate a valid result when put essentially into the relation or operation.
Conversely, the range defines the plethora of conceivable outputs that this very same function or relation can devise, considering its specified domain.
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Consider the sequence {3, 12, 21, 30, 39, 48, 57} What is a5
The value of the term a5 is 39
Calculating the value of a5From the question, we have the following parameters that can be used in our computation:
{3, 12, 21, 30, 39, 48, 57}
The expression a5 means the 5th term of the sequence
In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39
Hence, a5 = 39
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Use the frequency data in the table below to compute the phi correlation coefficient.
Therapist's Approach Satisfaction Totals
Cognitive-Behavioral Psychodynamic
Client Satisfied
by Therapy?
Yes 26 15 41
No 11 24 35
Approach Totals 37 39 N = 76
What is the Fobt for the regression line?
What is the critical value (Fcrit ) for the significance test of the regression line?
Based on the Fobt you calculated is the regression line statistically significant? (i.e., Should you reject the null hypothesis?)
Use the information you computed for the regression line significant test's source table to calculate the standard error of prediction (se). What is its value? (Round your answer to 2 decimal places)
Based on the information, we cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84).
How to explain the hypothesisIt should be noted that to establish whether the phi coefficient is statistically significant, we can compare it to a crucial value. However, the significance level (i.e., alpha) must be specified ahead of time.
Assume a 0.05 level of significance. We calculate the crucial value for a 2x2 contingency table with 1 degree of freedom and a significance level of 0.05 using a phi coefficient table or calculator.
We cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84). As a result, we find that there is no statistically significant relationship between the therapist's method and client satisfaction.
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QUESTION SIX Solve the following problems: (a) Find the gradient, x and y intercepts of 3x + 4y + 12 = 0. Sketch the graph. (6 Marks) (b) Find the gradient, x and y intercepts of the line I, passing through the points P (-1,4) and Q (3,0). Sketch the graph. (6 Marks) (c) A line 1₂ is perpendicular to 4. Find its gradient. (2 Marks) (14 Marks)
The sketches of the graphs are added as an attachment and the gradient of the perpendicular line l₂ is 1
Finding the gradient, x and y interceptsGiven that
3x + 4y + 12 = 0
Set x = 0 to determine the y-intercept
4y + 12 = 0
So, we have
y-intercept = -3
Set y = 0 to determine the x-intercept
3x + 12 = 0
So, we have
x-intercept = -4
For the gradient, we make y the subject in 3x + 4y + 12 = 0.
y = -3/4x - 12/4
y = -3/4x - 3
So, the gradient is -3/4
The sketch of the graph is attached.
Finding the gradient, x and y interceptsHere, we have the points P (-1,4) and Q (3,0).
The gradient is
gradient = (0 - 4)/(3 + 1)
gradient = -1
From the point, we have
x-intercept = 3
For the y-intercept, we have
(0 - 4)/(3 + 1) = (y - 4)/(0 + 1)
(y - 4)/(0 + 1) = -1
y - 4 = -1
y-intercept = 3
So, the equation is
y = -x + 3
The sketch of the graph is attached.
Finding the gradient of l₂We understand that l₂ is perpendicular to l
The gradients of perpendicular lines are
Gradient 1 = -1/Gradient 2
So, we have
l₂ = -1/-1
Evaluate
l₂ = 1
Hence, the gradient of line l₂ is 1
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Problems 2 and 3 refer to the following drawing.
2. The side AC corresponds to side AE of the other triangle.
3. The length of side BC is 15.
What are similar triangles?Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.
From the diagram given, we have;
2. Given that the triangles are similar, thus:
The side AC corresponds to side AE of the other triangle.
3. On comparing the corresponding length of the triangles, we have;
15/ 25 = 9/ BC
15BC = 9 x 25
= 225
BC = 225/ 15
= 15
The length of side BC is 15.
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How many lines are shown in the drawing
The given images shows us that we have a total of two lines
How to identify the lines?In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot. It has no length, shape or size.
A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.
A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.
Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.
From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.
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Just Need the blanks filled in PLEASE HELP
The Equation based on the function will be: t = (1/0.07) * ln(P/1,500,000)
How to explain the functionInitially, the exponential expression is extracted and formulated as follows:
It should be noted that to obtain e^(0.07t) = P/1,500,000
Secondly, in order to determine the value of t, take the natural logarithm of both sides of the equation such that:
Take ln(e^(0.07t)) = ln(P/1500000)
It can now be represented by 0.07t = ln(P/1500000)
Finally, on dividing both components of the term through 0.07, it results in the isolation of t where:
Equation: t = (1/0.07) * ln(P/1,500,000)
In conclusion, this function's inverse describes the number of years, since the year 1990, for a determined population figure, P - its formation being previously outlined above.
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use a unit 2 multiplayer to convert 5.4 square meters to square centameters
To convert 5.4 square meters to square centimeters is 54,000 cm²
How to convert convert 5.4 square meters to square centimeters?To convert 5.4 square meters (m²) to square centimeters (cm²),
We need to multiply it by 10,000 (since 1 meter = 100 centimeters).
5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²
Therefore, 5.4 square meters is equal to 54,000 square centimeters.
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A cone has an apex. True False
Answer:
True, a cone has an apex which is the point where the sides of the cone meet to form a tip.
Two buses leave a station at the same time and travel in opposite directions. One bus travels 8 mih slower than the other. If the two buses are 432 miles apart after 3 hours, what is the rate of each bus?
The rate of each bus which leave a station at the same time are 76 mi/h and 68 mi/h respectively.
Given that,
Two buses leave a station at the same time and travel in opposite directions.
Let x be the distance travelled by the the first bus in 3 hours.
Then the distance travelled by the other bus in 3 hours = 432 - x
Rate of first bus = x/3 miles per hour
Rate of second bus = (432 - x) / 3 miles per hour
One bus travels 8 mi/h slower than the other bus.
x/3 - (432 - x) / 3 = 8
(x - 432 + x) / 3 = 8
2x - 432 = 24
2x = 456
x = 228
Rate of one bus = 228/3 = 76 mi/h
Rate of second bus = (432 - 228)/3 = 68 mi/h
Hence the rate of each bus are 76 mi/h and 68 mi/h respectively.
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What term refers to the basic characteristics of a population segment such as gender age and income?
The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.
We have,
Demographics refers to statistical data that describes a population and its characteristics, such as age, gender, income, education level, marital status, and other relevant factors.
Demographic information is commonly used by businesses and organizations to analyze consumer behavior, market trends, and patterns in the population.
By understanding the demographics of a particular population segment, businesses can tailor their products and services to better meet the needs and preferences of their target audience.
Demographic information is also used by government agencies and policymakers to allocate resources, plan for future development, and assess the needs of the population.
Thus,
The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.
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2. Tell if the number shown is written in scientific notation. If it is, write correct, if incorrect
explain why and correct the mistake.
A. 0.5045 x 10
B. 2.804 x 10"
C. 12.04 x 10
The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.
What is Scientific notation?Scientific notation can be described as the way of writing very large as well as very small numbers.
It should be noted that the number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.
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