3.1 Q15
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 70°, it's height, f(x), in feet, can be modeled by:
[tex]f(x)=-0.06x^2 + 2.7x + 5.9[/tex]
where x is the shot's horizontal distance, in feet, from its point of release.
What is the maximum height of the shot and how far from it's point of release does this occur?
Answers
Find x-coordinate of the vertex (horizontal distance)
The function above is in standard form of ax² + bx + c = 0
In standard form of ax² + bx + c = 0, we could find the x-coordinate of the vertex by the formula of
[tex]x= -\cfrac{b}{2a} [/tex]
Extract the information of a and b from the function f(x) = -0.06x² + 2.7x + 5.9
a = -0.06
b = 2.7
Input the value of a and b to the formula of x-coordinate of the vertex
x = [tex]-\dfrac{b}{2a} [/tex]
x = [tex]- \dfrac{2.7}{2 \times (-0.06) \\} [/tex]
x = [tex]- \dfrac{2.7}{-0.12} [/tex]
x = [tex] \dfrac{2.7}{0.12} [/tex]
x = 22.5
The x-coordinate represents the horizontal distance. So the maximum height occurs when the distance is 22.5 feet far from its point of release.
Find y-coordinate of the vertex (the maximum height)
To find the maximum height, input the value of x-coordinate of the vertex to the function.
f(x) = -0.06x² + 2.7x + 5.9
f(22.5) = -0.06(22.5)² + 2.7(22.5) + 5.9
f(22.5) = -0.06(506.25) + 60.75 + 5.9
f(22.5) = -30.375 + 60.75 + 5.9
f(22.5) = 36.275
The maximum height is 36.275 feet
The maximum height reached by the shot is 36.375 feet. This occurs at a horizontal distance of 22.5 feet from its point of release.
Explanation:This is a question about the maximum height of a shot put. The equation presented here is a quadratic function, and it has the form of a parabola. The maximum value of a parabola that opens downwards (as in this case, where the coefficient of x2 is negative) is given at its vertex.
To find the 'x' coordinate of the vertex, use the formula -b/2a, where 'a' is the coefficient of x2 and 'b' is the coefficient of 'x'. In this case, 'a' is -0.06, and 'b' is 2.7. -b/2a = -(2.7)/(2*-0.06) equals 22.5 feet. This is the horizontal distance from the point of release where the shot reaches the maximum height. To find the maximum height, substitute the value of 'x' into the equation, f(22.5) = -0.06*(22.5)2 + 2.7*22.5 + 5.9. This gives the maximum height as 36.375 feet.Learn more about Maximum Height of Shot here:
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Related Questions
Evaluate the expression when y=-5
Y^2-8Y+4
Answers
(-5)^2 - 8(-5) + 4
= 25 - 8(-5) + 4
= 25 + 40 + 4
= 65 + 4
= 69
Hope this helps!
what is the simplified form of 3a4b-2c3?
Answers
The expression 3a4b-2c3 is already in its most simplified form because they are not like terms, thus cannot be combined.
Explanation:The given expression 3a4b-2c3 cannot be simplified further because it consists of variable components. Each of these components -- 3a, 4b, and 2c3 -- represent distinct and separate entities in the equation. Unlike in some mathematics problems, these components cannot be combined or simplified because they are not like terms. In algebra, like terms are terms that contain the same variables and powers. So only if the given equation was 3a + 2a or 4b - 3b, then they could be combined. But as it stands, 3a4b-2c3 is already in its most simplified form.
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The circle has a diameter of 16 inches. What is the area of the circle?
Answers
Since the diameter given is 16 inches, the radius is 8 inches.
Using the formula, we find that the area is pi*(8 inches)^2 = 64pi inches^2
One side of a square flower bed is 22 feet long. How many plants are needed if they are to be spaced 22 inches apart around the outside of the bed?
Answers
12*4 = 48 plants are needed for the outside border.
To find out how many plants are needed, we calculate the perimeter of the square flower bed, convert that to inches, and then divide by the spacing of the plants. In this case, about 48 plants would be needed.
Explanation:This problem can be solved using the properties of a square and unit conversion. Since a square has four equal sides and each side of the square flower bed is 22 feet long, the total perimeter of the flower bed would be calculated as 22 feet * 4, which is 88 feet. Next we need to convert these feet to inches since the plants are spaced 22 inches apart. There are 12 inches within a foot, so 88 feet equals 1,056 inches (88*12).
Once you have the total length in inches, you can determine the number of plants by dividing the total length in inches by the distance each plant is to be spaced. Thus, 1,056 inches divided by 22 inches gives us approximately 48 plants.
So, if you want to space your plants 22 inches apart around a square flower bed where each side is 22 feet, you will need 48 plants.
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What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Answers
Answer:
The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
Step-by-step explanation:
The given data set is
122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77
Arrange the data set in ascending order.
71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164
Divide the data set in equal parts.
(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)
Now divide each parenthesis in two equal parts.
(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)
Lower quartile is
[tex]Q_1=\frac{77+84}{2}=80.5[/tex]
Middle quartile is
[tex]Median=Q_2=98[/tex]
Upper quartile is
[tex]Q_3=\frac{114+122}{2}=118[/tex]
Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.
There are 3 grams of sodium in 1/2 of a liter of soda.how much is in 2/3 of a liter
Answers
The base of a triangle is 12 in. The height is 7 in. What is the area of the triangle? A) 19 in2 B) 28 in2 C) 42 in2 D) 84 in2
Answers
1/2(12)(7) = 42 in²
Hope this helps :)
Answer:
C. 42
Step-by-step explanation:
Each statement describes a transformation of the graph of y = log2x.
Which statement correctly describes the graph of y = log2(x + 3) - 9?
It is the graph of y = log2x translated 3 units down and 9 units to the left.
It is the graph of y = log2x translated 9 units down and 3 units to the right.
It is the graph of y = log2x translated 9 units down and 3 units to the left.
It is the graph of y = log2x translated 3 units up and 9 units to the left.
Answers
y = log_2(x); y = log_2(x + 3) - 9
You will see the picture clearly when you do this. The answer is that it moves 3 units towards the left and 9 units down.
Answer: Third one down.
Comment: Anything you put inside the brackets with an x moves the graph left or right depending on the sign. (x + 3) moves 3 units to the left. (x - 3) moves the graph 3 units to the left.
Anything outside the brackets moves the graph up or down. minus goes down. Plus goes up. The number must be on the right. - 9 goes nine units down.
it's C: It is the graph of y = log2x translated 9 units down and 3 units to the left.
A square with one side length represented by an expression is shown below. 6(3x+8)+32+12x. Use the properties of operations to write three different equivalent expressions to represent the lengths of the other three sides of the square. One of your expressions should contain only two terms
Answers
expression 2) 30x+48+32
expression 3) 30x+80
The length of each side of the square can be represented by the equivalent expressions 30x + 80, 10(3x + 8), and 2(15x) + 2(40), with the first expression being in the simplest form and containing only two terms.
The student is provided with an expression for the side length of a square and is asked to write equivalent expressions representing the lengths of the other three sides. Since all four sides of a square are equal, we simply need to simplify the given expression and use it to represent each side. The given expression is 6(3x+8)+32+12x.
First, we can simplify this by distributing and combining like terms:
6(3x+8) becomes 18x + 48
Adding the 32 gives us 18x + 48 + 32
Finally, add the 12x to get 18x + 12x + 48 + 32
Combining like terms results in 30x + 80.
Now we have our simplified expression, which is 30x + 80, to represent the length of each side of the square. For different but equivalent forms:
As two terms: 30x + 80 (this meets the requirement of containing only two terms)
Factored form: 10(3x + 8)
Expanded form by distributing a common factor: 2(15x) + 2(40)
These are three different equivalent expressions we can use to represent the lengths of each side of the square.
Need Help! I don't get it
Answers
that only happens if you drive it for 60 miles, what if you drive it for more, let's do a quick table on that,
[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 60&3.6(1)\\\\ &3.6\left( \frac{60}{60} \right)\\\\ 120&3.6(2)\\\\ &3.6\left( \frac{120}{60} \right)\\\\ 180&3.6(3)\\\\ &3.6\left( \frac{180}{60} \right) \end{array}[/tex]
and so on, now let's check if you less than 60 miles,
[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&3.6\left( \frac{40}{60} \right)\\\\ 20&3.6\left( \frac{20}{60} \right)\\\\ 10&3.6\left( \frac{10}{60} \right) \end{array}[/tex]
so, if you divide the amount of miles driven, by 60, when you have driven it for 120 miles, 120/60 is just 2, and the cost is for 2 gallons, or 3.6 * 2, which is 7.2 bucks, for 180 miles is 180/60 or 3 gallons for 3.6 * 3 bucks, and so on.
now, what if you drive it instead for "m" miles?
[tex]\bf \begin{array}{ccll} miles&cost\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ m&3.6\left( \frac{m}{60} \right)\\\\ \end{array}\implies c=3.6\left( \cfrac{m}{60} \right)\implies c=\cfrac{3.6m}{60} \\\\\\ c=\cfrac{3.6}{60}m\implies c=0.06m[/tex]
Can someone please help me with this assignment
Answers
Page 1:
1) Triangle ABC has vertices A(-2,1), B(0,5), and C (8,1). What type of triangle is triangle ABC
Answer: option A. acute triangle.
Explanation:
Determine the lengths of the three sides:
Side AB: √[(0+2)^2 + (5-1)^2 ] = √ [4 + 16] = √(20)
Side BC: √ [ (8-0)^2 + (1 -5)^2 ] = √ [ 64 + 16 ] = √(86)
Side AC: √ [ (8 + 2)^2 + (1 - 1)^2 ] = √100 = 10
Compare the square of the side length of the largest side with the sum of the squares of the other two sides.:
AC^2 = 100
BC^2 = 86
AB^2 = 20
BC^2 + AB^2 = 86 + 20 = 106
100 < 106 => AC^2 < BC^2 + AB^2 =>
all the angles are less than 90°, which means the triangle is actue.
That is becasue when the square of the largest side is equal to the sum of the squares of the smaller sides, there is a right angle and the triangle is a right triangle (Pytaghorean theorem). When the square of the largest side is less than the sum of the squares of the other two sides, the angle is less than 90°, and the triangle is acute.
2) Which set represents the side lengths of a right trianle?
Answer: option C: 9, 12, 15
Explanation:
Check whic set obeys Pythagorean theorem.
15^2 = 225
12^2 = 144
9^2 = 81
.
144 + 81 = 225 => 15^2 = 12^2 + 9^2 => right triangle
3) Which property disproves the statement in the student's notes?
Answer: option B) all angles of a rhombus are not congruent.
Explanation:
A rhombus is a quadrilateral whose four sides all have the same length. It is a quadrilateral.
The angles do not need to be congruent. Only the square, which is only one special case of rhombus, has the four angles congruent, but the masure of the angles of other rhombus are not equal.
4) What is the are of the figure?
Answer: 85 unit^2
Explanation:
1) Area of the rectangle = base * height = 4 * 9 = 36
2) area of the trapezoid = height * half of the sum of the bases = 7 * (3+7)/2 = 35
3) area of the rhombus = half the product of the diagonals = 7 * 4 / 2 = 14
Result: 36 + 35 + 14 = 85
That option is not among the choices. The nearest one is 84 unit^2.
Page 2 is the same page 1.
Page 3:
5) Question 8:
What line can be used to draw the altitude of the triangle FGH
Answer: option D: 3y = 7x + 16
Explanation:
1) All triangles have 3 altitudes (one for each vertex).
2) Now I am going to find the altitude of the vertex H (respect to base FG.
3) First calculate the slope of the segment FG:
slope = [y2 - y1] / [x2 - x1]
x2, y2 are the coordinates of the point G (6, -2) and x1, y1 are the coordinates of the point F (-8,4)
=> slope = [ -2 - 4] / [6 - (-8) ] = [-6] / [14] = - 3/7
4) Now calculate the slope of the perpendicular line (because the altitude is perpendicular to the base).
The lines of perpendicular lines obey the rule: slope line A = - slope line B / 2
So, the slope of the line perpendicular to the base is - [1 / (-3/7) ] = 7/3
5) The equation of the line with slope 3/7 that contains the point H (-4, - 4) is:
y - (-4) 7
--------- = -----
x - (-4) 3
=> 3(y + 4) = 7(x + 4)
=> 3y + 12 = 7x + 28
=> 3y = 7x + 28 - 12
=> 3y = 7x + 16 which is the answer
6) Question 8. How will be the volume affected
Answer: option c. the volume will be 9 times larger.
Explanation:
1) Formula of the volume of rectagular prism
Volume = length * width * height
2) Name, V the volume, l the length, w the width, h the heigth => V = l * w * h
3) Triple the length and the width:
New volume = 3l * 3w * h = 9 l * w * h = 9V
4) You have proved that the new volumen is 9 times the original volume, which is the option c.
7) Question 9
What is the approximate length of the median of the trapezoid ABCD.
Answer: option b. 7.8 units
Explanation:
1) The median of a trapezoid is half the sum of the two parallel segments
2) The two parallel segments are AB and CD
3) The length of the segment AB is:
AB^2 = (3+7)^2 + (7-2)^2 = 10^2 + 5^2 = 100 + 25 = 125
=> AB = √125 ≈ 11.18
4) The length of the sement CD is:
CD^2 = (3 + 1)^2 + (1+1)^2 = 4^2 + 2^2 = 16 + 4 = 20
=> CD = √20 ≈ 4.47
5) The median is [11.48 + 4.47] / 2 ≈ 7.83 => option b.
8) Question 10. Problem
Answer: option B. 34.8 feet
Explanation:
1) Variables:
Ha = 4 ft (heigth of Abigail)
α = 38°
s = 50 ft (length of the string)
Hk = ? (altitude of the kite)
2) formula of sine ratio:
sin α = opposite-leg / adjacent leg
3) solution
sin α = x / s => x = sinα * s = sin(38°) * 50 ft = 30.78 ft
Hk = x + Ha = 30.78 ft + 4 ft = 34.78 ft => aption B. 34.8 feet
If y varies inversely as x and y is 6 when x is 12 what is x when y is 14.4
Answers
y=k/x
k: It is the constant of variation or constant of proportionality.
2. So, keeping this on mind, you must calculate the value o the constant of variation "k", with the values given in the problem. Then, you have:
k=yx
k=(6)(12)
k=32
3. Now, you can apply the equation y=k/x and clear the "x" to find its value:
yx=k
x=k/y
k=32
y=14.4
4. Then, you have:
x=32/14.4
5. Therefore, the answer is:
x=2.22
the answer is option A. 5
(I will give Brainliest/5 stars to correct answer)
Find a ⋅ b.
a = 7i - 4j, b = 4i + 3j
A) <28, -12>
B) 16
C) -40
D) <11, -1>
Answers
= 28 -12
= 16 . . . . . matches selection B
a dot b = dot product between the vectors 'a' and 'b'
a dot b = 7*4 + (-4)*3
a dot b = 28 - 12
a dot b = 16
Answer: Choice B) 16
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas?
Answers
Hope this helped!
The tennis ball has a radius of 10 cm. Calculate the approximate volume of the tennis ball. Round to the nearest tenth
A. 4,186.7 cubic centimeters
B. 523.3 cubic centimeters
C. 2,356.2 cubic centimeters
D. 658.9 cubic centimeters
Answers
r = 10 cm^3 = 1000 cm^3 That let's out D
V = (4/3) * 3.14 * 1000
V = (1.3333) * 3.14 * 1000
V = 1333 * 3.14
V = 4185 cm^3
A <<<< ==== answer
Find the two numbers that have a
difference of 3 and a sum of 27.
Answers
15-12=3
15+12=27
The smaller one is 3 less, 12.
The two numbers are 12 and 15.
_____
This is what I call a "sum and difference" problem. You are given the sum of two numbers and the difference between them. Since you see this kind of problem many times and many ways in Algebra courses, it can be worthwhile to remember the solution--or at least, the derivation of the solution.
Let "a" and "b" represent the numbers. Let "s" and "d" represent their sum and difference, respectively. You are given
.. a +b = s
.. a -b = d
Add these two equations.
.. 2a = (s +d)
Divide by 2.
.. a = (s +d)/2 . . . . . . . . . one of the numbers, as computed above
If you subtract the second equation from the first, you get
.. 2b = s -d
.. b = (s -d)/2 . . . . . . . . . the other number
Of course, you also know
.. b = s -a
.. b = a -d
.. a = s -b
.. a = b +d
so that once you have found either of the numbers, you have several ways to find the other one.
2 cards are drawn from a standard deck of 52 playing cards. how many different 2-card hands are possible if the drawing is done without replacement?
Answers
[tex] _{52} C_{2} [/tex]= 1326
Final answer:
There are 1326 different 2-card hands possible when drawing without replacement from a standard deck of 52 playing cards, using combinations to calculate it.
Explanation:
To determine how many different 2-card hands are possible from a standard deck of 52 playing cards when drawing without replacement, we need to consider combinations since the order of the cards does not matter. Using the combination formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items and r is the number of items to choose, we calculate C(52, 2).
We have:
n = 52 (total number of cards)
r = 2 (number of cards to choose)
Therefore, the calculation is as follows:
C(52, 2) = 52! / (2!(52 - 2)!) = 52! / (2! * 50!) = (52 * 51) / (2 * 1) = 1326.
So, there are 1326 different 2-card hands possible when drawing without replacement from a standard deck of cards.
The length of a rectangle is 5 times the width. If the perimeter is to be greater than or equal to 108 meters. What are the possible values of the width?
Answers
perimeter is 2l + 2w
The perimeter must be ≥ 108 meters
5w + 5w + w + w ≥ 108
12w ≥108
divide both sides by 12
w ≥ 9
The width can be greater than or equal to 9 meters.
Hope this helps
The smallest possible value for the width of the rectangle is 9 meters, given that the perimeter must be greater than or equal to 108 meters and the length is 5 times the width.
The question asks for the possible values of the width of a rectangle where the length is 5 times the width and the perimeter is greater than or equal to 108 meters.
Step-by-step explanation:
Let's call the width of the rectangle w. The length is then 5w. The perimeter P of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
In this case, P = 2(5w) + 2w = 10w + 2w = 12w. Now, we know that P >= 108, so 12w >= 108.
To find the smallest value for w, we divide both sides by 12: w >= 9. Thus, the width of the rectangle must be at least 9 meters.
caros ran 5.25 miles each day for d days. h ran a total of 157.5 miles. which eqution represents the number of days carlos ran?
Answers
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. mc018-1.jpg How many roots of f(x) are rational numbers?
Answers
Answer: there are 3 root of f(x) which are rational numbers (2,0), (3,0) and (4.5,0)
Explanation:
Rational numbers are those that can be written in the form of p/q: q should not be equal to zero
since, the graph cuts x-axis at three points but rational are two
all integers are rational numbers
attached is the graph please have a look at it
Mora ate 8.5 Containers of Yogurt one week. Each Container Held 5.4 Ounces Of Yogurt . HOW Many Ounces Of Yogurt Did she eat in all
Answers
Final answer:
Mora ate a total of 45.9 ounces of yogurt after consuming 8.5 containers, with each container holding 5.4 ounces.
Explanation:
The student asked how many ounces of yogurt Mora ate after consuming 8.5 containers, with each container holding 5.4 ounces. Mora ate 8.5 containers of yogurt, with each container holding 5.4 ounces of yogurt. To calculate the total amount of yogurt consumed, we multiply the number of containers by the amount of yogurt each container holds.
To solve this, simply calculate 8.5 containers × 5.4 ounces/container = 45.9 ounces of yogurt in total. This is the total amount of yogurt Mora ate during that week.
In triangle NOP, Np is extended through Point P to Point Q, m < NOP =(x+17) degrees, m< PNO =(2x-4) degrees, and m< OPQ=(5x-17) degrees. Find m< OPQ
Answers
To find the measure of angle OPQ, set up an equation using the given angles in triangle NOP. Simplify the equation and solve for x. Substitute the value of x back into the expression for angle OPQ to find the measure of the angle.
Explanation:To find the measure of angle OPQ, we can set up an equation using the given angles in triangle NOP:
(x+17) + (2x-4) + (5x-17) = 180
Simplifying the equation, we get: 8x - 4 = 180
From this, we can solve for x: 8x = 184, x = 23.
Now that we have the value of x, we can substitute it back into the expression for angle OPQ: 5(23) - 17 = 108 degrees.
Thus, the measure of angle OPQ is 108 degrees.
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what is the maximum number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6
A. 3
B. 4
C. 5
D. 2
Answers
A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.
(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)
Write a number with one decimal place,that is bigger than 6 4/5 but smaller than 7 how can I solve this
Answers
The easiest way to solve this would be to convert 6 4/5 to a decimal. We know that to convert a fraction to a decimal, we must divide the numerator by the denominator.
4 / 5 = 0.8
0.8 + 6 = 6.8
So, 6 4/5 is 6.8 as a decimal.
See how it's easier now that we've converted the mixed number to a decimal?
There could be many numbers between 6.8 and 7. Some examples are:
6.81, 6.82, 6.83, 6.9, etc.
Three consecutive even integers add to −6. What are these integers?
Answers
PLEASE HELP!!!!
Which equation matches the graph of the greatest integer function given below?
A. y=[x]-3
B. y=[x]-2
C. y=[x]+2
D. y=[x]+3
Answers
the correct answere is B
Solve the equation using square roots. x2 -9=0
Answers
x^2 = 9
x = 3
3^2 - 9 = 0
9 - 9 = 0
0 = 0
The answer is x = 3
Hope this helps =)
Answer: x = 3, x= - 3
Step-by-step explanation:
x^2 - 9 = 0
=> x^2 = 9
=> x = 3, x= - 3
A polygon that has all sides the same measure and all angles the same measure is called what? A. Convex polygon B. Concave polygon C. Irregular polygon D. Regular polygon
Answers
A polygon that has all sides the same measure and all angles the same measure is called Regular polygon.
Hoped I helped!
Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) = 10(0.98)x to represent the amount of radioactive material that will remain after x hours in the container. Rounded to the nearest tenth, how much radioactive material will remain after 10 hours?
Answers
Answer: There is approximately 8.2 amount of radioactive material that will remain after 10 hours.
Step-by-step explanation:
Since we have given that
[tex]f(x)=10(0.98)^x[/tex]
where, f(x) represents the amount of radioactive material that will remain after x hours in the container.
Since we have given that x = 10 hours.
So, our equation becomes,
[tex]f(10)=10\times (0.98)^{10}\\\\f(10)\approx 8.17\\\\f(10)\approx 8.2[/tex]
Hence, there is approximately 8.2 amount of radioactive material that will remain after 10 hours.
A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station. Identify a problem with the study.
A) Some of the sample data are missing
C) The data are based on reported results
D) The correlation between the variables implies causality
Answers
This is a problem because when someone self-reports information it is not always accurate. In some instances, those who self-report are not always honest when filling out survey information.
The correct answer is D) The correlation between the variables implies causality.
What is a survey?A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics of interest.
Now it is said that, A radio station sent a letter in the mail to 1000 randomly chosen residents within its broadcast area. The letter contained one dollar and a survey. The survey asked recipients to track their radio habits over a week. The survey was to be filled out and sent back in to the radio station.
So, here the problem with the survey that the survey is the self filled thus there is a possibility that the people may not be honest while filling the survey.Hence causing casualities.
Thus the correct answer is D) The correlation between the variables implies causality
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