Answers
The transverse axis has a length of 5 units.
What is transverse axis and find its length?A transverse axis is a line that divides a conic section (such as an ellipse or hyperbola) into two symmetric parts. In the case of an ellipse, the transverse axis is the major axis, and it runs perpendicular to the minor axis.
To find the length of the transverse axis, we can use the equation (x − 1)²/a² + (y + 3)²/b² = 1, where a and b are the lengths of the major and minor axes, respectively.
The given equation is :
(x−h)²/a² + (y−k)²/b² = 1
Where h and k are the coordinates of the center of the ellipse.
Now we can substitute the given values in the equation
(x−1)²/25 + (y+3)²/9 = 1
To find the length of the transverse axis, we can take square root of the major axis value, a² = 25
√25 = 5
So the length of the transverse axis is 5 units.
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Related Questions
Simplify using the order of operations.
25) 25 ÷ 5 + 4 × 3 – 3
Answers
Answer: 14
Step-by-step explanation:
Climbing Mt. Everest is not an easy task! Not only is it a difficult hike, but the Earth's atmosphere
decreases exponentially as you climb above the Earth's surface, and this makes it harder to breathe. The air
pressure at the Earth's surface (sea level) is approximately 14.7 pounds per square inch (or 14.7 psi). In
Denver, Colorado, elevation 5280 feet, the air pressure is approximately 12.15 psi.
a.) write an exponential equation
b.) what is the air press at the top of mount everest, elevation 29,000 feet?
Answers
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi
Finding exponential equation and calculating air pressureTo write an exponential equation for the relationship between the air pressure and the elevation above the Earth's surface, we can use the form y = a x b^x,
where y is the air pressure,
x is the elevation,
and a and b are constants.
We can use the data given in the problem to find the values of a and b.
Let y = air pressure (psi)
x = elevation (feet)
We know that at sea level (x = 0), y = 14.7 psi
At Denver, Colorado, elevation 5280 feet, y = 12.15 psi
We can use these two points to find the values of a and b in the equation y = a x b^x
12.15 = 14.7 x b^5280
b = (12.15/14.7)^(1/5280)
b = 0.827
a = 14.7
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
b.) To find the air pressure at the top of Mount Everest, elevation 29,000 feet, we can substitute that value for x into the exponential equation.
y = 14.7 x 0.827^29000
y = 1.931 psi
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi. It's worth noting that this is a very low air pressure and the human body is not able to survive with such low pressure without proper equipment.
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I can’t fit the whole question but if anybody knows this it would be great
Answers
The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:
Shift right of 7 units and reflection over the x-axis.
What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The vertices of the original triangle are given as follows:
A(-3,-2), B(-6,-5) and C(-1,-4).
The vertices of the reflected triangle are given as follows:
A'(4,2), B'(1,5) and C'(6,4).
Hence the composite rule is given as follows:
(x,y) -> (x + 7, -y).
Meaning that the glide reflection is defined as follows:
x -> x + 7: translation of 7 units right.y -> -y: reflection over the x-axis.More can be learned about glide reflections at brainly.com/question/5612016
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State if the two triangles are congruent. If they are, state how you know.
Select the correct response:
Yes by SAS
They are not congruent.
Yes by AAS.
Yes by ASA.
Answers
The two triangles are not congruent
What does triangular congruency mean?According to the triangle congruency laws, triangles are considered congruent when their sides and angles are equal.
The rules include
Side - Side - Side = SSS
Side, Angle, and Side = SAS
Angle Side Angle = ASA
Angle, Angle, and Side. = AAS
Hypotenuse and one leg. = HL
In the problem no information is given about the sides and just one angle is given.
Even though, for the figure it can be deduced that one side is equal but the information is not enough to determine if the triangles are congruent
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motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. assume a production process produces items with a mean weight of 8 ounces.
Answers
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Rectangular pool is 7 m wide and 12 m long if you swim diagonally from one corner to the other how many meters are you swim approximately the answer to the nearest 10th
Answers
The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.
Given that, a rectangular pool is 7 meters wide and 12 meters long.
What is the Pythagoras theorem?
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
We know that, measure of each angle in a rectangle is 90°.
Let the length of diagonal of rectangular pool be x
So using Pythagoras theorem, we get
x²=12²+7²
⇒ x²=144+49
⇒ x²=193
⇒ x=√193
⇒ x=13.89
≈13.9 meters
The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.
Find the Banzhaf power distribution of the weighted voting system
[30: 18, 16, 13, 12]
Answers
The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.
What is the Banzhaf power distribution?List all the victorious coalitions, then tally the crucial voters, to determine a voter's power using the Banzhaf index. A crucial voter is someone whose vote, if it were altered from yes to no, would result in the measure's failure. The percentage of all swing votes that a voter may cast is used to determine that person's influence.
[30: 18, 16, 13, 12]
P₁, P₂ = 18 + 16 = 34
P₁, P₃ = 18 + 13 = 31
P₁, P₄ = 18 + 12 = 30
P₂, P₃ = 16 + 13 = 29
P₂, P₄ = 16 + 12 = 28
P₃, P₄ = 13 + 12 = 25
The Banzhaf power distribution of the weighted voting system will be 34, 31, and 30.
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Diego has 3 pencils, 4 pens, and 2 highlighters in his pencil case. What is the ratio of pencils and highlighters to pens in Diego's pencil case?
O 3:6
O
O
4:9
O 5:4
07:2
Answers
Then, ratio to amount of pens
Solution:
Sum of pencils n highlighters = 3 + 2 = 5
Pens = 4
Thus,
The ratio is:
5:4
What is the sum
of the rational expressions below?
Answers
Answer:
D. 4x² - x / x² - x - 2
Step-by-step explanation:
First cross multiply then sum the results:
cross:
x(x + 2) = x² + 2x
3x(x - 1) = 3x² - 3x
sum the results of the cross:
x² + 2x + 3x² - 3x
4x² - x (this goes at the top)
Then multiply the bottom:
(x - 1 )(x + 2)
x² + 2x - x - 2
x² - x - 2 (this stays at the bottom)
Fraction ends up like:
4x² - x / x² - x - 2
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3, 1)
(3,-1)
(5,-5)
Answers
The coordinates of the fourth vertex of the parallelogram are (11, -7).
What is a parallelogram?
A parallelogram is a quadrilateral with opposite sides that are parallel to each other. The opposite sides of a parallelogram are also equal in length.
The fourth vertex of a parallelogram can be determined by finding the vector that connects one vertex of the parallelogram to the opposite vertex, and then adding that vector to the third vertex given in the problem.
The vector that connects the first vertex (-3, 1) to the third vertex (5, -5) is (8, -6). To find the fourth vertex, we add this vector to the second vertex (3, -1) :
(3,-1) + (8, -6) = (11, -7)
Hence, the coordinates of the fourth vertex of the parallelogram are (11, -7).
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Use the information below to find the value of y. Explain your steps
Answers
Step-by-step explanation:
2y+y=180(Sum of supplementey angle)
3y=180
y=180\3
y=60Select the statement regarding ethical considerations in experimental designs that is not necessarily true: A. If a research team treats two consenting groups such that one group receives a dose of a drug, and the other group receives a placebo, the team must inform the test subjects after the experiment whether they received the drug or the placebo. B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent. C. A national survey, asking respondents about drinking and smoking habits, should remain confidential with regards to the identity of respondents when reporting its findings.
D. If a medical group is going to apply a treatment to a person, that person should be notified and should agree to the treatment first.
Answers
The statement regarding ethical considerations in experimental designs that is not necessarily true is that it is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
Therefore the answer is option B. It is unreasonable for a study to knowingly cause harm to an individual, even if that individual has given consent.
This statement is not necessarily true because there are some situations where knowingly causing harm to a person may be ethical in the context of medical research, such as in the case of trials for life-threatening diseases where no other treatments are available. However, in such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
In ethical considerations in experimental designs, it is generally accepted that participants should be fully informed of the risks involved in a study and should give their informed consent before participating. This means that they should be aware of what is going to happen during the experiment, what benefits and risks are associated with participating, and what their rights are as participants.
However, there are some situations where knowingly causing harm to a person may be considered ethical in the context of medical research, such as in trials for life-threatening diseases where no other treatments are available. In such cases, strict ethical review and oversight is usually required to ensure that the risks are minimized and that the participants are fully informed of the risks involved.
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males in the netherlands are the tallest, on average, in the world with an average height of centimeters (cm) (bbc news website). assume that the height of men in the netherlands is normally distributed with a mean of cm and standard deviation of cm.
Answers
The probability that a Dutch male is taller than 195 cm is 0.2525
Out of a random sample of 1000 Dutch men, people taller than 190 cm are 253 in number using statistics.
Mean = 183 cm
SD = 10.5 cm
Z score = ( Value - Mean ) /SD
Dutch male is shorter than 175 cm
Z score = ( 175 - 183)/10.5 = -0.762
from z score table probability is 0.223
Dutch male is taller than 195 cm
Z score = ( 195 - 183)/10.5 = 1.143
from z score table probability is 0.8735 for shorter than 195 cm
Hence probability that a Dutch male is taller than 195 cm = 1 - 0.8735
= 0.1265
Dutch male is between 173 and 193 cm
Z score = ( 173 - 183)/10.5 = -0.952 => 0.1705Z score = ( 193 - 183)/10.5 = 0.952 => 0.8295
0.8295 - 0.1705 =0.659
taller than 190 cm
Z score = ( 190 - 183)/10.5 = 0.6667
taller than 190 cm = 1 - 0.7475 = 0.2525
Hence in 1000 = 252.5 = 253
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The complete question is :
Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.a.What is the probability that a Dutch male is shorter than 175 cm?b.What is the probability that a Dutch male is taller than 195 cm?c.What is the probability that a Dutch male is between 173 and 193 cm?d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
Samantha bought an equal number of $11.00,$9.00 and $8.00 tickets for a concert. she spent $196 for all of the tickets. how many of each did she
Answers
Answer: Samantha bought 7 tickets for a concert
Step-by-step explanation:
$11.00 + $9.00 + $8.00 = 28
$196 / 28 = 7
The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y ? The mean is 20 and the standard deviation is 102.A) The mean is 20 and the standard deviation is 50.B) The mean is 22 and the standard deviation is 102.C) The mean is 22 and the standard deviation is 100.D) The mean is 22 and the standard deviation is 50.
Answers
By multiplying the mean of random variable X by two to four, the random variable Y's mean is calculated to be 20. (5). By dividing the X standard deviation (25), by 4, the standard deviation of Y is equal to 102.
The random variable X has a mean of 5 and a standard deviation of 25. A normal distribution's mean serves as its nucleus, and the standard deviation quantifies how much the values deviate from the mean. Y = 2 + 4X is the definition of the random variable Y. By adding 2 to the mean of X (5), we can determine the mean of Y, which equals 20. By dividing the standard deviation of X (25), by 4, we can determine the standard deviation of Y, which yields a standard deviation of 102 for Y. As a result, the standard deviation is 102 and the mean of Y is 20.
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What is the decimal expansion of the following fraction 1/3
Answers
The decimal expansion of the following fraction 1/3 would be; 0.33
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We need to find the expression of 1 divided by 3.
A negative divided by a negative is positive, then;
1/3 = 0.33
Therefore, The value of expression 1/3 would be; 0.33
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Describe the y-intercept and end behavior of the following graph: The graph starts on the top left and curves down to the right, crosses the x axis at negative 2, then crosses the y axis at negative 4 and continues decreasing to the bottom right. a (−2, 0); The graph approaches y = −6 to the right. b (0, −5); The graph approaches y = −6 to the right. c (−2, 0); The graph decreases to the left. d (0, −5); The graph decreases to the left.
Answers
The correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the graph of the function.
The correct alternatives are -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).Therefore, the correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).To solve more questions on graphs, visit the link below-
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Given sides b, c, and angle d
state the area of the triangle.
Answers
The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
What is triangle ?
Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.
Given
in the triangle with three sides a,b,c.
Let ABC be a triangle such that the length of the 3 sides of the triangle is AB = c, BC = a and CA = b.
The semi-perimeter of triangle ABC = s = (a + b + c)/2
Then, the area of triangle ABC = √[s × (s – a) × (s – b) × (s – c)].
Therefore, The area of triangle with three sides a,bc is equals to
√[s × (s – a) × (s – b) × (s – c)].
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What is the Puzzle code for puzzle 2.
Linear equation Digital Escape!!!
Please need the puzzle code for PUZZLE 2. WILL GIVE BRAINLIST.
Answers
All the equations are matched with the line graph are given below.
And the letter code is AEBG.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
All the equations are matched with the line graph:
A: y = 3x + 1 → Line 1
B: y = -2x + 2 → Line 3
G: y = -1/2x + 2 → Line 4
E : y = x+ 4 → Line 2
The letter code is AEBG.
Therefore, the letter code is AEBG.
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ions of a
use to make
vill she need
hi
↑
3 in.
Go Online You can complete your homework online.
2 A group of students is painting the flag of
Brunei for a geography project. Joseph is
responsible for painting only the
background colors of the flag. How many
square inches will he cover with white paint?
(Example 1)
4=bh t=72631
yellow
white
black
yellow
A=6120
81⁄2 in.
7 in.
Answers
The required area of the white part of the flag is 612 Square inches.
What is Rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to question:We have,
Width = 8(1/2) = 17/2 In
Length = 72 In
Area of the white part of the flag is
= 17/2 × 72
= 612 Square inches
Thus, required area is 612 Square inches.
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The white portion of the flag must have a 612 square inch area.
What is a rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and four equal vertices. Due to this, it is also known as an equiangular quadrilateral. Due to their equal and parallel opposite sides, rectangles are also known as parallelograms.The following is what we have:width = 8 (1/2) = 17 (2 inches).72 inches longThe white portion of the flag's area is= 17/2 × 72612 Square Inches612 square inches are therefore needed.To learn more about the area of square refer:
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help me please asap!!!
Answers
The scale factor for the dilation in this problem is given as follows:
2.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The equivalent side lengths in this problem are given as follows:
AD, with length 8 - 0 = 8.DE, with length 8 - 4 = 4.The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:
k = 8/4 = 2.
(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).
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Identifying Linear Equations Let x1, x2, ..., In be variables. Determine whether the following equations are linear or non-linear and explain why: (a) (x1 – 1)(x2 + 1) = 0 (b) 5x1 = 2x2 – 3x3 +4 (c) x1 + xż + x3 + ... + x n = 0 (d) sin(x3)x1 + x2 = 4 – cos^2(x3)21 (e) exı + e-x2 + ... +e" In = ln(5)
Answers
The following systems are :
a) Non-linear
b) Linear
c) Linear
d) Non-linear
e) Linear
a) Non-linear: The equation is non-linear because it contains a product of two variables (x1 - 1) and (x2 + 1). A linear equation only contains variables and their coefficients, not products of variables.
b) Linear: The equation is linear because it only contains variables and their coefficients.
c) Linear: The equation is linear because it only contains variables and their coefficients and the sum of variables.
d) Non-linear: The equation is non-linear because it contains the sine and cosine functions, which are non-linear.
e) Linear: The equation is linear because it only contains variables raised to a constant power (e raised to a constant power) and their coefficients.
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Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster. Explain your answer.
Answers
Answer:
Plane B
Step-by-step explanation:
Plane A: 2800/5 = 560 m/h
Plane B: 3885/7 = 555 m/h
1.
2.
3.
4.
7. Given: ZBAC = ZEDC, BC = EC
Prove: AABC = ADEC
Stat
EUC
3. Given: JK = LM, ZJKM = ZLMK
YO
1.
2.
3.
4.
B
Reasons
E
L
Answers
The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.
How may a triangle's congruency be demonstrated?Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved.The triangles are congruent if two of one triangle's sides and its included angle are the same as the corresponding sides and angles of another triangle.Triangles lining up, When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.The complete question is,
To what extent can the congruence of the triangles be demonstrated?
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Five Seconds of Summer’s tutoring service charges a base charge of $5 and $5 per hour.
Fall Out Boy’s tutoring service charges a base fee of $9 and $3 per hour. Whose service
would you rather use?
Make a table for your system of equations. Highlight the shared point in your table.
Solve your system graphically. Label your solution on the graph.
Solve the system, algebraically using substitution. Solve for both variables and box in your answers.
Choose your response to the would you rather question. Provide evidence and math to back up your choice. Could there be a scenario in which you would pick another option and tell me your other option
Answers
Answer: The cost of both services is equal when h = 2 hours.
Step-by-step explanation: The shared point on the table is when the cost of the two services is equal, i.e. when C1 = C2, where C1 is the cost of Five Seconds of Summer's service and C2 is the cost of Fall Out Boy's service.
To graphically solve the system, we can plot the two equations on the same coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x
We can then find the point of intersection of the two lines, which represents the point at which the cost of the two services is equal. We can label this point as (x, y) and our solution.
To solve the system algebraically using substitution, we can set C1 = C2 and solve for the number of hours (h) in terms of cost.
C1 = 5 + 5h = C2 = 9 + 3h
5 + 5h = 9 + 3h
2h = 4
h = 2
So, the cost of both services is equal when h = 2 hours.
From the above result, it is clear that Fall Out Boy's service is cheaper than Five Seconds of Summer's service. For 2 hours of tutoring, the cost of Fall Out Boy's service is $9 + 3(2) = $15 and the cost of Five Seconds of Summer's service is $5 + 5(2) = $15.
However, there could be scenarios where one service is cheaper than the other depending on the number of hours of tutoring required. For example, if a student requires more than 4 hours of tutoring, Five Seconds of Summer's service would be cheaper. And if a student requires less than 2 hours of tutoring, Fall Out Boy's service would be cheaper.
In conclusion, the best option would depend on the number of hours of tutoring required, and it is best to check both options and compare the cost before making a decision
Answer:
To compare the costs of the two tutoring services, we can set up a system of equations. Let x be the number of hours of tutoring.
Five Seconds of Summer's tutoring service:
y = 5 + 5x (base charge of $5 and $5 per hour)
Fall Out Boy's tutoring service:
y = 9 + 3x (base fee of $9 and $3 per hour)
We can make a table to compare the costs of the two services at different number of hours:
Hours (x) Five Seconds of Summer (y) Fall Out Boy (y)
0 5 9
1 10 12
2 15 15
3 20 18
4 25 21
The shared point in the table is when x = 0, y = 5 for Five Seconds of Summer's tutoring service and y = 9 for Fall Out Boy's tutoring service.
We can graph the two equations to compare the costs:
[Graph would be here if I were able to create one]
From the graph we can see that for any number of hours greater than 0, Five Seconds of Summer's tutoring service is cheaper.
We can also solve the system algebraically using substitution.
y
Several years ago, the average earnings for male workers between the uges of 25 and 34 with a high school diploma was $31,560. Comparing this
value in constant dollars to the average earnings 13 yr later showed that the average earnings have decreased to $28,700. Find the average rate of
change in dollars per year for this time period.
[ Hint: Use the ordered pairs (0, 31,560) and (13, 28,700).]
Answers
Using slope of the graph, The average rate of change in dollars per year for this time period is -220.
How is a slope determined?You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. Rise divided by Run gives you the slope. Rise/run on a slope Rise or run is a slope.
We have coordinates that represent the given information,
Let x = number of year,
Y = Change in income,
So, Our coordinates become = (0, 31560) and (13, 28700)
The average rate of change is defined as slope of the graph
Slope of graph = y2 - y1 / x2 - x1
⇒ 28700 - 31560 / 13 - 0
⇒ -2860 / 13
⇒ - 220
The value of slope is negative, which indicates depreciation.
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find exact value of sin -7pi/6??
Answers
A point is the measurement of the distance around a shape. * 1 point True False you will get brainless pls help
Answers
Answer:true
Step-by-step explanation:
Shawn is 23 years old, and Yu Yan is 15 years old. How many years ago was Shawn 3 times as old as Yu Yan was?
Answers
Answer:
11
Step-by-step explanation:
Now:
Shawn: 23
Yu Yan: 15
x years ago:
Shawn: 23 - x
Yu Yan: 15 - x
x years ago, Shawn was 3 times as old as Yu Yan.
23 - x = 3(15 - x)
23 - x = 45 - 3x
2x = 22
x = 11
Check:
11 years ago Shaw was 23 - 11 = 12, and Yu Yan was 15 - 11 = 4.
12 is indded 3 times 4.
Answer: 11
The College Board reported that in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution; use the empirical rule to find the percent of students who scored less than 494.
Feedback: Incorrect. The z-score for this situation is (494 - 686) / 96 = -2. Recall that 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. This question asks for the percent of students who scored less than 494 (below 2 standard deviations). The correct answer is 2.5%.
Answers
Totally correct about the mentioned before is 2.5%. This is because the z-score for this situation is (494 - 686) / 96 = -2. According to the Empirical Rule, approximately 95% of observations will fall within 2 standard deviations of the mean. In this case, the question is asking for the percent of students who scored less than 494, which is below 2 standard deviations, so the answer is 2.5%.
SAT Math Level 2 ScoreThe Empirical Rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data would get fall within 3 standard deviations of the mean. So if we know the mean and standard deviation of a normal distribution, we can use this rule to estimate the percentage of data that falls within a certain range.
In this specific question, the mean of Math Level 2 SAT subject test score was 686 with a standard deviation of 96. We were asked to find the percent of students who scored less than 494. To find this we first calculated the z-score which is (494 - 686) / 96 = -2.
Since the z-score is -2 it means that it's 2 standard deviation below the mean, and according to the Empirical rule 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. So the answer is 2.5%.
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