19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
how can you describe range?The range in statistics is the distinction between the greatest and lowest values within a set of data. It is a gauge of variation that reveals the degree to which values within a dataset are dispersed.
You simply take the difference between the two values to determine the range. The range is given by: When the dataset, for instance, has the values 2, 3, 5, 8, et 10, the lowest value is 2, and the highest is 10.
Range = Highest value – Lowest value = 10 – 2 = 8 .The range in this instance is hence 8.
given
The range is the discrepancy between the data set's maximum and minimum values.
The box plot shows that the range is between 40 and 59, with 40 being the smallest value and 59 being the maximum.
Maximum value - Minimum value equals 59 - 40, which equals 19.
You may determine the values of Q1 and Q3 to be roughly 45 and 59, respectively, using the box plot.
IQR = Q3 - Q1 = 59 - 45 = 14
When the IQR is 14 and the range is 19, the answer is:
19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
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The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 259 people entered the park, and the admission fees collected totaled $676.00. How many children and how many adults were admitted?
Let us call the number of children "c" and the number of adults "a." Based on the facts provided, we can then construct two equations: c + a = 259 (equation 1) (equation 1).
1.5c + 4a = 676 (2nd equation)
In equation 1, we may solve for one variable in terms of the other:
c = 259 - a
So, in equation 2, substitute this expression for "c":
1.5(259 - a) + 4a = 676
Distribute the 1.5:1:1:1:1:1:1:1:
388.5 - 1.5a + 4a = 676
Merge similar terms:
2.5a = 287.5
Multiply by 2.5:
a = 115
This translates to 115 adults being accepted. We can plug this number back into equation 1 to find "c":
c + 115 = 259
c = 144
As a result, 144 youngsters were hospitalised.
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Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven.
The probability that Karen’s second card will be a black card is 26/51.
What is a probability?Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are.
Let R represent the red cards and B represent the black cards.
We are given that a standard deck of playing cards consists of 52 cards. There are 26 black and 26 red cards in a playing deck.
The probability of the first card being red:
P(First R) = [tex]26/52[/tex]
The probability of the Karen’s second card being black:
P(First R) = [tex]26/51[/tex]
Full question "Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen’s second card will be a black card?"
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A seventh-grade class is selling oranges as a
class fundraiser. Each box has the same number
of oranges. Mr. Franclemont places an order for 4
boxes. As a thank-you gift, the class will give Mr.
Franclemont a free orange. All together, Mr.
Franclemont will receive 73 oranges.
Construct a model or diagram to represent this
relationship.
Write an equation that could be used to find b,
the number of oranges in each box.
Solve this equation to find the number of oranges
in each box.
Therefore, there are 18 oranges in each box.
What is equation?An equation is a mathematical statement that shows that two expressions are equal to each other. It typically consists of two sides separated by an equal sign (=), with mathematical expressions or variables on each side. Equations can be used to describe many different relationships and properties in mathematics, science, and engineering.
Here,
To represent the relationship described in the problem, we can use the following model or diagram:
4 boxes with b oranges per box, plus 1 free orange = 73 oranges in total
This can be written as the equation:
4b + 1 = 73
To solve for b, we need to isolate it on one side of the equation. We can start by subtracting 1 from both sides to get:
4b = 72
Then, we can divide both sides by 4 to get:
b = 18
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A single die is rolled twice. What is the probability that the first roll will be a 6 and the second roll will be a 2?
Answer:
1/6
Step-by-step explanation:
because the dice is most likly a 6 sided dice but if you need to simplify then it would be 1/2
HELP ME PLEASE BECAUSE THE QUATER IS ALMOST OVER
The terms and properties of operations that complete the statement and reasons for the equivalent expressions are;
3. Same
4.The properties of operations to write the equivalent expressions are; (-4), (-4) Distributive property
(-4), (-4), Associative property
(-4), (-3) Distributive property
5. When x = 2, and y = -5 -28·x + 12·y is -116 = -116
What are equivalent expressions?Equivalent expressions are expressions that have the same value for the values of the input variable.
3. The completed statement is presented as follows;
Equivalent expressions evaluate to the same value when a given set of values of x and y are substituted into both expressions.
4. The expressions in the question can be expanded to collect like terms as follows;
Expression; -28·x + 12·y
The common factor of 28 and 12 is 4, therefore, we get;
-28·x + 12·y = (4 × (-7))·x + (4 × 3)·y
To make the coefficient of the leading term positive, we get;
-28·x + 12·y = (-4 * 7)·x + (-4 * (-3))·y; Distributive property
Factoring the algebraic expression on the right, where the common factor is -4, we get;
(-4 * 7)·x + (-4 * (-3))·y = -4 × (7·x) + -4 × (-3·y); Associative property
= -4 × ((7·x) + (-3·y));
Therefore; -28·x + 12·y = -4 × (7·x + -3·y); Distributive property
5. Evaluation of the left and right side of the expression, where; x = 2, and y = 5, we get;
-28 × 2 + 12 × -5 = -116
(-4) × ((7 × 2) + (-3 × -5)) = -4 × 29 = -116
The completed equations are therefore;
-28·x + 12·y = -4 × (7·x + -3·y)
-28 × 2 + 12 × (-5) = -4 × (7 × 2 + -3 × (-5))
-116 = -116
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Given A(-1,-1), B(1,-2), C(1,2),
D(-1,3) and A(-2,-2), B'(2,-4),
C(2,4), D'(-2,6) with the center of
dilation at the origin, find the scale
factor.
Answer:
Step-by-step explanation:inconclusive
In what way are atoms of oxygen most different from autumns of nitrogen? A they have different temperatures B they have different colours C they have different states of matter D they have a different masses
Atoms of oxygen most different from atoms of nitrogen as they have different masses.
A subatomic particle known as an atom is made up of a nucleus composed of protons and neutrons, which is encircled by a swarm of electrons. The atom is the fundamental unit of the chemical elements, and the chemical elements are differentiated from one another by the count of protons present in their atoms. For instance, sodium is any atom that comprises 11 protons, and copper is any atom that includes 29 protons. The isotope of the element is characterized by the number of neutrons. Solid blue crystals can also be a form in which oxygen exists, with molecules that are diatomic.
Interestingly, Priestley was not immediately aware that he had discovered oxygen, and instead believed he had obtained a certain component of air. In a hermetic device, he observed the breakdown of mercury oxide and used a lens to direct sunlight onto the oxide.
In terms of the interaction between nitrogen and oxygen, these substances react in the presence of an electric current. Nitrogen is a stable molecule and does not readily react with other substances.
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An airplane is flying over the ocean at 2,500 feet in the air. A diver is swimming below and is 25 feet below the ocean surface. How far apart are the plane and the diver?
Answer:
2,525 FEET
Step-by-step explanation:
This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.
Answer:
The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
Step-by-step explanation:
Numbers in order:
4,5,6,6,7,8,9,9,10,10,12,12,14,15
List into two equal parts:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Find middle numbers:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Lower quartile: 6
Upper quartile: 12
Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
Use Distributive property to find an equivalent expression
1. 4(x+2)
2. (6+8)•x
3. 4(2x+3)
4. 6(x+y+z)
The distributive property allows us to distribute 4 to each term inside the parentheses, add the terms first, then distribute the result to x. It also allows us to distribute 6 to each term inside the parentheses, such as 6(x+y+z) = 6x + 6y + 6z.
What is distributive property?The distributive property is a mathematical property that applies to operations, such as addition and multiplication, that involve two or more terms. The distributive property states that the result of multiplying a term by a sum or difference of terms is the same as multiplying each term inside the parentheses by the term outside the parentheses and then adding or subtracting the results.
1. Using the distributive property, we can distribute the 4 to each term inside the parentheses:
4(x+2) = 4x + 42 = 4x + 8
Therefore, the equivalent expression is 4x + 8.
2. Using the distributive property, we can add the terms inside the parentheses first, then distribute the result to x:
(6+8)•x = 14•x
Therefore, the equivalent expression is 14x.
3. Using the distributive property, we can distribute the 4 to each term inside the parentheses:
4(2x+3) = 42x + 43 = 8x + 12
Therefore, the equivalent expression is 8x + 12.
4. Using the distributive property, we can distribute the 6 to each term inside the parentheses:
6(x+y+z) = 6x + 6y + 6z
Therefore, the equivalent expression is 6x + 6y + 6z.
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A rectangle has a diagonal of 2 cm and a length of 3(square root). Find its width
Answer:
1 cm
Step-by-step explanation:
To answer this question we use Pythagoras theorem. This is a² + b² = c², where a is the length, b is the width and c is the hypotenuse (diagonal).
As we are already given the diagonal, we have to rearrange the formula to apply to our question...
c² - a² = b²Now solve...
c = 2² = 4a = √3² = 34 - 3 = 1√1 = 1This means that our width is 1!
Hope this helps, have a lovely day! :)
There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3 to 5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
To solve this problem, we can set up a system of equations to represent the given information. Let R be the number of red tiles and B be the number of blue tiles. We are trying to find the value of R, the number of red tiles.
The first piece of information we are given is that the ratio of red to blue tiles is 3:5. This can be written as:
[tex]\dfrac{\text{R}}{\text{B}} =\dfrac{3}{5}[/tex]
The second piece of information we are given is that there are 12 more blue tiles than red tiles in the box.
This can be written as:
[tex]\text{B = R}+12[/tex]
We can solve this system of equations by substituting the second equation into the first equation and solving for R.
Substituting [tex]\text{B = R}+12[/tex] into the first equation, we get:
[tex]\dfrac{\text{R}}{\text{R}}+12 =\dfrac{3}{5}[/tex]
We can then simplify this equation to get:
[tex]\text{R} = 15[/tex]
Thus, there are 15 red tiles in the box.
This morning, Maya's car had 18.41 gallons of fuel. Now, 1.7 gallons are left. How
much fuel did Maya use?
X
Express the function graphed on the axes below as a piecewise function.
Answer:
y = 2/3x +6 for x< -3.
y = 2/3x +1 for x> 3.
Step-by-step explanation:
Explanations are given in attachment!
can you help me with this
The correct options for the average speed of both runners are:
B: Candace ran 4 meters per second
F: Candice ran at a faster rate
How to find the average speed between two coordinates?The formula for slope between two coordinates is:
Slope = (y2 - y1)/(x2 - x1)
For Antonio, we take two coordinates from the table to find the average speed.
The coordinates are: (8, 29) and (12, 41)
Thus:
Average speed = (41 - 29)/(12 - 4)
= 12/8 = 1.5 m/s
For candice, we take two coordinates which are:
(10, 42) and (15, 62)
Thus:
Average Speed = (62 - 42)/(15 - 10)
= 20/5
= 4 m/s
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If you flip three fairly coins what is th probability that you'll get a tail on the first flip a head on the second flip and another on the tail on the third flip
The probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.
What is probability?
Assuming that the coins are fair, meaning they have an equal probability of landing heads or tails, the probability of getting a specific sequence of outcomes is found by multiplying the probabilities of each individual outcome.
In this case, the probability of getting a tail on the first flip is 1/2, the probability of getting a head on the second flip is also 1/2, and the probability of getting a tail on the third flip is 1/2. Multiplying these probabilities together, we get:
(1/2) x (1/2) x (1/2) = 1/8
Therefore, the probability of getting a tail on the first flip, a head on the second flip, and another tail on the third flip is 1/8, or approximately 0.125.
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Note: Figure is not drawn to scale. If U = 4 inches, V = 4 inches, W = 8 inches, X = 6 inches, Y = 8 inches, and Z = 4 inches, what is the area of the object? A. 56 square inches B. 52 square inches C. 48 square inches D. 64 square inches
The clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.
What is Area ?Area is a measure οf the amοunt οf space inside a twο-dimensiοnal shape, such as a square, rectangle, triangle, circle, οr any οther shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, οr square meters.
Tο find the area οf the οbject, we need tο break it dοwn intο smaller shapes and add up their areas.
First, we can see that the οbject can be divided intο a rectangle with dimensiοns 8 inches by 4 inches (UWVZ), a triangle with base 4 inches and height 6 inches (VXY), and a trapezοid with bases 6 inches and 8 inches, and height 4 inches (WXYU).
The area οf the rectangle is:
A_rectangle = length × width = 8 in × 4 in = 32 square inches
The area οf the triangle is:
A_triangle = 1÷2 × base × height = 1÷2 × 4 in × 6 in = 12 square inches
The area οf the trapezοid is:
A_trapezοid = 1÷2 × (base1 + base2) × height = 1÷2 × (6 in + 8 in) × 4 in = 28 square inches
Therefοre, the tοtal area οf the οbject is:
A_οbject = A_rectangle + A_triangle + A_trapezοid
= 32 square inches + 12 square inches + 28 square inches
= 72 square inches
Therefοre, the clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.
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bias binding is to be sewn around the edge of a rectangular tablecloth measuring 73 in. by 46 in. if the bias binding comes in packages containing 13 ft of binding, how many packages of bias binding are needed for the tablecloth?
the required number of packages of bias binding for the tablecloth is 2.
As the rectangular tablecloth measures 73 in. by 46 in., the perimeter of the tablecloth can be calculated by the following formula:
Perimeter of the tablecloth = 2(Length + Width)= 2(73 + 46)= 2(119)= 238 inches
Therefore, the length of the bias binding required to sew around the tablecloth will be equal to the perimeter of the tablecloth. The length of the bias binding available in a single package is 13 feet, which is equal to 156 inches.Therefore, the number of packages required can be calculated as:
Number of packages of bias binding required= Length of bias binding required / Length of bias binding in a package= 238 / 156= 1.52
Therefore, 1.52 packages of bias binding will be needed for the tablecloth. However, we cannot purchase a fractional part of a package. Therefore, we need to round up the decimal to the nearest whole number. Hence, 2 packages of bias binding are required for the tablecloth.
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Solve the following quadratic function by utilizing the square root method.
Simplify your answer completely.
f(x) = 25×2-81
The solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.
Quadratic function solutionFirst, we need to rewrite the function in standard quadratic form:
f(x) = 25x^2 - 81
To solve this quadratic function using the square root method, we want to isolate the x^2 term and divide both sides by the coefficient of x^2, which is 25:
25x^2 - 81 = 0
25x^2 = 81
x^2 = 81/25
Taking the square root of both sides, we get:
x = ±(9/5)
Therefore, the solutions to the quadratic function f(x) = 25x^2 - 81 are x = 9/5 and x = -9/5.
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In a diagram, angle A and angle B are vertical angles, and angle B is a complementary angle with angle C. If angle A = 22°, write an equation
that you can use to solve for angle C. (2 points)
!! Please help!!!
The value of angle C is 68°.
Describe complementary angles?In geometry, complementary angles are two angles that add up to 90 degrees (a right angle). In other words, when two angles are placed adjacent to each other, and they form a right angle, they are considered complementary angles.
For example, if angle A is 40 degrees, then angle B, which is adjacent to angle A and together they form a right angle, is considered to be a complementary angle. Angle B would be 90 - 40 = 50 degrees.
Complementary angles can be found in many geometric shapes and objects, such as squares, rectangles, and triangles. In a right triangle, the two acute angles (the angles that are not the right angle) are always complementary.
Vertical angles are always congruent, which means that angle B is also 22°.
Since angle B and angle C are complementary, their sum is equal to 90°.
Thus, we can write the equation:
angle B + angle C = 90°
Substituting the known value of angle B, we get:
22° + angle C = 90°
Simplifying the equation, we get:
angle C = 90° - 22°
angle C = 68°
Therefore, the value of angle C is 68°.
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What value of b completes f(x)=2x^2+bx+74 If the vertex is (-6,2)
Answer:
The value of b will be completed when b = 24
Step-by-step explanation:
f(x) can also be determined as y.
(-6, 2)
y = 2x²+bx+74
Plug it in.
2 = 2(-6) ² + b (-6) + 74
2 = 2(36) - 6b + 74
2 = 72 - 6b + 74
2 + 6b = 72 + 74
6b = 70 + 74
6b = 144
b = 24
Find the equation of the exponential function that goes through the points (0,4) and (4,0.25).
The answer of the given question based on the exponential function is the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ.
What is Equation?An equation is a statement that two expressions are equal. It contains an equal sign (=) which separates the two expressions, and it can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
The general form of exponential function is:
f(x) = a(b)ˣ
where a is the initial value, b is the base, and x is the independent variable.
We can use the two given points to form a system of equations and solve for the values of a and b.
Using the point (0,4):
f(0) = a(b)⁰ = a = 4
Using the point (4,0.25):
f(4) = a(b)⁴ = 0.25
Now we can substitute a = 4 into the second equation and solve for b:
4(b)⁴ = 0.25
(b)⁴ = 0.25/4 = 1/16
b = (1/16)⁽¹/⁴⁾ = 0.5
Therefore, the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ
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Micheal is a swimmer. In 2009,he swam the men's 50-meter freestyle in 23.04 seconds. In the same year,he swam the 100 meter freestyle in 47.77 seconds. How much faster,in meters,was his 50-meter freestyle time then his 100-meter freestyle time?
Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.
What is Time, Speed and Distance?Time is the duratiοn between twο events. Speed is the measure οf hοw fast sοmething mοves οver a given distance. Distance is the amοunt οf space between twο pοints οr οbjects.
Tο find οut hοw much faster Michael swam the 50-meter freestyle than the 100-meter freestyle, we need tο calculate the difference between their speeds.
Let's first find οut Michael's speed in meters per secοnd fοr each race.
Fοr the 50-meter freestyle:
speed = distance / time = 50 meters / 23.04 secοnds ≈ 2.17 meters/secοnd
Fοr the 100-meter freestyle:
speed = distance / time = 100 meters / 47.77 secοnds ≈ 2.09 meters/secοnd
Nοw, tο find the difference in speed, we can subtract the speed οf the 100-meter freestyle frοm the speed οf the 50-meter freestyle:
2.17 meters/secοnd - 2.09 meters/secοnd ≈ 0.08 meters/secοnd
Therefοre, Michael was swimming abοut 0.08 meters per secοnd faster in the 50-meter freestyle than in the 100-meter freestyle.
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HELP PLSSS!!!
Write and solve an equation to find the value of x . Show work in the box below.
The value of x is ??
Step-by-step explanation:
(x+90°)=7x (vert opp angles)
x-7x=-90°
-6x/-6=-90°/-6
x=15
Triangle RGH is shown where m<RGH = (5x+1)°, m<GRH =(6x+6)°, and m<HRG = (11x-3)°.
The angle measures in triangle RGH are:
[tex]< RGH = 60\\ < HRG = 99\\ < RHG = 41\\[/tex]
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation.
To solve for the value of x and the angle measures in triangle RGH, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
Therefore, we can set up the equation:
[tex]< RGH + < HRG + < RHG = 180[/tex]
Substituting the given angle measures, we get:
[tex](6x+6) + (11x-3) + (5x+1) = 180\\[/tex]
Simplifying the equation, we get:
[tex]22x + 4 = 180\\x = 8\\[/tex]
Now that we know [tex]x = 8\\[/tex], we can substitute it back into the angle measures to find their values:
[tex]< RGH = (6x+6) = 54 + 6 = 60\\ < HRG = (11x-3) = 88 + 11 = 99\\ < RHG = (5x+1) = 41\\[/tex]
Therefore, the angle measures in triangle RGH are:
[tex]< RGH = 60\ degree\\ < HRG = 99\ degree\\ < RHG = 41\ degree\\[/tex]
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Solve for measure of angle a.
55°
25° a
a = [? ]°
If 2 secant lines intersect outside a circle:
2
Enter
Using the given secant line, we know that the required angle ∠a is 15° respectively.
What is secant?A secant in geometry is a line that crosses a curve at least two different points.
The Latin verb secare, which means to cut, is where the word secant originates.
A secant crosses a circle at precisely two points in a case of circle.
The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).
So, we know that:
c = 55° and b = 25°
And, the formula is:
∠a = c - b/2
Now, insert values as follows:
∠a = c - b/2
∠a = 55 - 25/2
∠a = 30/2
∠a = 15°
Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.
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Find the 25th term for the arithmetic sequence when the domain is x=1,2,3,4,5 (Use the formula from the previous question.)
5,7,9,11,13...
find the 25th Term
By answering the presented question, we may conclude that Therefore, the 25th term of the arithmetic sequence is 53.
What is Sequences?In mathematics, a sequence is an ordered list of items. Elements can be numbers, functions, or other mathematical objects. A series is commonly expressed by putting the phrases in parentheses and separating them with commas. A natural number series, for example, can be denoted as: (1, 2, 3, 4, 5, ...) Similarly, the even number series is labelled as follows: (2, 4, 6, 8, 10, ...) A series can be finite or infinite depending on whether it has a finite or infinite number of words.
To find the 25th term,
an = a1 + (n - 1)d
In this case, a1 = 5 and d = 2. Plugging these values into the formula, we get:
a25 = 5 + (25 - 1)2
a25 = 5 + 48
a25 = 53
Therefore, the 25th term of the arithmetic sequence is 53.
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A professor would like to use a 97% confidence interval to estimate the mean amount of time IRSC students
spend studying each week. The professor knows that distribution of time spent studying each week by IRSC
students is normally distributed with a standard deviation of 14.9 hours.
How large a sample should the professor select to ensure the confidence interval has a width of no more
than 1.7 hours. Round the solution up to the nearest whole number.
n=
The professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.
The Sample Size Calculation.To calculate the sample size needed for a confidence interval with a maximum width of 1.7 hours, we need to use the formula:
n = ((z * σ) / E)^2
where:
n is the sample size we need to find
z is the z-score corresponding to the desired confidence level (97% in this case)
σ is the population standard deviation (14.9 hours in this case)
E is the maximum margin of error we want in our confidence interval (1.7 hours in this case)
The z-score corresponding to a 97% confidence level is 1.8808 (which can be found using a z-table or calculator).
Substituting these values into the formula, we get:
n = ((1.8808 * 14.9) / 1.7)^2
n = 246.644
Rounding up to the nearest whole number, we get:
n = 247
Therefore, the professor should select a sample size of at least 247 students to ensure that the 97% confidence interval for the mean amount of time IRSC students spend studying each week has a width of no more than 1.7 hours.
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construct a rectangle ABCD with AB =6cm and diagonal BD= 7cm
What is an angle?
It is the opening that forms the intersection of two lines.
The sum of two angles:
Two angles are complementary if their sum equals 90°.Two angles are supplementary if their sum equals 180°.
What is a rectangle?
A rectangle is a polygon with four sides, with the characteristic that its opposite sides are equal.
What is the measure of the angle formed by the diagonals of the rectangle ABCD?
The area of a rectangle can be determined by knowing its diagonals and the angle they form between them.
A = D² Sen(γ)/2
Being;
D: diagonalγ: angle
Being;
A = (7)(6)
A = 42cm²
Apply the Pythagorean theorem to determine D.
D² = AB² + AD²
replace;
D² = (7)² + (6)²
D² = 49 + 36
D² = 82
Substitute in A;
42=82 Sen(γ)/2
Solve for γ;
84=82 Sen(γ)
γ = Sen⁻¹(84/82)
γ =
What is the image of the point ( 0 , 1 ) after a rotation of 270 ∘ counterclockwise about the origin?
The image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
A rotation of 270 degrees counterclockwise about the origin corresponds to a transformation in which every point in the plane is rotated 270 degrees counterclockwise about the origin.
To find the image of the point (0,1) under this transformation, we can use the following formula for a counterclockwise rotation of a point (x,y) about the origin by an angle of θ:
x' = x cos(θ) - y sin(θ)
y' = x sin(θ) + y cos(θ)
Plugging in the values x = 0, y = 1, and θ = 270 degrees, we get:
x' = 0 cos(270°) - 1 sin(270°) = 0 - (-1) = 1
y' = 0 sin(270°) + 1 cos(270°) = 0 + 0 = 0
Therefore, the image of the point (0,1) after a rotation of 270 degrees counterclockwise about the origin is the point (1,0).
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