Step-by-step explanation:
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = Largest value - Smallest value
Range = 92 - 3
Range = 89
To find the variance and standard deviation, we need to calculate the mean first:
Mean = (Sum of all values) / (Number of values)
Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11
Mean = 45.09 (rounded to two decimal places)
Next, we need to calculate the variance:
Variance = (Sum of squared differences from the mean) / (Number of values - 1)
Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)
Variance = 1071.45 (rounded to two decimal places)
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = Square root of variance
Standard deviation = Square root of 1071.45
Standard deviation = 32.74 (rounded to two decimal places)
The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.
draw a new of a square pyramid for which the base is 2 units long and the height of each triangular face is 5 units>
After answering the provided question, we can conclude that slant height of pyramid [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]
What exactly is a pyramid?A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The edges of the base form triangle faces known as sides, which connect to the top.
/\
/ \
/ \
/______\
5
|
|
|
|
|
2
The square pyramid in the diagram above has a two-unit-long square base and four five-unit-high triangular faces. The Pythagorean theorem can be used to calculate the slant height of each triangular face:
slant height [tex]= \sqrt((2/2)^2 + 5^2) = \sqrt(29) = 5.39 units.[/tex]
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(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^{T}[/tex]. Show with an example that the eigenvectors of A and [tex]A^{T}[/tex] are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
If λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
[tex]v^T A^T = \lambda v^T[/tex]
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
[tex]\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right][/tex]
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
[tex]v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T[/tex]
Now, for transpose of A:
[tex]A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right][/tex]
The eigen vectors are:
[tex]u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T[/tex]
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.
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Type the correct answer in each box. Assume π = 3.14. Round your answer(s) to the nearest tenth. 90° 30° In this circle, the area of sector COD is 50.24 square units. The radius of the circle is units, and m AB is units.
Therefore, the length of segment AB is approximately 7.4 units.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.
Here,
To find the radius of the circle, we can use the formula for the area of a sector:
Area of sector = (θ/360) x π x r²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.
We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:
50.24 = (90/360) x 3.14 x r²
50.24 = 0.25 x 3.14 x r²
r² = 50.24 / (0.25 x 3.14)
r² = 201.28
r = √201.28
r ≈ 14.2
Therefore, the radius of the circle is approximately 14.2 units.
Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:
AB = 2 x r x sin(θ/2)
where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.
We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:
AB = 2 x 14.2 x sin(30/2)
AB = 2 x 14.2 x sin(15)
AB ≈ 7.4
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Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Help pleaseeee!!
On January 1, 2014, the federal minimum wage was $7.25 per hour. Which graph has a slope that best represents this rate?
The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.
Which federal minimum wage was the highest?Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.
How are minimum wages determined?The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.
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in one of his experiments conducted with animals, thorndike found that cats learned to escape from a puzzle box:
In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually
To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:
B = f(log S1/S2)
where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.
In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.
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How do I solve? I don’t understand
Step-by-step explanation:
Use the 110 to find the 70 degree angle (they form a straight line = 180°)
then 70 + 64 + R angle = 180° ( sum of angles of a triangle)
then : R angle = 46°
then the R angle + 2x-10 = 90° ( because the two lines are perpendicular)
(2x -10)° + 46 ° = 90 °
x = 27
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11
If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.
The number of statistics book in bookcase is = 2;
The number of biology books in bookcase is = 5;
So, the total number of books is = 7;
The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.
After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.
So, the probability of choosing another statistics book on the second draw is 1/6.
In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:
So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);
⇒ (2/7) × (1/6)
⇒ 1/21
Therefore, the required probability is (a) 1/21.
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The given question is incomplete, the complete question is
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
(a) 1/21
(b) 10/21
(c) 11
(d) 21/11
The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
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Which construction is shown in the diagram below?
Answer:
Step-by-step explanation:
i think it B
What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
What is gravitational force?
Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.
The gravitational force that the moon produces on the Earth can be calculated using the formula:
[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]
where:
[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]
[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]
[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]
[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]
Substituting these values into the formula, we get:
[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]
Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
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Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
Expand and simplify completely
[tex]x(x+(1+x)+2x)-3(x^2-x+2)[/tex]
Answer:
x² + 4x - 6
Step-by-step explanation:
x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left
= x(x + 1 + x + 2x) - 3(x² - x + 2)
= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis
= 4x² + x - 3x² + 3x- 6 ← collect like terms
= x² + 4x - 6
Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
What is the end behavior of the polynomial function?
Answer: D. As x → -∞, y → -∞.
Step-by-step explanation:
The graph shows the function approaching negative infinity on the x-axis (left side). When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.
What are inequalities?
Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
in the right triangle round to your nearest tenth. 18 15 X help please
The value οf the given angle x = 39.8 degree
What is Trigοnοmetric Functiοns?Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.
The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.
In the figure tanx = p/h
[tex]x = tan^{-1(15/18)}[/tex]
x = 39.8
Hence the value οf the given angle x = 39.8 degree
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Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
The graph of y = 5x2 is
Answer:
................................
What does the point (5, 10) represent on the
graph?
Answer:
It means the point x = 5 and y = 10
Answer: The place 5 units right and 10 units up from the center of the graph (the origin).
Step-by-step explanation:
Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.
1 cubic meter = _____ cm cube
Answer:
1 cubic meter = 1000000 cm cubed
Step-by-step explanation:
[tex]1m^3*10^6=1000000cm^3[/tex]
Answer:
1 cubic meter = 10000000 cm cube
To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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Mia has a collection of vintage action figures that is worth $190. If the collection appreciates at a rate of 6% per year, which equation represents the value of the collection after 5 years?
The equation that represents the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
Explanation:
To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).
Therefore, the equation for the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
This can also be written as:
Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)
Therefore, the value of the collection after 5 years is $246.90.
Answer: 254.26
Step-by-step explanation:
Find the missing length indicated
The value of x is 5
Define the term Similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.
Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.
from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB
By using Thales's theorem, the ratio of the sides of triangles are;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5
Define the term Similar triangles?Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.
If matching sides are proportional and corresponding angles are congruent, two triangles are similar.
Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB
The ratio of triangle sides can be calculated using Thales' theory, and it is;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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i need the answer to this question
The measure of angle BAC is 55°, which is closest to option B (50°).
What is a tangent angle?The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:
[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]
[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]
Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:
[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]
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It is most similar to option B (50°) when the angle BAC is 55°.
What is a tangent angle?
The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.
This property can only be found in triangles with straight angles.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD
Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.
Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).
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the position vector r describes the path of an object moving in the xy-plane. position vector point r(t)
a) Velocity vector v(t) = i - 2tj, Speed s(t) = sqrt(1 + 4t²), Acceleration vector a(t) = -2j. b) Velocity vector v(1) = i - 2j, Acceleration vector a(1) = -2j
This problem is about finding the velocity, speed, and acceleration vectors of an object moving in the xy-plane, described by a position vector r(t). We can find the velocity vector by taking the derivative of the position vector, and the speed by taking the magnitude of the velocity vector. The acceleration vector can be found by taking the derivative of the velocity vector. We can then evaluate the velocity and acceleration vectors at a given point by plugging in the coordinates of the point. This problem requires basic vector calculus and understanding of the relationship between position, velocity, speed, and acceleration vectors.
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Complete question is attached below
Question 15 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:
Standard deck of 52 cards
4 suits (CLUBS SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
DIAMONDS
If a card is drawn at random from the deck, what is the probability it is a jack or ten?
0
4/52- 1/13
8/52 = 2/13
48/52- 12/13
Answer: 2/13
Step-by-step explanation:
There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:
P(Jack or Ten) = 8/52 = 2/13
So the answer is 2/13.
Step-by-step explanation:
a probability is airways the ratio
desired cases / totally possible cases
in each of the 4 suits there is one Jack and one 10.
that means in the whole deck of cards we have
4×2 = 8 desired cases.
the totally possible cases are the whole deck = 52.
so, the probability to draw a Jack or a Ten is
8/52 = 2/13
Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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A simple random sample with n = 25 provided a sample mean of 30 and a sample standard deviation of 4. Assume the population is approximately normal. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased?
Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.
What is confidence interval?In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.
Here,
To develop a confidence interval, we need to use the following formula:
Confidence Interval = sample mean ± margin of error
where the margin of error is calculated as:
Margin of Error = z* (sample standard deviation/ √n)
where z* is the critical value from the standard normal distribution table based on the chosen confidence level.
a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:
Margin of Error = 1.645 * (4 / √25) = 1.317
So, the 90% confidence interval for the population mean is:
30 ± 1.317, or (28.683, 31.317)
b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:
Margin of Error = 1.96 * (4 / √25) = 1.568
So, the 95% confidence interval for the population mean is:
30 ± 1.568, or (28.432, 31.568)
c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:
Margin of Error = 2.576 * (4 / √25) = 2.0656
So, the 99% confidence interval for the population mean is:
30 ± 2.0656, or (27.9344, 32.0656)
d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.
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