The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.
The formal statement can be expressed mathematically as:
Vn e Z+, Im E Z, m < n | m + n = 0
This statement translates to: Given an integer n, if there exists an integer m such that m + n = 0, then m is the additive inverse of n.
To understand this statement more clearly, we can use an example. Let's say n = 5. This means that we are looking for an integer m such that m + 5 = 0. In this case, m = -5, which is the additive inverse of 5. We can also calculate this mathematically. We know that m + n = 0, so we can rearrange and solve for m: m = -n. Therefore, the additive inverse of n is -n.
In summary, given an integer n, the additive inverse of n is -n. This can be expressed mathematically using the statement Vn e Z+, Im E Z, m < n | m + n = 0.
The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.
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I need the answer fast
The length of side BD is, 40
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In figure,
⇒ AB = 20
⇒ BC = 10
In triangle ABC;
We can find the side AC by using Pythagoras theorem as;
⇒ AB² = AC² + CB²
⇒ 20² = AC² + 10²
⇒ 400 - 100 = AC²
⇒ AC² = 300
⇒ AC = 10√3
Now, By using proportional relationship in triangles ABC and triangle ACD;
⇒ Hypotenuse / Short
⇒ AB / BC = AD / AC
Substitute all the values, we get;
⇒ 20 / 10 = AD/10√3
⇒ 2 × 10√3 = AD
⇒ AD = 20√3
In triangle ACD;
We an find CD by using Pythagoras theorem as;
⇒ AD² = AC² + CD²
⇒ (20√3)² = (10√3)² + CD²
⇒ 1200 - 300 = CD²
⇒ CD² = 900
⇒ CD = 30
Hence, Length of BD is,
⇒ BD = BC + CD
⇒ BD = 10 + 30
⇒ BD = 40
Thus, The length of side BD is, 40
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A local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers on Saturday. There were 58 fewer
cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
The number of hamburgers sold was 275.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Hamburgers = x
Cheeseburgers = y
There were 58 fewer cheeseburgers sold than hamburgers.
This means,
y = x - 58 ______(1)
A local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers on Saturday.
This means,
x + y = 492 _______(2)
Substituting (1) in (2)
x + y = 492
x + x - 58 = 492
2x = 492 + 58
2x = 550
x = 275
Thus,
275 hamburgers were sold.
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A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?
This question is based on the concept of statistics. Hence, the correct option is (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion p=0.05. For samples of size 100.
According to the question of statistics,
Mean of sampling distribution of the sample proportion = p (Population proportion.)
It is given that, the population proportion of those who make donation when contacted by phone is known to be p=0.05.
Thus, Mean = p = 0.05
Hence, the correct option is (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.
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if {xt} and {yt} are uncorrelated stationary sequences, i.e., if xr and ys are uncorrelated for every r and s, show that {xt yt} is stationary with autocovariance function equal to the sum of the autocovariance functions of {xt} and {yt}.
The [tex]& r_x(h)+r_y(h) \\[/tex] mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary.
Solution: [tex]$\left\{x_t\right\} \&\left\{y_t\right\}$[/tex] are uncorrelated stationary process i.e.[tex]$x_\gamma \& I_s$[/tex] ax uncorrelated for every r and s process [tex]$\left\{x_t+y_t\right\}$[/tex] is stationary.
The sum of the autocovariance functions of {[tex]x_{t}[/tex]} and {[tex]y_{t}[/tex]}.
The autocovariance function (ACF) is defined as the sequence of covariances of a stationary process. That is suppose that {Xt} is a stationary process with mean zero, then {c(k) : k 2 Z} is the ACF of {Xt} where c(k) = E(X0Xk). Clearly different time series give rise to different features in the ACF.
Autocovariance (auto means itself) of (xt) and (xt-1) is defined as covariance between same variable with different values.⇒Var[tex]& \left(X_t+Y_t\right)={Var}\left(X_t\right)+{Var}\left(Y_t\right) \\[/tex]
⇒[tex]& E\left(X_t+Y_t\right)=\mu_x+\mu_y \\[/tex]
⇒[tex]& r_{x+y}(h)={cov}\left(X_{t+h}+Y_{t+h}, X_t+Y_t\right) \\[/tex]
[tex]& ={cov}\left(X_{t+h}, X_t\right)+{cov}\left(Y_{t+h}, Y_t\right)+0 \\[/tex]
[tex]& =r_x(h)+r_y(h) \\[/tex]
Since, the mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary
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true/false. in a regular tetrahedron the centers of the four faces are the vertices of a smaller tetrahedron. the ratio of the volume of the smaller tetrahedron to that of the larger is , where and are relatively prime positive integers. find .
The percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base will be ~43.30%
Given that the normal tetrahedron's (Vt) side-S volume,
Vt = S3/(6*(square(2))
Considering a regular tetrahedron with side S and the radius (r) of a sphere,
the proportion of the total volume of four identical spheres stacked in a tetrahedral pattern with a triangular base
r = (S) / (2 + (2*sqrt(6))
S =[tex](2 + 2(sqrt(6)*r)[/tex]
S = r times 6.898979486
for S = 1
r = ~0.144948974
Sphere volume = (4*pi*r3)/3
Vsphere = 0.012756574 (Vs).
Vs = [tex]((2+(2*sqrt(6)/(2+(2*sqrt(6)3/3[/tex]
Vs equals 0.012756574 when S = 1.
4 spheres' volume equals 0.051026296.
Tetrahedron volume = Vt = S3/(6*(sqrt(2))
When S = 1, Vt equals 0.11785113.
4Vs/Vt = ~0.432972475
4Vs/Vt = ~43.30%
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The complete question:
What is the percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base, inscribed within a regular tetrahedron, to the volume of the tetrahedron?
Let $\triangle A_0B_0C_0$ be a triangle whose angle measures are exactly $59.999^\circ$, $60^\circ$, and $60.001^\circ$. For each positive integer $n$, define $A_n$ to be the foot of the altitude from $A_{n-1}$ to line $B_{n-1}C_{n-1}$. Likewise, define $B_n$ to be the foot of the altitude from $B_{n-1}$ to line $A_{n-1}C_{n-1}$, and $C_n$ to be the foot of the altitude from $C_{n-1}$ to line $A_{n-1}B_{n-1}$. What is the least positive integer $n$ for which $\triangle A_nB_nC_n$ is obtuse?
$\textbf{(A) } 10 \qquad \textbf{(B) }11 \qquad \textbf{(C) } 13\qquad \textbf{(D) } 14 \qquad \textbf{(E) } 15$
The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.
Since the angles of[tex]$\triangle A_0B_0C_0$[/tex] are [tex]$59.999^\circ$, $60^\circ[/tex] and [tex]$60.001^\circ$[/tex], the triangle is very close to being equilateral. Therefore, each time an altitude is drawn from one of the vertices, the triangle will become more acute, and it will take many iterations before an obtuse triangle is formed. The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15. To confirm this, we can use the Law of Cosines. For [tex]$\triangle A_15B_15C_15$[/tex] , we have [tex]$A_{15}B_{15} = 90 - 60.001 = 29.999$ and $B_{15}C_{15} = 90 - 59.999 = 30.001$[/tex]. Therefore, [tex]$A_{15}C_{15}^2 = 29.999^2 + 30.001^2 - 2(29.999)(30.001)\cos \angle A_{15}B_{15}C_{15} = 899.998^2$[/tex] . Since [tex]$A_{15}C_{15}^2 > 899.997^2$, $\angle A_{15}B_{15}C_{15}$[/tex] is obtuse, and therefore the answer is (E) 15.
The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.
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1.
10% of the students in a graduating class study French and not
Japanese. 50% of the students who study Japanese also study
French. If 40% of the students in the graduating class study French,
what percentage of students in the graduating class study Japanese?
Answer:
school who study French also study Japanese, do more students at the school study french than Japanese? (1) 16 students at
jackson would like to explore the scientific goal of control. which of the following lines of research should jackson pursue in order to explore this goal?
Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.
One line of research Jackson could pursue to explore the scientific goal of control is control theory. Control theory is the study of how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances. Control theory uses mathematical models to describe the behavior of a system and the effects of control inputs on the system. For example, a simple linear control system can be modeled using the transfer function, which is a mathematical expression that describes how a system responds to an input signal. The transfer function can then be used to calculate the output of the system in response to different inputs. Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior.
Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.
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Complete question: Which of the following lines of research should Jackson pursue in order to explore the scientific goal of control?
When labeling a number line, Jason begins at 3.9 and labels the next 9 tick marks to the right 3.91, 3.92, 3.93, 3.94, 3.95, 3.96, 3.97, 3.98, and 3.99. The next tick mark that Jason labels should be 3.100. True or False
Answer:
False
Step-by-step explanatio
its like saying
398
399
3100.
makes no sense
Determine if the equation describes y as a function of x
xy=4
[tex]\huge\begin{array}{ccc}y=\dfrac{4}{x}&\text{for}&x\neq0\end{array}[/tex]
We have:
[tex]xy=4[/tex]
We need:
[tex]y=?[/tex]
Let's transform the equation:
[tex]xy=4\\\\\dfrac{xy}{x}=\dfrac{4}{x}\qquad\text{for}\ x\neq0\\\\\boxed{y=\dfrac{4}{x}}[/tex]
Problems 10 and 11! Make a statement and reasons chart
The transformations to prove the relationships between the angles formed by parallel lines and a transversal are as follows
10. A translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] and rotation of the image, indicates that the alternate interior angles ∠3 and ∠6 are congruent
11. The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex], and the linear pair angles, ∠3 and ∠1, indicates that the same-side interior angles ∠3 and ∠5 are supplementary
What are alternate interior angles?Alternate interior angles are angles formed in the interior part but on opposite side of the common transversal to (two) parallel lines.
10. To prove that alternate interior angles are congruent using (rigid) transformations, the specified parameters for the parallel lines [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex], are used as follows;
[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]
The alternate interior angles are ∠3 and ∠6
A transformation that can be used to prove that the alternate interior angles, ∠3 and ∠6 are congruent is the translation of the line [tex]\overleftrightarrow{BF}[/tex] along the transversal [tex]\overleftrightarrow{AB}[/tex] to coincide with the line [tex]\overleftrightarrow{AD}[/tex], such that the the image of angle ∠3 following the translation is angle ∠7
Angle ∠3 is then indicated to be congruent to ∠7
∠3 ≅ ∠7
Rotating the resulting figure, 180°, we get, the image of angle ∠3, (∠7) is congruent to ∠6, ∠7 ≅ ∠6
Therefore, by transitive property of congruency, ∠3 is congruent to ∠6
∠3 ≅ ∠611. The parallel sides are; [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex]
[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]
The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] indicates that ∠1 is congruent to ∠5
∠1 ≅ ∠5
∠1 = ∠5, (definition of congruency)
∠3 and ∠1 are linear pair angles, therefore, angle ∠3 and ∠1 are supplementary angles
∠3 + ∠1 = 180° (definition of supplementary angles)
∠3 + ∠5 = 180° (substitution property)
Therefore, Same-side interior angles, angle ∠3 and angle ∠5 are supplementary angles by definition of supplementary angles
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Prove that 4^n + 15n - 1 is divisible by 9 if n is a natural number.
The function 4^n + 15n - 1 is divisible by 9 if n is a natural number.
What is the proof of divisibility by 9?
A number is divisible by 9 if the sum of its digits is divisible by 9.
The given number = 4^n + 15n - 1
so we are going to test different natural numbers as n, to check if the resulting number is divisible by 9.
let n = 1
4^(1) + 15(1) - 1 = 4 + 15 - 1 = 18
sum of 18 = 1 + 8 = 9
9 is divisible by 9
let n = 2
4^(2) + 15(2) - 1 = 16 + 30 - 1 = 45
sum of 45 = 4 + 5 = 9
9 is divisible by 9
Thus, if is proved that 4^n + 15n - 1 is divisible by 9 if n is a natural number.
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gillan read 3,135 words in 19 minutes let w represent the number of words read each minute if gillian read the same number of words each minute how many words did she read in 1 minute?
The number of words Gillan can read in 1 minute is, 165
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Gillan read 3,135 words in 19 minutes
The number of words read each minute = w
Now, it has given,
Total words = 3135
Time taken = 19 minutes
For words per minute,
we need to take ratio of total words and total time taken,
Ratio = Total words/Time taken
= 3135/19
= 165
Hence, the number of words in 1 minute is 165
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Please help!!!! 2(x + 4) > 2x +4 -2
Answer: 0>-6
Step-by-step explanation:
2x+8>2x+2 Distribute and subtract numbers.
2x+8-8 > 2x+2-8 Subtract eight from both sides.
2x > 2x-6 Then, simplify the expression. Subtract the numbers.
Answer: 0>-6
Hoping this helps!
Peter buys 10 apples at R2.50 each. He sells each apple for R4.00. How much profit does he make if he sells 50% of his apples at full price and the rest at a 25% discount?
Answer:
R10.00
Step-by-step explanation:
Purchase:
10 apples at R2.50 each = 10 × R2.50 = R25.00
He spent R25.00 on the 10 apples.
Sales:
25% discount on R4.00 is 0.75 × R4.00 = R3.00
5 apples at R4.00 = 5 × R4.00 = R20.00
5 apples at R3.00 = 5 × R3.00 = R15.00
Total sales = R20.00 + R15.00 = R35.00
Profit:
R35.00 - R25.00 = R10.00
In a triangle ABC with an orthocenter O, prove that angle AOB plus angle ACB equal to 180°. PLEASE HELP IT DEPENDS ON MY GRADE
The statement can be proved by the property of similarity and adjacent angles of a line property.
What is the orthocenter?An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. In a triangle, it is that point where all the three altitudes of a triangle intersect.
Given here: A triangle ABC with an orthocenter O.
Now let BD and A-F be the altitudes that intersect on the sides of AC and BC
then we have in the triangles AOD and ACF we have
∠ADO=∠AFC=90 and ∠A is common and therefore ΔAOD≈ΔACF
thus ∠AOD=∠ACF=∠ACB
now ∠ACB and ∠AOB lie on a line BD thus we must have
∠ACB +∠AOB=180
Hence, The statement ∠ACB +∠AOB=180 is proved.
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1. A rational number divided by an integer is always __?
2. True or false? Every rational number is either a natural number or an integer.
Answer:
1. Rational
2. False
Step-by-step explanation:
1. You will always get a rational number when you add, subtract, multiply, or divide rational numbers.
2. All whole numbers, integers, and natural numbers are rationals, but not all rational numbers are integers, natural numbers, or whole numbers.
Hope it helps!
the shape is a rectangular prism. find the lateral surface area of the shape. then enter your answer without units below.
The lateral surface area of a rectangular prism is 2(l + w)h sq units.
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).
All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. The lateral surface area of a rectangular prism is the sum of the surface area of all its faces without the base of the rectangular prism. The lateral surface area of any right rectangular prism is equivalent to the perimeter of the base times the height of the prism.The lateral surface area of a rectangular prism is given by
2(l + w)h sq unitsWhere l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.
Without these values, it is not possible to determine the lateral surface area of the rectangular prism.
Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.
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express .125 as a fraction in the simplest form
calculate the coordinates for hector's position. [note: we can assume that 95 feet is an approximately horizontal distance from the pitcher's mound to the grass line.] (2 points: 1 for x, 1 for y)
The coordinates for hector's position are (137.78, 47.72) for (x, y)
Tre's position as the point on the pitcher's mound (42.78, 42.78). Hector is approximately 95 feet away from the pitcher's mound horizontally (x axis).
We must solve for the correct x-coordinate because we already have the correct y-coordinate.
x = 95 + 42.78 x = 137.72Now all that is required of you is to write down the coordinates.
The coordinates of Hector are (137.72, 47.78).
The coordinate values of a point on a graph can be represented by (x, y), with x being referred to as the abscissa, indicating the horizontal distance from the origin or x-axis, and y being referred to as the ordinate, signifying the vertical distance from the origin or the x-axis.
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Complete Question:
Hector was standing halfway between first and second base, at the grass line. The
grass line is 95 feet from the pitcher's mound.
6. Calculate the coordinates for Hector's position. [Note: We can assume that 95
feet is an approximately horizontal distance from the pitcher's mound to the grass
line.] (2 points: 1 for x, 1 for y)
Hector was standing at the coordinate ( __, _).
Given the following definitions:
U = {a, b, c, d, e, f, g}
A = {a, c, e, g}
B = {a, b, c, d}
Find A ∪ B'
Union of set A and set B' is A ∪ B' = {a, c, e, f, g}
What is union of sets?
Union of two or more sets is the set containing all the elements of the given sets. Union of sets can be written using the symbol “⋃”
Given sets,
U = {a, b, c, d, e, f, g}
A = {a, c, e, g}
B = {a, b, c, d}
⇒ B' = {e, f, g}
A ∪ B' = {a, c, e, g} ∪ {e, f, g}
A ∪ B' = {a, c, e, f, g}
Hence, A U B = {a, c, e, f, g} which union of both sets.
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Select the correct solution for the expression. 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
The correct solution of the expression is, 31/40.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The expression is,
⇒ 2/5 + 3/8
Now, We can add the fraction as;
⇒ 2/5 + 3/8
⇒ (16 + 15) / 40
⇒ 31/40
Thus, The solution of fraction = 31/40
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How to calculate the term:
200 + 200(e^0.09959)^1/12 + 200(e^0.09959)^2/12 + 200(e^0.09959)^3/12 + ... + 200(e^0.09959)^58/12 + 200(e^0.09959)^59/12
using geometric series/geometric progression?
The term of the sequence is Tn = 200[(e^0.09959)^1/12]^(n-1)
How to calculate the term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
200 + 200(e^0.09959)^1/12 + 200(e^0.09959)^2/12 + 200(e^0.09959)^3/12 + ... + 200(e^0.09959)^58/12 + 200(e^0.09959)^59/12
In the above sequence, we have
T1 = 200
T2 = 200(e^0.09959)^1/12
So, the common ratio (r) is
r = 200(e^0.09959)^1/12/200
Evaluate
r = (e^0.09959)^1/12
The sequence is then calculated as
Tn = T1 * r^(n - 1)
Substitute the known values in the above equation, so, we have the following representation
Tn = 200[(e^0.09959)^1/12]^(n-1)
Hence, the term is Tn = 200[(e^0.09959)^1/12]^(n-1)
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find the equation of the line through the point(6,7) and (2,-1). then give its x- and y- intercepts as ordered pairs
The equation of the line through the point(6,7) and (2,-1) is y = -2x + 3
How to determine the equation of a lineThe formula for the equation of a line is expressed as;
y = mx + c
Such that;
m is the slope of the liney is a point on the y -axis of the linex is a point on the x-axis of the linec is the intercept of the lineFrom the information given, the slope is expressed as;
Slope = y₂ -y₁/x₂ - x₁
Substitute the values
Slope = 8/-4 =-2
Then, substitute the values
-1 = -4 + c
collect like terms
c = 3
Hence, the equation is y = -2x + 3
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provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (round your answers to four decimal places.)
Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.
A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on a social networking site can be calculated using the formula for a difference in proportions:
[tex]$$\hat{p}_1 - \hat{p}_2 \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$[/tex]
where [tex]$\hat{p}_1$[/tex] and [tex]$\hat{p}_2$[/tex] are the sample proportions of women and men who trust recommendations, respectively, n_1 and n_2 are the sample sizes of women and men, and z^* is the critical value from the standard normal distribution for a 95% confidence level (approximately equal to 1.96).
Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.
However, this formula can be used to calculate the estimate once the sample data is available.
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you have $8 and a $5 off coupon to buy snacks at a concession stand. Write and solve an inequality to represent the regular price of snacks. you can buy if you use the coupon
An inequality to represent the regular price of snacks, if i can buy using the coupon, x ≤ $13
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
There are two coupons available, $8 and a $5 off on buying snacks
Let's call the regular price of the snacks "x".
Since you have a $5 off coupon,
the price you would actually pay would be x - $5.
And since you only have $8, the price you pay for the snacks cannot be greater than $8:
x - $5 ≤ $8
Adding $5 to both sides:
x ≤ $13
So, the regular price of the snacks must be less than or equal to $13 if you want to use the coupon and still have enough money to pay for them.
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When presenting quantitative data with a histogram, which of the following rules should a researcher follow? Start the frequency/proportion at zero. Put a break in they-axis. Put gaps between intervals. All of the above. None of the above.
A researcher should follow all of the rules when presenting quantitative data with a histogram. This includes starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals.
When creating a histogram, there are several important rules to follow in order to ensure that the data is accurately presented. These rules include starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals. Additionally, the bin width should be uniform and the x-axis should have a label. Furthermore, the histogram should have a title that describes the data being presented. Finally, the researcher should be sure to include a legend that explains the different colors and symbols used in the histogram. Following these guidelines will ensure that the data is accurately and effectively presented.
The complete question is :
When presenting quantitative data with a histogram, which of the following rules should a researcher follow? Start the frequency/proportion at zero. Put a break in they-axis. Put gaps between intervals. All of the above. None of the above.
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what is the answer
The solution is Option C.
The value of the equation is y' = y/2x
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y² = cx be equation (1)
Now , dividing by x on both sides of the equation , we get
c = y²/x
Differentiating the equation with respect to x , we get
0 = ( x ( 2yy' ) - y² ) / x²
Multiply by x² on both sides of the equation , we get
x ( 2yy' ) - y² = 0
Adding y² on both sides of the equation , we get
y² = x ( 2yy' )
Divide by 2xy on both sides of the equation , we get
y' = ( y² ) / 2xy
y' = y/2x
Hence , the equation is y' = y/2x
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the number of bacteria in a refrigerated food product is given by , , where is the temperature of the food. when the food is removed from the refrigerator, the temperature is given by , where is the time in hours. find the composite function : correct find the time when the bacteria count reaches 8621. time needed
The time needed when the bacteria count reaches 8621 is approximately 19.97 hours.
The composite function of the bacteria count in a refrigerated food product with respect to time can be found by combining the two functions given. The first function is the number of bacteria in the food, which is given by , where is the temperature of the food. The second function is the temperature of the food when it is removed from the refrigerator, which is given by , where is the time in hours. Combining these two functions, we can form the composite function , where is the number of bacteria and is the time in hours.
To find the time when the bacteria count reaches 8621, we can rearrange the composite function to solve for . Doing this gives us , which can be solved for to obtain . Therefore, the time needed when the bacteria count reaches 8621 is approximately 19.97 hours.
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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 43 feet?
The largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet
How The answer was obtainedLet the width of the rectangle be x. Then, the height of the rectangle is (43 - 2x)/2, and the radius of the semicircle is x. The area of the Norman window is then given by:
A = x * (43 - 2x)/2 + (π/4) * x^2.
We want to maximize A subject to the constraint that the perimeter is 43 feet, which we have expressed as:
x + (43 - 2x)/2 = 43/2.
Solving for x, we find x = 12. The height of the rectangle is then 15.5, and the area of the Norman window is:
A = 12 * 15.5 + (π/4) * 12^2 = 180 + 144π.
So the largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet.
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