we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.
The Empirical Rule (or 3 sigma rule) states that for a normal distribution (bell shaped distribution) 68% of the data falls within one standard deviation (μ ± σ), 95% percent within two standard deviations (μ ± 2σ), and 99.7% within three standard deviations from the mean (μ ± 3σ).
Given that the mean (μ) = $2200, standard deviation (σ) = $400
a) The percentage of data within one standard deviation = μ ± σ = (2200 ± 400) = (1800, 2600)
Hence 68% of the land are between $1800 and $2600.
Number of farms = 68% × number of sample = 0.68 × 80 = 54.4 ≈ 54 farms
Hence we get the expected number of farms in the sample whose land value per acre is between $1800 and $2600 is 59.
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Question 7 of 35
Use the coordinates of the labeled point to find the point-slope equation of
the line.
-5
69
5
(2,-5)
The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope.
How do you write a point slope equation?When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.
An equation for a line stated using a single point on the line and the line's slope is a straightforward definition of point-slope form.
The slope is defined as the rise over run, or the proportion of the change in the y values over the change in the x values, and the point form is denoted by the letters (x,y).
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please help meeee…………..
The required measure of the angle ∠VYW is given as 59°.
Given that,
A Right angle is shown, where the measure of the complementary angle ∠VYW is to be determined.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
For complementary angle,
∠TYV + ∠VYW = 90
31 + ∠VYW = 90
∠VYW = 59°
Thus, the required measure of the angle ∠VYW is given as 59°.
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Liza is one year older than her sister. In four years she will be 3 times as old as she is now. How old is her sister now??
The required age of Liza's sister is given as 6 years.
Given that,
Liza is one year older than her sister. In four years she will be 3 times as old as she is now. How old is her sister now is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the age of Liza be x and of her sister be y,
According to the question,
x = y + 1
After 4 years,
4 + (y + 1) = 3(y + 1)
5 + y = 3y + 1
y = 2
The age of her sister now,
y = 2 + 4 = 6 years.
Thus, the required age of her sister is given as 6 years.
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Liz dives 10 feet below the surface of the water. Then she returns to the surface. Use the drop-down menus to write an expression that represents her overall change in depth.
The expression that represents her overall change in depth is given as follows:
-10 + 10.
How to represent the changes in depth?The changes in depth are represented using integer numbers, as follows:
Movement in the direction below the surface: negative value.Movement in the direction above the surface: positive value.Liz dives 10 feet below the surface of the water, hence the integer number is of:
-10.
Then she returns to the surface, that is, moving 10 feet in the direction of the surface, hence the integer number is given as follows:
10.
Then the addition operation that represents her overall change in depth
-10 + 10.
Which has a result of zero, as she finished at the same place that she started.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Solve using substitution.
4x − 10y = 10
x = –10
Answer:
x=−10,y=−5
Step-by-step explanation:
write the polynomial in standard form. then classify the polynomial by degree and by number of terms x + 2x^2
The equation is therefore in Standard Form: 2 Degree :Quadratic number of terms :Binomial
What is equation?There are numerous ways to define an equation in mathematics .In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation. Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two variables that are separated by the word "equal." Even the most elementary and simple algebraic equations use mathematical variables.
To construct a polynomial in standard form in this instance, you begin writing with the term having the highest degree, or exponent (in this example, the
2[tex]x^{2}[/tex] +x
word), and after that, in descending order. due to the two
[tex]x^{2}[/tex] is used to the greatest degree:
You look at the highest exponent, or degree, to categorize a polynomial. Considering that 2 is the highest exponent,
That is a quadratic equation. First few are as follows:
1- linear
2- quadratic
3- cubic
4- quartic
5- quintic
Count the terms in the polynomial to categorize it according to its term count: There are two terms in this polynomial,
2[tex]x^{2}[/tex]and x
. This is therefore a binomial.
Monomial is one term.
binary two terms
trinomial, 3 terms
4-plus terms; polynomial
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Nadia is hosting her sister Elizabeth birthday.Elizabeth favorite dessert is chocolate eclair.the local bakery charges $24 per box 8 eclairs, plus a delivery charger 5.95 per box. Nadia has received notice that 76 friends will attend, in addition to herself and Elizabeth. What is the total amount will have Nadia have to pay the bakery to deliver the eclair
Answer:
$292.36
Step-by-step explanation:
To calculate the total amount Nadia will have to pay the bakery to deliver the éclairs, you need to determine how many boxes of éclairs she will need to order and then add the delivery charge.
First, you need to determine how many éclairs Nadia will need to order to feed all of her guests. Since there are 8 éclairs per box and Nadia has 76 guests in addition to herself and Elizabeth, a total of 78 people, she will need to order 78 / 8 = <<78/8=9.75>>9.75 boxes of éclairs.
To calculate the total cost of the éclairs, you can multiply the number of boxes needed by the cost per box: 9.75 boxes * $24 per box = $<<9.75*24=234>>234.
To calculate the total delivery charge, you can multiply the number of boxes needed by the delivery charge per box: 9.75 boxes * $5.95 per box = $<<9.75*5.95=58.36>>58.36.
To find the total amount Nadia will have to pay the bakery, you can add the cost of the éclairs to the delivery charge: $234 + $58.36 = $<<234+58.36=292.36>>292.36.
Therefore, Nadia will have to pay the bakery a total of $292.36 to deliver the éclairs.
Answer:
[tex]\boxed{292.4625}.[/tex]
Step-by-step explanation:
To determine the total amount Nadia will have to pay the bakery to deliver the eclairs, you will need to first calculate the total number of eclairs that are needed. Since Nadia and Elizabeth will both be attending the party, and there will be a total of 76 friends attending, the total number of people at the party will be 76 + 2 = 78.
Next, you will need to determine how many boxes of eclairs Nadia will need to order. Since each box contains 8 eclairs, and there are 78 people at the party, Nadia will need to order 78 / 8 = <<78/8=9.75>>9.75 boxes of eclairs.
Since the bakery charges $24 per box of eclairs and Nadia needs to order 9.75 boxes, the cost for the eclairs will be 24 * 9.75 = $<<24*9.75=234>>234.
In addition to the cost of the eclairs, Nadia will also need to pay a delivery charge of $5.95 per box. Since Nadia needs to order 9.75 boxes, the delivery charge will be 5.95 * 9.75 = $<<5.95*9.75=58.4625>>58.4625.
To find the total amount Nadia will have to pay the bakery, you will need to add the cost of the eclairs and the delivery charge. The total amount Nadia will have to pay the bakery will be: $234 + $58.4625 = $<<234+58.4625=292.4625>>292.4625. Answer: \boxed{292.4625}.
Need help answer please!
Answer:
The second option/ B
Step-by-step explanation:
6 coins plus 4 coins is 10 coins, and you can’t forget the x amount of pennies.
hw to solve 6x-12/3+4=18/x
The two solutions of the equation:
(6x - 12)/3 + 4 = 18/x
Are x = 3 and x = -3
How to solve the equation?Here we have the following equation:
(6x - 12)/3 + 4 = 18/x
Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.
Now, let's start by simplifying the left side:
(6x - 12)/3+ 4 = 18/x
2x - 4 + 4 = 18/x
2x = 18/x
Now we can multiply both sides by x so we get:
2x^2 = 18
Now divide both sides by 2:
x^2 = 18/2
x^2 = 9
Finally, apply the square root in both sides:
√x^2 = ±√9
x = ±3
The two solutions are x = 3 and x = -3
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I need help with this please
all because all of the equianlangular triangles are equal
f(x) = ax^3 + bx^2 + cx + d In the polynomial above, a, b, c, and d are constants. If f(–5) = 3, which of the following must be true about f(x)? A x – 3 is a factor of f(x). B The remainder when f(x) is divided by x + 5 is 3. C x + 2 is a factor of f(x). D x + 5 is a factor of f(x).
The remainder when f(x) is divided by x + 5 is 3.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.
f(x) = ax^3 + bx^2 + cx + d
In the polynomial above, a, b, c, and d are constants and f(-5)=3.
- 5 is the root of the given polynomial when remainder is 3 so we get the one factor of the given polynomial and that is,
x-(-5)=(x+5)
That is if f(-5)=3 it means that the remainder when f(x) is
divided by (x-(-5))=x+5 is 3
Hence, The remainder when f(x) is divided by x + 5 is 3
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Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. Ŷ = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = .2683 Based on the above estimated regression equation, if advertising is $3000, then the point estimate for sales (in dollars) is?
The point estimate for sales when advertising is $3000 is $5412.
Based on the given information, the estimated regression equation is Ŷ = 12 + 1.8x, where Ŷ is the estimated value of the dependent variable (sales), x is the value of the independent variable (advertising), and the constants 12 and 1.8 are the coefficients of the regression equation.
If advertising is $3000, then the point estimate for sales (in dollars) is the value of Ŷ when x = 3000. Substituting this value into the estimated regression equation, we get:
Ŷ = 12 + 1.8 * 3000 = 12 + 5400 = 5412
So, the required amount is $5412.
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micky used 25% of his money on a new hat . The hat cost him $18 to purchase . How much money did Mickey have before he made his purchase.
Answer: $72
Step-by-step explanation:
x = money M had before he bought the hat
0.25x = 18
x = 18/.25 = 72
What is the volume in cubic centimeters of a right circular cone?; How do you find the volume of a right circular cone with a circumference?; How do you find the volume of a circular cone?; What is the volume of a cone if the height is 10 cm and the diameter is 6 cm?
The formula for the volume of a circular cone:
If the height(h) of the circular cone is given then,
V = 1/3 * π * r² * h
If the slant height(l) of the circular cone is given then,
V = 1/3 * π * r² * √(l² - r²)
the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters
We know that a right circular cone has a circular base with the apex above the center of the base.
For a right circular cone, with radius r and height h
The formula for the volume of a right circular cone is,
V = 1/3 * π * r² * h
We need to find the the volume of a right circular cone with a circumference.
We know that circumference C = 2πr
From circumference we find the radius of circular base.
Then using the formula for the volume of a right circular cone, we find the volume.
The volume of a circular cone:
If the height(h) of the circular cone is given then,
V = 1/3 * π * r² * h
If the slant height(l) of the circular cone is given then,
V = 1/3 * π * r² * √(l² - r²)
Now we need to find the the volume of a cone if the height is 10 cm and the diameter is 6 cm
From diameter, the radius of the circular base of the cone would be,
r = 6/2
r = 3 cm
also, h = 10 cm
So, V = 1/3 * π * 3² * 10
V = 94.25 cu.cm.
Therefore, the volume of a cone if the height is 10 cm and the diameter is 6 cm is 94.25 cubic centimeters
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2. Which is the slope value of the line that passes through the ordered pairs (16, -9) and (16, 13)?
m = 22
m = 0
m = 4
undefined
Answer:
slope is undefined
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (16, - 9 ) and (x₂, y₂ ) = (16, 13 )
m = [tex]\frac{13-(-9)}{16-16}[/tex] = [tex]\frac{13+9}{0}[/tex] = [tex]\frac{22}{0}[/tex]
since division by zero is undefined then slope of line is undefined.
When computing standard error, if the sample size increases while the variability remains the same, then the standard error:
A) decreases
B) increases
C) remains the same
D) is about average
E) none of the above; there is no such thing as standard error
If the sample size increases while the variability remains the same, then the standard error decreases.
Standard error is defined as the measures of the preciseness of an estimate of a population mean. It can be calculated by dividing the sample standard deviation by the square root of the sample size.
SE = SD / √n
where SE = standard error
SD = sample standard deviation
n = sample size
Variability refers to the statistical dispersion of data which is expressed through the range, variance, or standard deviation.
Increasing the sample size, n, while having the same variability, will result to a lower value for the standard error.
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rhombuses are special parallelograms true or false; which polygon is a pentagon?; a square is a special rhombus; why is a parallelogram not the same type of quadrilateral is a trapezoid; a square is a specific type of parallelogram true or false; why is a square a special parallelogram
Yes Rhombuses are special parallelograms is true statement. Yes square is also a special rhombus. True square is a specific type of parallelogram.
What is parallelograms?
A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
A parallelogram has adjacent angles that add up to 180 degrees.
rhombuses is a quadrilateral with all the four sides having equal lengths.
In a rhombus, the opposite sides are parallel and equal. Hence, it is a parallelogram.
So rhombuses are special parallelograms this statement is true.
A square is a special rhombus Yes that is true
The sides of a square and a rhombus are both the same length. A rhombus only has its opposite angles equal, whereas a square has all of its angles at 90 degrees.
why is a parallelogram not the same type of quadrilateral is a trapezoid?
Since they both have four sides, it is obvious that a trapezoid and a parallelogram are quadrilaterals. There are at least one set of parallel sides in a trapezoid. Two sets of parallel sides make up a parallelogram. Therefore, a trapezoid is not a parallelogram if it has only one pair of parallel sides.
a square is a specific type of parallelogram this statement is true.
A square is a quadrilateral in two dimensions that has four equal sides and four equal angles. It is a unique parallelogram with equal angles and sides.
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Which expression is equivalent to Z +( z 6?
None of the solutions are appropriate since the result of the equation z + (z+6) will be equal to 2z + 6.
An expression is defined.A mathematical expression is the result of combining a number of mathematical symbols with an arithmetic operator, a variable, and a constraint.
In a different sense, expression is highly helpful in identifying the root or end value of a constraint.
for instance, 3x + 5y
The expression restriction is denoted by the symbols = or, >.
Given the phrase,
z + (z+6)
opening the bracket
z + z + 6
⇒ 2z + 6
Hence
"2z + 6 will be the value of the equation z + (z+6)."
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identify features of graphs and tables for linear and nonlinear relationships (example: coordinates of points; x/y intercept)
If you graph a linear characteristic you may get a immediately line. There also are nonlinear functions. If you graph the coordinates of a nonlinear characteristic you may now no longer get a immediately line.
One of the very best ways (however now no longer the handiest way) to differentiate among a linear and a nonlinear characteristic is to have a take a observe the graph of the characteristic.
A linear equation is an equation with variables whose graph is a line. The graph of the linear equation is a hard and fast of factors withinside the coordinate aircraft that every one are answers to the equation. If all variables constitute actual numbers you can graph the equation via way of means of plotting sufficient factors to understand a sample after which join the factors to encompass all factors.
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Struggling again.., any help will be appreciated :(
Step-by-step explanation:
since triangles are congurent
4z- 32 = 36
z = 68/4
z= 17
6x - 29 = 115
6x = 144
x = 24
and u can find y by triangle property...... similarly.....I'm too lazy to do that
a circle with circumference \blue{10}10 start color #6495ed, 10, end color #6495ed . It has an arc of length 92\dfrac{9}{2} 2 9 start fraction, 9, divided by, 2, end fraction . What is the central angle of the arc, in degrees? ∘^\circ ∘ degrees
The value of the central angle of the given arc of the circle is ; θ = 162°
What is the central angle of the arc?The central angle of an arc of a circle is defined as an angle between two radii with the vertex at the center. The central angle of an arc is also called the central angle subtended by the arc.
We are given the circumference of the circle as 10 and the length of the arc as 9.
Now, the formula for circumference of a circle is;
C = 2πr
where r is radius
The formula for length of the arc is;
L = θ/360 * 2πr
Plugging in the relevant values, we have;
9/2 = (θ/360) * 10
θ = (360 * 9)/(10 * 2)
θ = 162°
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What number makes the expressions equivalent?
12(−1.4m+0.4)=?m+0.2
The number -84 makes the expression 12(−1.4m+0.4) = 0.2(?m+0.2) equivalent.
Calculating for the unknown numberTo calculate for the unknown number represented by the question mark (?), we first expand the left hand side of the equation and then compare with the expression at the right hand side of the equation.
From the left hand side;
12(−1.4m+0.4) = -16m + 4.8 {by expansion}
12(−1.4m+0.4) = 0.2 × -84m + 0.2 × 0.2 {factor out 0.2 from both terms}
12(−1.4m+0.4) = 0.2(-84m + 0.2) {use bracket}
Therefore, by comparing 0.2(-84m + 0.2) with 0.2(?m+0.2), we observe the unknown number represented by "?" is -84 which makes the expression equivalent for 12(−1.4m+0.4) = 0.2(?m+0.2)
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Possible question
What number makes the expressions 12(−1.4m+0.4) = 0.2(?m+0.2) equivalent?
For a graph where would I put my point at?
(3,2)
Answer:
See below
Step-by-step explanation:
You start at the origin which is the very middle of where the x and y axis cross. The first number tells you to go right 3 spaces and the second number tells you to go 2 spaces.
10. State the amplitude, period, horizontal translation, vertical translation, and equation of the axis. (Graph each of the following)
a. y= 4cos4(theta-90 degrees) +3
b. y= 8sin2(theta−180 degrees) -8
You can compute amplitude as well, but this is quicker. There will be a reflection in the x axis, as shown by the negative sign before the number 2.
what is amplitude?The maximum displacement or distance made by a point on a vibrating body or wave relative to its equilibrium location is known as the amplitude in physics. It is equivalent to one-half of the vibration path's length.
Amplitude:
[tex]Found right in the equation the first number:\\ y=-2-cos2(x+4)-1[/tex]
You can compute it as well, but this is quicker. There will be a reflection in the x axis, as shown by the negative sign before the number 2.
Period:
[tex]First find k in equation:\\ y=−2cos2−(x+4)−1[/tex]
Then use this equation:
[tex]period=2\pi /k\\period=2\pi /2\\period=\pi[/tex]
Phase Shift:
[tex]y=-2cos2(x+4)-1[/tex]
The graph will move 4 units to the left, according to this section of the equation.
Vertical Translation:
[tex]y=-2cos2(x+4)-1[/tex]
The -1 tells you that the graph will shift 1 unit down.
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Let S be a nonempty subset of Z and let R be a relation defined on S by x R y if 3 (x + 2y). (a) Prove that R is an equivalence relation. (b) If S = (-7, -6, -2,0,1,4,5,7), then what are the distinct equivalence classes in this case?
R is equivalence relation and cl (-7) = cl(5)
cl (-6) = cl (0)
cl (-2) = cl(1) = cl(4) = cl( 7)
What is equivalence relation?A reflexive, symmetric, transitive binary connection is an equivalence relation. One such illustration of an equivalence relation is the relation of equipollence between line segments in geometry.
demonstrate the equivalence of R. We must demonstrate
1). reflexive
x +2x = 3x and 3/ 3x = 3/x +2x
(x,x) ∈ R
R is reflexive
2). symmetric
let (x,y ) ∈ R
x + 2y = 3a for some a ∈ R
consider y +2x = y + 2(3a - 2y)
6a - 3y = 3(2a - y) = 3k
3/y +2x
so (y,x) ∈ R
R is symmetric
3). transitive
(x,y) and (y,x) ∈ R
3/x+2y and 3/y+2x
x+2y =3a and y +2x = 2b for some a,b
consider x+2z = 3a - 2y + 2 (3b-y/2)
3a +3b -3y
3(a+b-y)
3/x+2z
(x,z) ∈ R
R is tansitive
so R is equivalence relation
b).S = (-7, -6, -2,0,1,4,5,7)
cl (x) = { y∈ z , x∈ y }
cl (x) = {y∈ z , x +2y = 3a}
cl (x) = {y∈ z , y = 3a - x /2}
cl (-7) = {y∈ z , y = 3a +7 /2}
cl (-7) = cl(5)
cl (-6) = cl (0)
cl (-2) = cl(1) = cl(4) = cl( 7)
R is equivalence relation
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Lisa creates a designer bracelets with gemstones are most recent included six bracelets and takes $12 to make one bracelet right and talking equation to represent how many stones are used for the order
Equation s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.
How to form an equation for a word problem?
Follow these steps:
Understand the problem. Understand all the words used in stating the problem. Understand what you are asked to find.
Translate the problem to an equation. Assign a variable (or variables) to represent the unknown.
Carry out the plan and solve the problem.
According to the given question:
Leslie's most recent order included a total of 6 bracelets.
It takes 12 stone to make one bracelet.
Let the total number of stones be s.
If one bracelet requires 12 stones then 6 bracelets requires 12 x 6 stones
Therefore, s = 12 x 6 or s/12 = 6
On solving to get value of s we get 12 x 6 = 72 stones.
Hence s/12 = 6 represents the equation on how many stones were used for the order. On solving we get 72 stones.
Complete question:
Leslie creates designer bracelets with gemstones. Her most recent order included a total of 6 bracelets. It takes 12 stone to make one bracelet.
Write and solve an equation that represents how many stones were used for the order.
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Show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write . c. If possible, identify the direction of the velocity vector and show it as a labeled vector. d. Write a short description of a real object for which this is the correct free-body diagram. Use Examples and 5.6 as models of what a description should be like.
A) Acceleration Direction
The net force is acting down the surface, as seen in the figure. As a result, the acceleration vector should likewise be directed down the surface.
Labeling the vector of acceleration
The acceleration vector is depicted below:
B) Determine the velocity vector
According to the free-body diagram, an item should be on an inclined surface with a tension force pulling it down. When a kinetic frictional force is directed up to the surface, the item is said to be sliding down the slope. As a result, the velocity vector should be oriented upside down.
Determine the direction of the velocity vector
The velocity vector is indicated in the picture below:
C) Describe a real-world thing
The diagram shows an item on an inclined surface, with the kinetic force directed up to the surface. As a result, the item may be thought of as a box being pulled down by a rope down an inclined slope.
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Full Question
Problems 35 through 40 show a free-body diagram. For each:
a. Redraw the diagram
b Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write
c. If possible, identify the direction of the velocity vector and show it as a labeled vector.
d Write a short description of a real object for which this is the correct free-body diagram. Use Examples 5.4, 5.5, and 5.6 as models of what a description should be like.
A is a 7x7 matrix with three eigenvalues. One eigenspace is two-dimensional, and one of the other eigenspaces is three dimensional then it is possible that A is not diagonalizable. Select one: True False
A is a 7x7 matrix with three eigen values. One eigenspace is two-dimensional and one of the other eigenspaces is three dimensional, then it is possible that A is not diagonalizable. The given statement is true.
There are three eigen-spaces, since A has three eigen values, the dimension of each of the eigen value is atleast one as there is atleast one non-zero eigen vector in them.
It is given that one of the eigen space has dimension 2 and other one has dimension 3.
A 7 x 7 matrix is diagonalizable if and only if the sum of the eigenspaces' dimension is 7. The given matrix is diagonalizable if and only if the third eigen space has dimension 2.
In A, if the sum of dimensions of eigenspace is not equal to the number of columns, then A is not diagonalizable.
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Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 80% of all such components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested until a defect-free component is obtained.
(a) What is the smallest possible y value, and what experimental outcome gives this y value? What is the second smallest y value, and what outcome gives rise to it?
The smallest value of y is ______ . The outcome corresponding to this is______ .
The second smallest value of y is_________ . The outcome that corresponds to this is ______ .
(b) Determine the probability of each of the five smallest y values. You should see a pattern that leads to a simple formula for P(y), the probability distribution of y.
P(y = 1) =
P(y = 2) =
P(y = 3) =
P(y = 4) =
P(y = 5) =
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To determine the probability of each of the five smallest y values, we can use the probability of each possible outcome and the number of ways that outcome can occur.
P(y = 1) = probability that the first component is defect-free = 0.8
P(y = 2) = probability that the first component is defective and the second component is defect-free = (1 - 0.8) * 0.8 = 0.16
P(y = 3) = probability that the first two components are defective and the third component is defect-free = (1 - 0.8) * (1 - 0.8) * 0.8 = 0.032
P(y = 4) = probability that the first three components are defective and the fourth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.0064
P(y = 5) = probability that the first four components are defective and the fifth component is defect-free = (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * (1 - 0.8) * 0.8 = 0.00128
We can see that the probability of each y value is simply the probability of the previous y value multiplied by (1 - 0.8) = 0.2. This means that the probability distribution of y is given by the formula P(y) = 0.2^(y - 1) * 0.8.
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Reflecting across Both Axes Suppose (-7,3) is reflected across the x-axis, and then the y-axis. What will be the new coordinates? A. (-7,-3) B. (-7,3) C. (7,-3) D. (7,3)
The coordinates after the reflection of the points will be(7, -3).
What is reflection over axes?The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse.
Given that, (-7,3) is reflected across the x-axis, and then the y-axis.
When reflected across x-axis, it will be (-7, -3)
And again when reflected across y-axis it will be (7, -3)
Hence, The coordinates after the reflection of the points will be(7, -3)
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