The respective probabilities are -
(a).P(vet concludes-no virus ,if no chicken is infected)=0.988,
(b).P(vet cincludes virus,if no chicken is infected)= 0.012,
(c).P(vet cincludes virus, if every chicken is infected)=0.99 ,
(d).P(vet cincludes virus, if 20% chickens are infected)= 0.383.
This problem involves the probability of binomial distribution as there are only two outcomes of the event, either the bird is infected or its not infected.
Now, let us suppose in this problem, that x is a random variable indicating the no. of chickens infected.
According to question , P(false positive test)=0.05,
P(false negative test)=0.10 where false positive test means that the bird is not infected and still the vet says that its infected.
false negative test means that the bird is not infected and the vet declares it to be infected.
Now, P(bird is not infected) = 1- P(bird tested false positive) = 1-0.05=0.95
Similarly, P(bird is infected) = 1 - P(bird tested false negative) 1- 0.10=0.90
Now, in the question , the vet declares the flock as infected if at least 3 out of 10 chickens are infected.
So, in (a) , t]if the vet does not declare the birds as infected means less than 3 birds would only be infected.
so, P(vet declares as uninfected) = P(x=0) + P(x=1) + P(x=2)=
10C0 (0.05)^0 (0.95^10) + 10C1 (0.05)^1 (0.95)^9 + 10C2(0.05)^2 (0.95)^8
Upon calculating this , we get 0.988.
Now, for (b) , P(no virus and vet declares it to be present)= 1- P(no virus and vet does not declare it to be infected)= 1-0.988 = 0.012.
(c) - the probability that every chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is present in the flock = 1- P(every chicken is infected and the vet declares as not infected) = 1- bin (10,0.9,2)
=1- 10C0(0.9)^0(0.1)^10 + 10C1(0.9)^1(0.1)^9 + 10C2(0.9)^8(0.1)^2 = 1- 0.001 = 0.99.
(d) . Now here, we need to calculate P(x>=3) =
1- [10C0(0.22)^0(0.78)^10 + 10C1(0.22)^1(0.78)^9 + 10C2(0.22)^8(0.78)^2]
=0.383.
So, in this way we get answers as (a)-0.988 , (b)- 0.012, (c)-0.99 , (d) - 0.383.
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divide 1hr on the ratio 5 7
Answer:
25:35
Step-by-step explanation:
5 + 7 = 12
60 ÷ 12 = 5
5 × 5 = 25
5 ×7 = 35
ratio = 25:35
in fact, you don't get an amount starting with an 8 or 9 until the 40th invoice. do you suspect that the invoice amounts are not genuine? compute an appropriate probability to support your answer.
a) It is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.
b)It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05) ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.
Now, According to the question:
Part (a) Step 1: Given Information
Given, p = 0.097
Formula used:
The expected value
μ = 1/p
Part (a) Step 2: Simplification
The number of independent trials required until first success is distributed geometrically.
A geometric distribution's expected value is
μ = 1/p = 1/0.097 = 10.3039
Hence, it is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.
Part (b) Step 1: Given Information
Given, p = 0.097
Formulae to be used
Geometric probability:
P(X = k) = [tex]q^k^-^1p = (1-p)^k^-^1p[/tex]
Addition rule:
P(A ∪ B) = P(A) + P(B)
Complement rule:
P(A°) = P(not A) = 1 - P(A)
Part (b) Step 2: Simplification
Consider, p = 0.097
Compute the binomial probability definition at k = 1, 2,and3....40 :
P(X = 1) = [tex](1 - 0.097)^1^-^1(0.097)[/tex] = 0.097
Using the complement rule:
P(X ≥ 40) = 1 - P(X ≤ 39) = 1 - 0.9813 = 0.0187 = 1.87%
It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05) ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.
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The given question is incomplete, The complete question is:
Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .
a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?
b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.
Ellen has a pencil 2x+15cm long. Tom has a pencil 5x+25cm long. How much longer is Tom's pencil than Ellen's?
Tom's pencil is longer than Ellen's pencil with (3x+10)cm
What is subtraction?Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 minus 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.
Ellen's pencils length = 2x+15
Tom's pencil length = 5x+25
Tom's pencil will be longer than Ellen's with;
(5x + 25 ) - (2x+15)
= 5x + 25 -2x - 15
collect like terms
5x -2x +25-15
3x +10
therefore Tom's pencil is longer than Ellen's pencil with ( 3x+10) cm
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two cards are selected with replacement from a standard deck of 52 cards. find the probability of selecting a spade and then selecting a heart.
The probability of selecting a spade and then selecting a heart from a standard deck with replacement is 0.625.
When selecting two cards with replacement from a standard deck of 52 cards, the probability of selecting a specific card on the first draw does not affect the probability of selecting a specific card on the second draw. Therefore, we can simply multiply the probability of selecting one card of a specific suit by the probability of selecting a different card of a specific suit.
The probability of selecting a spade on the first draw is
13/52 = 1/4 = 0.25
since there are 13 spades in a deck of 52 cards.
The probability of selecting a heart on the second draw is also
13/52 = 1/4 = 0.25
since there are 13 hearts in a deck of 52 cards.
Therefore, the probability of selecting a spade and then selecting a heart is:
(0.25) * (0.25) = 0.0625
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please HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
[tex]\mathrm{A.\;\;\boxed{V = \dfrac{m}{D}}}\\\\\\\\\mathrm{B.\;\;\boxed{8.8496\;cm^3}}[/tex]
Step-by-step explanation:
Object density formula is
[tex]D = \dfrac{m}V}\\[/tex]
with the variables defined as in the question
A.
B.
For osmium, we have D = 22.6 gm/cm³We are given the mass as 200 gm, so m = 200Plug these values into the equation to get the volume of 200gms of osmiumclasswork
If tan x = 1, evaluate Sin x+ cos x, leaving your answer in surd form
Answer:
sin x + cos x = [tex]\sqrt{2}[/tex]
Step-by-step explanation:
given
tan x = 1 , then
x = [tex]tan^{-1}[/tex] (1) = 45°
the exact values of both sin45° and cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin x + cos x
= sin45° + cos45°
= [tex]\frac{1}{\sqrt{2} }[/tex] + [tex]\frac{1}{\sqrt{2} }[/tex]
= [tex]\frac{2}{\sqrt{2} }[/tex]
rationalise the denominator by multiplying numerator/ denominator by [tex]\sqrt{2}[/tex]
= [tex]\frac{2(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]
= [tex]\frac{2\sqrt{2} }{2}[/tex]
= [tex]\sqrt{2}[/tex]
What is the value of x?
The value of x is 15 units.
What are Corresponding Angles ?
When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
For instance, angle p and angle w are the comparable angles in the image below.
Step-by-step explanation:
In the given triangle RSQ and ΔRST it is given that
∠RTS ≅ ∠SRQ ≅ 90°
∠RSQ is common in two triangles Δ RSQ and Δ RST.
Therefore two angles are equal so both the triangles are common.
From this property we opposite sides of the corresponding angles will be in the same ratio.
SR/SQ = ST/SR
x/(9 + 16) = 9/x
By cross multiplication on each side of the equation
x² = 25×9 = 225
x = √225 = 15
Therefore measurement of x is 15 units.
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what is the equation of the line that passes through displaystyle 1 10 1 10 and is perpendicular to the equator displaystyle y frac 1 3x 5y 3 1 x 5
The equation of the line is y = -3x + 5.
To find the equation of a line that passes through two points and is perpendicular to the equator, we need to calculate the slope of the line that passes through the two points first.
The slope of the line passing through (1,10) and (1,10) is 0. This means that the line is perpendicular to the equator, whose slope is undefined.
Next, we need to calculate the y-intercept. If we assume that the line passes through the point (1,10), then the y-intercept is 10.
Finally, we can use the slope and the y-intercept to write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0 and the y-intercept is 10, so the equation of the line is y = 0x + 10, which simplifies to y = 10.
Since the slope of the line is 0, we can also write the equation of the line in the form y = -3x + b, where b is the y-intercept. In this case, the y-intercept is 10, so the equation of the line is y = -3x + 10, which simplifies to y = -3x + 5.
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Mrs. mccall is renting a truck for one day. the two choices she had are company a and company b. what is the minimum number of miles that mrs.mccall would need to drive in order to make renting from campany b a better deal?
On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles in order to make renting from Company B a better deal
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have -
Company A charges = $35 per day
plus = $0.45 per mile.
Company B charges = $60 per day
plus = $0.25 per mile.
McCall would need to drive 126 miles in order to make renting from Company B a better deal
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A car rolls forward 5 ft. The car wheel has a 16 in radius. Through what angle (to the nearest tenth of a degree) does the wheel turn?
Answer:
214.9°
Step-by-step explanation:
You want to know the angle of rotation that moves a point on a circle of 16 inch radius a distance of 5 feet.
Arc lengthThe relation between the length of an arc and the central angle in radians is ...
s = rθ
The distance of 5 ft is equal to 60 inches, so we have ...
60 = 16θ
AngleSolving for θ gives ...
θ = 60/16 = 15/4 . . . . radians
The angle in radians can be converted to an angle in degrees by multiplying it by 180°/π:
15/4 radians = (15/4)·(180°/π) ≈ 214.9°
The wheel turned through an angle of about 214.9°.
Suppose that A and B are two independent events for which P(A) = 0.31 and P(B) = 0.76. What is the probability of (A|B), (B|A), (A and B), and (A or B)?
The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.
When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.
P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356
P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)
P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)
P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144
Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.
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if ACB= (11x-32) find the value of x
Answer:the final answer is 7
Step-by-step explanation:
How do you solve absolute value Grade 7?
In grade 7, one common method to solve absolute value equations is by isolating the absolute value on one side of the equation and then solving for the two possible solutions.
Here is a step-by-step process to solve an absolute value equation:
Isolate the absolute value on one side of the equation by adding or subtracting the same value to both sides of the equation.
For example, |x| = 3 can be rewritten as x = 3 or x = -3
Split the equation into two separate cases, one for when the value inside the absolute value sign is positive, and one for when it is negative.
Solve each case separately.
Check your solutions by plugging them back into the original equation and making sure they are valid solutions.
Write your answer in interval notation if the solutions are continuous or list them as individual values if they are not.
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PLS GIVE ME THE EQUATION FOR THIS QUESTION. I WILL MARK BRAINLIEST.
Answer:
x + y ≥ 6 (Melissa exercises for at least 6 hours per week)
x ≤ 11 (Melissa spends at most 11 hours doing cardiovascular work)
y ≤ 4 (Melissa spends at most 4 hours on weight training)
To graph this region, you can plot the constraints on the x-y coordinate plane and shade the area that satisfies all of them.
The first constraint x+y>=6 can be represented by the line y = -x +6
The second constraint x<=11 can be represented by the line y = 11
The third constraint y<=4 can be represented by the line y = 4
The shaded area will be the region that is above and to the right of the line y = -x + 6, below the line y = 11 and below the line y = 4.
Kind of hard to shade a graph without having it in front of me. Hope this helps!
Answer:
livirav737 has provided the correct answer first.
I am merely providing the graph
Step-by-step explanation:
Plotted using online graphing tool Geogebra
The heavily shaded region with ABCD as its corners represents the region corresponding to all 5 inequalities
Note
Though not explicitly stated
You must also have the two additional constraints
x ≥ 0, y ≥ 0
These are called non-negativity constraints to ensure that x and y are not negative. The number of hours exercised on each platform cannot be less than 0
In this particular case, these are not necessary but standard practice is to include them whenever you have a system of inequalities with non-negative variables
How many 1/4 are in 3
Answer:
there are 12 fourths in 3 .
when canned peaches are delivered to a grocery store, the clerk stocks the new cans in front of the old. if each can sold is accounted for as to its cost, a) lifo (last-in, first-out). b) average. c) random. d) fifo (first-in, first-out).
According to the given statement If each can sold in accounted for as to its cost Last in first out.
Why do we determine the average?The average is determined by adding together all of the numbers as well as dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value. We constantly encounter the average computation in our daily lives.
Which 4 averages are there?The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or dispersion.
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Find the equation of the linear function represented by the table below in
slope-intercept form.
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
we see that with every increase of x by 1 y increases by 3.
so, the slope "a" is 3.
to get b we use one of the given points, e.g. (1, 5) :
5 = 3×1 + b = 3 + b
b = 2
so, our function is
y = 3x + 2
Find the sum of the geometric sequence if the first term is -8, the common ratio is -3 and there are 10 terms
Answer:
Step-by-step explanation:
The sum of a geometric sequence can be found using the formula
Sn = a₁ (1 - rⁿ⁻¹)/ (1 - r)
where a₁ is the first term, r is the common ratio, and n is the number of terms.
In this case, a₁ = -8, r = -3, and n = 10.
Plugging these values into the formula, we get
Sn = -8 (1 - (-3)⁹⁻¹) / (1 - (-3))
Sn = -8 (1 + 3⁹) / 4
Sn = -8 (1 + 19683) / 4
Sn = -8 × 19684 / 4
Sn = -4920
What length of rope would enable the goat to eat 10 square yards of grass? Show all your reasoning.
Legth of rope=7 m
Length of shed=8m
Breadth of shed=14m
Note-Goat is tied to corner of shed
The length of the rope must be, at least, 5.9 meters.
How to find the length of the rope?The rope will allow the sheep to move in an almost perfect circle (except for the part where the shed is) so we will have 3/4 of a circle.
So here we just need to find the length L of the rope such that:
10 yd² = (3/4)*pi*L^2
Where (3/4)*pi*L² is the area of 3/4 of a circle of radius L.
and pi = 3.14
Solving for L we will get:
L = √( 10 yd²*(4/3*3.14)) = 6.4 yd
Writting this in meters, we will get:
1 yd = 0.9144 m
then:
L = 6.4* 0.9144 m = 5.9m
The rope must be at least 5.9 meters long.
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we roll a pair of standard dice until the sum of the two numbers on which they land is 5 or 7 or 9. what is the probability that we observe a sum of 5 or 9 before a sum of 7 ?
The probability that we observe a sum of 5 or 9 before a sum of 7 is 7/18
The term probability is referred as the number of ways of achieving success. the total number of possible outcomes
Here we have given that we roll a pair of standard dice until the sum of the two numbers on which they land is 5 or 7 or 9.
As we all know that the sample space for the rolling of two dice that is the pair of dice is written as n(s) = 36
Then the probability of getting the sum of 5 is written as,
=> 4/36
Similarly, the probability of getting sum of 7 is written as,
=> 6/36
And the probability of getting sum of 9 is written as,
=> 4/36
Then the total probability is calculated as,
=> 14/36
When we simplify this one then we get,
=> 7/18
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Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer to Problem 13 is 34.5
Answer to Problem 15 is 22.9
==================================================
Work Shown for Problem 13
sin(x)/17 = sin(91)/30
sin(x) = 17*sin(91)/30
sin(x) = 0.56658036
x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)
x = 34.51210645 or x = 180-34.51210645
x = 34.51210645 or x = 145.48789355
x = 34.5 or x = 145.5
If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).
If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)
In short, x = 34.5 is valid while x = 145.5 is not valid.
Therefore, the only possible answer is 34.5
---------------------------------------------
Work Shown for Problem 15
sin(x)/20 = sin(119)/45
sin(x) = 20*sin(119)/45
sin(x) = 0.38871987
x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)
x = 22.87486940 or x = 180-22.87486940
x = 22.87486940 or x = 157.1251306
x = 22.9 or x = 157.1
If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.
If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1
The only possible answer is therefore 22.9
---------------------------------------------
Side notes:
Make sure your calculator is in degree mode. Unfortunately some calculators like to default to radian mode. A quick check is to see if sin(30) produces the result 0.5Arcsine is the same as inverse sine, which is denoted as [tex]\sin^{-1}[/tex] on many calculators.Do absolute value functions pass the vertical line test?
No, absolute value functions do not pass the vertical line test.
The vertical line test is a way to determine if a graph represents a function. A graph represents a function if and only if no vertical line intersects the graph more than once.
An absolute value function is defined as:
y = |x|
The graph of this function is a V-shape, with the vertex at the origin. The graph of the function is defined for all x-values, but the graph is not a function because a vertical line can intersect the graph at two points, one for x and the other for -x, for example if the vertical line x=2, it will intersects the graph at (2,2) and (2,-2), thus it does not pass the vertical line test.
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The manager at Apex Gym wants to know when the new pricing model (higher per-class fee but lower membership fee) will be better than the old pricing model used last year. He uses a table to calculate the members’ costs for different numbers of classes.
The completed table to show the member cost for different numbers of classes is :
No. of classes Cost under old model Cost under new model
2 170 110
4 200 170
5 215 200
6 230 230
7 245 260
How to find the member costs ?Assuming that the number of classes is x, then the formula to find the cost with a certain number of classes with the old model is:
= 15 x + 140 membership fee
4 classes :
= 15 x 4 + 140
= $ 200
5 classes :
= 15 x 5 + 140
= $ 215
6 classes :
= 15 x 6 + 140
= $ 230
7 classes :
= 15 x 7 + 140
= $ 245
Cost under new model would take the formula:
= 30 x + 50 membership fee
4 classes :
= 30 x 4 + 50
= $ 170
5 classes :
= 30 x 5 + 50
= $ 200
6 classes :
= 30 x 6 + 50
= $ 230
7 classes :
= 30 x 7 + 50
= $ 260
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A circle centered at $P$ with radius $10$ and a circle centered at $Q$ with radius $8$ are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$
If the two circle centered at P and Q with radius 10 and 8 respectively , and if the common external tangent intersects line PQ at R , then the length of QR is 72 .
The radius of the circle that is centered at P is = 10 ;
the radius of circle that is centered at Q is = 8 ;
the common external tangent intersects the line PQ at R ,
Let XYR be external tangent with X on the Circle with center P , and at point Y on circle with center Q .
we extend , the line PQ to point R ,
we get , that triangle XPR is similar to triangle YQR ,
it means that , [tex]\frac{RQ}{RP} =\frac{QY}{PX}[/tex] ;
let the length of RQ be = x , then
length of RP will be = [tex]x+18[/tex] ;
we get ; [tex]\frac{x}{x+18} =\frac{8}{10}[/tex] ;
⇒ [tex]10x=8x+144[/tex] ;
⇒ [tex]2x=144[/tex] ;
⇒ [tex]x=72[/tex] .
Therefore , the length of QR is 72 .
The given question is incomplete , the complete question is
A circle centered at P with radius 10 and a circle centered at Q with radius 8 are externally tangent. A common external tangent intersects line PQ at R. Find QR .
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"What set of reflections would carry hexagon ABCDEF onto itself?. . Hexagon ABCDEF on the coordinate plane with pointA at negative 1, 1, pointB at negative 3, 1, pointC at negative 4, 2, pointD at negative 3, 3, pointE at negative 1, 3, and pointF at 0, 2. . .x-axis, y=x, x-axis, y=x .. y=x, x-axis, y=x, y-axis .. y-axis, x-axis, y-axis .. x-axis, y-axis, y-axis ."
A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
What is a combination of reflections?
Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.
Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.
One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.
This would take the hexagon from its original position to itself.
Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.
This would also take the hexagon from its original position to itself.
Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
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What is the greatest possible error for a measurement or 25 miles?
The greatest possible error for 25 miles is 12.5 miles.
What is the greatest possible error?Half of the unit of measure to which a measurement is rounded is the largest possible error. The maximum error is 2 units when a measurement is taken to the nearest whole unit 4.
Given, A value of 25 miles.
Now, we know the greatest possible error is half of the unit of measure.
Therefore, The greatest possible error for 25 miles is,
= (25/2) miles.
= 12.5 miles.
As 12.5 miles is half the value of 25 miles.
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H(x) = 1/8 x^3 -x2 what is the average rate of change of h over the Interval-2 < x< 2
The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.
Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:
(h(2) - h(-2)) / (2 - (-2))
First, we have to find h(2) and h(-2) by substituting these values in the function:
h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5
h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5
So, the average rate of change is:
(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25
Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25
What is the solution of the system?
4g + h = -4
12g + 2h = -4
Enter the coordinate pair in the blanks in alphabetical order (g, h) (_, _)
The coordinate pair of the given solution of the system would be= (g, h) (1,-8).
What is the substitution equation?Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.
4g + h = -4 ---->. eq 1
12g + 2h = -4 ----> eq 2
Make h the subject of formula;
h = -4 - 4g -----> eq 3
Substitute equation 3 into equation 2;
12g + 2( -4 - 4g) = -4
12g - 8 -8g = -4
4g -8 = -4
4g = -4 +8
4g = 4
g = 4/4= 1
Solve for g = 1 in equation 1;
4(1) + h = -4
4 + h = -4
h = -4-4
h = -8
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A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length 2000. What is the length of each side of the octagon
A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square. To find the length of the side of the octagon, we can use the Pythagorean theorem to calculate the length of the hypotenuse of the isosceles right triangle.
In an isosceles right triangle, the two legs have the same length and the hypotenuse is the side opposite the right angle. Since the square has sides of length 2000, half of the side of the square is the leg of the isosceles right triangle.
So the leg of the isosceles right triangle is 2000/2 = 1000.
Applying the Pythagorean theorem to find the hypotenuse of the isosceles right triangle:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
c = sqrt(1000^2 + 1000^2)
c = sqrt(1000000)
c = 1000*sqrt(2)
So the length of each side of the octagon is 1000sqrt(2)
if a gallon of paint costs $36.50 and it covers 350 square feet on average, what is the cost of painting the room walls with two coats of paint?
The cost of painting the room walls with two coats of paint would be $84.38
To determine the cost of painting the room walls with two coats of paint, you would need to know the total square footage of the walls you are planning to paint. Once you have that information, you can calculate the total cost by multiplying the number of gallons of paint required by the cost per gallon. For example, if the room has 800 square feet of walls, you would need 2.28 gallons of paint (800/350 = 2.28) and the total cost would be $84.38 (2.28 x $36.50). If you want to know the cost of one coat, you will need to divide that number by 2.
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