The event definition that corresponds to exactly one outcome of the experiment is selecting a specific number on the die and drawing a specific card from the set. For example, if the event definition is "rolling a 3 on the die and drawing the card numbered 7," this corresponds to exactly one outcome in the experiment.
In this experiment, there are six possible outcomes for rolling the die (numbers 1 to 6) and ten possible outcomes for drawing a card (numbers 1 to 10).
When we specify a particular number on the die and a particular card from the set, we narrow down the possible outcomes to only one combination. This means that there is only one way this event can occur, making it a single outcome event.
For instance, if we define the event as "rolling a 4 on the die and drawing the card numbered 5," there is only one instance where this can happen.
If the die lands on 4 and the card drawn is number 5, then the event has occurred. Any other combination of numbers on the die or cards from the set would not satisfy this event definition.
Therefore, by specifying a particular number on the die and a specific card from the set, we create an event definition that corresponds to exactly one outcome in the experiment.
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4.3 help me please i would appreciate it so so much
Answer:
x = 150 , y = 30 , z = 60
Step-by-step explanation:
x and 30° are same- side interior angles and sum to 180° , that is
x + 30 = 180 ( subtract 30 from both sides )
x = 150
-------------
x and y are a linear pair and sum to 180° , that is
x + y = 180
150 + y = 180 ( subtract 150 from both sides )
y = 30
----------------
since EF and EG are congruent then Δ EFG is isosceles with base angles congruent , then
2 = y = 30
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
z is an exterior angle of Δ EFG , then
z = ∠ 2 + ∠ y = 30 + 30 = 60
Which function is decreasing on the same interval as the function graphed here?
f (x)
61
N
-2
O A.
O B.
O c.
O D
4
2
-2
10
-41
2
A.
★
k (2) = -2x2 – 82 + 5
भ
Ko
j (±) = 22 + 4 – 4
=
9 (‡) = 322
- 12x + 18
h (x) = 2x2 + 8x + 3
The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.
To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.
Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.
Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.
Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).
Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).
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Kaylib’s eye-level height is 48 ft above sea level, and Addison’s eye-level height is 85 and one-third ft above sea level. How much farther can Addison see to the horizon? Use the formula d = square root 3h/2, with d being the distance they can see in miles and h being their eye-level height in feet.
Answer is [tex]2\sqrt{2}[/tex] mi
Given,
Kaylib’s eye-level height is 48 ft
Addison’s eye-level height is 85 and one-third ft above sea level.
From the formula d= [tex]\sqrt{3h/2}[/tex],
get the difference as:
[tex]d=\sqrt{(3*(85+1/3))/2} - \sqrt{(3*48)/2}[/tex]
=[tex]\sqrt{256/2} - \sqrt{3*24}[/tex]
=[tex]\sqrt{128} - 6\sqrt{2}[/tex]
=[tex]8\sqrt{2} - 6\sqrt{2}[/tex]
d=[tex]2\sqrt{2}[/tex]
Therefore, Addison sees [tex]2\sqrt{2}[/tex]mi to the horizon
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For what values of a and b is x^64 + ax^b +25 a perfect square for all integer values of x?
For the expression [tex]x^64 + ax^b + 25[/tex] to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = [tex]y^2.[/tex]
To determine the values of a and b such that the expression[tex]x^64 + ax^b[/tex] + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.
A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of[tex](x^n)^2,[/tex] where n is an even integer.
Let's examine the given expression: [tex]x^64 + ax^b[/tex] + 25
For it to be a perfect square, the quadratic term [tex]ax^b[/tex]must have the same exponent as the leading term[tex]x^6^4.[/tex] This means b must be equal to 64.
So we have:[tex]x^64 + ax^64 + 25[/tex]
Now, we can rewrite this as:[tex](x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2[/tex]
By comparing this with the standard form of a perfect square, ([tex]x^n +\sqrt{k} )^2[/tex], we can deduce that √a must be equal to x^32 and [tex]\sqrt{25}[/tex] must be equal to [tex]\sqrt{k.}[/tex]
Therefore, we have: [tex]\sqrt{a} = x^3^2[/tex]and[tex]\sqrt{25} = \sqrt{k}[/tex]
From the second equation, we know that k = 25.
Now, substituting the value of k back into the first equation, we have: [tex]\sqrt{a} = x^3^2[/tex]
To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =[tex]y^2[/tex], where y is an integer.
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Select the correct answer from the drop-down menu.
Right triangle MNR is represented with the right angle at vertex M. Angle R measures 34 degrees and angle N measures 56 degrees. Point Q lies on segment RN and point P lies on segment MP. Segments MQ and PQ are drawn. Angle MQP measures 56 degrees.
In the figure, sin ∠MQP =
.
sin ∠MQP = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{MQ}{MP}[/tex].
To determine the value of sin ∠MQP, we need to use the given information about the triangle.
Since we know the measures of angles MQP and MQN, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle QMP.
Let's calculate it:
Angle MQP + Angle MQN + Angle NQM = 180 degrees
56 degrees + 90 degrees + Angle NQM = 180 degrees
Simplifying the equation:
146 degrees + Angle NQM = 180 degrees
Subtracting 146 degrees from both sides:
Angle NQM = 180 degrees - 146 degrees
Angle NQM = 34 degrees
Now, we have all the angles needed to calculate sin ∠MQP.
The sine function relates the lengths of the sides of a right triangle to its angles.
In this case, we are interested in the side opposite to ∠MQP, which is side MQ, and the hypotenuse, which is side MP.
Therefore, sin ∠MQP = opposite/hypotenuse = MQ/MP.
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Given circle C with diameter AB
, find the value of x.
A circle with three chords. Point C is in the center, point D is a 2 o clock, point B is at 3 o clock, and point A is at 9 o clock. Segment AB is passing through C. Segment BD and AD do not pass through C. Angle ABD is labeled 70 degrees. Angle DAB is labeled x.
Enter your answer in the box.
The value of x is 70 degrees.
To find the value of x, we can use the properties of angles in a circle.
In the given circle, we have a diameter AB passing through the center of the circle, labeled as point C. Point D is located at 2 o'clock, point B at 3 o'clock, and point A at 9 o'clock.
We are given that angle ABD is labeled as 70 degrees. Since angle ABD is an angle formed by a chord (AB) and a tangent (BD), we can apply the property that the measure of an angle formed by a tangent and a chord is equal to half the measure of the intercepted arc.
In this case, angle ABD intercepts the arc AB. Since AB is a diameter, it subtends a 180-degree arc. Therefore, the measure of angle ABD is equal to half the measure of the intercepted arc AB, which is 180 degrees divided by 2, resulting in 90 degrees.
Now, let's focus on angle DAB, labeled as x. Since angle DAB and angle ABD are vertical angles (angles formed by the intersection of two lines), they have the same measure. Therefore, x is also equal to 70 degrees.
In conclusion, the value of x is 70 degrees.
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The number of visitors to a certain
Web site triples every month. The
number of visitors is modeled by the
expression 8100.3m, where m is the
number of months after the number
of visitors was measured. Evaluate
the expression for m =-4.
When m = -4, the expression 8100.3m evaluates to -24300.12.
How to find the expression for m =-4.To evaluate the expression 8100.3m for m = -4, we substitute the value of m into the expression:
8100.3m = 8100.3(-4)
Now, we can calculate the value:
8100.3(-4) = -24300.12
Therefore, when m = -4, the expression 8100.3m evaluates to -24300.12.
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Given =(5,-2, 3) and >= (1, 1, 2) find an ordered triple that represents 3u - 2v.
The ordered triple representing [tex]3u - 2v[/tex] is [tex](13, -8, 5)[/tex].
To find an ordered triple representing [tex]3u - 2v[/tex],
where [tex]u = (5, -2, 3)[/tex] and [tex]v = (1, 1, 2)[/tex],
we can perform the following operations:
[tex]3u = 3(5, -2, 3)[/tex]
[tex]3u = (15, -6, 9)[/tex]
[tex]2v = 2(1, 1, 2)[/tex]
[tex]2v = (2, 2, 4)[/tex]
Now, subtracting 2v from 3u gives:
[tex]3u - 2v = (15, -6, 9) - (2, 2, 4)[/tex]
[tex]3u - 2v = (15-2, -6-2, 9-4)[/tex]
[tex]3u - 2v = (13, -8, 5)[/tex]
Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).
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Question 2 of 5
Which inequality represents the values of r that ensure triangle ABC exists?
A
2x + 4
B
OA. <<
OB. <<
C. 1 < 1 < 5
D. 2 < < 6
18
6x
-C
کے
An inequality that represent the values of x that ensure triangle ABC exists is: A. 7/4 < x < 11/2.
What is the Triangle Inequality Theorem?In Mathematics, the Triangle Inequality Theorem is a type of theorem which states that the sum of any two side lengths of a triangle must be greater than the measure of the third side.
Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:
b - c < a < b + c
Where:
a, b, and c represent the side lengths of this triangle.
By applying the Triangle Inequality Theorem to the side lengths of this triangle, we have:
2x + 4 + 6x > 18
8x > 18 - 4
x > 14/8
x > 7/4
6x - (2x + 4) > 18
4x > 18 + 4
x > 22/4
x > 11/2
Therefore, we have 7/4 < x < 11/2.
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PLEASE HELP TODAY!!!!!!!!!11
Answer:
Measure of AC is 150°
Step-by-step explanation:
Given : ∠ABC = 75°
To Find : Arc AC
Solution :
Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc.
So, using this theorem
ABC=1/2 arc (AC)
->75=1/2 arc (AC)
->75= * 2=arc(AC)
->150=arc(AC)
Arc AC = 150°
BAM, Measure of AC is 150°
your welcome :)
im probably wrong cause i needed like 50 people to help but i hope this helps </33333333
L{(2+6)te^((2+0)t)+(3+0)sin3t}
The Laplace transform of the given function is L{(2+6)te^((2+0)t)+(3+0)sin3t}. Simplifying the expression inside the Laplace transform, we get L{8te^(2t)+3sin3t}.
The Laplace transform of te^(at) is (s-a)^(-2) and the Laplace transform of sin(at) is a/(s^2+a^2). Substituting these values into the expression, we get:
L{8te^(2t)+3sin3t} = 8(s-2)^(-2) + 3(3/(s^2+9)) = 8/(s-2)^2 + 9/(s^2+9)
This is the simplified form of the Laplace transform of the given function.
pls brainliest
10. John has taken many science tests. His scores are shown below.
What is the range of his test scores?
X
X
X
X
X
79 80 81
X
X X
x x
X
82
X
X X
83
84
85
Answer: 6
Step-by-step explanation:
85-79=6
Answer:
6
Step-by-step explanation:
85-79=6
a body move according to the law S(t)=62.6 + 54 t^2_0.2 t^5 , were t is time in second. then determine the velocity and acceleration in the body at this distance.
The velocity of the body is[tex]v = 108t + t^4[/tex], and the acceleration of the body is a = [tex]108 + 4t^3[/tex].
Given:S(t) = [tex]62.6 + 54t^2 + 0.2t^5[/tex]We are supposed to determine the velocity and acceleration of the body at a given distance.Solution:Velocity v is the derivative of displacement with respect to time, that is[tex],v = S'(t).[/tex]
Let us find the derivative of S(t)dS(t)/dt = [tex]d(62.6)/dt + d(54t^2)/dt + d(0.2t^5)/dt[/tex]We know that d/dt(C) = 0 (where C is a constant)The derivative of 62.6 is zero.[tex]d(54t^2)/dt = 108tandd(0.2t^5)/dt = t^4[/tex]Using the above derivations, the velocity of the body at any given time t is given by,[tex]v = dS(t)/dt = 108t + t^4.[/tex]
The acceleration of the body is the derivative of velocity with respect to time, that is,[tex]a = v'(t)[/tex]Again, let us differentiate[tex]v w.r.t t,dv/dt = d(108t)/dt + d(t^4)/dt = 108 + 4t^3[/tex]Using the above derivation, the acceleration of the body at any given time t is given by[tex],a = dv/dt = 108 + 4t^3.[/tex]
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Select a personal or professional example of a measurement you use routinely. Convert the measurement either from U.S customary units to metric units, or from metric units to U.S. customary units. You may choose more than one measurement and may choose among weight, length, temperature, etc. Show each step of your conversion and be sure to include all units from the original and converted measurements (for example, yards to meters, degrees Celsius to degrees Fahrenheit).
A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.
For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:
150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms
Therefore, 150 pounds is approximately equal to 68.0388 kilograms.
In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.
It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.
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Select the correct answer.
What is the quotient when (16x4 + 40x3 − 24x2) is divided by 8x2?
A.
2x2 + 3x − 5
B.
2x2 − 5x + 5
C.
2x2 + 5x − 3
D.
2x3 + 5x2 − 3
The quotient when (16x^4 + 40x^3 − 24x^2) is divided by 8x^2 is 2x^2 + 3x - 5.
To find the quotient when (16x^4 + 40x^3 − 24x^2) is divided by 8x^2, we perform polynomial long division.
We divide each term of the dividend by the divisor and simplify the result. The steps are as follows:
2x^2
8x^2 | 16x^4 + 40x^3 - 24x^2
- (16x^4 + 0x^3)
40x^3 - 24x^2
- (40x^3 - 0x^2)
-24x^2
The division process ends here, as the degree of the remaining term (-24x^2) is less than the degree of the divisor (8x^2).
Therefore, the quotient is 2x^2.
Hence, the correct answer is option A: 2x^2 + 3x - 5.
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Elana spent $25 for two shirts that each cost the same amount of money. The shirts were marked $4.00 off the original price. The equation 2(p−4)=25 can be solved to find p, the original price of the shirts. What was the original price?
in the figure below the length of segment CB is 64 units and the length of segment BG is 137 units. What is the length of segment EA
The length of segment EA, considering the trigonometric ratios in this problem, is given as follows:
146 units.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.As the tangent of 45º is of 1, on a triangle with an angle of 45º, the two sides have equal measure, hence the length of BA is given as follows:
BA = 64.
Applying the segment addition postulate, the length of AG is given as follows:
AG + 64 = 137
AG = 137 - 64
AG = 73.
73 is adjacent to the angle of 60º, while EA is the hypotenuse, hence the length of EA is given as follows:
cos(60º) = 73/EA
1/2 = 73/EA
EA = 2 x 73
EA = 146 units.
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Given: (↔AB) ║ (↔CD)
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of (↔AB) is (?) . If the coordinates of point D are (5 , 5), the equation of line (↔CD) is y =(?) x +(?).
can someone please help me figure out what the (?) is.
The y-intercept of line ↔AB is 56/5.
The equation of line ↔CD is y = (-7/5)x + 12.
To find the y-intercept of line ↔AB, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Given the coordinates of point A (8, 0) and point B (3, 7), we can calculate the slope of line ↔AB:
slope (m) = (y₂ - y₁) / (x₂ - x₁)
= (7 - 0) / (3 - 8)
= 7 / -5
= -7/5
Now, we can substitute the slope (-7/5) and the coordinates of point A (8, 0) into the slope-intercept form to find the y-intercept:
0 = (-7/5)(8) + b
Simplifying:
0 = -56/5 + b
To isolate b, we can add 56/5 to both sides:
b = 56/5
Therefore, the y-intercept of line ↔AB is 56/5.
Moving on to line ↔CD, given the coordinates of point D (5, 5), we can use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁)
Substituting the coordinates of point D (5, 5) and the slope from the previous calculation (-7/5), we have:
y - 5 = (-7/5)(x - 5)
Expanding and simplifying:
y - 5 = (-7/5)x + 7
Rearranging the equation to slope-intercept form:
y = (-7/5)x + 7 + 5
y = (-7/5)x + 12
Therefore, the equation of line ↔CD is y = (-7/5)x + 12.
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The distance between a building on the ground and a pilot in the cockpit is 72 ft. The angle of elevation from the building to the pilot is 38°. What is the distance along the ground between the building and the pilot? Round your answer to the nearest tenth.
The distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).
To find the distance along the ground between the building and the pilot, we can use trigonometry.
We have the following information:
Angle of elevation (θ) = 38°
Distance from the building to the pilot (opposite side) = 72 ft
We need to find the adjacent side, which represents the distance along the ground.
Using the trigonometric function tangent (tan), we can set up the following equation:
tan(θ) = opposite/adjacent
tan(38°) = 72/adjacent
To find the adjacent side, we rearrange the equation:
adjacent = 72 / tan(38°)
Using a calculator, we can evaluate this expression:
adjacent ≈ 72 / 0.7813 ≈ 92.19 ft
Therefore, the distance along the ground between the building and the pilot is approximately 92.19 feet (rounded to the nearest tenth).
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Select the correct answer from each drop-down menu.
Trapezoids 1 and 2 are plotted on the coordinate plane. Are they similar?
-8 -6
Trapezoid 1
8
6
2-
-4-20
2-
N
6
X
similar to trapezoid 2 because trapezoid 1
cannot be
Res can be
mapped onto trapezoid 2 by a series of transformations.
Text
Trapezoid 1 is similar to trapezoid 2 because trapezoid 1 can be mapped onto trapezoid 2 by a series of transformations.
What are the properties of similar geometric figures?In Mathematics and Geometry, two geometric figures such as trapezoids are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
This ultimately implies that, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar;
Scale factor = √10/√2 = 5/2.5 = 7/3.5
Scale factor = 2.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Guided application Every minute, Mr Williams completes 8 questions on his homework. Two bu Bus A Miss Hymers completes 6 questions on her homework every Bus B minute Pane en How many minutes does it take each of them to do this? Both b If they both complete the same amount of questions and both work for an exact number of minutes, what is the lowest What number of questions they could have done?
Mr. Williams takes (total number of questions) / 8 minutes to complete his homework, Miss Hymers takes (total number of questions) / 6 minutes to complete her homework, and the lowest number of questions they could have done is 24.
To find the number of minutes it takes for each of them to complete their homework, we can divide the total number of questions by the number of questions they complete per minute.
For Mr. Williams, he completes 8 questions per minute, so if we divide the total number of questions by 8, we will get the number of minutes it takes for him to complete his homework.
Similarly, for Miss Hymers, she completes 6 questions per minute, so if we divide the total number of questions by 6, we will get the number of minutes it takes for her to complete her homework.
To find the lowest number of questions they could have done if they both completed the same amount of questions and worked for an exact number of minutes, we need to find the least common multiple (LCM) of 8 and 6. The LCM of 8 and 6 is 24. Therefore, the lowest number of questions they could have done is 24.
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Please awnser asap I will brainlist
The equation that represents the total cost of purchasing currency is 1.40x + 1.50y = 3400.00.
The equation that represents the relationship between the number of currency A and number of currency B is x = 5y.
x = 2000 and y = 400
There are 2000 of currency A and 400 of currency B
How to determine the number of currency?In order to write a system of linear equations to describe this situation, we would assign variables to the number of currency A and currency B, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of currency A.Let the variable y represent the number of currency B.Since she budgeted $3400.00 for spending money on an upcoming trip and currency A is trading at $1.40 per euro, and currency B is trading at $1.50 per pound, a system of linear equations to describe this situation is given by;
1.40x + 1.50y = 3400.00
x = 5y
1.40(5y) + 1.50y = 3400.00
8.5y = 3400
y = 3400/8.5
y = 400
x = 5y
x = 5(400)
x = 2000
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Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?
On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3).
A: A Is congruent to B and B Is congruent to C
B: A Is congruent to A, B Is congruent to B, C Is congruent to C
C: Each triangle is a right triangle.
D: Each triangle is an isosceles triangle.
The reflected figure is labeled figure C is B: A is congruent to A, B is congruent to B, C is congruent to C. The correct answer is B: A is congruent to A, B is congruent to B, C is congruent to C.
To explain why figure A is congruent to figure C, we need to understand the transformations that were applied to create each figure.
In the given scenario, figure A was translated 3 units to the right and 2 units up to create figure B. This means that every point in figure A was shifted horizontally by 3 units to the right and vertically by 2 units up to obtain the corresponding points in figure B.
Next, figure B was reflected over the x-axis to create figure C. This reflection flips the figure vertically, so the y-coordinates of each point are negated while the x-coordinates remain the same.
Now, if we compare the coordinates of figure A and figure C, we can see that the x-coordinates of each point in figure C are the same as in figure A, while the y-coordinates are negated. This means that the two figures have the same shape and size, just positioned differently on the coordinate plane.
Therefore, we can conclude that figure A is congruent to figure C because they have the same shape and size, even though they are located in different positions on the coordinate plane.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The scale factor and the value of x for each figure is given as follows:
A) Scale factor of 1/3, x = 7 m.
B) Scale factor 0.4747, x = 4.5 in.
How to obtain the scale factor and the value of x?For Figure A, we have that the ratio between the areas is given as follows:
510/4590 = 1/9.
As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:
1/3.
Then the value of x is obtained as follows:
x = 21 x 1/3
x = 7 m.
For Figure B, we have that the ratio between the areas is given as follows:
16/71 = 0.22535.
The scale factor is then the square root of 0.22535, which is given as follows:
0.4747.
Then the value of x is given as follows:
x = 9.5 x 0.4747
x = 4.5 in.
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rattlesnake and paxon colleges play 4 games againt eachother. the probabilities that rattlesnake and paxon will win wach game are 2/3 and 1/3. what is the probability if paxon losses all four games
The probability that Paxon loses all four games is 16/81.
In the games played between the Rattlesnake and Paxon colleges, the probability of each team winning the game is 2/3 and 1/3 respectively.
We find the probability that Paxon loses all four games.
Firstly, we can find the probability of Paxon losing a single game as:
P(Paxon loses) = 1 - P(Paxon wins)
P(Paxon loses) = [tex]1-\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex]
To find the probability that Paxon loses all four games, we can assume that the events of losing a game are independent of each other.
This means that losing one game doesn't affect the probability of losing another game.
P(Paxon loses all 4 games) = P(Paxon loses game 1) × P(Paxon loses game 2) × P(Paxon loses game 3) × P(Paxon loses game 4)
P(Paxon loses all 4 games) = [tex](\frac{2}{3} )\times(\frac{2}{3} )\times(\frac{2}{3} )\times(\frac{2}{3} )[/tex]
P(Paxon loses all 4 games) = [tex]\frac{16}{81}[/tex]
Therefore, the probability that Paxon loses all four games is 16/81.
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HELPPP!!!
Does your residual plot show that the linear model from the regression calculator is a good model? Explain your reasoning.
A careful examination of the residual plot is crucial in determining the goodness of fit for the linear model.To determine whether the linear model from the regression calculator is a good model, we need to analyze the residual plot.
A residual plot is a graphical representation of the differences between the observed values and the predicted values from the linear model.
If the residual plot exhibits random scatter around the horizontal line (y = 0) with no discernible pattern, it suggests that the linear model is a good fit for the data. This indicates that the model captures the underlying linear relationship between the variables adequately, and the residuals have no systematic bias or trend.
However, if the residual plot displays a distinct pattern, such as a curved shape, a funnel shape, or an increasing/decreasing trend, it indicates that the linear model may not be appropriate. In such cases, the model may not be capturing all the relevant information or may be missing higher-order relationships.
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Please help and answer ASAP please will mark Brainlest
What is the value for x?
Enter your answer in the box.
x =
Answer:
x=45
Step-by-step explanation:
i hope its right good luck :)
i think im wrong
Find rectangular coordinates of the polar coordinates (3,-2)
Find the polar coordinates of the rectangular coordinates (2, 5pi/4)
Step-by-step explanation:
The equation of rectangular coordtion given polar coordinates are
[tex]x = r \cos( \alpha ) [/tex]
[tex]y = r \sin( \alpha ) [/tex]
R is 2, and alpha is 5pi/4
So
[tex]x = 2 \cos( \frac{5\pi}{4} ) = - \sqrt{2} [/tex]
[tex]y = 2 \sin( \frac{5\pi}{4} ) = - \sqrt{2} [/tex]
So our rectangular coordinates are
[tex]( - \sqrt{2} , - \sqrt{2} )[/tex]
To convert from rectangular coordinates to polar coordinates
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex] \alpha = \tan {}^{ - 1} ( \frac{y}{x} ) [/tex]
Since the point (3,-2), is in the fourth quadrant, our angle should be within (270 and 360 degrees)
[tex]r = \sqrt{ {3}^{2} + ( - 2) {}^{2} } = \sqrt{13} [/tex]
[tex] \alpha = \tan {}^{ - 1} ( - \frac{2}{3} ) [/tex]
We about about
[tex] \alpha = 326.31[/tex]
So our polar coordinates are
[tex]( \sqrt{13} ,326.31)[/tex]
The second entry is in degrees. If you need to convert to radians, let me know
Adjust the recipe in the chart below. If the answer is a fraction then enter it like this example: ex. 1/2 If it is a mixed fraction like 1 1/2 c then type a space between the whole number and the fraction.
Do not enter decimals, only use whole numbers and/or fractions.
Answer:
Ingredient | 4 servings | 2 servings | 8 servings
-------------------------------------------------------------------
flour (c) | 1 | 1/2 | 2
sugar (c) | 3/4 | 3/8 | 3/2
butter (T) | 1 | 1/2 | 2
salt (t) | 1/4 | 1/8 | 1/2
Step-by-step explanation:
4 servings:
1 c flour
3/4 c sugar
1 T butter
1/4 t salt
2 serving = 4 servings / 2 =
1 c flour/2 = 1/2 c flour
3/4 c sugar/2 = 3/8 c sugar
1 T butter/2 = 1/2 T butter
1/4 t salt/2 = 1/8 t salt
8 servings = 4 servings * 2 =
1 c flour * 2 = 2 c flour
3/4 c sugar * 2 = (3*2)/4 = 3/2 c sugar
1 T butter * 2 = 2 T butter
1/4 t salt * 2 = 2/4 = 1/2 t salt
Table:
Ingredient | 4 servings | 2 servings | 8 servings
-------------------------------------------------------------------
flour (c) | 1 | 1/2 | 2
sugar (c) | 3/4 | 3/8 | 3/2
butter (T) | 1 | 1/2 | 2
salt (t) | 1/4 | 1/8 | 1/2
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The perimeter of the triangle is 52 units where x = 4.5
How to find the perimeterTo find the perimeter we have to find x. To solve for both x and the perimeter we use the knowledge of tangents to a circle
The formula below exists due to relationship between tangents
2x = 9
x = 4.5
Also, QU = 4, and UR = 13
The perimeter is solved by adding all the sides
= (9 + 4) + (9 + 13) + (4 + 13)
= 13 + 22 + 17
= 52 units
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