Answers
The correct answers are: a reflection across the x-axis and a translation 1, unit right, a rotation of 180° about the origin and a translation of 1 unit left.
How to check for congruence?To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.
For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
Therefore, the correct answers are:
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit left.
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Related Questions
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
Answer:
1) y² - 5y = 750
2) 750 -y(y -5) = 0
3) (y + 25)(y -30) = 0
Step-by-step explanation:
Area of rectangle = 750 ft²
length = y ft
width = (y - 5) ft
Area of rectangle = 750
length * width = 750
y (y -5) = 750
Expand the equation,y*y - 5*y = 750
y² - 5y = 750
y(y - 5 )= 7500 = 750 - y(y -5)
750 - y(y-5) = 0
y² - 5y = 750y² - 5y - 750 = 0
Sum = -5
Product = -750
Factors = -30 , 25 {-30 + 25 = -5 & (-30)*25 = -750}
y² - 30y + 25y - 750 = 0 {Rewrite the middle term using the factors}
y(y - 30) +25(y - 30) = 0
(y - 30)(y + 25) = 0
A group of 5 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: 6 of Spades, Jack of Diamonds. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.)
Recall, while using your calculator, that E10 means to move the decimal place 10 places to the right.
Answers
a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.
b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is equals to the 0.1025.
Five friends group are playing poker one night. They have a standard 52-card deck. So, here total possible outcomes
= 52
Now, the designated cards are 6 of Spades, Jack of Diamonds. So,
a) Number of cards are in the deck that are not one of the designated cards = 52 - 2 = 50
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.
b) Number of cards are in the deck = 52
Number of cards that need to be dealt in order for each player to have 7 cards
= 5× 7 = 35
Thus total possible number of ways
= ⁵²C₃₅ = 21945588357420
Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.
c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards
= 2250829575120/21945588357420
= 0.10256410256
Hence, required probability is 0.10256.
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Complete question:
A group of 5 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over. The designated cards are: 6 of Spades, Jack of Diamonds. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
a) In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)
b) In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?
c) What is the probability of a successful hand that will go all the way till everyone gets 7 cards? (Round your answer to 4 decimal places.) Recall, while using your calculator, that E10 means to move the decimal place 10 places to the right.
The equation below describes a parabola. If a is negative, which way does the parabola open?
y= ax?
Answers
If a is negative, the parabola opens down. Option C is the correct option.
What is a parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its concepts are covered here.
A polynomial function of the second degree is a quadratic function. A quadratic function has this general form:
y = ax² + bx + c
A parabola is a name for a quadratic function's graph.
A parabola resembles the letter "U" or an upside-down "U" in general shape.
If the leading coefficient is greater than zero, the parabola opens upward; if the leading coefficient is less than zero, the parabola opens downward. This simple rule can be used to determine whether the graph of a quadratic function opens upward or downward.
Given equation is
y = ax²
The leading coefficient is a and it is a negative number. Thus the parabola opens down.
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Let X and Y be continuous random variables with joint density f
X
,
Y
(
x
,
y
)
=
e
−
y
,
f
o
r
0
<
x
≤
y
<
[infinity]
and 0 otherwise.
Find rho
X
Y
.
Answers
The correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y.
The correlation coefficient of two continuous random variables X and Y is a measure of how similar the two variables are in terms of their behavior. In this case, X and Y have a joint density of e−y, for 0 < x ≤ y < ∞ and 0 otherwise. This implies that the correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y. This means that there is a perfect linear relationship between the two variables, meaning that as one variable increases, the other will also increase by the same amount.
To calculate the correlation coefficient, we need to calculate the covariance and variances of X and Y. The covariance is calculated by integrating the joint density of X and Y over the given range. The variance of X and Y is then calculated by taking the square root of the expected value of the squares of the differences between the expected value of X and Y and their respective observed values. Since the joint density of X and Y is always positive for x ≤ y, the correlation coefficient of X and Y will always be 1.
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The set {0,1,2,3,4,5,6,7,8,9,} has how many subsets?
Answers
Answer:
Step-by-step explanation:
The set {0,1,2,3,4,5,6,7,8,9} has 2^10 = 1024 subsets. To see why, note that each element can be either in or out of a given subset, so there are 2 choices for each of the 10 elements, giving 2x2x2x2x2x2x2x2x2x2 = 1024 possible subsets.
Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.
a(t) = 19ti + etj + e -tk, v(0) = k, r(0) = j + k
Answers
The position vector of a particle that has an acceleration, a(t) = 19t i + eᵗ j + e⁻ᵗ k, is equals to the 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.
We have, The acceleration vector function of a particle is defined as, a(t)
= 19t i + eᵗ j + e⁻ᵗ k and intial velocity and position is, v(0) = k, r(0) = j + k.
We have to calculate the position vector of a particle. Now, as we know, the acceleration of a particle is equals to derivative of velocity of particle with time. In other words, velocity is integration of acceleration with respect to time.
Mathematically, v(t) = ∫a(t)dt , let C be integration constant ( vector).
v(t) = ∫a(t)dt = ∫[ (19t) i + (eᵗ) j + (e⁻ᵗ) k] dt
=> v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + C
At t = 0 , v(0) = k
=> k = 19(0²/2) i + e⁰j - e⁻⁰ k + C
=> k = 0 + j - k + C
=> C = 2k - j
so, v(t) = 19(t²/2) i + eᵗ j - e⁻ᵗ k + 2k - j
= 19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k
Now, Position of a particle is determined by integrating the velocity of particle with respect to time, r(t) = ∫v(t)dt , let D be integration constant ( vector). So, r(t)
= ∫[19(t²/2) i + (eᵗ - 1) j - (e⁻ᵗ - 2) k ] dt
= 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + D
At t = 0, r(0) = j + k
=> j + k = 19 (0³/6) i +e⁰ j - 0j - e⁻⁰ k +2× 0k +D
=> j + k = 0 + j - k + D
=> D = 2k
so, r(t) = 19 (t³/6) i + eᵗ j - t j - e⁻ᵗ k + 2t k + 2k
= 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k
Hence, required position vector is 19 (t³/6)i + (eᵗ - t )j - (e⁻ᵗ - 2t - 2)k.
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eighty-two percent of all women who submit to pregnancy tests are pregnant. a new pregnancy test gives a false positive result with probability 0.02 and a correct positive result with probability 0.95. define the events: p: {a woman is pregnant} and : {the pregnancy test is positive}. a)
Answers
The probability that a woman is actually pregnant given that the test is positive is 0.974 (or 97.4%).
a) To find the probability that a woman is actually pregnant given that the test is positive, we can use Bayes' theorem:
P(p|+) = P(+|p) P(p) / P (+)
where P(p) is the prior probability of a woman being pregnant (which is 0.82), P (+) is the probability of a positive test result, and P(+|p) is the conditional probability of a positive test result given that the woman is pregnant.
We are given that the test has a false positive rate of 0.02, which means that P(+|~p) = 0.02 (where ~p denotes "not pregnant"). We are also given that the test has a correct positive rate of 0.95, which means that P (+|p) = 0.95. Therefore, we can calculate:
P (+) = P(+|p) P(p) + P(+|~p) P(~p)
= 0.95 * 0.82 + 0.02 * (1 - 0.82)
= 0.802
Substituting into Bayes' theorem, we get:
P(p|+) = 0.95 * 0.82 / 0.802
= 0.974
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PLEASE please please help, it will mean the world to me, and if you are right I will give brainliest. And try to show work! Mr Smith is putting a brick border around his irregular shaped garden. Before installing the border, he must cut the bricks to fit the angles of the garden. Use the given measures to answer this question. What are the angle measures of each vertex of the yard? Show your work.
Answers
The value of x is 24. The angle measures of each vertex of the yard are m∠A = 160°, m∠B = 142°, m∠C = 120°, m∠D = 156°, m∠E = 31°, m∠F = 111°.
What is a polygon?
A polygon is a closed polygonal chain made up of a finite number of straight line segments and is a type of plane figure in geometry. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.
The formula of the sum of interior angles of a polygon is (n - 2)×180°, where n is number of sides.
The number of sides of the given irregularly shaped garden is 6.
The sum of the interior angles of the garden is (6 - 2)×180° = 720°
Also given:
m∠A = (7x - 8)°, m∠B = (4x + 46)°, m∠C = (5x)° , m∠D = (6x + 12)°, m∠E = (x + 7)°, m∠F = (5x - 9)°.
The sum of the interior angles of the garden is
(7x - 8)° + (4x + 46)° + (5x)° + (6x + 12)° + (x + 7)° + (5x - 9)°
Therefore,
(7x - 8)° + (4x + 46)° + (5x)° + (6x + 12)° + (x + 7)° + (5x - 9)° = 720°
Combine like terms:
(7x +4x + 5x + 6x + x + 5x) + (-8 +46 + 12 + 7 - 9) = 720
28x + 48 = 720
Subtract 48 from both sides:
28x = 672
Divide both sides by 28:
x = 24
Putting x = 28 in the given angles:
m∠A = (7×24 - 8)° = 160°
m∠B = (4×24 + 46)°= 142°
m∠C = (5×24)° = 120°
m∠D = (6×24 + 12)°= 156°
m∠E = (24 + 7)° = 31°
m∠F = (5×24 - 9)° = 111°
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Find the value of X, round to the nearest tenth
Answers
Answer:
[tex]x=8.3[/tex]
The first option listed
Step-by-step explanation:
We can use the cosine function to evaluate [tex]x[/tex].
The definition of the cosine function is
[tex]\cos \theta=\frac{A}{H}[/tex]
Note
[tex]\theta[/tex] is the angle
[tex]A[/tex] is the side adjacent to the angle
[tex]H[/tex] is the hypotenuse
In this example we are given the hypotenuse and the angle.
Knowing these 2 values we can evaluate the adjacent side ([tex]x[/tex]).
Lets solve for [tex]A[/tex].
[tex]\cos \theta=\frac{A}{H}[/tex]
Multiplying both sides by [tex]H[/tex] lets us isolate [tex]A[/tex] ([tex]x[/tex]).
[tex]A=H*\cos \theta[/tex]
Numerical Evaluation
We are given
[tex]\theta = 41\textdegree\\H=11[/tex]
Inserting those values into our equation for [tex]A[/tex] ([tex]x[/tex]) yields
[tex]A=11*\cos 41[/tex]
[tex]A=8.30180534[/tex]
Rounding to the nearest tenth gives us
[tex]A=8.3[/tex]
[tex]x=8.3[/tex]
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Solve this equation.
Answers
Answer:
[tex]\dfrac{4a^6b^5}{c^3}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{8a^4b^{-3}c^{12}}{2a^{-2}b^{-8}c^{15}}[/tex]
Separate like terms:
[tex]\dfrac{8}{2} \cdot \dfrac{a^4}{a^{-2}}\cdot \dfrac{b^{-3}}{b^{-8}} \cdot \dfrac{c^{12}}{c^{15}}[/tex]
Divide the numbers:
[tex]4\cdot \dfrac{a^4}{a^{-2}}\cdot \dfrac{b^{-3}}{b^{-8}} \cdot \dfrac{c^{12}}{c^{15}}[/tex]
[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]4 \cdot a^{4-(-2)} \cdot b^{-3-(-8)} \cdot c^{12-15}[/tex]
Simplify the exponents:
[tex]4 \cdot a^6 \cdot b^5 \cdot c^{-3}[/tex]
[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]4 \cdot a^6 \cdot b^5 \cdot \dfrac{1}{c^3}[/tex]
Simplify:
[tex]\dfrac{4a^6b^5}{c^3}[/tex]
Write the equation of the function whose graph is shown y= ___ (x + ____) sqrt + ____
Answers
The equation of the function of the given graph is y = (x - 5)² + 3 shown.
What is Parabola?The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) is the x and y-coordinates of the vertex.
According to the given graph, we have data as follows:
Points on the x and y-axis = (8, 12).
Vertex (h, k)= (5, 3).
Substitute the values of h = 5 and k = 3 in the above equation
y - 3 = a(x - 5)²
y = a(x - 5)² + 3
If the parabola contains the point (0, 0)
Substitute the point (8, 12) in the above equation
12 = a((8-5)² + 3
12 = a(3)² + 3
12 - 3 = 9a
9a = 9
a = 1
4a = -3
a = -3/4
So, the equation becomes y = (x - 5)² + 3
Hence, the required equation is y = (x - 5)² + 3 which represents the given parabola.
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Monaco has an area of 499 acres and a population of 39,000 people. Vatican City has a population of 1,000
people and an area of 0.44 square kilometers. Which city has the highest population density?
a. What is the population density of Monaco? Round to a whole number.
(1)
b. What is the population density of Vatican City? Round to a whole number. (Hint: To compare the population
density of Vatican City with Monaco, they need to be measured in the same units!)
(1)
c. Which location has the highest population density?
(0.5)
Answers
a. The population density of Monaco is 19,307 people per square kilometer.
b. The population density of Vatican City is 37 people per square kilometer.
c. The Vatican City has the highest population density
What is population density?
Population density is measured by dividing the total area of a region in question by the total number of people that live there.
a. To find the population density of Monaco, we need to divide the population by the area, and then convert acres to square kilometers (since Vatican City's area is given in square kilometers).
499 acres x 0.00404686 square kilometers/acre = 2.02 square kilometers
The population density of Monaco is therefore:
39,000 people / 2.02 square kilometers = 19,307 people per square kilometer.
Rounded to the nearest whole number, the population density of Monaco is 19,307 people per square kilometer.
b. To find the population density of Vatican City, we first need to convert its area to acres:
0.44 square kilometers x 247.105 acres/square kilometer = 108.7 acres
The population density of Vatican City is then:
1,000 people / 108.7 acres = 9.2 people per acre
To compare with Monaco's population density, we need to convert this to people per square kilometer:
9.2 people per acre x 0.00404686 square kilometers/acre = 37.3 people per square kilometer
Rounded to the nearest whole number, the population density of Vatican City is 37 people per square kilometer.
c. Therefore, Vatican City has the highest population density, with a density of 37 people per square kilometer compared to Monaco's density of 19,307 people per square kilometer.
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Over 1000 people try to climb mt Everest every year. Of those who try to climb Everest, 31 precent succeed. The probability that a climber is at least 60 years old is 0.04 The probability that a climber is at least 60 years old and succeeds in climbing Everest is 0.005.
Answers
P(success I at least 60 years old) = 0.125.
What is the probability?The possibility of an event in time is known as a probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?
Given:
Over 1000 people try to climb mt Everest every year.
Of those who try to climb Everest, 31 percent succeed.
The probability that a climber is at least 60 years old is 0.04.
The probability that a climber is at least 60 years old and succeeds in climbing Everest is 0.005.
P(success I at least 60 years old) = 0.005/0.04 = 0.125
Therefore, the probability is 0.125.
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Two circles have a 24-cm common chord, their centers are 14 cm apart, and the radius of one of the circles is 13 cm. Make an accurate drawing, and find the radius for the second circle in your diagram. There are two solutions; find both.
Answers
That hypotenuse is the radius of the second circle which is equal to 15.
The segment joining the centers of the circles bisects the common chord.
So in the circle with radius 13, the common chord, the segment joining the centers of the circles, and the radius to an endpoint of the common chord form a right triangle with hypotenuse 13 and one leg 12; that makes the distance from the center of that circle to the common chord 5.
Since the length of the segment joining the two circles is 14, the distance from the center of the other circle to the common chord is 14-5=9.
Then in that other circle, we have a right triangle with legs 9 and 12, making the hypotenuse 15.
And that hypotenuse is the radius of the second circle which is equal to 15.
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f ( x ) = { 2 x + 4 , x ≤ − 2 4 + 1 2 x , − 2 < x < 2 − x + 5 , 2 ≤ x Which of the following is the graph of the function shown above? A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, minus 3) and passes through (5, 0). The third line with 2 open circles at (2, 6) and (minus 2, 3) W. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, minus 3) and passes through (5, 0). The third line with 2 open circles at (2, 3) and (minus 2, 5) X. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at a closed circle (2, 3) and passes through (5, 0). The third line with 2 open circles at (minus 2, 3) and (2, 5) Y. A line starts at a closed circle (minus 2, 0) and passes through (minus 4, minus 4). The second line starts at an open circle (2, 3) and passes through (5, 0). The third line with an open circle at (minus 2, 3) and a closed circle at (2, 5) Z. A. W B. X C. Y D. Z
Answers
Answer:
The correct graph of the given function is option C. Y.
Step-by-step explanation:
The correct graph is option B (X) because it satisfies all the conditions specified in the function definition.
The first segment of the graph starts at x=-2 and goes to the left, passing through the point (-4,-4) and representing the equation 2x+4. The second segment of the graph starts at x=-2 and goes to the right, passing through the point (2,3) and representing the equation 4+1/2x. The third segment of the graph starts at x=2 and goes to the right, passing through the point (5,0) and representing the equation -x+5.
Option A (W) has a line that passes through the point (2,6), which is not on the graph of the function, and option C (Y) has a line that passes through the point (2,5), which is also not on the graph of the function. Option D (Z) has an open circle at (-2,3), which should be a closed circle according to the function definition, and a closed circle at (2,5), which should be an open circle according to the function definition.
In the figure below, triangle HIJ and triangle KML are similar. The figures are not drawn to scale. What is the length of overline ML , in units?
Answers
The measure of side ML of the triangle MLK is ML = 6 units
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔMLK
Let the second triangle be represented as ΔHJI
The measure of side HJ = 20 units
The measure of side HI = 36 units
The measure of side JI = 24 units
And ,
The measure of side LK = 5 units
The measure of side MK = 9 units
The measure of side ML = A units
Now , the triangles are similar
So , the corresponding sides of similar triangles are in the same ratio
The measure of side MK / measure of side HI = The measure of side ML / measure of side JI
Substituting the values in the equation , we get
A / 24 = 9 / 36
Multiply by 24 on both sides of the equation , we get
A = ( 24 x 9 ) / 36
A = 24 / 4
A = 6 units
Hence , the measure of side ML of triangle is 6 units
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determine whether the number described is a statistic or a parameter. in a survery of hospital employees, feel that they are overworked.
Answers
In a survery of hospital employees here it is parameter or statistic data is given in Question
Parameters are numeric values that characterize the population as a whole. A statistic is a number that describes the characteristics of a sample.
For example, median income in the United States is a demographic parameter. Conversely, the median income for the US sample is a sample statistic. Both values represent median income, but one is a parameter to the statistic. Easy to remember parameters and stats! Both are summary values that describe the group and have a convenient mnemonic device to remind you which group is being described. Notice their initials.
Parameter = Population
Statistics = Sample
A population is the entire group of people, things, animals, trades, etc. that are being studied. A sample is part of a population.
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square root of 64 minus 10 plus 13
Answers
Answer:
11
Step-by-step explanation:
[tex]\sqrt{64}[/tex] -10 + 13
8 - 10 + 13
-2 + 13
11
8 - 10 = -2
-2 + 13= 11
Answer eleven
determine the volume of the solid with a circular base of radius a whose cross sections are squares that are perpendicular to the base.
Answers
The volume of the solid is [tex]4a^2h[/tex].
Each square cross-section has a side length equal to the diameter of the circle, which is 2a.
Therefore, the area of each cross-section is
[tex](2a)^2 = 4a^2[/tex]
The volume of the solid can be found by integrating the area of the cross sections over the height of the solid.
Since the cross-sections are perpendicular to the base, the height of each cross-section is equal to the thickness of the solid, which we can denote as dx.
Thus, the volume of the solid is given by the integral of the cross-sectional area with respect to x, from x = 0 to x = h, the height of the solid:
V = ∫ (0 to h) [tex]4a^2 dx[/tex]
V = [tex]4a^2[/tex] ∫(0 to h) dx
V = [tex]4a^2[/tex] (0 to h)
V = [tex]4a^2[/tex] (h - 0)
V = [tex]4a^2h[/tex]
Therefore, the volume of the solid is [tex]4a^2h[/tex]
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the geometric distribution arises as the distribution of the number of times we flip a coin until it comes up heads. consider now the distribution of the number of flips until the -th head appears, where each coin flip comes up heads independently with probability . this is known as the negative binomial distribution, and we also write . find . hint: here counts the number of flips including the flip with the -th head. mark the correct expression for , below.
Answers
The correct expression for P(X = k) will be [tex]P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^k[/tex]
Given,
The geometric distribution arises as the distribution of the number of times we flip a coin until it comes up heads. consider now the distribution of the number of flips until the -th head appears, where each coin flip comes up heads independently with probability.
The negative binomial distribution describes the probability of getting the -th success (in this case, heads) on the th trial, given a probability p of success on each trial.
We can write this as:
[tex]P(X = k) = \binom{k-1}{r-1} p^r (1-p)^{k-r}[/tex]
where k is the number of flips needed to get r successes, including the rth success.
In this case, we want the distribution of the number of flips until the rth head appears,
so we can set p = 1/2,
since the coin is fair.
We also need to adjust the formula to count the number of flips, including the flip with the rth head.
Since we need r heads to appear, the last head must appear on the rth flip, so we can write:
[tex]P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^r \left(\frac{1}{2}\right)^{k-r+1}[/tex]
Simplifying the expression,
we get:
[tex]P(X = k) = \binom{k-1}{r-1} \left(\frac{1}{2}\right)^k[/tex]
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fill in the blank. the ___performs all arithmetic operations (for example, addition and subtraction) and all logic operations (such as sorting and comparing numbers). (please use acronym) multiple choice question.
Answers
The CPU (Central Processing Unit) performs all arithmetic operations (for example, addition and subtraction) and all logic operations (such as sorting and comparing numbers).
The acronym that fills in the blank is CPU, which stands for Central Processing Unit. The CPU is essentially the brain of a computer, responsible for processing all the information that flows through the system.
Arithmetic operations are those that involve mathematical calculations, such as addition, subtraction, multiplication, and division. These are relatively straightforward tasks for the CPU, which can perform them quickly and accurately.
Logic operations, on the other hand, involve comparing and manipulating data based on various conditions.
CPU has the ability to perform logic operations is a crucial aspect of computing, as it allows computers to make decisions and process information based on a set of rules or conditions.
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jaden has a spinner with 8 sections labeled with letters, each section is the same size, as shown below. jaden spins the arrow 75 times, which result is most likely to be the number if times the arrow will land on a section labeled s or t?
Answers
The probability that the arrow will land on a section labeled S or T is 7/8.
What is Probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.
Therefore, it is likely that the arrow will land on one of these sections around 56 to 57 times out of 75 spins. It is impossible to predict exactly how many times the arrow will land on S or T, as this is a probability-based outcome. Generally speaking, with such a large number of spins, the result should be close to the probability of 7/8.
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En una progresión aritmética sabemos que a2 =1 y a5 =7. Halla el término general y los términos a8 , a15 y a20
Answers
The general rule of the arithmetic sequence is given as follows:
[tex]a_n = -1 + 2(n - 1)[/tex]
The terms are given as follows:
[tex]a_8 = 13[/tex][tex]a_{15} = 27[/tex][tex]a_{20} = 37[/tex]What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
The difference between the 3 terms is of 6, hence the common difference is given as follows:
3d = 6
d = 2.
As the 2nd term is of 1, the first term is of:
[tex]a_1 = 1 - 2 = -1[/tex]
Hence the rule is given as follows:
[tex]a_n = -1 + 2(n - 1)[/tex]
The terms are given as follows:
[tex]a_8 = -1 + 2 \times 7 = 13[/tex][tex]a_{15} = -1 + 2 \times 14 = 27[/tex][tex]a_{20} = -1 + 2 \times 19 = 37[/tex]More can be learned about arithmetic sequences at https://brainly.com/question/30544915
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b) How much
2. The original price of a MacBook is $1400. Students get a 10% discount. How much will
after the discount?
Show work
nswer:
Answers
Answer:
$1400 divided by 10 = $140
$1400 - $140 = $1260
A corporation has four factories, each of which manufactures sport utility vehicles and pickup trucks. The number of units of vehicle produced at factory in one day is represented by in the matrixA = | 100 90 70 30 || 40 20 60 60 |Find the production levels if production is increased by 10%
Answers
If the production is increased by 10%, the new production levels for sport utility vehicles and pickup trucks are:
Factory 1: 110 sport utility vehicles
Factory 2: 99 sport utility vehicles
Factory 3: 77 sport utility vehicles, 66 pickup trucks
Factory 4: 33 sport utility vehicles, 66 pickup trucks
To find the production levels if production is increased by 10%, we need to multiply each entry of the matrix by 1.1:
A' = 1.1A = | 110 99 77 33 || 44 22 66 66 |
The matrix A' represents the new production levels. The entry in the first row and first column of A' (110) represents the number of sport utility vehicles produced at the first factory after the 10% increase in production. Similarly, the entry in the second row and third column of A' (66) represents the number of pickup trucks produced at the third factory after the 10% increase in production.
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27
Select the correct answer.
Number of Players on the Team Time Taken to Complete Game (in minutes)
Teams with varying numbers of players are playing a group card game. The time taken by each team to complete one game is given in the table.
What is the relationship between the two variables?
2
3
4
5
O A. positive linear association
O B. exponential relationship
O C.
negative linear association
32
26
20
14
Answers
The relationship between the two variables negative linear association.
What is Linear Association?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Given:
The data table is organized as follows:
1 2 3 4 5
32 26 20 14 8
We see that more the number of members in the team increase, the more the times decrease.
The correlation is a negative linear association, we conclude.
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There are 9 girls and 6 boys taking golf lessons. Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
Answers
Answer:
2:5
Step-by-step explanation:
We know
There are 9 girls and 6 boys taking golf lessons.
So, there are a total of 15 taking a golf lesson.
Write the ratio that compares the number of girls taking golf lessons to the total number of students taking golf lessons.
The ratio is
6:15 = 2:5
So, the ratio is 2:5
A recent study showed that tea drinkers have lower stress levels than coffee drinkers. Tea drinkers are known to have a higher proportion of yoga practitioners than coffee drinkers, and they exercise on average two hours per week more than their coffee-drinking counterparts. What is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers?
Answers
The additional factors that might have an effect on the stress levels of tea drinkers are called confounding variables. Confounding variables are variables that are not the main focus of the study but may have an impact on the results.
The term used to describe these additional factors that might have an effect on the stress levels of tea drinkers is "confounding variables." Confounding variables are extraneous factors that can affect the relationship between two variables of interest and can lead to incorrect conclusions about the relationship. In this case, the higher proportion of yoga practitioners and the increased exercise among tea drinkers could be considered confounding variables because they may be influencing the observed relationship between tea drinking and lower stress levels, rather than tea consumption alone.
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If sin(θ)>0 and sec(θ)<0, in which quadrant does θ lie?
Answers
Answer:
Quadrant II
Step-by-step explanation:
sin (∅) > 0 means sin (∅)is positive
sec (∅) < 0 means sec (∅) is negative
thus,
∅ lies in quadrant II
Jaxson works in a department store selling clothing. He makes a guaranteed salary of $250 per week, but is paid a commission on top of his base salary equal to 15% of his total sales for the week. How much would Jaxson make in a week in which he made $1800 in sales? How much would Jaxson make in a week if he made
�
x dollars in sales?
Answers: Base salary 520:
When selling for X:0.15
Total sales:250+0.15 or 0.15+250
Answers
Answer:
Step-by-step explanation:
250 per week base
15%of 1800 he made is = 270
270+250 =520
He made 520$ in the week he made 1800$ in sales
Jaxson's salary is a combination of a fixed $250 plus 15% commission on his weekly sales. For $1800 in sales, he will earn $520. If the sales amount is x dollars, then he will earn $250 + 0.15*x dollars in a week.
Explanation:Jaxson's income consists of a guaranteed base salary of $250 per week and a commission of 15% on his total weekly sales. If Jaxson made $1800 in sales in a week, his total income for the week would be his base salary plus his commission i.e., $250 + 0.15*$1800 = $520.
Similarly, if Jaxson made x dollars in sales in a week, his total income for that week would be his base salary plus his commission on the sales i.e., $250 + 0.15*x dollars.
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