The leg-leg (LL) theorem of congruency states that if the legs of a right triangle are equal to the legs of a second right triangle, then the two triangles are congruent.
We know that two triangles are congruent if and only if they have three pairs of equal sides.
In the case of the LL congruence theorem,
the two triangles have two pairs of equal sides (the legs) and one pair of equal angles (the right angles).
Therefore by the Side-Angle-Side (SAS) congruence criterion, the 2 triangles are congruent.
Alternatively
If the legs are of equal length then
Their squares would be equal to
Hence, the sum of these squares too would be equal.
Now taking a root over these would give us the hypotenuse for these triangles, which in turn should be equal.
Hence, by SSS congruence criteria
the triangles would be congruent.
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what is the square root of 10
Answer:
3 or 3.16227766017
Step-by-step explanation:
One card is selected at random from a deck of cards. What is the probability that the card selected is a spade or a queen?
the probability that the card selected is a spade or a queen is given by P= 0.25
In a deck, there are:
total card = 52
spade = 13
Required
Determine the probability that a selected card is a spade
This is represented as: P(Spade) and it is calculated using:
P= card / spade
Substitute 13 for Spade and 52 for Cards
P = 13/52
= 0.25
Hence, the required probability is 0.25
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Prove that for any natural number n: The number 3^n+2 - 2^n+2 + 3^n - 2^n is divisible by 10.
Answer: (___)•10
By algebra properties, the power expression 3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ is divisible by 10 as it is equivalent to (3ⁿ - 2ⁿ⁻¹) · 10.
How to determine if a given expression is divisible by a given number
According to number theory, a natural number is divisible by another natural number if the result is a natural number. In this case we must determine if a power expression is divisible by 10 according to algebra properties.
First, write the whole expression:
3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ
Second, use algebra properties until the multiple is found:
(3ⁿ⁺² + 3ⁿ) + (- 2ⁿ⁺² - 2ⁿ)
3ⁿ · (3² + 1) + 2ⁿ · (- 2² - 1)
3ⁿ · 10 - 2ⁿ · 5
3ⁿ · 10 - 2ⁿ⁺¹⁻¹ · 5
3ⁿ · 10 - 2ⁿ⁻¹ · 10
(3ⁿ - 2ⁿ⁻¹) · 10
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This is a missing assignment please help.
Answer:
The answer is A:22
We can start by finding out 5^2 which is just 5 times 5 because it is 5 times itself 2 times (as the little two tells us how many times to multiply 5 by itself). The answer is 25. 25-3=22
5×5-3
=25-3
=22 is the answer
Rewrite as equivalent rational expressions with denominator
5, Brittney is conducting an experiment in class to determine the probability of getting four heads when flip-
four coins. What is the sample space of her experiment?
Answer:
16 possible outcomes
Step-by-step explanation:
The sample space of Brittney's experiment is the set of all possible outcomes of flipping four coins. Since each coin can either land on heads or tails, there are two possible outcomes for each coin. Therefore, there are a total of 2^4 = 16 possible outcomes for the experiment. These outcomes can be represented as a list, with each outcome represented by a string of four "H"s and "T"s, where "H" represents a heads and "T" represents a tails. For example, one possible outcome of the experiment could be "HHHT" (two heads, one tails, one heads), and another could be "TTTT" (four tails). The complete sample space of Brittney's experiment would include all 16 possible outcomes.
1. A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems.
a.
What is the probability one of these cars selected at random had neither a CD player nor
an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
C.
What is the probability a car with an alarm system had a CD player?
D.
Are having a CD player and an alarm system disjoint events? Explain.
henry flips 10 coins then lays them on a desk. he then chooses one of the coins at random, and if it is tails, he flips it to heads.
As per the concept of probability, the probability of getting head is 99.5%.
The term probability in statistics is known as the possible way of getting the particular event.
Here we have given that
And we need to find the probability of getting head.
Here we know that the number of coins is 10.
So, the sample space for the 10 coins is calculated as,
Here we already know that for each of the 10 coin tosses, we have either a head (H) or a tail (T).
so, the total number of probability of 10 coins is 210 strings in the sample space.
Here we know that the only option of all tails doesn't have head in it.
So, the number tosses that have head in it is calculated as,
=> 210 - 1
=> 209
Therefore, the probability is calculated as,
=> P = 209/210
=> P = 0.995
Therefore, the probability in percentage is 99.5%
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what is 24divided by 2
Answer:12
Step-by-step explanation:
24/2 = 12 bc 12*2=24
07, The present age of Queens University College is three times that of GAGE University College. After 5 years, the difference of their ages will be 30 years. Find the present ages of Queens and GAGE University College?
Answer: Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.
Step-by-step explanation: Let Q be the present age of Queens University College and G be the present age of GAGE University College.
Since the present age of Queens University College is three times that of GAGE University College, we can write the equation Q = 3G.
After 5 years, the difference of their ages will be 30 years, so we can write the equation Q + 5 = G + 30.
Substituting the first equation into the second equation, we get 3G + 5 = G + 30.
Solving for G, we find that G = 15.
Substituting this value into the equation Q = 3G, we find that Q = 3 * 15 = 45.
Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.
Professor Bowdidge taught four business statistics classes during the fall semester with the following grade averages for each class: 74%, 82%, 86%, and 91%. Calculate the mean (round to the nearest hundredth). A. 83.00% B. 83.12% C. 85.00% D. 83.25%
By using the mean formula, the mean grade across all four classes was 83.25%.
What is mean?The mean is a measure of central tendency that represents the average value of a set of data
What is formula to calculate mean?The formula for calculating the mean:
Mean = (x1 + x2 + x3 + ... + xn) / n
Where:
x1, x2, x3, ..., xn are the individual values in the set
n is the total number of values in the set
Mean = (74 + 82 + 86 + 91) / 4
Mean = 333 / 4
Mean = 83.25
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Someone please help me! Find the cotangent! Thank you!
The value for cotangent of ∠V is 55.6°.
What is pythagora's theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.Cotangent = adjacent / opposite
Pythagoras theorem,
WV² = XW² + VW²
9² = x² + (√57)²
x² = 81 - 57
= 24
x = √24
= 4.89
cot (v) = √24 / √57
v = cot⁻¹ (0.6488)
v = 55.6°
Hence, the value for cotangent of ∠V is 55.6°.
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A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field
F(x, y, z) = z2i + 3xyj + 5y2k.
Use Stokes' Theorem to find the work done.
Refer to the images uploaded. Please let me know if this answer works out for you. I also would appreciate a rate :)
What is the inverse of this function f(x)=-1/2sqrtx+3, x>_-3
The inverse of the function f(x) = -1/2√x + 3, x ≥ -3 is y = (6 - 2x)²
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=-1/2sqrtx+3, x>_-3
Express properly
So, we have
f(x) = -1/2√x + 3, x ≥ -3
Write out the function
f(x) = -1/2√x + 3
Express as an equation
y = -1/2√x + 3
Swap x and y
This gives
x = -1/2√y + 3
Subtract 3 from both sides
-1/2√y = x - 3
So, we have
√y = 6 - 2x
Take the square of both sides
y = (6 - 2x)²
Hence, the inverse is y = (6 - 2x)²
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L'expression -6x + 8 est la forme réduite de :
-3x + 3x + 2 *4 ou 2x - 8x *5 + 3 ou 2x - (5x - 6) + (-3x + 2) ou - (3x + 5) + (-2x + 3) - x
Answer:
2x - (5x - 6) + (-3x + 2)
Step-by-step explanation:
L'expression -6x + 8 est la forme réduite de:
-3x + 3x + 2 *4
= 0x + 8
= 8
pas vrai
__________________________
2x - 8x *5 + 3
= 2x - 40x + 3
= -38x + 3
pas vrai
__________________________
2x - (5x - 6) + (-3x + 2)
=2x - 5x + 6 - 3x + 2
= -6x + 8
Corriger
__________________________
- (3x + 5) + (-2x + 3) - x
= - 3x - 5 - 2x + 3 - x
= - 6x + 2
pas vrai
(veuillez pardonner mon français.)
Read the following prompt and type your response in the space provided.
Give an example of a problem involving multiplication of fractions that can be made easier using the associative property. Explain how it makes the problem easier.
One example of a problem involving multiplication of fractions that can be made easier using the associative property is as follows:
Given the expression (2/3) * (4/5) * (6/7), we can use the associative property to rearrange the terms and simplify the expression. Specifically, the associative property states that the order in which we perform operations does not change the result. In this case, we can rearrange the terms as follows:
(2/3) * (4/5) * (6/7) = (4/5) * (2/3) * (6/7)
Then, we can simplify the expression using the commutative property of multiplication (which states that the order of the terms does not affect the result of the multiplication):
(4/5) * (2/3) * (6/7) = (2/3) * (4/5) * (6/7)
Finally, we can simplify the expression by multiplying the fractions:(2/3) * (4/5) * (6/7) = (12/21).
Using the associative property allows us to rearrange the terms and simplify the expression, making the problem easier to solve.
apply dijkstra's algorithm to find the shortest path from vertex a to vertex g in h. for full credit you must show your work, follow dijkstra's algorithm approach explicitly, and indicate both the shortest path and cumulative weight at the end
On solving the provided question, Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.
What is Dijkstra's algorithm?In a graph that may, for instance, represent a network of roads, Dijkstra's Method is an algorithm for determining the shortest routes between nodes. Computer scientist Edsger W. Dijkstra created it in 1956, and it was published three years later. Algorithms come in a wide variety.
Here is how the algorithm is described:
Mark the remaining distances with infinite and your chosen beginning node with a current distance of 0.Make current node C the non-visited node with the shortest current distance. You should double the distance between your current node C and each of its neighbors, N, by the weight of the edge that connects C and N. Make it the new current distance of N if it is less than the current distance of N. C is the current node; mark it as visited.
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I had to re-put the question for you shining dream
The equation that correctly represents the given problem is;
¹/₂p - 2 = 18
How to solve algebra word problems?We are told that p is the time it takes Tomás to bike to the park.
Now, we are given that;
Time taken by Tomás to bike to the community center = 2 minutes less than half the time it takes him to bike to the city park.
Time taken by Tomás to bike to the community center = 18 minutes
Thus, correct equation can be expressed as;
¹/₂p - 2 = 18
And if we need to solve p, we can just make p the subject of the equation and solve accordingly.
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The complete question is;
Which equation represents this problem?
The time it takes Tomás to bike to the community center is 2 minutes less than half the time it takes him to bike to the city park. It takes Tomás 18 minutes to bike to the community center.
Let p = the time it takes Tomás to bike to the park.
Find the solution of y = log(x + 3) and y = 1.
Answer:
x=7
Step-by-step explanation:
y = log(x + 3) and y = 1.
Substitute y =1 into the equation
1 = log(x + 3)
Raise each side to base 10 since log (x+3) has a base 10 implied
10^1 = 10^ log(x+3)
10 = x+3
Subtract 3 from each side
10-3 = x+3-3
7 =x
multiply by 6, 7, 8, and 9 fill in the puzzle so that the product in each column and row is the same
Multiply by 6, 7, 8, and 9 fill in the puzzle so that the product in each column and row is the same is 3024.
What is Multiply?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
[tex]\begin{aligned}& 6 \times 8=48 \\& 6 \times 9=54 \quad \text { find the common } \\& \text { multiple } \\& 9 \times 7=63 \quad 6 \times 7 \times 8 \times 9=3024 \\&\end{aligned}[/tex]
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What is 71/5 as a decimal
Answer:
Step-by-step explanation:
71/5 70/5 = 14 with 1/5 = .2 this together = 14.2
It is known that the probability p of tossing heads on an unbalanced coin is either 1/4 or 3/4. The coin is tossed twice and a value for Y , the number of heads, is observed. For each possible value of Y , which of the two values for p (1/4 or 3/4) maximizes the probability that Y = y? Depending on the value of y actually observed, what is the MLE of p?
On solving the provided question we can say that NILE is not unique for this case
What is Probability?Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.
Note: the probability is equal to the mass function for Y :2
since, ML criteria, we choose p which maximizes the probability.
If Y 0, L (p) is maximized at p 0.25.
If Y 2, L (p) is maximized at p 0.75.
[tex]But if Y 1, L (p) has the same value at both as shown above; that is,[/tex]
L (0.25) L (0.75) for y — 1.
NILE is not unique for this case
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Use the marginal tax rate chart to answer the question.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Determine the effective tax rate for a taxable income of $192,700. Round the final answer to the nearest hundredth.
32.00%
21.77%
24.00%
18.57%
PLEASE HELP
Answer: B. 21.77%
Step-by-step explanation: See picture. I'm currently taking the test right now
Answer:
(b) 21.77%
Step-by-step explanation:
Using the given tax rate table, you want to know the effective tax rate on a taxable income of $192,700.
TaxThe tax will be the sum of the taxes due in each of the brackets. This sum can be simplified to make the tax computation a little less work.
tax = 0.10(10275) +0.12(41175 -10275) +0.22(89075 -41175) +0.24(17050 -89075) +0.32(192700 -170050)
= 10275(0.10 -0.12) +41175(0.12 -0.22) +89075(0.22 -0.24) +170050(0.24 -0.32) +192700(0.32)
= 192700(0.32) -(10275(0.02) +41175(0.10) +89075(0.02) +170050(0.08))
= 192,700(0.32) -19708.50
tax = 41955.50
Effective rateThe tax as a percentage of the taxable income is ...
tax/income × 100% = 41955.50/192700 × 100% ≈ 21.77%
The effective tax rate is about 21.77%.
__
Additional comment
We can use this same idea to simplify the tax table all around. The various tax computations are shown in the second attachment. Interestingly, the tax due is the maximum of the computations for the different brackets. The graph shows the effective tax rate (%) as a function of income. The effective rate for $192,700 is marked.
Because the tax tables are written with discontinuities, there can be some confusion about the amount that fits in each bracket. For example, the tax on 10276 is not 10% of 10275 plus 12% of zero. Rather it is 10% of 10275 plus 12% of (10276 -10275), for a total of $1027.62.
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Please answer these questions!
Answer:
Step-by-step explanation:
1)
She takes medicine at the moment 0
24(1/2)^0
24 · 1
24 mg
2)
24 (1/2)^1
24 (1/2)
12 mg
The history of melting point data for a certain product indicates that the long-term average melting point has been 95 degrees. It is desired to test to see if the average is still 95 degrees or whether it has changed. a) Set up the statistical test at a 0.01 significance level and draw the conclusion using the sample data that follows: the average of a sample of 16 randomly chosen melting points is 94.32 degrees. Assume that the distribution of melting points is normal with σ = 1.20 . b) What is the critical region for this test, both in terms of the sample average and the z-score?
As per the desire to test to see if the average is still 95 degrees or whether it has changed. The results will be as follows:
a) The null hypothesis and the alternative hypothesis must be identified before we can set up the statistical test at a 0.01 significance level. The average melting point, which is still 95 degrees, has not altered, according to the null hypothesis. The other theory is that the average melting point, which was 95 degrees, has changed.
Next, we must establish the test's critical value. The critical value will be the amount that corresponds to a p-value of 0.01 because we are choosing a significance level of 0.01. We may use the usual normal distribution to determine the critical value because we are presuming that the melting point distribution is normally distributed with a standard deviation of 1.20.
Using the sample data, we discover that a sample of 16 melting points has an average temperature of 94.32 degrees. A one-sample z-test can be used to examine whether this sample average differs noticeably from the 95 degree long-term average.
where x is the sample average (94.32), is the long-term average (95), σ is the standard deviation of the melting points (1.20), and n is the sample size (16).
Plugging these values into the formula, we get:
z = (94.32 - 95) / (1.20 / √16) = -0.83
We are unable to rule out the null hypothesis because the z-score is smaller than the critical value. As a result, we draw the conclusion that 95 degrees still serve as the average melting point.
b) The range of values that would be deemed statistically significant at the 0.01 significance level constitutes the critical region for this test. The range of values that would be regarded as significantly different from the long-term average of 95 degrees is the critical zone in terms of the sample average. The range of values that would be associated with a p-value of less than 0.01 is known as the critical zone in terms of the z-score.
The required z-score value for a one-sided test with a significance level of 0.01 is 2.326. Therefore, any number more than 2.326 is the critical zone in terms of the z-score. This relates to a range of values that are significantly higher than 95 degrees based on the sample average.
The essential z-score values for a two-sided test with a 0.01 significance level are -2.326 and 2.326. Therefore, any value between -2.326 and 2.326 constitutes the key zone in terms of the z-score. This relates to a range of values that are significantly higher or lower than 95 degrees, based on the sample average.
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The distance between the points (10, -2) and (4, 6) is 10.
True
False
=
Answer:
True
Step-by-step explanation:
Use the distance formula: x^2 + y^2 = d^2; where d=distance
x = x2 - x1
y = y2 - y1
(10, -2), (4, 6) ==> (x1=10, y1=-2), (x2=4, y2=6)
x = 4 - 10 ==> plug in 4 for x2 and 10 for x1
x = -6
y = 6 - (-2) ==> plug in 6 for y2 and -2 for y1
y = 6 + 2
y = 8
(-6)^2 + (8)^2 = d^2 ==> plug in x and y back into the distance formula
36 + 64 = d^2
100 = d^2 ==> simplify
d = [tex]\sqrt{100}[/tex]
distance = 10 ==> True
Jack decides to estimate the volume of a coffee cup by modeling it as a right cylinder. Jack measures its radius as 2.2 cm and its volume as 117 cubic centimeters. Find the height of the cup in centimeters. Round your answer to the nearest tenth if necessary.
The Support Vector Classifier includes a tuning parameter C that controls the bias-variance trade-off. Which of the following statements is correct?
a) As C increases, the margin becomes smaller, which increases bias but potentially decreases variance
b) As C increases, the margin becomes smaller, which decreases bias but potentially increases variance
c) As C increases, the margin becomes larger, which increases bias but potentially decreases variance
d) As C increases, the margin becomes larger, which decreases bias but potentially increases variance
The correct answer is D) As C increases, the margin becomes larger, which decreases bias but potentially increases variance.
In the Support Vector Classifier (SVC), the parameter C controls the trade-off between the model's complexity and the amount of training error that it is allowed to have. A larger value of C means that the model will be more complex, and therefore will have a larger margin.
This will decrease the bias of the model but may increase the variance.
On the other hand, a smaller value of C means that the model will be less complex and will have a smaller margin, which will increase the bias of the model but potentially decrease the variance.
So, in summary, as C increases, the margin becomes larger, which decreases bias but potentially increases variance.
Hence, the correct answer would be an option (D).
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If Ellie has 3 more quarters than nickels and they have a combined value of 195 cents, how many of each coin does she have?
Using system of linear equation, the number of quarter is 7 and nickel is 4
System of Linear EquationSystem of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
To solve this problem, we need to write a system of linear equation.
let;
x = quartersy = nickels1 nickel = 5 cent
1 quarter = 25 cent
25x + 5y = 195 ... eq(i)
x = 3 + y ...eq(ii)
Put eq(ii) into eq(i)
25(3 + y) + 5y = 195
75 + 25y + 5y = 195
75 + 30y = 195
30y = 195 - 75
30y = 120
y = 4
put y = 4 in equation (ii)
x = 3 + 4
x = 7
The number of quarter is 7 and nickel is 4
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a. Bared an the information in the figure, which of the two cities have nearest to each other?
Select choice
b. Based on the information in the figure, which of the two cities are farthest apart from each other?
Select Choice
c. If you were going to use the information from 5 Sate's sketch to plan a road trip between these cities, what is an assumption that you would have to make?
Select Choice
The City A and Abilene are nearest to each other
The Austin and Abilene are farthest apart from each other
Here the two angles of the triangle = 59 degrees and 64 degrees
The sum of the angles in a triangle is 180 degrees
Then the third angle will be
59 + 64 + x = 180
123 + x = 180
x = 180 - 123
x = 57 degrees
The third city name is not visible so consider it as city A
Part a
Here the smallest angle is 57 degrees
Opposite side of the angle will be the smallest distance
That is the distance between city A and Abilene
Part b
Here the largest angle is 64 degrees
The opposite side of the angle will be largest distance
That is the distance between Austin and Abilene
Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other
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