Which postulate proves these two
triangles are congruent?

A. HL
B. SSA
C. ASA
D. SAS

e6z = xyz,  implicit differentiation of the following equation-

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. 

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

According to our question-

Given e6z = xyz

To find ∂z/∂x → consider z as a function of x and take y to be a constant

So differentiating with respect to x, we get

e6z × 6 × ∂z/∂x = z × y + xy × 1 × ∂z/∂x

[using the chain rule on the LHS and the product rule on the RHS]

Factor out the ∂z/∂x:

∂z/∂x [6e6z - xy] = yz

∂z/∂x = yz / [6e6z - xy]

Do the same thing to find ∂z/∂y except consider z to be a function of y and take x to be a constant

Differentiating with respect to y:

e6z × 6 × ∂z/∂y = z × x + xy × 1 × ∂z/∂y

∂z/∂y [6e6z - xy] = xz

∂z/∂y = xz / [6e6z - xy]

Therefore, ∂z/∂x = yz / [6e6z - xy] and ∂z/∂y = xz / [6e6z - xy]

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Answer:

64

Step-by-step explanation:

53+11

50+10=60

3+1=4

64

The value of s for the given value is 24.05.

Given is an equation v² = u²+2gs, we need to find the value of s if v = 25, u = 12 and g = 10,

So,

25² = 12² + 2(10)s

625 = 144 + 20s

20s = 481

s = 24.05

Hence the value of s for the given value is 24.05.

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The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

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The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

To estimate the increase in the daily cost if one additional chocolate bar is produced per day, we need to calculate the marginal cost at the current production level.

Given that the cost function is represented , we can find the marginal cost by taking the derivative of the cost function with respect to the number of chocolate bars produced (x).

So, let's find the derivative:

d(co-eas.co)/dx = eas.co + co-as. s

Now, let's substitute the current production level, x = 510, into the derivative:

d(co-eas.co)/dx = e(510)as.co + co-a(510)s.s

Since we only need to estimate the increase in cost for one additional chocolate bar, we substitute x = 511 into the derivative:

d(co-eas.co)/dx = e(511)as.co + co-a(511)s.s

The result will give us the increase in the daily cost when one additional chocolate bar is produced per day.

Without specific values for the coefficients (e, a, c, and s) and the initial cost (co), it is not possible to provide a numerical estimation for the increase in the daily cost. The options given in the question cannot be calculated based on the information provided.

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The measure of the angles are 91.375°and 88.625°. Both the angles are obtained by the supplementary angle principal.

Supplementary angles are two angels whose total is 180 degrees. When a straight line is crossed by a line, two angles develop on each of the examined straight line's sides.

Two sets of additional angles make up those two-two angles. That is, if supplementary angles are placed next to each other, the exterior sides of their exterior sides will form a straight line.

The given data in the problem is;

∠1 = 9y-2

∠2 = 7y+16

The sum of the supplementary angle is 180

⇒9y-2 +7y+16 = 180

⇒16y +14 =180

⇒16y= 166  

⇒ y=10.375

The measure of the angle 1 is;

∠1 = 9y-2

∠ 1 = 9 ×10.375 -2

∠ 1 = 91.375°

The measure of the angle 2 is;

∠2 = 7 × 10.75 +16  

∠2 = 88.625°

Hence, the measure of the angles are 91.375°and 88.625°.

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The value of the reflex angle in this figure is 273 degrees

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

In this given figure, there's acute angle and an obtuse angle, therefore a reflex angle must be present.

To find the reflex angle in the figure, we have to trace the green part of the figure which will give us;

180° + 93°

i.e the sum of angle on a straight line with an obtuse angle

Reflex angle = 180 + 93 = 273°

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Answer:

Any real value.

Step-by-step explanation:

Ok, so I am just gonna simplify the question a little bit.

\(\frac{x-8+3}{5}\) = (x - 5)/5 or x/5 - 1..
Wait a minute, the question doesn't make sense.
The question is true for any value of x as | x | > 0 and - | x | will be < 0 no matter what.

Therefore, the inverse Laplace transform of the potential function \(\( H(s) \) is:\( h(t) = 20e^{(-200 + 3090i)t} + 20e^{(-200 - 3090i)t} \)\)

Step 1: Factorize the denominator of \(\( H(s) \):The denominator \( s^2 + 400s + 6290000 \)\) cannot be factored further, so we move to the next step.

Step 2: Express\(\( H(s) \) using partial fractions:\( H(s) = \frac{A}{s - s_1} + \frac{B}{s - s_2} \)\)

To find A and B, we need to solve for the values of s_1 and s_2, which are the roots of the denominator equation \(\( s^2 + 400s + 6290000 = 0 \)\).

Using the quadratic formula, we find that the roots are complex:\(\( s_1 = -200 + 3090i \) and \( s_2 = -200 - 3090i \).\)

Step 3: Substitute the values of s_1 and s_2 into the partial fraction decomposition:

\(\( H(s) = \frac{A}{s - (-200 + 3090i)} + \frac{B}{s - (-200 - 3090i)} \)\)

Step 4: Find the values of A and B:

We multiply both sides of the equation by the denominator to eliminate the fractions and then substitute the values of s_1 and s_2:

\(\( 40(s+200) = A(s - (-200 - 3090i)) + B(s - (-200 + 3090i)) \)\)

Simplifying the equation, we get:

\(\( 40s + 8000 = As + A(-200 + 3090i) + Bs + B(-200 - 3090i) \)\)

Matching the coefficients of like terms, we get the following system of equations:

\(\( A + B = 40 \)\( A(-200 + 3090i) + B(-200 - 3090i) = 8000 \)\)

Solving this system of equations, we find that A = 20 and B = 20.

Step 5: Write the partial fraction decomposition:

\(\( H(s) = \frac{20}{s - (-200 + 3090i)} + \frac{20}{s - (-200 - 3090i)} \)\)

Step 6: Find the inverse Laplace transform using lookup tables:

The inverse Laplace transform of each term can be looked up in the Laplace transform table. The inverse Laplace transform of \(\( \frac{20}{s - (-200 + 3090i)} \) is \( 20e^{(-200 + 3090i)t} \), and the inverse Laplace transform of \( \frac{20}{s - (-200 - 3090i)} \) is \( 20e^{(-200 - 3090i)t} \).\)

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The highest point scored is by Carlos with 19 points. Mario's highest was 15. so, Carlos scored 4 points more than Mario.

In the 7th game, Carlos scored 19 points which is the highest point of his game. In the 1st game, Mario scored 15 points which was the highest point he scored. Therefore, Carlos had the highest scoring game between the two of them. Carlos scored 4 points more than Mario did in his highest-scoring game. You can also construct a box plot for this question which will help you visualise this better. The box plot can be made by drawing a number line and marking the following points: minimum, first quartile, median, third quartile and maximum.

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The full question is:

Mario and Carlos, two brothers, play for the same basketball team. Here are the

points they scored in 10 games:

Game 1 2 3 4 5 6 7 8 9 10

Mario 15 X X 12 7 11 12 11 10 11

Carlos 10 X 9 12 15 X 19 11 12 12

(Xs mark games each one missed.) Which brother had the

highest-scoring game? How many more points did he score in

that game than the other brother did in his highest-scoring game?

the distance from the point (5, 31, -69) to the y-axis is 5 units.

To find the distance from a point to the y-axis, we only need to consider the x-coordinate of the point.

In this case, the point is (5, 31, -69). The x-coordinate of this point is 5.

The distance from the point (5, 31, -69) to the y-axis is simply the absolute value of the x-coordinate, which is:

|5| = 5

Therefore, the distance from the point (5, 31, -69) to the y-axis is 5 units.

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Control procedures are those that enable researchers to rule out specific causes for results other than the hypotheses they intend to test.

In a controlled experiment, every factor besides the independent variable is kept under control or constant to ensure that it has no impact on the dependent variable.

This experiment involves the systematic manipulation of an independent variable (the cause) and the measurement of the dependent variable (the effect). This ensures that any extraneous variables are controlled.

This experiment aids the researcher in determining whether the experimental group and control group differ from one another.

For example, during the medication effect test, the group that receives the medication is referred to as the experiment group. Those who don't get any medication are referred to as the control group.

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To improve the model's performance in predicting thyroid cancer occurrence, two potential steps to consider are: generating synthetic samples using SMOTE and collecting more data for the positive cases. option b and d

The given problem scenario involves imbalanced classes, with a significantly higher number of negative instances compared to positive instances. This class imbalance can lead to biased model performance, such as poor recall for the minority class (positive instances in this case). Here are the two selected steps and their rationale:

B) Generating synthetic samples using SMOTE: SMOTE is a technique used to address class imbalance by creating synthetic samples of the minority class. It generates new instances by interpolating between neighboring instances of the minority class. By using SMOTE, the positive class can be over-sampled, increasing the representation of thyroid cancer cases in the training data. This can help the model learn better decision boundaries for positive instances and improve recall.

D) Collecting more data for the positive cases: Increasing the number of positive instances in the training data can provide the model with more information to learn from. Collecting additional data specifically for positive cases, such as acquiring more samples of individuals diagnosed with thyroid cancer, can help in better capturing the characteristics and patterns associated with cancer occurrence. This can lead to a more balanced representation of the classes and potentially improve recall.

While options A (under-sampling instances from the positive class) and E (using Bagging) are also strategies to address class imbalance, they may not be as effective in this specific scenario. Under-sampling positive instances may further reduce the information available for learning, and Bagging, although useful for ensemble learning, may not directly address the class imbalance issue or improve recall.

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Answer:

78000000

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

7x3=21

2x2=4

4x5=20

21-20=1

Answer:

it can be written as 0.44y=40

44% can be written as 0.44

Step-by-step explanation:

to solve for y divide both sides by 0.44

to get y is equal to 100

True. An individual can assign a subjective probability to an event based on their knowledge and personal beliefs about the event.

Subjective probability is a measure of an individual's degree of belief or confidence in the likelihood of an event occurring, based on their subjective assessment of the available information.

Subjective probabilities can be influenced by various factors, including personal experiences, biases, and individual judgment. They are subjective in nature because they are based on an individual's own perception and interpretation of the event, rather than being derived from objective or empirical data.

Subjective probabilities are often used in decision-making under uncertainty, where individuals assess the likelihood of different outcomes based on their subjective understanding of the situation. While subjective probabilities may vary among individuals, they play an important role in decision-making processes, allowing individuals to make informed judgments and choices based on their personal knowledge and beliefs.

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Answer:

To solve for the sum, add all whole numbers together.

Step-by-step explanation:

16 + 9 = 25 and 5 + 16 is 21.

Subtracting these values will give you positive 4, but that's extra.

Answer:

9+16=25 AND 5+16=21

Step-by-step explanation:

Use the Order of Opperations to calculate the answer.

Answer:

x=67 y=113 x=52

Step-by-step explanation:

85+28= 113

180-113=67

67= x

67+28=95

95+85=180

y= 28+ 85 =113

113+15= 128

180-128=52

52=x

f(x) = -10

set the equation equal to -10 and solve for x:

-10 = -x-1

Add 1 to both sides:

-9 = -x

Divide both sides by -1:

x = 9

Answer:

okay so,

Step-by-step explanation:

My computer screen is broken and I could not see the equation for 11, 13, and 16

10. 81

12. -1/5 or -0.2

14. 9/64 or 0.140625

15. 27

17. -8

18. 1

Answer:

1.  81

2.  1/144

3.  -5

4.  1/64

5.  9/64

6.  27

7.  0

8. -16

9.  3

Answer:

the new side lengths are 10.5 , 9 and 6 inches

the new triangle has the following sides: 5, 4, 3 inches

the perimeter of the first triangle is 36 inches

the perimeter of the second triangle is 12 inches

area of the first triangle is 54 inches squared

area of the second triangle is 6 inches squared

Step-by-step explanation:

first question:

sides are 7,6,4. multiply each one by 3/2 or 1.5

7 x 1.5 = 10.5 or 12/2

6 x 1.5 = 9

4 x 1.5 = 6

the new side lengths are 10.5 , 9 and 6 inches

second question:

multiply each side by 1/3

the sides are 15, 12, 9, so:

15 x 1/3= 5

12 x 1/3 = 4

9 x 1/3 = 3

the new triangle has the following sides: 5, 4, 3

normal sides are 3 and 4

hypotenuse is 5

question a: (calculate perimeter)

the perimeter of a triangle: you add all the sides

the first triangle has 15, 12, 9 for its sides so:

15+12+9 = 36

the perimeter of the first triangle is 36

the second triangle has 5,4,3 for its sides so:

5+4+3 = 12

the perimeter of the second triangle is 12

question b: (calculate the area of both triangles)

area of a triangle: h x b/2: height times base divided by 2

the first triangle has sides, 15,12,9

height is 9 and base is 12, so:

9 x 12/2 = 54 inches squared

area of the first triangle is 54 inches squared

the second triangle has sides, 5,4,3

height is 3 and base is 4, so:

3 x 4/2 = 6 inches squared

area of the second triangle is 6 inches squared

The dependent variables in the following scenario are whether the bacon becomes moister and more flavorful and the independent variable is the cooking method.

In statistics, a dependent variable is one whose value is determined by another set of variables called independent variables. To put it simply, the dependent variable is the thing that is being tested or calculated. The dependent variable is sometimes known as the "outcome variable." In the given scenario, the chef was curious as to whether or not frying or microwaving the bacon would produce a moister and more flavorful final product. The bacon is the result of the experiment, hence it is a dependent variable.

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The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The requried value of ∂y/∂x at the point (1,3) is 7/2, which is option E.

We are given the curve in the xy-plane as:

f(x)g(y) = 24 + x + y

Substituting the point (1,3) in the above equation, we get:

f(1)g(3) = 24 + 1 + 3

f(1)g(3) = 28 ----- (1)

Now, we are also given the values of f(1), f'(1), g(3), and g'(3):

f(1) = 4

f'(1) = -2

g(3) = 7

g'(3) = 1

We need to find the value of ∂y/∂x at the point (1,3).

Using the product rule of differentiation, we can differentiate both sides of equation (1) with respect to x:

g(3) f'(1) + f(1) g'(3) ∂y/∂x = 0

Substituting the given values, we get:

7(-2) + 4(1) ∂y/∂x = 0

-14 + 4 ∂y/∂x = 0

∂y/∂x = 14/4

∂y/∂x = 7/2

Therefore, the value of ∂y/∂x at the point (1,3) is 7/2, which is option E.

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Let's rewrite every line in the slope-intercept form:

Since their slopes are equal, we can conclude that those lines are parallel.

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Firstly, we needt to identify the coordinates of the vertices of the quadilateral

Afterwards, we then perform the translation

The translation simply means we add 2 to the x-value and add 4 to the y-value

So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)

Let us identify the vertices;

K'

K (-4,-2)

L (-1,-2)

M (-1,-5)

N (-4,-5)

After translation, we have;

K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)

Answer:

700  

Step-by-step explanation:

35/x = 5/100

cross-multiply:

5x = 3500

x = 700