Chaim tried to prove that AUTS ~ AUDE in the following figure, but his proof is wrong.
E
D
41
т
37
S
What is the first mistake Chaim made in the proof?
Statement
Reason
1 ZSUT ZEUD Vertical angles are congruent.
2 ST | DE
Given
3 ZUST. ZUED Alternate interior angles formed by parallel lines are congruent (2).
AUTS AUDE Angle-angle similarity (1,3)
4
Choose 1 answer

To find the volume of the composite figure, we first need to break it down into simpler shapes. We can see that the composite figure is made up of a rectangular prism and a triangular prism.

The rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 7 cm. Therefore, its volume is:

Volume of rectangular prism = length x width x height = 6 cm x 4 cm x 7 cm = 168 cubic cm

The triangular prism has a base of 3 cm, a height of 8 cm, and a length of 10 cm. Therefore, its volume is:

Volume of triangular prism = (1/2) x base x height x length = (1/2) x 3 cm x 8 cm x 10 cm = 120 cubic cm

To find the volume of the composite figure, we add the volumes of the rectangular prism and the triangular prism:

Volume of composite figure = Volume of rectangular prism + Volume of triangular prism = 168 cubic cm + 120 cubic cm = 288 cubic cm

Therefore, the volume of the composite figure is 288 cubic centimeters.

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We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁).

This procedure calculates the slope of a line using the coordinates of two points. It takes four numeric parameters as input: the x coordinate of the first point, the y coordinate of the first point, the x coordinate of the second point, and the y coordinate of the second point. The slope of a line is a measure of its steepness and is defined as the change in y divided by the change in x between two points on the line.

To calculate the slope of a line using the coordinates of two points, we need to first find the difference between the y-coordinates of the two points and the difference between the x-coordinates of the two points.

We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁). The resulting slope value can be positive, negative, or zero depending on the direction and steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing from left to right. A slope of zero indicates a horizontal line.

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-21,  -23, -27, -28, -28, -29 order them least to greatest and then find the middle if there is not a middle then put -27.5 as your answer for the median. For the mean add up all the number then you should get -156 then divide it by 6 which should give you -26 for the mean.  and for the mode you should get -28 as the one that occurs the most often.

mean: -26

median: -27.5

mode: -28

Yes, the new method for detecting avobenzone in sunscreen is valid/accurate at a 95% confidence level.

The standard reference material provided by the FDA contains 0.250 mg of avobenzone per gram of sunscreen. The working group analyzed the standard and obtained measurements of avobenzone content in six samples, which were found to be 0.256, 0.279, 0.328, 0.305, 0.312, and 0.230 µg/g.

To determine the validity and accuracy of the new detection method, we need to assess if the measurements obtained from the samples are within an acceptable range of the known avobenzone content provided by the standard.

At a 95% confidence level, we can calculate a confidence interval to evaluate the accuracy of the new method. The confidence interval is a range within which we can reasonably expect the true avobenzone content of the sunscreen samples to fall. If the known avobenzone content provided by the standard falls within this confidence interval, it indicates that the new method is valid and accurate.

By performing the necessary calculations, we can determine the confidence interval. Comparing the range of the measurements obtained from the samples (0.230 to 0.328 µg/g) with the known avobenzone content provided by the standard (0.250 mg/g), we find that the measurements overlap with the known value. Therefore, we can conclude that the new method is valid/accurate for the detection of avobenzone in sunscreen at a 95% confidence level.

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Answer:

Yes, very. This has happen to me so many times. I hate it

Have a nice day <3

^_^

Answer:

3 and 4

Step-by-step explanation:

13 is between the perfect squares of 9 and 16, which are 3^2 and 4^2 respectively.

The angle that the wire makes with the ground is 36.87° with horizontal.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

The given situation is making a right-angle triangle,

By Pythagoras' theorem in the triangle.

Base = √(100² - 60²) = 80 foot

By tan trigonometric function,

tanx = 60/80

x = 36.87°

Hence "The wire's angle with the ground is 36.87° with respect to the horizontal".

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The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.

Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.

In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.

In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.

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If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

\(\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}\)

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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The expression by using a Double-Angle Formula or a Half-Angle Formula are: For part (a), the expression can be simplified to 1 - 2sin²(37°), and for part (b), the expression can be simplified to 1 - 2sin²(4θ).

(a) cos^2(37°) - sin²(37°)

Let us use the formula cos(2A) = 2cos²A − 1.

If we take A = 37°, we get:

cos(74°) = 2cos²(37°) − 1

Substituting cos²(37°) = 1 − sin²(37°), we obtain

cos(74°) = 2(1 − sin²(37°)) − 1

Simplifying cos(74°) = 1 − 2sin²(37°)

Hence the expression cos²(37°) - sin²(37°) can be simplified as 1 - 2sin²(37°).

Using Double-Angle Formula, we get cos(74).

b) cos^2(8θ) - sin²(8θ)

Let us use the formula cos(2A) = 2cos²A − 1.

If we take A = 4θ, we get:

cos(8θ) = 2cos²(4θ) − 1

Substituting cos²(4θ) = 1 − sin²(4θ), we obtain

cos(8θ) = 2(1 − sin²(4θ)) − 1

Simplifying

cos(8θ) = 1 − 2sin²(4θ)

Hence the expression cos²(8θ) - sin²(8θ) can be simplified as 1 - 2sin²(4θ).

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Answer: 30 sandwiches

Step-by-step explanation:

you multply 4 times 10 and you get 40 then you buy 30 sandwiches becuase you have 40 bucks left

Answer:

Step-by-step explanation:

y=1/2-5x

Answer:

Step-by-step explanation:

Using points on the graph to get the equation

Slope intercept form:

From the graph, point (0, -5) we can see y-intercept is b = -5

An calculating the slope using two points (-6, -3) and (6, -7):

So the line is:

The smallest angles of the triangle is angle A

In triangle ABC

The length of the side AB = 6.2 units

The length of the side AC = 9.5 units

The length of the side BC = 5.1 units

The opposite angle of AB is angle C, the opposite angle of AC is angle B and the opposite angle of BC is angle A

We know length of the line is BC which is 5.1 units which is the smallest side of the triangle. Then the opposite angle of BC will be the smallest angle in the triangle ABC

The opposite angle of the side BC is angle A, which is the smallest angle in the triangle

Hence, the smallest angles of the triangle is angle A

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Answer:

m = -1/2

Step-by-step explanation:

m = y1 - y2/x1 - x2

2 - 0/0 - 4

-2/4

Simplify

-1/2

4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), ¬X V Y is a tautology.

4.2 No, it does not necessarily follow that Y must entail ¬Z. Y does not necessarily entail ¬Z.

4.3 The tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.

4.1 If X is contingent (neither a tautology nor a contradiction) and Y is a tautology (always true), the sentence ¬X V Y must be a tautology. This is because the disjunction (∨) operator evaluates to true if at least one of its operands is true. In this case, since Y is a tautology and always true, the entire sentence ¬X V Y will also be true regardless of the truth value of X. Therefore, ¬X V Y is a tautology.

4.2 No, it does not necessarily follow that Y must entail ¬Z. Logical equivalence between X and Y means that they have the same truth values for all possible interpretations. Inconsistency between X and Z means that they cannot both be true at the same time. However, logical equivalence and inconsistency do not imply entailment.

Y being logically equivalent to X means that they have the same truth values, but it does not determine the truth value of ¬Z. There could be cases where Y is true, but Z is also true, making the negation of Z (¬Z) false. Therefore, Y does not necessarily entail ¬Z.

4.3 No, it does not necessarily follow that Z is also a tautology. The fact that X and X → Z are both tautologies means that they are always true regardless of the interpretation. However, this does not guarantee that Z itself is always true.

Consider a case where X is true and X → Z is true, which means Z is also true. In this case, Z is a tautology. However, it is also possible for X to be true and X → Z to be true while Z is false for some other interpretations. In such cases, Z would not be a tautology.

Therefore, the tautologies of X and X → Z do not provide sufficient information to conclude that Z itself is a tautology.

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The area of the shaded region based on the information will be 201cm².

It should be noted that the radius of the outer circle will be:

= Diameter / 2

= (8 + 8 + 4 + 4)/2

= 24 / 2

= 12cm

The area of the circle = πr²

= 3.14 × 12²

= 3.14 × 144

= 452.16 cm²

The area of the circle with radius 8cm = 200.96 cm²

The area of the circle with radius 4cm =50.24cm².

The area of the shaded region:

= 452.16 - 200.96 - 50.24

= 200.96 cm²

Therefore, the area of the shaded region based on the information will be 201cm².

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To find all subgame perfect Nash equilibria (SPNE), we need to analyze each decision node in the game tree and determine the best response for each player at that node.

Starting from the final round (bottom of the tree) and working our way up:

At the node labeled "N", Player 1 has two options: "H" and "S". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(H, h): Player 1 gets a payoff of 3, Player 2 gets a payoff of 0.

(S, h): Player 1 gets a payoff of 2, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "H" rather than "S" and Player 2's payoff is higher when choosing "h" rather than "H", the subgame perfect Nash equilibrium for this node is (H, h).

Moving up to the next round, we have a decision node labeled "a". Player 1 has two options: "C" and "T". Player 2 has only one option: "h". The payoffs associated with each combination of choices are as follows:

(C, h): Player 1 gets a payoff of 4, Player 2 gets a payoff of 0.

(T, h): Player 1 gets a payoff of 5, Player 2 gets a payoff of 5.

Since Player 1's payoff is higher when choosing "T" rather than "C" and Player 2's payoff is higher when choosing "h" rather than "C", the subgame perfect Nash equilibrium for this node is (T, h).

Finally, at the topmost decision node labeled "S", Player 1 has only one option: "S". Player 2 has two options: "C" and "T". The payoffs associated with each combination of choices are as follows:

(S, C): Player 1 gets a payoff of 0, Player 2 gets a payoff of 2.

(S, T): Player 1 gets a payoff of 3, Player 2 gets a payoff of 3.

Since Player 1's payoff is higher when choosing "S" rather than "N" and Player 2's payoff is higher when choosing "C" rather than "T", the subgame perfect Nash equilibrium for this node is (S, C).

In summary, the subgame perfect Nash equilibria for this game are (H, h), (T, h), and (S, C).

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Answer:

Step-by-step explanation:

The arc length formula is

\(L=\frac{\theta}{360}*2\pi r\)

Theta is the angle that intersects arc HJ. That measure is 180-122 which is 58 degrees. We put that into the formula along with the radius measure of 10 to get:

\(L=\frac{58}{360}*2\pi (10)\) which gives us, rounded to the nearest hundredth,

L = 10.12 units

Answer:

its 847>×+18 enjoy hope it work

Answer:

Hi there,

$294 per year = $24.50 per month

Kim paid $24.50 + $3.50 = $28 per

month with her old phone plan.

Hope this helps :-)

Step-by-step explanation:

Answer:

1. 0/10

2. -9/0

Step-by-step explanation:

you want to do the second y- the first y / the second X-the first x

The required area of the circle with diameter 15.8 cm is 196.06 cm^2.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To find the area of a circle, we use the formula: pi * (radius)^2. The diameter of the circle is given as 15.8 cm,

so the radius can be calculated by dividing the diameter by 2,

giving us a radius of 15.8 cm / 2

= 7.9 cm.

Plugging the radius into the formula, we get:

pi * (7.9 cm)^2

= 3.14 * 62.41.

Finally, rounding the answer to the nearest hundredth, we get: 62.41 * 3.14

= 196.06 cm^2.

Thus, requi9red answer is 196.06 cm^2.

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Answer:The winner recieved 4,500 more votes than the loser

Step-by-step explanation:

Answer:

5,250

Step-by-step explanation:

The first step is to set up a porportion like this one

\(\frac{?}{15,000} \frac{65}{100}\)

Next, you cross multiply and divide. 15,000 times 65 is 975,000

Then divide this by 100 which is 9750. This is the number of votes the winning candidate received. Subtract this number from 15,000 to get 5,250. Hope this helps!

Answer:

35 units ^2

Step-by-step explanation:

First, draw lines or count how many units are between each point. Don't go diagonal, just up/down or left/right, like from point B to point A.

So I counted 5 units from point B to A, 5 units from C to D, 7 units from A to D, and 7 units from B to C.

Now, you choose two sides - one that goes up/down and one that goes left/right. This is your base and your height.

So you should have 5 and 7. Now, the equation of a rectangle is base times height (b* h) so you multiply 5 and 7 together to get your answer, 35 units ^2

I hope this helps :)

Answer:

Monica had 17 cookies to begin with

Step-by-step explanation:

10 divided by 2 is 5

Answer:

No solutions / "no"

Step-by-step explanation:

y = 3x + 2

y = 3x - 6

Since both equations are equal to y, you can set them equal to each other.

3x + 2 = 3x - 6

subtract 3x from both sides

2 = -6

This equation is not true, therefore your answer is no solutions.

Answer:

Step-by-step explanation:

\(\dfrac{x}{2}=\dfrac{y}{3}\\\\\)

Cross multiply,

3x = 2y    ------------(I)

\(\dfrac{y}{4}=\dfrac{z}{4}\\\\4*\dfrac{y}{4}=\dfrac{z}{4}*4\\\\y=z\)

y = z --------------(II)

Plugin y =z in (I)

3x = 2z

3x/2 = z  ----------------(III)

x + 2y - z = 10

From (I) and (III)

\(x + 3x - \dfrac{3x}{2}=10\\\\4x - \dfrac{3x}{2}=10\\\\Multiply \ the \ entire \ equation \ by \ 2\\\\2*4x - 2*\dfrac{3x}{2}=10*2\\\\8x - 3x = 20\\\\5x = 20\)

Divide both sides by 5

x = 20/5

x = 4

Plugin x = 4 in (I)

3*4=2y

12 = 2y

2y = 12

y = 12/2

y  = 6

z = y

z = 6

Answer:

shaded area = total area - the two triangles areas

total area = 5*9 = 45 cm²

first tri area = 1/2 * h *b

= 0.5 * 5 * 2 = 5 cm²

second tri area = 0.5 * 6 * 5 = 15 cm²

shaded area = 45 - 15 - 5 = 25 cm²