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Step-by-step explanation:

AB and DC are parallel

AD and BC are parallel

It can't be a rectangle bcz sides AB and BC are not perpendicular to each other

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

hope this helps:)

Answer:

At least two of the lateral faces are congruent.

Step-by-step explanation:

Because the words "at least" are used this means that at a minimum 2 of the faces are congruent. Because the base is in the shape of a triangle, this will definitely be true.

hope this helps:)

The Cartesian equation of the curve is x = -y^2 - 4y - 3. The graph is a downward-opening parabola with the range -4 ≤ y ≤ 0.

To eliminate the parameter t and find the Cartesian equation, we solve y = t - 2 for t, giving t = y + 2.

Substituting this into x = 1 - t^2 yields x = 1 - (y + 2)^2 = -y^2 - 4y - 3. This equation represents a downward-opening parabola. The range of y is determined by the given parameter range, -2 ≤ t ≤ 2, which corresponds to -4 ≤ y ≤ 0.

Plotting the graph, we observe that the parabola intersects the x-axis at x = -3 and opens downward. The y-values range from -4 to 0. Please note that the sketch provided is a rough visualization and may not be precise to scale.

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Answer:

(4.5 , -1.125)

Step-by-step explanation:

y= -1/4x

× +2y=4

step 1. substitute y = -1/4x into the second equation.

Rearranging × + 2y = 4 we get  x = 4 - 2y

now substitute

x = 4 + 2(1/4)

x = 4 + 0.5

x = 4.5

step 2. plug in the value of x into the first equation and solve for y.

y= -1/4x

y= -1/4(4.5)

y = -1.125

tadah!

We can write an equation for the interior angles, and we will see that x = 13

We want to find the value of x, we can see two adjacent angles on a rectangle, then the sum of these two is equal to 180°, we can write:

3x + 78 + x + 50 = 180

4x + 128 = 180

4x = 180 - 128

4x = 52

x = 52/4 = 13

The value of x is 13.

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Sebastian, this is the solution to the first problem you uploaded:

Let's recall that the interior angles of a triangle add up to 180 degrees.

Then if E =

The probability of X being odd when using a fair coin is 0.

When using a biased coin with a probability of 10/1 of coming up heads, the probability that X is odd is 1/9.

Let's analyze the probability of X being odd in both scenarios: with a fair coin and with a biased coin.

1. Fair Coin:

When flipping a fair coin, the probability of getting heads (H) or tails (T) is 1/2 for each flip. We can break down the possible sequences of flips as follows:

X = 1 (H)

X = 2 (TH)

X = 3 (TTH)

X = 4 (TTTH)

Notice that to obtain an odd number of flips, we need to have tails (T) at least once before getting heads (H). In the sequences above, we see that the first flip is always heads (H), so the number of flips is always even.

Therefore, the probability of X being odd when using a fair coin is 0.

2. Biased Coin:

Now, let's consider a biased coin with a probability of 10/1 of coming up heads (H) on each flip. The probability of getting tails (T) on each flip is then 1 - 10/1 = 1/10.

Similar to before, we can break down the possible sequences of flips:

X = 1 (H)

X = 2 (TH)

X = 3 (TTH)

X = 4 (TTTH)

This time, the first flip has a 10/1 probability of being heads (H). Therefore, the number of flips X can be odd since it's possible to get tails (T) before getting heads (H).

To calculate the probability of X being odd, we need to find the sum of the probabilities of the sequences with an odd number of flips. This can be done by considering the geometric series:

P(X is odd) = (1/10) + (1/10)(1/10) + (1/10)(1/10)(1/10) + ...

Using the formula for the sum of an infinite geometric series:

P(X is odd) = (1/10) / (1 - 1/10) = (1/10) / (9/10) = 1/9

Therefore, when using a biased coin with a probability of 10/1 of coming up heads, the probability that X is odd is 1/9.

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The charity organization will donate $100 + $10.

The dependent and independent variables are the two types of variables that are involved in a mathematical equation. In this problem, f is the independent variable, and c is the dependent variable.

An independent variable is the variable that is changed or controlled to test the effects on the dependent variable.

In the equation c = f + 10, f is the independent variable and c is the dependent variable.

This equation is an example of a linear equation where y is a dependent variable and x is an independent variable. The equation means that the amount of money that the charity organization contributes (c) is dependent on the amount of money that you raise during the fundraiser (f).

For every dollar raised, the charity organization will contribute an additional ten dollars. That is, c will always be equal to the amount of money raised (f) plus 10.

If f is zero, then c is also zero plus 10, which means the charity organization will donate ten dollars.

If f is $50, then c will be $60 since the charity organization will donate $50 + $10. If f is $100,

then c will be $110

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Answer:

9,000 m2

Step-by-step explanation:

If the longer rope has three times the length of the shorter rope, the perimeter and the sides of the triangle formed by the longer rope are three times the perimeter and sides of the triangle formed by the smaller rope.

The area of an equilateral triangle is:

\(Area = \frac{side^{2} * \sqrt{3}}{4}\)

So, if the side is three times bigger, the area will be 9 times bigger (3^2).

The area of the small triangle is 1000 m2, so the area of the bigger triangle is 9 * 1,000 = 9,000 m2

Answer:

The coordinates of D' and F are;

Explanation:

Given the triangles DEF mapped onto D'E'F'.

Given then the coordinate;

Let us find the translation used to map triangle DEF to D'E'F'.

Applying the translation to point D;

Also to get F;

The coordinate of point F is;

Therefore, the coordinates of D' and F are;

Answer:

28 inches

Step-by-step explanation:

\(P = 2(l+w)\)

\(P=2(9+5)\)

\(P=2(14)\)

\(P=28\)

Answer:

Step-by-step explanation:

If AS is an angle bisector, then angle XAS is congruent to angle PAS; mathematically, that looks like this:

3x + 15 = 2x + 30 and x = 15.

3(15) + 15 = angle XAP, which is 120.

Because angle XAS is congruent to angle PAS, then the sides across from those congruent angles also should be congruent. Let's check it, just to make sure:

XS = PS --> 2(15) + 9 = 39 and 4(15) - 21 = 39. So that checks out. Because AS is congruent to itself by the reflexive property, then what this means is that triangle XAS is congruent to triangle PAS, making angle x and P the same measure. Looking at the whole big triangle, triangle XAP, if angle XAP measures 120, then angle X = angle P = (180 - 120) / 2, so angle X = 30.

Answer ran 2 3/4 miles in 1/3 of an hour

2 3/4 miles =11/4 miles in 1/3 of hour

11/4 miles divided by 1/3 hr

11/4 ÷ 1/3

11/4 * 3/1 =33/4 =8 1/4 miles in 1 hr

The outcome is random if we know the possible values it can have, but not which particular value it takes.

Randomness refers to the property of a process or system where the outcome is uncertain, unpredictable, and not predetermined. In a random process, we know the set of possible outcomes.

But we cannot determine which particular outcome will occur until it actually happens. For example, when flipping a fair coin, the possible outcomes are heads or tails.

But we do not know which one will come up until the coin is flipped. Randomness is a fundamental concept in probability theory and is used to model and analyze a wide range of phenomena.

Including games of chance, genetics, and quantum mechanics.

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The best way to select five students from a list of 626 students available such that it exhibits a random process is to List each name on a separate piece of paper; place them all in a hat, and pick five.

The selection process which should be undertaken by the student government, should be one which is inclusive and representative. Hence, the five students to be selected which makes up the sample of the total student should be chosen at random and transparently.

Hence, listing the names of each student on a Seperate piece of paper, placing it in a hat and making 5 selections showcase randomness and transparency, hence, it should be the adopted selection process.

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The money in the account at the end of the 4 years is $1034

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Now we are given that the initial amount deposited in the account is $1000

This account is giving 0.85% And we have to figure out how much amount will be there

We use compound interest formula to find the amount

\(A= P(1+r/n)^{nt}\\\\A= 1000(1+0.0085)^{4}\\A = 1000(1.034)\\A= 1034\)

Hence the amount will be after 4 years is $1034.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Let's represent the numbers as variables to better understand the given information.

Let:

The first number be 'x'.

The second number be 'x - 2' (2 less than the first number).

The third number be 'y'.

The fourth number be 'y + 1' (1 less than the fourth number).

So, the representation of the given information is as follows:

First number: x

Second number: x - 2

Third number: y

Fourth number: y + 1

Please note that I have used 'y' for the third number since it wasn't explicitly defined in the statement.

Certainly! Let's consider an example to illustrate the given conditions.

Let's assume:

The first number, 'x', is 10.

The second number is 2 less than the first number, so it would be 10 - 2 = 8.

The third number, 'y', is 5.

The fourth number is 1 less than the third number, so it would be 5 - 1 = 4.

So, in this example, the sequence of numbers would be: 10, 8, 5, 4.

Please note that this is just one example that satisfies the given conditions. If you have a different set of numbers or additional information, please let me know, and I can assist you accordingly.

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Answer:

450/500 = 0.9sorry if it's wrong

Step-by-step explanation:

Answer:

D. 280/500 = 0.56

Step-by-step explanation:

280 are intended for people over 16 and 320 use a rechargeable battery.

320-150 = 170 (intended for those under the age of 16)

The answer would be D because you need to take the highest number of products (280) that would satisfy the requirements.

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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By using the concept of permutation, it can be calculated that

Number of ways in which the marbles of different sizes can be arranged in a line = 362880

What is permutation?

The technique which is used to determine the possible arrangements that can be made among the members of the set when the order of arrangement is taken into account

Here the concept of permutation is used

Number of red marbles = 2

Number of yellow marbles = 2

Number of green marbles = 5

Total number of marbles = 2 + 2 + 5 = 9

Here, the marbles are of different sizes

So the first marble have 9 choices, second marble have 8 choices and so on

Number of ways in which the marbles of different sizes can be arranged in a line = 9 \(\times\) 8 \(\times\) 7 \(\times\) .... \(\times\) 1

         = 9!

         = 362880

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Answer:

12, 24, and 60.

Step-by-step explanation:

It says multiples. Not factors, so it can't be 1 or 2. Neither of the numbers can make the number 10. 4 can make 40, but 6 can't.

Answer:

12, 24, 60

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

they always look for does kind of movies

Answer:

x = 33

Step-by-step explanation:

∡ CBE = ∡DBA = 57°

The sum of the interior angles of a triangle results 180°

∡BDA = it´s a right angle = 90°

Then:

57° + 90° + x = 180°

147° + x = 180°

x = 180° - 147°

x = 33°

The real zeros of the polynomial function P(x) = x⁵ − 50x³ + 49x are -1, 0, and 1.

To find the zeros of this function, we can factor it by first factoring out an x to get P(x) = x(x⁴ − 50x² + 49). Then, we can factor the quadratic expression inside the parentheses using the difference of squares formula, which gives us P(x) = x(x² − 1)(x² − 49). Simplifying further, we have P(x) = x(x − 1)(x + 1)(x - 7)(x + 7).

Therefore, the zeros of P(x) are the values of x that make each factor equal to zero. This gives us x = -7, -1, 0, 1, and 7. Since all of these values are real, we conclude that the number of real zeros of P(x) is 5.

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Answer:

900+ hours

Step-by-step explanation:

Answer:

3x³- 8x² + 2x +3

Step-by-step explanation:

All you need to do is multiply everything in the second bracket with the first bracket like you would normally do with double brackets.

3x³-3x²-5x²+5x-3x+3=

3x³-8x²+2x+3

Answer:

The error is that the question equals -13-13.

Step-by-step explanation:

This is absolute value, so anything inside of the bars is positive. Since the first -13 has bars around it it would be positive. But since the second - is outside of the 13 with bars, the 13 stays negative, so it would be 13-13. Hope this helps! :)