Which of the following statements must be true in order to prove that a quadrilateral is a parallelogram?

Answer:

12

\( {x}^{2} - {y}^{2} = (x - y) \times (x + y) = 3 \times 4 = 12 \)

Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.

To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.

We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.

Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.

Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have

√-2 = a/b

Squaring both sides gives

-2 = a^2/b^2

Multiplying both sides by b^2 gives

-2b^2 = a^2

This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means

-2b^2 = (2k)^2

Simplifying, we get

-2b^2 = 4k^2

Dividing both sides by -2 gives

b^2 = -2k^2

This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.

By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.

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The critical t-value is approximately 1.753.

To find the critical value for a 96% confidence interval with a sample size of 15, we need to determine the t-value from the t-distribution table. The t-distribution table is a statistical tool used to determine the probability of a t-value given the degrees of freedom (df) and the desired level of significance (α).

In this case, we have a sample size of 15, which means our degrees of freedom are 14 (n - 1). Looking at a t-distribution table for 14 degrees of freedom and a 96% confidence interval.

This means that if we were to construct a confidence interval from a sample size of 15, the margin of error would be calculated by multiplying the critical t-value of 1.753 by the standard deviation of the sample and dividing by the square root of the sample size. The resulting interval would contain the population mean with 96% confidence.

It's essential to note that the critical value will change as the sample size and confidence level change. Therefore, it's crucial to use the correct table to find the corresponding critical values for a given dataset's sample size and confidence level.

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The probability that three of the dice show prime numbers and the rest show composite numbers is \(\frac {5}{16}\).

Given that, six 6-sided dice are rolled.

The prime numbers on dice are 2, 3, and 5. The composites are the rest. Keep in mind that 1 by definition isn't directly composite, but it isn't prime, so we don't count it when we're counting primes.

We know that the primes are {2, 3, 5}. This means for a single die, we have a \(\frac{3}{6}=\frac{1}{2}\) chance that it shows a prime. Out of the six dice, we want to know how many ways we can choose three to show primes. This is equal to (6 3)=20 possible ways. For all of the dice to show the successful outcome.

P(success)=Ways to pick prime dice. P(prime dice are prime, composite dice are composite)

= \(20\cdot (\frac{1}{2})^6\)

= \(\frac {20}{64}\)

= \(\frac {5}{16}\)

Therefore, the probability that three of the dice show prime numbers and the rest show composite numbers is \(\frac {5}{16}\).

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The answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.

Given:

x = 3 , y = 1/3 and z = 5 and expression  12x - 3y / 4x - z.

substitute the x,y,z values in expression.

= 12(3)-3(1/3) / 4(3)-5

= 36 - 3/3 / 12 - 5

= 36 - 1 / 7

= 35/7

= 5.

Therefore the answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.

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When the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

The volume of the wall is determined as follows;

V = h x w x t

where;

Initial volume of the wall when some blocks are removed to make a window is 2 feet high by 2 feet wide.

V1 = (6 - 2) x (6 - 2) x (t)

V1 = 16t  ft³

Second volume of the wall when some blocks are removed to make a window is 4 feet high by 4 feet wide.

V2 = (12 - 4) x (12 - 4) x (t)

V2 = 64t  ft³

V2 = 4(16t  ft³)

V2 = 4(V1)

Thus, when the window is expanded to be 4 feet high by 4 feet wide, the volume of the wall quadruples or increases by factor of 4.

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Answer:

2

Step-by-step explanation:

because the other numbers are closer to each other than 2

Answer:

2

Step-by-step explanation:

In a data set, the outlier is the data point that differs significantly from all other data points- it's normally very different from all other points.

In the data set, we can see that all but one of the points are between 9-14.

Hence, we can safely say that the outlier is 2.

To better visualize this, we can plot all the points.

As you can see, all the scores are clumped together, except for "2."

36 number of ways to set out the letters without the i's together.

Order of the letters matters, so, this is a permutation problem.

Now we will determine in how many ways we can arrange these letters.

There are 2 repeating i's, so, we can arrange the letters:

5!/2! = 120/2

= 60 ways.

We also have the following equation:

60 = (number of ways to arrange the letters with the i's together) + (number of ways without the i's together).

To find the no. of ways to set out the letters with the i's together.

We have: [i-i] [d] [g] [t]

We see that with the i's together, we have:

4! = 24 ways to arrange the letters.

Thus, the number of ways to set out the letters without the i's together is:

60 – 24 = 36.

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We have the following linear equation:

5x - 2y = -10

In the standard form, we have:

-2y = -5x - 10

y = 5x/2 - 5

For x = 0, we have y = -5, and, for y = 0, we have x = 2

Therefore, to graph this equation, we just need to draw a line passing through (0,-5) and (2,0).

Answer:

Step-by-step explanation:

Sin (90 - ∅) = Cos ∅

90 -54 = 36

Sin 36 = Sin (90 - 54)

            = Cos 54      --------->(I)

Now, Sin (36) - Cos (54) = Cos 54 - Cos 54   {From 1}

                                        = 0

2) tan (90-∅) = Cot ∅

Tan 80 = Tan (90 - 10)

            = Cot 10  ----------(II)

Tan 80 - Cot 10 = Cot 10 - cot 10   -----------(from (II)}

                         = 0

Are you korean?

≧∇≦

ฅ'ω'ฅ

Answer:

7.25cm

Step-by-step explanation:

Let the complete question be;

Jill cuts a piece of cardboard in the shape of a trapezoid. The area of the is 43.5sp cm. If bases are 3.5cm and 8.5cm long, what is the height.

Area of a trapezoid = 1/2(a+b)*h

a and b are the parallel sides (bases)

h is the height

Given

a = 3.5cm

b = 8.5cm

A = 43.5 sq.cm

Required

Height h

Substitute the given values into the expression

Area of a trapezoid = 1/2(a+b)*h

43.5 = 1/2(3.5+8.5)*h

43.5 = 1/2 * 12h

43.5 = 6h

h = 43.5/6

h = 7.25cm

Hence the height is 7.25cm

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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The percent of the possible subcommittees that Michael is a member of is David is 8/20 or 40%. the correct option is (B) 40%.

Now, we are required to determine the percentage of possible subcommittees that Michael and David are both members of which will 40%.

The number of ways to pick 3 members out of 6 is 6C3 = 20.The number of ways to select 3 members including both Michael and David is 4C1 × 2C1 = 8

Total possible subcommittees=20

The number of ways in which Michael and David can be members in the same subcommittee is 8.

Thus, the percent of the possible subcommittees that Michael is a member of is David is 8/20 or 40%.

Therefore, the correct option is (B) 40%.

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Answer:

612 266.56 centimeters im pretty sure

Step-by-step explanation:

just times them all

Answer:

Tens place: 8

Tenths place: 5

Ten thousandths place: 2

Answers:

tenths place = 5

ten-thousandths place = 2

======================================================

Explanation:

Refer to the place value chart shown below.

The 5 is in the tenths place which is one spot to the right of the decimal point. The ten-thousandths place is four spots to the right of the decimal point.

Answer:

0.50 cents

Step-by-step explanation:

If the ratio is 2:1 then the bigger share would be 2 times bigger than the smaller share.

The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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Answer:

10% out of 100%.

Or 4/40=1/10 which is 10%.

Shen has ridden her bike for 10% of the course

The angle that is complementary to angle X is 90 degrees minus angle X.

1. Complementary angles are two angles whose sum is 90 degrees.

2. Let's assume that angle X is given.

3. To find the angle that is complementary to angle X, we need to subtract angle X from 90 degrees.

4. The formula to find the complementary angle is: Complementary Angle = 90 degrees - angle X.

5. Substitute the value of angle X into the formula to calculate the complementary angle.

6. For example, if angle X is 45 degrees, the complementary angle would be: 90 degrees - 45 degrees = 45 degrees.

7. Similarly, if angle X is 60 degrees, the complementary angle would be: 90 degrees - 60 degrees = 30 degrees.

8. Therefore, to find the complementary angle to any given angle X, subtract that angle from 90 degrees.

9. The result will be the measure of the angle that is complementary to angle X.

10. Remember that complementary angles always add up to 90 degrees.

11. By using this approach, you can find the complementary angle for any given angle X.

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Answer:

c i think

Step-by-step explanation:

Answer:

C.) x7      ;)

Step-by-step explanation:

:))))))))))))))

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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The sequence is 5,9,13,17,...

Determine the common difference for the sequance

The correct interpretation is with a one unit increase in x.2, the response increases by 18.385, on average.

The coefficient for x.2 represents the average change in the response variable for a one unit increase in x.2, while holding other variables constant.

In this case, the coefficient indicates that, on average, when x.2 increases by one unit, the response variable increases by 18.385. This implies a positive linear relationship between x.2 and the response.

Furthermore, the statement that the average of x.2 is 18.385 indicates that the average value of x.2 in the given data is 18.385.

Finally, when x.2 is 0, the value of the response is also 18.385, suggesting that this serves as a reference point or baseline for the response variable.

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Answer:

8 in

Step-by-step explanation:

Area of a square = l×w

Since it is a square then l and w are equal to each other.

So we can instead just say l^2 = A

l^2 = 68.2

l = square root of 68.2

l = 8.26

The price for 1 scoop of ice cream and the price for 1 topping is $1.20 and $0.35 respectively.  

Suppose the price for 1 scoop of ice cream = x

The price for 1 topping = y

An equation of the form ax+by+c=0 is called a linear equation where a, b and c are real numbers.

According to the question

3x+y=3.95.......(1)

2x+2y=3.10.......(2)

Multiply equation (1) by 2 on both sides

6x+2y=7.90.....(3)

Subtracting the equation (2) from equation(3)

4x=4.80

x=1.20

So, y = 0.35

So, the price for 1 scoop of ice cream =$1.20

The price for 1 topping = $0.35

Hence, the price for 1 scoop of ice cream and price for 1 topping is $1.20 and $0.35 respectively.  

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Answer:

B

Step-by-step explanation:

Answer: Answer:

A. is your answer

When using the Slope Method, your answer is y - 5 = 4(x - 2).

Feel free to give brainliest.

Have a great day everyone!

Answer:

Correct.

Step-y-step explanation:

The rise-over-run formula for the slope of a straight line is the basis of the high-low method.

What is slope of a straight line?

The slope of a straight line by joining two points is the rise over run formula. The subtraction between the two points of the y-coordinates is called the rise. And the subtraction between the two points of the x-coordinates is called the run. The slope can be calculated by dividing the rise by run.

The slope of a line either goes in the upward direction or in the downward direction or left direction or right direction. It determines the direction of the line. When the straight line goes in the upward direction, it means the rising line and slope is positive. When it goes in the downward direction, it means a falling line and slope is negative.

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