Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (2, 3, 4), (6, 2, 5), (7,4,8) STEP 1: Compute the following two vectors. (2, 3, 4) - (1, 1, 1) = (7, 4, 8) - (6, 2,5) Are these two vectors equal? Yes No STEP 2: Compute the following two vectors. (6, 2,5) - (1, 1, 1) = (7,4, 8) - (2, 3, 4) = = Are these two vectors equal? Yes No STEP 3: Compute the cross product of the two vectors from above. STEP 4: Compute the norm of the cross product to compute the area of the parallelogram.

Answer: 454.5

Step-by-step explanation:

-2, 20, -200, 2,000 ==> 4 numbers

Mean: (-2+20+(-200)+2000)/4=

(18-200+2000)/4=

(-182+2000)/4

1818/4=454.5

Answer:

4 Chips $12 and 6 cans of soda $12.

Step-by-step explanation:

Each chip cost $3*4=12 and Soda cans cost $2*6=12

12+12=$24. You can also figure a few of different ways, this is one of them.

Based on the equidistant chords theorem, the value of m and n in the circle are:

m = 7/4 = 1.75

n = 1/2 = 0.5

The equidistant chords theorem states that, two chords are congruent if they are equidistant to the center of the same circle.

Given:

Thus, since US = RU, therefore chords PO and EW are congruent based on the equidistant chords theorem.

Therefore:

3m + 2 = -m + 9

Add like terms

3m + m = -2 + 9

4m = 7

m = 7/4

m = 1.75

20n - 14 = -2(2n + 1)

20n - 14 = -4n - 2

20n + 4n = 14 - 2

24n = 12

n = 12/24

n = 1/2 = 0.5

Therefore, based on the equidistant chords theorem, the value of m and n in the circle are:

m = 7/4 = 1.75

n = 1/2 = 0.5

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-2/5x - 9 < 9/10

-2/5x-9+9<9/10+9

-2/5x<99/10

(5/-2)*(-2/5 x)<(5/-2)*(99/10)

x>-99/4

By using the given domain and range, we will see that the false statements are:

What we know about the function f(x) is:

The domain is: -10 ≤ x ≤ 20

The range is: -40 ≤ f(x) ≤ -10

Which statements are false:

1)  f(0)= 0

This is false, because the maximum value of the range is -10, so f(0) can't be equal to zero.

2. f(1) = 13

Same reasoning than above, 13 is outside of the range.

3. f(-15) =- 20

The smallest value on the domain (possible inputs) is -10, so the input -15 is not in the domain.

4)  f(-9) = 88

88 is outside the range of the function, so this is false.

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Answer:

Step-by-step explanation:

-2x + 9 < x - 9                     Add 9 to both sides

-2x + 9 + 9 < x - 9 + 9        Combine

-2x + 18 < x                         Add 2x to both sides

-2x+2x + 18 < x + 2x           Combine

18 < 3x                                 Divide by 3

18/3 < 3x/3

6 < x

Challenge To travel on vacation, a family wants to rent a car. Company A bills $70.50 plus 17 cents each mile. Charges from Company B are $30.50 plus 8 per mile. For every x miles that Company A charges, Company B is (39.24x)

Before figuring out their difference for x miles, we must first determine their difference for one mile.

Difference per mile = ($70.50 + $0.14) - ($30.50 + $0.90)

= $70.64 - $31.40

= $39.24

Difference for x miles = $39.24 × x miles

= $(39.24x)

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Answer:

see below (I hope this helps!)

Step-by-step explanation:

We can split this into 2 cases:

3x + 2 > 9 or -(3x + 2) > 9

3x > 7 or 3x + 2 < -9

x > 7/3 or x < -11/3

Applying the inscribed angle theorem, we have:

a. x = 55° b. x = 60°  c. x = 92°    d. x = 84°

These theorem states that:

Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.

Intercepted arc measure = central angle measure.

Therefore, we have:

a. x = 180 - 35 - 90 [tangent theorem]

x = 55°

b. x = 1/2(120) [inscribed angle theorem]

x = 60°

c. x = 2(46) [inscribed angle theorem]

x = 92°

d. m(FE) = 2(42) = 84°

m(EB) = 180 - FE = 180 - 84

m(EB) = 96°

m(AB) = 180 - m(EB) = 180 - 96

m(AB) = 84°

x = m(AB) = 84° [central angle theorem]

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The Python methods is used to perform chi-square goodness of fit tests is option (a) chisquare from scipy.stats submodule

The chisquare method from the scipy.stats submodule in Python is used to perform chi-square goodness of fit tests. This test is a statistical technique used to determine if an observed categorical frequency distribution differs from a theoretical distribution. The chisquare method takes two arguments: the observed frequency distribution and the expected frequency distribution.

It returns the chi-square test statistic and the p-value. If the p-value is less than the significance level, we reject the null hypothesis that the observed distribution and the expected distribution are the same. This method is widely used in various fields, including biology, finance, and social sciences, to test the hypothesis about the distribution of categorical data.

Therefore, the correct option is (a) chi-square from scipy.stats submodule

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Integration by parts is a technique used to evaluate the integrals of a product of two functions.

This method is commonly used when the integral cannot be solved using other techniques. The formula for integration by parts is given by:

∫u dv = uv - ∫v du where u and v are functions of x, and du/dx and dv/dx are the derivatives of u and v with respect to x.

Using the formula of integration by parts, we get:

6. ∫f(In x)² dx

Let u = In x and dv = f(In x) d(In x)

Then, du = (1/x) dx and v = ∫f(In x) d(In x)

So, we get:

∫f(In x)² dx= u*v - ∫v du

= In x * ∫f(In x) d(In x) - ∫∫f(In x) d(In x) (1/x) dx

7. ∫fx³ dx

Let u = x² and

dv = f(x) dx

Then, du = 2x dx and v = ∫f(x) dx

So, we get:

∫fx³ dx= u*v - ∫v du

= x² * ∫f(x) dx - ∫2x * ∫f(x) dx

8. ∫√9-x² dx

Let u = √9-x² and dv = dx

Then, du = (-1/2) (9-x²)^(-1/2) (-2x) dx and

v = x

So, we get:

∫√9-x² dx= u*v - ∫v du

= x√9-x² + 9*∫(1/√9-x²) x dx

= x√9-x² + 9*In| x + √9-x² | + C

9. ∫2x fe²x sinx dx

Let u = 2x and dv = fe²x sinx dx

Then, du = 2 dx and v = (-1/2) fe²x cosx

So, we get:

∫2x fe²x sinx dx= u*v - ∫v du

= (-1/2) 2x fe²x cosx - ∫(-1/2) fe²x cosx 2 dx

= -x fe²x cosx - ∫fe²x cosx dx

10. ∫fx² √x-1 dx

Let u = √x-1 and

dv = fx² dx

Then, du = (1/2) (x-1)^(-1/2) dx and

v = (1/3) f(x)³

So, we get:

∫fx² √x-1 dx= u*v - ∫v du

= (1/3) f(x)³ √x-1 - ∫(1/3) f(x)³ (1/2) (x-1)^(-1/2) dx

Therefore, using the formula of integration by parts, we can evaluate the given integrals as shown above.

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To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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In a test of hypothesis the p-value was 0.24. If the level of significance is 10 %. The potential type of statistical error is a) Type II error.

In hypothesis testing, Type I error occurs when the null hypothesis is incorrectly rejected, while Type II error occurs when the null hypothesis is incorrectly accepted. The p-value of 0.24 is greater than the significance level of 0.10, which means there is not enough evidence to reject the null hypothesis.

Therefore, the potential error would be a Type II error, as the null hypothesis may be true but erroneously accepted. Therefore the option a is correct answer of the question.

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Answer:

The ratio between Roberto and David is 3:11

Step-by-step explanation:

If Roberto were to have 18 cards when we start, then David would have 24. Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio of Roberto's cards to David's cards will be 3:11.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The number of Roberto's baseball cards is 3/4 the number of David's cards. If Roberto gives 1/2 of his cards to David.

If Roberto were to have 18 cards when we start, then David would have 24.

Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio between Roberto and David is 3:11

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The direction of Beatriz relative to the starting point of her trip is approximately \(278.806^{\circ}\).

After a careful reading of the statement, we find that final position (\(\vec r\)) by the end of the second day is found by means of this vector sum:

\(\vec r = \vec r_{1} + \vec r_{2}\) (1)

Where:

If we know that \(\vec r_{1} = (200\,km \cdot \cos 300^{\circ}, 200\,km\cdot \sin 300^{\circ})\) and \(\vec r_{2} = (150\,km\cdot \cos 250^{\circ}, 150\,km\cdot \sin 250^{\circ})\), then final position of Beatriz relative to origin is:

\(\vec r = (200\,km\cdot \cos 300^{\circ}, 200\,km\cdot \sin 300^{\circ})+(150\,km \cdot \cos 250^{\circ}, 150\,km\cdot \sin 250^{\circ})\)

\(\vec r = (48.670, -314.159)\,[km]\)

And the direction relative to the starting point (\(\theta\)), in degrees, is found by following inverse trigonometric relation:

\(\theta = \tan^{-1} \frac{r_{y}}{r_{x}}\) (2)

If we know that \(r_{x} = 48.670\,km\) and \(r_{y} = -314.159\,km\), then the direction of Beatriz relative to the starting point of her trip is:

\(\theta = \tan^{-1} \left(\frac{-314.159\,km}{48.670\,km} \right)\)

\(\theta \approx 278.806^{\circ}\)

The direction of Beatriz relative to the starting point of her trip is approximately \(278.806^{\circ}\). \(\blacksquare\)

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Answer:

Step-by-step explanation:

h × b × \(\frac{1}{2}\) = A   (this is the formula)

2 × 3 × \(\frac{1}{2}\) =  3m²

I believe you forgot to mention some information...but hope this helps...

To prove that in a collection of 51 integers there is a subset of 11 where the difference of two of them is a multiple of 5, we can use the Pigeonhole Principle.

Consider the residues of the integers modulo 5, which can take values from 0 to 4. Let's assume that none of the 51 integers has a difference that is a multiple of 5. In other words, no pair of integers in the collection has a difference that leaves a residue of 0 when divided by 5.

Now, we can divide the 51 integers into five subsets based on their residues modulo 5. Each subset will contain the integers with the corresponding residues 0, 1, 2, 3, or 4.

Since we have 51 integers and only five possible residues, by the Pigeonhole Principle, at least one of the subsets must contain at least 51 / 5 = 10 + 1 = 11 integers. Let's assume, without loss of generality, that the subset with residue 0 contains 11 or more integers.

Within this subset, any pair of integers will have a difference that leaves a residue of 0 when divided by 5. Hence, we have found a subset of 11 integers where the difference of two of them is a multiple of 5.

Therefore, we have proved that in a collection of 51 integers, there is always a subset of 11 where the difference of two of them is a multiple of 5.

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Answer:

110 cards were sold on Mother's Day

Step-by-step explanation:

Bob's gift shop sold 20% of all the cards sold on Mother's Day.

Let the number of cards sold on Mother's day be m

Bob sold 20% of m or 0.2m

We know that 0.2m is 22, so now we can solve for m

110 cards were sold on mothers day

Note

We know that 0.2 is 1/5, so instead of dividing each side by 0.2, we could have multiplied both sides by 5

-Chetan K

(a)   AX=B

      2x - y + 3z = 4

      3x + 4y - 5z = 2

       x - 2y + z = -1

(b)   A^−1 = [9/25 1/25 14/25; -1/5 3/20 1/4; -2/25 -1/25 3/25]

(c)   X = [2; -1; 1]

(a) The matrix equation for the given system AX=B is:

2x - y + 3z = 4

3x + 4y - 5z = 2

x - 2y + z = -1

The coefficient matrix A is:

A = [2 -1 3; 3 4 -5; 1 -2 1]

The variable matrix X is:

X = [x; y; z]

The constant matrix B is:

B = [4; 2; -1]

(b) The inverse of matrix A is:

A^−1 = [9/25 1/25 14/25; -1/5 3/20 1/4; -2/25 -1/25 3/25]

(c) The solution to the matrix equation is:

X = A^−1B

X = [9/25 1/25 14/25; -1/5 3/20 1/4; -2/25 -1/25 3/25] * [4; 2; -1]

X = [2; -1; 1]

The given system of equations can be represented as a matrix equation AX=B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. The inverse of matrix A can be found using various methods, and it is denoted by A^−1. Finally, the solution of the matrix equation can be found by multiplying the inverse of A with B, i.e., X=A^−1B. In this case, the solution matrix X is [2; -1; 1].

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Answer:

120

Step-by-step explanation:

10 choose 3

theres really no simple way to do that with work unless you have a fancy calculator.

Answer:

It is 63 or 63/1. Billy used change in x over change in y, and the correct formula for slope is the change in y over the change in x.

He might have done it backwards.

1/63

and could be 63 miles in 1 hour

63/1.

Because the graph looks good. (i think)

a. Income tax is the amount of money that an individual is required to pay to the government based on their income.

b. Ramesh's total income in 13 months, including the festival expense, is found as Rs 593,857.

c.   Ramesh's annual income tax, considering the investment in citizens' investment fund, is Rs 85,000.

a. Income tax is described as the amount of money that an individual is required to pay to the government based on their income.  found  using a specific tax rate applied to different income brackets.

b.

Monthly income = Salary + Dearness allowance

= Rs 43,689 + Rs 2,000

= Rs 45,689

Total income for 13 months = Monthly income * 13

= Rs 45,689 * 13

= Rs 593,857

c.

Total income after deducting citizens' investment fund = Total income - Investment amount

= Rs 593,857 - Rs 2000

= Rs 591,857

Hence, the income tax based on the revised total income is:

Tax for income upto 5 lakh which is 1% of the income

= 0.01 * 500000

= Rs 5,000

Tax for income from 5-7 lakh which is the 10% of the income

= 0.1 * 200000

= Rs 20,000

The Tax for income from 7-10 lakh: 20% of the income

= 0.2 * 300000

= Rs 60,000

The Tax for income from 10-20 lakh is 30% of the income

= 0.3 * 0

= Rs 0

The total income tax = Rs 5,000 + Rs 20,000 + Rs 60,000 + Rs 0 + Rs 0

= Rs 85,000

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The tulip bed's area is a portion of the rose bed's territory. To determine this proportion, multiply the result by 100 after dividing the tulip bed's area by the rose bed's area.

One must first measure the size of each bed in order to determine the proportion of the tulip bed's area to the rose bed's area. The length and width of a bed are measured, and then these two dimensions are multiplied together to determine the area of the bed. Divide the size of the tulip bed by the size of the rose bed once the areas of each bed are known. You will receive the decimal value of the proportion of the tulip bed's area to the rose bed's area as a result. Divide the decimal amount by 100 to get the percentage itself. You will then be given the proportion of the tulip bed's area to the rose bed's area.

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The complete question is

The area of the tulip bed is what percent of the area of the rose bed territory.

Answer:

the answer is c I believe

Step-by-step explanation:

5(10) 50 + 25 is 75 equals 25 and 10 + 5 is 15 so 75 + 15 is 90. so the answer is c

The sizes large and small, are 8 and 6, respectively.

If everyone receives the same number of slices and the pizza is agreed upon by everybody, then each individual will receive 5/8ths of the total number of slices on the pizza. Depending on the size of the pizza and the eatery, that number may vary.

Large is 12 slices at a size of 7.5.

Medium is 8 slices or 5 per slice.

6 thin slices for $3.75 each

Individual Pan 4 slices, each at 2.5

very large 10 slices = $6.25 apiece

We've already reviewed the sizes large and small, which are 8 and 6, respectively.

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The full question:

There are 5 pizzas and 8 people how many slices do they get each?

Answer:

21, 9

Step-by-step explanation:

If girls are x, then boys are x + 12

x + x + 12 = 30

2x + 12 =  30

2x = 18

x = 9

There are 9 girls and 21 boys