Write the quadratic equation in factored form
x 2 + x - 12 = 0

The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10

Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.

By question-

The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.

In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows

Income plainness = chance change in volume demanded/ chance change in income

The chance change in volume demanded is

( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200

The chance change in income is 20

thus, the income plainness of demand for eatery reflections is

Income plainness = 200/ 20 = 10

Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.

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Answer:

1/2

Step-by-step explanation:

When you roll a 6-sided die, there are 6 possible outcomes:

1, 2, 3, 4, 5, 6

3 of the outcomes are even, and 3 of the outcomes are odd.

p(A) = p(even) = 3/6 = 1/2

p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2

The function that models the independent variable, x, in terms of y, is:

\(x = ln(\frac{y}{2.56})/ln(1.04)\)

Here we have the relation:

\(y = 2.56*(1.04)^x\)

We want to write x in terms of y, so we just need to isolate x.

We have:

\(\frac{y}{2.56} = (1.04)^x\)

Now we can apply the natural logarithm in both sides, so we get:

\(ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x\)

Now we can just isolate x.

\(x = ln(\frac{y}{2.56})/ln(1.04)\)

That is the function that models the independent variable, x, in terms of y.

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Answer:

14 squared

Step-by-step explanation:

Answer:

amor no te enojes conmigo hacienda

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

To find the perimeter of an isosceles trapezoid, follow these steps:

1. Identify the given measurements: In an isosceles trapezoid, know the lengths of the two parallel sides (the bases) and the two non-parallel sides (the legs).

2. Add the lengths of the bases: Add the lengths of the two parallel sides (bases) of the trapezoid.

3. Multiply the sum by 2: Multiply the sum from step 2 by 2 to account for both sides of the trapezoid.

4. Add the lengths of the legs: Add the lengths of the two non-parallel sides (legs) of the trapezoid.

5. Add the results: Add the results from steps 3 and 4 to find the perimeter of the isosceles trapezoid.

Mathematically, the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

Alternatively, know the lengths of all four sides of the trapezoid, simply add them together to find the perimeter.

Keep in mind that the measurements used in the formula should be in the same unit (e.g., centimetres, inches) for accurate results.

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Answer:

Step-by-step explanation:

P = a + b + 2c

where a is the top, b is the bottom, and c is a leg of the trapezoid. The perimeter is the sum of the outer edge of the shape, so you just need to add the lengths of the sides.

The least number of trips that Ava must make in order to deliver 250 cartons of books is 10 trips.

The least number of trips that Ava must make in order to deliver 250 cartons of books can be found by dividing the total number of cartons by the number of cartons that her car can hold per trip.

This can be written as:
Least number of trips = Total number of cartons / Number of cartons per trip

Substituting the given values into the equation, we get:
Least number of trips = 250 cartons / 26 cartons
Least number of trips = 9.62

Since Ava cannot make a fraction of a trip, we need to round up to the nearest whole number. Therefore, the least number of trips that Ava must make in order to deliver 250 cartons of books is 10.

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The pseudoinverse is a generalized inverse of a matrix, denoted by A+. To prove the properties of the pseudoinverse, we first need to verify that the given matrix satisfies the Penrose conditions, which are:

1. AA+A = A
2. A+A A = A+
3. (AA+)T = AA+
4. (A+A)A = A+A

Once we have verified that these conditions are satisfied, we can then proceed to prove the properties of the pseudoinverse. These properties include:

1. AA+A is symmetric and idempotent
2. A+A is symmetric and idempotent
3. AA+A is the unique matrix that satisfies the Penrose conditions
4. A+A is the unique matrix that satisfies the Penrose conditions
5. If A has full column rank, then A+A = (AA)−1

To summarize, in order to prove the properties of the pseudoinverse, we need to first verify that the given matrix satisfies the Penrose conditions. Once we have done that, we can then proceed to prove the various properties of the pseudoinverse, which include its symmetry, idempotency, uniqueness, and relation to the original matrix.
. In this case, we will verify that the given matrix satisfies the four Penrose conditions.

Let A be an arbitrary matrix and B be its pseudoinverse. We need to prove the following properties:

1. AB = A
2. BA = B
3. (AB)A = A
4. (BA)B = B

Step 1: AB = A
To prove this property, we need to multiply matrix A by its pseudoinverse B. By definition, the pseudoinverse is a unique matrix B that satisfies this property. Since the Penrose conditions require this equality, it holds true.

Step 2: BA = B
Similar to Step 1, we need to multiply matrix B by A. The pseudoinverse definition and Penrose conditions require that the product of BA should equal B, so this property is also satisfied.

Step 3: (AB)A = A
We already know that AB = A (from Step 1). Now, we need to multiply the result (AB) by A again. Since AB = A, this simplifies to AA = A. For this property to be satisfied, A must be an idempotent matrix, meaning that A*A = A. The pseudoinverse ensures this property is true by definition and according to the Penrose conditions.

Step 4: (BA)B = B
Similar to Step 3, we know that BA = B (from Step 2). Now, we need to multiply the result (BA) by B. Since BA = B, this simplifies to BB = B. The pseudoinverse ensures this property is true by definition and according to the Penrose conditions.

By verifying that the given matrix satisfies all four Penrose conditions, we have proved the properties of the pseudoinverse.

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In the research question, the explanatory variable is "drinking espresso in the afternoon," which refers to the factor or condition that researchers manipulate or observe. It represents the potential cause or influencing factor being studied.

The response variable, on the other hand, is "headaches," which refers to the outcome or behavior that researchers are interested in understanding or measuring. It represents the effect or result that is expected to be influenced by the explanatory variable.

Therefore, in this research question, the explanatory variable is "drinking espresso in the afternoon," and the response variable is "headaches." The researchers are investigating whether there is a relationship between drinking espresso in the afternoon (explanatory variable) and experiencing headaches (response variable).

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Answer:

\( - \frac{1}{2} ( - 6x + 8y) \\ = \frac{1}{2} (6x - 8y) \\ = 3x - 4y\)

Answer:

3:2

Step-by-step explanation:

The ratio of boys to girls will be 12:8

But, this can be simplified, since both numbers are divisible by 4.

12/4 = 3

8/4 = 2

So, the simplified ratio of boys to girls is 3:2

Answer:

3:2

Step-by-step explanation:

Answer: 41 degrees

Step-by-step explanation:

so, we know that a triangle is 180 degrees. since we know that one angle is 80 degrees, we can subtract that from the equation. now, we are trying to find what X is so that we can find the angle. here is how i did it:

i rewrote it and removed the parentheses.

4x + 1 + 4x + 19 = 100

then, i collected like terms and calculated it.

8x + 20 = 100

then, i moved the constant to the right.

8x = 100 - 20

then, i simply calculated it.

8x = 10

solution: x = 10

so, we just insert X into the angle for A. that gets us 4(10) + 1 = angle A

40 + 1 = angle A, hence angle A = 41 degrees.

Answer: hope this helps I guess?

Step-by-step explanation:

The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.

We are given the vector-valued function r(t) = (4t, 3t², 4t³).

To find r'(t), we need to take the derivative of each component of r(t) with respect to t:

r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)

r'(t) = (4, 6t, 12t²)

To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):

r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)

| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14

T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)

To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:

r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)

r''(t) = (0, 6, 24t)

Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):

r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)

r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)

r'(t) ร r''(t) = 144t³

Therefore, we have:

r'(t) = (4, 6t, 12t²)

T(1) = (2/7, 3/7, 6/7)

r''(t) = (0, 6, 24t)

r'(t) ร r''(t) = 144t³

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There are 15,120 ways to distribute the first, second, third, and two fourth prizes among the five different people in the group of nine.

To determine the number of ways to distribute the prizes, we can break down the process step by step: First Prize: There are 9 people in the group, and one of them can be chosen for the first prize. So there are 9 options for the first prize. Second Prize: After the first prize has been awarded, there are 8 remaining people who can be chosen for the second prize. So there are 8 options for the second prize. Third Prize: After the first and second prizes have been awarded, there are 7 remaining people who can be chosen for the third prize. So there are 7 options for the third prize.

Fourth Prizes: There are two fourth prizes to be given. After the first three prizes have been awarded, there are 6 remaining people. The first fourth prize can be given to any one of them, leaving 5 people for the second fourth prize. So there are 6 options for the first fourth prize and 5 options for the second fourth prize. Multiplying the number of options for each step together: Total number of ways = 9 * 8 * 7 * 6 * 5 = 15,120 . Therefore, there are 15,120 ways to distribute the first, second, third, and two fourth prizes among the five different people in the group of nine.

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Answer: 6.89 per pound (assuming you meant which is the better deal)

Step-by-step explanation:

There are 16 ounces in a pound so you can multiply, 3.5 x 2 (since it is 3.5 for 8 ounces) to get 7. Therefore $6.89 for a pound is cheaper.

Answer:

Line up the numbers on the right - do not align the decimal points.

Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.

Add the products.

Step-by-step explanation:

Answer:

like up the numbers on the right

Step-by-step explanation:

multiply as if you were multiplying regularly up and down then bring down the decimal point after

Answer:

4/35x5/16=1/7x1/4=1/28 the final answer is1/28

Answer:

simplify: 7x^2+9x-3

It is equal to 32y+32 if you wanted to simplify it.

Answer:

32y + 32

Step-by-step explanation:

8 × 4y + 8 × 4

Answer:

-50 m

Step-by-step explanation:

its negative elevation because he is going down

The radius of convergence of the given series is infinity.

To find the radius of convergence, we use the ratio test, which involves computing the limit of the ratio of successive terms. Applying the ratio test to the given series, we get:

limit as n approaches infinity of [((n+1)!)^k/(k(n+1))!][k!/(n!)^k][x^(n+1)][(kn)!/k!][n!/(kn)!]*[x^n]

Simplifying the expression, we get:

limit as n approaches infinity of [(n+1)/(kx)]*|x|

Since the limit is infinity, the radius of convergence is infinity. This means that the series converges for all values of x.

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The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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The minimum score needed is 538.

To find the minimum score needed to get into ABC University, we need to determine the score that corresponds to the top 2.5% of the distribution.

First, we need to find the Z-score corresponding to the top 2.5% of the distribution. The Z-score represents the number of standard deviations a value is away from the mean in a normal distribution.

Using a standard normal distribution table or calculator, we can find that the Z-score corresponding to the top 2.5% is approximately 1.96 (rounded to two decimal places).

Next, we can use the formula for Z-score to find the minimum score:

Z = (X - μ) / σ

Where:

Z is the Z-score,

X is the score we want to find,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

Rearranging the formula to solve for X:

X = Z * σ + μ

Plugging in the values:

X = 1.96 * 36 + 467

Calculating the result:

X ≈ 71.04 + 467 ≈ 538.04

Rounded to the nearest whole number, the minimum score needed to get into ABC University is approximately 538.

Therefore, the minimum score needed is 538.

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