Mrs. Sage will print a copy of the class alphabet book for each student. The book is formatted in1/2 pages with a title page, a page for each letter and an end page. If there are 70 students, how many reams of paper will Mrs. Sage need for the books?

Final answer:

The original equation, after multiplication and simplification, results in -10x^2y^2 - 16y^2 + 8x^-1y^3. This process demonstrates the use of the distributive property and exponent rules in algebra.

Explanation:

The question requires us to multiply -2x-3y by (5yx5+8xy-4y2x2). Proceed by applying the distributive property, which involves multiplying each term inside the parentheses by -2x-3y. Here are the steps:

Multiply -2x-3y by 5yx5 to get -10x2y2.

Multiply -2x-3y by 8xy to get -16y2.

Multiply -2x-3y by -4y2x2 to get 8x-1y3.

Therefore, the final result of the multiplication is -10x2y2 - 16y2 + 8x-1y3.

The result is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

To multiply [tex]\(-2x^{-3} y\) by \(5yx^5 + 8xy - 4y^2x^2\)[/tex], we distribute [tex]\(-2x^{-3} y\)[/tex] to each term inside the parentheses.

[tex]\[ -2x^{-3} y (5yx^5) + (-2x^{-3} y)(8xy) + (-2x^{-3} y)(-4y^2x^2) \][/tex]

Simplify each term:

[tex]\[ = -10yx^2 + (-16)x^{-2}y^2x + 8x^{-1}y^3 \][/tex]

[tex]\[ = -10yx^2 - \frac{16y^2}{x^2} + 8x^{-1}y^3 \][/tex]

[tex]\[ = -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex]

Thus, the final result of the multiplication is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

This expression cannot be further simplified, as it represents the result of multiplying each term in the first expression by each term in the second expression and then combining like terms.

Therefore, the correct option is B. [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].

Complete Question:

Answer:

The inequality would be r/7 ≤ 18 and the solution would be r ≤ 126

Step-by-step explanation:

We start by writing the inequality

r/7 ≤ 18

We know to use division between r and 7 since it asks for the quotient and we know to use a ≤ sign since it says "is no more than"

To solve, simply multiply both sides by 7

r ≤ 126

The inequality will be r/7 ≤ 18

Since it's a quotient, we'll need to divide the expression and this will be:

= r/7 ≤ 18

Now the value of r will be gotten thus:

r/7 ≤ 18

Cross multiply.

r ≤ 18 × 7

r ≤ 126

Therefore, this mean that the value of r will be 126 or numbers lower than 126

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The measurement of ∠y = ∠DBC will be 40°.

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given is ∠ABC = 110°

Let ∠ABD = x , ∠DBC = y, ∠CBE = z

∠ABD + ∠DBC + ∠CBE = 180°

x + y + z = 180°

and

∠ABD + ∠DBC = 110°

x + y = 110°

Then -

z = 180° - (x + y)

z = 180 - 110

z = 70°

Since DB and EC are equally inclined -

x = z = 70°

Then -

x + y = 110°

y = 110° - 70°

y = 40°

Therefore, the measurement of ∠y = ∠DBC will be 40°.

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0-9 = 10 numbers

 1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10 * 9 *8*7 = 5040 different combinations

The number of different possible passwords are possible

Given that each digit can be used once, then:

So, the number of passwords is:

n = 10 * 9 * 8 * 7

Evaluate the products

n = 5040

Hence, there are 5040 different possible passwords

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To convert 1559 cm to inches, divide by 2.54, and the result should be reported with the same number of significant figures as the given measurement, which is four. Thus, 1559 cm is equal to 613.8 inches.

To convert 1559 cm to inches using the conversion factor 1 inch = 2.54 cm, we divide 1559 by 2.54. The number 1559 has four significant figures because all non-zero digits are considered significant. Since the conversion factor 2.54 cm per inch is exact and does not limit the number of significant figures, the result should also be reported with four significant figures.

The calculation would be as follows:

Answer:

1,802,862.

Step-by-step explanation:

We have been given that the population of state is 1,821,000 decreasing by 0.2% every year. We are asked to find the population of state after 5 years.

We will use exponential decay function to solve our given problem.

[tex]y=a\cdot b^x[/tex], where,

y = Amount left after x years,

a = Initial amount,

b = For decay b is in form (1-r) where r represents decay rate in decimal form.

x = Number of years.

Let us convert our given rate in decimal form.

[tex]0.2\%=\frac{0.2}{100}=0.002[/tex]

Upon substituting our given values in above formula we will get,

[tex]y=1,821,000 \cdot(1-0.002)^5[/tex]

[tex]y=1,821,000 \cdot(0.998)^5[/tex]

[tex]y=1,821,000 \cdot 0.990039920079968[/tex]

[tex]y=1,802,862.69[/tex]

Since we can not have 0.69 of a person, therefore, we will round down our answer.

[tex]y=1,802,862.69\approx 1,802,862[/tex]

Therefore, the population of state after 5 years will be 1,802,862.

Answer:

B) −4

Step-by-step explanation:

The correct transformation that preserves the size and shape of an object, resulting in congruent images, is an isometric transformation. Examples include translation, rotation, and reflection, all of which maintain the object's proportions and dimensions.

A transformation that preserves the size and shape of an object's original image, such that the image is congruent to the pre-image, is known as an isometric transformation. This transformation includes operations like translation (a shift from one place to another), rotation (turning around a center), and reflection (flipping over a line). All these transformations keep the object's dimensions and proportions unchanged. The key property of isometric transformations is that they maintain congruency and preserve distances and angles.

An example of an isometric transformation is when a square is rotated 90 degrees around its center. The square's shape and size remain the same, even though its orientation has changed. This contrasts with dilation, which changes the size of the object, and affine transformations, which can alter both shape and size, such as through stretching or skewing. The correct answer to the student's question is B. isometric.

A) f(x) = 15x + 25; f(6) = 115

We are given the equation:

sin θ = 3 / 4

To find for the value of θ, simply compute using the calculator:

θ = sin^-1 (3 / 4)

θ = 48.60° = θ1

To find for the other value, subtract the answer from 180°, so:

θ2 = 180° - 48.60°

θ2 = 131.40°

So the angles are 48.60° and 131.40°

The angles θ for which sin(θ) equals 3/4 between 0° and 180° are approximately 48.6° and 131.4°.

The student's question relates to the topic of trigonometry. Specifically, finding the angles θ for which the sine equals 3/4. To answer this, in the first quadrant, we can use the arcsin function to get θ = arcsin(3/4). Using a calculator, θ ≈ 48.6°. In the second quadrant, the sine is still positive, so θ = 180° - arcsin(3/4) ≈ 131.4°. Thus, the solution is 48.6°, 131.4°. It's worth noting that using a calculator's arcsin function usually gives a result in the first quadrant (0° - 90°) so we have to calculate the second quadrant angle ourselves.

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Answer: Carbon occurs as a solid, liquid, and gas.

Carbon is found everywhere.

Carbon is versatile and easily combines with other elements.

Carbon bonds with other elements to form macromolecules.

Answer:

C. Circumcenter.

Step-by-step explanation:

We have been given an image of a triangle KLM  and we are asked to choose the term that describes point N.

We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.

Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM nad option C is the correct choice.  

1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]

2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]

- Independent probability: This is the probability of two events occurring together, assuming that one event's occurrence does not affect the other. Mathematically, if A and B are independent events, then [tex]\( P(A \cap B) = P(A) \times P(B) \).[/tex]

- Conditional probability: This is the probability of an event occurring given that another event has already occurred. Mathematically, if A and B are events with[tex]\( P(B) > 0 \)[/tex], then the conditional probability of A given B is [tex]\( P(A|B) = \frac{P(A \cap B)}{P(B)} \).[/tex]

Let's illustrate these concepts with an example:

Suppose we have a deck of cards (52 cards total), and we're interested in two events:

A: Drawing a red card

B: Drawing a queen

First, let's find the independent probabilities:

1. Probability of A (drawing a red card):

  - There are 26 red cards out of 52 total cards, so [tex]\( P(A) = \frac{26}{52} = \frac{1}{2} \).[/tex]

2. Probability of B (drawing a queen):

  - There are 4 queens out of 52 total cards, so[tex]\( P(B) = \frac{4}{52} = \frac{1}{13} \).[/tex]

Now, let's find the probability of both events occurring together (A and B):

3. Probability of A and B (drawing a red queen):

  - There are 2 red queens (hearts and diamonds) out of 52 total cards, so [tex]\( P(A \cap B) = \frac{2}{52} = \frac{1}{26} \).[/tex]

For independent events,[tex]\( P(A \cap B) = P(A) \times P(B) \):[/tex]

[tex]\[ \frac{1}{26} = \frac{1}{2} \times \frac{1}{13} \][/tex]

Now, let's find the conditional probability of A given B:

[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{26}}{\frac{1}{13}} = \frac{1}{2} \][/tex]

1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]

2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]

In summary, we first calculated the independent probabilities of A and B, then found the probability of A and B occurring together, and finally calculated the conditional probability of A given B using the given formulas and calculations.v

complete question

how can you interpret the independent or conditional probability of two events

Complementary angles add up to 90 degrees. Angle b can be found by subtracting the measure of angle a from 90 degrees.

The question states that angle a and angle b are complements, and that the measure of angle a is 36 degrees. In mathematics, complementary angles are two angles whose measures add up to 90 degrees. So, if angle a is 36 degrees, angle b can be found by subtracting 36 from 90, which gives us 54 degrees. Therefore, angle b is 54 degrees.

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$27 / 4 = 6.75 dollars per hour

4 / 24 = 0.148 = 0.15 hours per dollar

Answer is A