(X^3+x^2+x+2)/(x^2-1)

The equation for the parabola with a focus at (-4,3) and a directrix at y=5 in terms of y is y = (-1/8)x² - x/8 + 6.

The vertex of the parabola is the midpoint between the focus and directrix, which is (−4, 4).

Since the directrix is a horizontal line, the parabola will open downward.

Using the distance formula, the distance between a point (x, y) on the parabola and the focus (-4, 3) is equal to the distance between the point and the directrix y = 5.

√((x + 4)² + (y - 3)²) = |y - 5|

Squaring both sides yields:

(x + 4)² + (y - 3)² = (y - 5)²

Expanding the squares and simplifying, we get:

x² + 8x + 16 = -8y + 64

Rearranging terms, we have:

8y = -x² - 8x + 48

Dividing by 8, we get the equation of the parabola in terms of y:

y = (-1/8)x² - x/8 + 6

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Answer:

To find the value of a5, we need to know the formula for the nth term of the sequence. We know that a1 = 2, so we can start by finding the common difference (d) between consecutive terms. an-1 + 5 = a1 + (n-2)d + 5 Simplifying this equation, we get: an-1 = a1 + (n-2)d Substituting a1 = 2, we get: an-1 = 2 + (n-2)d We also know that a5 is the 5th term of the sequence, so n = 5. Substituting n = 5, we get: a4 = 2 + (5-2)d a4 = 2 + 3d We don't have enough information

the area of section A, which has side lengths of 7 inches each.

To determine the area, we will use the following terms:

Area = Side length × Side length

Area = 7 inches × 7 inches

7 inches × 7 inches = 49 square inches

So, the area of section A is 49 square inches (OA).

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17-x

Because he sends more than you we subtract your value,x,from his 17,mostly because we are unaware of the number of texts you send.Which means 17 minus x will give you the amount of texts he sends more.

Answer:

14

Step-by-step explanation:

A = length x width

l = length

w = 3l + 2

A = l(3l + 2) = 56

3l² + 2l - 56 = 0

Now you have a polynomial you can solve by factoring or using the quadratic equation to find the 2 roots of l:

using the quadratic equation with a = 3, b = 2, c = -56

l = 4, -14/3

Disregarding the negative root,

l = 4

Therefore, w = 3(4) + 2 = 14

Answer:

The probability of the coin landing heads up on any given flip is 1/2, and the probability of it landing tails up is also 1/2. Therefore, we can use the binomial distribution formula to calculate the probability of getting exactly 27 heads out of 90 flips: P(27 heads) = (90 choose 27) * (1/2)^27 * (1/2)^63 = 1.452 x 10^-9 So the probability of getting exactly 27 heads out of 90 flips is approximately 1.452 x 10^-9.

is would be 50 percent! you're welcome

Based on the given information, Mike's grandmother deposited $6,000 into the savings account.

What is simple interest?

Simple interest is a method of calculating interest on a principal amount, where the interest is calculated only on the original amount of the loan or investment, without taking into account any interest that may have been previously earned. The formula for calculating simple interest is I = P * r * t, where I is the interest earned, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.

We are given that the interest rate is 8% and the interest earned after 10 years is $4,800. So we can write:

4,800 = P * 0.08 * 10

Simplifying the equation, we get:

4,800 = 0.8P

Dividing both sides by 0.8, we get:

P = 6,000

Therefore, Mike's grandmother deposited $6,000 into the savings account.

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Answer:

Step-by-step explanation:

A dilation maintains the shape of a figure but changes its size.

A reduction would mean the new figure will be a smaller version of the original.

An enlargement would mean the new figure will be a bigger version of the original.

This particular question doesn’t include a photo so depending on these definitions, one can easily identify the correct answer.

Answer:

In geometry, a dilation is a transformation that changes the size of a figure while keeping its shape the same. Imagine taking a picture of a shape and then making it bigger or smaller without changing its proportions or angles.

If a dilation makes the figure smaller than the original, we call it a reduction. This means that the new figure is a scaled-down version of the original. Conversely, if a dilation makes the figure larger, we call it an enlargement. In this case, the new figure is a scaled-up version of the original.

So, to summarize, dilations can change the size of a figure while preserving its shape, and we can describe the resulting figure as either a reduction or an enlargement depending on whether it is smaller or larger than the original.

Step-by-step explanation:

To find the length of the hypotenuse of a right triangle, we need to use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, we have two sides with lengths given by the expressions 5x + 7 and 3x. When x = 14, we can substitute this value into the expressions to find the lengths of the sides:

a = 5x + 7 = 5(14) + 7 = 77

b = 3x = 3(14) = 42

Now we can use the Pythagorean Theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2 = 77^2 + 42^2 = 5929 + 1764 = 7693

Taking the square root of both sides, we get:

c = sqrt(7693) ≈ 87.7

Therefore, when x = 14, the length of the hypotenuse of the triangle is approximately 87.7 units. I

The mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

So, we've said the:

12$ =1hours

initial forty hours a week

Then after a week, 18 dollars per hour.

We must ascertain the function that represents Bailey's income.

Then, the formula for regular earnings:

regular hour × regular rate=regular eaning

40(12)=480$

overtime hours × overtime rate=overtime pay

Regular earning +overtime pay=total earnings

The overtime hours in this case are unknown.

Because of this, we are unable to determine total earnings.

Therefore, the mathematical function model for Bailey's income is: Regular earning +overtime pay=total earnings

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Correct question:
Each week, Bailey earns $12 per hour for the first 40 hours she works, and $18 for each hour of work after 40 hours. Her weekly earnings are a function of the amount of time she works.

Which function models the amount of money that Bailey earns?

Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.

To find the original price of the couch, we need to first understand what a 25% discount means.

A discount is a reduction in price from the original or regular price of an item. A discount is usually given as a percentage of the original price. For example, a 25% discount means that the price of an item has been reduced by 25% of its original price.

Let's use this information to solve the problem at hand.

Let x be the original price of the couch. The discount given is 25%, which means that the price paid by Mrs. Smith is 75% of the original price. Mathematically, we can write this as:

75% of x = R13 450.00

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 75% or 0.75 (which is the decimal equivalent of 75%).

75% of x / 0.75 = R13 450.00 / 0.75

x = R17 933.33 (rounded to the nearest cent)

Therefore, the original price of the couch was R17 933.33.

In conclusion, Mrs. Smith paid R13 450.00 for a couch that originally cost R17 933.33. This means that she received a discount of R4 483.33, which is 25% of the original price.

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The difference between t-distribution T0 and t0 is nothing, They are the same thing option B.

The central limit theorem explains the connection between the original population and the sampling distribution of means. Keep in mind that we must first determine the variance of the original population if we are to determine the variance of the sampling distribution.

A point estimate of the mean may be calculated without knowing the variance of the sampling distribution, but other, more complex estimation methods demand that you either know or estimate the variance of the population.

If you stop and think for a second, you'll see that it seems bizarre to know the population's variance when you don't know the mean. As the population variance and standard deviation must be calculated, it is necessary to know the population mean.

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The nurse is responsible for giving Medication G in a quantity of 30 mL, which is approximately equivalent to 1.014 fluid ounces.

First, we need to convert 0.6 g to mg:

0.6 g = 600 mg

Next, we need to calculate how many mL are needed to deliver 600 mg of Medication G. From the label, we know that there are 100 mg of Medication G in 5 mL, so we can set up a proportion:

100 mg / 5 mL = 600 mg / x mL

Cross-multiplying, we get:

100x = 5 * 600

Simplifying, we get:

x = 30 mL

Finally, we can convert 30 mL to fluid ounces. There are 29.5735 mL in one fluid ounce, so:

30 mL / 29.5735 mL/oz ≈ 1.014 fl oz

Therefore, the nurse should administer 30 mL (or approximately 1.014 fluid ounces) of Medication G.

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a. To test whether the population mean daily number of texts for one age group differs from the population mean daily number of texts for another age group, we should use the following alternative hypothesis:
H1: μ1 ≠ μ2

b. To compute the p-value, we need to perform the following steps:
1. State the null hypothesis: H0: μ1 = μ2
2. Calculate the test statistic:
  t = (sample mean - hypothesized mean difference) / (population standard deviation / √n)
  Assuming the hypothesized mean difference is 0, and plugging in the given values:
  t = (sample mean - 0) / (population standard deviation / √30)
3. Find the p-value using a t-distribution table or calculator, and round to four decimal places.
c. If the p-value is less than the level of significance (α), we reject the null hypothesis and conclude that there is a significant difference in the population mean daily texts between the two age groups.

If the p-value is greater than or equal to α, we do not reject the null hypothesis and cannot conclude that there is a significant difference.
d. For the critical value approach, we compare the test statistic (t) with the critical value (±1.96).

If the test statistic falls in the rejection region (outside of ±1.96), we reject the null hypothesis and conclude that the population mean differs.

If the test statistic falls within the acceptance region (inside ±1.96), we do not reject the null hypothesis and cannot conclude that the population mean differs.

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The price that would generate more revenue for the company will be $5 because p(5) > p(17) based on the revenue generation on the graph.

As we change the price of the product, the quantity sold may also change. This means that the revenue curve will not be a straight line, but rather a curve that increases and then decreases as we move from lower to higher prices. The price point that generates the highest revenue will be the one at which the revenue curve reaches its maximum value.

It is important to note that the price point that maximizes revenue may not necessarily be the same as the price point that maximizes profit, as profit is influenced by both revenue and costs. Therefore, companies must carefully consider both revenue and cost factors when determining the optimal price point for their products.

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The discriminant shows that the volume will reach 2750 shares in 24.6 weeks, but will never reach 4000 shares in a week.

What is the volume of a company's stock and will it ever reach certain values using the given equation and discriminant?

To determine if the volume will ever reach a certain value, we need to solve the equation V = 250t - 5t^2 for t and see if there are any real solutions for t that satisfy the condition.

a) For V = 2750, we have:

2750 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 2750 = 0

Using the quadratic formula, we can find the solutions for t:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(2750))) / (2(5))

t = (250 ± sqrt(62500 - 55000)) / 10

t = (250 ± sqrt(7500)) / 10

t ≈ 24.6 or t ≈ 5.4

Since one solution is positive and the other is negative, the only solution that makes sense in this context is t ≈ 24.6 weeks. Therefore, the volume will reach 2750 shares in 24.6 weeks.

b) For V = 4000, we have:

4000 = 250t - 5t^2

Rearranging and simplifying, we get:

5t^2 - 250t + 4000 = 0

Using the discriminant, which is b^2 - 4ac in the quadratic formula, we have:

b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500

Because the discriminant is positive, there are only two possible solutions for t. Therefore, the volume will reach 4000 shares in a week at some point. However, we need to solve the equation to find the exact solutions:

t = (-(-250) ± sqrt((-250)^2 - 4(5)(4000))) / (2(5))

t = (250 ± sqrt(62500 - 80000)) / 10

t = (250 ± sqrt(-17500)) / 10

There are no real solutions for t that satisfy the condition because the square root of a negative number is not a real number. Therefore, the volume will never reach 4000 shares in a week.

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Answer:

The correct answer is D. Enough to feel rested.

Answer:

Step-by-step explanation:

Step 1: Substitute d for 75

|500-50t| - 75 = 0

Step 2: Move the constant to one side

|500-50t| = 75

Step 3: Separate the equation into two possible cases

500−50t=75

500−50t=−75​

Step 4: Solve the equation for t

t = 17/2 = 8.5

t = 23/2 = 11.5

Solution:

D: 8.5 seconds and 11.5 seconds

Answer:

x∈( -5; +∞)

Step-by-step explanation:

[tex]x > - 5[/tex]

[tex]x∈( - 5;+ ∞)[/tex]

We predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25°F on the basis of the line of best fit.

Intercept is the point on the graph where the line crosses the x-axis or the y-axis. This point is calculated by solving the equation of the line for the given axis. It is used to determine the relationship between two variables.

To predict the number of hot cocoas to be sold at 25° Fahrenheit, we need to use the line of best fit equation.

The equation of the line of best fit can be determined by calculating the slope and y-intercept of the line and then using the point-slope form of a line.

The slope of the line can be calculated using the formula

m = (y₂-y₁) / (x₂-x₁)

For this graph, the slope can be calculated as

m = (104-94) / (12-0)

= 10/12

= 0.83

The y-intercept of the line can be calculated using the formula y = mx + b, where m is the slope and b is the y-intercept.

For this graph, the y-intercept can be calculated as

b = 104 - 0.83(12)

= 94.04

Therefore, the equation of the line of best fit is y = 0.83x + 94.04

Substituting the given temperature, 25°F into the equation, we get

y = 0.83(25) + 94.04

= 114.79 hot cocoas

Hence, based on the line of best fit, we predict that Dylan will sell 114.79 hot cocoas if the day's high temperature is 25 degree Fahrenheit.

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If your dependent variable is measured on a ratio scale, you should use statistical procedure of parametric test. The correct answer is D).

Parametric tests are statistical tests that assume a normal distribution of data and require interval or ratio scale measurements. Examples of parametric tests include t-tests, ANOVA, and linear regression. Non-parametric tests, on the other hand, do not assume a normal distribution of data and can be used for nominal, ordinal, interval, or ratio scale measurements.

Examples of non-parametric tests include the chi-square test for goodness of fit and the chi-square test for independence. However, these tests are not appropriate for ratio scale measurements, so you should use a parametric test. So, the correct option is D).

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--The given question is incomplete, the complete question is given

"what type of statistical procedure should you use if your dependent variable is measured on a ratio scale? select one:

A) chi-square test for goodness of fit

B) chi-square test for independence

C) non-parametric test

D) parametric test"--

Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows: a = 2500 × 0.6^(n-1) (n-1)

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given :

We can use the fact that each word is produced by multiplying the previous term by the common ratio r to determine the value of r. Thus:

1500/2500 = 0.6 = r

We can keep adding r to the preceding term to find the next two terms:

900 × 0.6 = 540

540 × 0.6 = 324

540 and 324 are the next two terms as a result.

Finally, using the first term a1 = 2500 and the common ratio r = 0.6, we can formulate the explicit rule for the sequence as follows:

a = a1 × r^(n-1) (n-1)

The clear rule is as follows: a = 2500 × 0.6^(n-1) (n-1).

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Answer:

To solve this problem, we need to first find the numbers that are multiples of 4 or 6 between 1 and 15, inclusive.

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The number 12 is a multiple of both 4 and 6, so we only count it once.

So, there are a total of 4 possible outcomes that meet the condition of being a multiple of 4 or 6.

Therefore, the probability of getting a multiple of 4 or 6 is:

P(multiple of 4 or 6) = 4/15

Answer: 4/15.

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The value of x is 45° for the Newton bounces a ball off of a wall to Descartes as shown in figure.

An angle that is exactly 90 degrees, or a quarter turn, is called a right angle. It is made up of two lines that are perpendicular to one another or line segments that cross at a point, forming four equal angles.



If we consider the figure below we can find some angles and AD is a Straight line;    (Refer the below figure 2)

⇒ ∠AOB + ∠BOC+ ∠DOC = 180°

⇒ x° + 90° + x° = 180°

⇒ 2x° = 180° - 90°

⇒ x° = 90°/ 2

⇒ x° = 45°

Therefore, the value of x is 45°

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Complete question-

According to the figure, x is 45° when Newton bounces a ball off of a wall and Descartes.

Right angles are angles that are exactly 90 degrees, or a quarter turn. It is composed of two parallel lines or line segments that cross at a place to produce four equal angles. It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

If we look at the graphic below, we can see that AD is a straight line and there are certain angles;

∠AOB + ∠BOC+ ∠DOC = 180°

x° + 90° + x° = 180°

2x° = 180° - 90°

x° = 90°/ 2

x° = 45°

Therefore, the value of x is 45°

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The complete question is attached below,

Answer: We can start by factoring the given expression for the area of the rectangle:

Area = 144x^2 - 81

Area = (12x)^2 - (9)^2

Area = (12x + 9)(12x - 9)

We can see that the area is expressed as the product of two binomials (12x + 9) and (12x - 9), which represent the length and width of the rectangle, respectively. Therefore:

Length = 12x + 9

Width = 12x - 9

Note that we can check that the product of the length and width indeed equals the area:

Length x Width = (12x + 9)(12x - 9) = 144x^2 - 81 = Area

So, the expressions for the dimensions of the rectangle are:

Length = 12x + 9

Width = 12x - 9

Step-by-step explanation:

Answer:

81 eggs

Step-by-step explanation:

already had 9 eggs

6 crates x 12 eggs in each crate

= 72 eggs

72+9=81

Answer: (c) 0

Step-by-step explanation:There is no variable x involved, so we can say that this polynomial is of degree 0.

Polynomial as having a constant term of 5 and no other terms involving x.

If p(x)=x^5 then degree of polynomial is 5

degree of polynomial = highest degree of x

Answer:

Step-by-step explanation: