Let g(x.y)= 15x2 +2y2. Compute g(3,3), g(0,-2), and g(a,b). g(3,3)= _____

For given equation x = (-b ± √(b²-4ac))/2a the equation in the form c= is: c = -x²(a/b) - x.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.

What is goal of equation?

The goal of solving an equation is to determine the value or values of the variable that make the equation true. Equations are used extensively in mathematics and science to describe relationships between quantities and to solve problems.

Starting with the equation:

x = (-b ± √(b²-4ac))/2a

We can simplify and rearrange it to the form c= as follows:

Multiply both sides by 2a to get rid of the denominator:

2a x = -b ± √(b²-4ac)

Add b to both sides:

2a x + b = ± √(b²-4ac)

Square both sides:

(2a x + b)² = b² - 4ac

Expand the left side:

4a² x² + 4abx + b² = b² - 4ac

Simplify:

4a² x² + 4abx = -4ac

Divide both sides by 4a:

x² + bx/a = -c/a

Rearrange to the form c=:

c = -x²(a/b) - x

Therefore, the equation in the form c= is:

c = -x²(a/b) - x

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. 0.587 in scientific notation is 5.87 x 10^-1.

Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.

For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.

Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.

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The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

We have to given that;

Parallel lines EN, BH, and RK, with transversal PW are shown.

And, m ∠ BMV = 108° and m ∠KVS = 72°

Now, We get by definition of vertically opposite angle;

m ∠ BMV = m ∠PWN = 108°

Hence, By definition of alternate angle we get;

⇒ m ∠PWN = m ∠WPN = 108°

Thus, The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

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The y-values that a function approaches when the x-values are extremely large or extremely small is called the function's asymptotic behavior.

When we talk about the asymptotic behavior of a function, we are referring to what happens to the values of the function as the input (x-values) either tends to positive infinity or negative infinity.

In other words, we are interested in how the function behaves when the input values become extremely large or extremely small.

To understand asymptotic behavior, let's consider two types of asymptotes: horizontal and vertical asymptotes.

Horizontal Asymptotes:

A horizontal asymptote is a horizontal line that a function approaches as the x-values become extremely large or extremely small. We usually denote horizontal asymptotes as y = c, where c is a constant.

For example, let's consider the function f(x) = (2x^2 + 3) / (x^2 - 1). As x approaches positive or negative infinity, we can observe the following behavior:

As x becomes extremely large or extremely small, the function becomes closer and closer to the line y = 2. Therefore, we say that y = 2 is a horizontal asymptote for this function.

Vertical Asymptotes:

A vertical asymptote is a vertical line that the function approaches as the x-values approach a particular value. It typically occurs when there is a division by zero or when the function tends to infinity at a specific point.

For example, consider the function g(x) = 1 / (x - 2). As x approaches 2 from either side (but never equal to 2), we can observe the following behavior:

As x approaches 2 from the left (x < 2), the function g(x) becomes increasingly negative, tending towards negative infinity.

As x approaches 2 from the right (x > 2), the function g(x) becomes increasingly positive, tending towards positive infinity.

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(d) Probability of at least one major earthquake in the next 49 years is 0.9884, and (e) the probability of no major earthquakes in the next 49 years is 0.0116.

We will use the Poisson distribution to compute the probabilities. First, we need to find the value of λ (average number of earthquakes in a given time period).

(d) Compute the probability of at least one major earthquake in the next 49 years:

1. Calculate λ for 49 years:

(2.0 earthquakes / 22 years) * 49 years = 4.45 (rounded to the nearest hundredth)

2. Compute the probability of no major earthquakes (P(0)) in the next 49 years using Poisson distribution formula:

P(0) = (e^(-λ) * (λ^0)) / 0! = (e^(-4.45) * (4.45^0)) / 1 = 0.0116 (rounded to 4 decimal places)

3. Compute the probability of at least one major earthquake:

P(at least 1) = 1 - P(0) = 1 - 0.0116 = 0.9884

So, the probability of at least one major earthquake in the next 49 years is 0.9884 (rounded to 4 decimal places).

(e) Compute the probability of no major earthquakes in the next 49 years:

As calculated in step (d), the probability of no major earthquakes in the next 49 years is 0.0116 (rounded to 4 decimal places).

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Distribute

50+30(2x+10)

50+30×2x+30×10

50+60×+300

add the number

50+300+60×

350+60x

60x+350

common factors

10(6x+35)

The sum of the measures of the interior angles is 1260 degrees

From the question, we have the following parameters that can be used in our computation:

An interior angle = 140 degrees

The sum of interior angles of a regular polygon is:

S = (n - 2) × 180

Where n is the number of sides of a polygon

Also, we have

S = 140n

Substitute the known values in the above equation, so, we have the following representation

140n = (n - 2) × 180

Expand

140n = 180n - 360

This gives

40n = 360

Divide

n = 9

Recall that

S = (n - 2) × 180

So, we have

S = (9 - 2) × 180

Evaluate

S = 1260

Hence, the sum of the measures of the interior angles is 1260 degrees

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Answer:Each of the shaded sections represents 25% of the total number of students in the class, and since we have evenly distributed the 12 students among them, each shaded section now represents 30% of the students (i.e., 25% + 5% = 30%).

Step-by-step explanation: To model this situation, we need to determine the total number of students in the class. We can use the given percentage to set up a proportion:

40% = 12 students / x total students

To solve for x, we can cross-multiply and simplify:

0.4x = 12

x = 12 / 0.4

x = 30

Therefore, there are 30 students in the class.

To evenly distribute the 12 students in the 4 shaded sections, we can divide 12 by 4 to get the number of students for each section:

12 students / 4 sections = 3 students per section

Answer:

3x + 5 = 4x - 40

x = 45

5y - 50 = y

4y = 50

y = 25/2

Leslie’s annual social security deduction is $3551.70.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Leslie’s  annual salary is $57,285. 50 and her annual social security deduction is 6.2% of the annual salary. We can say:

Annual social security deduction = 6.2/100 * 57,285. 50

Annual social security deduction = $3551.70

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The ordered pairs of the inequality expression is (0, 4)

From the question, we have the following parameters that can be used in our computation:

The inequality expression  y>1/2x+3

To determine the ordered pairs of the inequality expression, we set x - 0 and then calculate the value of y

Using the above as a guide, we have the following:

y > 1/2 * 0 + 3

Evauate

y > 3

This means that the value of y is greater than 3 say y = 4

So, we have (0, 4)

Hence, the ordered pairs of the inequality expression is (0, 4)

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Therefore, the perimeter of the rectangle is 38 units that is option C.

A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.

Here,

First, we need to find the distance between points A and B to determine the length of the rectangle:

Distance AB = |yB - yA|

= |8 - 2|

= 6

Next, we need to find the distance between points B and C to determine the width of the rectangle:

Distance BC = |xC - xB|

= |6 - (-7)|

= 13

Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.

Therefore, the perimeter of the rectangle is:

Perimeter = 2 * (length + width)

Perimeter = 2 * (13 + 6)

Perimeter = 2 * 19

Perimeter = 38

So the answer is (C) 38.

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We will use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence and assuming that the events are independent and randomly distributed.

For this problem, we will assume that the number of days with 0.01 inch or more precipitation in Lewiston, Idaho, follows a Poisson distribution with parameter λ = 8.7.

(a) To find the probability that there are exactly 9 days with 0.01 inch or more precipitation, we can use the Poisson probability mass function:

P(X = k) = e^(-λ) * λ^k / k!

where X is the random variable representing the number of days with 0.01 inch or more precipitation, λ is the parameter of the Poisson distribution, and k is the number of events we are interested in.

Plugging in the values, we get:

P(X = 9) = e^(-8.7) * 8.7^9 / 9! ≈ 0.151

Therefore, the probability that there are exactly 9 days with 0.01 inch or more precipitation is approximately 0.151.

(b) To find the probability that there are at most 9 days with 0.01 inch or more precipitation, we can use the cumulative distribution function of the Poisson distribution:

P(X ≤ k) = ∑i=0^k e^(-λ) * λ^i / i!

Plugging in the values, we get:

P(X ≤ 9) = ∑i=0^9 e^(-8.7) * 8.7^i / i! ≈ 0.503

Therefore, the probability that there are at most 9 days with 0.01 inch or more precipitation is approximately 0.503.

(c) To find the probability that there are more than 9 days with 0.01 inch or more precipitation, we can subtract the probability of having 9 or fewer days from 1:

P(X > 9) = 1 - P(X ≤ 9) ≈ 0.497

Therefore, the probability that there are more than 9 days with 0.01 inch or more precipitation is approximately 0.497.

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The probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.

To find the probability of getting two numbers whose sum is 12 when a single number cube is rolled twice, we'll first need to identify the favorable outcomes.

A number cube has six faces, numbered from 1 to 6. When it is rolled twice, there are 6 x 6 = 36 equally-likely outcomes. To find the probability, we can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

The first step is to identify the favorable outcomes, which are the pairs of numbers that add up to 12. Since we are dealing with a number cube that has faces numbered 1 to 6, there is only one possible pair that satisfies this condition: (6,6).

Now that we have determined the favorable outcome, we can find the probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (for the pair 6,6) / 36

Thus, the probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.

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The perimeter of a rectangle is 34 units.

To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.

The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.

The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.

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Answer:

238 ft²

Step-by-step explanation:

Base area is l*w and there are two of these so 2(7*7) = 98

Then there 4 faces that have dimensions 4(7*5)=140

98+140=238

The theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

The theoretical probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.

In this case, Alexandria rolled the number cube 60 times and recorded her results in the table.

Looking at the table, we can see that the number 1 came up 16 times and the number 2 came up 20 times.

So the number of favorable outcomes is 16 + 20 = 36.

And the total number of possible outcomes is 60.

Therefore, the theoretical probability of rolling a one or two is:

P(1 or 2) = favorable outcomes/total outcomes = 36/60

Simplifying the fraction, we get:

P(1 or 2) = 3/5

So the theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

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A. True. A compound event may consist of two dependent events. Dependent events are those in which the outcome of the first event affects the outcome of the second event. For example, drawing a card from a deck and not replacing it before drawing a second card would be an example of dependent events.

Answer: Linear Function: y = -10x + 15    Exponential Function:  

y = 15(1/3)(to the power of x)

Step-by-step explanation:

Linear Function:

First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)

In which, it should be (5 - 15)/(1 - 0)

So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is

y = mx + b,

In which, it would become y = -10x + 15

Exponential Function =

The exponential function is y = ab(to the power of x)

Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)

Know let's solve for each variable.

1. 15 = ab(0)

2. 15/b(0) = a

3. 15 = a

Know we know that a is 15, we can solve for b.

1. 5 = (15)b(1)

2. 5/15 = b(1)

3. 1/3 = b

Know we know that b is equal to 1/3, let's plug it into the equation.

y = 15(1/3)(to the power of x)

Answer:

30%

Step-by-step explanation:

If there are only 2 categories:

Students at lunch and students studying, then the whole is 100%

100% - 70% = 30%

Helping in the name of Jesus.

Nataly saved s/64.

The original prices for the items are:

Skirt: s/78

Blouse: s/65

Jacket: s/240

The discounted prices Nataly paid are:

Skirt: s/69

Blouse: s/52

Jacket: s/198

To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:

savings = (78 - 69) + (65 - 52) + (240 - 198)

savings = 9 + 13 + 42

savings = s/64

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The equation in two variables that describes how the amount of cat food in the bag changes over time is: A = 10 - 0.3t
Where A represents the amount of cat food left in the bag after t days, and t represents the number of days that have passed since Simon bought the bag.

The variable A is the dependent variable because it depends on the value of t. As time passes and t increases, the amount of cat food left in the bag decreases. The variable t is the independent variable because it is the input that determines the value of A.

For example, after one day (t = 1), Simon will have used 0.3 pounds of cat food and there will be 9.7 pounds left in the bag (A = 10 - 0.3(1) = 9.7). After two days (t = 2), he will have used 0.6 pounds of cat food and there will be 9.4 pounds left in the bag (A = 10 - 0.3(2) = 9.4), and so on.

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2x²t + 7xy

    To simplify, we will combine like terms.

    Given:

5xy - x²t + 2xy + 3x²t

    Reorder like terms:

5xy + 2xy + 3x²t - x²t

    Combine like terms:

    ➜ 5 + 2 = 7

    ➜ 3 - 1 = 2

7xy + 2x²t

    Reorder by degree:

2x²t + 7xy

Answer:

y = 1 + 2√7 or y = 1 - 2√7

Step-by-step explanation:

To complete the square, you need to add and subtract the square of half of the coefficient of the y term.

First, you can factor out a 1 from the y^2 - 2y term:

y^2 - 2y - 27 = 0

y^2 - 2y = 27

Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):

y^2 - 2y + 1 - 1 = 27

The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.

Now you can rewrite the left side as a perfect square:

(y - 1)^2 - 28 = 0

Add 28 to both sides:

(y - 1)^2 = 28

Take the square root of both sides (remembering to include both positive and negative square roots):

y - 1 = ±√28

y = 1 ± 2√7

So the solutions are:

y = 1 + 2√7

y = 1 - 2√7

Answer: y=± 2√7+1

6.29

Step-by-step explanation: Use the formula

(b/2)^2  in order to create a new term. Solve for y by using this term to complete the square.

The new price per share is $111.48.

Stock price is the current market value of a share of a publicly traded company's stock. It represents the price at which buyers and sellers agree to trade shares in the open market. Stock prices are determined by a variety of factors, including the company's financial performance, industry trends, and overall market conditions. The stock price is often used as an indicator of investor sentiment about the company and its future prospects.

To find the new price per share, follow these steps:

1. Note the initial stock price: $109.99
2. Note the increase in stock price: $1.49
3. Add the increase to the initial stock price: $109.99 + $1.49 = $111.48

The new price per share is $111.48.

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The amount of interest paid for missing the payment in the eight month would be C. $87.28

First, find the total cost of the computer including the sales price :

= 875 x ( 1 + 0. 05 )

= 875 x 1. 05

= $ 918. 75

Then, find the monthly rate of interest :

= 14. 25 / 12

= 1. 1875 %

This leads to an eight month interest rate of :

= 8 x 1. 1875 %

= 9. 5 %

The interest to be paid:

= 9. 5 % x 918. 75

= $ 87. 28

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Full question is:

You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. 58.19

The mean of the given stem and leaf plot is 24.5 and the median of the data is 25.

The stem and leaf plot represents the given data as:

| 2 | 4, 5, 6, 9

| 3 | 1, 4, 5, 5, 7, 8

| 4 | 2, 5, 7, 8, 9

To find the mean, we need to add up all the values and divide by the total number of values.

Mean = (24 + 25 + 26 + 29 + 31 + 34 + 35 + 35 + 37 + 38 + 42 + 45 + 47 + 48 + 49) / 15

= 367 / 15

= 24.5

To find the median, we need to arrange the data in order and find the middle value. As there are 15 data points, the median will be the average of the 8th and 9th data points.

Data in order: 24, 25, 25, 26, 29, 31, 34, 35, 35, 37, 38, 42, 45, 47, 48

Median = (35 + 37) / 2

= 36.

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Answer:

366 times

Step-by-step explanation:

The position of the particle at time t = 1 is x = 4 units.

To find the position of the particle at time t = 1, we need to integrate the given velocity function v(t) with respect to time from 0 to 1:

x(t) = ∫v(t)dt (from t = 0 to t = 1)

= ∫([tex]3t^2[/tex]+ 6t)dt (from t = 0 to t = 1)

= ([tex]t^3 + 3t^2[/tex]) (from t = 0 to t = 1)

[tex]= (1^3 + 3(1^2)) - (0^3 + 3(0^2))[/tex]

= 4

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