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What is the value of y in the triangle?

The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

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Numerical integration is a numerical analysis technique for calculating the approximate numerical value of a definite integral.

In general, integrals can be either indefinite integrals or definite integrals. A definite integral is an integral with limits of integration, while an indefinite integral is an integral without limits of integration.A numerical integration formula is an algorithm that calculates the approximate numerical value of a definite integral. Numerical integration is based on the approximation of the integrand using a numerical quadrature formula.

The numerical quadrature formula is used to approximate the value of the integral by breaking it up into small parts and summing the parts together.Equations for the calculation of integration by trapezoidal rule (1/2)h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h= Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The basic principle is to replace the integral by a simple sum that can be calculated numerically. This is done by partitioning the interval of integration into subintervals, approximating the integrand on each subinterval by an interpolating polynomial, and then evaluating the integral of each polynomial.

Based on the given table of unequally spaced data, we are to calculate the approximate numerical value of the definite integral. To do this, we will use the integration formula as given by the trapezoidal rule which is 1/2 h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h = Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes.  The table can be represented as follows:x            0.1 0.3 0.5 0.7 0.95 1.2f(x)      1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012Let Δx = 0.1 + 0.2 + 0.2 + 0.25 + 0.25 = 1, and n = 5Substituting into the integration formula, we have; 1/2[1(1)+2(0.9048+0.7408+0.6065+0.4966)+0.3867]1/2[1 + 2.3037+ 1.5136+ 1.1932 + 0.3867]1/2[6.3972]= 3.1986 (to 4 decimal places)

Therefore, the approximate numerical value of the definite integral is 3.1986.

The approximate numerical value of a definite integral can be calculated using numerical integration formulas such as the trapezoidal rule. The trapezoidal rule can be used to calculate the approximate numerical value of a definite integral of an unequally spaced table of data.

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Answer:

Step-by-step explanation:

for the table you just add 45 to all the numbers, so it will be 135, and 270

you will just have to graph that.

Answer:

$90 to rent and 15$ per guest. equation is y=15x+90. initial value is 90, rate of change is 15.

Step-by-step explanation:

Answer: C: 4.9

The original answer is 4.8989, so I rounded 8 to the nearest hundredth and got the answer of 4.9. Having a Mathematics calculator also helps with math like this.

Answer:

Around 376.99

Step-by-step explanation:

the formula is 2πrh+2πr²

so if we plug in everything we get 2π(4)(11)+2π(4)²

When we simplify that, we would get 376.99

Answer: \(12^6\) because when multiplying numbers with the same base, you add the exponents.

Step-by-step explanation:

\((12^0)(12^6)=12^{0+6}=12^{6}\)

Answer:

₹4064

Step-by-step explanation:

Given data

P= ₹4000

r= 8%

t= 2 years

Required

The final amount A

we will apply the simple interest formula

A=P(1+rt)

substitute

A= 4000(1+0.08*2)

A= 4000(1+0.16)

A= 4000*1.016

A= ₹4064

Hence the amount is  ₹4064

Answer:

2

Step-by-step explanation:

5 . solving the inequality

6.the graph takes all values ​​less than -1, without taking -1

so

which can be represented as

7. solving

and the graph is

The correct option is C) changes. When moving from one explanatory variable to two explanatory variables, the formula for the standard error of the regression coefficient changes.

The standard error of the regression coefficient depends on the number of explanatory variables, and adding a variable changes the number. The formula for the standard error of the regression coefficient when there is one explanatory variable assumes that all of the variation in the response variable is due to the explanatory variable. However, when there are two explanatory variables, some of the variation in the response variable may be due to the other variable, and the standard error must account for this.

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Cluster Sample is the sampling method used in this type of data collection.

Cluster sampling is a sampling technique used in statistics that divides the total population under consideration into externally homogeneous but internally heterogeneous groupings known as clusters. Each cluster essentially serves as a miniature representation of the overall population.

Using simple random sampling, some clusters are picked after the clusters have been identified, while the remaining clusters are left out of the study. A researcher must determine the right sampling strategy for each cluster after identifying the clusters.

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The count in a bacteria culture was 600 after 15 minutes and 2000 after 40 minutes. The count of bacteria is given in this problem and is said to be growing exponentially. We are required to calculate the initial count of the bacteria.

Let N0 be the initial count of bacteria, k be the growth constant, and t be the time taken. According to the law of exponential growth, the number of bacteria increases exponentially with time. Hence we can write, Number of bacteria N = N0ekt

According to the given problem, When t = 15, N = 600 When t = 40, N = 2000

Substituting these values in the above equation, we get

600 = N_0ek15,  and  2000 = N_0ek40

Dividing the above two equations, we get 600/2000 = ek15 - ek40

=> 0.3 = e-k25ln(0.3) = -k25=> k = 0.064

Based on the above values of k, we can calculate the initial count of bacteria as follows:

N_0 = 600/e0.064 × 15

=> N_0 = 150 bacteria.

Hence the initial count of bacteria was 150.

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Answer:

The answer is D.

Step-by-step explanation:

Here, the meaning of the y-intercept in the context of the problem is the initial value of the investment is $400.

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

I think you should start with a table and then write all your points for x then in the next column your answers for y.

Then take your medium and start drawing.

I suggest your x's should start from 0 and increase by 1 or 2

Then when you reach a certain point then go back to 0 and start doing your negatives.

For example if y = 2x

x | y

0|0

1 | 2

2| 4

3|6

4|8

....

then

16|32

0|0

-1|-2

-2|-4

Thanks for this question. I am working my way up to brainliest answer and Master Answerer. This answer took a lot of time to type so I hope I get good review.

:)

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Step-by-step explanation:

Answer:

enlargement

Step-by-step explanation:

if scale factor > 1 then enlargement

if scale factor 0 < SF < 1 then reduction

here SF = \(\frac{6}{5}\) = 1.2 > 1 so enlargement

Answer:

Enlargement

Step-by-step explanation:

Due to the scale factor properties stating that a SF value must be more than one to become an enlargement factor, we know that 6/5 is more than one whole. Thus, the SF is enlargement.

Answer:

0.15

Step-by-step explanation:

We can divide both sides to single out the x:

x = \(\frac{3.75}{25}\)

Simplifying that gives:

x = 0.15

Answer: I believe the answer is: x=15

Step-by-step explanation: 15*.25=3.75

Answer:

no

Step-by-step explanation:

no

Answer:

See below

Step-by-step explanation:

Lines given

1. ......................................

2. ......................................

3. ......................................

4. ......................................

5. ......................................

Answer:

The slope of the line modeled by 3x − 2y = 6 is 3/2 ------ True

The slope of the line modeled by 4y = x is 4 ---------- False

The slope of the line modeled by y = 7 is undefined -------- False

The slope of the line modeled by equation x = 8 is undefined ------- True

The slope of the line modeled by −2x − 5y = 4 is −2/5 , and the y-intercept is −4/5  --------- True

Step-by-step explanation:

The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

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Answer:

- 3a -16b

Step-by-step explanation:

Answer:

x=3

PAW = 40

Step-by-step explanation:

-11x+173-x+43=180

-12x+ 216 = 180

12x = 36

hi

Let's call money invested at 7%  X and the one at  4% Y

So we have :

X+Y = 27 000                       (1)

0.07X + 0.04 Y =  1 530       (2)  

As X+Y = 27 000 then   Y = 27 000 -X

then   we have in line (2)

0.07X + 0.04 ( 27 000 -X) =  1 530

0.07X +  1080 -0.04 X = 1 530

0.07X - 0.04X = 1530 - 1080

          0.03X =  450

                 X = 450 / 0.03

                 X =  15 000

Now  X = 15 000

so Y = 27 000 - 15 000 =  12 000

Answer is :   15 000 dollars were invested at  7% and 12 000 at  4%

Let's check  to be sure  :  

15 000 * 0.07 =  1 050

12 000 *0.04 =     480

and  1 050 + 480 = 1 530  

The parabola opens upward and the vertex represents the minimum value, the range of the function is all real numbers greater than or equal to 12.

The range of a quadratic function can be determined by finding the vertex and the leading coefficient of the quadratic equation.

In the given quadratic function, \[ f(x)=2 x^{2}+16 x+28 \], the leading coefficient is 2.

Since the leading coefficient is positive, the parabola opens upward. This means that the vertex represents the minimum value of the function, and the range will extend from the minimum value to positive infinity.

To find the vertex, we can use the formula: \[ x = -\frac{b}{2a} \]

In this case, a = 2 and b = 16. Plugging these values into the formula, we get:

\[ x = -\frac{16}{2(2)} = -4 \]

To find the corresponding y-value or the minimum value of the function, we substitute this x-value back into the equation:

\[ f(-4) = 2(-4)^2 + 16(-4) + 28 = 12 \]

So, the vertex is (-4, 12).

Since the parabola opens upward and the vertex represents the minimum value, the range of the function is all real numbers greater than or equal to 12.

Using interval notation, we can write the range as \[ [12, \infty) \]. This means that the range includes all values from 12 to positive infinity, including 12 itself.

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By using function, it can be concluded that-

The predictor variables are bed, bath, floor

What is function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

In a function y = f(x), x is the independent variable and y is the dependent variable.

The price of an apartment is dependent on the number of bedrooms, bathrooms and the floor of the apartment

So the required function is p = f(bed, bath, floor) where p is the price of the apartment

The predictor variables are bed, bath, floor

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