I don’t really understand how to do this… summer brain

Answer:

0 & -16,x=0

Step-by-step explanation:

The function is discontinuous at x = 0, x = 1/4 and x = -1/4.

To create the extended function, add f(x) = 0.

A function is discontinuous when the f(x) cannot be defined.

An extended function aims to make the function continuous at some values of the variable.

It is given that:

\(f(x)=\frac{2x^{2}+16x}{16x^{3}-x}\)

The function becomes discontinuous when the denominator becomes zero.

∴ 16x³ - x = 0

⇒ x(16x² - 1) = 0

⇒ x = 0 and 16x² -1 = 0

This is further simplified:

16x² -1 = 0

x² = 1/16

x = ±1/4

This means that the function is discontinuous at x = 0, x = 1/4 and x = -1/4.

The function can be extended as follows:

\(f(x)=\frac{2x^{2}+16x}{16x^{3}-x}\\f(x)= \lim_{x \to 0} \frac{2x^{2}+16x}{16x^{3}-x}\\= \lim_{x \to 0} \frac{x(2x+16)}{x(16x^{2}-1)}\\= \lim_{x \to 0} \frac{2x+16}{16x^{2}-1}\\\)

We do not have to add anything to f(x) to extend it. Hence zero can be added to it.

Therefore, we have found that the function is discontinuous at x = 0, x = 1/4 and x = -1/4, and that we can create the extended function by adding 0.

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Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

To determine which point is a solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2, we can test each point to see if it satisfies both inequalities.

a) Point E at (4, -2):

Substituting the coordinates into the inequalities:

-2 > -2(4) + 10 -> -2 > -8 + 10 -> -2 > 2 (False)

-2 > (1/2)(4) - 2 -> -2 > 2 - 2 -> -2 > 0 (False)

b) Point K at (2, 3):

Substituting the coordinates into the inequalities:

3 > -2(2) + 10 -> 3 > -4 + 10 -> 3 > 6 (False)

3 > (1/2)(2) - 2 -> 3 > 1 - 2 -> 3 > -1 (True)

c) Point B at (4, 7):

Substituting the coordinates into the inequalities:

7 > -2(4) + 10 -> 7 > -8 + 10 -> 7 > 2 (True)

7 > (1/2)(4) - 2 -> 7 > 2 - 2 -> 7 > 0 (True)

d) Point D at (-7, 1):

Substituting the coordinates into the inequalities:

1 > -2(-7) + 10 -> 1 > 14 + 10 -> 1 > 24 (False)

1 > (1/2)(-7) - 2 -> 1 > -3.5 - 2 -> 1 > -5.5 (True)

Based on the analysis, point D at (-7, 1) is the only solution to the system of inequalities y > -2x + 10 and y > (1/2)x - 2. Therefore, the correct answer is option d) D.

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Therefore , the solution for this problem is that standard deviation can be used as risk management investing.

The standard deviation is a metric that reveals the amount of variation (such as spread, scattering, and spread) from the mean. The standard deviation represents a "average" departure from the mean. Because it uses the exact units of measurement from the data set, it is a well-liked measure of variability. Similar to variance, there is little variation when data points are near the mean, but there is much variation when data points are widely scattered from the mean.

Here,

Standard deviation is one of many ways to measure risk in finance.

It states the level of dispersion of some data values (like stock returns) around its mean.

The higher the standard deviation the more diverse or wider the returns will be, that is, more risk.

If the mean is 8% with a standard deviation of 13%, you can calculate the probability of the expected returns to be in between -5% and 21% (8% +\- 13%). Actually even outside the interval.

(The probability will depend on the distributions of returns)

Therefore , the solution for this problem is that standard deviation can be used as risk management investing.

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Answer:

53.87 because 4 cant round the 6

Step-by-step explanation:

Answer:

53.87

Step-by-step explanation:

4 cannot round the 6

Answer:

the next three numbers should be 8, 4, 0

Step-by-step explanation:

it reduces by 4 each time

24 - 4 = 20

20 - 4 = 16

16 - 4 = 12

12 - 4 = 8

8 - 4 = 4

4 - 4 = 0

First term =a=24

common difference=d=20-24=-4

Formula

a_5

a_6

a_7

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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At a price of $44, 30 units of good x are exchanged. This can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50).

At a price of $44, the quantity of good x that is exchanged can be calculated by subtracting the quantity supplied at price $15 (q0=10) and the quantity supplied at price $31 (q*=30) from the quantity demanded at price $44 (q1=50). The quantity supplied at price $15 is 10 units, the quantity supplied at price $31 is 30 units, and the quantity demanded at price $44 is 50 units. Therefore, the quantity exchanged at price $44 is 50 units minus 10 units (q0) minus 30 units (q*) which equals 10 units. Thus, the quantity of good x exchanged at price $44 is 10 units.

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Terms are 4b, 7b, 5 coefficient are 4 , 7 and constant = 4, 7 , 5

What are the parts in expression?

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given expression:

4b+7b+5

As. term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.

Terms are 4b, 7b, 5

Now, coefficient is a number that is multiplied by a variable in an expression.

coefficient are 4 , 7

As a constant is a fixed numerical value,

So, constant = 4, 7 , 5

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Jamie's final shift in score is -96 after changing it by -12 points for 8 consecutive turns.

The unit approach is a form of conundrum that entails figuring the value of just one unit, multiplying such a value, and then assessing the necessary value. To put it plainly, the unit technique is employed to determine a single product value from either a supplied multitude. One pen gets 400 dollars, so 40 pens would spend 400 rupees. There could be a routine condition for carrying this out. essentially one nation. anything bearing a distinctive component. Algebra of matrices or operators, linear programming, numerical modeling, and its coproduct and reciprocal all seem to be identical.

given

Score for each turn: -12

There are 8 turns.

Jamie's overall total

Total Jamie's score = Each turn's tally Number of turns

Jamie's overall total is -12 8.

Jamie's final total is -96.

Jamie's final shift in score is -96 after changing it by -12 points for 8 consecutive turns.

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The polar equation is symmetric with respect to the polar axis. The polar equation is not symmetric with respect to the pole. The polar equation is not symmetric with respect to the line theta = π/2. The polar equation is not symmetric with respect to any of these.

To test for symmetry with respect to the polar axis, we replace theta with -theta and see if the equation remains the same.

r = 5/(4 - 3sin(theta))

r = 5/(4 - 3sin(-theta))

r = 5/(4 + 3sin(theta))

Since the equation is not the same, the polar equation is not symmetric with respect to the polar axis.

To test for symmetry with respect to the pole, we replace r with -r and see if the equation remains the same.

r = 5/(4 - 3sin(theta))

-r = 5/(4 - 3sin(theta + π))

-r = 5/(4 + 3sin(theta))

Since the equation is not the same, the polar equation is not symmetric with respect to the pole.

To test for symmetry with respect to the line theta = π/2, we replace theta with (π/2) - theta and see if the equation remains the same.

r = 5/(4 - 3sin(theta))

r = 5/(4 - 3sin((π/2) - theta))

r = 5/(4 + 3cos(theta))

Since the equation is not the same, the polar equation is not symmetric with respect to the line theta = π/2.

Therefore, the polar equation is not symmetric with respect to any of these.

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--The complete question is, Test the polar equation for symmetry with respect to the polar axis, the pole, and the line r = 5 /(4 - 3 sin(theta)) a. symmetric with respect to the polar axis

b. symmetric with respect to the pole

c. symmetric with respect to the line theta = π / 2

d. not symmetric with respect to any of these--

The inequality will be 3(h+8) < 45 and the number of hats that Bill have is less than 7

HATS Bill has h hats

If he buys 8 more hats then the number of hats he has = h + 8

then multiplies his total by 3  then the number of hats he has = 3(h + 8)

Still Bill has fewer hats than Jim, Jim has 45 hats

then the inequality will be 3(h+8) < 45

3(h+8) < 45

3h + 24 < 45

3h < 21

h < 7

Therefore, the inequality will be 3(h+8) < 45 and the number of hats that Bill have is less than 7

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Answer:

x=3.5

Step-by-step explanation:

2x + 5 =12

2x = 12 - 5

2x= 7

2x÷ 2 = 7÷2

x=3.5

statistical calculations are important in risk management and insurance because they help to quantify and model risk, predict future outcomes, and manage risk effectively.

Variance is important in risk management and insurance because it helps to assess the volatility or fluctuation of returns, which is important in determining how much risk an individual or company is willing to take. Random Variable :Random variables are essential in risk management because they help to determine the probability of specific outcomes. This is particularly important for insurance companies that need to calculate premiums and manage risk on behalf of policyholders .Expected Value: Expected value is critical to risk management because it helps to calculate the average outcome of an event over a large number of trials. This helps to predict future outcomes and manage risk. Probability Distributions :Probability distributions are important in insurance and risk management because they help to quantify and model the likelihood of different outcomes and events. This is critical in assessing and managing risk. Standard Deviation :Standard deviation is important in risk management because it helps to measure the amount of variability or dispersion of data around the mean or expected value. This is important in determining the level of risk associated with an investment or policy decision .

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Answer:102 children and 337 adults swam at the publice pool that da

Step-by-step explanation:

let the number of children be x

and

the number of adults be y

such that the total number of people who came to use the public swimming pool be expressed as

x + y = 439----- Equation 1

and price  for swimming be expressed as

1.75x + 2.50y =1021----- Equation 2

Step 2

x + y = 439----- Equation 1

1.75x + 2.50y =1021----- Equation 2

First make x the subject formulae and put in equation 2

x= 439-y

1.75 (430-y) + 2.50y = 1021

Solving gives

768.25-1.75y+2.50y=1021

2.50y-1.75y=1021-768.25

0.75y=252.75

y =252.75/0.75  

y=337

To find x, put the value of y = 337 in equation 1

x+y= 439

x= 439-337

x=102

Therefore 102 children and 337 adults swam at the public pool that day

Answer:

Step-by-step explanation:

In a two tailed test, the alternative hypothesis contains the "unequal to" symbol. It is used when we are testing for a difference. This means that the test is regardless of direction. Therefore, the left tail and the right tail of the curve is considered when making decisions. This simply means that there are two critical regions for the test. Therefore, a two-tailed test is one where:

B. results in either of two directions can lead to rejection of the null hypothesis

Given data:

In a rectangle the opposite sides are always parallel and equal.

3/8 pints of milk will fill an empty mug of the same size.

In this question, we have been given Pia poured 1/4 pint of milk into an empty mug.

The milk filled 2/3 of the mug.

We need to find the pints of milk that will fill an empty mug of the same size.

Let 'm' pints of milk will fill an empty mug of the same size.

From given data, we get proportion.

⇒ (1/4) / (2/3) = m / 1

We simplify above equation to find the value of m.

⇒ (2/3) m = 1/4

⇒ m = (1/4) × (3/2)

⇒ m = 3/8

Therefore, 3/8 pints of milk will fill an empty mug of the same size.

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Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

Answer:

192

Step-by-step explanation:

-3(-4(2) - 7(8))

= -3(-8 - 56)

= -3(-64)

= 192

*Negative x negative = positive

You should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

To solve this problem, we can use the present value formula for an ordinary annuity: PV = PMT * [1 - (1 + r)^-n] / r

Where:

PV = present value

PMT = periodic payment

r = interest rate

n = number of payments

In this case, we have:

PV = unknown

PMT = $3,000

r = 5%

n = 10 years (first payment in 3 years, so there are 10 payments after that)

Plugging these values into the formula,

we get:

PV = $3,000 * [1 - (1 + 0.05)^-10] / 0.05

PV = $22,627.84

Therefore, you should invest $22,627.84 if you want to receive payments of $3,000 at the end of each year for 10 years, with the first payment 3 years from now, if the money is compounded at 5% annually.

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In summary, it takes approximately 4.92 hours for 2 milligrams to be left in the body and the half-life of the drug is approximately 2.29 hours.

To determine when 2 milligrams is left in the body, we can substitute A = 2 into the equation given: 2 = 10(0.8)^t. Then, we can solve for t by dividing both sides by 10 and taking the natural logarithm of both sides to isolate t: t = ln(2/10) / ln(0.8). Using a calculator, we find that t is approximately 4.92 hours.

To find the half-life of the drug, we need to determine the time it takes for half of the initial dose (10 milligrams) to be eliminated from the body. This occurs when A = 5 milligrams. We can use the same equation and substitute A = 5: 5 = 10(0.8)^t. Then, we can solve for t using the same method as before: t = ln(0.5) / ln(0.8). Using a calculator, we find that t is approximately 2.29 hours.

In summary, it takes approximately 4.92 hours for 2 milligrams to be left in the body and the half-life of the drug is approximately 2.29 hours.

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A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\(\sigma\))= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

Option A

Step-by-step explanation:

The equation of line is

Solution:

Given that line passes through the point (4, –6) and has a slope of Negative three-fourths

Given point is (x, y) = (4, -6)

The equation of line passing through point (x, y) and slope "m" is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Substitute (x, y) = (4, -6) and  in eqn 1

The required equation of line is given as:

Thus the equation of line is found

Answer:

a

Step-by-step explanation:

Answer:

24 hours

Step-by-step explanation:

Divide 200 by 5.50

200÷5.50=36.36 (round to the nearest decimal)

Divide 68 by 5.50

68÷5.50=12.36 (round to the nearest decimal)

So if he worked 12.4 hours to gain $68,

We then can minus 12.4 from 36.4

36.4-12.4=24

He will need to work 24 more hours in order to have enough money

Answer:

Answer:    \(\frac{1}{2}\)

Step-by-step explanation:

(-7, 7) is (x1, y1)

(-1, 10) is (x2, y2)

\(\frac{10 - 7}{-1 - (-7)}\)  =   \(\frac{3}{6}\)  

Simplify 3/6.

\(\frac{3}{6}\)  divide by  \(\frac{3}{3}\)  equals \(\frac{1}{2}\)

True. Line graphs are not suitable for representing central tendencies and variation between categorical data.They are effective in showing changes and patterns in numerical data.

Line graphs are typically used to display trends over time or the relationship between two continuous variables. However, when it comes to categorical data, which consists of distinct categories or groups, line graphs are not appropriate for representing central tendencies and variation.

Central tendencies, such as the mean or median, are measures that describe the average or typical value within a set of data. Variation refers to the spread or dispersion of the data points. Categorical data does not have a natural numerical scale or order, making it difficult to determine central tendencies and variation using line graphs.

For categorical data, alternative graphical representations like bar charts, pie charts, or stacked column charts are more suitable. These graphs provide a visual representation of the frequencies or proportions of different categories, allowing for a better understanding of the distribution and comparison between categories. Such graphs are effective in capturing the central tendencies and variation in categorical data.

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The quotient (2x^3+ 6x²- 6x + 2)divided by (2x-3) is: \(x^2 + 4x + 3\).

Quotients are often used in algebra to solve equations and expressions involving division. They are used in everyday life such as when calculating the average speed of a journey.

\(x^2 + 4x + 3\)

\(---------\)

\(2x - 3 | 2x^3 + 6x^2 - 6x + 2 \\ - (2x^3 - 3x^2)\)

    \(----------\)

         \(9x^2 - 6x \\- (9x^2 - 13x)\)

             \(-----------\)

                   \(7x + 2\)

The quotient is:

\(x^2 + 4x + 3\)

Therefore, (2x^3 + 6x² - 6x + 2) divided by (2x-3) is equal to (x^2 + 4x + 3) with a remainder of (7x + 2).

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According to the information in the table, the row of f(x) is completed by increasing twice the previous number. On the other hand, the function g(x) is completed by increasing 23.

To complete the table we must take into account the values shown in the initial part. There we can identify the pattern that the functions follow. In the case of f(x) we can identify that the value corresponds to twice the previous number:

On the other hand, the second row g(x) corresponds to the number 23:

Then the values that complete the table are:

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