Which of the following points lie in the solution set to the following system of inequalities? y > â’3x 3 y > x 2 (2, â’5) (â’2, 5) (2, 5) (â’2, â’5).

The slope (m) will be "279.33". A further solution to the question is provided below.

At one moment this same instantaneous modification rate would be the same with the functionality derivative assessed somewhere at the time. In certain other terms, the pitch of such tangent line towards the curvature is somewhere at a level equivalent to that as well.

According to the question,

As we know,

⇒  \(Slope (m) = \frac{y_2-y_1}{x_2-x_1}\)

By substituting the values, we get

⇒                  \(=\frac{838-0}{6-3}\)

⇒                  \(=\frac{838}{3}\)

⇒                  \(=279.33\)

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The instantaneous rate of change is the rate of change at a particular point or instant in the graph. The instantaneous rate of change of P at \(t=4\) is 250

I've added as an attachment, the graph that represents the population of the fish.

To determine the instantaneous rate of change at \(t=4\), we simply calculate the slope (m) of the tangent line using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Because of the scale of the graph, I will use the following estimated points from the tangent line

\((x_1,y_1) = (3,0)\)

\((x_2,y_2) = (4,250)\)

So, the slope is:

\(m = \frac{250 - 0}{4 - 3}\)

\(m = \frac{250}{1}\)

\(m = 250\)

Hence, the instantaneous rate of change of P at \(t=4\) is 250

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If the arrival times of Caryl's school bus are distributed on a normal curve, the standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

The standard deviation is a statistic that measures the amount of variation or dispersion from the central tendency of a set of data values. A low standard deviation indicates that the data is tightly clustered around the mean or average, while a high standard deviation indicates that the data is more spread out.

The standard deviation is particularly useful when dealing with normally distributed data, as it allows us to estimate the probability of a certain range of values occurring. In this case, Caryl can use the standard deviation to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

Hence, option c. standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

(1, 28 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) ]

here (x₁, y₁ ) = G(- 2, 46) and (x₂, y₂ ) = L(4, 10), thus

midpoint = (\(\frac{-2+4}{2}\) , \(\frac{46+10}{2}\) ) = (\(\frac{2}{2}\) , \(\frac{56}2}\) ) = (1, 28 )

Front-end estimation is a particular way of rounding numbers to estimate sums and differences.

To use front- end estimation, add or subtract only the numbers in the greatest place value. Then add the decimals rounded to the nearest tenth.

Step-by-step explanation:

In front end estimation we are going to replace the original number with a number that is close by but only has one non zero digit. Examples: {20, 300, -50, 1,000, 80,000}. For example take the number 32, the choices to replace it with are 30 or 40 (they both have only one non-zero digit).

The required expression is given by 179.2 - 10.6d.

There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day

Volume, is defined as the ratio of the mass of object to its density.

the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.

since the amount of water is getting consumed day by day
therefore, the expression can be given as
  =  179.2 - 10.6d

Thus, the required expression is 179.2 - 10.6d.

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Answer: 35 hours

Step-by-step explanation:

If Jerome spends 4 hours studying science for every 5 hours studying math, that means he studied 9 hours total (4 + 5 = 9) for every 5 hours of math.

      4 hours + 5 hours = 9 hours

Using this information, we can divide 63 by 9 to find how many times he studied math in the 63-hour period.

      63 hours / 9 hours = 7 times

Lastly, we can multiply 7 times by 5 hours to find the total number of hours.

      7 times * 5 hours = 35 hours

We can check our work by setting up a proportion.

      \(\displaystyle \frac{\text{5 hours of math}}{\text{9 total hours}} =\frac{\text{35 hours of math}}{\text{63 total hours}}\)

      \(\displaystyle 0.55556 = 0.55556\) ✓

The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.

First, we will find the equations showing the level of mercury in each body of water.

For the first water body:

Initial measure of mercury = 0.05 ppb.

Rate of rising = 0.1 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.05 + 0.1y.

For the second water body:

Initial measure of mercury = 0.12 ppb.

Rate of rising = 0.06 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.12 + 0.06y.

We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.

As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:

0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.

Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

Dunno what the RACE method is, never heard of it before but.

3x is positive, has a variable.

-3 is negative, has no variable.

-3x^2 is negative, has a variable, and an exponent.

-5x is negaitive, has a variable.

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

To calculate the future value of a three-year uneven cash flow given below, using an 11% discount rate, we need to use the formula;

Future value of uneven cash flow = cash flow at year 1/(1+discount rate)¹ + cash flow at year 2/(1+discount rate)² + cash flow at year 3/(1+discount rate)³ + cash flow at year 4/(1+discount rate)⁴

Given the cash flows;

Year 0: $0

Year 1: $600

Year 2: $500

Year 3: $400

Then the Future value of uneven cash flow

= $600/(1+0.11)¹ + $500/(1+0.11)² + $400/(1+0.11)³

= $600/1.11 + $500/1.23 + $400/1.36

=$540.54 + $405.28 + $293.00

=$1,238.82

Therefore, the future value of a three-year uneven cash flow given below, using an 11% discount rate is $1,238.82.

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Answer:

(-4+i)+4i = -4+(i+4i)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are going to assume that the balance compounds every year

applying the compound interest formula we have

\(A= P(1+r)^t\)

where

A, final amount

P, Principal= $100

r, Rate= 3%= 0.03

T, time= 2years

substituting our values into the formula we have

\(A= 100(1+0.03)^2\\A=100(1.03)^2\\A=100*1.0609\\A=106.09\\\)

The final amount/ her balance after two years is $106.09

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Penetration equation is given by  B(x) = B₀ * exp(-x / λ).

To determine the magnetic field penetration (B(x)) inside a superconducting plate, we need to consider the penetration equation. The penetration equation is written as:

B(x) = B₀ * exp(-x / λ),

where B₀ is the magnetic field at the surface of the superconducting plate, x is the distance from the surface, and λ is the penetration depth.

(a) To show that B(x) inside a superconducting plate perpendicular to the axis and of thickness d is given by this equation, we can follow these steps:

Step 1: Assume that the magnetic field is perpendicular to the surface of the superconducting plate (i.e., along the axis).

Step 2: When x = 0 (i.e., at the surface of the plate), the magnetic field is B₀:

B(0) = B₀ * exp(-0 / λ) = B₀ * exp(0) = B₀.

Step 3: As x increases and penetrates inside the superconducting plate, the magnetic field decreases due to the exp(-x / λ) term in the penetration equation.

Step 4: At the other surface of the plate (i.e., at x = d, where d is the thickness of the plate), the magnetic field will be:

B(d) = B₀ * exp(-d / λ).

Thus, we have shown that the magnetic field penetration (B(x)) inside a superconducting plate perpendicular to the axis and of thickness d is given by the penetration equation B(x) = B₀ * exp(-x / λ).

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Answer:

Step-by-step explanation:

First Pair.

If you divide the top equation by 3 you get

x + 2y = 12

x + y = 7          From that I get that y = 5

Second pair

Do the same thing to the top equation only this time divide by 6

x + 2y = 4                

x + y = 7

If you subtract again you get y = - 3

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

9. No

10. Yes

Step-by-step explanation:

The first one is not, since you have (3, 3) and (3, 9).  In a function, each x maps to a single y.

The second one is since every x appears only once.

Answer:

im grade 6 I don't no whats that sorry

100% percent of the espressos were single-shot.

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios, proportions, and rates. It is denoted by the symbol "%". For example, if you have 25 out of 100 items, you can express this as 25% to represent the proportion of items that you have.

The total number of espressos sold yesterday afternoon was 5. If 5 of them were single-shot, then 100% * 5 / 5 = 100% of the espressos were single-shot.

Hence, 100% percent of the espressos were single-shot.

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Answer:

0

Step-by-step explanation:

2(n - 1) + 4n = 2 ( 3n - 1 )

2n - 2 + 4n = 6n - 2

6n - 2 = 6n - 2

6n - 6n = -2 + 2

0 = 0

The t value needed to develop the 95% confidence interval for the population mean sat score is 1.998.

We are given the sample of 64 sat scores, which is n=64.

Average score is given as 1200.

Sample Standard deviation of sat scores is 200.

We have to find the t value to develop 95% confidence interval.

We will use t test, as population standard deviation is not known.

To find t value, first we will calculate the degrees of freedom,

Degrees of freedom, df=n-1

df=64-1

df=63

From the t table for  df=63 and 95% confidence Level, we have the t value as 1.998.

Therefore, the t value needed to develop the 95% confidence interval for the population mean sat score is 1.998.

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Answer:

X=3-(y/2)=8

Step-by-step explanation:

suppose the numbers is X

3 less than half the product of a number is 8

X= 3- (y/2)=8

Answer:

Step-by-step explanation:

13. 2/3

14. 0

15. 5/2

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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The equations are solved to give;

46. x = 5

48. h = 1

50. The inequality is 7 ≤ d/ -5

An algebraic expression is described as a mathematical expression that is composed of terms, factors, coefficients, constants and variables.

They are described as expressions made up of arithmetic operations which includes;

Given the expression;

46.  |2x + 5| = 3x

Take the absolute value, we have;

2x + 5 = 3x

collect like terms

2x - 3x = - 5

-x = -5

x = 5

48.  (3h + 8) + 2 = 13

expand the bracket

3h + 8 + 2 = 13

collect like terms

3h = 13 - 10

3h = 3

Make 'x' the subject of formula

h = 1

50. Seven is at most the quotient of a number d and -5.

This is expressed as;

7 ≤ d/ -5

Hence, the values are x = 5, h = 1 and 7 ≤ d/ -5

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Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

To determine if the LCM of two numbers is the product of the two numbers using their prime factorization, you need to check if the numbers are coprime.

Coprime numbers have no common prime factors except for 1. If the numbers are coprime, their LCM will be equal to the product of the two numbers.

To tell if the LCM of two numbers is the product of the two numbers, you need to compare the prime factorization of the two numbers. If the prime factors of both numbers are unique (meaning they do not share any common factors), then the LCM will be the product of the two numbers. However, if the two numbers share some common prime factors, then the LCM will have to include those factors at their highest power. So, to find the LCM of the two numbers, you need to take the highest power of each prime factor that appears in either number and multiply them together. If the product of these highest powers matches the product of the two numbers, then the LCM is equal to the product of the two numbers.

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The Height of the utility pole is : 16.971

Given that a 12-foot ladder is leaning against a wall and the top slips down the wall at a rate of 2ft/s.

We need to find how fast will the foot be moving away from the wall when the top is 9 feet above the ground?

Let the distance between the foot of the ladder and the wall be x. The distance between the top of the ladder and the ground is (12 - x).

The ladder, wall, and ground form a right-angled triangle. Therefore, x² + (12 - x)² = 12² Simplify:

x² + 144 - 24x + x² = 1442x² - 24x = 0x(2x - 24) = 0x = 0, 12

Since the distance cannot be zero, x = 12 - 9 = 3 feet

When the top of the ladder is 9 feet above the ground, the distance between the foot of the ladder and the wall is 3 feet. Differentiating the equation with respect to time, we get:

2x(dx/dt) - 24(dx/dt) = 0dx/dt (2x - 24) = 0When x = 3, dx/dt (2(3) - 24) = -36ft/s

When the top of the ladder is 9 feet above the ground, the foot is moving away from the wall at a rate of 36ft/s.

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Given: A 12-foot ladder is leaning against a wall. The top of the ladder slips down the wall at a rate of 2ft/s.

The top of the ladder is 9 feet above the ground.

To find: How fast will the foot be moving away from the wall when the top is 9 feet above the ground?

Solution: Let y be the distance between the wall and the foot of the ladder

Let x be the distance between the top of the ladder and the ground

From the given data, the ladder makes a right-angled triangle with the wall.

So, we have: y² + x² = 12²

Differentiating w.r.t t, we get:

2y (dy/dt) + 2x (dx/dt) = 0

When the top of the ladder is 9ft above the ground, we have:

x = 9fty² + x² = 12²y² + 9² = 12²y² = 12² - 9²y² = (12 + 9)(12 - 9)y² = 63y = √63 ft

So, when the top of the ladder is 9ft above the ground, we have:

y = √63 ft

Let v be the velocity of the foot when the top is 9 feet above the ground.

We know that:

dx/dt = 2 ft/s (given)

Substituting the values in equation (2),

we get: 2 (dy/dt) + 2 (9) (2) = 0(2) (dy/dt) = -36dy/dt = -18 ft/s (negative because the foot is moving away from the wall)

Therefore, the foot is moving away from the wall at a rate of 18 ft/s when the top is 9 feet above the ground.

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