What is the equation of the line that passes through the point (-1,2) and has a slope of -1?

2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.

In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.

It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.

So, we got:

r = 3.5%/100% = 0.035

We have our exponential function:

P(t) = 2500*(1 - 0.035)^t

The number after 5 years is provided by substituting t = 5, we will get:

P(5) =  2500*(1 - 0.035)^5 = 2,092.1

Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.

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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years

This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.

This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.

In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.

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Answer: x+6

Step-by-step explanation:

5x-3(x-2)-x .......................... Question

5x-3x+6-x ........................... Distribute

1x+6 ..................................... Combine like terms

x+6 ...................................... Multiply by 1

Answer: x+6

Step-by-step explanation:

5x-3(x-2)-x

5x -3x +6 -x

x + 6

The 95% confidence interval estimate of the population mean is 98.10< μ < 98.30.

Given that

sample mean = ~x = 95.2

sample standard deviation = s = 0.7

sample size = n = 175

Degrees of freedom = d.f = n - 1 = 175 - 1 = 174

αt /2,d.f = 1.974.

The explanation for step 1

At 95% confidence level

 α= 1-0.95% =1-0.95 =0.05

α /2=0.05/ 2= 0.025

αt /2,d.f = t0.025,174 = 1.974

αt /2,d.f = 1.974

The explanation of Step 2

Margin of error = E = t/2,df x (s /Vn )    =  1.974 x ( 0.7/ V175)   = 0.10

Margin of error = E = 0.10

The 95% confidence interval estimate of the population mean is,

~x- E < μ < ~x + E

98.2 - 0.10< μ < 98.2 + 0.10

98.10< μ < 98.30

Margin of error = E = 0.10

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Answer:

q = -4

Step-by-step explanation:

0.0009 = 9 × 10^(-4)

q = -4

Answer:  l +d ≤ 14

Step-by-step explanation:

The minimum number of packages of shingles that would be needed to do the job would be = 0.285 package.

An area of an object is defined as the total area that is being covered by the shape of that object.

This given object has the total of five sides with two triangles, and three rectangles.

The top part of the object is what is needed to be roofed therefore the area of the 2 rectangles should be determined as follows.

Area of rectangle =2( l ×w)

l = 14cm

w = X cm ( this is calculated using the Pythagorean theorem)

w² = 4.1² + 4²

w² = 16.81 + 16

w² = 32.81

w = √ 32.81

w = 5.7cm

Area of rectangle = 2× (14 × 5.7)

= 2× 79.8 = 159.6 cm²= 1.596m²

If 1 package of shingles = 5.6 m²

X package = 1.596m²

make X package the subject of formula = 1.596× 1/5.6

= 0.285 package.

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Answer:

[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]

Step-by-step explanation:

See picture below :)

The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).

The general solution of the mentioned differential equation will be calculated as follows -

Firstly rewriting the differential equation in standard form:

(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]

Calculating the integrating factor to make the LHS as a total derivative:

As known, formula for integrating factor is:

mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]

= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]

= (x+1)(x+2)

Now multiplying both sides of the equation by the integrating factor:

(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

LHS will be a total derivative. Rearrange the equation for the same -

d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

Integrating both sides of the equation:

(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx

= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C

Now find the equation for y:

y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)

Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.

The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).

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Answer:

  20%

Step-by-step explanation:

You want to know the percentage change from 1120 to a final number that is 100 less, 130 more, and 254 less.

The percentage change is given by ...

  percent change = change/(original amount) × 100%

Here, the total amount of change is the sum of the given changes:

  -100 +130 -254 = -224

Then the percentage change is ...

  -224/1120 × 100% = -20%

The percent decrease is 20%.

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The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.

In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.

We have to check there be two integers whose sum is 15.

As we know that,

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.

There are total 10 elements.

We have to choose two element from the given set which sum is equal to 15.

If we choose 3 and 12 then there sum is 15.

Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.

So the given set have two integers whose sum is 15.

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convert 2.8hours to hours, minutes and seconds is 2.8 hours = 2 hours 48 minutes 0 seconds

The conversion of 2.8 hours into hours, minutes and seconds is relatively simple. To begin, we must first convert 2.8 hours into minutes. To do this, we multiply 2.8 by 60, which equals 168 minutes. Now, we need to convert those minutes into hours and seconds. To do this, we divide the 168 minutes by 60, which gives us 2 hours. We then take the remainder, which is 48 minutes, and divide it by 60, which gives us 0 seconds. Therefore, 2.8 hours is equivalent to 2 hours 48 minutes 0 seconds.

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Answer: h = 92

Step-by-step explanation:

148 - 180 = 32

32 + 56 = 88

88 - 180 = 92

The correct option for the graph shown are-

The question's line traverses the origin and (4,-12).

The line's rate of change is;

m = -12 - 0 / 4 - 0

m = -3

The slope of the line or its rate of change is -3.

The line's equation is provided by;

y - 0 = -3(x - 0)

y = -3x

This relationship is linear as a result.

The relationship is proportionate if we take any value of x because there will only ever be one value of y.

Therefore, the following claims are accurate:

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Answer:

The answer is (-4x + 15y - 6xy)

Step-by-step explanation:

(3x + 4y - 3xy + 5x + 3y - 2xy)

= 8x + 7y - 5xy

(2x + y - 3xy + 10x - 9y - 8xy)

= 12x - 8y - 11xy

Now,

(8x + 7y - 5xy) - (12x - 8y - 11xy)

8x + 7y - 5xy - 12x + 8y + 11xy

= -4x + 15y - 6xy

Thus, The answer is (-4x + 15y - 6xy)

Answer:

5x + 10× - 30= 180 degree

15x =150

x= 10

The predicted value of the twin born first has an IQ of 104 is 106.2..

We have given that,

sample size n = 10

x = 98.13

y = 100.6

r = 0.904

p-value = 0.000

y'= 14.68 + 0.88x

significance level = 0.05

and we have to find predicted value of the twin born first has an IQ of 104.

We know that x represents the IQ score of the twin born first.

Therefore value of x is 104.

Hence the predicted value P will be,

P = 14.68 + 0.88(104)

  = 14.68 + 91.52

P = 106.2

Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.

The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.

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Step-by-step explanation:

The length of each side of the given square is 3.306 yards.

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

In geometry, a square is a flat shape with four equal sides and four right angles (90°).

A square is a unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

So, we have the area of the square as:

1.21 yards²

Area formula of square: A = s²

Now, calculate to find the length of the square as follows:

A = s²

1.21 = s²

s = 4/1.21

s = 3.306

Therefore, the length of each side of the given square is 3.306 yards.

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The expression that has the element of A*B*B is Option A - (b,2,3)

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

The "elements" of a set are the objects that make up the collection. Sets are equal if and only if they have the same elements, therefore a = A denotes that 'a' is one of A's elements. For sets, repetition and order are irrelevant.

Given, A={a.b} and B=[1,2,3]

Since the required expression was supposed to have the element of A*B*B the correct option would be A since it has elements b from A, 2 from B, and 3 from B, fulfilling all the required elements.

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The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.

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Answer:

2x=9+7

2x=16

x= 2/16

x=8

​

Step-by-step explanation:

Answer:

A: 74.9

B: 51.4

C: 53.7

Sorry I don't have enough time for the rest

Step-by-step explanation:

all angles should add up to 180

The algebraic expression for "9 less than the quotient of z and 8" exists 9 - z / 8.

Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions.

Similar to this, when we describe an algebraic expression in English and it has a variable, we are doing so (an expression with a variable).

A mathematical expression made composed of integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Let the given expression be "9 less than the quotient of z and 8".

simplifying the expression, we get

= 9 - z / 8

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The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

The gradient vector field of a function

Suppose that  a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.

In which:

fx(x,y) is the partial derivative of f relative to variable x.

fy(x,y) is the partial derivative of f relative to variable y.

The function in this problem is defined as follows:

f(x,y) = xe^(9xy).

The partial derivative relative to x  as follows:

fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).

The partial derivative relative to y  as follows:

fy(x,y) = 9x²e^(9xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

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a. The polynomials are given as follows:

1. 2x^4 + 18x³ - 4.

2. -8x³ + 4x + 2.

3. 2x² - x - 10

4. 3x³ + 10x² + 9x + 2.

b. The resulting degrees are given as follows:

1. 4.

2. 3.

3. 2.

4. 3.

c. The end behavior of each polynomial is given as follows:

1. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

2. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> -∞.

3. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

4. As x -> -∞, f(x) -> -∞, as x -> ∞, f(x) -> ∞.

The polynomials are obtained doing the operations and then combining the like terms.

Hence:

(6x³ + 3x² - 4) + (2x^4 - 3x² + 12x³)

2x^4 + (6 + 12)x³ + (3 - 3)x² - 4.

2x^4 + 18x³ - 4.

(10 + 4x - 3x³) - (5x³ + 8)

10 + 4x - 3x³ - 5x³ - 8

-8x³ + 4x + 2.

(x + 2)(2x - 5)

2x² - 5x + 4x - 10

2x² - x - 10

(x + 2)(3x² + 4x + 1)

3x³ + 4x² + x + 6x² + 8x + 2

3x³ + 10x² + 9x + 2.

The degree of a polynomial is given by the highest exponent in it's equation.

The end behavior of a polynomial is calculated as the result of elevating negative infinity and then positive infinity to the highest exponent of the polynomial, considering the leading coefficient.

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Answer:About 155 results (0.47 seconds)

Tax and Tip - Illustrative Math Taskshttps://tasks.illustrativemathematics.org

Step-by-step explanation:

this may help

The correct hypothesis relation is  is H₀ : μ ≥ 2,412. and Ha : μ < 2,412

According to the United States Census Bureau, the average area = 2, 412 square feet

Then the null hypothesis is

H₀ :μ ( mean ) area is greater than or equal to 2,412

H₀ : μ ≥ 2,412.

But, according to Jane, in her area, still families want a small home comparison to average.

Alternative hypothesis is that, mean area is less than 2,412 .

Ha : μ < 2,412.

Therefore,  H₀ : μ ≥ 2,412. and Ha : μ < 2,412

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Average speed of Usain Bolt is 10.41 m/s.

The distance travelled by an object in relation to the amount of time it takes to travel that distance can be used to define speed. In plainer terms, it is a gauge of how quickly an object moves.

Average speed = (Total distance travelled)/(Total time required)

SI unit of speed is m/s.

Distance Travelled by Usain Bolt = 100m

Time required to travel this distance =  [tex]9\frac{3}{5}[/tex] = 48 ⁄ (5 sec)

Average speed = (Total distance travelled)/ (Total time required)

Average speed = 100/ (48/5)

                          = 500/48

                          = 10.41 m/s

Therefore, average speed of Usain Bolt is 10.41 m/s.

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64.5 divided by 12.3 using rounding 60 divided by 10 gives 5.33.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given numbers are,

64.5 and 12.3.

When 64.5 is divided by 12.3.

The 64.5 can be rounded as 64

And 12.3 can be written after rounded as 12

Now divide 64 by 12.

64 / 12 = 5.333

The value of 64.5 divided by 12.3 is 5.33.

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