2x+1=7x+3-8x+1=
I need help simplifying this

Answer:

X = 15 = Erin's age

Y = 18 = Alex's age

Step-by-step explanation:

X = Erin's age

Y = Alex's age

33 (combined ages) - 3 (how many years Erin is younger than Alex) = 30

30 ÷ 2 = 15

15 + 0 = 15 (Erin's age)

15 + 3 = (Alex's age)

X = 15 = Erin's age

Y = 18 = Alex's age

The expression for the sequence 48, 49, 50, 51, is aₙ = n + 47

The sequence is an arithmetic progression. Therefore, the expression of the sequence can be ascertain with the arithmetic formula as follows:

aₙ = a + (n - 1)d

where

Therefore,

a = 48

d = 49 - 48 = 1

Hence,

aₙ = 48 + (n - 1)1

aₙ = 48 + n - 1

aₙ = 48 - 1 + n

aₙ = n + 47

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By applying the operation of addition we observed that the sum of two number are belong to the given set

take any two numbers suppose a and b

and applying the operation addition

Irrational numbers are not closed under addition.

The closure property of addition in irrational numbers say that sum of two irrational number is always a rational number, But this is not true. It is not necessary that the sum is always irrational some time it may be rational.

This can be understood with the help of an example:

let (2+√2) and (-√2) be two irrational number. Their sum is (2+√2)+(-√2) = 2, which is clearly a rational number.

Hence, irrational numbers are not closed under addition.

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The standard error of the distribution of sample proportion is 0.0490.

What is the standard error of the distribution?

The standard error of a statistic's sampling distribution, denoted as x, describes how much the computed statistics should differ from one another when calculated from a sample of similar size and drawn from similar population models.

We have,

Population parameter (P) = 0.4,

n = 100,

The standard error (S.E.) =?

The formula of standard error (S.E.) =  [tex]\sqrt{\frac{P(1 - P)}{n} }[/tex]

By using the formula:

S.E. = √0.4(1 - 0.4)/100

S.E. = √0.0024

S.E. = 0.0489

S.E. = 0.0490

Hence, the standard error of the distribution of sample proportion is 0.0490.

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The farmer will produce 700kg of rice this year, which is 30%(percentage) less

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

A farmer produces 1000kg of rice.

This year the production of rice decreased by 30%

30% of 1000 will be 1000*30/100 = 300

So total production this year will be 1000-300 = 700KG

Hence, the farmer will produce 700kg of rice this year.

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Proved that a quadrilateral is a square then the quadrilateral is also a rectangle.

A quadrilateral is a closed shape created by uniting four points, any three of which cannot be collinear. Four sides, four angles, and four vertices make up a quadrilateral.

Quadrilaterals have a few characteristics as follows:

Each side of figure has four sides.

Each of them has four vertices.

The Two diagonals are present.

The sum of all interior angles is 360 degrees.

Given to prove if a quadrilateral is a square, then the quadrilateral is a rectangle.

The Square has four equal sides, and all four angles.

Rectangle has equal opposite sides, and all four angles are the right angle.

Thus, the two sides of the square can be increased to form a rectangle.

Hence, We have Proved that if a quadrilateral is a square then the quadrilateral is also a rectangle.

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The mean of a observed values approaches the population mean more and more as the number of data points gathered rises.

The average calculated from the group members, distribution, or population is known as the population mean.

Thus, choose a population with a finite mean and a random sample of observations. The mean of a observed values approaches the population mean to a greater extent as the number of data gathered rises.

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The moment of inertia of a cube with mass m = 0.500kg and side lengths s = 0. 030m about an axis which is both normal (perpendicular) to and through the center of a face of the cube is I = 2.205x10^-4 kg/m^2.

Here Given mass m = 0.5 kg

And side length = 0.03 m

Moment of inertia I = mass x radius of rotation squared

I = mr^2

In this case, the radius of rotation is about an axis which is both normal (perpendicular) to and through the center of a face of the cube.

Calculating from the dimensions of the the box, the radius of rotation r = 0.021 m

Therefore, I = 0.5 x 0.021^2 = 2.205x10^-4 kg/m^2

Hence the answer is the moment of inertia of a cube with mass m = 0.500kg and side lengths s = 0. 030m about an axis which is both normal (perpendicular) to and through the center of a face of the cube is I = 2.205x10^-4 kg/m^2.

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The coordinate will make perpendicular AB to CD is D(x, x/3 + 3). We have used the slope concept to solve this problem.

The slope of a line segment between two points (x1,y1) and (x2,y2) is given by the ratio of change in the y coordinate to the change in the x coordinate.

Slope = (y2 - y1)/(x2- x1)

Slope of line AB = (-5-4)/(2-(-1)) = -9/3 = -3

Let the slope of another segment CD be m.

As the product of two perpendicular segments is equal to -1.

So,

-3m = -1

m = 1/3.

Let,s assume point D is (x,y)

Slope of segment CD = (y - 4) / (x-3)

(y - 4) / (x-3) = 1/3

3(y-4) = (x-3)

3y = x+9

y = x/3 + 3

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Among smokers, the etiologic fraction of disease due to smoking is: a score of 0.83 for lung cancer and 0.18 for coronary thrombosis.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

The death rate per 100,000 for lung cancer is 7 among nonsmokers and 71 among smokers.

The death rate per 100,000 for coronary thrombosis is 422 among nonsmokers and 599 among smokers.

Lung cancer's relative risk (RR) is equal to 71/7 =  10.1

Lung cancer population etiological factor (PEF) =

0.55(10.1 -1) /0'.55 (10,1 -1)+1

= 0.83

Coronary thrombosis' relative risk (RR) is 599/422, or 1.42.

The population etiological factor (PEF) for coronary thrombosis

= 0.55 (1.42-1)/0'.55. (1.42 -1)+1

= 0.18

Hence, Among smokers with a score of 0.83 for lung cancer and 0.18 for coronary thrombosis.

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As per the given standard deviation, the standard error is 5

Standard deviation:

Basically, standard deviation means the root-mean square deviation as it is the square root of means of the squared deviations from the arithmetic mean.

Given,

A sample of size 16 is randomly selected from a population of size 90.

Here we need to determine the standard error of the mean if the population standard deviation equals 20.

As per the given question, we know that,

Number of population is 16

And the standard deviation = 20

So, the standard error is calculated as,

=> Error =  20/√16

=> error = 20/4

=> error = 5

Therefore, the standard error is 5.

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The constant of proportionality in the equation c = 8m will be; 8.

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

We have been given C = 8m is an equation and the relationship between c and m is direct.

This means that dividing both sides of the equation by m, we have;

C/m = 8m/m

c/m = 8

Therefore, the constant of proportionality is 8

It is found that the constant of proportionality for which c = 8m will be 8.

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The odd for the event happening is 0,45%.The probability of event happening is quite posssible but it has less probability the event is not on the odds than the event is not happening.

Probability of event happening always count as two probability where it is 0 and 1 ,or the event is happening and not. To count odds for the event happening you can use this formula: odds = event happening : total probability/experiment x 100%. As per given the odds is 47 and total experiment is 47, the calculation will be:

odds = [tex]\frac{21}{47}[/tex] x 100% = 0.44680851063%

odds = 0,45%

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No matter what the shape of the parent population is, as long as our sample size is 10 or greater, we can conclude that the sampling distribution of the sample mean is approximately normally distributed. This statement is False.

We know that,

the Central limit theorem says that no matter what the distribution of the population is, as long as the sample is "large", meaning of size 30 or more, the sample mean is approximately normally distributed. If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size.

So therefore we need sample size greater than 30 and we have given 10 or greater.

Hence the given statement is false.

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The two functions are a part of the same family of functions

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

Equations

y= -80(x-1)^{2} + 80

y=-0.49(x-12)^2 +70

These equations can be re-expressed properly as follows

So, we have the following representation

y= -80(x-1)² + 80

y=-0.49(x-12)² +70

From the above representations, we can see that the degrees of both equations are 2

This means that the equations are quadratic equations

This is so because a quadratic equation is represented as y= a(x - h)² + k

Hence, the two functions are a part of the family of quadratic equation  functions

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Place value of 432 is 400 +30+02 .

What is place value?

In math, each digit in a very variety features a place value. Place value is outlined because the price pictured by a digit in a very variety on the premise of its position within the variety.

Main body:

The place value of a digit will increase by 10 times as we move  left on the place worth chart and reduces by ten times as we tend to move right.

The place of digit 4 will be hundreds.

The place of digit 3 will be tens.

The place of digit 2 will be ones.

Hence place value of 432 is  400 +30+02 .

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Answer:

Step-by-step explanation:

In the pic below:-

The quotient is (x + y) (3x -y) for the expression[tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex]    .

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is

[tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex]      

The factor of equation 3x³-7x2y-7xy²+3y³ are,

(x + y) (3x - y) (x - 3y)

The given expression can be written as,

[tex]\frac{(x + y) (3x - y) (x -3y)}{x-3y}[/tex]

=(x + y) (3x -y)

The required quotient for the given expression [tex]\frac{3x^3-7x^2y-7xy^2+3y^3}{x-3y}[/tex] is (x + y) (3x -y).

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We can determine if a function is linear or quadratic by, if the function is exponential if the variable is in the exponent. It is a quadratic equation if the variable is not in the exponent. The function is a linear function if it lacks an exponent.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

We can determine if a function is linear or quadratic by,

For data presented as ordered pairs, you can calculate the model's degree by identifying differences between dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.

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The explanation about counterexample for the conjecture is describe below.

The term counterexample alludes to an occasion or model that offers the expression bogus. This is utilized in rationale to check in the event that an assertion is valid or not. Counter model will quite often counter the explanation being talked about with admirable sentiments.

The inquiry needs to show the relationship that might exist among perimeter and area of a rectangle.

The counterexample gave the aspects that gave the border which is 40 however neglected to give area of 1 square unit

Thus, A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

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The Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 [tex]cm^3[/tex].

What is pyramid ?

 A three-dimensional shape is a pyramid. Flat triangular sides that are joined at a common point known as the apex define the polygonal base of a pyramid. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

Here slant height l = 16cm and sides of the rectangular base is ,

length l = 15cm and width w = 9 cm.

Side length = 9/2 = 4.5cm

Using Pythagorean theorem ,

=> Height h =  [tex]\sqrt{16^2-4.5^2}[/tex]

=> height h = 15.35 cm

Now volume of pyramid is ,

=> V = 1/3 * Base area * height cubic unit

=> V = 1/3 *15*9*15.35

=> V = 690.75 [tex]cm^3[/tex]

Hence the Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 [tex]cm^3[/tex].

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Because it only considers the worst possible outcomes, the maximin decision criterion has the least downside risk.

Wald's maximin model is a non-probabilistic decision-making model in game theory and decision theory.

It says that while choosing a course of action, the decision-maker should choose the one whose greatest (highest) loss is better than the least (minimum) loss of all other options that are feasible under the current conditions. The approach that maximizes one's own lowest payout is referred to as "maximin" in non-zero-sum games.

When given a choice between numerous options, the maximin approach instructs managers to consider each option's worst-case outcome. This presupposes that each choice has a number of possible outcomes.

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Answer:

x= -1.5

Rounded: x= -2

Step-by-step explanation:

3(-6x)+5=32

-18x+5=32

      -5. -5

-18x=27

/-18.  /-18

x=-1.5

And I guess I round to a whole number

x=-2

Hopes this helps please mark brainliest

3(-6x) + 5 = 32

multiply out left side:

-18x + 5 = 32

subtract 5 from both sides:

-18x = 27

divide both sides by-18:

x = -3/2

or

x = -1.5

When the null hypothesis is rejected in ANOVA analysis, we can test for differences between treatment means by doing a t-test.

It is statistically possible to compare the means of two or more groups of data using the ANOVA approach. It includes comparing the null hypothesis, which states that the means of the groups are equal, to the alternative hypothesis, which states that at least one of the means is different. If the null hypothesis is disproved, it signifies that the group means deviate significantly from one another.To test for these differences, we may use a t-test, which is a statistical test used to evaluate if the means of two groups are significantly different from one another. With the use of a t-test, we may assess if there are any statistically variations in terms of the 2 groups.

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The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t) using the eigen value method.

The coefficients of a set of linear equations are represented by coefficient matrices. These matrices are frequently used to streamline the process of calculating equations  by arranging the coefficients in a standardized manner. The coefficient matrix is frequently designated as A, with the dimensions matching to the number of equations and variables in the system. A system of three equations with three variables, for inspection , would have a 3x3 coefficient matrix. The elements in the matrix reflect the coefficients of each variable in each equation and may be used to solve the problem using various approaches such as Gaussian elimination or matrix inversion.

How to solve?

x1' = -3x1 + 2x2

x2' = -3x1 - 2x2

The characteristic equation is (-3-λ)(-3+λ)+4=0, which simplifies to λ^2-9+4=0, or λ^2-5=0. This has solutions λ = +-sqrt(5).

For λ = +sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 + 2sqrt(5)x2

x2 = -(3/2)x1 + (1/sqrt(5))x2

eigenvector x2 = (1/sqrt(5))x1.

For λ = -sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 - 2sqrt(5)x2

x2 = -(3/2)x1 - (1/sqrt(5))x2

Dividing both sides by (1+3/2sqrt(5)), we get the eigenvector x2 = (-1/sqrt(5))x1.

The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t).

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The average rate of change of g(x) over the interval [-3, 3] is 2.

For a function f(x), we define the rate of change over an interval (a, b) as:

(f(b) - f(a))/(b - a)

Here we have the interval [-3, 3] and the function:

g(x) = x^2 + 2x + 8

Then the average rate of change over that interval will be:

[ g(3) - g(-3)]/(3 - (-3))

The values in the denominator are:

g(3) = 3^2 + 2*3 + 8 = 9 + 6 + 8  =23

g(-3) = (-3)^2 + 2*-3 + 8 = 9 - 6 + 8 = 11

Replacing that we get:

[23 - 11]/(3 + 3) = 12/6 = 2

The average rate of change over that interval is 2.

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The equation which represents this scenario would be y = 2x + 1.

What is a linear function?

The term linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

Miguel runs 1 mile in the first week and in the second week he runs 2 runs farther than his distance for the previous week,

Let the distance covered in the previous week be 'x' distance then his goal can be represented as '2x'.

Then the given scenario can be represented by

                 y = 2x + 1.

Hence, the equation which represents this scenario would be y = 2x + 1.

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Answer:

[tex]\textsf{1.} \quad 2[/tex]

[tex]\textsf{2.} \quad -4[/tex]

[tex]\textsf{3.\quad und\:\!efined}[/tex]

[tex]\textsf{4.} \quad 0\;\;\textsf{(zero)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{3-(-1)}{2-0}=\dfrac{4}{2}=2[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{6-(-10)}{2-6}=\dfrac{16}{-4}=-4[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{5-2}{3-3}=\dfrac{3}{0}=\textsf{und\:\!efined}[/tex]

Given points:

Substitute the given points into the slope formula:

[tex]\implies \textsf{Slope}=\dfrac{3-3}{5-2}=\dfrac{0}{3}=0[/tex]

Answer:

The required function formula is,

D(t) = 160 - 25 t

Given,

The total distance of her from the safe zone = 160 meters,

And, after 3 seconds she is 85 meters far away from the safe zone,

Thus, the total distance she covered in 3 seconds = 160 - 85 = 75 meters, Since, she drove at a constant speed,

Also,

Thus, the distance she will cover in t seconds = 25 t

( Because, Distance = Speed × Time )

Hence, the total distance of her from the safe zone after t seconds, D(t) = 160 - 25t

Which is the required function formula.

Step-by-step explanation:

The monthly payment needs to pay is  15,505.3.

What is the percent deposit?

Deposit Percentage refers to the percentage of total Deposit Exposures represented by any Deposit Lender's Deposit Exposure.

We have,

Car price to pay 137,825,

saved up a 10%

The rest can pay in 8 monthly deposits.

So, firstly we divide the total price amount by 10 to get the deposit amount,

137,825 /10 = 13,782.5

then minus this amount from the total amount,

137,825 - 13,782.5 = 1,24,042.5

again divide this amount by 8 to get monthly deposit,

monthly each payment = 1,24,042.5/8

= 15,505.3

Hence, the monthly payment needs to pay is  15,505.3.

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