What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2
1 over the quantity x plus 3 times the quantity x plus 4
1 over the quantity x plus 3 times the quantity x minus 2
1 over the quantity x plus 4 times the quantity x minus 2
1 over the quantity x plus 3 times the quantity x plus 1

Answer:

The rule for a reflection over the y -axis is (x,y)→(−x,y) .

A'(-(x) ; y)

A'(-(-5) ; 3)

A'(5 ; 3)

The inequalities solution is given below as

[tex]8 x-y \leq 32 \\\\&-3 x+5 y \leq 25 \\\\& \Rightarrow {[8 x-y \leq 32] \times 5 } \\\\& {[-3 x+5 y \leq 25] \times 1 } \\\\& \Rightarrow 40 x-5 y \leq 160 \\\\&-3 x+5 y \leq 25 \\\\& 37 x \leq 185 \\\\& x \leq \frac{185}{37} \leq 5[/tex]

substitute $x=5$ into eqn(11)

[tex]-3 x+5 y \leq 25\\\\$-3(5)+5 y \leq 25\\\\& -15+5 y \leq 25 \\\\\& 5 y \leq 25+15 \\\\& 5 y \leq 450 \\\\& y \leq \frac{40}{5} \\\\& -y \leq 8 \\\\[/tex]

(5,8)

z=-4 x+5 y

[tex]& \frac{\partial z}{\partial x}=-4(i)-5 y \\[/tex]

=-4-5 y

when y=8

[tex]\frac{\partial z}{\partial x} & =-4-5(8)[/tex]

=-4-40

=-4-40

=-44

[tex]& \frac{\partial z}{\partial y}=-4 x-5(i) \\[/tex]

when x=5

[tex]\frac{\partial z}{\partial y}=-4 x-5 \\[/tex]

[tex]\frac{\partial z}{\partial y} & =-4(5)-5 \\[/tex]

=-20-5

=-25

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The required value of the given expression of limit is 1/2.

In mathematics, a limit is a fundamental concept that describes the behavior of a function as its input approaches a certain value or point. In particular, the limit of a function at a point is the value that the function approaches as its input gets arbitrarily close to that point, whether from the left or the right.

Here,
Given expression,
[tex]=\lim_{x \to \\ \pi /3} sin(3\sqrt{2}x/\pi - sec(3x/4) + \pi/6)[/tex]

Put x = π/3
= sin (3√2 × π/3 × 1/π - sec (3/4 × π / 3) + π /6)
= sin(√2 - sec(π/4) + π/6)
= sin(√2 - √2 + π/6)
= sin(π/6)
= 1/2

Thus, the required value of the given expression of limit is 1/2.

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A complex number is a number of the form a + bi, where a and b are real numbers

Given is that {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients.

Yes, the given statement -

" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.

Therefore, the given statement -

" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.

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1)

The value of x is 30.5.

The measure of each angle is:

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

The measure of ∠b is 60.7.

The measure of ∠d is 43.1.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

1)

Since line m and line n are parallel.

(2x + 25) and 86 are alternate interior angles.

So,

2x + 25 = 86
2x = 86 - 25

2x = 61

x = 30.5

And,

∠2 and 86 are opposite angles.

So,

∠2 = 86

∠1 and ∠3 are opposite angles.

So,

∠1 = ∠3

And,

∠3 + 86 = 180

∠3 = 180 - 86

∠3 = 94

∠3 and ∠4 are alternate interior angles.

So,

∠3 = ∠4 = 94

∠1 and ∠6 are exterior alternate angles.

∠2 and ∠5 are exterior alternate angles.

So,

∠1 = ∠6 = 94

∠2 = ∠5 = 86

2)

Line m and line n are parallel.

So,

∠b and 60.7 are alternate interior angles.

∠d and 43.1 are alternate interiro angles.

So,

∠b = 60.7

∠d = 43.1

Thus,

1)

The value of x is 30.5.

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

∠b = 60.7

∠d = 43.1

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The student's claim is incorrect, and SAS information is sufficient to prove the congruence of the triangles.

What is triangle ?

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has various properties and formulas associated with it, such as its area, perimeter, angles, and side lengths. Triangles can be classified into different types based on their angles and side lengths, such as acute, right, obtuse, isosceles, and equilateral triangles. Triangles also have applications in various fields, including engineering, architecture, and physics.

The error in the student's reasoning is that they have misunderstood the SAS (Side-Angle-Side) congruence criterion. SAS criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. The order of the vertices of the triangle does not matter.

In the given case, if we have AJ = AR and KL = QP, and the included angle JAK is congruent to the included angle RAQ, then we have the SAS information to prove that triangles AJK and ARQ are congruent. The student's argument that the triangles are not congruent because J does not map onto R and L does not map onto P is incorrect, as the order of the vertices does not matter. The correct mapping is to move J to R and L to P by using a translation, and the triangles will coincide.

Therefore, the student's claim is incorrect, and SAS information is sufficient to prove the congruence of the triangles.

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The proper choice is D, and it provides the best-fitting regression model for the data plot under consideration.

A model that uses a linear regression has an output-input connection that is a straight line. The most straightforward to understand and even see in action in the actual world is this. Even when a relationship isn't quite linear, our brains nevertheless attempt to recognize the pattern and associate that relationship with a crude linear model.

The number of responses to a marketing effort could serve as one illustration. We might receive five responses out of 1,000 emails sent. If a linear regression can be used to describe this relationship, then we can anticipate ten responses from 2,000 emails sent. Your chart may be different, but the basic premise is the same: we link a predictor and a goal and presume that they are related.

There is typically a regression model running in the background to support a claim like this, whether it is connected to exercise, happiness, health, or any other claim.

Moreover, a mean squared error can be used to describe the model fit. In essence, this provides us with a numerical representation of how well the linear model fits.

Predicting a patient's length of hospital stay, the association between income and crime, the birth rate and education, or the relationship between sales and temperature are more serious instances of linear regression.

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Therefore, the following exponential probability density function P(4 ≤ x ≤ 6) is 0.1406 (rounded to four decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is a mathematical concept that quantifies the degree of uncertainty of an outcome in a given situation or experiment. Probability is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here,

(a) The formula for P(x ≤ x0) is the cumulative distribution function (CDF), which gives the probability that the random variable x is less than or equal to a certain value x0. For the exponential probability density function given, the CDF is:

F(x) = P(x ≤ x0) = ∫[0,x0] f(x) dx = ∫[0,x0] (1/5)e*(-x/5) dx

(b) To find P(x ≤ 4), we substitute x0 = 4 into the CDF formula and evaluate the integral:

P(x ≤ 4) = F(4) = ∫[0,4] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 4

= -e*(-4/5) + 1

≈ 0.3297 (rounded to four decimal places)

(c) To find P(x ≥ 5), we note that P(x ≥ 5) = 1 - P(x < 5), where P(x < 5) is the probability that x is less than 5. Using the CDF formula, we have:

P(x < 5) = F(5) = ∫[0,5] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 5

= -e*(-1) + 1

≈ 0.6321

Therefore, P(x ≥ 5) = 1 - P(x < 5) = 1 - 0.6321 = 0.3679 (rounded to four decimal places).

(d) To find P(x ≤ 6), we use the CDF formula with x0 = 6:

P(x ≤ 6) = F(6) = ∫[0,6] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 6

= -e*(-6/5) + 1

≈ 0.4703

(e) To find P(4 ≤ x ≤ 6), we note that P(4 ≤ x ≤ 6) = P(x ≤ 6) - P(x < 4), where P(x < 4) is the probability that x is less than 4. Using the CDF formula, we have:

P(x < 4) = F(4) = ∫[0,4] (1/5)e*(-x/5) dx

= [-e*(-x/5)] from x = 0 to 4

= -e*(-4/5) + 1

≈ 0.3297

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Complete question:

Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0 (a) Write the formula for P(x ≤ x0). (b) Find P(x ≤ 4). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(4 ≤ x ≤ 6). (Round your answer to four decimal places.)

The solution is, the average speed of the boat relative to the water is 9 mph

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time

here, we have,

Let x represent the speed of the boat.

The rate of the current was 7 mph,

Assuming the boat travelled against the current while going upstream, the total speed would be x - 7

Assuming the boat in the direction of the current while going downstream, the total speed would be x + 7

Time = speed × time

Since she travelled 32 miles upstream and 32 miles downstream, then,

Time taken to go upstream = 32/(x -7)

Time taken to go downstream = 32/(x + 7)

Since the total time of the trip was 18 hours, then

32/(x -7) + 32/(x + 7) = 18

Cross multiplying by (x - 7)(x + 7), it becomes

32(x + 7) + 32(x - 7) = 18[(x - 7)(x + 7)

32x + 224 + 32x - 224 = 18(x² + 7x - 7x - 49

32x + 32x = 18x² - 882

18x² - 64x - 882 = 0

Dividing through by 2, it becomes

9x² - 32x - 441 = 0

9x² + 49x - 81x - 441 = 0

x(9x + 49) - 9(9x + 49) = 0

x - 9 = 0 or 9x + 49 = 0

x = 9 or x = - 49/9

Since the speed of the boat cannot be negative, then x = 9

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The Area of Trapezoid of figures given below.

The area of a trapezoid is found using the formula, A = ½ (a + b) h,

where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.

Given:

1. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (22+ 11) x 12

= 33 x 6

= 198 m²

2. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (38+ 24) x 26

= 806 mm²

3. Area of Trapezoid

= 1/2 ( a+ b) x h

= 1/2 (105 + 212) x 78

= 12363 Km²

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Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The cost of renting from Low Price Rentals can be calculated as follows:

Rental fee + Cost per mile × Distance driven = $49 + $0.16 ×60 = $58.60

The cost of renting from Easy Rental can be calculated as follows:

Rental fee + Cost per mile × Distance driven = $25 + $0.50×  60 = $55.00

Therefore, the correct answer is: Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60. So, option 1 is the correct answer.

Hence, Easy Rental, because it will charge $55.00 for the trip, while Low Price Rentals will charge $58.60

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Answer:

the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.

Step-by-step explanation:

The capital value (present sale value) CV of property that can be rented on a perpetual basis for R dollars annually is given by the formula:

CV = ∫₀^∞ R e^(-it) dt

where i is the prevailing continuous interest rate.

To show that CV = R/i, we can evaluate the integral:

CV = ∫₀^∞ R e^(-it) dt

We can use the formula for the exponential integral, which is:

∫ e^(ax) dx = (1/a) e^(ax) + C

Using this formula, we can integrate the exponential function in the integral and obtain:

CV = [ (-R/i) e^(-it) ] from t = 0 to t = infinity

Since e^(-infinity) = 0, we have:

CV = [ (-R/i) e^(0) ] - [ (-R/i) e^(-i*0) ]

Simplifying this, we get:

CV = [ (-R/i) ] - [ (-R/i) ] = R/i

So we have shown that CV = R/i, as required.

Now, to find the capital value of property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year, we can use the formula CV = R/i with R = $10,000 and i = 0.06:

CV = $10,000 / 0.06 ≈ $166,667 (rounded to the nearest whole number)

Therefore, the capital value of the property that can be rented at $10,000 annually when the prevailing continuous interest rate is 6%/year is approximately $166,667.

Answer:

a. If every teacher is given a $1000 raise:

i. The mean salary of the teachers will increase by $1000.

ii. The median salary will also increase by $1000.

iii. The extremes of the salary range will remain the same.

iv. The quartiles will shift up by $1000.

v. The standard deviation of the salaries will not be affected.

vi. The interquartile range (IQR) will remain the same.

b. If every teacher received a 5% raise:

i. The mean salary of the teachers will increase by 5% of the current mean salary.

ii. The standard deviation of the salaries will increase, since the relative difference between the salaries will become larger.

Note: To calculate the new mean salary, you can use the formula:

New mean salary = Old mean salary * (1 + percentage raise)

So, if the old mean salary is $38,500, and every teacher receives a 5% raise, the new mean salary would be:

New mean salary = $38,500 * (1 + 0.05) = $40,425

This means the mean salary of the teachers will increase by $1,925.

To calculate the new standard deviation, you can use the formula:

New standard deviation = Old standard deviation * square root(1 + percentage raise)

So, if the old standard deviation is $7,000, and every teacher receives a 5% raise, the new standard deviation would be:

New standard deviation = $7,000 * square root(1 + 0.05) = $7,266

This means the standard deviation of the salaries will increase by $266.

The statement that the Property damage liability pays for injuries to a driver or their passengers caused by an uninsured or underinsured driver is false.

Auto insurance policy is a contract between the insurance company and the person being insured which protects the person under any financial loss caused by accident or theft.

There are mainly six types of auto insurance coverage that the company basically provide.

They are Property damage liability, Bodily injury liability, PIP, Uninsured and underinsured motorist coverage, collision and comprehensive.

Property damage liability pays for the damage that the person insured causes to someone else's property, which include someone else's car, buildings or so.

The given coverage in the statement is the Uninsured and underinsured motorist coverage.

Hence the given statement is false.

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The Segment Addition Postulate states that if C is between D and E, then DC + CE = DE. In this case, we can use this postulate to solve for T by substituting the given values into the equation and solving for T.

First, we will repeat the question in our answer: Let C be between D and E. Use the Segment Addition Postulate to solve for T.

Next, we will substitute the given values into the equation: DC + CE = DE

Since we are solving for T, we will rearrange the equation to isolate T on one side of the equation: T = DE - DC - CE

Finally, we will substitute the given values for DE, DC, and CE into the equation and solve for T: T = (DE) - (DC) - (CE)

T = (T + DC + CE) - (DC) - (CE)

T = T

Therefore, the value of T is equal to itself, and the Segment Addition Postulate has been used to solve for T.

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The description corresponds to an experiment.

Mathematics is the sciences and study of quality, structure, space, and change. Mathematician's are seek out patterns, formulate new conjectured, and establish truth by the  rigorous seduction from appropriately choden axioms and definitions.

An experiment is a type of scientific research method in which a researcher manipulates one or more variables and measures the effects of the manipulation on other variables. In this example, the researcher divided the thirty university students into two groups and manipulated one variable (free tutoring in mathematics) to measure the effects on another variable (final mathematical examination scores). Therefore, this is an experiment.

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The age of Julia is 13 years.

Integers are whole numbers, including both positive and negative numbers, that do not have any fractions or decimals. In mathematics, integers are often used to represent real-world quantities such as age, time, and money.

In this problem, Julia is the oldest of three siblings whose ages are consecutive integers. We can represent this using the equation x + (x+1) + (x+2) = 42, where x is Julia's age.

To solve this equation, we can use the distributive property to expand the left side of the equation to 3x + 3 = 42.

We can then subtract 3 from both sides of the equation to get 3x = 39. Finally, we can divide both sides by 3 to get x = 13.

Therefore, Julia's age is 13.

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Complete Question:

Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.

Answer:

A = 20 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 5 and h = 8 , then

A = [tex]\frac{1}{2}[/tex] × 5 × 8 = [tex]\frac{1}{2}[/tex] × 40 = 20 ft²

Answer:

C. 13.77 m

Step-by-step explanation:

The sum of the three angles of a triangle is 180°

In the given triangle, two of the angles are 37° and 90°

Third angle = 180 - (37 + 90) = 53°

By the law of sines, ratio of a side to the sine of the opposite angle is the same for all sides and their opposite angles

∴
[tex]\dfrac{a}{\sin 90} = \dfrac{11}{\sin 53}\\\\\sin 90 = 1\\\sin 53 = 0.7986\\\\\rightarrow \dfrac{a}{1} = \dfrac{11}{0.7986}\\\\a = 13.7735\\\\a\approx 13.77\; m[/tex]

Answer:i think the answer is D but it could be C but i know for a fact it is definitely not A or B

Step-by-step explanation:

Answer:

x = 13 or x = 1

Step-by-step explanation:

To solve the equation (x - 7)^2 = 36, we can take the square root of both sides:

(x - 7)^2 = 36

sqrt((x - 7)^2) = sqrt(36)

x - 7 = ±6

Solving for x, we get:

x - 7 = 6 or x - 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.

The formula for the volume of a d-dimensional sphere of radius r is:

V_d(r) = (π^(d/2) / Γ(d/2 + 1)) * r^d

It should be noted that in the formula, Γ is the gamma function.

Let's break down the formula:

π^(d/2) is pi raised to the power of d/2.

Γ(d/2 + 1) is the gamma function evaluated at d/2 + 1.

r^d is the radius raised to the power of d.

Putting it all together, we get the formula above.

For a 2-dimensional sphere (a circle) of radius r, we have d=2, so:

V_2(r) = (π^(2/2) / Γ(2/2 + 1)) * r^2

= (π / Γ(3/2)) * r^2

= (π / (1/2) * √π) * r^2

= 2πr^2

For a 3-dimensional sphere of radius r, we have d=3, so:

V_3(r) = (π^(3/2) / Γ(3/2 + 1)) * r^3

= (4/3) * π * r^3

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commission percentage = 2.18%

Percentage is a way of expressing a proportion or a fraction as a fraction of 100. It is denoted by the symbol "%". For example, if there are 50 red marbles out of 100 marbles in a jar, the percentage of red marbles in the jar would be 50%.

To find the salesperson's commission as a percent of the total monthly sales, we first need to calculate the total monthly sales for September and October combined:

Total monthly sales = September sales + October sales

Total monthly sales = $85,460 + $74,570

Total monthly sales = $160,030

Next, we can divide the commission earned by the total monthly sales and multiply by 100 to get the commission as a percentage:

Commission percentage = (Commission earned / Total monthly sales) x 100

Commission percentage = ($3,485 / $160,030) x 100

Commission percentage = 2.18%

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Therefore , the solution of the given problem of fraction comes out to be the restaurant could make 48 cups of pudding from the 8 quarts they have.

An whole can be represented by any set of related sums or fractions. In standard English, a percentage is used to represent the quantity of a specific size. 8, 3/4. Also wholes are fractions. Numbers are expressed in mathematics using the ratio of it's own portion to the bottom. These fractions are all made up of basic numbers. Due to variances in actual percentage calculations, numerators, and numerators, a difficult fraction contains a fraction. A measurement that reflects a portion of the whole is a percentage.

Here,

There are different ways to approach this problem, but one possible method is to use unit conversions to find how many cups are in 8 quarts, and then divide by 1/6 of a quart per cup.

1 quart = 4 cups (by definition of quart)

Therefore, 8 quarts = 8 x 4 cups = 32 cups

1/6 of a quart = 1/6 x 4 cups = 2/3 cups

Therefore, the number of cups of pudding that could be made is:

32 cups / (2/3 cups) = 48 cups

Therefore, the restaurant could make 48 cups of pudding from the 8 quarts they have.

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Answer:

No, 3,816+467 is not a good estimate! 3,816 is very far from 8,000. 467 is a very low number to be added to 3,816. most likely when you add the two you will get a low number. when you add the two you get 4,283 which is not even close to the number you are trying to reach!

Step-by-step explanation:

hope this helps!

1. The y-intercept when the coordinate is 9,1 and the slope is 4 8= -35

2. The y intercept when the coordinate is -3,-3 and the slope is -1= -6

The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Coordinate geometry allows for a variety of operations, like measuring the distance between two points, segmenting lines into m:n pieces, determining a line's midpoint, calculating a triangle's area in the Cartesian plane, and more.

1.To find the y-intercept, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

Given the point (9,1) and slope 4 8, we can plug in these values to get:

1 = (4 8)9 + b

Simplifying this equation, we get:

1 = 36 + b

b = -35

Therefore, the y-intercept is -35.

2. Again, using the slope-intercept form of a linear equation, we have:

y = mx + b

Given the point (-3,-3) and slope -1, we can plug in these values to get:

-3 = (-1)(-3) + b

Simplifying this equation, we get:

-3 = 3 + b

b = -6

Therefore, the y-intercept is -6.

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Answer:

4/6 and 2/6

Step-by-step explanation:

2/3 = 4/6

1/3 = 2/6

4/6 + 2/6 = 6/6 = 1

Answer:

Step-by-step explanation:

hashhshd

Answer:

≈ 7.8

Step-by-step explanation:

Specific gravity of steel = Density of steel / Density of water

Density of steel = 487 pounds per cubic foot

Density of water = 62.4 pounds per cubic foot

Specific gravity of steel = 487 / 62.4

Specific gravity of steel ≈ 7.8

Therefore, the specific gravity of steel is approximately 7.8.

Based on given question, average rate of change or slope is-0.004 and

the predicted price for 7500 shirts is $47.

The ordered pairs for the historical data are:

(12000, 29) and (18000, 5)

To find the slope (average rate of change) between these two data points, we can use the formula:

slope = (change in y) / (change in x)

slope = (5 - 29) / (18000 - 12000)

slope = -24 / 6000

slope = -0.004

Rounding to three decimal places, the slope is -0.004.

To find the linear equation, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Using the point (12000, 29) and the slope we just calculated, we get:

p - 29 = -0.004(x - 12000)

Simplifying and solving for p, we get:

p(x) = -0.004x + 77

Therefore, the equation for the price p they can charge for x shirts is p(x) = -0.004x + 77.

To predict the price they can charge for 7500 shirts, we can substitute x = 7500 into the equation:

p(7500) = -0.004(7500) + 77

p(7500) = 47

Therefore, the predicted price for 7500 shirts is $47.

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Answer:

Step-by-step explanation:

2517.02