the lines p and q intersect at point O.
what is the balue of x?
​

(i) The area of the path is 120x - 4x² square meters.

(ii) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² is (900 - 120x + 4x²) × 40

To find the area of the path and the remaining portion of the garden, we need to first find the dimensions of the inner square after the path has been constructed.

Let the width of the path be "x" meters. Then the dimensions of the inner square garden will be (30-2x) meters on each side.

(i) The area of the path can be found by subtracting the area of the inner square from the area of the outer square.

Area of outer square = 30 × 30 = 900 sq.m.

Area of inner square = (30-2x) × (30-2x) = 900 - 120x + 4x² sq.m.

Area of path = Area of outer square - Area of inner square

= 120x - 4x² sq.m.

(ii) The remaining portion of the garden is the area of the inner square.

Area of remaining portion = (30-2x) × (30-2x) sq.m.

= 900 - 120x + 4x² sq.m.

The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² can be found by multiplying the area of the remaining portion by the rate.

Cost of planting grass = Area of remaining portion × Rate

= (900 - 120x + 4x²) × 40

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The mean number of days to fix defects is 3.2 days.

The random variable in this case is the number of days it takes to fix defects in a pair of eyeglasses. Therefore, the correct answer is:
rv X = the number of days to fix defects

The corresponding histogram for this frequency table would be right-skewed. This is because there is a higher probability of it taking fewer days to fix the defects, with the probability decreasing as the number of days increases.

To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability and then sum the results. The formula for this is:

mean = ∑(x * P(x))

Where x is the number of days and P(x) is the probability of it taking that number of days.

Using the data from the table, we can calculate the mean as follows:

mean = (1 * 0.1) + (2 * 0.2) + (3 * 0.3) + (4 * 0.25) + (5 * 0.1) + (6 * 0.05)

mean = 0.1 + 0.4 + 0.9 + 1 + 0.5 + 0.3

mean = 3.2

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Step-by-step explanation:

When 508,000,000 is written in scientific notation, it will be represented as:

5.08 x 10^8

Therefore, the value of the exponent is 8.

Based on the given information, the sample space for the event can be represented using a tree diagram, where the first level consists of the three pants (black, blue, and tan) and the second level consists of the five shirts (white, black, green, blue, and red). Each branch represents a possible combination of a pair of pants and a shirt.

To find the total number of outcomes in the sample space, we can simply multiply the number of options for pants (3) by the number of options for shirts (5), giving us a total of 15 possible outcomes.

For Natalie selecting a pair of pants and shirt that are the same color, the favourable outcomes would be the combinations where the pants and shirt are either both black or both blue. These can be listed as:

Black pants and black shirt

Blue pants and blue shirt

For Natalie selecting a black shirt, the favourable outcomes would be the combinations where the shirt is black. These can be listed as:

Black pants and black shirt

Blue pants and black shirt

Tan pants and black shirt

For Natalie selecting a blue article of clothing, the favourable outcomes would be the combinations where either the pants or the shirt (or both) are blue. These can be listed as:

Black pants and blue shirt

Blue pants and white shirt

Blue pants and black shirt

Blue pants and green shirt

Blue pants and blue shirt

Tan pants and blue shirt

In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.

Descriptive analytics is a method used to collect, analyze and summarize data. In the case of the aerospace industry, descriptive analytics can be used to track the response and resolution of technical support calls. This helps to provide insights into the quality of service and make decisions about future changes to optimize the process.

In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.

By analyzing this data, the producer can gain insights into the most common types of technical support issues, the average response and resolution times, and any trends or patterns in the data. This information can then be used to improve the technical support process, identify areas for improvement, and develop strategies to prevent future technical support issues.

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To find out how many of each product Derrick can buy, we can use algebra. Let's call the number of headphones x and the number of cell phone cases y. We can set up an equation to represent the situation:

26x + 14y = 150

Now we can solve for one of the variables in terms of the other. Let's solve for y:

14y = 150 - 26x

y = (150 - 26x)/14

Now we can plug in different values for x and see what values of y will result in a total cost of at least $150. For example, if x = 1, then y = (150 - 26)/14 = 8.86. This means that Derrick could buy 1 pair of headphones and 8 cell phone cases for a total cost of $150.

Similarly, if x = 2, then y = (150 - 52)/14 = 7. This means that Derrick could buy 2 pairs of headphones and 7 cell phone cases for a total cost of $150.

We can continue plugging in different values for x until we find a combination of products that will cost at least $150. Alternatively, we could use a graphing calculator or an online graphing tool to graph the equation and find the intersection points with the line y = 150. These intersection points will represent the combinations of products that will cost at least $150.

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The perimeter of a regular octagon, we use the expression 8s, where s represents side length. The perimeter of a regular octagon with side length 1.5 feet is equals to the 12 feet.

Regular octagon is a polygon with eight sides. The perimeter of a polygon is equals to the sum of all its sides. All eight sides of regular octagon are same measure. So, in other words the perimeter of Regular octagon is equal to eight times the length its side. Here,

Side length of a regular octagon

= 1.5 feet

=> Perimeter = 8 × 1.5 feet [An octagon has 8 sides]

=> Perimeter = 12 feet

Hence, required perimeter is 12 feet.

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The equation 3x² - 12x - 15 = 0 when solved by factoring has the solutions x = 5 and x = -1

The equation 3x² - 12x - 15 = 0, is a representation of the equation in the question.

The aforementioned problem is a quadratic equation, and factoring is one way to solve this kind of issue.

Divide 3 from the equation.

As a result, we have the following

x² - 4x - 5 = 0.

Expanding the equation, we get

x² + x - 5x - 5 = 0.

Factoring the equation, we get

x(x + 1) - 5(x + 1) = 0

The result is

(x - 5)(x + 1) = 0.

We can solve for x by getting

x = 5 and x = -1.

Thus, the equation's answers are 5 and -1.

And it means that there are actually two solutions to the equation.

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Explanation:

There are 4 white marbles out of 4+10 = 14 total

4/14 = 2/7 is the probability of randomly picking a white marble.

(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.

Use a calculator to find that 4/49 = 0.0816 approximately.

That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.

603 white-tailed deer are expected to live in the rectangular area. To find the total number of white-tailed deer in the rectangular area, we need to find the area of the rectangle first. The area of a rectangle is given by the formula:

Area = length × width

In this case, the length is 2.25 miles and the width is 6.7 miles. So, the area of the rectangle is:

Area = 2.25 × 6.7

Area = 15.075 square miles

According to the given information, there are about 40 white-tailed deer per square mile in each of 35 Texas counties. We need to find how many white-tailed deer are expected to live in a rectangular area that measures 2.25 miles by 6.7 miles.

Now, we can find the total number of white-tailed deer in the rectangular area by multiplying the area by the number of deer per square mile:

Total number of deer = 15.075 × 40

Total number of deer = 603

Therefore, there are expected to be 603 white-tailed deer in the rectangular area.

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If you travel 200 miles in four hours, then your average speed for the trip is 50 miles per hour. This is calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).

So, if you travel 200 miles in four hours, your average speed is 50 mi/h.

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Answer:

B. y=7x

Step-by-step explanation:

A direct proportion is where the ratio is constant. The ratio will stay the same. Therefore, y = 7x, this ratio will stay constant making it a direct proportion.

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The total excise tax per pack is $2.15.

The total excise tax is the sum of the federal excise tax and the state excise tax.

Excise tax is the tax that is levied at the moment of manufacture of a good or service. Excise tax is usually levied on alcoholic or tobacco products.

Total excise tax = federal excise tax + state excise tax

$3,80 + $17.70 = $21.50

The total excise tax per pack can be known by dividing the total excise tax by the total number of packs.

Total excise tax per pack = $21.50 / 10 = $2.15

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The first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.

A system of equations can be classified as consistent, dependent, or inconsistent. A consistent system has at least one solution. A dependent system has infinitely many solutions, and an inconsistent system has no solution.

The first system of equations, y=-x+1 and y=-x, is inconsistent. This is because there is no value of x that can make both equations true at the same time. The graphs of these equations would be parallel lines that never intersect, meaning there is no solution.

The second system of equations, y=x+2 and y=x, is consistent and dependent. This is because there are infinitely many solutions that make both equations true. The graphs of these equations would be the same line, meaning every point on the line is a solution.

The third system of equations, y=x and y=2x, is consistent and independent. This is because there is only one solution that makes both equations true. The graphs of these equations would be two lines that intersect at one point, meaning there is only one solution.

In summary, the first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.

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The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.

Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.

Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:

y - 5 = -6(x - 3)

Simplifying the equation, we get:

y - 5 = -6x + 18

y = -6x + 23

Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.

Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.

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15. The student got 18 questions correct.

16. The weight of vitamin C in that tablet is 14%.

17. The secretary's salary has been increased by 60%.

18. The typist's original typing speed was 21 words per minute.

19. The salesperson made $1,022.40 in commission.

20. The salesperson's monthly earnings will be $19,546.

15. On a 45 questions exam, a student gets 40%.

The number of correct questions that the student got is
= 40% × 45 questions

= 18 questions

16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C.

The percent of the weight of this tablet is vitamin C is
= 35mg/250mg × 100%

= 14%

17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually.

The percentage the secretary's salary has been increased by
= ($17,920/$11,200 × 100%) - 100%

= 160% - 100%

= 60%

18. A typist was able to increase his speed by 120% to 42 words per minute.

Her original typing speed was
= 42/120%  × 100%

= 42/1.2

= 21 words per minute

19. A salesperson makes a commission of 12% on the total amount of each sale. In one month, she makes a total of $8,520 in sales.

In that month, she made a commission of
= $8,520 × 12%

= $1,022.40

20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. In a particular month, she sells $22,800 worth of merchandise.

Her monthly earnings will be
= $850 salary + 82% × $22,800

= $19,546

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The greatest common factor of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6) is 6y^(5)w^(2)u^(6).

The greatest common factor (GCF) of two expressions is the largest expression that divides both of the expressions. To find the GCF of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6), we need to find the highest power of each variable that divides both expressions.

The GCF of the coefficients 18 and 30 is 6.

The highest power of y that divides both expressions is y^(5).

The highest power of w that divides both expressions is w^(2).

The highest power of u that divides both expressions is u^(6).

So, the GCF of the two expressions is 6y^(5)w^(2)u^(6).

Therefore, the greatest common factor of the two expressions 18y^(7)w^(2)u^(8) and 30y^(5)w^(4)u^(6) is 6y^(5)w^(2)u^(6).

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Answer:

12ft: 1sec

Step-by-step explanation:

180ft : 15sec

180÷15=12

15÷15=1

soooo it's

12ft : 1sec in the lowest term

As the variance/mean ratio is significantly greater than 1, the population is found to be a clumped distribution.

A clumped distribution, also known as an aggregated distribution, is a pattern of dispersion or arrangement of individuals within a population where they are found in groups or clusters. This means that individuals within a population are more likely to be found in certain areas, while other areas may have few or no individuals.

From the table in the attached image, it can be seen that

the variance= sum of (x -  0.6)^2/ sum of frequency

= 362.88/288

= 1.26

Variance/mean = 1.26/0.6 = 2.1 which is greater than 1

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Answer:

Step-by-step explanation:

The solution of inequality is n < - 9

The value [tex]Cos\theta[/tex] is 20/29 and it can be determined by using the Pythagoras theorem.

Given that,

The value [tex]Sin\theta[/tex] is [tex]\frac{21}{29}[/tex],

We have to determine,

The value of [tex]Cos\theta[/tex]?

According to the question,

To determine the value of [tex]Cos\theta[/tex] following all the given below.

The formula of [tex]Sin\theta[/tex] is,

[tex]Sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

On comparing to the given value of [tex]Sin\theta[/tex] is,

[tex]Sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]sin\theta=\dfrac{21}{29}[/tex]

Here, Hypotenuse = 29, and Perpendicular = 21

Then,

The formula of [tex]Cos\theta[/tex] is,

[tex]Cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

Let, the base be x,

The value of base finding by using Pythagoras theorem,

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](29)^2=(21)^2+(x)^2[/tex]

[tex]841=441+x^2[/tex]

[tex]x^2=841-441[/tex]

[tex]x^2=400[/tex]

[tex]x=20[/tex]

The value of the base is 20.

Therefore,

[tex]Cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]cos\theta=\dfrac{20}{29}[/tex]

Hence, The value [tex]Cos\theta[/tex] is 20/29.

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The inequality that represents the set of solutions above the straight line is: x-3y<5

What is a linear inequality?

A linear inequality is an inequality in which one side is a linear expression in one or more variables, and the other side is a constant, or another linear expression. The solution set of a linear inequality is a region in the coordinate plane that satisfies the inequality.

Calculate the inequality to represent the set of solution by shaded region:

A linear inequality can be represented by a shaded region on the coordinate plane. The boundary of the region is a straight line, and the shaded region represents all the points in the plane that satisfy the inequality. In this case, the line that intersects the x-axis at (5,0) and the y-axis at (0, -5/3) represents the boundary of the region.

To find the inequality that represents the set of solutions above the line, we first need to find the equation of the line. We can use the point-slope form of the equation of a line, which relates the slope of the line and a point on the line to the equation of the line.

We know that the line passes through the points (5,0) and (0, -5/3), so we can calculate the slope of the line by using the formula:

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

where (x1, y1) and (x2, y2) are the two points through which the line passes.

m = (-5/3 - 0) / (0 - 5) = 1/3

Now we can use the point-slope form of the equation of the line to write the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the two points through which the line passes.

Using the point (5,0) as (x1, y1), we get:

y - 0 = (1/3)(x - 5)

y = (1/3)x - 5/3

3y = x - 5

To represent the set of solutions above the line, we need to use the greater than symbol. So the inequality that represents the set of solutions above the straight line is:

x-3y<5

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Answer:

Air

Step-by-step explanation:

it's asking you to look at the chart and find which substance is densest by comparing it to how fast sound can move through it (the speed of sound in the substance). In my opinion copper is not the densest material because sound moves through it the fastest; which means the particles in copper are not as densely held together. Air however, shows that sound can only travel 330 meters per second which is incredibly slow compared to the other listed materials, so by that logic it must be the densest.  

Answer:

Answer is C

Step-by-step explanation:

using long divison:

The possible rational zeros for the given function are ±1, ±2, ±3, ±6.

The Rational Zero Theorem states that if f(x) = anxn + an-1xn-1 + ... + a1x + a0 is a polynomial with integer coefficients, then any rational zero of f(x) must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

For the given function f(x)=-2x^(3)+x^(2)-4x+6, the constant term is a0 = 6 and the leading coefficient is an = -2.

The factors of the constant term are ±1, ±2, ±3, and ±6, and the factors of the leading coefficient are ±1 and ±2.

Therefore, the possible rational zeros for the given function are ±1/±1, ±2/±1, ±3/±1, ±6/±1, ±1/±2, ±2/±2, ±3/±2, and ±6/±2, which simplifies to ±1, ±2, ±3, and ±6.

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The two binomials that Camden must have multiplied and got the product of 49x^(2)-100 are (7x+10) and (7x-10).

To find the two binomials that Camden must have multiplied to get the product of 49x^(2)-100, we can use the process of factoring. Factoring is the process of breaking down a larger expression into two or more smaller expressions that can be multiplied together to get the original expression.

One way to factor the expression 49x^(2)-100 is to look for two binomials that have a difference of squares. A difference of squares is an expression of the form a^(2)-b^(2), which can be factored into (a+b)(a-b).

In this case, we can see that 49x^(2) is a perfect square, as it is equal to (7x)^(2), and 100 is also a perfect square, as it is equal to 10^(2). Therefore, we can factor the expression 49x^(2)-100 into (7x+10)(7x-10).

So, the two binomials that Camden must have multiplied are (7x+10) and (7x-10).

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Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \]

To find the expression for \( f(x) \), we need to use the fact that the zeros of a polynomial are the values of \( x \) that make the polynomial equal to zero. This means that if \( -1, 4, \) and \( 3+2i \) are zeros of \( f(x) \), then the factors of \( f(x) \) are \[ (x+1)(x-4)(x-(3+2i))(x-(3-2i)) \] Now, we can simplify the last two factors by multiplying them together: \[ (x-3-2i)(x-3+2i) = (x-3)^2 - (2i)^2 = x^2 - 6x + 9 - 4i^2 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13 \] So, the expression for \( f(x) \) is \[ f(x) = (x+1)(x-4)(x^2 - 6x + 13) \] Now, we can use the fact that \( f(1) = -144 \) to find the value of the leading coefficient of \( f(x) \). Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \] This is the final answer.

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The gradient of line A is 4/72% or 0.0555.The gradient of line B is -2/6 or -0.3333.

Value is the worth of something, or the amount of importance, good qualities, or benefits that something has. It is determined by the amount of effort, time, and resources that have been put into it. Value can also refer to a person's moral or ethical principles and standards. It is the measure of worth that someone places on something or someone. Ultimately, value is subjective, as it is based on individual opinion.

The gradients of lines A and B indicate the rate of change of the line in relation to the x-axis. The gradient of line A is positive, which indicates that the line is increasing as it moves along the x-axis. This means that the y-value of the line is increasing as the x-value increases. On the other hand, line B has a negative gradient, which means that the y-value of the line is decreasing as the x-value increases. This means that the line is decreasing as it moves along the x-axis. This is why the gradients of lines A and B are different.

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The unit rate for inches per mile is 0.8 inches.

The length of road B is 9.6 inches on map.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.

Road in inches = 1 1/5 = 6/5 inches

Road in miles = 1 1/2 miles =

Inches per mile = 6/5 / (3/2)

                         = 6/5 x 2/3

                         = 4/5

                         = 0.8 inches

If the road B is 12 miles long, on the map it would be;

= 0.8 x 12

= 9.6 inches

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